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Isotachophoresis : some fundamental aspects
Citation for published version (APA):Beckers, J. L. (1973). Isotachophoresis : some fundamental aspects. Eindhoven: Technische HogeschoolEindhoven. https://doi.org/10.6100/IR80190
DOI:10.6100/IR80190
Document status and date:Published: 01/01/1973
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ISOT ACHOPHORESIS SOME FUNDAMEN TAL ASPECTS
J. L. BECKER
ISOTACHOPHORESIS SOME FUNDAMENTAL ASPECTS
PROEFSCHRIFT TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL EINDHOVEN, OP GEZAG VAN DE RECTOR MAGNIFICUS, PROF. DR. IR. G. VOSSERS, VOOR EEN COMMISSIE AANGEWBZEN DOOR HET COLLEGE VAN DEKANEN IN HET OPENBAAR TE VERDEDIGEN OP DINSDAG 19 JUNI 1973 TE 16.00 UUR
DOOR
JOZEFLEONARDUSBECKERS geboren te Maastricht
1973 DRUKKERIJ J. H. PASMANS, 's-GRAVENHAGE
DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR
Prof.Dr.Ir. A.I.M. Keulemans, promotor
Dr.Ir. F.M. Everaerts, co-referent.
~ 1973 by J.L. Beckers, Maastricht, The Netherlands.
Aan Eusje.
Aan mijn ouders.
5
CONTENTS.
INTRODUCTION.
THEORETICAL PART
1 PRINCIPLES OF THE ELECTROPHORETIC METHODS.
1.1 The principle of isotachophoresis.
1.2 The principle of zone electrophoresis.
1.3 The principle of moving boundary electrophoresis.
1.4 The principle of isoelectricfocusing.
1.5 Discussion.
2 GENERAL EQUATIONS IN ELECTROPHORETIC PROCESSES.
2.1
2.2
Introduction.
The general equations.
2.2.1 The equilibrium equations.
2.2.2 The electroneutrality equations.
2.2.3 The mass-balances for all ionic species.
2.2.4 The modified OHM's law.
3 A MATHEMATICAL MODEL FOR ISOTACHOPHORESIS.
3.1 Introduction.
3.2 Basic equations.
3.2.1 The equilibrium equations.
3.2.2 The isotachophoretic condition.
3.2.3 The mass-balance of the buffer.
3.2.4 The electroneutrality equations.
3.2.5 The modified OHM~s law.
3.3
3.4
3.5
Procedure of computation.
Procedure of iteration.
Discussion.
4 MOVING BOUNDARY ELECTROPHORESIS.
4.1 Introduction.
9
11
12
14
15
16
16
18
18
21
22
23
26
28
29
29
30
31
32
32
34
35
43
44
6
4.2 A model of moving boundary electrophoresis.
4.2.1 The electroneutrality equations.
4.2.2 The modified OHM's law.
4.2.3 The mass-balances for all cationic species.
4.3 Procedure of computation.
4.4 Exper imen ta 1.
5 VALIDITY OF THE ISOTACHOPHORETIC MODEL.
5.1 Introduction.
5.2 The concept of mobility.
5.2.1 Relaxation and electrophoretic effects.
5.2.2 Partial dissociation.
5.2.3 Solvation.
5.2.4 The relationship between entropy and ionic mobility.
5.2.5 The relationship between volume and ionic mobility.
45
46
46
46
47
50
55
55
57
58
59
60
62 5.2.6 Discussion. 63
5.3 The influence of the diffusion on the zone boundaries. 64
5.4 The influence of axial and radial temperature differences.64
5.5 The influence of the activity coefficients on the concen-
tration. 66
5.6 Some calculations.
6 SOME PHENOMENA IN ISOTACHOPHORETIC EXPERIMENTS.
6.1
6.2
6.2.1
6.2.2
6.3
6. 4.
Introduction.
Some effects in the use of non-buffered systems.
The HI-MI boundary.
The MI-MII boundary. Enforced isotachophoresis.
Water as a terminator.
67
74
74
74
75
80
83
7
EXPERIMENTAL PART. 89
7
8
8.1
8.2
8.3
9
9.1
9.2
9.2.1
9.2.2
9.2.3
9.2.4
9.2.5
9,3
9.4
9.4.1
9.4.2
9.4.3
9.5
INTRODUCTION. 90
DETERMINATION OF PK VALUES IN METHANOLIC SOLUTIONS.
The determination of the pH in methanolic solutions. 93
.The determination of the pK values in methanolic solutions. . 99 97 Exper~ments.
THE QUALITATIVE SEPARATION OF CATIONS BY ISOTACHOPHORESIS.
Introduction. 100
Aqueous systems. 103
The system WHCL. 103
The system WHI0 3 • 104
The system WKAC. 104
The system WKCAC. 107
The system WKDIT. 107
Combinations of systems. 108
Methanolic systems. 110
The system MHCL. 110
The system MKAC. 114
The system MTMAAC. 114
Discussion. 116
10 THE QUALITATIVE SEPARATiON OF ANIONS BY ISOTACHOPHORESIS.
10.1 Introduction. 119
10.2 Aqueous systems.
10~2.1 Separations according to mobilities.
10.2.1.1 The system Hist/HCl.
10.2.1.2 The system Imid/HCl.
10.2.2
10.3
10.3.1
10.3.2
10.3.3
10.4•
Separations according to pK values.
Methanolic systems.
The separation of fatty acids.
The separation of dicarboxylic acids.
The separation of inorganic ionic species.
Discussion.
119
119
119
123
124
131
131
133
137
137.
8
11 THE SEPARATION OF NUCLEOTIDES BY ISOTACHOPHORESIS.
11. 1
11.2
11.3
11.4
11.5
Introduction.
The structure of the nucleotides.
Experiments.
An enzymatic reaction.
Discussion.
12 QUANTITATIVE ASPECTS IN THE SEPARATION BY ISOTACHO-
PHORESIS.
138
138
138
145
146
12 .. 1 Introduction. 148
12.2 Theoretical. 149
12.3 Reproducibility. 151
12.4 The determination of the calibration constant. 152
12.5 Quantitative aspects in the separation of mixtures. 153
12.6 Detection limits. 158
12.7 Discussion. 163
13 FURTHER DEVELOPMENTS. 164
REFERENCES. 168
LIST OF SYMBOLS AND ABBREVIATIONS. 173
APPENDIX A: The computerprogram X3. 177
APPENDIX B: Isotachophoretic equipment with sample valve. 182
APPENDIX C: Isotachophoretic equipment with injection block. 183
SUMMARY 185
SAMENVATTING 186
DANKWOORD 187
LEVENSBERICHT 187
9
INTRODUCTION
In the middle of thenineteenthcentury WIEDEMANN 1- 2
and BUFF 3 reported on the phenomenon that charged par
ticles migrate as a result of an applied electric field.
The charged particles have a characteristic velocity and
their mobility is defined as: "The velocity in an elec
tric field E of unit-strength".
In general different ionic species have different
characteristic mobilities and therefore different veloci
ties in an electric field. This can be used for their se
paration. Techniques based on this principle are known as
electrophoretic techniques.
Four main types can be distinghuished in electrophoresis,
viz.: -Isotachophoresis
-Isoelectricfocusing
-Moving boundary electrophoresis
-zone electrophoresis.
All these different types of electrophoresis can be
carried out in different ways, e.g. on paper, on thin
layers, in gels, in blocks and in capillary tubes. All
these methods have advantages and disadvantages. The in
fluence of e.g. the production of heat, electroendosmosis
and moreover the use of aggressive and volatile solvents
can be troublesome. Limitations in the use of high volta
ges and electric currents are the result.
1)
See list of symbols.
10
In the course of time numerous workers have investi
gated the phenomenon of isotachophoresis and its appli-5-11 cations. The separation of isotopes , the measurement
12-18 . of transference numbers , the separat~on of ionic . 19-28 29-34
spec~es , the use of counter-flow , . 36-38 . . 39-40 pH grad~ents · , and the use of spacers have been
dealt with, although optimum results often could not be
obtained by defective equipment.
Better results are obtained by EVERAERTS. EVERAERTS41 (1968)
and MARTIN and EVERAERTS 35 (1967) described an analytical
method, based on the principle of isotachophoresis in capil
lary tubes. Ionic species migrate under the influence of
an electric field in a closed system, filled with an elec
trolyte. Cooling is easy and even volatile and aggressive
solvents can be used. A thermocouple serves as a detector.
Although several papers describing the isotachophoretic
separation of ionic species have been published, a more de
tailed research on the possibility to separate ionic spe
cies by isotachophoresis has not been made.
The aim of this work is to give a contribution in the
applicability of isotachophoresis for the qualitative and
quantitative analyses of ionic species. In the first part a mathematical model for isotacho
phoresis and moving boundary electrophoresis is given and
experimental values are compared with calculated values in
order to check the models. In the second part data are gi
ven of separations of anions and cations with water and
methanol as solvents.
T H E 0 R E T I C A L P A R T
"Anything will prove interesting
as soon as you take an interest in it."
12
CHAPTER 1
PRINCIPLES OF THE ELECTROPHORETIC METHODS
1.1 THE PRINCIPLE OF ISOTACHOPHORESIS.
For the explanation of the principle of isotachophore
sis we will consider the separation of anionic species in
capillary tubes. For the separation of anions, the capil-
lary
ding
than
tube and anode compartment, are filled with the lea
electrolyte. The leading anion has a mobility higher
b . f c i l) . f any mo ill. ty o the sample an ons • The catJ.ons o
the leading electrolyte have a buffering capacity. The ca
thode compartment is filled with an electrolyte, called
terminator. The anions of the latter must have a mobility
lower than any of the sample anions. The sample is intro
duced by means of a sample tap, between the leading elec
trolyte and the terminating electrolyte (Appendix B).
After the introduction of the sample an electric current
is passed. After some time a steady state is obtained with
all ionic species of the sample separated in serried zones
in order of their mobilities. The first zone contains the
sample anionic species with the highest mobility, the last
zone that with the lowest mobility. All these zones migrate
with a velocity equal to the velocity of the leading zone.
It follows that each zone has a characteristic electric
field, according to the relation v = m. E, where the velo
city V must 'be equalised with the velocity of the leading
zone. The boundaries between two zones are sharp, because of
the self-correcting effect of the isotachophoretic system41 .
1) Speaking about mobilities in experiments, always the effec-
tive mobilities are meant, as these determine the actual
velocities in an electric field; see also Section 5.2.
13
The producti.on of heat in a zone is determined by the
product of E and I. Working at a constant current density,
zones with ionic species of high mobilities will have a smaller production of heat, than zones containing ionic
species of lower mobilities' this results in lower tempera
tures. As the zones are generally ordered according to de
creasing mobilities, the temperature of the succeeding zones
will increase. The temperatures are detected with a thermo
couple. The step heights in the electropherograms are a
measure of the temperature and hence allow the identification
of the ionic-species. All zones have a specific concentration
as already indicated by KOHLRAUSCH 51 Therefore the length of
the zones is a measure for the amount of the ionic species
present in the sample.
Figure 1.1 shows the voltages., the electric field strengths
and the temperatures of the different zones. The stepheight H
• -I Al I A2 I A:3 I A4 e
rnA ) rnA > mA3 > rnA 1 2 4
v
f
E
I I ~ ~
;,......__.; r---:
T ___. temperature
t of the zone
differential signal
FIG. 1.1 The voltages, electric field strengths and tempe-
ratures of the different zones in isotachophoresis.
14
is used for the identification and the length L is a measure
for the quantities.
Because this method is characterised by equal velocities
of all zones, in the steady state, the method is called "Iso
tacho-electrophoresis." In practice the name "Isotachophore
sis" is used. This method is comparable with displacement
chromatography.
1.2 THE PRINCIPLE OF ZONE ELECTROPHORESIS.
In zone electrophoresis the whole system is filled with
one-electrolyte (back-ground electrolyte). The sample is in
troduced into this back-ground electrolyte. The separation
of anionic species is considered. The ionic species of the
back-ground electrolyte have certain mobilities and when an
electric current is passed these ionic species will migrate
with their specific velocities. Also the sample ions migrate
under. the influence of the electric field applied, each io
nic species with its own characteristic velocity dependent
on the conditions chosen.
A flow of ions of the electrolyte, supervened by a flow
of sample ionic species is obtained. As the back-ground elec
trolyte can provide in the current transport, no serried
zones of the sample ions can be expected and there is not a self-correcting effect of the boundary. Due to the diffusion
the peaks are wide and unsharp (tailing) and adsorption phe
nomena can cause "trailing".
Figure 1.2 shows the voltages electric field strengths
and temperatures of the different zones. The back-ground
electrolyte supervened by a slow sample ionic species shows
a higher electric field strength over the zone than in the
case of a quicker sample ionic species. If the influence of
the back-ground electrolyte on the conductivity of the zone,
is large in comparison with that of the sample ions, a near
ly constant electric field strength and pH can be expected
15
v
I Eri'---'----'---....:.__L.,___j ___l ~ ;
:-.1; : ! i---< '----' ----,
T'L~~;...____._i . ~ :
~ i.. :-----.. u. : : :---f
FIG. 1.2 The voltages, electric field strengths and tempera
tures of the different zones in zone electrophoresis.
and ~11 sample ions will have their own constant velocities
during the experiment. Identification is possible by diffe
rences in the "retention times" of the ionic species.
This technique is comparable with elution chromatography.
1.3 THE PRINCIPLE OF MOVING BOUNDARY ELECTROPHORESIS.
In this method the sample fills the electrode compart
ment behind the leading electrolyte. A partial separation
is obtained dependent on the time of the analysis. An elec
tropherogram may have the following shape (Figure 1.3):
T
I FIG. 1.3 An electropherogram in moving boundary electrophoresis.
16
Substance A1 , more mobile than the other substances of
the sample is separated from A2 and A3• Substance A2 mixed
with A~ forms the second sample zone after the pure A1 zone. The 3t zone contains the mixture A1, A2 and A3 • This method
is comparable with the frontal analysis method in chromato
graphy.
In moving boundary electrophoresis, the zones generally
contain more ionic species of the sample. The composition of
the sample plays an important role in the determination of
the concentrations, pH's and conductivities of t~e zones. This
in contrast with isotachophoresis where all these quantities
are independent of the quantitative composition of the sample.
1.4 THE PRINCIPLE OF ISOELECTRICFOCUSING.
In this method a column contains a buffer solution,
that creates a pH gradient in the tube. When a sample,
consisting of a mixture of amphiprotic molecules (with
a particular pi value) is introduced, the particles will
move until they reach a pH in the tube equal to their pi values.
At this point the effective mobilities are equal to
zero. In the stationary state the particles will be sepa
rated, if they have different pi values, according to their pi values.
1.5 DISCUSSION.
Although in this chapter four main types of electro
phoresis have been distinghuished, often a sharp distinction
between these types can not be made in practice. Disturbances
during the experiments are often caused because not all con
ditions are fulfilled, required for a specific type of elec-
17
trophoresis. During isotachophoretic experiments all other
types can exist.
The first stage in the separation by isotachophoresis is
a moving boundary procedure in the sample compartment, i.e.
all ionic species have a velocity determined by e.g. the
actual pH, the ionic strength, the temperature, the visco
sity, the effective mobilities and the electric field strength.
After some time, when a steady state is reached, the ionic
species are separated and we can speak of isotachophoresis.
If the differences between the mobilities are too small
and/or if the differences in concentrations are too large,
mixed zones can be expected and we can not speak of isotacho
phoresis properly.
If the influence of a back-ground electrolyte (solvent effect at low and high pHs) is too great, zone electrophoretic
phenomena can be expected. The use of spacers (ampholytes)
during isotachophoretic experiments gives a combination of
isotachophoresis and isoelectricfocusing. Some phenomena
will be discussed further on.
18
CHAPTER 2
GENERAL EQUATIONS IN ELECTROPHORETIC PROCESSES
2.1 INTRODUCTION.
Experiments based on the principle of electrophoresis 1-4 50-54 have been described for a long time ' . Already in
1897 KOHLRAUSCH51 gave a mathematical model for electro
phoretic processes. Using the divergence theorem, the con
tinuity equations can be derived and using the principle
of electroneutrality and assumptions such as constant re
lative mobilities, he formulated the socalled "Beharrliche
funktion":
= Constant.
This regulating function prescribes that at any point the
sum of the concentrations divided by the mobilities must
be constant.
In this chapter the general equations in electrophoretic
processes will be discussed. They will be used for the mathe
matical models of isotachophoresis (Chapter 3) and moving
boundary electrophoresis (Chapter 4).
2.2 THE GENERAL EQUATIONS.
For the derivation of the general equations in electro
phoretic processes we will consider the movement and forma
tion of zone-boundaries, when a electric field is applied
over an existing zone-boundary between two electrolyte
solutions. On one side of the boundary a mixture of several
anionic and cationic species and on the other side a "single
electrolyte" is present.
19
The anode is placed in the single electrolyte. Only the
migration of the anionic species is considered, whereby the
effective mobility of the anionic species of the single elec
trolyte is assumed to be higher than any of the anionic
species of the mixture (Figure 2.1).
e
< FIG. 2.1 A zone boundary between a mixture of several anionic
and cationic species and a "single electrolyte".
After some time all anionic species have the same
counterion (BL) because the cationic species B1 to Br
are moving in the opposite direction.
Furthermore a number of boundaries will be formed. Two
types of boundaries have to be distinghuished viz. the
concentration and the separation boundaries.
For the concentration boundaries the number of anio
nic species is equal on both sides of the boundaries,
whereas for separation boundaries one particular ionic
species is present on one side of the boundary only.
In general r+1 boundaries will be present if an electric
current is passed across the original boundary as shown
in Figure 2.1, considering the separation of anionic spe
cies, viz. one concentration boundary, r-1 separation
boundaries and the boundary between the single electrolyte
and the zone containing the anionic species with the highest
effective mobility of the mixture (Figure 2.2).
The velocity of the concentration boundary is neglected 61-63 .
• The boundary between AL and A1 has a veloc1ty equal
e A - A-1 .• r 1 .. r-1 -
t -concentration boundary
20
A1 +A2 Al AL-
- -BL
' t t t r-1 separation I t
boundary boundaries L.E.-A1
< FIG. 2.2 Zone boundaries formed when an electric current is
passed across a zone boundary as shown in Fig. 2.1.
to the velocity of the AL and A1
ionic species. The velo
cities of the separation boundaries are equal to the veloci.,..
ties of the ionic species with the lowest effective mobility
in those zones. These anionic species are not present in the
preceding zones.
Speaking about ionic species in the model we mean amphi
protic polyvalent particles, containing different chemical
groups with different equilibrium constants. For such a
particle, the following equilibria can be set up:
-ZA -(i-1)
A r + H 0 ~ .. !::::====; .. r 2
ZA - (n-1)
r + H 0 ~=::::p 2 pK n
ZA -1 A r
r
ZA -i A r
r
ZA -n A r
r
2.1
21
ZA The particle Ar r, with the highest positive charge zA ,
r is taken as a reference in all computations.
The pK's are increasing from pK 1 to pKn. A similar reac
tion can be given for the buffering counterions B. Nearly
all general equations are similar for both the ionic species
to be separated (anions) and the buffering counter-ions
(cations).
For the derivation of the equations the following assump
tions are made: the electric current is constant; the cross
section of the tube is constant; the influence of the diffu
sion, hydrostatic flow and electroendosmosis is negligible;
the activity coefficients and the influence of the radial
temperature differences can be neglected.
The generalequations describing electrophoretic processes
are: the equilibrium equations.
the electroneutrality equations
the mass-balances for all ionic species
the modified OHM's law.
These equations will be considered in more detail.
2.2.1 The eguilibrium equations.
The chemical equilibrium equations determine all pH
depending quantities such as the effective mobilities. Con
sidering the reaction 2.1 the general expression for the
equilibrium constant will be (for the Uth zone):
2.2
So:
22
KAr,U,i • cA ,U,zA -i+l r r
CA ,U,zA -i = r r cH,U
Substituting the expressions for c -l.'+l etc., up to A 1 U 1 ZA
in eqn. 2.3 r r
c = A ,u,zA -i r r
The total concentration of an anionic species is:
c A ,U,zA r r
nA .;;:--r
( 1 + <-i=l
i
j"[ KAr,u ,j )
(ca,u>i
2.3
2.4
2.5
Similar equations can be derived for the buffering counterions.
2.2.2 The electroneutrality equations.
In accordance with the principle of electroneutrality,
the arithmic sum of all products of the concentrations of·
all forms of all ionic species and the corresponding valences, present in each zone, must be zero.
While the first zone contains one ionic species of the
sample, each zone following always contains one ionic species th . more. The U zone will contain U ionic species of the sample
consequently. The ionic species are numbered in order of decreasing effective mobilities. For the Uth zone can be written:
23
u
~{ r=1
{ ( ZA - i) • cA U - . } } + ' ,zA ~ r r r
0
Substituting eqns. 2.4 and 2.5 in eqn. 2.6, both for the
sample ionic species and counterions:
i
1f K . . _
1 A ,U,J
-·) J- r ~ . i
(cH,u> } +
} + i
1 +
i
~B i=1
i
1 + 1f KB,U ,j j=1
i=1
2.2.3 The mass-balances for all ionic species.
2.6
2.7
0
In the stationary state the amount of all ionic species
passing .a separation boundary is equal to the amount rea
ching the separation boundary. For the Uth separation boun-
24
dary this means that U-1 balances for the anions and 1 ba-1)
lance for the bufferions can be obtained •
The zone-boundary U/U-1 has a velocity of EU.mA u· u'
The quantities written with a bar ,m, indicate that they do
not apply to ions, but to the equilibrium mixtures of all
forms of the constituent, consequently the effective mobili
ties of the ionic species are meant. As the boundary velocity
is determined by the Uth ionic species, the subscript figure
r in rnA is replaced by a "u". r
For the effective mobility TISELius 64 pointed out that
a substance consisting of several forms with different mo
bilities in equilibrium with each other will generally mi
grate as a uniform substance with an effective mobility:
n n
m = ~ ~ 2.8 i=O i=O
provided that the time of existence of each ionic species
is small in comparison with the duration of the experiment.
In this effective mobility, factors such as the relaxation
effect, the electrophoretic effect, the influence of the
temperature are neglected (see also Section 5.2).
1) The sample ionic species Au 1 the ionic species with the
lowest effective mobility of the sample, determines the
velocity of the Uth zone and is not present in the u-1th
zone.
25
Substituting the eqns. 2.4 and 2.5 in the eqn. 2.8 delivers:
'
t Eu t1 To
EU-1 t
cB,U cB,U-1 t T T1
t cA c
r'u 0 Ar,U-1
FIG. 2.3 Migration paths of the different ionic species over
a zone boundary.
1
} + m A ,U,zA
r r
n i Arlf < K .
+ "<: ~j_=_1 ____ A_r~._,u __ ,_J
i=1
The amount of the buffer ions, just passing the moving
boundary is (Figure 2.3):
The amount just leaving the boundary is:
1!.2 B
2.9
2.10
2.11
26
Those amounts must be equal and the mass-balance for the
buffer will be:
In a similar way for the mass-balances of the anionic spe
cies can be derived:
2.2.4 The modified OHM's law.
Working at an equal current density:
I/G = Constant = E0 • Au
The electric conductivities for the zones are the somma
tion of all: ci . mi • 1zi1 , consequently:
( lzA -il .cA i.mA U · r ,u,zA - r' ,zA -~
r r r +
Substitution of the eqns. 2.4 and 2.5 in eqn. 2.15 gives:
2.13
2.14
2.15
27
i
nAr 1f K .
~ ~ . j = 1 Ar 1 U 1 J ~ lzA -1.1 . rnA . + lzA l·m
U i=l r i r 1012A -1. r Ar 1012A [ ~ ______________ (_c_H_~u __ l 1~. ____________ r _________________ r_
r=J
ci U} + rl
~r i=l 1 +
i
jill KBIUij
i .mB 1 U1 zB-i ~+lzBI .mB 1 U 1 zB (cH
1U) t
------------~~~l.-------------------------.cB 1 U +
1 + ~ i=l
1T KBIU I j j=l
I/G 2.16
28
CHAPTER 3
A MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
3.1 INTRODUCTION.
In Chapter 2 the general equations, describing the movement and formation of zone boundaries, are discussed
for the case that a stabilised electric current is passed
across a zone boundary, between a mixture of anionic and
cationic species on one side and a single electrolyte on
the other side. Generally r+1 zone boundaries were obtained
for the separation of anionic species. No complete separa
tion of the anionic species can be obtained in this way.
In principle an isotachophoretic system is a similar
one. The sample (mixture of anionic and cationic species) is
introduced between a leadingelectrolyte and a terminator
electrolyte (Figure 3.1).
The first stage is a separation procedure as will be
described in Chapter 4. In the steady state all the ionic
species of the sample are separated and each sample zone
contains only one ionic species of the sample.
A.r AI. .r AL e ---- ----- (9 - -- ---B.r B1 .• r BL
mA.r < mA 1.. r < mA
L
FIG. 3.1 Original situation when a sample is introduced in an
isotachophoretic electrolyte system.
29
Each zone has correlation formulae only with the zone
in front of it. Calculations of pH, concentration and other
parameters are possible. For the mathematical model of iso-41-43 63 65
tachophoresis ' ' the general equations (Chapter 2)
will be combined with the isotachophoretic condition, which
prescribes that all zone velocities must be equal.
3.2 BASIC EQUATIONS.
In analogy with the general equations and with the same
assumptions we will give here the equilibrium equations, the
mass-balance of the buffer, the electroneutrality equations
and the modified OHM's law, combined with the isotachophore~
tic condition, for the description of the isotachophoretic
model.
Only the mass balance of the buffer will be used as the
anionic species of the sample are only present in their own
zone (the separation of anions is considered).
3.2.1 The equilibrium equations.
In a similar way as described in Chapter 2 we can derive:
KA__ . --v' ~
1) 3.1
1)
3.2
The subscript figure refering to the Vth zone is used
only for the hydrogen ions. For the other symbols this
indication is superfluous as the indication Av always
refers to the Vth zone.
30
i
n~ 1f KIV . t ( 1 + ~ j=1 ,J
c A = c . ) v Av•ZAv i=1 {cH, v> i 3.3
3.2.2 The isotachophoretic condition.
In the steady state all zones move with a velocity equal
to that of the leading zone, therefore:
3.4
-The mAL and mAv are the effective mobilities of the leading
ion in the leading zone and the sample .ions IV in the Vth
zone respectively.
t i=l
n~ 1 + <
&,1
i JT K . j=1 IV·J
(cH v> i ) + mA_
-v'zAv
3.5
For all other ionic species a similar expression for
the effective mobilities can be derived. The isotachopho
retic condition is the essential difference between iso
tachophoresis and other electrophoretic methods.
31
3.2.3 The mass-balance of the buffer.
The movements (AX) of the zone boundaries L V and V W
per unit of time are equal (Figure 3.2):
AX 3.6
t tl to t t1 t 0 0 0
l AX AX
B2X I B1X
vw
62
FIG. 3.2 Migration paths and movement of the zone boundaries
in an isotachophoretic system.
The distances over which the buffer ions move during one unit of time in order to reach the zone boundaries
are respectively:
B1X EL.mB L
3.7
B2X = Ev.m~ 3.8
Therefore the amounts of the buffer that pass the zone
boundaries L-V and v-w, are the amounts of the buffer pre
sent in the volumes 6 1 and 6 2 respectively, at t=O.
The 9mounts of the buffer entering and leaving a zone must
be equal, therefore:
32
Combining the eqns. 3.9 and 3.4 gives:
t - -cB • { 1+mB /rnA_)
L L --r, 3.10
3.2.4 The electroneutrality equations.
In accordance with paragraph 2.2.2 for the electroneutrality
can be written:
i Tr KA.__ • j~:\ ---v' J
i {cH,V)
3.2.5 The modified OHM's law.
Working at an equal current density:
+
= 0
3.12
33
The electric conductivities for the zones are the somma
tion of all: ci.,zil'mi1 consequently:
nA
(cOH L.mOH L+cH L"mH L+ <L ( lzA -i\.cA_ _ .• rnA -i> + I I I I &o L --L I z A l. L I z A
L L
I/G. 3.13
Substitution of the eqns. 3.2 and 3.3 gives:
i 1T KB ]'
j!d1 Ll ) + IZB I i L
(cH,L)
nB
~L
1 + i=1
= I/G 3.14
34
A similar expression can be set up for the sample zone.
Assuming the left-hand side term of the eqn. 3.14, QL
and QV for the leading and Vth zone respectively, the
function RFQ defined as:
must be zero according to equation 3.12.
3.3 PROCEDURE OF COMPUTATION.
The procedure of the computation is the following.!)
If all mobilities and pK values are known, and the to
tal concentration of the leading ionic species and the
pHL are chosen, all computation constants2 ) of both the
leading ions and the buffer ions in the leading zone can
be calculated.
From an equation similar to 3.3 thecA z can be L' A_
calculated out of the total concentration L and with
eqn. 3.2 all partial ionic concentrations of the ionic
species AL. With eqn. 3.11 the total buffer concentration
in the leading electrolyte zone can be obtained, and with
an eqn. similar to 3.3 and 3.2 the partial concentrations
of the buffer. Furthermore QL and the left-hand side term
of the buffer correlation (eqn. 3.10) can be acquired.
All quantities of the leading electrolyte are known now.
1) With the equations derived in section 3.2 a computer
program has been developed. In Appendix A the program
is shown. An example of the in- and output is given.
The language used is ALGOL 60.
Calculations were made with the P9200 time sharing
computer.
2) Computation constants are e.g. the effective mobili
ties and the continual products in the equilibrium
equations.
35
Assuming a certain Pliv for the following zones, all
computation constants for those zones can be calculated,
in a similar way as indicated for the leading zone. With
the eqn. 3.10 the total concentration of the buffer can
be found and with the eqns. 3.2 and 3.3 all other par
tial concentrations. With eqn. 3.11 the total concentra
tion of the sample ionic species and with the eqns. 3.2
and 3.3 all partial concentrations can be obtained.
With equation 3.14 the QV can be obtained and the eqn.
3.15 will give the value of the function RFQ for the
assumed pH. This value must be zero for the correct Pllv· In fact more zero-points are possible. The way found the
correct Pllv zero-point will be dealt with in the next sec
tion.
3.4 PROCEDURE OF ITERATION.
As mentioned in Section 3.2.5., the function RFQ
must be zero for the correct Pllv value. For several cases
this function RFQ is computed as a function of the Pllv·
In Figure 3.3 this function is plotted for .the se
parations of univalent cations and anions. Also the buf
fering counterions were univalent. In Figure 3.4 the
function is shown for polyvalent sample ionic species and
bufferions. In Figure 3.5 the function is shown for a
system, where in the leading electrolyte zone, the leading
ion buffers in stead of the counter ion. Only in the sample
zones, the counter ion acts as a buffer and in general this
means that a larger pH shift between pHL and Pliv is present. This is used in disc.-electrophoresis according to ORNSTEIN and DAVIS25 , 26 •
In the Figures 3.3, 3.4 and 3.5, the anionic and cationic separations are indicated by e and ~ respectively. The func-
36
TABLE 3.1 pK values and ionic mobilities of the ionic species,
used for the calculation of the relationship between
RFQ and p~.
Fig. Leading zone
Buffer ionic s:eecies Leadin9: ionic s:eecies
m.10 5 pKs n z cone. m.10 5 pKs n z pHL
cm2(_vs mole(_l cm2t._vs
3.3.a 0,50 3 1 0 0.01 75,0 14 1 1 3 3.3.b 19,0 11 1 1 0.01 0,76.5 -2 1 0 11 3.3.c 0,50 4 1 0 0.01 75,0 14 1 1 4 3.3.d 30,0 10 1 1 0.01 0,76.5 -2 1 0 10 3.3.e 0,50 6 1 0 0.01 75,0 14 1 1 6 3.3.f 19,0 6 1 1 0.01 0,76.5 -2 1 0 6 3.3.g 0,50 10 1 0 0.01 75,0 14 1 1 10 3.3.h 30,0 4 1 1 0.01 0,76.5 -2 1 0 4 3.3.i 0,50 11 1 0 0.01 75,0 14 1 1 11 3.3.j 30,0 3 1 1 0.01 0,76.5 -2 1 0 3 3.3.k 0,50 12 1 0 0.01 75,0 14 1 1 12 3.3.1 30,0 2 1 1 0.01 0,76.5 -2 1 0 2
3. 4. a 50,0,50,70 2,4,8 3 1 0.01 75,0 14 1 1 5 3.4.b 0,40 4.75 1 0 o.o1 75,0 14 1 1 5 3.4.c 19,0 6 1 1 o.o1 0,76.5 -2 1 0 6 3.4.d 19,0 6 1 1 0.01 0,76.5 -2 1 0 6
3.5 19,0 8 1 1 0.01 0,40 4.75 1 0 4.75
Fig. Sam:ele ionic s:eecies Fig. (a)
m.10 5 pKs n z pKs 2·
em (_Vs
3.4.a 50,0 .!! 1 1 3.3.a 3,5,6,7 50,0 10 1 1 3.3.b 9,10,11,12 50,0 14 1 1 3.3.c 3,4,5,6,8,10,12 70,30,0,30 4,6,8 3 2 3.3.d 1-6,9,12
3.4.b 70,30,0,30 4,6,8 3 2 3.3.e 3,5,7,9,13 70,50,0 5,7 2 2 3.3.f 1,6,10,11,12 50,0 14 1 1 3.3.g 4,8,10,13
3.4.c 0,50 4 1 0 3.3.h 1,4,5,10 0,50,70 4.5,5 2 0 3.3.i 2,4,8,10,11 50,0,30,60 3,5,7 3 0 3.3.j 4,5,8
3.4.d 50,0,30,60 2,4,8, 3 1 3.3.k 2,4,8,12 50,0,50 3,9 2 1 3.3.1 1,4,5,8 70,70,0,50,70 2,4,6,8 4 2
3.5 30,0,30 2,9 2 1
(a) because in this cases the assumed mobilities for the mono-valent cations and anions were resp. 50,0 and 0,50, only the pK values of the sample ionic species are given.
j· 2
1
0
~
tl 5
-1
3
2
1
0
~ t
-1
7
10
pH =3 L
pHV
FIG. 3.3.a
pH =4 L
2
-pll.v
FIG. 3.3.c
37
e pHL=ll
3
12
2 11
10
1 0
~ 9
5 10 - pHV
FIG. 3.3.b
-1
e
12
3
2
I 9
1
0
~ 1-6
5 - PRy
FIG. 3.3.d -1
3
2
1
0.
~· 1 - PlV
FIG. 3.3.e -1
1~ 4 l 13
2
1. 0
~
5 10 - PlV
) ;)/ FIG. 3. 3 .g
-I
38
e
3
2 1
1
0
~
t
I -1
e
3
2
1
0 ~
t
-1
6
5
4 10 5
12 10
1
pHL=6
FIG.
pH =4 L
-FIG,
PlV
3.3.f
Pllv
3.3.h
3 0 11
2
1 r
\ 01, r...: !l:l t
5 1 -Pflv FIG. 3.3.1
-1
pHL=12
2
4 12
8
1 \ I
01 I ~
\ i 5 10 Pflv
-1 FIG. 3.3.k
39
e 8
4 5
2
1
01
~
5
-1 \\.\
e
2
1
4 ~ a 1
01
I \ ~ t' \
5\
-1 \~
10
pH =2 L
10
pH =3 L
-FIG.
Pflv 3.3.j
- pHV
FIG. 3. 3. 1
2
1 0
~
-1
-2
e
3
2
ill'l
\~ I'"-
ll'l
("f)
1
0 ...,_, cz:
-1
~I\
pH =5 L
- PJV
FIG. 3.4.a
pH == 6 L
10 -plfv
FIG. 3.4.c
40
14 p~=S
2
1
0
~ t
10 - PJV
-1
-2 ~n I I FIG. 3.4.b
e pHL=6
3
co .. 2 co 1.0 .. ..
<;!' <;!'
I ..
N N
1 0
~
t ---..p
-1 FIG. 3.4.d
41
tions are indicated by a number, representing the pK values
of the sample ionic species. All assumed pK values and ionic
mobilities for the leading electrolyte and the sample ionic
species are given in Table 3.1.
For all these electrolyte systems different functions
were obtained. Some show no real zero-points, sometimes two
zero-points are present and some show discontinuities.
All those properties depend on quantities such as pK values
and mobilities. Although not all possible functions have
been computed, we can conclude that all systems have one
common property viz., in the case of a cationic separation
the correct zero-point was always the transition between a
e
2
1
0
~
t 5
- Pf\r -1
-2
FIG. 3.5 The relationship between the function RFQ and the
p~ for a disc. electrophoretic system.
42
negative and a positive value of the function RFQ in the
direction of higher pHs and for the anionic separations it
was the transition between a positive and a negative va
lue of RFQ. (For the false zero-points negativ~ concentrations were obtained).
The way to find the correct zero-point is therefore:
In the computer program first a Pliv is searched for, with
a positive (resp. negative) value for RFQ and then for a
Pliv with a negative (resp. positive) value for the Plivr for anionic (resp. cationic) separation. The correct Pliv at which the function QV is zero, within a certain deviation,
is obtained by iterating between those two values. If no
pair of positive-negative resp. negative-positive QV values
can be obtained in a traject of 6 pH values from the pHL then "NO REAL ZERO-POINTS" will be printed.
The procedure of iteration is shown in Figure 3. 6.
PRINT RESULTS
FIG. 3.6 Flow chart of the iteration procedure of the com
puter program x 3 .
43
3.5 DISCUSSION.
Sometimes, the function RFQ shows no real zero-point,
i.e. the function is always positive (e.g. Fig. 3.3. a,
3.3. band 3.3. c). Mainly this effect can be observed
at low pHs for the cationic and at high pHs for anionic
separations. The exact pHs at which this phenomenon occurs
depends on the pK values and mobilities of all ionic species
and a general treatment to determine them can not be given.
The importance of this fact is that theoretically the
mathematical model is not valid at those pHs. Practically
it means that at those pHs the influences of the hydrogen
and hydroxyl ions are such that we do not have real isotacho
phoresis. The isotachophoretic condition is lost, i.e. isota
chophoresis is transferred into e.g. a moving boundary procedure.
In the next chapter a. model of moving boundary electro
phoresis will be given. This model is necessary in order to
understand some other phenomena in isotachophoretic experi
ments.
44
CHAPTER 4
MOVING BOUNDARY ELECTROPHORESIS
4.1 INTRODUCTION.
If the separation in isotachophoresis is completed,
only one ionic species of the sample is present in each
sample zone. The parameters of each zone are related
with those of its preceding zone. Calculations of the
pH, concentration and other parameters are possible. A
mathematical model for the buffered systems already has
been given in the previous chapter.
If the separation is not completed, i.e. mixed zones
are present, and/or if the influence of the back-ground
ions is too great, the conditions for real isotachophoresis
are lost and the model described is not valid any more.
Especially this can occur in non-buffered systems. In this
case the separation procedure can be better understood by
using a model similar to the moving boundary technique.
Several authors 55- 60 gave already a mathematical model
for the moving boundary system, but it is very difficult to
work with an exact model. Some simplifications have to be
made. Each zone does not consist of one ionic species of
the sample, but the number of ionic species in the zones
increases to the rear-side. Only the first sample zone,
following the leading electrolyte zone, contains one ionic
species from the sample. All zones have correlations with
both the preceding and following zone, which explains the
difficulties in computation.
A simpler model was used by BROUWER and POSTEMA61 • They
described a model of separation during isotachophoresis,
45
which is moving boundary electrophoresis in principle. Con
centration effects, the influence of the pH and the tempe
rature were neglected. Although this is not a general model,
it can be used for non-buffered systems of monovalent, fully
ionised ionic species.
In this chapter we will describe a model similar to that 61 of BROUWER and POSTEMA . The influence of the temperature
is taken into account. With the formulae a computer program
is made and calculations are compared with the results of
experiments. Moreover some phenomena in isotachophoresis
of non-buffered systems can be explained.
4.2 A MODEL OF MOVING BOUNDARY ELECTROPHORESIS.
To carry out experiments with moving boundary electro
phoresis the capillary tube can be filled with an electrolyte
of a strong acid, when a separation of cations is desired.
The cation present has a mobility higher than the mobility
of any other cation of the sample. The sample is situated at
one end of the capillary tube, i.e. in the anode-compartment.
For the derivation of the formulae the following assump
tions are made: fully ionised monovalent cations and anions
are considered; the contribution of the back-ground ions to
the conductance of a zone is negligible; the influence of
differences in pH, and concentrations are negligible; the
electric current is stabilised; the diffusion, hydrodynamic
flow and electroendosmosis are negligible; the solution ini
tially present in the capillary tube and anode compartment is
of well known constant composition.
The formulae needed to be considered are; the electro
neutrality equations; the modified OHM's la~·; the mass
balances of all cationic species.
46
4.2.1 The electroneutrality equations.
If the influence of the back-ground ions can be neglected
and when all ionic species are fully ionised the concentra
tion of the counter ions will always be equal with the con
centrations of the cations present in a zone. This if mono
valent ionic species are considered of course.
4.2.2 The modified OHM's law.
+ The influence of the H and OH ions are neglected. It
follows that:
1) I/G = Constant
4.2.3 The mass balances for all cationic species.
In the stationary state the amount of each ionic species
passing a separation boundary is equal to the amount reaching
the separation boundary. For each ionic species and all sepa
ration boundaries can be written:
4.2
Substituting:. v0 4.3
1)
The subscript letter U refers to the uth zone. The Uth zone
contains U ionic species of the sample. The temperature cor
rection for the mobilites TC0 is taken uniform for all spe
cies.
47
4.4
Introducing: Su- 1 ,u
4.3 PROCEDURE OF COMPUTATION.
Combining egns. 4.1 and 4.6, for a separation boundary
will be obtained:
U-1
~ r=1
4.5
4.6
The left-hand side term will be zero for r=U, because the
ionic species U is not present in the U-1th zone. This means
its concentration is zero. Therefore the left-hand sum can be
extended to u. After simplification eqn. 4.7 will give:
~ = 0 4.8 ·r=l
48
or:
This is a modification of the "Dole-polynomals" (ref.66,55).
Solutions are valid if:
< 1
If the composition of the leading electrolyte and the
sample solution are known all parameters can be computed
with the eqns. 4.9 and 4.10 if the Su- 1 ,u were known.
4.10
The velocity of the concentration boundari~s can be neglected.
ted.
The parameters of the first zone can be calculated in
two ways: both with the eqns. 4.9 and 4.10 and with the
isotachophoretic conditions as described in Chapter 3.
In the computation we chose arbritarily a Su-1 ,U of 1 and
computed all quantities. If the parameters of the first
zone in this way obtained did not agree with those of the
isotachophoretic calculation, we recomputed up to the
last zone with the quantities obtained for the first zone
with the isotachophoretic calculation (the S's are constant).
With the formulae a computerprogram is made. Experiments
are carried out in order to check this model. To this end,
all concentrations should be determined in each zone. Be-
49
cause this gives difficulties another possibility is to measure
the speeds of the zones by means of a detector.
Each zone has its specific constant speed: Vu=Eu.mA .TCU.
For practical reasons we use the relative speeds in ste}id of
the absolute speed:
4.11
If the distance between the injection-point and the
point of the detection is called P, the time needed for
each ionic species to be detected will be:
P/VU = P/(mA .TCu.EU) or P u
4.12
The relation between speeds and times for the detection is:
The times of the detections can be measured, taking the
time from the starting-point of the analyses up to the time
of appearing of the step height of that specific ionic spe
cies in the electropherogram.
The speed of the leading electrolyte is equal to the
speed of the first zone following the leading electrolyte
( isotachophoretical condition ) • Thus:
4.14
So we can use the ratio t 1/tu from the electropherograms r
to check the computed Vu/VL <vu>·
50
4.4 EXPERIMENTAL.
As indicated in the previous section the time of de
tection can be used as a parameter, characteristic for mo
ving boundary systems. The relative time tL/tU is a mea
sure for the voltage drops over the zones and therefore
for all other quantities such as the concentrations and
the conductivities of the zones.
To check the model some experiments have been carried
out and the experimental values of tL/tU are compared with
the theoretical values of Vu/VL obtained with a computer
program.
The values of tL/tu were taken from the electrophero-
f d 'ff . f + + .+ T + d T + grams o 1 erent m1xtures o Na , K , L1 , ma an ea .
The leading electrolyte was 0.01 N HCl in water. The elec
tric current was stabilised at 70 1uA.
The experimental data are given in Table 4.1. In Figure
TABLE 4.1 Theoretical and experimental values of the relative
time of detection for some cations in a moving
boundary electrophoretic system.
K Na Tma Li Tea
a) concentrations 0.01 0.01 0.01 0.01 0.01 tL/tU theoretic 1. 000 0.904 0.863 0.793 0.717
measured 1. 00 0.90 0.85 0.79 0.70
b) 0.02 0.01 0.01 0.01 0.01 1.000 0.848 0.805 0.736 0.664 1. 00 0.84 0.79 0.73 0.65
c) 0.02 0.02 0.02 0.01 0.01 1. 000 0.889 0.845 0.753 o. 671 1. 00 0.88 0.83 0.75 0.66
d) 0.02 0.01 0.01 0.02 0.02 1. 000 0.872 0.837 0.793 o. 723 1. 00 0.87 0.83 0.78 0.71
e) 0.02 0.01 0.02 0.01 0.02 1.000 0.877 0.845 0.767 0.708 1. 00 0.87 0.84 0.76 0.70
51
4.1 those results are represented in a graph (the dotted
lines represent the experimental values).
The experimental values agree very well with the calcu
lated values, and it may be concluded that the model is a
suitable one.
G. I
f. " " ' IJ l e. K
I• I llo .... u
(dl
'
(bl
Tao
' ' (c
FIG. 4.1 Graphical representation of the theoretical and ex
perimental values for the times of detection for
some cations in a moving boundary electrophoretic
system (see Table 4.1).
' '
The relative time of detection for a mixture of 2 cations
of a certain known concentration is constant and depends on
the mobilities. By this it is possible to determine the mo
bility of a cation from its relative time of detection.
In Figure 4.2 all relative detection times (calculated)
are noted as a function of a mobility of an ionic species, if
introduced as a mixture with K+ (O.OlN) for some concentrations
of the sample ionic species. (The leading electrolyte is O.OlN
HCl). If the relative time of detection is measured the mobi-
52
so
= 1 t
D.S 1,8
FIG. 4.2 Graphical representation of the calculated relative
times of detection as a function of the mobilities
for different concentrations of the sample, mixed
with 0.01 M KCl, after the leading electrolyte 0.01
N HCl.
lity can be found in this graph. In this way measurements were
carried out with Na+, Tma+ and Tea+. The results are given in
Table 4. 2. As can be seen this procedure is corre'ct for the
measurement of mobilities. Figure 4.2 shows that for smaller
concentrations of the ionic species, mixed with 0.01 M KCl in
one sample, the relationship is a linear one.
This corresponds with the theory, as in that case the
elution phenomena prevail i.e. a uniform voltage gradient
is present over the whole of the capillary and consequently
53
the relative times of detection are a linear function of the
mobilities.
TABLE 4.2 Theoretical and experimental mobilities of some
cations.
concentration tL/tu 5 m. 10 5 m. 10
in the sample theoretical measured
K-Na: 0.01 0.01 0.8375 50.5 51.25 0.01 0.005 0.7930 51.5
K-Tma:0.01 0.01 0.7900 45.0 45.7 0.01 0.005 0.7200 45.5
K-Tea:0.01 0.01 0.6770 30.0 32.2 0.01 0.005 0.6000 33.2
f
Trru:
FIG. 4.3 Separation of a mixture of cations in moving boun
dary- electrophoresis. All initial concentrations
were 0.01 M. The electric current was stabilised
at 70 1uA. The leading electrolyte was 0.01 M HCl
in methanol (95% b.w.).
54
With moving boundary also separations of mixtures can
be carried out. In Figure 4.3 the electropherogram is given
of the separation of a mixture of Tma, NH4 , K, Na, Ca, Li, + Co, Mn, and Cu after the leading ion H •
The separation is quite good, but interpretation will
be difficult if the sample is unknown due to the fact that
the retention times are not constant and the step heights
are dependent to both the mobilities and the concentrations
in the sample.
Of course we would like to know the information of all
step heights and all retention times in the elec~ropherogram
but practically this is too difficult and in this way moving boundary electrophoresis hardly can be used.
55
CHAPTER 5
VALIDITY OF THE ISOTACHOPHORETIC MODEL
5.1 INTRODUCTION
In Chapter 3 a mathematical model of isotachophoresis
has been given and based on this model a computer program
has been developed for the computation of quantities such
as the concentrations of sample and buffer ionic species,
the electrical conductivities of the zones, the pH's of the
zones and the effective mobilities of the ionic species in
the zones during the steady state. For the calculations the
composition of the leading electrolyte zone and data on
ionic mobilities and pK values of all ionic forms must be
Rnown.
In this model the activity coefficients, the influence
of the temperature (different in each zone), the relaxation
and electrophoretic effects, the diffusion, the hydrostatic
flow and the electroendosmosis were neglected.
In this chapter some of those factors will be discussed.
For some of them corrections will be made in the calculations
and the results of these calculations will be compared with
the results of some experiments in order to check the validi
ty of the model.
5.2 THE CONCEPT OF MOBILITY.
The concept of mobility plays an important part in elec
trophoretic techniques. Differences in effective mobilities
determine whether ionic species can be separated or not.
The concentrations and voltage gradients of the different
56
zones in relations with the quantities of the leading zone
are also fixed by the mobility values.
The absolute mobility (m0
) is defined as the average
velocity of an ion per unit of field strength. This absolute
ionic mobility is a characteristic constant for each ionic
species in a certain solvent and is proportional to the
equivalent conductance at zero concentration:
A;t. 0
= 5.1
The effective mobility of an ionic species is related
with the absolute mobili.ty. TISELius 64 pointed out that the
effective mobility was the summation of all products of the
degree of dissociation and the ionic mobilities.
Other influences on the effective mobility are the re
laxation and electrophoretic effects as described by ONSAGER67 .
By the formulae of ONSAGER a correction is made for the ion
ion interactions. The influence of the solvent (e.g. solvation
and influence of the dielectric constant) is also very impor
tant.
Summarising we can state that the effective mobility of
an ionic species depends on factors such as the ionic radius,
solvation, dielectric constant and viscosity of the solvent,
shape and charge of the ion, pH, complex-formation, concen
tration, degree of dissociation and temperature. All those
factors can influence each other and therefore it is very
difficult to give a mathematical expvession for the effective
mobility. Speaking about effective mobilities we will use the
expression:
=~ i
5.;2
57
where ai =the degree of dissociation; Yi= a correction
factor according to the influence of relaxation and elec
trophoretic effects and m. = the absolute ionic mobility. ~
These effects will be described in more detail.
5.2.1 Relaxation and electrophoretic effects.
ONSAGER derived for the rela~ation and electrophoretic
effects the following expression:
5.3
where:
~~.· 0.98S·I06
.~·(1n+l·ln-I)A* + 29(ln+l +In_ I) (DT)+ I + .J q o (DT)t'lo
q = ln+l·ln-1 lri +A; ln+l + ln-1 In+ lA; + ln-l..:tri 5.5
For water as a solvent:
5.6
For methanol as a solvent:
5.7
To compare the effects in different solvents for diffe
rent charges of the cations, we calculated the effective
mobility according to this expression for monovalent and
divalent cations in water and methanol, for a hypothetical
absolute mobility of 50.10-5cm2 /Vs at a concentration of
0.01 N. The results are shown in table 5.1. Those effects
are even stronger for solvents with smaller dielectric con
stants and for cations with higher charges.
58
TABLE 5.1 Theoretical effective mobilities of mono- and di
valent cations in water and methanol (95,% b.w.).
1-1
2-1
50
50
Water
5 meff" 10
46
43
5.2.2 Partial dissociation.
Methanol
50
50
37.5
25
Two main types of interactions can be distinghuished,
protolysis and complex formation.
PPotoZysis.
A proton takes part in the dissociation reaction. The
degree of dissociation depend's on the pH and the equilibrium
constant, e.g.:
5.8
K (pK 4. 75) 5.9
CompZe~ foPmation.
Now a particle different from a proton takes part in the
dissociation reaction, e~g.:
59
The degree of complex formation depends mainly on the
partial concentrations. Sometimes however, both types affect 3+ the mobility such as for Al :
---- Al ( OH) ( H 0) 2+ 2 5
1)
If the value of the dielectric constant decreases, the
interionic forces increase. This results especially for ca
tions with a higher charge in a stronger complex formation.
Therefore the pK values of the dissociation depend on the
dielectric constant.
5.2.3 Solvation.
To describe the exact effect of the solvation is difficult.
In general, ions with large radii and a low charge have a
small degree of solvation, whereas highly charged ions with
small radii have a large degree of solvation~ In general, ions
with a large degree of solvation have a small mobility.
In water and methanol, the mobilities of the alkali metal
ions decrease in the sequence Cs+:>Rb+:>K+:>Na+:>Li+, i.e. in
the order of their decreasing radii. The differences between
the mobilities however, seem to be favoured in methanol. In
water Cs+, Rb+ and K+ ions are very difficult to separate,
while in methanol the differences in mobility are such that
these cations can be separated easily. A similar effect shows
also the series of J-, Br-, Cl- and F-. Also the mobilities 2+ 2+ 2+ 2+ • of Ba , Sr , Ca and Mg ions diminish 1n the order of
their decreasing-radii.
1)
Not all steps of dissociation are given.
60
Organic cations often have high mobilities in methanol.
Even the large cation Tba+ has a rather high mobility, about
equal to the mobility of the very small cation Li+. This
indicates that the Tba ion is hardly solvated, probably due
to the screening effect of the groups surrounding the charge.
In water, however, the Tba+ ion has a rather low mobility.
The cation Tma+ has the highest mobility in methanol, except
for H+.
When the absolute ionic mobility is ~nown and when for the
influence of the degree of dissociation and electrophoretic and
relaxation effects can be corrected, the effective mobility can
be computed. As the exact data for many ionic species are unknowl
many authors have looked for correlations between the ionic mo
bilities and parame~ers such as the radius of the molecule, the
ionic volume and the entropy of the ions.
Some of those approaches will be discussed.
5.2.4 The relationship between entropy and ionic mobility.
E.K. ZOLOTAREv68 has tried to relate the entropy to the
ionic mobility in aqueous solutions. Combination of the by
KAPUSTINSKIIS 103 derived formulae:
s A/rw + B 5.13
and +
m = n:-e I 6. 1r .n0• rw
gives:
s k 1 .m + k2
(this formula is valid for equally charged substances).
61
In Table 5.2 the entropy and the ionic mobility of some ionic
species are noted. The relationship between the entropy and
the ionic mobility is graphically presented in Figure 5.1.
TABLE 5.2 The entropy and the ionic mobility of some ionic
species.
Ionic species m.10 5 s Ionic species m.10 5 s
NH+ 74 27 Ba2+ 63.8 3 cs 4 78 31.8 Cd 54 -14.8 Li 38.7 3.4 ca 59.3 -13.2 K 73.5 24.5 Co 51 -37.1 Ag 62 17.7 Ni 50.5 -38.2 Tl 76 30.4 cu 54.5 -23.6 Na 50.5 14.4 Fe 54 -27.1 Rb 76.5 29.7 Zn 54 -25.5
Pb 70-73 5. 1 Hco; 44.5 22.7 Mg 53 -28.2 J03 41 27.7 Sr 60 -9.4 Hc
3o 4 40.2 36.7 Mn 52 -20
HS 50 31.6 HS0 3 30.3 - 78.4 19.2 50 Br CHO~ 54.6 21.9 Cl 76.5 13.2 Br0 3
56 40.9 F 54.7 -2.3 Cl03 65 39 J 77 26.1 Cl04 68 43.5 CN 78 28.2 N0 3
71.5 35
In Figure 5.l.a the relationship for uni- and divalent
metal ions is given and a linear relationship can be found,
in accordance with the theory. A similar relation for anio
nic species is less evident (Figure 5.1.b).
By using entropy values a reasonable estimation for the io
nic mobility can not be given.
62
-1
50
+1
5
1 II
-m
(a) (b) -10 -50
FIG. 5.1 The relationship between the entropy and ionic mo
bility for some cations (a) and anions (b) (see
Table 5.2).
5.2.5 The relationship between volume and ionic mobility.
In general it is said that for a "steady flow" of molecules
the STOKES' law may be applied for the computation of the force
of resistance (assuming a spherical particle in an infinite
fluidum69 ). If the ionic radius is not too small the following
formulae can be deduced104- 106 :
:1: m
0 = n. e I 6. n .n
0• rw 5.16
For smaller particles(3-5 R> 70- 71 a modified expression can
be given, viz.· +
m0
= n:e I 5.n.n0.rw.(flf
0)
where flf0
is a friction factor correcting for non-spherical
63
particles and rw is the v.d. Waals' radius. For water (21°C)
this means:
From this formula it can be concluded that the ionic mo
bility is a function of shape, charge and radius of the ion 71 72
and the viscosity of the solvent. EDWARD and BONDI have
computed the contribution of the differen~ groups in the
molecules to the V (by this to the r ) from the covalent radius w w 73
according to L.PAULING and the v.d. Waals' radii and angles •
PERRIN74 derived the formulae for the friction factors, from
the ratio of the axes of prolate and oblate ellipsoids.
EDWARD 75 showed the possibility to compute the friction factors
from the diffusion constants.
In the papers mentioned, reasonable results were obtained
for the computed values in comparison with the experimental
values. Deviations were found for small ions and strongly po
lar groups. Nonspherical and non-ellipsoid ions, such as the
"knobby-shape" ions can be computed too. Very irregular ions
cannot be computed because their friction factors are unknown.
In general they will show lower mobilities than spherical ions
with an equal volume.
5.2.6 Discussion.
In this section some approaches are given, for the estima
tions of the ionic mobilities. Quite a different approach has 98 been made by LINDEMANN • He gives an approach based on the
kinetic theory of gases and pictures the ions as suffering
repeated collisions with solvent molecules, at each of which
it retains a fraction of its velocity depending on the relative
mass. Between collisions it moves freely under the influence of
the electric field. A relation is thus established between mo
bility of the ion and its mean free path between collisions.
64
I Although some effects, affecting the effective mobility can
be described mathematically and although the iorhc mobilities
can be treated theoretically from data such as entropy and the
STOKES' law, difficulties in the estimation of mbbilities are
present practically. The mathematical models cannot be applied
to all ionic species. Specific interactions give differences
between experimental and theoretical values, especially in the
use of non-aqueous solvents.
Experimental measurements have to be carried out for the
determination of the mobility. For the comparison of experimen
tal and theoretical values in order to check the isotachophoreti<
model, those ionic species are taken, from which average data in
the literature agree quite well.
Yet, inaccuracies in mobilities can cause differences betweer
theory and practise. Better agreements will be obtained when morE
accurate data would be available.
5.3 THE INFLUENCE OF THE DIFFUSION ON THE ZONE BOUNDARIES.
In the model for isotachophoresis the influence of the
diffusion has been neglected. By this influence the sharp
ness of the boundary is counteracted and the zone boundary
will have a certain width. The neglection of this influence
is only allowed if the zone width due to this effect is very
small in comparison with the zone length.
Several authors {41,63,77,76) give an approximation for this
effect and show that the zone boundary width due to the
diffusion is smaller than 0.1 mm; for longer zone len9ths this
can be neglected.
5.4 THE INFLUENCE OF AXIAL AND RADIAL TEMPERATURE DIFFERENCES.
During electrophoretic experiments radial differences in
65
temperature exist in the zones and axial differences in tern
perature between the different zones. Several quantities such
as mobilities and pK values depend on the temperature. Also
the concentrations and pH of the zones are affected by tempe
rature. HJERTEN 107 and ROUTs 63 described the influences of the
temperature in radial direction and remarked that a parabolic
shape of the zone boundary can be expected.
Another important point is the difference in pK values of
the ionic species due to the different temperatures of the
zones. In Figure 5.2 some pK values of ionic species are
shown as a function of the temperature.
() 0
80 12 n
1 I 8
60
-pK 5 10
FIG. 5.2 Relationship between temperature and pK values of
some ionic species.
(l=pK 1 glutamic acid; 2=pK 1 glycine; 3=pK formic acid;
4=pK2
glutamic acid; 5=pK1
oxalic acid; 6=pK acetic acid;
7=pK2 histidine; 8=pK imidazole; 9= pK3
citric acid;
lO=pK tris; ll=pK arnrnediol; 12=pK o-boric acid.)
66
From Figure 5.2 it can be concluded that esp~cially the
positively charged ionic species such as imidazoie, tris and
histidine, used as buffering counter ions for th~ separation
of anionic species show a strong temperature dependence.
Therefore it can be expected that for the separations of very
low mobile anions this influence can not be neglected.
In the evaluated computer program different mobilities and pK
values can be put in and also corrections for this effect
can be made.
5.5 THE INFLUENCE OF THE ACTIVITY COEFFICIENT ON THE CON
CENTRATION.
When a equilibrium is considered as follows:
HA 5.18
the pH and pK are defined as:
pH 5.19
5.20
The activities are defined as:
5.21
where aA is the activity, cA is the molar concentration and
Ya is the activity coefficient of the component A.
These activity coefficients can be calculated from the
DEBYE-HUCKEL limiting law as:
5.22
67
Although it is possible to compute all activity coefficients
and to develop a computer program including those coefficients
they are neglected in our isotachophoretic model.
In fact this means that the following definitions are used:
pH = - log [ H+] 5. 23
and
pK = pH + log [ A ] I [ AH] 5.24
Interpreting all pHs as -log(H+] and all pKs as pKcs, (see
Section 8.2), correct computations can be carried out. The
pKc can be calculated from the pKa by correction for the activi
ty coefficients and repeated calculations give the exact values.
5.6 SOME CALCULATIONS.
Working at a stabilised electric current, the conductivity
of a zone determines the characteristic voltage gradient over
the zone. The heat production for a unit of volume corresponds
with I.E and determines the temperature of the zone in the
steady state.
For a check of the theory the difference between the tempe
rature inside the capillary ~ube and the temperature of the
air (air-cooling) should be known. The difference in temperature
measured by a thermocouple (dTth) is different. However, a linear
relationship between the dTth and real difference in temperature . d78 ~s measure •
As a linear relationship between the conductivity of a zone
and the temperature inside the capillary tube can be expected,
also a linear relationship can be expected for the relationship
between the conductivity of the zones and the detected tempera
ture by means of a thermocouple. This is used for a check of the
theory.
68
In this section some calculations of the parameters of the
different zones will be made, and the results will be compared
with the results of some experiments. Calculations were made
both for anions and cations, correcting for the ~nfluence of
the activity coefficients, relaxation and electrophoretic
effects and for the different temperatures in the zones. The
temperatures in the zones are estimated from the thermocouple
signals and the relationship between thermocouple temperatures
and the temperatures in the capillary tube 78 •
Calculations were made for the cations Ba, Ca, Mg, Fe, K,
Ag and Na. Those cations are chosen because the slope pf the
functionA~ = F(\rc*} agrees reasonably with the expected slope
according to the ONSAGER's relationship. If other influences
such as complex formation exist, the decreasing effect on the
mobility should be greater and calculations would not be valid
as the computer program does not deal with e.g. complex forma
tion.
For the anionic calculations, those acids are chosen
of which data such as ionic mobilities and pK values are
rather well-known.
The concentrations, pHs, step heights, and zone resis
tances are noted in Table 5.3 for the cations in the system
TABLE 5.3 Some experimental and calculated values for ca
tions for the system WKAC {see Section 9.2.3).
Cation 1/A. 10 3 1/A-10 3 Calculated pH Step height without with concentration of {mm) correc- correc- the ionised part tions tions (mole/1)
K+ 0.874 0.8930 0.0100 5.390 220 Ag+ l. 029 1.0440 0.0094 5.362 260 Na+ \.272 1. 2825 0.0086 5. 320 302 Ea 2+ 1. 013 1 . 1152 0.0048 5.364 264
ca 2+ 1.077 1. 1818 o. 0046 5.353 284 ~lg2+ 1. 210 l. 3215 0.0044 5.331 314
Fe 2+ 1. 188 l. 2969 0.0045 5.334 312
69
TABLE 5.4 Some experimental and calculated values for anions
for the system Hist/HCl (see Section 10.2.1.1).
Ionic species 1/A.103 1jX.1o3 Calculated pH Step height without with concentration of (mm) correc- correc- the ionised part tions tions (mole/1)
Acetic acid 2.036 2.195 o.0082a 6.12 366
Benzoic acid 2.504 2.689 0.0078 6.13 430
m-nitro-Benzoic acid 2.561 2.749 0.0078 6.13 440
p-nitro-Benzoic acid 2.560 2.764 0.0078 6.13 442
Capric acid 3.075 3.246 0.0070 6.19 511
Caprylic acid 3.064 3.235 0.0070 6.19 510
Chloric acid 1.230 1. 349 0.0097 6.04 24 3
Crotonic acid 2.414 2.591 0.0078 6.14 416
Formic acid 1. 4 74 1.608 0.0092 6.06 276
Glycolic acid 1. 996 2.160 0.0084 6.10 360 Hydrofluoric acid 1. 468 1. 600 0.0092 6.06 277
Iodic acid 1. 977 2.142 0.0085 6.09 358
Lactic acid 2.268 2.4 50 0.0081 6.11 391
Nicotinic acid 2.526 2.697 0.0076 6. 16 436
Nitric acid 1. 120 1. 225 0.0099 6.03 220
Nitrous acid 1. 115 1. 219 0.0099 6.03 217
Methacrylic acid 2.295 2.469 o.ooao 6.12 404
Pelargonic acid 3.100 3.286 0.0070 6.20 494
Picric acid 2.648 2.832 0.0077 6. 14 446
S-ch1oro-Propionic acid 2.283 2.461 0.0081 6. 12 399
Salicylic acid 2.334 2.512 0.0080 6.13 408 Sulphamic acid 1. 623 1. 766 0.0090 6.07 304 Sulphanilic acid 2.483 2. 672 o. 0078 6.13 420
!-Valerie acid 2.660 2.831 0.0075 6. 16 460
Adipic acid 1. 543 1.869 0.0045b 6.06 334
Maleic acid 1.689 1. 900 0.0030 0.0027a 6. 11 312
dl-Malic acid 1. 402 1. 655 0.0042 6.07 286 Malonic acid 1. 257 1. 520 0.0047 6.04 280 Oxalic acid 1.098 1.331 0.0049 6.03 236 Pimelic acid 1. 626 1. 972 0.0044 6.07 345 Succinic acid 1.511 1. 759 0.0013 0.0038 6.09 304
'Sulphuric acid 0.996 1.204 0.0050 6.02 224 Tartaric acid 1. 257 1. 521 0.0047 6.04 280
Tartronic acid 1. 203 1.458 0.0048 6.04 256
a Concentration of the mono-valent anions
b Concentrations of the di-valent anions
70
TABLE 5w5 Some experimental and calculated values for anions
in the system Imid/HCl (see Section 10.2.1.~).
Ionl..c species
Acetic acid
Benzoic acid
m-nitro-Benzoic acid
p-nitro-Benzoic acid
Capric acid
Caprylic acid
Chloric acid
Crotonic acid
Formic acid
Glycolic acid
Hydrofluoric acid
Iodic acid
Lactic acid
Nocotinic acid
Nitric acid
Nitrous acid
M~thacrylic acid
Pe1argonic acid
Picric acid
1/L 10 3
without corrections
l. 5049
1.9019
1. 9610
1. 9608
2.2575
2. 25'67
0.9482
1. 7952
1.1259
1.5239 1,1236
1.5171
1.7388
1.8520
0.8594
0.8536
1. 7407
2.2594
1. 7893
e-chloro-Propionic acid 1.7398
Salicylic acid 1.7894
Sulphamic acid 1.2454
Sulphanilic acid
i-Valeric acid
Adipic acid
Maleic acid
dl-Malic acid
Malonic acid
Oxalic acid
Pimelic acid
Succinic acid
Sulphuric acid
Tartaric acid
Tartronic acid
1.8972
1.9680
1. 1783
1. 0679
1.0014
0.8422
1. 2458
1. 0411
0.7681
0.9611
0.9182
1/L1o3
with corrections
l. 5821
l. 9711
2.0357
2.0299
2.3104
2.3016
1.0156
1.8668
1.2013
1.6009
1.1985
1. 5920
1.8144 1.9182
0.9232
0.9137
1.8715
2.3100
1:8493
1. 8140 1. 8632
1.3194
1.9654
2.0322
1. 3499
1.2207
1.1510
l. 0831
0. 9634
1. 4228
1.1946
0.8931
1. 1083 1.0642
Calculated concentration of the ionised part (mole/1)
0. 0075a
0.0065
0.0064
0.0064
0.0059
0.0059
0.0093
0.0068
0.0087
0.0074
0.0087
0.0074
0.0069
0.0066
0.0097
0.0098
0.0068 0.0059
0.0068
0.0069 0.0068
0.0082
0.0066
0.0064
0.0042b
0.0042
0.0045
0.0046
0.0049
0.0041
0.0044
0.0051
0.0046
0.0047
a Concentration of the mono-valent anions
b Concentration of the di-valent anions
pH
7.13
7.18
7.19
7.19
7.23
7.23
7.03
7.17
7.06
7.13
7.06
7. 13
7.16
7.18
7.01
7.01
7.16
7.23 7.17
7.16
7.17
7.08
7.18
7.19
7.07
7.06
7.04
7.18
7.01
7.08
7.05
6.99
7.03
7.02
I Step height , (mm)
281
340
340
345
400
400
190
326
216
286
218
290
314
342
174
170
312
393
350
316
323 244
344
360
252
216
222
204
180
264
224
169
216
,195
380
-e E -::J:
I 200
71
380
-E e -::J:
l 100
(a) (b)
0.9 1,1 1.3 0.9 1,1 t.l ---- 1/}.·103 - VA·103
FIG. 5.3 Relationships between measured step heights and
calculated zone resistance for sorne cationic species
in the system WKAC, without corrections (a) and with
corrections (b).
WKAC (see Section 9.2.3) and for the anionic separations
in the systems Hist/HCl and .rmid/HCl (see Section 10.2.1)
in the Tables 5.4 and 5.5 respectively.
Firstly calculations were made without any correction.
The relationship between the experimental measured step
heights and the uncorrected calculated conductivities of
the zones are represented in respectively the Figures 5.4.
a, 5.5.a and 5.6.a. Although one continuous relationship
must be expected, two distinghuishable curves are obtained,
for those relationships.
This.can be understood easily.
72
-
-
FIG. 5.4 Relationships between the measured step heights and
the calculated zone resistance for some anions in
the system Hist/HCl, without corrections (a) and
with corrections (b).
If the zone resistance are computed without applying
corrections for the Onsager relation, there will be devia
tions with the real electrical resistances actually present.
The zone resistances calculated will be smaller than the
actual resistances because the relaxation and electrophoretic
effects are neglected, which decrease the mobility. Conse
quently the resistance of the zones increase.
As these effects are stronger for divalent ionic species, two
different curves can be expected, as shown in the Figures
5.3.a, 5.4.a and S.S.a. The influence of the different tempe
ratures on pKs and ionic mobilities and the influence of the
activity coefficients do not differ so much for mono- and
di-valent ionic species.
73
:
(a)
. ..
(b)
FIG. 5.5 Relationships between the measured step heights and calculated zone resistances for some anions in the
system Imid/HCl, without corrections (a) and with corrections (b).
After corrections have been made for the influences of
temperature activity coefficients and the Onsager relation,
only one curve is obtained for both the mono-, and divalent
ionic species (Figure S.3.b, S.4.b and S.S.b), in accordance
with the theory. In all cases the calculated pH values of the
zones before and after applying the corrections do not differ
appreciably. For most ionic species they differ by not more
than 0.01 of a pH unit. Therefore no pH measurements were
used as a check on the theory. Reasonable values were obtained
however, by EVERAERTS and ROUTs 65 •
74
CHAPTER 6
I
SOME PHENOMENA IN ISOTACHOPHORETIC EXPERIMENTS
6.1 INTRODUCTION.
In the experimental work in isotachophoresis sometimes
strange effects have been obtained. This can be caused be
cause not all conditions are fulfilled to obtain an isotacho
phoretic system. In this chapter some of those phenomena will
be discussed.
6.2 SOME EFFECTS IN THE USE OF NON-BUFFERED SYSTEMS.
A non-buffered system in isotachophoresis for the separa
tion of cations can consist of a strong acid as a leading
electrolyte, such as HCl and a-terminator such as tris.
After the introduction of a sample and the separation of the
ionic species, a series of zones is obtained containing one
ionic species of the sample each. Two kinds of separation
boundaries can be distinghuished viz., the first boundary be
tween the leading ion H+ and the zone of the ion M;, of the
sample with the highest mobility (the boundary of the type
HI-MI, Section 6.2.1) and the other separation boundaries
between two zones of sample cations (the boundary of the type
MI-MII' Section 6.2.2). These two types of boundaries have a
different character in general.
6.2.1 The HI-MI boundary.
The zone of the cation M; always will contain H+ ions.
Essentially this means it is a mixed zone of a cation M;
and H+ ions. The H+ ions are more mobile than the M; ions
and therefore the hydrogen ions will pass the boundary HI-MI.
75
(Note: in a buffered system they will be taken away by the
buffer, according to the equilibrium state).
Those hydrogen ions passing this boundary migrate into
the leading electrolyte zone (HCl) and create a H+ zone be~ tween the leading electrolyte zone and the first sample zone
M;. Evidently the extra H+ zone has the same H+ concentration
as the leading electrolyte zone. In fact this is a moving
boundary procedure. For the M; zone the isotachophoretic con
dition is not valid anymore. The speed of this zone is smaller
than that of the leading electrolyte zone. The step heights
will be smaller due to the effect of the H+ ions. If the H+ + concentration in the MI zone is low, the effect mentioned
above is very small and practically no disturbances can be
expected. If the pH is low in the M; zone, the original H+
zone is elongated and the result is: longer times for the detection and lower step heights.
In Figure 6.1.a-d the electropherograms are shown, of
Al 3+ as a terminator after 0.01 N HCl as a leading electro
lyte in methanol, as practically obtained. Figure 6.1.a
shows the original situation, viz. the original leading ion + 3+ zone H (1} and the terminator solution Al (3), which contains
also H+ ions.
In the Figures 6.1.b-d an increasing amount of H+ ions(2) be
tween the original solution of H+(1} and the mixed zone Al 3+
-H+ is obtained after a longer time of analysis. The original
concentration boundary, which will be present too, is neglected.
6.2.2 The MI-MII boundary.
Now two mixed zones are close together, both consisting of
a cation of the sample and H+ ions. The H+ ions of the M~ zone
76
FIG. 6.l.a-d Simplified electropherograms of the leading elec-3+ troplyte HCl and the terminator Al in methanol,
after different times.
+ will pass the boundary and will migrate into the MI zone.
Computation of the pH relation for the two zones (for hypothe
tical values) including the mass balances for the H+ and the
OH ions and the dissociation constant of water, gives imagi
nary data, assuming a stationary state. So no stationary state
will exist.
If the pH is about 7 the influence on a stationary situa
tion will be small and practically no disturbances can be ex
pected. If the concentrations of the hydrogen or hydroxyl ions
are large, elution phenomena will be dominant. If the pH of
the second cation-zone is low, the H+ concentration will pass + + the boundary and a mixed zone of MI and the H coming from the
M; zone is created.
The step height in the electropherogram will decrease
and this results in two zones of the cation M~, viz. the + + +
original M* zone and the mixed zone of H and MI. After some
time the H coming from the M; zone has covered the whole
M+ zone. I
A situation as described was obtained using a leading
electrolyte of 0.01 N HCl in methanol and a terminator of 3+ + Al . The sample K was introduced. Figure 6.1.e shows the
original situation. The first zone is the leading zone con
sisting of H+ (1), the second the original K+ zone(2) and the
last zone contains Al 3+ including H+ ions (3).
77
Jl£_~ 3 t _j2~ 3 t
1 1 ;
-time e
FIG. 6.l.e-h Simplified electropherograms of the leading elec
troplyte HCl, and the terminator Al 3+. The sample
K+ is introduced. The solvent was methanol.
In Figure 6.l.f. the hydrogen ions have partially penetra
ted the K+(2A) zone, where in Figure 6.l.g the hydrogen ions
nearly have reached the leading zone. In Figure 6.l.h an en
larged leading zone (lA) can be seen.
In Figure 6.l.i-l a similar procedure is shown for a lea
ding electrolyte of KCl (1), a sample containing Na+ ions (2)
and a terminator of Al 3+ (and H+) (3). The H+ ions coming from
the Al 3+ zone enter the Na+ zone (2A) and finally reaches the
K+ zone ( lA).
Cll i ilill bfJt bti b8 ·;;; ! 3 : :3 : : 3 i3 t 1 ! 2 i t 1 !2! 2a i t 1 ~ 2a i t 1 'toi 2a i
-time k
FIG. 6.l.i-l Simplified electropherograms of the leading elec
trolyte KCl and the terminator AlJ+ in methanol
after different times. The sample introduced was Na+.
To check the influence of a low pH in the terminator
quantitatively, experimental values are compared with theoretical
values, as calculated with the model as described in Section 4.2.
As a terminator, mixtures of HCl and KCl at different pHs are
used with a leading electrolyte 0,01 N HCl in water. The elec
tric current was 70 1uA. The ratios tL/tu are taken as a check.
78
•+.--~----~--~--~--~----r------ pHT
FIG. 6.2 Theoretical and experimental relationship between
the pH of the terminator solution and the relative
times of detection, for solutions of KCl as a
terminator, in a moving boundary system.
In Figure 6.2 the relationship between the pH of the terminator
and the tL/tU is given for the theoretical and experimental va
lues (triangles). A good agreement is obtained, showing that a
model of moving boundary is a better description than isotacho
phoresis for this model.
If the influence of back-ground electrolytes such as hydro
gen ions is too great elution phenomena will appear after some
time. The zone boundaries become more and more unsharp and af
ter a long time they release each other. The elution effects
are often caused by electrode reactions when the electrode
compartments are not refreshed in time; using Cl as a counter
ion in methanol (95% b.w.) the following reactions can be
expected:
HOCl
2 Cl !!!!!!::::;;;;; Cl2
+ 2e HCl +
79
In experiments with a non-buffered system the produced
H+-ions disturb the analyses. As an example the separation
is given of Cs, Na and Li, with a leading electrolyte 0.01 N
HCl and the terminator CdC1 2 • (See Figure 6.3.a).
In Figure 6.3.b the separation of the same mixture in the
same system is given, after that the terminator electrolyte
was not refreshed for some time. The terminator solution was
more and more acid and a flow of hydrogen ions migrate through
all zones towards the cathode compartment.
8 ~ ~ H ~ ~
~ ~ 8 00
t
Cd
8 ~ ~ H Cd ~ ~
~ ~ 8 00
t TIME TIME
(a) (b)
FIG. 6.3 The separation of a cationic mixture in a non-buf
fered electrolyte system with refreshed terminator
(a) and unrefreshed terminator solution (b).
From the phenomena described above it can be concluded,
that it is not advisable to work in non-buffered electrolyte
systems, where regular refreshing of the electrode compart
ments is necessary. The use of terminator solutions at low
pHs is undesirable, for cationic separations. Similar problems
can be expected for anionic separations 57
80
6.3 ENFORCED ISOTACHOPHORESIS.
The pH of the zones depends strongly on the,pK values of I
the buffer ions and the sample ions. Separating 1 strong acids
the pH is nearly equal to the p~ but for weak ~cids large pH
shifts can be present. Problems can be expected when the pHof
the zones is not increasing regularly.
When the pH of a zone is lower than the pH of the preceding
zone, the effective mobility of the ionic species of the prece
ding zone, will be smaller in that zone, i.e. if some of the
ions are left behind, they cannot reach there own zone and the
self-correction of the sharpness of the front is lost. In course
of time the zonelength will decrease and mixed zones are the
result.
An example of this phenomenon63 is the bicarbonate zone
before a zone of cacodylic acid. The pH in the cacodylic acid
zone is lower than the pH of the bicarbonate zone, and the
effective mobility of the bicarbonate ions is higher in the
pure bicarbonate zone than in the cacodylic acid zone. The
bicarbonate zone vanishes.
Furthermore a pH can be chosen that the ionic species in
a particular zone has an effective mobility higher than the
effective mobility of the leading ion, but a smaller effec
tive mobility in the leading electrolyte zone. The ionic spe
cies can not pass the boundary with the leading electrolyte
(pH shift) but has a larger effective mobility and therefore
a smaller step height. This can be called an enforced isota
chophoretic system, because the zones are not ordered to de
creasing effective mobilities.
An example of such a system can be the leading electro
lyte consisting of a mixture of potassium acetate 0.01 N and
81
acetic acid at pH 4. 75 and a sample of bicarbonate. The bicar
bonate's effective mobility is higher than that of the acetic
acid but the pH of KAC/HAC is such that the carbonate cannot
pass that boundary.
In Figure 6.4 the electropherograms are given for this system
at two different times of detection. The step heights of the
bicarbonate zones are smaller than the step height of the
leading electrolyte zone, where the zone length decreases
during time, because of the lower pH of the cacodylate zone •
.......
"' 'tl ..., ... m u ..., <11 "' u
'tl u "' 'tl ..... ..... ..... u c:: 9 u <11 0 "' .<l ..... u .. rn u ..... "' rn ... ..., u "'
..., "' ..... ..., Q) u ~ 0 u < .,. <
- TIME -TIME (b)
FIG. 6.4 Electropherogram of the bicarbonate zone between the
leading electrolyte zone KAC/HAC (pH 4.75) and caco
dylic acid (b). The same separation after a longer
time (a).
Disc electrophoresis.
In disc electrophoresis 26 the first stage of the separa
tion consists of an isotachophoretical system whereby the
sample introduced is concentrated in small zones. Generally
the leading electrolyte consists of an acid (e.g. acetic acid)
which buffers at a low pH (4.75) and a buffering counter ion
82
(e.g. tris) which does not act as a buffer in the leading zone
(pK = 8).
Only in the following zones the counter ions buffer and they create high pH's where the proteins have a s
1
ufficient
mobility. In the literature56- 59 different treatments for
the zone pHs are considered and from comparisons with weak
acids pHs of 8-9 are assumed in the protein zoneJ.
11
pP;:ionic apeeies•lO
effective mobilities
FIG. 6.5 Relationship between pH in the sample zone and effec
tive mobility of the sample ionic species for diffe
rent pR values of the ionic species. The leading
electrolyte is a mixture of 0.01 N potassium acetate
and acetic acid at a pH of 4.75. The countering
buffer ion is tris with a pR of 8.
83
We computed for some weak acids (hypothetical pK values) the
pHs in the sample zones for a system as described above at a
pHL of 4.75; the pHs in the zones as a function of the effective
mobilities are shown in Figure 6.5 for several pKs of the
ionic species. As can be seen, the pH strongly depends on zone the pK values and on the mobilities of the ionic species.
Especially for rather mobile ionic species large pH shifts
can be obtained. For low mobilities the shift in pH is not as
high as is assumed in the literature. For some acids with
charges of -10 to -100 and pKs of 7 to 8, pHs were computed
to be 5.72 to 6.4. If it is allowed to use the model for the
calculation of the pHs, it means that the proteins do not
move in an isotachophoretic way, but are in fact pushed along
by the terminator solutions, where a high pH is present.
Also this can be called enforced isotachophoresis.
6.4 "WATER" AS A TERMINATOR.
In Section 3.5, we mentioned that sometimes no real values
for the P"v could be obtained, because the isotachophoretic
conditions was lost at low pHs for the cationic and at high
pHs for the anionic separations. This can be caused, because
the pH increases in anionic separations and decreases in
cationic separations until va~ues were hydroxyl, respectively
hydrogen ions can carry the electric current and the
"water" acts as a back-ground electrolyte. Zone electrophore
sis is the result. When the substances are more mobile than
the< "water", it can act as a terminator.
Some experiments are carried out to study this phenomenon.
Analysing some nucleic bases this phenomenon was observed.
Nucleic bases have a rather low mobility and show low pK va
lues. The step heights of those substances have been deter
mined in a system of the leading electrolyte consisting of
a mixture of potassium acetate and acetic acid at different
pH's and are noted in Table 6.1.
84
TABLE 6.1 The stepheights of some cations after a leFding electrolyte of 0.01 N potassium acetate and acetic acid at different pH's. I
pHL 4.0 4.3 4.5 !4. 91
CATIONS Step heights (nunl
Adenine 30 69+90
Adenosine 12 12+37 85+120 156
Guanine 11.5 13 85
Uridine 12 12 77 119
Cytidine 12 12+40 103 145
Guanosine 12 12 80 120
In Table 6. 1 we can see that at low pH's of the leading
electrolyte (in the sample zones the pH is even lower) all
substances show the same step heights. Some substances show
double peaks. At higher pH's the substances show different
stepheights, but the differences are too small to separate
all of them together. Furthermore the "water" peak at pH
4.91 is about 160 and it is dubious whether the step heights
measured are pure isotachophoretic step heights or the step
heights of a mixed zone of the substances with much H+, as the
pH can be lowered very much.
It can be concluded that substances with low pK values
and small mobilities can not be separated at low pH's.
Also some experiments have been done with amino acids and
similar results have been obtained. At low pH's the amino
acids had the same step heights. Also v.HOUT 79 fou~d the
same step heights for amino acids for an electrolyte system
at pH 5. For some fully ionised cations the calculated Pfiv's are
shown in Table 6.2. If the Pfiv is not given in the table, no
85
real zero-points were present.
From the table it can be seen that the substances with low
pK values can not be separated by isotachophoresis (pK 3 and
2) where fully ionised cations can be analysed at lower pH's.
TABLE 6.2 Calculated pHs of the sample zones for cations after
the leading electrolyte potassium formate/formic
acid and sodium formate/formic acid at different
pHs.
PHr, a) 3.0 3.5 3.75 4.0 4.1 4.2 4.5 s.o
Cations pHs of the sample
m.10 5pK zone (theoretic)
50 14 3.34 3.61 3.87 3.98 4.08 4.38 4.88
30 14 3.55 3.68 3.80 4.12 4.65
10 14
30 6 3.54 3.67 3.79 4.10 4.49
30 5 3.48 3.60 3.70 3.93 4.13
30 4 3.38 3.51
30 3
30 2
PHr, b) 3.25 3.5 3.75 4.0
38.8 14 3.068 3.368 3.637 3.896
30 8 3. 458 3.749
20 8
a) pHL of the leading zone Potassium formate {0.01N) and
formic acid.
b) pHL of the leading zone Sodium formate (O.OlN) and
Formic acid.
86
In order to see what happens separating thosel cations,
experiments were carried out with tris as a termi:nator and I
Li as the sample ion after leading electrolytes consisting
of 0.01 N potassium formate and formic acid resp. sodium
formate and formic acid at different pH's.
TIME
FIG. 6.6 Electropherograms for Li between tris as a terminator
and the leading electrolyte sodium formate/formic acid
at different pH's •
. In Table 6.2, Li (mobility 38.8) always shows real zero
points with the leading electrolyte sodium formate/formic
acid, whereas tris ( mobility about 30 ) does not show real
zero-points at pH 3.25 and 3.5. In Figure 6.6 the electropherograms are given for those systems. Indeed Li shows at
these pHs normal step heights but tris shows at pH 3.5 a retardation. At pH 3.25 a large and a lowered step height is
present between Li and tris (zone electrophoresis).
Tris shows no real zero-points at pH 3.75 for the system
87
E< :c <:!) .... ~ :c p, ~ E< Ul
1
TUIE
FIG. 6.7 Electropherogram for Li between tris as a terminator
and the leading electrolyte potassium formate/formic
acid at pHL 3.75.
potassium formate, and already at this pH the electrophero
gram (Figure 6.7) shows a large and a low step height between
Li and tris.
E X P E R I M E N T A L P A R T
It is a necessary principle in experimen
tal work to eliminate every complication,
and to make experiments as simple as
possible.
A.L. Lavoisier.
90
CHAPTER 7
INTRODUCTION
Numerous techniques are available for the quantitative
and qualitative analyses of ionic species and each techni
que has its own advantages and limitations. Because of mu
tual interactions of the ions, simultaneous separations are
sometimes tricky.Great differences in concentrations may be a source of difficulties and sometimes complicated pre-treat
ments of the sample are necessary.
Isotachophoresis is a technique with many advantages in
comparison with other well known techniques. Simultaneous
separations of ions are possible, but until now the possibi
lities of analysing ions by isotachophoresis have not been
fully studied. In the first part of this thesis the theory of
isotachophoretic processes has been described and in this
part experiments will be dealt with, showing the possibilities
of this method.
In isotachophoresis ionic species can be separated if their
effective mobilities differ sufficiently. The effective mobi
lity is defined as:
(eqn. 5. 2) .
The degree of dissociation ai, depends mainly on the pK values,
the temperature and the pH in the zones. The values yi' a correction factor for the decreasing effects on the mobility
due to the relaxation and electrophoretic effects as described
by ONSAGER67 , depend mainly on the ionic concentrations. The
values of mi depend on several factors such as solvation, ra
dius and charge of the ions and dielectric constant and vis
cosity of the solvents.
91
All those parameters influence the effective mobility and
a well. considered choice of the electrolyte system, makes a
good separation possible.
The use of different solvents (the influence of the dielec
tric constant and solvation) or different buffers (the change
of pH and the influence of the complex formation) allows nu
merous possibilities.
The separation of ionic species can be carried out in diffe
rent ways, viz.:
- The differences in absolute ionic mobilities can be used
for the separation of the ionic species. A particular
pH of the buffered system is chosen such that all ionic
species are almost completely dissociated. We will call
those separations: "separations according to mobilities".
The differences in the pK values of the ionic species
can be used for the separation. A particular pH is
chosen such that most ionic species are not completely
dissociated, especially when many ionic species have
about the same ionic mobility. According to eqn. 5.2 a
pH is chosen in such a way that maximal differences in
effective mobilities are obtained. Those separations
will be called: "separations according to pK values".
- Other solvents can be applied in order to obtain a com
plete separation. This can be used if the ionic species
have about the same ionic mobilities and pK values, and/
or are.not or only slightly soluble in a certain solvent.
Furthermore other factors as complex formation, prec~p~
tation102 and other specific interactions can be used.
We will not look into their possibilities, although they
automatically affect the effective mobility.
92
The experiments described successively in the next chapters com
prise the qualitative and quantitative cationic and anionic
separations according to mobilities and pK values with both water and methanol as solvents1).
As methanol is used as a non-aquous solvent and the pK va
lues must be known in order to choose the buffe~ system, the
pH (pK) measurements in non-aqueous media will be discussed
briefly.
l) Most data have been published already (ref. 42-47 ).
Copyright by Elsevier Publishing Company, Amsterdam,
The Netherlands.
93
CHAPTER 8
DETERMINATION OF PK VALUES IN METHANOLIC SOLUTIONS
8.1 THE DETERMINATION OF THE pH IN METHANOLIC SOLUTIONS.
The operational definition of the pH determined electro
metrically in water, is based on EMK measurements of cells
of the type:
Indicator I aqueous solution I KCl, ref. electrode
electrode of standard; pHs
Indicator I aqueous solution I KCl ref. electrode
electrode of sample; pHx '
In general the indicator electrodes are glass electrodes and
the reference electrodes are calomel electrodes.
The Es and the Ex can be expressed as (25°C):
0.05916 log aH,s + Ej,s
0.05916 log aH + E. ,x J ,x
Combinations of the eqns. 8.1 and 8.2
- log aH,x - log aH + Ex - Es ,s 0.05916
The operational definition of the pH is:
E - E X S
pHS + 0.05916
E. - E. J,X J 1 S
0.05916
8.1
8.2
8.3
8.4
94
Comparison of the equation 8.3 and 8.4 shows th~t:
- log aH ,s
and
E. = E. ] 1 X ] 1 S
In general this is not exactly true. Bates et.al. of the N.
B.s. 83 have determined the pHs of some standard buffer solu
tions for which:
If the solution x has about the same ionic strength, in the
same solvent as used for the standard solution, Ej,s can be considered as equal to E. and then pHx can be interpreted J,X as -log aH,x'
For the pH measurements in methanolic solvents, the same
procedure can be followed. Because of the different liquid
junction potentials for aqueous buffer solutions and unknown
methanolic solutions, there must be looked for standard buffer
solutions in the same kind of methanolic solutions as used for
the unknown solution. Using this standard solution the two
liquid junction potentials will cancel each other again and
the measured pH can be interpreted in terms of hydrogen ion
activity. de LIGNY et a1 84 • 85 determined the pH (-log cH. y:) for some standard solutions in methanolic solvents according to the
method of the N.B.S. for water solutions.
1)
In the determination of the pHx of standard solutions for 1)
Here the asterisk menas that the quantities refer to the
solutions considered, and not to aqueous solutions.
95
methanolic solvents corrections have to be made for the slight
association of ions to ion-pairs. FUOSS and ONSAGER86 , 87 de
veloped a method for the calculations of the closest. approach
b and the dissociation constant K of an incompletely disso
ciated electrolyte in water, but because for the methanolic
solvents no accurate determinations of the conductivity of
electrolytes were available DE LIGNY et al. did not correct
for the ion-pair association. • For the estimation of the log Ycl de LIGNY et al used the
Gronwall-LaMer-Sandved equation:
• (n*e> 2 ln y = -
2DkT
+ 2 3 1024{ (n-el ~
bDkT .
K - ln (1+0.002.c.M1) +
:1: 2 5 1040! (n e) I
• (~X3 - 2Y3) + l ~ bDkT
The pH values for some buffers are noted in Table 8.1 as
determined by de LIGNY.
In those experiments the reference electrode (calomel) is
placed in a KCl solution of the same solvent as the buffers
are prepared in. Using the values mentioned de LIGNY deter
mined the liquid-junction potential between the buffer solu
tions in methanol and a saturated KCl solution in water.
8.5
The liquid junction potentials between standard solutions
in methanol-water mixtures and a saturated KCl solution in wa
ter are noted in Table 8.2. When the pH of a solution of metha
nol water mixtures is measured by means of a pH meter, stand
ardised by a KCl solution in water, the error due to the li
quid-junction potential can be calculated by:
E.* - E d pH~= J (meth-water) j(water) 8.6
0.05916
96
TABLE 8.1 p~ values for the oxalate and succinate ~uffer in
methanolic solutions as determined by de Ligny et al.
% methanol pHx
0 10 20 30 40 50 60 70 80 90
100
2.15 2.19 2.25 2.30 2.38 2.47 2.58 2.76 3.13 3.73 5.79
0.01 M H2
Succ+0.01 M LiHSucc I
% methanol pHx
0 10 20 30 40 50 60 70 80 90
100
4.12 4:3o 4.48 4.67 4.87 5.07 5.30 5.57 6.01 6.73 8.75
TABLE 8.2 Liquid junction potentials between standard solutions
in methanol and a saturated KCl solution in water.
% methanol E~ % methanol E~
0 0.0046 0 0.0041
39.13 0.0091 43.31 0.0083
70 o. 0114 64.2 0.0132
84.2 -0.009 84. 1 -0.0091
84.21 -0.0082 84.2 -0.0086
94.2 -0.0435 94.19 -0.0485
100 -0.1338 100 -0.1329
100 -0.1347
For higher percentages of methanol this d pH can be very
high. In order to calibrate the pH meter for measurements in
methanolic solutions also a standard buffer solution in water 89 X
can be used • Then the correct pH can be computed from the
read pH, by subtracting a correction factor o. The values are noted in Table 8.3.
97
TABLE d.3 6-Correction term for some methanol-water mixtures.
% methanol pHx units
0
43.3
64
94.29
0.11
0.22
-0.86
The liquid-junction potentials at the boundaries standard
solution (alcoholic-water mixtures)/saturated KCl solution (aq)
are independent of the nature of the buffering solution.
In the pH~ measurements carried out in this chapter, the
same procedure is used as described by de LIGNY. Standard buffer
solutions and pHx values used as determined by this author.
8.2 THE DETERMINATION OF pK VALUES IN METHANOLIC SOLUTIONS.
The determinations of pK values can be carried out in
several ways. The most important ones are:
- the conductivity method.
- the electrometric way.
- the spectrometric way.
- the colorimetric way.
In this paragraph the electrometric method will be discussed
for the determination of pK values.
According to RORABACHER90 et al. some definitions can be used
for the pK. The activity equilibrium constant is defined as:
x a A I 8.7
98
TABLE 8.4 Experimentally determined pK! values of some ionic
species in 95 % methanol.
Ionic species pK: Io.ni.c speci.es !If pKm
Aceti.c acid 7.9 Maleic acid 4.6 - ?
Adipic acid' 7.55-9.1 Malonic acid 5.9 -9.7
Azelaic acid 7.6.5-9.0 Monoethanolamine 9.6
Benzoic acid 7.5 Myristic acid 8.1
Butyric acid 8.0 Orotic acid 8.8
Caproic acid 8.0 Oxalic acid 4.5 -8.3
Caprylic acid 8.0 Palmitic acid 8.0
Diethanolamine 9.6 Pimelic acid 7.6 -8.95
Formic acid 6.45 Pyruvic acid 5.9
Glutaric acid 7.5 -9.2 Salicylic acid 6.2
Hippuric acid 6.95 Suberic acid 7.6 -8.95
Histidine 6.0-10.15 Succinic acid 7.25-9.4
Imidazole 6.55 Triethanolamine 7.9
Lauric acid 7.9 Tris 9.05
Linoleic acid 7.9 i-Valeric acid 8.05
The equilibrium constant based on concentrations is:
8.8
and the mixed-mode equilibrium constant is defined as:
8.9
By this: 2 I y HA 8.10
In the electrometric method for the determination of pK
values, the concept of the HNP is used. The HNP (half aeutra-
99
lisation point) is the point in the acid-base titration at
which half the amount of acid {or base) has been
According to eqn. 8.3 this means that the pK: mined. The thermodynamic equilibrium constant can
neutralised. is deter
be computed from the mixed-mode constant by correcting for the activity
coefficients {eqn. 8.10).
8.3 EXPERIMENTS.
In order to choose an optimum electrolyte system in isotachophoresis, the pK values of the buffers and the pK
values of the sample ionic species must be known. Some pK: values of anionic species and bases have been de
termined in 95% methanol on the electrometric way. The re
sults are listed in Table 8.4.
100
CHAPTER 9
THE QUALITATIVE SEPARATION OF CATIONS
BY ISOTACHOPHORESIS
9.1 INTRODUCTION.
As mentioned before, the effective mobilities of cations
can easily be influenced. This can be an advantage especially
if the cations to be separated have the same or almost the
same effective mobility in an electrolyte system. By changing
the system, it may be possible to separate ~uch ionic species.
In this chapter the qualitative simultaneous separation of
some cations both using water and methanol as a solvent will
be described. Buffered as well as non-buffered systems have
been used. The conditions for all those electrolyte systems
are summarised in Table 9.1. The step helghts1 ) found in the
electropherograms of the experiments in water and methanol are
given in Tables 9.2 and 9.3 respectively. All these step heights
refer to o1uA.
For some electrolyte systems a scheme is given showing
which cationic species can be separated simultaneously. The
interpretation of the diagrams is as follows. Ions placed
in one circle and ions placed in circles directly connected
by lines, cannot be separated from each other. An example is 2+ 2+ given (Figure 9.1, system WHCL). Ba and Pb cannot be se-
parated because they are placed in the same circle, whereas
1)
The step height in an isotachopherogram is a qualitative
measure for the ionic species, where the distance between
two successivepeaks gives all necessary quantitative information.
TABLE 9. 1 Conditions of the different systems for the separation
of cations.
Aqueous systems Methanolic systems
WHCL WHI0 3 WKAC WKCAC WKDIT MHCL MKAC TMAAC
Leading electrolyte 0.01 N 0.01 N 0.01 N 0.01 N 0.01 N 0.01 N 0.01 N 0.01 N
HCL HI03 KAC+ KOH + KOH + HCL KAC + TmaAc+
Acetic Caco- Diiodo- Acetic Acetic
acid dylic tyrosi- acid acid
acid ne
pH of the leading 2 1.9 5.39 6.37 7.39 6.35 6.85 1-' 0
electrolyte 1-'
Terminator solution 0.01 N 0.01 N 0.01 N 0.01 N 0.01 N 0.01 N 0.01 N 0.01 N
Tris Tris Tris Tris Tris CdC12 CdC1 2 CdC12 Electrical current 100 70 70 70 70 50 50 50
<;uA) Recorder adjustments
Integral signal (mV) 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Differential signal 20 20 20 20 20 20 20 20
(1
uv)
Paper speed 5 5 5 5 5 5 5 5
(mm/min)
102
TABLE 9.2 Step heights (mml of cations in aqueous systems.
System
CATION WHCL t1HI0 3 WKAC WKCAC WKDIT
+ 60 72 H+
K + 216 290 220 280 300 Na+ 292 400 302 384 410 ;Li+ 352 492 378 476 504 NH4 215 292 220 282 303 Ag+ 260 338 t.l.m. Tl + 217 295 .Tma+ 302 437 340 430 442 Tea+ 400 560 432 540 568 Tba + t .1. m. t.l.m. t .1. m. 808 Tr~s 434 625 490 610 680 Im+ 306 412 310 432 c) 551 Cs+ 208 Rb + 213 ,Guan+ 285 391 294 372 399 S.C. 324 450 343 434 477
2+ 290 416 318 407 co2+
Ni2+ 291 415 318 403 t.l.m. Mg2+ 294 408 314 . 396 430 cu2+ 290 404 387 442 t.l.m. ca 266 372 284 362 388
2+ 285 412 320 420 440 Mn 2+ Cd 2+ 318 420 341 446 t .l.m. Fe2+ 294 a 410 312 508 t.l.m. sn2+ 248-270 ) - 1276 b) t.l.m. Pb2+ 250 t.l.m. 371 486 t.l.m. Ba2+ 255 352 264 338 368 Zn 294 404 320 415 t.l.m.
3+ t.l.m. t.l. m. 1128 b) t.l.m. t .l.m. Fe 3+ ~a3+ 241 366 322 402 634 ce 3+ 246 368 325 416 834 cr3+ 312 a) 498 390 t.l.m. t .l.m. ,Al 272 380 360 t.l.m.
t.l.m. means "too little mobile" a) double step b) estimated value from experiment at a lower
current deni:li ty c) the step height for imidazole at pH 6.53 is 472 mm
103
ca2+ and Al 3+ cannot be separated because they are connected 2+ 2+ 3+ directly by a line. If Ba , Ca and Al are present, they
form a mixed zone together. Li+ and Tea+ can be separated be
cause they are not connected by a line.
The experiments were carried out with an instrument described
in Appendix B.
The effective mobilities of some cations are sometimes very
low. The increment in electrical resistance during the analy
sis, due to the movement of the zones with small conductivi
ties into the capillary tube, require higher potentials than
available. In this case the term "too little mobile" is used
for these cations.
The sample tap volume (about 20 1ul) is rather large
and corresponds to the contents of about a 14-cm length of
the capillary tube. If the concentrations of the sample ions
are chosen to be too high, a complete separation according to
the isotachophoretic principle, cannot be expected.
The average time for most analyses was about 45 minutes.
9.2 AQUEOUS SYSTEMS.
9.2.1 The system WHCL.
The leading electrolyte used is HCl in water and tris
in water is used as the terminator.
Many mono-, di- and tri-valent ions have about the same
step heights. Their effective mobilities are nearly equal,
so that separations are impossible with the apparatus avai
lable. Ions can be separated in this system if they differ
in step height by about 20 mm in this system (Table 9.2).
Separations of mixtures containing cations with low pK
values are difficult; this is explained in Chapter 6.
104
Figure 9.1 shows which cations can be separated s'imultaneously I
in this system.
FIG. 9.1 Simultaneous separation of cations in the system WHCL.
Figure 9.2 shows the electropherogram for the separation of a mixture consisting of Tl+, La 3+, ca2+, Fe2+, cd2+ and Li+.
The leading ion is H+ and Tris+ is the terminating ion.
9.2.2 The system WHI0 3 •
In this system the leading electrolyte is HI0 3 in water
and the buffering effect of this electrolyte is small. The
sequence of the stepheights of the cations is similar to the
sequence in the system WHCL.
The most important shifts ( Section 9.5) in step heights are 3+ 3+ 3+ 2+ . . those of Cr , Ce and La • The Pb ~on does not m2grate
noticeably.
9.2.3 The system WKAC.
The leading electrolyte is a solution of potassium acetate
in water, adjusted to pH 5.39 by adding acetic acid. This pH
is chosen because in the following zones the pH decreases to
wards the pK values of acetic acid, producing a maximum buffe
ring effect.
The differences in step heights of the cations, for complete
separations, must be about 20 mm in this system.
105
Tl
Tris
t
Li
Cd Fe 2
Ca
H
FIG. 9.2 Electropherogram of the separation of cations in the system WHCL.
08 A ~
FIG. 9.3 Simultaneous separation of cations in the system WKAC.
106
Figure 9.3 shows which ions can be separate~ simultaneous
ly. Comparing the step heights in this system with those of
the other systems, some shifts in the step heights must be . 2+ 3+ 3+ noted. The most 1mportant ones are those of Pb 1 Ce 1 La 1
Al 3+ and cr3+, which are all polyvalent ions. The reason for
the shifts can be found in the higher pH of the system and /or
a stronger complex formation.
Figure 9.4 shows the electropherogram for the separation of 2+ 2+ + .2+ 2+ a mixture of Ba , Ca 1 Na 1 N1 , Cd 1
2+ + + . Pb and Tea .K 1s
the leading ion and Tris+ the terminating ion.
Ba
' E-< ::: ..., .... "' ::: ~ Ni Ca
"' E-< Cd ,, "'
'------'K
- TIME
FIG. 9.4 Electropherogram of the separation of cations in the
system WKAC.
107
9.2.4 The system WKCAC.
The leading electrolyte is KOH in water, adjusted to pH
6.37 by adding cacodylic acid. Tris+ is used as a terminator.
This higher pH was chosen so as to investigate the influence
of an increasing pH.
In the WKCAC system, all ions have lower effective mobilities,
in general, and it is not clear whether this is due to the
higher pH of the system, to complex formation or to a combi
nation of these effects.
The effective mobilities of Al 3+, cr3+ and Fe3+ are too
low. Imidazole shows a typical shift in step height. It has
a pK value of 6.95 and at higher pHs its effective mobility
will decrease (eqn. 5.2). To check this effect, some experi
ments were carried out with the same buffer at a pH of 6.53.
For some cations of strong electrolytes the step heights were
identical while the step height of imidazole increased.
Figure 9.5 shows which cations can be separated simultane
ously. In Figure 9.6 the electropherogram is given for the . 2+ 2+ + 2+ 2+ 2+ separation of the cat1ons Ba , Ca , Na ,. Ni , Mn , Cu
and Tea+. The leading ion is K+ and the terminating ion is
Tris+.
8 8 FIG. 9. 5 Simultaneous separation of cations. in the system WKCAC.
9.2.5 The sxstem WKDIT.
The leading electrolyte is KOH in water, adjusted to a
pH of 7.39 by adding diiodotyrosine. The terminating ion is
Tris+. In this system many ions do not migrate at all (Table
9.2), and sometimes precipitates are formed.
108
Tris Tea
t
TIME
FIG. 9.6 Electropherogram of the separation of cations in the
system WKCAC.
While all possible step heights were measured, the effects
mentioned above were such that no separations in this system
could be achieved. For some special purposes however, this sys
tem could be useful, e.g. in combinations with other systems.
9.3 COMBINATIONS OF SYSTEMS.
Some systems, suitable for separations of cations, are
109
given and in each system about 7 to 9 cations can be separa
ted simultaneously. Because shifts in step heights appear in
the different systems, a suitable system can be found for a
specific problem. However, mixtures can be found with such a
composition that total separation in one system is impossible.
Combining a set of systems may solve this problem.
An example of this is given below.
Suppose the mixture to be separated consists of K+, Na+, .+ + 2+ b 2+ i 2+ 2+ Fe2+, Cd2+, cu2+ and L1 , Tea 1 Ba , P , N 1 Ca ,
cr3+. It is clear that a separation in one electrolyte
system is impossible. The electropherograms, showing many
mixed zones, are as follows:
Ca Fe In the system WHCL: H K Ba Ni Cd Li Tea Tris
Pb Na Cr Cu
Pb Fe cr
In the system WKAC: K Ba Ca Ni Cd Li Tea Tris Na Cu
Cd
In the system WKCAc 1 >: Cu
K Ba Ca Na Ni Li Tea Tris Fe Pb
The quantities of the cations given in italics are known
directly from the electropherograms, viz. K, Ba, Li, Tea, Ca,
Cd, Na and Ni. Further we can compute:
Cr = (Cd+Cr)WHCL - CdWKAC
1) 3+ In this system Cr is too little mobile.
110
Pb = (Ba+Ca+Pb)WHCL -BaWKAC - CaWKCAC
Cu = (Cu+Li+Pb+Cr)WKAC - Pb - Cr - LiWHCL com. com.
1
= (Cd+Cu+Li+Fe+Pb)WKCAC - CdWKAC - Cucom. - Pbcom. - LiWHCL. Fe
So complex mixtures can be analysed by combining the systems
in an appropiate manner. In this chapter only the qualitative
aspects are described.
9.4 METHANOLIC SYSTEMS.
The methanol (95%, technical grade) was prepared by
running it over a column filled with a mixed-bed ion exchanger (Merck V).
9.4.1 The system MHCL.
The leading electrolyte is HCL in methanol and the ter
minating electrolyte is a solution of Cdcl2 in methanol. For
further conditions see Table 9.1. The step heights of the
cations in the methanolic systems are given in Table 9.3.
The differences in step heights required for a complete sepa
ration must be about 8-10 rom.
In comparison with the aqueous systems, especially for
monovalent cations, separations can be achieved much more
successfully in methanol. Trivalent cations are difficult
to separate. Their electropherograms show very wide, some
times double, steps, because clusters can be formed. For this reason, only the separations of monovalent and divalent
cations were investigated.
CATION
H+
K+
Na+
Li+
Rb+
Cs+ Ag+
NH+ 4 +
Tris Tl+
Tma +
Tea +
Tba+
Guan +
S.C.+
Im+
TABLE 9.3 Step heights (mm) of cations for the methanolic
systems.
System System
MHCL MKAC MTMAAC CATION MHCL MKAC
124 Ni 2+ 262 510
195 195 198 Mg2+ 240 397
222 230 230 Zn 2+ t.l.m. 821
257 270 260 Pb2+ t.l.m. 946
180 188 Ba2+ 232 335
168 173 ca2+ 241 425
1031 Cd2+ 628 1025
179 193 Co 2+ 272 497
292 321 317 cu 2+
383 t.l.m.
218 Mn2+ 296 483
154 151 150 Fe2+ 390 t.l.m.
170 177 186 Fe3+ 340 t.l.m.
265 260 250 Al 3+ 256 t.l.m.
192 203 198 cr3+ 290 t.l.m.
209 191 184 ce3+ 310 t.l.m.
176 599 La 3+ 330 t.l.m.
MTMAAC
560
436
960
1080
350 ..... .....
456 .....
540
520
112
06 0-0~ .. e0 e d3e e '
FIG. 9.7 Simultaneous separation of cations in the ~ystem MHCL. I
Cu
t Cs
Li
8 :c (!) H M :c
"' M 8
"'
H
- TIME
FIG. 9.8 Electropherogram of the separation of the alkali metals
in the system MHCL.
113
Figure 9.7 shows which cations can be separated simulta
neously. In Figure 9.8 the electropherogram of the separation
of the alkali metal ions Cs+, Rb+, K+, Na+ and Li+ is given.
The leading ion isH+ and the terminating ion is cu2+. In
Figure 9.9 the electropherogram is given for a mixture consis-+ + + + +
ting of the cations Tma 1 Tea , NH4 , K 1 Na 1
2+ 2+ 2+ . + Co 1 Mn and Cu • The leading ion 1s H and
c 2+ L.+ a 1 J. I
the terminating
ion is Cd2+.
Cd C
Tma
t
- TIME
FIG. 9.9 Electropherogram of the separation of cations in the
system MHCL.
114
9.4.2 The system MKAC.
In this system the leading electrolyte is potassium aceta
te in methanol adjusted to a pH of 7.4 by adding acetic acid.
The pH is measured with a glass electrode and a c~lomel elec
trode, filled with an aqueous saterated solution of KCl, as
a reference electrode. The terminator used is Cdcl2 in metha
nol. There are big differences in comparison with 1 the step
heights of the cations in the system MHCL. Divalent cations
in particular, show great shifts in step heights. The tri
valent cations have such a low effective mobility that they
do not migrate in an appropiate way.
Figure 9.10 shows which cations are simultaneously sepa
rated in this system. In Figure 9.11 the electropherogram is given for the separation of a mixture consisting of Guan+, Na+,
.+ B 2+ 2+ 2+ d i 2+ h 1 d' ' ' + d h L~ , a , Mg , Ca an N • T e ea ~ng ~on 1s K an t e terminating ion is zn2+.
FIG. 9.10 Simultaneous separation of cations in the system MKAC.
The most important metals in blood are easily separated
in this system. Quantitative separations however, can be more
difficult because of the big differences in concentrations.
For this reason, other types of detectors with higher resolution power must be used.
9.4.3 The system MTMAAC.
In the preceeding system, the leading ion is K+ and
cations with mobilities higher than that of K+ cannot be
determined. Because many ions are more mobile thanK+, we
115
Zn Ni
t
Ba Mg
TIME
FIG. 9.11 Electropherogram of the separation of cations in the
system MKAC.
carried out some experiments with the leading electrolyte
tetra methyl ammonium acetate. Tetra methyl ammonium is the
highest mobile cation used in our experiments. In Table 9.3
it can be seen that most step heights agree with those of the
system MKAC. All divalent cations are a little slower possibly
due to higher pH.
116
9.5 DISCUSSION.
In this chapter the qualitative data of some dationic
experiments carried out on isotachophoresis are described.
The possibility of separating cations depends on tlhe type
of detector and injection system used. In using a tap, the
sample ions are introduced separately from the ter~inating
and leading electrolytes. This can be seen as an advantage,
as the total length of the capillary tube can be used for
the separations of the sample ions according to the concen
trations and effective mobilities of the various ions.
If the sample is introduced by an injection, for in
stance with a Hamilton syringe, the sample ions are mixed
with the terminating and/or leading ion. In this case the
length of the capillary tube, available for the separation
must also be used for the separation of the sample ions
from the leading and/or leading ions also.
Sometimes this is difficult especially when the effec
tive mobilities of the sample ions do not differ much from
those of the leading and/or terminating ions.
The large volume of the tap is a disadvantage, but
smaller concentrations can be handled. In combining systems,
only the combination of aqueous systems has been considered.
The possibilities are much extended when methanolic systems
can be applied as in our case, where the apparatus is fully
lined with PTFE.
Differences in step heights as found in the various systems
must be carefully interpreted. The influence of counter-ion
and pH always produces changes in the step height of the ca
tions for the different systems. Complex formation and sol
vation effects will shift the step heights in relation to other
cations. An example of this is given below.
Figure 9.12 shows clearly the influence of the various sy-
400- T•a/
Li
300
Na
I(
I I
I
I
WHCI WKAC
117
... Pb
Li
I(
I L----- TN
MHCI MKAC
FIG. 9.12 Step height differences of some cations for the
different systems.
118
sterns on the step heights of the strong cations, K, Na and Li.
T9e behaviour of these cations in the various sys~erns is si
milar. Highly charged cations such as Ce, Al and Pb show
shifts in step heights due to the effects of pH arid complex . I
formation in water. '
Large shifts are also shown for Ba and Tea fo~ the aque-1
ous and rnethanolic systems due to the effect of solvation arid
change of dielectric constant. In rnethanolic systems the in
fluence of a change in pH on the divalent cations is remarkable.
119
CHAPTER 10
THE QUALITATIVE SEPARATION OF ANIONS
BY ISOTACHOPHORESIS
10.1 INTRODUCTION
In this chapter some data are given for the separations
of anions in aqueous and methanolic solutions. For the ex
periments a similar apparatus is used as described in Appen
dix B. To demonstrate separationa "according to mobilities"
the pHs of the buffered systems are chosen as 6 and 7. Most
organic and inorganic acids have pK values not higher than
5.5 so that the acids will be almost.completely ionised, at
the pHs mentioned above. To demonstrate the separations
"according to pK values" some anions, inseparable in the
systems at pHs 6 and 7 are selected and for those anions
another optimum system pH is computed and some experiments
are carried out at lower pHs. Furthermore some data of experi
ments carried out in methanol, are presented.
10.2 AQUEOUS SYSTEMS.
10.2.1 Separations according to mobilities.
10.2.1.1 The system Hist/HCl.
The leading electrolyte was a mixture of histidine and
hydrochloric acid at a pH 6.02. The concentration of the
leading ion Cl- was 0.01 N. The current was stabilised at
70 1uA. The step heights measured for all ionic species are
_given in Table 10.1. The step heights refer to 0 1uA.
Many anions have the same or almost the same step heights
because their effective mobilities are almost equal, i.e.
they can not be separated. From our experiments we can state
TABLE 10.1 Step heights (mm) of anions for the systems Hist/HCl
and Imid/HCl. All step heights refer to 0 pA.
Ionic species System System Ionic species Hist/ Imid/ HCl HCl
Adipic acid 334 252 Malonic acid Acetic acid 366 281 Mandelic acid Acetylsalicylic acid 474 380 Methacrylic acid Allomucic acid 319 250 Molybdic acid Azelaic acid 365 274 Naphtalene-2-sulphonic Benzoic acid 430 340 acid Benzoic acid, m-amino 454 340 Nicotinic acid Benzoic acid, o-amino 408 Nitric acid Benzoic acid, p-amino 454 350 m-Nitrobenzoic acid Benzyl-dl-aspartic acid 531 440 p-Nitrobenzoic acid Benzoic acid, 5-bromo- Nitrous acid
2,3-dihydroxy 460 316 Orotic acid Butyric acid 428 356 Oxalic acid Cacodylic acid 620 400 Pelargonic acid Caffeic acid 526 420 Periodic acid Capric acid 511 400 Peroxodisulphuric acid Caproic acid 478 386 Phenidon Caprylic acid 510 400 Phenylacetic acid Carbonic acid 520sl. 320sl. a-Phosphoric acid Chloric acid 243 190 o-Phtalic acid Chromic acid 259 173 Picric acid Cinnamic acid 500 368 Pimelic acid Citric acid 292 200 Propionic acid, a-chloro Crotonic acid 416 326 Pycrolonic acid
System System Hist/ I mid/ HCl HCl
280 204 456 364 404 312 335 185
496 358 436 342 220 174 1-'
440 340 "' 0
442 345 217 170 454 310 236 180 494 393 358 250 212 162 t.l.m. t .l.m. 448 366 408 _266 328 246 446 350 345 264 399 316 t.l.m.
Table 10.1 continued
Dichromic acid 2,4 -Dihydroxybenzoic acid EDTA Formic acid Galacturonic acid (D) Glucoronic acid Glutamic acid Glycolic acid Glyoxylic acid Guanidoacetic acid Hippuric acid Hydrofluoric acid a-Hydroxybutyric acid 4,5-Imidazoledicarboxy-
lic acid Indolylacetic acid Iodic acid 2-Ketogulonic acid Kynurenic acid Lactic acid Laevulinic acid Maleic acid Malic acid dl
249 459 334 276 t.l.m. 509 476 360 399 t.l.m. 490 277 470 326
.t.l.m. 358 496 470 391 430 312 286
t.l.m. means too little mobile
174 354 285 216
420 386 286 290 t .l.m. 391 218 375 240
t .l.m. 290 395 383 314
216 222
Pyrazine-2,3-dicarboxylic acid
Pyrazole-3,5-dicarboxylic acid
Pyrophosphoric acid Pyrosulphuric acid Pyrosulphurous acid Salicylic acid Succinic acid Sulphamic acid Sulphanilic acid Sulphosalicylic acid Sulphuric acid Sulphurous acid Tartaric acid Tartronic acid Tiglic acid Trichloroacetic acid Trimethylacetic acid Uric acid i-Valeric acid y-oxoimino-Valeric acid Vanadic acid Vitamin c Xanthurenic acid
298
301
224 224 408 304 304 420 283 224 286 280 256 410 399 470 424 460 466 320sl. 510 484
235 204
172 323 224 244 344 228 169 170 216 195 332 316 363 360 360 382 184 390 353
sl. means that an indefinite step height was obtained. The signal slopes slowly to an end-point.
122
I that anions can be separated if they differ by about 10% in
step height when using a thermometric detector.!
Figure 10.1 shows the electropherogram for 1
the separation
of a mixture of nitric, oxalic, tartronic, formic, citric,
maleic, adipic, iodic, tri-Cl-acetic, and mand~lic acid.
Vitamin c was used as the terminator.
In Figure 10. 2 the electropherogram is gi vein for the se
paration of sulphate, chlorate, chromate, malonate, pyrazole
3,5-dicarboxylate, adipate, acetate, a-chloropropionate and
'0 .... ()
'0 '" ~ .... () .... ()
() '" '0 .... '" '0 .... " () .... () 0 () .... () '" ...
v .... '0 0. '" ...,
.... .... .... () " .~ "' () '0 () .... '" '0 '" <'( .... .: !'-< .. " "' ....
'" "' .... 0 ..., ::.: '" "-..... X :> :s
'0 () .... '" ()
'" () .... () .... .... '" "' ... "
.... () ..., 0 () .... .... '" ..., v
()
"' () .... <( " I
..., .... ; () I
" ...,
t
- TIME
FIG. 10.1 Electropherogram of the separation of anions in the
system Hist/HCl.
123
t
- TIME
FIG. 10.2 Electropherogram of the separation of anions in the
system Hist/HCl.
phenylacetate. The terminator used was vitamin c. The
sample tap volume was about 20 1ul.
10.2.1.2 The system Imid/HCl.
The leading electrolyte was a mixture of imidazole and
124
hydrochloric acid at pH 7.05. The concentration of the
leading ion, Cl-, was 0.01 N. The current was st~bilised at
70 ;uA in all experiments.
The absolute mobility of the counter ion is ~arger than
the mobility of the counter ion in the system Hi~t/HCl. This
means that all zone resistances are lower; conse~uently, all
step heights decrease. However, the step heights correlate
correctly with the calculated zone resistances (Section 5.6).
Some step height shifts are remarkable. This can be as
cribed to a dissociation which is more completed in the sys
tem Imid/HCl. Some examples of shifts are citric acid (pK3=
6.4), orthophosphoric acid (pK2=7.21) and chromic acid (pK2=
6.49). All step heights are given in Table 10.1.
In Figure 10.3 the electropherogram is shown for the se
paration of a mixture of sulphate, oxalate, chlorate, formate,
pyrazole 3,5-dicarboxylate, adipate, iodate, s-chloropropio
nate and nicotinate. The terminator used was vitamin c. In
this system ions can be separated simultaneously if the dif
ferences in their step heights are about 10%.
10.2.2 Separations according to pK values.
As mentioned above, separations of anions can be carried
out by using the differences between pK values, especially
if the anions have about the same absolute mobilities. A pH
is chosen in such a way that different effective mobilities
are obtained according to eqn. 5.2. The choice of the pH of
the leading electrolyte is limited. A minimal effective mo
bility of the ionic species is required. If the pH of a zone
is more than one unit lower than the pK values of the ionic
species in that zone, such a low effective mobility is ob
tained that the potential required rises above the maximal
potential of the stabilised direct-current power supply.
125
<I> +' .. ..... <I> >. +' ~ .. 0 fi .0 ... c
<I> .. fo. +' u .. I 'tl .... 0 'tl !-1
"' <I> "' +'
"' <I> 0. ..... .... 0 'tl " ...: .. ...
:>-.,. <I> +' .. ... 0 .....
.<:: u
<I> 4l +' +'
"' "' .... .<::
"' r:. ~ ..... c " tt.
t
- TIME
FIG. 10.3 Electropherogram of the separation of anions in the
system Imid/HCl.
Another limitation is due to the buffering capacity of
the counter-ion. A maximal buffering effect is obtained if
pKB + 1 > pH zone > pKB -1.
If the pH of the leading electrolyte is chosen, the pH's
of the succeeding zones can be such that the buffering ca
pacity of the counterion will be low in these zones. The re
lationship between the pK of the ionic-species and the pH
/
•
I
/ I
I
126
I I
I I
I
- pKionic species
I
I I
FIG. 10.4 Relationship between the pH of the zone and the pK
value of an anionic species for a pHL of 5.75 and
a pKB of 6.
of the zone is shown in Figure 10.4 for a pKB value of 6 and
a pH value of the leading electrolyte (p~) of 5.75.
Figure 10.4 shows clearly that a buffer will have a low buf
fering capacity when its pK value is more than one unit lower
than the pK of the ionic species.
To demonstrate the possibility of separations according
to pK values, eleven anions that cannot be separ~ted in the
system Hist/HCl (pHL=6.02) were selected. With a computer program, the effective mobilities were computed for five
systems at lower pHs and the step heights for the different
systems were measured for the eleven anions.
Table 10.2 shows the conditions for the different systems.
127
TABLE 10.2 conditions of the electrolyte
tions according to pK values.
System Leading electrolyte
A 0.01 N HCl + pyridine
B 0.01 N HCl + pyridine
c 0.01 N HCl + aniline
D 0.01 N HCl + aniline
E 0.01 N HCl + aniline
--
--\
\ \
\
i ! • -- r ! ..
D c
systems for the separa-
\ \
\
8
\ \
pHL
5.5
5.0
5.0
4.5
4.0
'\ \
I ( uA)
70
70
70
70
70
A
FIG. 10.5 Graphical representation of the step heights measured
in the various systems (see Table 10.3 for 1 .•• 11 and
Table 10.2 for A •.• E ).
No.
1
2
3
4
5
6
7
8
9 10
11
TABLE 10.3 Experimental and calculated values of anions for the
systems A toE (see Table 10.2 for A toE).
The mobilities are given in 10- 5 cm2;vs.
S;£Stem A S;£Stem B S;£stem C S;£Stem D S;£Stem E meff H (nun) meff H(mm) meff H(nun) meff H(nun) meff H(mm)
26.33 428 22.39 21.42 590 16.76 722 13.81 810 28.13 424 24.36 455 23.41 533 18.62 629 15.44 722 29.59 403 25.94 432 25.08 518 20.20 618 16.85 688 31.20 380 27.81 413 27.08 478 22.19 547 18.65 624 32.21 377 30.45 382 30.24 428 26.78 477 23. :n 522 34.58 338 33.26 363 33.15 394 30.25 435 26.86 449
31.16 377 30.80 377 30.79 429 29.80 426 27.99 433
31.97 372 31. 16 360 31.12 398 29.15 404 26.41 409 30.24 380 30.24 373 30.24 418 30.24 408 30.24 408
34.26 361 34.10 347 34.09 379 33.60 382 32.49 392 36.60 344 36.60 343 36.60 370 36.60 372 36.60 370
1 = Trimethylacetic acid; 2 = p-Aminobenzoic acid~ 3 = Butyric acid~
4 = Crotonic acid; 5 = Benzoic acid; 6 = 6-chloro-Propionic acid;
7 = p-Nitrobenzoic acid; 8 = Sulphanilic acid; 9 = Picric acid;
10 = Salicylic acid; 11 = Trichloroacetic acid.
..... 1\J Q)
129
41> 41> ... ... "'41>
"' ... ...
f ~ 41>111 uo ... <tN ::> If':
..... ..-141) t!l >-Ill
,!:I +10 41><: e:..-. I E ..;Ill ... I
G> ... Q. +>41> .....
I>< <:"' i'l 0 0 e-< +IN til 0<:
G> .... Q) Ulll 't) .... ....
0 ..... .<: (J
- TIME
FIG. 10.6 Electropherogram of the separation of anions in the
system Hist/HCl ( separation according to mobilities ) •
In Table 10.3 the calculated effective mobilities and the mea
sured step heights are given.
In figure 10.5 the step heights are plotted for the different
systems. Figure 10.5 shows that the differences in step heights
are much greater, at lower pHs of the leading electrolyte.
This allows better separations.
1
- TIME
130
~ ..... k 0 .... t3
FIG. 10.7 Electropherogram of the separation of anions in the
system E (Table 10.3) according to pK values. The same
sample is introduced as in Fig. 10.6.
Some separations were carried out. Figure 10.6 shows the
electropherogram for the separation of a mixture of trichloro
acetate, a-chloropropionate, benzoate, crotonate, p-aminoben
zoate and trimethylacetate at a pHL value of 6.02. The termi
nator was glutamate and the leading ion was chloride.
No complete separation could be achieved. In Figure 10.7 the
separation is shown for the same mixture in system E {Table
•
131
10.3) at a pHL .value of 4. Trimethylacetate was used as a.
terminator. A complete separation could be obtained easily.
10.3 METHANOLIC SYSTEMS.
To study the suitability of methanol as a solvent for
the separations of anions, experiments have been carried
out with methanol. From pK measurements (chapter 8) we
chased as a leading electrolyte a mixture of Tris and HCl • in methanol at pHL 9. The concentration of the chloride ion
was 0.01 M. This means that a combination of a "separation
on pK values"and a "separation on mobilities" is used, as most
acids have pK: values of 8 to 9. Before use the methanol was
purified by running it over a mixed-bed ion exchanger (from
methanol, technical grade, 95% b.w.). The step heights measu
red are noted in Table 10.4 for some substances. Simultaneous
separations are possible if the differences in step heights
are about 7% (related to 0 ;uA). Some groups of anions will be considered in more detail.
10.3.1 The separation of fatty acids.
Already in Section 10.2 some fatty acids have been measured
in aqueous systems, but many of them have about the same effec
tive mobility and some of them are not sufficiently soluble in
water. The solubility in methanol is much better and also the
differences in mobility seem to be better (see Table 10.4 for
the step heights). In order to look for an optimUm pH we also
measured the step heights for some saturated fatty acids at
different mixtures of HCl and Tris as a leading electrolyte.
The electric current was stabilised at 70 ;uA in all ex
periments. The step heights of the fatty acids measured at
three different electrolyte systems are listed in Table 10.5.
These step heights are related to that of the leading zone.
132
I TABLE 10.4 Step heights (mm) of anions in methanol. The sf.ep heights
refer to the step height of the leading zone (:173 mm).
Ionic species H (mm) Ionic species H (mm)
Acetic acid Acetic acid, Acetic acid, Adipic acid Azelaic acid
88 phenyl 240 tri-chloro 76
260 272
Benz'Oic acid Benzoic acid, o-amino Benzoic acid, p-amino Benzoic acid, m-amino Benzoic acid, 5-bromo,
3-4,di-hydroxy Benzoic acid, 2,4 di-
hydroxy Butyric acid Cacodylic acid Capric acid Caproic acid Caprylic acid Crotonic acid Hydrogenfluoric acid Formic acid Hippuric acid Lactic acid Lauric acid
216 304 412 308
264
224 176 800 380 296 336 180 148
37 256 232 408
Linoleic acid Maleic acid Malic acid, dl Malonic acid Mandelic acid, dl Myristic acid Oleic acid Oxalic acid Palmitic acid Pelargonic acid Pimelic acid Pyruvic acid Salicylic acid Salicylic acid, acetyl Salicylic acid, sulfo Stearic acid Suberic acid Succinic acid Sulphanylic acid Sulphonic acid,
2-naphtalene Valerie acid
a) double step
508 176-344a) 244 120-188a) 210 440 504 112-3CJOa) 480 360 264 96+298a) 112 108+220a) 108 508 280 224 200
162 274
The step height of the leading zone is 138,87 and 86 mm
respectively for the systems A, B and c. The differences between the step heights in system A are
larger than in the systems B and C because the effective mo
bility of the buffer ionic species decreases at higher pH.
In all systems a complete separation could easily be obtained
however. In Figure 10.8 the separation of some fatty acids is
shown for the system A. As a terminator a solution of cacody
lic acid is used. Cacodylic acid contains some impurities.
After running it.as a terminator during so~e experiments, most
impurities migrated from the solution and the electropherograms
did not show any impurity.
133
TABLE 10.5 Step heights of fatty acids in methanol. The step heights
refer to that of the leading zone.
System A B c
Leading electrolyte 0.02 N Tris 0.0085 N Tris 0.01 N Tris 0.01 N HCl 0.01 N HCl 0.018 N HCl
Ionic species Step heights in mm
Formic acid 37 21 18 Acetic acid 88 64 78 Butyric acid 128 91 110 !-Valerie acid 137 122 Caproic acid 148 104 132 Caprylic acid 168 114 144 Pelargonic acid 180 124 148 Capric acid 190 126 156 Lauric acid 204 136 172 Myristic acid 220 146 184 Palmitic acid 240 156 204 Stearic acid 252 166 222 Terminator solutions Litocholic acid 216 256 Cacodylic acid 400
10.3.2 The separation of dicarboxylic acids.
In the separation of dicarboxylic acids strange effects
were obtained. Measuring them at various times, different step
heights were obtained. Especially oxalic gave different steps
for fresh and aged solutions.
Experiments showed the following:
Fresh solutions of oxalic acid gave a step height of 300
mm, where as a 2-days-old solution gave a step height of 112 mm.
Between those times electropherograms were obtained showing
2 step heights one at 112 and the other at 300 mm, where the
zonelengths were different according to the time after prepa
ration. These steps are stable, i.e. when a mixture of oxalic
134
'0 ..... 0
"' 0
..... ..... :>. '0 0 0
"' ~ u u
"" ....
!i: (,!) H ~ :X:
"' ~ fii
1
FIG. 10.8 Separation of a mixture of saturated fatty acids.
acid and another substance, with a step height between those
of oxalic acid, is introduced, the e1ectropherogram shows 3
different steps in accordance with those of oxalic acid and
that substance.
Figure 10.9 shows the electropherogram of a mixture of
oxalic acid and dl-malic acid, one day after the preparation
of the solution. The electrolyte system A was used (Table
135
(a) (b) (.)
! ~
- TIME '-----__J
STEP HEIGHT
FIG. 10.9 Electropherograms of dl-malic acid (a), oxalic acid (b)
and a mixture of oxalic acid and dl-malic acid (c).
10.5). The terminator was cacodylic acid.
Also pK measurements of oxalic acid showed the disappearance
of one pK step during the time. A: fresh solution gave 2 pK
values and a 2-days-old solution only one~ In Figure 10.10
the titration curves are given for those cases.
From the solutions of oxalic acid in methanol, the me
thanol has been evaporated for a great deal and after addi
tion of water, these have also been measured in aqueous sys
tems. Here the products of the old methanolic solution gave
a higher step height than normal. The product from the fresh
methanolic solution gave the normal step height of oxalic
acid in aqueous systems. Old solutions of oxalic acid gave
after some hours in water two step heigh;ts, in accordance with
10
5
old solution
I I
I I I I
I I
fresh solution
// I I .
/ /
, ... , _.....,.;
I I
I
I I I I I ,
I I
I
!i: s "' "' "' ., t;
f
3
"" ... ~ ... ... <II
"" i ... u ' .. ~
2 "" ~ ' .... "'
- ml NAOCH, -TIME
FIG. 10.10 Titration curves of a two-days-old and a fresh solution
of oxalic acid. ( in methanol )
FIG. 10.11 Electropherograrn of a fresh solution of di-hydroxy
maleic acid in methanol.
1-' w 0\
41
"" .... .. 0 .... ... (.)
137
the above mentioned. After about one day the number step ~eight
of oxalic acid was come back.
It may be concluded that oxalic acid shows a spontaneous
conversion to its mono-ester in methanolic solutions.
Other dicarboxylic acids showed similar effects, but on a
smaller scale. Dicarboxylic acids such as di-hydroxy-maleic
acid showed a large number of step heights and it will be
clear that the analyses of such substances will give problems.
Figure 10.11 shows the electropherogram of a fresh solution of
di-hydroxy maleic acid in methanol with a solution of 0.02 N
Tris and 0.01 N HCl in methanol as a leading electrolyte. The
terminator was cacodylic acid.
10.3.3 The separation of inorganic ionic species.
In general the inorganic anions were sparingly soluble
in methanol. By the lower dielectric constant the complex
formation is much larger in comparison with water and also
the greater effect of the activity coefficients and decrea
sing effects on the mobility make methanol,not the best so
lution for isotachophoretical experiments of inorganic ionic
spec:i,.es.
10.4 DISCUSSION.
In this chapter the possibility to separate anionic spe
cies :i,.n water and methanol has been studied. Especially for
larger organic molecules, methanol is a better solvent. In
organic anions can be analysed better with water as a sol
vent. Also combinations of these systems can be a help to
get rid of particular problems.
138
CHAPTER 11
THE SEPARATION OF NUCLEOTIDES BY ISOTACSOPHORESIS
11.1 INTRODUCTION.
91-96 Many authors have dealt with methods for the sepa-
ration of nucleotides, some of whom used the principle of
electrophoresis. Although electrophoresis is an obvious
method for the analysis of nucleotides (charged .particles),
problems can be expected when zone electrophoresis is used,
where a swamping.back-ground electrolyte is needed.
Because of this requirement no general way of detection
can be used. Specific methods such as UV absorption and colour reactions are the most suitable for detection.
In this chapter the possibility to separate them by isotacho
phoresis is described.
11.2 STRUCTURE OF THE NUCLEOTIDES.
The nucleotides studied are the mono-, di- and tri-phos
phates of adenosine, cytidine, guanosine and uridine. This
group of substances are the materials for the nucleic acids
and play an important role in carbohydrate, lipid and vita
min metabolisms. The adenosine and guanosine phosphates are
derived from the purine bases adenine and guanine and the
cytidine and uridine phosphates are derived from the pyri
midine bases cytosine and uracil. As an example the structure
of the 5-monophosphates of the nucleosites are given below.
11.3 EXPERIMENTS.
The· nucleotides are amphiprotic substances' at intermediate pHs they are negatively charged and show a behaviour simi-
_J:) _9 ~ or-c~lo('
c.-s·-MP
l.J o- N olo-CHd OH OH
u-s:.. MP
139
NHz I . co
-9- ~ O-r0-CH2
0 OH
A-5'-Mp
N~N) 0-N~N)_
o~r-o-c~ OH OH
G-5:_MP
lar to acids. Exact data of pK values and mobilities are not
known in the literature but it can be expected that a separa
tion on pK values. will be the most successful one. The pH of
the electrolyte system, regulates the degree of dissociation
of the nucleotides and thus is an important factor affecting
the effective mobilities.
To choose an optimum pH for the separations we measured the
step heights for some nucleotides in systems at different
pHs, in water. The conditions of the electrolyte systems are
listed in Table 11.1. In Table 11.2 the step heights measured
are given for the different systems. All these step heights
were measured with the same thermocouple. Small differences
between the step heights as shown in the pictures and as lis
ted in Table 11.2 can be present because different thermocou
ples, mounted at different places on the capillary tube (in
System pH
WAdCl 3.4
WaNCl 3.7
WAnCl (I) 4.2
WAnCl (II) 4.6
WPyrCl 5.0
WHisCl 6.0
WimCl 7.0
TABLE 11.1 Conditions of the different electrolyte systems for the
separation of nucleotides.
Leading electrolyte Electric current Terminator
(;uA)
0. 01 N HCl+ 70 Caproic acid
Adenosine
0. 01 N HCl+ 70 Caproic acid
a-Naphtylamine
0. 01 N HCl+ 70 Pivalic acid
Aniline
0. 01 N HCl+ 70 Pivalic acid
Aniline
0. 01 N HCl+ 70 cacodylic acid
Pyridine
0. 01 N HCl+ 70 Cacodylic acid
Histidine
0. 01 N HCl+ 70 Benzyl-dl-asparigine
Imidazole
..... ""' 0
TABLE 11.2 Step heights of the nucleotides for the different systems.
The step heights (mm) are given from the top of the step
height of the leading zone (Table 11.1).
Ionic species WAdCl WaNCl WAnCl (I) WAnCl (II) WPyrCl WHisCl WimCl
AMP 536 476 400 310 304 290 162
AOP 318 268 224 170 164 186 108
ATP 204 184 150 118 100 146 82
GMP 388 350 352 290 290 300 162
GOP 230 2"10 176 152 140 192 112 ..... ,. GTP 172 160 120 104 100 160 88
.....
CMP 740 624 472 346 300 250
COP 356 312 276 192 184 100
CTP 176 188 168 124 108 142 68
UMP 328 318 324 264 270
UOP 172 164 168 136 178 100
UTP 120 104 98 130 78
142
order to have the possibility of using several lengths for the
separation) are used. Figure 11.1 shows the graphicalrepresen
tation of the step heights in the different systems.
80
60
40
2
t E-<
8 H ril :.:: c. ~
Cytidine
Adenosine
Guanosine
Urid1ne
phosphates
~ ~~--------~------------~~--------------_.--------------~ 3.4 4.0 s.o 6.0 -pH
FIG. 11.1 Graphical representation of the step heights in the
different systems (Table 11.1).
7.0
l=CMP; 2=AMP; 3=GMP; 4=CDP; 5=UMP; 6=ADP; 7=GDP; 8=ATP;
9=CTP; lO=UDP; ll=GTP; 12=UTP.
t
"' ..... 0 Ill
0 .... ,.;
~ 0
~
l"
143
t
"' ..... 0 Ill
0 ..... .... >< 'g 0 Ill u
1>. 0 ::>
QJ
"' .... .... 0 .... ti
- TH\E (a)
- TIME (b)
FIG. 11.2.a Separation of pyro-phosphate, ATP, ADP and AMP in the
system WHisCl at pH 6.0.
FIG. 11.2.b Separation of UTP, UDP and UMP in the system WHisCl
at pH 6.0.
At higher pHs (5 to 7) the differences in step heights are
rather small and the systems are not suitable for the sepa
ration of complicated mixtures. The separation of the mono
di- and tri-phosphates of each nucleotide is always possible.
Figure 11.2 shows e.g. the electropherograms of the adenosine
and uridine phosphates respectively, at pH 6. In the sample
144
of Figure 11.2.a also pyrophosphate was presend. The time
of separation was here about 20 minutes.
I At lower pHs the step heights diverge and larger diffe-
rences in step heights are obtained. This is d~e to the fact
that many of them have pK values in this pH range. Those sys
tems are more suitable for the separation of the nucleotides
t
- TillE
FIG. 11.3 Separation of a mixture of nucleotides at pH 3. 7
l=UTP; 2=UDP; 3=GDP; 4=ADP; 5=UMP; 6=GMP; 7=AMP; 8=CMP; 9=Caproic acid.
145
in complicated mixtures. As an example the electropherogram
of the separation of the nucleotides UTP, UDP, GDP, ADP, UMP,
GMP, AMP and CMP is given in Figure 11. 3. A complete separa
tion could be obtained in 30 minutes at pH 3.7.
Lower pHs hardly can be used, because the low effective
mobilities at those pHs require more kV's than available.
Not all nucleotides could be separated at these pH's but
the use of a UV detector at more wavelengths can solve this
problem.
11.4 AN ENZYMATIC REACTION.
As an example of an enzymatic reaction we studied the
conversion of glucose to G6P and 6PG, according to the re
actions:
ATP + Glucose ~-~~~ G6P + NADP - ...
ADP +·G6P
6PG + NADPH
11.1
11.2
In the first r~action the enzyme hexokinase regulates the
conversion, where the coenzyme ATP phosphorylates the glu
cose to G6P. The enzyme G6P dehydrogenase catalyses the
oxidation of G6P to 6PG in the presence of the coenzym NADP.
The reaction product is 6 phospho-glucorono-lacton. The
hydrolysis of the lacton is relatively slow without the
enzyme lactonase. Both reactions have been carried out and
the step heights of all substances in those reactions are
listed in Table 11.3. In this table also the step heights of ATP, ADP and AMP are given to relate all values with
measurements noted in Section 11.2.
At a pH of 4 the step heights of 6PG and NADPH are
equal. Therefore the electrolyte system at pH 5 is chosen
146
TABLE 11.3 The step ~eights of some substances in systems at dif
ferent pHs. The step heights (mm) refer to the step
heights of the leading zone.
Leading electrolyte
Anionic species
ATP
ADP
AMP
NADP
G6P
NADPH
6PG
pH 4 pH 5
0.01 N.HCl 0.01 N HCl
+ aniline + pyridine
Step heights (mm)
43 30
64 47
116 87
82 65
87 72 43
} 52 33
I pH 6 o.oi N HCl
+ histidine
40
54
81
68
71
47
35
to follow the conversion. In Figure 11.4 the electropherogram
of a mixture consisting of ATP, ADP, NADP and glucobe is given.
At this pH (5) the glucose does not migrate and in the elec
tropherogram only the step heights of ATP, ADP and NADP are
present. (Figure 11.4.a)
The terminator was cacodylic acid. After the addition of
hexokinase (also containing the G6P dehydrogenase) an electro
pherogram was obtained as shown in Figure 11.5.b• The ATP is
converted completely to ADP and G6P; the G6P is partially con
verted in NADPH and 6PG. A small amount of the NADP is not
converted.
11.5 DISCUSSION.
Although the principle of isotachophoresis differs totally
in comparison with zone electrophoresis, the results corres
pond remarkably with those of zone electrophoretic analyses91 - 9 ~
147
t_ TlME (a)
FIG. 11.4 Electropherograms of a mixture of ATP, ADP, NADP and
glucose before (a) and after (b) conversion.
A comparison of the results of zone electrophoresis and
isotachophoresis can be made.
For the separation of complicated mixtures of nucleotides
by isotachophoresis the use of counterflow of electrolyte and/
or combination of more systems can be necessary.
Especially a counterflow of electrolyte can be applied if
the differences in concentrations between the ionic species
in the sample are large and the differences in effective mo
bilities are small.
148
CHAPTER 12
QUANTITATIVE ASPECTS IN THE SEPARATION
BY ISOTACHOPHORESIS
12.1 INTRODUCTION.
Until now only qualitative aspects of the sepa~ations
by isotachophoresis of different kinds of ionic species
are described. The value of an analytical method depends
strongly on the quantitative results of the method. In
this chapter some quantitative data are given.
In the experiments some anionic species are used, which
do not cause difficulties such as complex formation.
For the experiments we did not use the apparatus, used for
the qualitative experiments. There the sample inFroduction
was made by a sample tap. The reproducibility however is
much better by using an injection block. Therefore an appa
ratus is used as describedby EVERAERTS andVERHEGGEN97 {Appen
dix C). Here the sample introduction is made by a Hamilton
syringe in an injection block. The injection block is shown
in Figure 12.1.
In principle the use of calibration curves for quantitative
analyses is possible. In isotachophoresis where each zone has
its own determined concentration in the zones, independent of
the sample concentrations, the length of a zone ~s a measure
for the concentration in the sample. As will be shown, the
concentration of the sample ion species can be calculated from
a calibration constant. If this constant is determined, there
is no need for the determination of calibration curves.
149
12.2 THEORETICAL~
In the quantitative determination of ionic species a linear relationship between zonelength and amount of the ionic
species should be obtained. Calibration curves for all ionic species present in a sample must be determined however. The introduction of a calibration constant, characteristic for
all ionic species in a chosen system, simplifies the quanti
tative determinations. The calibration constant can be determined as follows.
The amount of an ionic species introduced in the apparatus
is given by
Q = v. . . c ~nJ.
12.1
The amount of that ionic species in the capillary tube will
be therefore:
Combining of eqns. 12.1 and 12.2:
or
vinj • c = 0
cact • L
v ... c ~nJ = constant =
cact • Lt K cal
12.2
12.3
12.4
where Kcal is the calibration constant and Lt (seconds) is the zone length as detected between two successive signals
of the measuring thermocouple. In chapter 3 equations are
given for the calculation of the actual concentration of
an ionic species in its zone. This means that once the cali-
150
7
-5cm
151
bration constant Kcal is known the concentration of a sample can be calculated from the zone length. Not all
calibration curves for each ionic species have to be deter
mined s~parately.
In order to check the reproducibility of the analyses and
to determine the calibration constants mentioned above, quan
titative experiments were carried out in two different systems
with water as a solvent.
The calibration constant is not a constant for all systems;
factors such as variations in the concentration of the leading
electrolyte, temperature and changes in the electrical current
density, result in different potential gradients and hence
affect the migration velocity in the system. This effect produces different zone lengths for the same amounts of the
ionic species in the different systems.
12.3 REPRODUCIBILITY.
To estimate the reproducibility, the zone length of
formic acid (injected volume 3 1ul of a 0.05 N solution)
was measured ten times, in different experiments. The le;{
ding electrolyte was a solution of histidine and HCl at a pH
6.02. The Cl- concentrations was 0.01 N.
FIG. 12.1 Injection block and compartment for the terminal electro
lyte. 1=injection block; 2=bolt for fitting septum;
3=septum~ 4=piece of Perspex for fitting capillary tube; 5= screw for mounting injection block; G=bolt for fitting
piece 4 and capillary tube; 7=capillary tube; S=rubber
0-ring; 9=high-tension cable; lO=piece of Perspex for
mounting high-tension cable; ll=cover for electrode
compartment; 12=electrode compartment;. 13=connection
of electrode compartment with plunger compartment;
14=connection towards drain; lS=PTFE-covered plunger.
152
The electric current was stabilised at 70 1
UA.. The termi
nator was a solution of glutamic acid. The average zone length I
found was Lt = 311 seconds from ten experiments and the stan-
dard deviation was 4 s. Owing to the asymmetry of the step I
response, the zone length depends on the type of terminator I
used. Some experiments were therefore carried out with the
same sample but with acetic acid as a terminator. The average
zone length then found was Lt = 307, from five experiments
and the standard deviation was 3 s. There was no significant
difference compared with the value obtained from experiments
with glutamic acid as a terminator. Glutamic acid is therefore
used as a terminator in all the other experimentE;.
12.4 DETERMINATION OF THE CALIBRATION CONSTANT.
The calibration constant was determined from experiments
carried out with histidine and hydrochloric acid at pH 6.02
as the leading electrolyte. The concentration of the leading
ion Cl- was 0.01 N. The electric current was stabilised at
70 1uA. All zone lengths are listed in Table 12.1.
The third column in Table 12.1 shows the actual total con
centrations of the ionic species calculated by using the com
puter program mentioned earlier. The last two columns show
the deviations from the average Kcal· Reasonable values were
obtained, which might be improved if more precise values were
available for the mobilities.
A similar determination of the calibration constant was
carried out with imidazole and hydrochloric acid at pH 7.05
as the leading electrolyte. The concentration of the leading
ion (chloride) was 0.01 N. The electric current was stabili
sed at 70 1uA. All zone lengths measured in this system are
listed in Table 12.2. The last two columns show the deviations
153
TABLE 12.1 Calibration constants and zone lengths for anions,
with histidine/hydrochloric acid as the leading
electrolyte (Section 10.2.1.1).
Ionic species COncen- Concen- Inj-ected Detected tration tration volum.e zone· length in the sample in the zo-ne lull (ll)
(mole/ll (mole/ll
Succinic acid
Acetic acid
Adipic acid
Formic acid Io<lic acid
Lactic acid
B-chloro-
0.01
0.05
0.025
0.05
o.o5 0.031
Propionic acid o. 05
Succinic acid 0. 01
Sulphamic acid 0. 05
Tartaric acid 0.025
Acetic acid 0.05
Adipic acid 0.025
Iodic acid 0.05
Maleic acid 0.05
Tartaric acid 0.025
Acetic acid
Formic acid
0.05
0.05
0.0051
0.0085
0.0046
0.0093
o. 0085
0.0081
o. 0081
o. 0051
0.0090
0.0048
o. 0085
~.0046
o.oo85 o. 0057
0.0048
0.0085 0.0093
3
3
3
2
2
2
Average
163
358.5
335
311 350
222
370
119
335
320
234
223
231
349
213
120
105
Calibration constant
0.4812
0.4923
0.4867
o. 5186
o. 5042
0.5112
0.5005
o. 4943
0.4975
0.4883
o. 5028
0.4874
o. 50!13
o. 5027
0.4891
0.4902
o. 5120
0.4985
Deviation from averaqe 11:
081
J(cal"106 \
•1.73 -3.5
-0.62 -1.2
-1.18 -2.4
2.01 4.0
0.57 1.1
1.87 3.7
0.20 0.4
-0.42 -0.8
-0.10 -0.2
-1.02 -2.0
0.43 0.9
-1.11 -2.2
1.08 2.2
0.42 0.8
-0.94 -1.9
-0.83 -1.7
1.35 2.7
0.93 1.9
from the average Kcal· In this system also reasonable constancy of the calibration constapt was obtained.
It should be hold in mind that the influence of the activity coefficients are neglected in the calculation of the
actual concentration of the_ ionic species.
12.5 QUANTITATIVE ASPECTS IN THE SEPARATION OF MIXTURES.
In the previous Section of this chapter the concept of
the calibration constant has been introduced and for two
different systems this calibration constant was determined.
Deviations from the Kcal were within 2%.
154
During the experiments carried out to deter~ine this Kcal• only single electrolytes were introduced as a sample. In
practice, the most important factor is the accuracy of the
method in the separation of mixtures, especially if the ionic
species of the sample differ in concentration. 1
I In order to get an idea about the accuracy of the method in
analysing mixtures, experiments were carried ou~ with mixtures
of some anions.
In Table 12.3 the results of quantitative experiments of·
mixtures of formate and acetate are given. The results are
graphically presented in Figure 12.2. Linear relationships between injected amounts and lengths of the zones are ob
tained as can be expected from the theory. Remarkable is
that also for small and large amounts of the sample, zone
lengths are obtained fitting quite correctly the calibra
tion curves. The results also agree with those of the calibration constants
in the preceding part.
TABLE 12.2 Calibration constants and zone lengths for anions,
with imidazole/hydrochloric acid as the leading
electrolyte (Section 10.2.1.2).
Ionic species Cone en- Concen• Injected Detected Calibration trat!on tration volume z.one length constant in the sample in the zone (~1) (S)
(Kcal•l04l (mole/ll (mole/ll
Acetic acid 0.05 o. 0075 467 0.4283
Adipic acid 0.025 o. 0042 407 0.4388
ForJI'tic acid 0.05 0.0087 398 0.4327
Hydrofluoric acid o.os o. 0087 409 0.4215
Iodic acid 0.05 0.0074 465 0.4364
Lactic acid o. 343 0.0069 340 0.4386
Maleic acid 0.05 0.0046 735 o. 4437
Tartaric acid 0.025 0.0042 416 o. 4290
Acetic acid 0.05 0.0075 308 o. 4329
Formic acid 0.05 0,0087 255 o. 4508
Maleic acid o. 05 0.0046 491 o. 4428
Acetic acid 0.05 o. 0075 154 0. 4 329
Formic acid 0.05 0.0087 129 0.4455
Averaqe 0.4365
Deviation average Kcal
Kcal'I06
-0.82 -1.9 0.23 0.5
-0.38 -0.8
-1.50 -3.4
-0.01 o.o
o. 21 0.5
0.72 1.6 -o.7s -1.7
-o. 36 -0.8
1. 43 3. 3
0.63 1.4
-0.36 -0.8
0.90 2.1
o.u 1.5
155
TABLE 12.3 Injected amounts and zone lengths of mixtures of formate
and acetate in the system Hist/HCl ( Section 10.2.1.1 ).
Injected amount (mole.l0 6 )
Formate
0.075 o.osos 0.037 0.025 o. 014 0.009
0.1005 0.112 0.125 0.136 0.141
0.150 0.100 0.075 0.050 0.027
0.200 0.225 0.250 0.273
Acetate
0.075 0.1005 0.112 0.125 0.136 0.141
0.0505 0.037 0.025 0.014 0.009
0.150 0.200 0.225 0.250 0.273
0.100 0.075 0.050 0.027
zonelength ( s )
Formate
156 100
76 51 27 15
205 234 251 270 281
310 202 147
93 47
410 462 501 547
Acetate
181 236 274 309 331 337
122 92 61 33 23
360 487 542 603 641
239 179 118
63
TABLE 12.4 Injected amounts and zone lengths of mixtures of formate
and acetate in the system Hist/HCl (Section 10.2.1.1),
for different injected volumes;
Injected Injected amount
volume (mole.I0 6 )
(ul) Q
3
3
1.5
1.5
3
5
9
10
Formate Acetate
0.15
0.075
0.15
0.075
0.075 0.075
0.125 0.125
0.225 0.225
0.25 0.25
Zone length
( s )
Lt
Formate Acetate
305
155
150
207.5
243
268
365.5
184.1
186
257
304
329
Lt/ Q
( s/mole • 10-7 )
Formate Acetate
203
207
200
166
108
107.2
244
245
248
206.5
135
131.6
156
500
1 0 - INJECTED AMOUNT 0 • 0 2
(mole .10 6 )
FIG. 12.2 Relationships between injected amounts and zone lengths
for formate and acetate in the system Hist/HCl.
5 10 - injected volume (pl)
FIG. 12.3 The theoretical and practical relationship between the
ratio zone length I injected amount and the injected
volume.
157
TABLE 12.5 Injected amounts and zone ,lengths in the system Hist/
HCl for separations of some mixtures. The injected
volumes were 3 ~1.
Injected amounts (g.-equiv.10 6 ) Zone length (s)
Cl - - - Po 3- Cl - P0 3-HCOO CH 3COO 4 HCOO CH 3coo 4
0.600 0.075 not separated 0.050 0.100 :214 0.075 0.075 164 0.150 0.075 162 0.300 0.075 154 0.125 0.025 53 o. 250 0.025 53 0.500 0.025 53 0.555 0.014 23 0.273 0.014 29 0.136 0.014 29 0.429 0.043 0.043 87 120 0.500 0.025 o. 025 44 72 0.400 0.100 0.100 201 257 0.500 0.013 0.013 17 28
0.05 0.05 0.02 94 111 57 0.375 0.019 0.019 0.008 18 42 23 0.273 0.027 0.027 0. 011 60 80 40 0.470 0.012 0.012 0.004 13 27 11
0.06 182
Ill
1
acetate phosphate
formate
INJECTED AMOUNT 6 (mole.10 )
FIG. 12.4 Relationships between injected amounts and zone lengths
for the separations of soJne mixtures in the system Hist/HCl.
158
Some experiments were carried out introducing different
numbers of 1ul's. Not more then 31ul can be inj~cted by use of this type of injection block (Table 12.4 and 1 Figure 12.3).
In many natural samples large amounts, e.g. chl?ride, are
present with smaller amounts of other ionic species. For that
reason some experiments are carried out with mi~tures of chlo
ride, formate, acetate and phosphate.
Table 12.5 shows the experimental values. The data are
graphically presented in Figure 12.4. Also here an excellent
reproducibility and accuracy are obtained.
Also by v. HOUT 79 , quantitative data about mixtures of some
amino acids are given by isotachophoresis, showing a good
accuracy although at the high pHs the presence of Hco3- can
be troublesome.
12.6 DETECTION LIMITS.
From our experiments we can state that the minimum detec
table zone length is about 5 mm, using thermometric detection.
This value can vary depending on the heat production of the
adjacent zones, the electric current, the type of solvent
used and some minor factors.
The concentration of an ionic species in the capillary
tube is about 0.01 g-equiv./1 under the conditions used and
the cross-section of the capillary tube is about 1.6.10-3 cm2 •
This means the minimum amount of an ionic species that can be
detected is about 8.10-9 g-equiv. If the volume of the sample
injected is 3 1u1 the minimum concentration in the sample
that can be detected about 2.7.10- 3 g-equiv./1. To illustratE
the above, the results are given of a separation of mixtures
of oxalate, formate, acetate and s-chloropropionate in the
system Hist/HCl (Section 10~2.1.1) in Table 12.6.
159
TABLE 12.6 Injected amounts and zone lengths for mixtures of
some ionic. species in the system Hist/HCl (Section
10.2.1.1).
Oxalate Formate Acetate S-CI-Propionate
moles injected 15.10-9 30.10-9 30.10-9 45.10- 9
Zone length 64 62 72 111 (s) 64 61 72 108
63 61 71 107 64 61 71 108 64 63 72 110
Average 64 61.5 71.5 109 •
moles injected 10.10-9 20.10-9 20.10-9 30.10-9
Zone length 43 39 47 71 (s) 43 41 47 74
43 41 47 73 Average 43 40 47 73
moles injected 5.10-9 10.10-9 10.10-9 15.10-9
Zone length 20 20 22 37 (s) 21 20 22 37
21 19 21 39 Average 21 20 22 38
In Figure 12.5 the electropherogram is given of a sepa
ration of a mixture of 0.005 N oxalate, 0.01 N formate, 0.01 N
acetate and 0.015 N B-chloropropionate in the system Hist/HCl. Figs. i2.5.a, 12.5.b and 12.5.c correspond to injected
volumes of 1,2 and 3 1
u1 respectively. This means that the amounts detected are 5.10-9 , 10-8 , 10-8 and 1. 5 10-8
moles resp. for the different anions, if 1 1u1 is injec-
ted. It can be stated that the Figs. 12.5.b and 12.5.c
show a complete separation of the mixture to be separated
both quantitatively and qualitatively. All quantitative
information can still be deduced from figure 12.5.a for it
should be remembered that for quantitative analyses the
transition of zone boundaries is required. The differential
signals give an exact indication of the amounts of the
160
I 4
a b c TIMB
(l=chloride; 2=oxalate; 3=formate; 4=acetate;
5= a-chloro-propionate; 6=glutamate)
FIG. 12.5 Electropherograms of the separation of some anionic
species in the. system Hist/HCl (Section 10. 2.1.1). The
injected volumes were 1 (a), 2 (b), and 3 ~1 (c).
·161
ionic species introduced1). This in contrast to a similar
gaschromatogram which would represent an incomplete sepa
ration.
<II ... <II <II
<II 1). ... ... .... <II <II ~ e ... ...
~ <II 0 ll r..
C) < H
"' :t:
"' "' ·£-< (II
1
TIME
FIG. 12.6 Electropherogram of the separation of anions in the
system Hist/HCl (Section 10.2.1.1) at low concentration
of the leading ion (10-J g-equiv./1) and pH 6.02.
1)
The time interval between two successive peaks, measured with
a stopwatch is given in seconds. The use of electronic equip
ment for measuring the time intervals more accurately can
decrease these limits. The introduction of another type of
detector (with a higher resolving power) can decrease these
limits still further.
162
The detection limit can be decreased by usin~ a leading
electrolyte with a lower concentration. If the concentration , -3
of the leading ion is decreased towards 10 g-e~uiv./1 the I
minimum detectable amount of an ionic species wopld be
8.10- 10 g-equiv./1, i.e. a minimum concentration in the -4 sample of 2. 7.10 g.equiv./1, when a volume of .3 1u1 of
the sample is injected into the system.
The detection limit for the concentration in the sample can
be decreased by injecting a larger volume, e.g. with a sample
tap. The sample taps that we commonly use nave a volume of ca.
30 1ul. Consequently the minimum detectable concentration in
the sample will decrease by a factor of 10. If the average
concentration of the ionic species of interest in the sample is low, a sample tap is therefore recommended. 1)
To study the possibility of carrying out analyses with a leading electrolyte of concentration 10- 3 g-equiv./1, some
experiments were performed with histidine arld HCl at pH 6.02
as the leading electrolyte. The concentration of the leading
ion {Cl-) was 0.001 N. Because the driving pot~ntial availa
ble is limited, the electric current must be decreased to
7 /uA.
Figure 12.6 shows the electropherogram of the separation of
nitrate, chlorate, formate, cit~ate and adipate, with acetate
as the terminator. A complete separation was easily obtained.
A disadvantage may be that very small signals are obtained from the thermocouples, when the driving current is lowered too much. The signals must be amplified so that the signal-to
noise ratio decreases as can be seen in Figure 12.6.
1)
Large amounts of other ionic species present in the
sample can disturb a separation because the steady
state is difficult to obtain.
163
12.7 DISCUSSION.
It is shown that reproducible analyses can be carried out when
the sample is introduced into the apparatus with a syringe.
However, the construction of the injection block still causes
some disadvantages, regarding the introduction of the sample.
The sample introduced is mixed with the leading electrolyte
and the sample will not form a plug separated from both
the leading electrolyte and the terminator, as in the case
when a sample tap is used.
This effect was made visible by injection of dyes.
The position of the leading electrolyte behind the sample,
between the septum and the plunger compartment (Figure
12.1) is another disadvantage. The leading ions behind the
sample have to overtake the sample ions in order to give a
separation, which means that the length of the capillary
tube available for the separation is not used only for the
separation of the sample ions. In particular, difficulties
can be expected if the mobility of the leading ions does not
differ very much from at least one of the ions present
in the sample.
The time required for tne analyses depends on the length
of the capillary tube needed for the separation, the elec
tric current used, the type of the leading electrolyte and
counter ion present, the pH, the difference in mobilities
of the sample ionic species and so on.
The time required for analyses was about 45-60 minutes under
the conditions described above.
164
CHAPTER 13
FURTHER DEVELOPMENTS
In this thesis the quantitative and qualitative aspects
of isotachophoresis have been discussed and some;examples
o.f anionic and cationic separations have been given. Also the possibility to use other solvents was studied.
Although the accuracy has been proved to be about 2%,
some problems arise in the analyses of several samples.
In practice, samples of all kinds have a large variety
in concentrations of the components. This makes a problem.
In Section 5.6 it has been shown that in the stationary state each zone has a characteristic temperature and as
it takes some time before that this temperature can be detected by the thermocouples, due to the axial conduction
of heat and the heat-transport through the capillary tube
of teflon, a minimal zonelength of about 5 mm is required
in order to detect that zone. This means that for detection of the component with the lowest concentration, a
very long capillary tube should be required even to contain the sample. For a completed separation still longer capillaries are necessary. In practice it means that only
mixtures can be separated of which the components do not
differ more then a factor 30 to 40 in concentration.
some tools are available to solve that problem. Firstly
the use of an electric or mechanical regulated counter flow
of electrolyte can be a help to optimalise the separation length of the capillary tube, through which a lar,ger sample
volume can be analysed in a relatively smaller length of
the capillary tube.
165
Another possibility can be found in the use of a de
tector with a higher resolving power, i.e. a detection of
smaller zonelengths. Also the minimal detectable amount of the
ionic species will be decreased then (Section 12.6).
Such a detector could be found by the use of U.V. and the
measurement of the conductivity of the zones. The use of U.V.
already has been described by ARLINGER and F.OUTS108 but can
be used only for substances showing UV absorbance. Sharp and
quick responses have been obtained.
A.O. EVERAERTs80- 82 constructed a detector based on the principle of the measurement of the conductivity. By this
the minimal amount of the sample to be detected can be lowered
by at least a factor of 50, in comparison with a thermometric
detection. Also the differences in concentrations of the com
ponents in the samples can be increased at least by a factor
50 under similar circumstances.
In order to demonstrate the advantages of such a detector two
electropherograms are given, showing the separation of iden
tical mixtures of anions but detected in two ways. Figure 13.1
shows the electropherogram of a mixture consisting of sulphate,
chlorate, chromate, malonate, pyrazole 3-5 di-carboxylate,
adipate, acetate and 6-chloro-propionate. The leading electro
lyte was a mixture of 0.01 N HCl and histidine at pH 6. The
terminator was phenyl-acetate. A thermometric detection was
used. Especially the last zones could not be detected clearly
because the zonelength was too short. In Figure 13.2 the same
mixture and the same amount of the sample are used, but the
conductivity detector was applied. Very sharp and clear steps
are obtained. In Figure 13.2 the paper speed was twice as
high as in Figure 13.1)
With such a detector many problems as indicated elsewhere
in this thesis can be solved. Some problems however, in mea
suring the conductivity of a zone, are present. The e!l.ectro
des act as bipoles and troubles like gasproduction can be
the result. At this very moment the development and improve-
Q1 ..., "' Q1 .... >< ..., >< "' Q1
.8 ..., ..., Q1 "' I< () c
"' "' 0 t) I .... I .... "' .... >< 0 '0 c I< Q1
I 4) "' ..., . ..<:: I "' Q) "' "' 0 .... ..., ... ~ "'
.., 0
"' .... .8 .... 4) ..<::
~ .... 0 I< 0 I "' N ca,U
"' I I< + .... >< Q1 Q1 4) <I>
f <I> '0
"' ..., ..., ..., ..., ..., I
f "' "' "' "' "' a 6 ... -a ..., "' 0 Q1 .... I< .... .... :i "' ~ ..<:: ..<:: .1! u u e<
"' !l: !l:
.., Q1 Q1 Q1 4) 4) ..,
""' ,.... .. ...,...,..., ..., '0 ,....
0'\ !l: "'"'"' "' ... .. 0'\ Cli!"' -a ... :<:
"' 000 0 llo .. ........... .... ....
E-o .\\!.<:.<: :l ..<:: ~ Ul -UU Ul t) Ul
Q1 'tl .... I< 0 .... .t: u
- TIME - Tll·IE
FIG. 13.1 Electropherogram of anionic species in the system Hist/HCl with a thermometric detector.
FIG. 13.2 Electropherogram of anionic species in the system Hist/HCl with a conductivity detector.
167
ment of this detector goes on. When such a detector is avai
lable isotachophoresis will be suitable in a wide field of
application.
In many other techniques based on the principle of elution,
the zones become wider and more unsharp during the analysis.
An important point is then the sample introduction that must
be as sharp as possible. It will be clear now that in some
cases isotachophoresis will be an excellent injection method
of the sample for those techniques. This has already been
applied in disc-electrophoresis; also this can be applied in
techniques as e.g. liquid-chromatography.
After all, we can state that isotachophoresi.s will be suitable
in a wide field of application, both. on an analytical and
preparative scale, for the qualitative and quantitative
analysis and isolation of charged particles.
168
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173
LIST OF SYMBOLS AND ABBREVIATIONS
A ionic species A empirical constant for a given series of ions
of the same charge
a activity
B buffer ionic species B
b
c
empirical constant for a given series of ions of the same charge
distance of closest approach
concentration
actual concentration of the ionic species in the capillary tube
D dielectric constant
E
e
H
I
electric field strength electric motoria force
charge of an electron
faraday constant
friction factor
constant
step height
electric current ionic strength
K equilibrium constant
m
calibration constant gas constant per molecule
constant
length of a zone
length of a zone
mobility molality
M1
molecular weight of the solvent
n + n ,n
0
p
number of pK values of a molecule
valency of a cation, anion
cross section area of the capillary tube
distance between point of injection and point of detection
mole/1
mole/!
V/cm v c C/g-equiv.
mm
llA g-equiv./cm3
em
s
cm2/Vs mole/kg
em
174
Q total amount of an ionic species
q electrolyte constant
rw s T
TC
v
vd WAALS radius
entropy
absolute temperature temperature correction
voltage drop· velocity
injected volume
vd WAALS molecular volume
x3 ,x5 function of K.b
Y3 ,Y 5 function of K.b
z maximum number of positive charges for an ionic species
a degree of dissociation
a• reaL degree of dissociation
e ratio of two electric field strengths
y activity coefficient correction factor according to ONSAGER
K function of the concentration
equivalent conductance
electric conductivity of a zone
equivalent conductance of an ionic species
viscosity
Subscripts.
A ionic species A
.B ionic species B
c concentration
com computed
H ionic species H+
mole
cm2/ohm.equiv.
1/ohm.cm
cm2/ohm.equiv.
g/cm.s
i a number indicating the step of dissociation summation index
ind indicator electrode
175
j a number indicating the step of dissociation liquid junction
L leading zone
OH ionic species OH-
o at zero concentration
r indicates what kind of ionic species is meant
ref reference electrode
s
u v X
z
standard solution
uth zone
vth zone
sample solution
a number indicating the maximum possible charge
Superscripts.
()i to the ith degree
r relative
t total
z maximal number of positive charges of an ionic species
x refers to the equivalents in stead of molecular quantities
refers to quantities in a certain solution
Some examples.
CA . r'U,z-~
the concentration of the ionic species A , th r
with z-i positive charges in the U zone.
the concentration of the H+ ions in the uth zone
to the ith degree
Abbreviations.
AMP,
CMP,
GMP,
G6P
ADP,ATP
CDP, CTP
GDP, GTP
Adenosine, mono-, di- and tri-phosphate
Cytidine, mono-, di- and tri-phosphate
Guanosine, mono-, di- and tri-phosphate
Glucose-6-phosphate
Guan
HNP
Im
NADP
6PG
Tba
Tea
Tma
Tris
S.C.
UMP, UDP, UTP
176
Guanidine
Half neutralisation point
Imidazole
Nicotamide-adenine-dinucleotideiphosphate
6-phospho-Gluconic acid
Tetrabutylammonium
Tetraethylammonium
Tetramethylammonium
Trishydroxymethylaminomethane
Succinyl choline
Uridine, mono-, di- and tri-phosphate
177
APPENDIX A
With the formulae derived in Chapter 3 a computer program is
evaluated as shown in this appendix. The language used is
Algol. For the computations of all concentrations, conducti
vities, pHs, and effective mobilities the following input is
required:
-1 or 1 (anionic resp. cationic separations)
pHL , the number t of the zones, cA , L
nA ,mA ,zA ' L L'zA L
L all pKs and ionic mobilities of the ionic species AL,
and all pKs and ionic mobilities
for the following zones:
nAy,mH,V'mOH,V'mAy,zAy'zAy' all pKs and ionic mobilities of Av· n~,m~-z~,z~ and all pKs and ionic mobilities of ~·
INPUT
~t.4.s.J.o.o2.1.o.o.4.75.41•2oo.Jso.1.19.1·B·O·
2 •. )50.200.3()1 1·2 ·2·0·9· 778 .. 30·1·19·1·8·0· 1.Jso.2oo.o.o.7.Jo.1.19.t.a.o. 2·3S0.2oo.o.o.7.~o.a.Jo,1,19·1·B·O·
PROGRAM
0010 'ljE:GI~·
01 00 'RE:4L' PHL .. CS TLI • ,"t,;,LI, MaHL.I'I-CL .. M:'L '3 • rPL. -1HL• f • TU'.ol • 0110 KTLI.KI'Ll•KlLl,l'(ltvl.I .. KTU3 .. KM.R .. KIL3,Kli"'I.B .. ~ .. ~·~ .. Ol:<:ID C :JLI.·I£ULI .. ML.I1 .. CJUJ .. CSTL'h'£UU,,;"'! .. J31 .. 8Cd~.tt<JL. 0125 S•9H,9L .. 0130 t<JLT .. ~·JJ 0150 '1\ITE:GE:-t' 1\,\JLI .. I.J,!'(,:U,zi,z:l .. L,V .. MJ 0170 '~EAL''4R~~Y'PKLI .. MLI .. PKL3 .. MLR,KLI .. KU3 .. MH.MJH,M01 .. ~(0110J, 01 7:a C:Sf'3,CSfi .. C.H .. C8LJ, -EIR .. -E:JhPH .. ~H .. HP.IoMl1 .. M31,KTB.o 0173 KIMhKl9.oKi'B.ol<lMl.oKll.ot<Ml•KTl to: 10 J..KI..-<3, 0180 PKI .. Ml.ot>Ki':l.o:'flto: 10 .. 0:10 H 0190 '1\lff.GF..r'<\~.~AY' \ll.o'H.oZI•-J.om-Jto:tOH
178
0195 S:=RE4DJ i ();aOO PHL:=f£~0JC\: =.~E4DJCSTLI: =READJ '1...1: =!£.1\DJ M0LI: =REAI!lJ 0~0 1 l I : =R£.!\D J
0210 'F~' I: =1 'STEP'1 'U ~TIL' ·'ILl '01.1' 0220 '3EGPJ'P.><LIU J:=.~£.~DJMLHI l:=R£.1\DJ'Ei\IJ' J 0230 MJHL: =RE~DJ MiL: ~E4DP.JLJJ: =RE4DJM0L'3: =KEADJ 0231 l'3:=RE40J 0240 'F0R' I :=I'SI'EP'1'UNTIL' .~U3'00' 0250 'BEGV.I'PKLBC I l: ::;'iE~OH11JH I J: ~E4DJ 'E'V' J 0260 'r~~'I:=l'STEP'l'UNTIL'4'00' 0270 '8EGii~' NH I l: =.REL\DJI'IH[l J :=REAl.lJMJH[ I 1: ::::~EADJ·:'1<Jl til: =;~EADJ 0275 Zl'IU 1: =READJ 0280 'F"<~' J:=l 'STt:t''1 'U•\IflL' .\II [ Il'IJJ' 0290 'BEGI:\1' PI<H I ,JJ: =KEl\DJ MIC hJJ::::f~EL\0; 'E-l>' J OJOO ,'i3[ll:=RE~D;MI.J3( I l: =KE~DJ 0305 Z8~(1l:=REAOJ
0310 'F0f~' J: =1 'S TEP'I 'LJ'IriL' ~3[ I J'D;'' 0320 'BEG! ~'PK3U .. Jl:=READJM3ChJl: =KEA£H 'E:\0' J 0330 'E:'i>' J 0400'CI::Ii'+E'IT' iJE~EKE.~I'Iki 1E ZJ•\EJ 0410 HPL: =tot<-PHLH,1HL:=10t <-14+PHLH OlleO KLHO 1:=1 JI<TLI: :::><;4..1: =KILl: =Kli'1 ... I: =OJ 0430 'F"J~' I:=t'STEP'l'U.~riL':\ILI'O:J' 0440 ''lEGPJ' KLI[ I J: =KLH I -1 l*lOt< -Pt<:LIC I J)/tf>LJ•H:=ll -IJ 0450 KTLI: =KTLI +KLI C I H r<ILI: =KILl +KLI (I l*<ltU 0460 KMLit=KM...I+KLHI l*i"1LICI l*SIG"<:l~H 0470 KI:-LI ::::KI,1...1 +KLH I J*AIJSC(}K)*MLHI JJ 0480 'E\ID'; 0490 C0LI: ::CSTLI/<1 +t<TLI > nEULI :::C,:)Lh<ZI+KILI H 0500 :1...11 : =< Mi:ILI *S IG \IC Z I> +K!"LI> I< I +KTL I >J 0510 P·U \lfTEXT<' <' LJ0PELECT.K.,LYTl:,•\IE' >' )J 'III.J:i{J 0520 Pr~l>lrT£XTC'<'PHL= '>'HF'IXT<6 .. :J,PHL>J 0530 Pr{l-.JTTF:XTC'C' Mic:f.3LI= '>'>WIJ<TC6 .. 4,i"LIIH'ILC-O 0535 KL3CO J: =I JKTL'3: =Ki"L8: =KIL-1: =Kii'I .. B: =OJ 0540 'Ji'~' I: =0' STEP' 1 'U -..!riL' •-ILl 'I)J' 0550 '8E:G1•'-l'F'IXHS,o,zi -I HrL:HC5,2 .. KLH I J:t<CJLI H '\I!..Gr{J 'E\D' J 0560 P~I~TfEXTC'C' CSTLI= '>'HF"LtHCS .. ~,CSTLIH\ILC:~nl.C·U 0570 'F<'H' I: =1 • STf..P' 1 'U"'T IL' ~IJ3 '1).1' 0560 '·3i':GI 'I' KLf1C I l: =i<lJ3CI-ll*lOt C -t>KU3CI ])/1-t->LJQ.~: =l8-I; 0590 KTLIJ:=KfL9+KL9CIJlKILq::::KIUl+KL8CIJ*~J
0600 ;<:-11Jh =K:'4.H+:<L'3C I l1<1'4 .. HCI 1*SIG\IC:JV J
0610 t<I1'1 .. .':3: =KPUJ+KU3( I 1*1\~SCH>t::•t.iHI H 0620 'E·'Il' J 0630 rH =1 +KfL"iJ 'li:UL'3: =<ZI3+KlLB>I:H 0640 CSTL'3: =-C,\IEULl +riPL-rJHL)/,\£ULfHGlJL<J: =C':>TL3/'t.J 0650 i'1 .. B1 :=CMJL.'3*SIG:.!CZ~>+KMI.J1>1r'H 0660 BC,H:=Cl +4:-JSCML'il >II¥3S<i't..Il > >*'::::>TU:h 0670 r:=C0LhC~i35Cll ):!c,"l,JLI+Kl·"LIH 0680 TJ~~:=C;JU1*<<¥-3S<ll3 >*MJL''i+KIM...13> J 0690 KJL:=HPL*:-t-tL+JHL*:-1-JHL+T+fU'.IIJ 0700 ~I \IHr:xrc' C' >t:HL.:-3= '>' HFIXf(6,4 .. •1..31 H 'JIJ~~~
179
0710 'r:~'IS =O'STEP'l 'U"lriL'NL9'00' 07'20 'BEGI\I'F'IXT<5 .. o,zB-I>JF'UlfCS .. 2 .. t<U3CIJ:f<CJLqH'l..CKJ 'E'\()' J 0730 P.~I>-JTTE:XTC' C' CS'TUJ::: '>' >JrWH<S .. 2,CSTU3>; 'i..Ct{r-Jl.C;H 0740 P!U·\ITTE:XT<' <' LA.f.!04.::: '>' )JF'Llr<S .. 2 .. Kdl.) J 0750 .\IJ.J;.iJc>ILC~J,\jLCRJ
0800'C\'J:-t"'E.\ff' BEREKENI~ VJLGE•\JOE Z0\ESJ 0610 'F~R'L:=t'STEP'l'U'\ITIL'A'DO' O!iaO 'qEGIN' 'SWI fCH' SYSn::-1: =Lt .. l.2 .. LJ,L4 .. L.S .. L6,L7 ,LS; 0821 VI=LJM:=2;K:=1J 0830 PHCV l: =PHLJ 0640 L1: HPCVl1=10t<-PHCVl>J~HCVJ:=10tC-14+PHCVl>J 0650 KICV .. OJ:=IJKTICVl:=KMICVl:=KIICVl:=KIMICVl:=OJ 0860 'F'i~~· I: =1 'STEP'1 'U;IITIL 'i\jl[V l '00' 0870 '9EGIN' QR:=ZVIICVJ-IJ 0880 KI[V,Il:=KICV .. I-1l*10t<-PKICV .. Il)IHPCVJJ 0890 KTICVJ:=KfiCVJ+KICV .. IJJ 0900 KMICVJ:=KMICVJ+KICV .. Il*MICV•ll*SIG~C~K)J 0910 KIICVJ:=KII[Vl+Kl[V,Il*JRJ 0~20 KIMICVJ:=KIMICVJ+KlCV .. Il*ABSCQ~>*MlCV .. IlJ 0930 • f:,\j[). J 0940 Mil CVl: =C~HV l*SlG\IC Zl 'lj[IJ)>+KMICV ])IC1 +KTHV 1 >; 0950 KBCV .. Ol:=IJKTBCVl:=KMBCVl•=KIBCVJ:=KIMBCVl:=OJ 0960 'F'JR'l:=1'STEP'1'U\ITIL'·\13[VJ'DO' 0970 '8EGL'J'.·JJ<:=ZBIICVJ-IJ 0980 KBCV,IJ:=KB[V .. I-11*10t<-PKiCV,Il>IHPCVJJ 0990 KT9CV11=KTBCVl+~3CV .. tlJ 1000 KMBCVl:=KMBCVl+KBCV,.ll*MBCV .. I l*SlGNCQlUJ 1010 KIBCV1:=Kl9[V1+l<f:HV .. ll*J~J 1!V-0 KIM3[Vl:=KIM3CV l+Ki-UV,I l*"r:lSC.H>*MBCV• I H 1 030 • [i\j[). J 1040 MB1 CVJ: =<MJfHVH•SIG,\j(Zi3\I[V l >+X!"BCV l> I< 1 +Kr8CV ])J 1050 CSTBCVl:=9C~~/CJ~3S<M31CVl>l4.q3<MI1CVJ>>J 1060 CB0CVl:=CST8CVll<t+KT9CV1>J 1070 IIEU3[V 1: =CZ9·'1j[V )+i<l13[V 1 >:4o.::•H[V lJ 1080 T: =CB0CV 1*<4-'35< Zi3:11[V 1 >*:'4.1·HV 1+KII'BCV l>; 1090 ~UHVl: =<Zl \I[V l+KI Hv 1>1< 1 +KTHV l>J 1100 CSTHVJ:=-C\!KlBCVJ+HP[V J-,JHCVJ>/,..£UHV 1J 1110 C01CVl:=CSriCVJ1<1+KTICVJ>J 1120 T!.JW:=C•iHCVl*<Ac:!SCZl 'IICV l>*M,H CV l+KIMHV J>; 1130 KJLT: =HP[V l*MYCV l+J"'[Vl*:-'MrUV l+rU'.J+TJ 1140 iW•J: =< i'<Lll *K~L T> I C-411 [ V l *KJL. > -t; 1150 'GIJU'SYSTEi"'[MlJ 1160 L7: P:U'Ijf'fi~Xr< 'C 'V;1<.H l·J:'£' >' > ;F IXrcs .. O .. L>; 1165 PiU\ITn:xrc•c• .-,J.J :'~E~L ZE:I<J PJHTS '>'HIILGKJ\II..C:{J 1110 'GI1fJ'SYSTEMC8lJ 1200 12: 'IF'' -S*~:.)>=O' THEil' '13E:GI·II' ~L: =PHCV Ht'l: =JJPHCV l: =PH[ V 1+0-~J 1210 t<:=1J'Gt<H1'SYSTEM[l H'E'iJ' 1220 'ELSE' ''3E:Gl.J'PHCV 1: =PHCV 1-S*D·iHK: =K+1 J' IF' K<JO'THEII' 1222 'G~TJ'SYSTE:r-1[1 l'EL'iE' 'Gvln1'SYST£,'1[7 lJ '£,\10' J 1230 LJ: 'IF'' -S*RF'J<=O' THE \I' 'c:!EG I 'l' JH: =PHCV JJM: =4iPH[V l: =CQH+(}L> 12J 1240 K::::1J'G::H.1'SYSrEMC1H'E:·v•
180
1250 'ELSE''BEGI~'PHCVl:=PHCVl~·2JK:=K+1J'IF'K<JO'THEN' 1252 'G0T~'SYSfEMC1l'ELSE''G0T0'SYSTEMC7lJ'E~'J 1260 L4: 'IF' ·S*f'F.J>::()'THEN' 'BEGI.'.I'QL:=PHCVJJ 'G6T0'SYSTEMC5 lJ 'END' 1270 'ELSE' 'BEGl"'QH:=PHCVlJ'G3TriJ'SYSTEMC5JJ'Ei\D' J 1280 1..5: 'IF'A8SCQH-QL><10tC·6>'THEi>l''BEGIN'M:=6J 1290 PHCVJ:=CQL+QH)/2J'G0T0'SYSTEMC1 lJ 'E;'V' 1300 'ELSE' '13EGI . ..,'PHCVl:=C:lL+QH>I2J 'G<Jf0'SYSTEMC 1 JIJ 'END' J 1400 L6: PRiilrfTEXTC' C' Vm..GE'DE Z0:-£' >' >JFIXf<5~0 .. L)J~"'I..CRJ 1410 PRI...,TTEXTC'C'PHV= '>'>JFIXTC6 .. 3 .. PHCVJ>J 1420 PRINTTEXTC'C' MgBI: '>'>JFIXTC6 .. 4 .. MI1CVl>J~RJ 1430 'F0.~' l:::()'STEP'l 'UNTIL'!U[Vl'DIJ' 144> '3EGIN'FIXTC5.tO,zi'JCVJ ... l>JFL-JTC5 .. 2 .. KI CV.t I l*C01 CV])J 1450 •'ll..£:iH 'E:-.D' J 1460 P~INfTEXTC' C' CSTI= '>' HFL0TC5 .. 2.tCS'fiCVl>J•:'III..CtU 1410 NlC~JPrtiNTTEXTC'<' MaBB= '>'>JrlXTC6.t4,M81CVl>J 1480 Nl.C!U 1490 'rid;~' II=O'STEP'l'U;'IffiL'>BCVl'00' 1500 '3EGIN'FIXTC5 .. o .. ZBNCVJ-I>JFL0TCS .. 2.tKBCV .. Il*CB~CVl>J 1510 :-ILCRJ 'E'IJ' J 1520 PRIWTEXTC' C' CSTB= '>' >JFL0TC5 .. 2 .. CSTI3CV]) J 1530 NLCRJ~J 1540 PRINTTEXTC' C' 1550 PIUWTEXTC' C' 1555 L8: K:=lJ 1560 1700 1800
OUTPUT
LJ0PELECTK~L YTZ('l>£
L<\MBD4 RFO=
PHL= +4.800 M:BLI= 0 +·94250'- 2
-1 +.10575'- 1 CSTLI= +.20000'·
M.Jli.B= +18·9880 +1 +·10559'- 1 0 +.66624'- 5 CSTLB= +.10566'-
L<\M30<\= +.63975'+ 0
'>'>J~TC5 .. 2 .. KvLT>J '>' >JF'L0T<S .. 2 .. RF\U J .UfU
i'll.Cr<J • E 'I) • J
V0LGENDE Z01\E +1 PHV= +8.707 M0Bl=
+1 +.50943'- 8 0 +.16384'- 1
-1 +·13924'- 2 CSTI= +.17776'-
+3.1162 +I +•13975'- 2
0 +. 71232'- 2 CSTB= +.85206'- 2
tA!'SIJA +o69343 1 - 1
V0LGE:IIDE Z0 '£ +2 PHV= +6.800
0 +.10276'- 1 -1 +.77890'- 2 CSTI= +•18065'-
~BI=
+17.6613 +I +.77889'- 2
0 +.59041.- 3 CSTB= +·63794'- 2
lAMBDA +•38172'+ 0
Vm.GEI'!IJE z•3.'£ +3 PHV= +6.734 MJBI=
0 +·91646'- 2 -1 +·49642'- ~
-2 +o26889'- 3 CSTl= +·14398'-
~JB9= +18·0237 +I +·55019'- 2 0 +o2980'2'- 3 CSTB= +.57999'- 2
Lt\f'IBDA +•22003'+ 0
181
RrQ= +.35763'- 6
-12·9352
RFQ= -·13039'- 6
-7·4560
RrQ= -.57742'- 1
182
APPENDIX B
i For all qualitative analyses an apparatus is use1 as shown
schematically in Figure B.l. Basically the electrophoretic
equipment consists of a thin-walled narrow hole 1ube, made
of teflon. The internal diameter is 0.45 mm and the outside
diameter is 0.75 mm. The teflon capillary tube is mounted
in a liebig cooler; the water cooling is possible by the
inlet and outlet A. The capillary tube is connected with the
electrode compartments. The sample introduction ~s made by
a four-way sample tap. The detection is made by thermocouples
(Band C). The signals of the thermocouples are amplified
(D) and registered by a recorder (E).
· ... -~· .. _.,.... ' . '·. ·:·.\; •. ·. . . : .
FIG. B.l Schematic diagram of the isotachophoretic equipment
with sample valve. A=thermostated water; B=integral
thermocouple; C=differential thermocouple; D=ampli
fiers; E=recorder; FGHI=sample tap (H:rinsing and
refilling of the capillary tube, F:rinsing and refil
ling of the terminator compartment, G and F:for the
sample introduction).
183
A direct current power-supply, maximal 22 kV, delivers a
constant electric current of 0-200 ~A. The electrodes are
made of platinum. To prevent electroendosmosis one electrode
compartment is closed by a serum cap.
At this moment the differential thermocouple C is not used,
because the differential signal is obtained, differentiating
the signal of thermocouple B.
APPENDIX C
The quantitative analyses are carried out with an apparatus
as shown in Figure c.197 • A capillary tube is connected with
the electrode compartments (7-8). The sample introduction
is made by an injection block {7). To prevent electroendos
mosis the electrode compartment 8 is provided of a membrame.
Compartment 5 can be used for a counterflow of electrolyte.
184
19
FIG. C.l Bloc diagram of the isotachophoretic equipment.
!=recorders; 2=differentiator; 3= Knick amplifiers, type A; 4=regulator for the counterflow; 5=equipment
for the counter-flow; 6=level control; ?=injection bloc; S=counter electrode; 9=thermocouple; lO=Al bloc
with capillary tube; ll=Pt sensor; 12=load; 13=regu
lator for thermostating; 14=thermostated water;
15=teflon-lined valves; 16=current stabilised power
supply; !?=reservoirs; lS=magnetic valves; 19=mano
meter; 20=pressure regulator; 2l=air (2 atm).
185
SUMMARY
In this thesis, some aspects of the analytical method
"isotachophoresis" are discussed.
In the first part a theoretical model is decribed, and with
the derived formulae a computer program is developed. With
this program quantities such as concentrations, pHs and
conductivities of the zones can be computed. Calculated
values fit experimental values. Corrections for the relaxation
and electrophoretic effect and for the differences in tempera
tures in the zones were necessary.
Sometimes no real values were obtained in the calculations.
In those cases disturbances were present in the experiments.
A model of moving boundary electrophoresis was more satis
factorily.
In the second part the results of quantitative and qualitative
experiments for several ionic species are given. As a detector,
a thermocouple was used.
In order to obtain a separation we can use:
- differences in mobilities
- differences in pK values
- different solvents.
Using differences in mobilities and pK values, experiments
were carried out with anions and cations in different electrolyte
systems at different pHs, with water and methanol as solvents.
Also some separations of nucleotides were studied.
Some quantitative experiments were carried out with anions.
The concept of the "calibration constant" is introduced,
whereby the determination of calibration curves is superfluous.
186
SAMENVATTING
In dit proefschrift worden enige aspecten van dejelectro
foretische an~lyse methode "isotachoforese" behafdeld.
In het eerste gedeelte wordt een theoretisch model beschreven.
Uitgaande van de afgeleide vergelijkingen werd een computer
programma samengesteld, waarmee alle benodigde parameters
berekend kunnen worden. De met dit programma berekende
waarden stemden goed overeen met experimenteel bepaalde
waarden. Wel bleken correcties voor de invloed van relaxatie
en electroforese effect, en voor de verschillen in temperatuur
tussen de verschillende zones noodzakelijk te zijn.
Berekeningen gaven in sommige gevallen geen reele waarden.
In de overeenkomstige experimenten werden dan verstoringen
bemerkt. Een model van moving boundary electroforese bleek
in deze gevallen beter te voldoen.
In het tweede gedeelte worden de resultaten van kwalitatieve
en kwantitatieve experimenten voor de verschillende ion
soorten beschreven. Als detectie methode werd een thermo
koppel gebruikt.
Om een goede scheiding te verkrijgen kan gebruik gemaakt
worden van: verschillen in mobiliteiten
verschillen in pK waarden
- verschillende oplosmiddelen.
Gebruik makende van genoemde punten werden scheidingen
verricht van kationen en anionen in de verschillende
electrolyte systemen met verschillende pH~s, waarbij zowel
water als methanol als oplosmiddel gebruikt werd.
Ook werd de scheidinq van eniqe nucleotiden bekekfen.
~eneinde de kwantitatieve mogelijkheden van de methode te
onderzoeken werden experimenten met anionen verricht. Het
begrip "kalibratie konstante" werd ingevoerd, waardoor
ijkkurven overbodig worden.
187
DANKWOORD
Veel dank is verschuldigd aan LKB-produkten AB, Zweden,
voor het verstrekte promotie stipendium, en verder aan
allen die op enigerlei wijze aan de tot stand koming
van dit proefschrift hebben bijgedragen.
LEVENSBERICHT
Op aanraden van de Senaat volgt hier een kort levensbericht
van de schrijver.
Hij werd op 22 augustus 1944 geboren te Maastricht. In 1960
behaalde hij het MULO-B dipl?ma waarna hij de H.T.S. te
Heerlen bezocht. In 1964 werd het H.T.S. getuigschrift
behaald (afdeling Chemische Techniek).
Van 1964 tot 1966 vervulde hij zijn militaire dienstplicht.
In 1966 began hij de ingenieursstudie aan de Technische
Hogeschool te Eindhoven, waar hij in september 1970
afstudeerde aan de sectie Instrumentele Analyse. Hierna
ving hij een onderzoek aan over isotachoforese, dat de basis
voor dit proefschrift zou vormen.
STELLINGEN.
1 Het gebruik van een isotachoforetisch systeem betekent
nog niet een isotachoforetische scheiding. Het gebruik
der naam "isotachoforese" voor electroforetische schei
dingen waarbij mengvormen optreden, dient daarom ver
meden te worden.
R.J. Routs, Thesis, T.H.E., 1971.
F.M. Everaerts en W.H.M. Kbnz, J.Chromatog.
65, 2871 1972 •
2 De micro bepaling van zuur en base dissociatie konstan
ten m.b.v. papier electroforese, zoals beschreven door
D. Waldron-Edwards is niet zinvol.
D. Waldron-Edwards, J.Chromatog. 20, 556, 1965.
3 De theoretische achtergrond van disc(ontinue) electro
forese zoals beschreven door L. Ornstein is onjuist.
L. Ornstein, "Disc electrophoresis, Background
and theory", Ann. N.Y.Acad.Sci., 121, 2, 1964.
4 De interpretatie van de scheiding van NH4+/H+ in het
artikel van 0. Hello is discutabel.
0. Hello, J.Electroanal.Chem. 19, 37, 1968.
5 Het gebruik van komplex-vorming in electroforetische
scheidingen verdient meer aandacht.
V. Jokl, J.Chromatog. 71, 523, 1972.
V. Jokl en L. Valaskova, J.Chromatog.
72, 373, 1972.
v. Jokl en z. Pikulikova, J.Chromatog.
74, 325, 1972.
6 Het gebruik van relatieve retentietijden bij geprogram
meerde gaschromatografische analyses voor identificatie
doeleinden dient onder voorbehoud te geschieden.
~~· __ .......... ~~
L.L. Engel, A.M. Neville, J.C. Orr en
P.R. Raggatt, Steroids, 337, 1970.
7 De aannarne door V.D. Mochel van een stereoregulariteit
in een door hem "zonder speciale zorg" bereid poly
butadieen is onjuist en berust op een foutieve inter-13 pretatie van C NMR spectra.
V.D. Mochel, J. Polym. Sci., A-1, 1009, 1972.
8 De, met ons huidig wetenschappelijk wereldbeeld, onver
klaarbare feiten en verschijnselen, dienen terdege onder
zocht te worden. Vooroordelen en onwil mogen geen belet
sel vormen voor een noodzakelijke herziening van het
wereldbeeld.
J. v. Belle: Zienswijze (op o.a. UFO's)
BRES PLANETE 1 tot 39
R. Charroux: Vergeten werelden, Vergeten woorden,
Onbekend verleden
E. von Daniken: Goud der goden, Waren de goden
astronauten, Terug naar de sterren
I. Hobana en J. Weverbergh: UFO's in Oost en
West I en II
L. Pauwels en J. Bergier: De eeuwige mens
E. von Khuon: Geleerden over von Daniken
9 Het gebruik van de natuurlijke stemming i.p.v. de evenre
dige stemming verdient meer aandacht teneinde een juiste
klankweergave te krijgen. Effecten als het "quinte de
loupe" dienen vermeden te worden.
10 De uitspraak "het slechtste beleid onder deze omstandighe
den is een ongewijzigd beleid" kan slechts als een demago
gische uitspraak beschouwd worden.
Keerpunt 72.
Eindhoven, 19 juni 1973.
J.L. Beckers.
