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Interaction of sodium hyaluronate with a
biocompatible cationic surfactant from lysine: a
binding study
Matej Bračič,a Per Hansson,b Lourdes Pérez,c Lidija F. Zemljič,a and Ksenija Kogejd*
aInstitute for the Engineering and Design of Materials, University of Maribor, Smetanova 17,
2000 Maribor, Slovenia.
bDepartment of Pharmacy, Biomedical Centre, Uppsala University, SE-75123 Uppsala, Sweden
cDepartment of Chemical and Surfactant technology, Instituto de Química Avanzada de Cataluña,
CSIC, Jordi Girona 18-26, 08034 Barcelona, Spain
dDepartment of Chemistry and Biochemistry, Faculty of Chemistry and Chemical Technology,
University of Ljubljana, 1000 Ljubljana, Slovenia.
Keywords: sodium hyaluronate, biocompatible cationic surfactant, fluorescence measurements,
binary-surfactant-mixture binding model; competitive adsorption.
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Abstract 207 words
Mixtures of natural and biodegradable surfactants and ionic polysaccharides have attracted
considerable research interest in recent years because they prosper as antimicrobial materials for
medical applications. In the present work, interactions between the lysine derived biocompatible
cationic surfactant, abbreviated as MKM, and the sodium salt of hyaluronic acid (NaHA) are
investigated in aqueous media by potentiometric titrations using the surfactant sensitive electrode
(SSE) and pyrene based fluorescence spectroscopy. The critical micelle concentration (CMC) in
pure surfactant solutions and the critical association concentration (CAC) in the presence of
NaHA are determined in dependence on the added electrolyte (NaCl) concentration. The
equilibrium between the protonated (charged) and deprotonated (neutral) forms of MKM is
proposed to explain the anomalous binding isotherms observed in the presence of the
polyelectrolyte. The explanation is supported by theoretical model calculations of the mixed-
micelle equilibrium and the competitive binding of the two MKM forms to the surface of the
electrode membrane. It is suggested that the presence of even small amounts of the deprotonated
form can strongly influence the measured electrode response. Such ionic-nonionic surfactant
mixtures are a special case of mixed surfactant systems where the amount of the nonionic
component cannot be varied independently as is the case with some of the earlier studies.
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1. Introduction
Aqueous mixtures of ionic surfactants and polyelectrolytes of opposite charge are of great
scientific and practical interest. They are used in a variety of technological fields in the form of
different advanced products, e.g. as household products (detergents, paints, and cosmetics),
coatings, wastewater treatment agents, pharmaceutical products, and many others.1,2 Their great
potential for the medical field use has been reported in the literature,3,4,5 e.g. in controlled drug
release or in direct treatment of acute inner organ injuries.3,4 In particular, natural and
biodegradable surfactants and ionic polysaccharides have attracted a lot of interest in recent
years.6,7,8,9 They prosper as alternative materials for medical applications where wound healing
properties and antimicrobial activity is needed, since a wide variety of common antimicrobial
chemical agents used in the medical field until now, such as metals and their salts, 10,11
iodophors,12 phenols and thiophenols,13 and antibiotics,14 is toxic to humans and harmful to the
environment.
When preparing aqueous mixtures for applications, special attention has to be paid to the
interactions between ionic surfactants and polyelectrolytes of opposite charge, since these can
alter the unique properties of each of the components in the mixture. Understanding of these
interactions is therefore crucial for optimizing the performance of the polyion-surfactant ion
mixtures. Within this frame, the purpose of this work is to perform a fundamental study of
interactions of a cationic surfactant derived from lysine with a completely ionized hyaluronic acid
(HA) in aqueous solutions. HA is a biocompatible and biodegradable polysaccharide consisting
of repeating β 1-4 D-glucuronic acid and β 1-3 N-acetyl-D-glucosamine. Due to its
biocompatibility and also to its excellent wound healing abilities, it is used in various
applications, the most notable being wound dressings, cosmetics, and pharmaceutical
products.15,16,17 The lysine-based cationic surfactant used in this work is an Nε-myristoyl-lysine
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methyl ester, abbreviated as MKM.18 It is a biodegradable amino-acid based surfactant exhibiting
excellent antimicrobial properties and low toxicity.18 Amino acid based surfactants constitute an
important class of natural surface-active molecules and are of great interest in organic and
physical chemistry as well as in biology and medicine. Their physicochemical properties
resemble those of conventional cationic surfactants, but they are more environmentally friendly
and non-toxic to eyes and skin.6
The critical micelle concentration (CMC) and the critical association concentration (CAC)
values of MKM in pure solutions and in the presence of hyaluronate anion, respectively, were
determined by potentiometric titrations using the surfactant sensitive electrode (SSE) and by
fluorescence measurements using pyrene as a probe. All measurements were performed in
aqueous solutions without and with added NaCl. From the SSE data, binding isotherms where
constructed in order to study the binding behavior. The results are interpreted by taking into
account the acid-base equilibrium between the protonated and deprotonated forms of MKM. The
importance of this special feature of the studied system is highlighted by theoretical model
calculations of the micellar equilibrium and of the SSE signal in solutions in the absence and
presence of the polyelectrolyte.
2. Materials and methods
2.1. Materials
The sodium salt of HA, NaHA (molecular weight: Mw = 0.6-1.1 MDa; monomer unit molecular
weight: Mm = 401.3 g/mol; for structure see Scheme S1 in Supporting Information, SI) was
purchased from Lex, Slovenia. All aqueous NaHA solutions for potentiometric and fluorescence
measurements were prepared by suspending NaHA in triple-distilled water (or in aqueous NaCl
solution) and stirring for 30 min at ambient temperature in order to obtain clear solutions.
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MKM (M = 407.0 g/mol; for structure see Scheme S1, SI) was synthesized as reported in
reference 18, where some biological and chemical properties of cationic surfactants derived from
lysine were also described. All aqueous MKM solutions were prepared by suspending MKM in
triple-distilled water (or in aqueous NaCl solution) and stirring for 15 min at around 40 °C. The
heating step is necessary because the dissolution of MKM in water at lower temperatures is slow
and its solubility moderate.
In view of the biodegradability of MKM,18 the stability of the surfactant in water was checked
by high pressure liquid chromatography (HPLC) and by nuclear magnetic resonance (NMR)
measurement (for instrumentation details see SI). 16 mg of MKM were dissolved in water and
stirred, first for 2 hours at 45°C and then for 18 hours at room temperature. Aliquots of 0.5 mL of
this solution were taken at the beginning (i.e. after 0 hours) and after 2, 4, and 20 hours. 4 HPLC
chromatograms were recorded at each time interval (t). These chromatograms were all identical;
therefore, only one is shown for the initial (t = 0 h) and final time (t = 20 h; c.f. Figure S1 in SI).
In Table S1, the height and area of the main peak observed at a retention time of around 13.5
minutes is reported at each t. After this treatment, the samples were lyophilized in order to
remove water, the obtained solid MKM was dissolved in deuterated methanol and an 1H NMR
spectrum was recorded. The 1H NMR spectra of MKM taken before (t = 0 h) and after (t = 20 h)
the described treatment in water are shown in Figure S2 in SI. It can be seen that also the NMR
spectra are identical. The HPLC and 1H NMR results thus show that no chemical degradation of
MKM is taking place in water at room temperature within the period of 20 hours. This time is
more than sufficient to perform the herein reported measurements without fear of MKM
degradation. Nevertheless, each measurement series was performed with freshly prepared MKM
solutions and immediately after their preparation.
2.2. Methods
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SSE-potentiometric titrations. The potentiometric titrations using the SSE were used to
determine the CMC values of MKM and the binding isotherms of MKM binding by NaHA, both
as a function of NaCl concentration. The SSE was prepared following the procedure described in
the literature.19 The active part of the electrode is a poly(vinyl chloride) (PVC) membrane
containing so called carrier complex (CC) that is formed between a cationic and an anionic
surfactant in aqueous solutions. For CC preparation, a 0.4 M solution of sodium dodecyl sulphate
(SDS) was slowly added to a 0.005 M solution of MKM under continuous stirring until a 1:1
molar ratio between the surfactants was achieved. This resulted in precipitation of an insoluble
CC from water. The resulting white precipitate was repeatedly washed with water in order to
remove NaCl (the by-product of the reaction between MKM and SDS) and vacuum dried at 50-
60 °C. A solid membrane with the composition 23 wt. % of PVC, 76 wt. % of dioctyl phthalate
(DOP), and 1 wt. % of CC was then prepared in the following way: CC was dissolved in 5 mL of
tetrahydrofuran (THF) by heating, followed by a sequential addition of PVC and DOP. The clear
viscous THF solution was cast into a petri dish and the solvent was left to evaporate overnight at
room temperature, producing a thin solid membrane of approximately 1 mm thickness. A piece of
the PVC membrane was glued to the bottom of a hard 1 cm diameter PVC tube by using a dense
THF solution of PVC as an adhesive. The PVC tube was filled with the reference solution (1
104 M MKM in 0.01 M NaCl) and an Ag/AgCl electrode was inserted in order to provide
electrical contact. The saturated calomel electrode (SCE) was used as the reference electrode.
After inserting the electrodes into the solution, the potential difference (E) between the SSE and
SCE was recorded after each addition of the MKM titrant solution into a given volume of the
solvent using the pH meter MA 5740, Iskra. The stability criterion for taking a reading after each
addition was dE/dt = 0.1 mV/30 s. The solution was continuously stirred with a magnetic stirrer
and a constant temperature of 25 °C was maintained during the titration. The response of the SSE
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to surfactant ion concentration in water without added NaCl was linear in a wide MKM
concentration range (from around 5.0 x 10-6 to 4.9 x 10-4 M, the CMC value of MKM in water)
with a slope of 56 mV/decade, which is close to the theoretical value at 25 °C (59.2 mV/decade).
For the CMC determination, a 5 x 10-3 M MKM solution was added stepwise to 10 mL of water
or aqueous NaCl solution with a micro burette. The titrations were performed at the following
salt (NaCl) concentrations (csalt): csalt = 0, 0.01, 0.05, and 0.1 M.
Titrations for the binding studies were performed in the same manner as described above.
Instead of water or aqueous NaCl, a 5 x 10-4 M NaHA solution in the selected solvent was used as
the initial solution and a MKM solution in the same solvent together with the same volume of a 1
10-3 M NaHA solution, in order to keep the NaHA concentration in the cell constant during the
measurement, were added in a stepwise manner. The stability criterion for taking a reading after
each addition was dE/dt = 0.1 mV/180 s.
The apparent degree of MKM binding by NaHA (βapp) was calculated as βapp = (cst cs
f)/cp,
where cst and cs
f are the total and free surfactant (MKM) concentrations, respectively, which are
obtained from potentiometric curves20,21 measured in the absence and presence of NaHA, and cp is
the concentration of the polyion (NaHA) expressed in moles of monomer units per volume.
Fluorescence measurements. Fluorescence measurements were performed to determine the
surfactant’s CMC and its CAC in the presence of NaHA. Pyrene (Aldrich, optical grade) was
used as the external fluorescence probe to monitor the formation of MKM micelles. The pyrene
saturated aqueous solutions, without or with NaCl, were prepared as described previously22 and
were used for the preparation of the MKM and NaHA solutions. The emission spectra of pyrene
were recorded in a 1 cm quartz cuvette at a constant temperature of 25°C by using a
luminescence spectrometer LS 50 from Perkin-Elmer. The wavelength of the excitation
electromagnetic radiation was 330 nm. All spectra were recorded in the wavelength region 350-
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450 nm. The excitation and emission slit widths were 2.5 mm and the scan rate was 200 nm/min.
The stock MKM solution (c = 5 x 10-3 M) was added in small volume increments into a pyrene
saturated solution in the cuvette. The emission spectra were recorded after each addition until the
CMC (or CAC) of MKM was reached and exceeded. Nine scans were accumulated for each run
and spectra were fully corrected before the ratio of the fluorescence intensities of the first and
third vibronic bands, I1/I3, was calculated. The peaks appeared at approximately 373 and 384 nm.
All measurements were performed in water and in 0.01, 0.05, and 0.1 M NaCl.
2.3. Theory
2.3.1 Model of MKM self-assembly
Polyelectrolyte-free solutions of MKM are modelled using the Poisson-Boltzmann (PB)
approach.23,24 The protonated (S+) and deprotonated (S0) forms of MKM are considered to form
mixed micelles of a single aggregation number N (N=N +¿+N0¿, where N+¿¿ and N 0 are the
numbers of S+ and S0 per micelle, respectively). The chemical potential of surfactant species i in
micelles (μimic) is:23
μimic=μi
0 , mic+μimix+μi
surf+μiel. (1)
where μi0 , mic is the standard chemical potential of a hydrocarbon tail in the micellar core. The term
μimix is due to the entropy of mixing, which has two contributions: RTln xi from mixing S+ and S0
in the micelles and RTN
ln cmic from the translational entropy of the micelles. Here, xi is the mole
fraction of i in the micelle, R is the ideal gas constant and T is the absolute temperature. The term
μisurf (¿ai γ i, where a i is the area in the surface region of the micelle and γi is a proportionality
constant with units of surface tension) comes from the contact energy between hydrocarbon and
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water at the micelle surface and μiel is the contribution from the electrostatic free energy of
forming a micelle. For surfactant monomers in the aqueous region we have:
μiw=μ i
0 ,w+RTln c i (2)
with μi0 , w being the standard chemical potential of the surfactant monomer in water and c i its
concentration. By taking into account the conservation of mass and introducing an acid constant
Ka relating the protonated and deprotonated surfactant forms to the concentration of hydrogen
ions, the equilibrium of the system is determined by the following set of equations:
c i=x i cmic
1N e(∆ μ0+ μi
surf+ μiel )/RT (i = +, 0) (3)
cSt =N cmic+c+¿+c0¿ (4)
¿ (5)
Ka=c0¿¿ (6)
In eq. 3,∆ μ0 is equal to the difference μi0 , m−μi
0 , w. Eq. (5) is valid when dissociation of MKM is
the only source of hydrogen ions in the system. For the dilute micellar solutions considered here,
the activity of a dispersed ion is set equal to its concentration.
To model the self-assembly of MKM in polyelectrolyte solutions, the polyion-dressed micelle
(PDM) approach developed earlier was used.25,26,27 PDM is a complex between a surfactant
micelle and (part of) a polyion chain. The electrostatic free energy of a dilute solution is divided
into separate contributions from micelle-free regions (containing polyelectrolyte) and regions
containing PDMs. The latter, in turn, consists of an external free energy due to the net charge of
the complex and an internal free energy due to the interaction between the bare micelle and the
polyion charges in the complex. The external part is calculated using the PB model with the PDM
described as a uniformly charged sphere. Expressions for the contribution to the chemical
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potential (μiel ,ext) are the standard ones within the PB theory.23,24 The internal contributions to the
chemical potential of S+ and S0 in PDM can be written as25,26,27 (for details see SI, section S2):
μ iel ,∫¿
k BT=N
x+¿ lBh
4 r ¿¿¿¿¿ (i = +, 0) (7a)
g+¿=¿¿ (7b)
g0=−x+¿¿¿ (7c)
where k B is the Boltzmann constant, ε 0 εr is the permittivity of the medium, h is a model
parameter related to distribution of charges on the micelle (see below and SI, section S2), and lB
is the Bjerrum length: lB=e2
4 π kB T ε0 εr. The total chemical potential of surfactant i in PDM is:
μimic=μi
0 , mic+μimix+μi
surf+μiel ,ext+μi
el ,∫¿+f ∆ μ p¿. (8)
The first three terms on the right-hand side of eq. (8) have the same meaning as in eq. (1) and the
last term corresponds to the PB-model free energy change ∆ μp of transferring f polyion charged
segments per micelle charge from the free state to the micelle surface. The equilibrium
composition is obtained by combining eqs. (4) – (6) with the following equation:
c i=x i cmic
1N e¿ ¿ (i = +, 0) (9)
As a result, c+¿¿ and c0 are obtained as functions of cSt from which the degree of surfactant
binding to the polyelectrolyte (β), is calculated:
β=cSt −
c+¿−c0
c p¿ (10)
For comparison with experimental data an apparent degree of binding (app) is defined as:
βapp=cSt −
c+¿app
c p¿ (11)
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where c+¿app¿ is the surfactant concentration in a polyelectrolyte-free solution (below the CMC)
giving the same electrode signal (E) as that in the polyelectrolyte solution (see below).
2.3.2 Model of the SSE response
To calculate theoretically the SSE response, we assume that the main contribution to the
measured signal comes from the charge transfer between the solutions on each side of the
electrode membrane. In equilibrium models, the interference of an ion j of the same charge sign
and valence as the potential determining ion i is often handled by means of a selectivity
coefficient Kj.28 This can be interpreted as the equilibrium constant of the ion exchange reaction
in which i is replaced by j in the membrane. Under the condition that the total concentration of i
and j in the membrane is constant one obtains the familiar Nikolskii-equation for the measured
electromotive force:29
E=constant+ R TF
ln (ci+K j c j) (12)
with F being the Faraday constant. Eq. (12) is applicable to monovalent ions when the
composition of the solution on the reference side of the membrane is kept fixed. The form of the
equation remains the same when the overall membrane potential is assumed to be the sum of the
phase boundary potential and a membrane diffusion potential under steady state, but K j then
equals the product of the ion exchange constant and the ratio of the ion mobilities in the
membrane.29 The uncharged form of MKM (S0) does not contribute to the electric potential itself
but, when present in the membrane, it modulates the signal by affecting the chemical potential of
S+. Because of its dominating hydrophobic groups the concentration in the membrane is expected
to be quite high even at low concentrations in the solution. In principle, it can reduce the activity
of S+ in the membrane either by expelling it (competitive binding) or by lowering its activity
coefficient without replacing it. It may also affect the dynamics of the charge transfer process,
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e.g. by changing the mobility of S+ in the membrane. To the best of our knowledge there are no
reports in the literature of such types of interference by non-ionic surfactants. Since we are not in
a position to identifying the dominating potential generating mechanism we will assume that the
effect is captured by a generalized form of eq. (12):
E=E¿+ RTF
ln ¿ (13)
E¿ is a constant, c Na is the concentration of sodium ions in the solution, and K Na and K0 are
‘interference’ coefficients for sodium ions and S0, respectively. It will be demonstrated that eq.
(13) in combination with the above model of surfactant self-assembly captures the main
qualitative features observed experimentally. In SI (section S3) we describe the competitive
binding mechanism reproducing the form of eq. (13) to a constant near.
2.3.3 Model calculations
The non-linear PB equation is solved numerically by means of a computer program (PB cell)
written by Bengt Jönsson. The program also calculates the electrostatic contribution to the
chemical potentials in the thermodynamic model by Jönsson and Wennerström.24 The PDM is
modelled as a uniformly charged sphere with a radius 17 Å carrying N+¿ (1−f ) ¿ net charges. Instead
of attempting to determine the optimal value from the free energy expression we simply set f=1
for β+¿≤ 1¿, and f=1
β+¿¿ for β+¿>1 ¿, with β+¿¿ being the number of bound S+ per polyion charge.
The fully dissociated HA is modelled as a uniformly charged cylinder with a radius of 5 Å and a
linear charge density corresponding to one negative charge per 10 Å. Both, micelles and polyions
are in contact with infinitely large solution of monovalent salt at T = 298 K; the dielectric
constant (ε r) of the medium is set to ε r=78.5. When evaluating eqs. (3) and (9), we set
Δ μ0=−13.5 RT/mole (molarity scale), a typical value for a C12 surfactant,30 γ+¿=0.018¿ J/m2,24 and
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γ0=0.010 J/m2 (see the previous models of mixed aggregates of charged an uncharged
amphiphiles24). The dominating contribution to the free energy change of transferring polyion
chain segments to the micelle surface is considered to come from the entropy gain in releasing
the counterions. Hence, we put ∆ μp=−f μp−TS, where μp
−TS is the entropic part of the electrostatic
chemical potential of a polyion (per charge). PB calculations provide the following values of μp−TS
(in units of RT/mole): 0.55, 0.40, 0.31, and 0.26, in solutions containing 0.005, 0.01, 0.05 and 0.1
M salt respectively. In all calculations, we use pKa = 7.8 (suitable for MKM in the unimer form18),
N=56, and h=2.5. The latter is obtained from an optimization of the free energy of PDM for a
C12 surfactant by means of a procedure described in SI (section S2). In the calculation of the SSE
response, we use K Na=0.001 and K0=500. The ion concentrations in eq. (13) are converted to
activities by multiplying with activity coefficients (¿10−0.5√C salt /(1+√Csalt)). The correction has only a
marginal effect on the result.
3. Results and discussion
The synthesis and basic characterization of MKM was described recently.18 However, its
micellization process was followed only in aqueous solution without added salt by measuring the
self-diffusion coefficients at 25°C by NMR. It is well known that CMC of ionic surfactants
depends considerably on the added salt concentration. Therefore, we first report CMC values of
MKM in dependence on NaCl concentration (Section 3.1). Section 3.2 is devoted to the
discussion of experimental binding isotherms in NaHA solutions at various csalt values and
Section 3.3 to their model treatment.
3.1. Determination of CMC values
The response of the SSE electrode to the total concentration of MKM (i.e. the E vs. log cst
curve) in the absence of NaHA is presented in Figure 1 for all investigated csalt. The dependencies
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Figure 1. Plots of the electromotive force (E) as a function of the total MKM concentration (cst)
in aqueous solutions without and with added NaCl. Slopes of the linear parts of the curves below
the CMC are reported in the Figure. To highlight the difference between the curves those for
0.01, 0.05 and 0.10 M NaCl have been shifted vertically to start at the same value as the salt free
curve. The original curves are presented in SI (Figure S9).
are linear at low surfactant concentrations and display a break at a well-defined concentration as
expected for surfactant solutions below and above the CMC. The determined CMC values, taken
as the concentration at the break point, are reported in Table S2 (SI, section S4.1) and plotted in
Figure 2 as a function of the ionic strength I (= csalt + CMC) at the CMC. For the moment they
should be considered as apparent CMC values. The reason for this is that the electrode response
curves contain anomalies.
First of all, the slope below the break point is smaller than the theoretical value at 25°C (
dE /dlogcSt = 59 mM/decade) and depends on csalt (see values reported in Figure 1). This is not a
behavior expected for ionic surfactants. Normally, the addition of salt lowers the CMC whereas
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the slope of the E vs. log cst line below the CMC is not affected by csalt. Secondly, the slope above
the break point is negative and becomes more negative the higher the csalt. While the single-ion
activity of ionic surfactants is known to decrease above the CMC, an observation largely
attributable to a decreasing entropic penalty of binding counterions at a higher total surfactant
concentration, the effect is known to disappear when salt is added. In particular, the effect should
be absent at 0.1 M NaCl, where in contrast the experimental slope of the electrode response curve
above the CMC is the most negative. Because of the importance also for the construction of
surfactant binding isotherms in polyelectrolyte solutions, it is necessary to examine in detail the
origin of this ʻanomalousʼ behavior to see in what ways it affects the results. Therefore, the
potentiometric CMC values were compared with those obtained by the pyrene fluorescence
method. The formation of hydrophobic domains (such as micelles) is indicated by the change in
the pyrene polarity ratio, I1/I3, which is obtained from pyrene emission spectra22 (see examples of
such spectra reported in Figure S7 in SI). Plots of the I1/I3 ratio as a function of the MKM
concentration are shown in Figure 3 for all salt concentrations. The I1/I3 value is high below the
CMC (I1/I3 = 1.55-1.65) indicating a highly polar microenvironment of pyrene, it starts to
decrease as the micelles begin to form and finally stabilizes at a considerably lower value (I1/I3
1.1-1.2). The I1/I3 ratio around 1.2 indicates solubilization of pyrene in the hydrophobic interior
of surfactant micelles. The CMC values were determined at the point where the I1/I3 values
started to decrease and are plotted in Figure 2 together with the CMC data from potentiometric
measurements. It can be seen that potentiometric (SSE) and fluorimetric data are in good
agreement (see also the CMC values reported in Table S2 in SI). This indicates that the break
point in the SSE curves indeed coincides with the appearance of the hydrophobic domains in
solution. It is therefore interesting to point out that the CMC value in water (CMC = 4.9 10-4 M
by both methods) is approximately 3-times lower than the one determined previously by NMR
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Figure 2. Upper panel: CMC values of MKM in aqueous NaCl solutions at 25°C in dependence
on the logarithm of the ionic strength, I (= csalt + CMC), as determined by the SSE potentiometric
titrations (full triangles) and by pyrene fluorescence measurements (open triangles). The straight
line is the best fit to the experimental data and can be described by the equation
CMC=−3.28−1.25 log I (see text). Lower panel: CAC values of MKM in aqueous NaCl
solutions at 25°C in dependence on I as determined by the SSE potentiometric titrations.
measurements (CMC = 1.6 10-3 M18) and 4-6-times lower than the one obtained by
conductivity measurements (CMC = 2-3 10-3 M6,31). In reference 31, a considerably lower
CMC (= 2.3 10-5 M) in comparison with these values was determined by surface tension
measurements with the Wilhelmy plate. This finding was explained therein as a consequence of
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the multilayer adsorption of the surfactant’s amine groups on the platinum surface of the plate,
which supposedly affected the wetting properties of the plate and hence the measured surface
tension. However, the reasons for the above discrepancies in CMC values may also be that the
bulk methods (like NMR and conductivity) are less sensitive than the fluorescence and SSE
potentiometric ones for detecting the formation of hydrophobic domains at low surfactant
concentrations. NMR measures the self-diffusion coefficients of species in solution and low
solute concentrations (around 1 10-3 M) may present some limitations for the reliability of the
NMR determination. Another interpretation is that the values determined by the present methods
(and those obtained previously by surface tension31) are influenced by a small fraction of MKM
monomer present in the deprotonated form even at a neutral pH (note that pKa value of the
monomer MKM is 7.818). Thus, mixed micelles of the protonated (positively charged, S+) and
deprotonated (uncharged, S0) forms may exist in solution at concentrations low enough not to
Figure 3. The I1/I3 fluorescence ratio of pyrene in aqueous MKM solutions in the absence (water)
and in the presence of NaCl.
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markedly influence the concentration of the free MKM molecules, and therefore do not affect the
measured NMR self-diffusion coefficient or conductivity (note that the uncharged MKM has a
negligible effect on solution’s conductivity). Nevertheless, even at such low concentrations they
may very well be detectable by the pyrene method, which is very sensitive to the presence of
hydrophobic domains. It will be demonstrated below that the break point in the SSE response
curve should in fact correspond to the onset of mixed micelle formation of the two forms of
MKM, S+ and S0. Further support for this interpretation is provided by the plateau values of I1/I3
below the CMC. Usually, the I1/I3 values below the CMC increases with increasing salt
concentration because of a more polar environment when a larger number of ions from NaCl is
present in solution.22 The trend is just the opposite in Figure 3: the lowest I1/I3 ( 1.56) value is
detected in 0.1 M NaCl. This suggests that the concentration of S0 increases with increasing csalt.
The above results are in excellent agreement with recent studies of Fegyver et al.32,33 on the
impact of the nonionic surfactant additive on association between polyelectrolytes and oppositely
charged surfactants. Those studies revealed formation of mixed ionic-nonionic surfactant
micelles in polyelectrolyte-free solutions at very low surfactant concentrations by using pyrene
fluorescence spectroscopy, whereas the conductivity measurements detected micelles at orders of
magnitude higher surfactant concentrations. An important difference between the studies of
Fegyver et al.32,33 and ours is that the nonionic surfactant with a different chemical nature
compared to the ionic surfactant was used therein. The uncharged component could thus be added
to the mixed surfactant solution independently, for example so that its concentration was kept
constant. On the contrary, the concentration of nonionic surfactant (S0) is determined by the
inherent S+-S0 equilibrium in these solutions in the MKM case.
Let’s turn back to the ʻanomalousʼ behavior of MKM. Another indication of MKM’s
anomalous self-assembly comes from the variation of the apparent CMC with csalt (Figure 2,
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upper panel). The observation that CMC decreases with increasing csalt is a phenomenon typical
for ionic surfactants (see also Figure S8 in SI, where data for a conventional cationic and anionic
surfactant, cetylpyridinium chloride (CPC)34 and SDS,35 respectively, are included). The presence
of an electrolyte reduces the net repulsion between charged head groups of surfactant molecules
in the micelle and consequently micellization starts at a lower surfactant concentration.30
However, the trend indicated by the solid line in Figure 2 (upper panel) is not typical. This line is
described by an equation of the form CMC=−3.28−1.25logI , whereas for conventional ionic
surfactants like CPC or SDS the linear dependence is normally obtained on a double logarithmic
plot36,37 and is described by an equation of the form logCMC=−a−blogI (where constants a and
b have positive values). This is clearly demonstrated for CPC and SDS in Figure S8 in SI (lower
panel). As one can appreciate from Figure S8, the apparent CMC values of MKM do not fit such
functional relationship. Rather, they decrease less steeply with increasing I in comparison with
conventional surfactants, which may indicate that the micellar equilibrium is influenced by the
acid-base equilibrium.
Returning to the anomalous electrode responses displayed in Figure 1 that might also be
accounted for by proposing formation of MKM pre-micelles (dimers, trimers, etc., in equilibrium
with free monomers). It is easy to see that the formation of MKM pre-micelles would lower the
activity of the surfactant and reduce the slope of the curves below CMC. However, this cannot
account for the negative slopes above the CMC. As already pointed out the observed increase of
the effect with increasing csalt is not consistent with micellar equilibrium of regular cationic
surfactants. On the other hand it is possible to account for it if a fraction of MKM is deprotonated
but still interacts with the surfactant electrode membrane.
3.2. Binding isotherms
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The degree of binding of MKM to NaHA was determined by the use of SSE. The SSE
potentiometric titration curves (E vs. log cs) obtained in pure MKM solution and in the presence
of NaHA are presented in Figure 4 for the case of 0.01 M NaCl. Other curves are shown in Figure
S9 in SI. The curve obtained in the presence of NaHA almost fits the calibration line
(measurement in pure MKM) for cs < 6 10-5 mol/L and starts to deviate from it at higher
surfactant concentrations due to MKM binding by NaHA. In the region where binding is strong
and cooperative the free surfactant concentration in mixed solution with the polyelectrolyte
usually almost does not change. Because the potential of the SSE depends on the free (monomer)
MKM concentration in solution, also the value of the measured E should be more or less
constant. In the MKM case, however, E in this region clearly decreases with increasing MKM
Figure 4. SSE potentiometric titration curves for pure MKM and for MKM in the presence of
NaHA (cp = 5 10-4 mol/L) in 0.01 M NaCl; the values of Δcs and csf, needed for the calculation
of the degree of binding, are indicated (see text).
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concentration (c.f. the negative slope of the curve in the range 6 10-5 M < cst < 5 10-4 M).
This result suggests that the free MKM concentration even decreases in the region of cooperative
binding, which ultimately leads to negative slopes of the experimental surfactant binding
isotherms (see Figure 5). This is generally not observed in surfactant/polyelectrolyte mixtures.
More extended discussion related to this observation is given below.
Figure 5. Binding isotherms (degree of binding app as a function of csf) for MKM binding by
NaHA (cp = 5 10-4 mol/L) in water (open circles) and in solutions with added NaCl: csalt = 0.01
(diamonds), 0.05 (squares), and 0.1 mol/L (triangles). The arrows indicate CMC values of MKM
determined by potentiometry: 1 - water, 2 - 0.01 M NaCl, 3 - 0.05 M NaCl, and 4 - 0.1 M NaCl.
Normally, the difference between the curves in Figure 4 should give the information on the
amount of MKM bound by the polyion (designated as cs) and enable the calculation of app (=
(cst - cs
f)/cp = cs/cp) and construction of binding isotherms. Apparent binding isotherms obtained
in this way are shown in Figure 5 for all salt concentrations. Some features are characteristic for
cooperative binding of surfactants by polymers.20 Binding is negligible (app 0) at MKM
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concentrations lower than a certain value: for example, in water app is virtually zero for csf below
4 10-5 mol/L. At higher surfactant concentrations, app increases rapidly (i.e. csf does not change
appreciably), indicating strongly cooperative interaction, and finally levels of at some point
indicating that cooperative binding to the polyelectrolyte is no longer possible.
The free surfactant concentration at the point of the steep increase in app is referred to as the
critical association concentration (CAC) or ‘CMC’ in the presence of the polyion. The CAC
values determined from the isotherms in Figure 5 are reported in Table S2 in SI and plotted in
Figure 2 versus I. They increase with increasing I, contrary to CMC values, a finding related to
the screening effect of simple electrolyte on attractive interactions between polyions and
oppositely charged surfactant cations. Strong interactions are indicated by a pronounced
reduction of CAC in comparison with the CMC values (CMC values are indicated by arrows in
Figure 5). In the NaHA-MKM system, the largest lowering of CAC (around 1 order of
magnitude) is observed in solutions with no added NaCl.
At the highest NaCl concentration (csalt = 0.1 mol/L), no levelling off of the isotherm is
indicated; rather, app continuously increases to values above 1. The reason for this observation is
the coincidence of the CMC and the CAC values of MKM in 0.1 M NaCl (CMCCAC = 1 × 10-4
mol/L; c.f. Table S2 and arrow 4 in Figure 5). The free micelle formation starts instantly after (or
simultaneously with) the saturation of the polyion by MKM, with SSE registering both processes.
The slopes of the experimental binding isotherms in Figure 5 deserve special attention due to
their pronounced negative value in the region of cooperative binding, which is not typical for the
binding of conventional surfactants by polymers. The “back swing” of the isotherms even
increases with increasing salt concentration and seems to indicate that the free MKM
concentration decreases as the cooperative binding of MKM to NaHA is taking place.
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Possible explanations for negative slopes in the NaHA-MKM system could be the following:
(1) the presence of a non-ionic surfactant (with different chemical structure as MKM) that is not
detected by the SSE but takes part in the aggregate formation at the polyion together with MKM;
this option was excluded based on the chemical analysis of the solid MKM; (2) polyion
properties (its charge density) change significantly during the binding process. In order to get an
increasing negative slope, the charge density should increase upon surfactant binding, which
seems highly unrealistic in the case of cationic surfactant binding to an anionic polyelectrolyte;
(3) some other equilibrium process, such as the above mentioned acid-base equilibrium plays an
important role. In the following, we present results of model calculations favoring the latter
explanation.
3.3. Results of theoretical modelling
To investigate theoretically the importance of the equilibrium between the protonated (S+) and
deprotonated (S0) MKM on the results we used the model described in Section 2.3 to calculate
the concentrations of free surfactant monomers (C+¿¿ andC0¿ in the solution in equilibrium with
micelles as functions of the total surfactant concentration. The result obtained for the systems
containing 0.1 M salt in the absence of the polyelectrolyte is presented in Figure 6. Shown in the
figure is also the concentration of hydrogen ions ([H+]), the mole fraction of S+ in the micelles (
x+¿¿) and the total fraction of surfactant in the micelles (N Cmic /Cst ). As can be seen, the fraction
in micelles starts to increase fairly abruptly when the total surfactant concentration is about 10-4
M. Below that concentration, which is interpreted as the critical micelle concentration (CMC),
essentially all surfactant exists in the form of free monomers. Below CMC, the concentrations of
H+ and free S0 are the same since (by neglecting the dissociation of water) all H+ in the system
derives from the reaction S+¿→ S 0+H+¿¿ ¿. Because of the rather high pKa, they are present at much
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lower concentration than S+. Nevertheless, at the CMC the micelles contain about equal amounts
of S+ and S0 (x+¿¿ = 0.47), which is explained by the fact that micelles of low charge density are
favored by the electrostatic free energy. Above CMC the concentration of H+ increases faster
with increasing surfactant concentration than below CMC showing that, despite the fact that the
ratio C0/C+ of free monomers decreases faster than below CMC (in agreement with Eq. 6), the
total concentration of S0 in the system increases in this range. Again this is an effect of the
electrostatic free energy favoring low charge of the micelles. Note that this is not in conflict with
the result that x+¿¿ increases and C0 decreases above CMC since the fraction partitioned to
micelles increases for both S+ and S0.
Figure 6. Theoretically calculated concentrations of free S+ (C+), S0 (C0), H+ ([H+], left axis), and
mole fraction of S+ (x+) and total fraction of surfactant in micelles (N Cmic /Cst ) (right axis) as a
function of total surfactant concentration at 0.1 M salt in polyelectrolyte-free solutions.
The result in Figure 6 of the largest significance for the interpretation of the data from the
electrode measurements in Figure 1 is that C0 starts to decrease immediately above the CMC. C0
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decreases in part because incorporating uncharged surfactants in charged micelles lowers the
electrostatic free energy of the micelles (and thus the electrostatic interactions give a negative
contribution to the chemical potential of S0 in micelles), and in part because it is favored by the
entropy of mixing in the micelles. Before dealing with how the decrease affects the response of
the SSE, we note that the onset of micelle formation appears to have a much less dramatic effect
on C+ than on C0. This can explain the discrepancy between the experimental CMC values
reported here and those obtained from measuring bulk properties (NMR self-diffusion and
conductivity) in salt-free solutions. This is further discussed in SI, section S6. The theoretically
calculated CMC values depend, of course, on the standard free energy of transferring a
hydrocarbon tail from water to the micelle core (Δ μ0). The latter value was adjusted to give a
CMC in agreement with experiments at 0.1 M salt. However, the value (13.5 RT/mole) is of the
same order of magnitude as values used earlier for surfactants of comparable hydrophobicity in
connection with the PB theory. E.g., the values 11.4 and 14.4 RT/mole (molarity scale) were
assigned to dodecyl (C12TAB) and tetradecyltrimethyl ammonium bromide (C14TAB),
respectively, in an earlier study.38 By taking into account the contribution from the methylene
groups in the spacer in the MKM head group, the value used is fully reasonable. This value and
the values of the other parameters are used also for the lower salt concentrations. The following
CMC values are obtained at 0.0005, 0.01, 0.05 and 0.1 M salt, respectively: 2.2×10-4, 1.7×10-4,
1.1×10-4 and 9.4×10-5 M. In agreement with the results in Figure 2, the CMC decreases with
increasing salt concentration but the trend is weaker than in the experiments. The agreement
could have been improved by using, e.g., the cell model at the lowest salt concentrations, by
optimizing the aggregation number instead of using a fixed value, or by adjusting the value
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assigned toγ0. However, since our purpose is to demonstrate qualitative features rather than to
seek quantitative agreement we choose not to embark on that task.
We return now to the concentration of free surfactant and how it affects the SSE signal.
According to Figure 6, the concentration of free S+ increases monotonically as a function of the
total concentration, a result expected for solutions of mixed micelles of the present type. It is
indeed difficult to imagine a mechanism that would decrease C+ above the CMC when salt is
present in excess. Thus, we conclude that the lowering of the SSE signal above CMC (Fig. 1)
does not reflect a lowering of the activity of S+ in the solution. The only other charged species
displaying a variant activity in the solution is H+, which is expected to interfere with the S+-
response in the same way as sodium ions. However, since the activity of it increases above the
CMC (and more rapidly than below) it cannot give rise to a reduction of the membrane potential.
Furthermore, it is present at very low concentrations and should be outcompeted by the sodium
ions. The remaining component displaying a varying activity is S0, which is not expected to give
rise to a membrane potential itself. However, by partitioning to the membrane it can affect the
response indirectly by lowering the local activity of S+ or, alternatively, increasing its mobility.
Figure 7 shows the electrode response functions calculated by means of eq. (13) using the data
behind Figure 6 and the corresponding ones for the other salt concentrations. To facilitate
comparison with the experimental data in Figure 1, the curves have been adjusted slightly in the
vertical direction. We emphasize that the adjustment has no influence on the shape of the curves.
The model captures on a qualitative level the two most intriguing features observable in Fig. 1,
namely the deviation from the Nernstian slope at low surfactant concentrations (< CMC) and the
turnover to negative slopes at higher concentrations (> CMC). The quantitative agreement with
experiments decreases with decreasing salt concentration. In particular, the slope below the CMC
approaches the Nernstian value (59 mV/decade) slower with decreasing salt concentrations than
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Figure 7. Theoretically calculated electrode response (E) as a function of the total surfactant
concentration (cst) in the surfactant solutions at different salt concentrations (in mol L -1) as
indicated. The dashed line: Nernstian response function (slope at 25°C: 59 mV/decade).
in the experiments, leading also to lower maximum E values. At low surfactant concentrations,
the interference by Na+ is responsible for the slight bending of the curves (mainly at the higher
salt concentrations). Apart from that, the slope deviates from the Nernstian below CMC because
C0 increases slower than C+.
The model of polyion-dressed micelles (PDM) was used to calculate the concentration of
micelle-bound and free surfactant in solutions containing polyelectrolyte and simple salt. The free
polyelectrolyte chain is modelled using parameters suitable for fully dissociated HA as described
in section 2.3.3. All other parameters are the same as used to model the polyelectrolyte-free
system. When the degree of S+ binding to the polyelectrolyte ¿ is below unity, the concentrations
of all species and x+ vary with the total surfactant concentration qualitatively in the same way as
in the polyelectrolyte-free solutions. When β+¿¿ is larger than unity, C+ starts to increase faster
with increasing total surfactant concentration due to the entropic penalty of binding surfactant
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counterions to PDM. This is accompanied by an increase in C0 and a decrease in x+. The same
qualitative behavior is observed at all salt concentrations investigated. The results are used to
calculate the electrode response functions in the same way as in the polyelectrolyte-free case.
Figure 8 shows the result obtained for the 0.01 M salt case (solid line). For surfactant
concentrations below the CAC, the response is the same as in polyelectrolyte-free solutions
(dashed line). Above the CAC, the signal first drops and then increases again as expected from
the variation of C0 just described. A comparison with Fig. 4 shows that the calculated curve
captures the main features observed experimentally. The theoretically calculated curves for the
other salt concentrations are presented together with the corresponding experimental curves in SI
(Figure S9). It can be mentioned here that the experimental curves in
Figure 8. Theoretically calculated electrode response (E vs. log cS) as a function of the total
surfactant concentration, cst, in the presence and absence of the polyelectrolyte at 0.01 M salt.
E* = 257 mV.
Fig. 1 plotted without vertical adjustment display a shift towards lower E with increasing salt
concentration (at 0.01, 0.05, and 0.1 M salt the shift is ca. 25, 25 and 35 mV, respectively, from
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the salt free curve). The reason for this salt effect, which is not captured by eq. (13), is not
understood.
Figure 9 shows theoretically calculated binding isotherms for all salt concentrations studied.
Shown are both the apparent binding isotherms (βapp=f ¿; curves to the left) calculated from eq.
(11) and the actual binding isotherms (β=f (C+¿¿); curves to the right) calculated from eq. (10).
Note that the former ones are constructed from the curves in Fig. 8 (and the corresponding ones
for the other salt concentrations) in the same way as the experimental binding isotherms in Fig. 5
were constructed from the data in Figs. 4 and S7. In agreement with experiments, the slope of the
apparent binding isotherms calculated from theory is negative in a large binding range above
CAC and changes rather abruptly to positive values at high degrees of
Figure 9. Theoretically calculated binding isotherms. Left branch: Apparent degree of surfactant
binding, app, plotted vs. the apparent free concentration of S+. Right branch: true degree of
binding, , of MKM plotted vs. its free monomer concentration. In both cases, free monomer
concentration is designated as csf.
binding. In contrast, in the binding isotherms showing the actual degree of binding (“β”) the
slope is never negative. The apparent binding isotherm for the highest salt concentration does not
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‘swing back’ as much as in the experiment but the effect is most pronounced for this salt
concentration and the curve even intersects the other ones, in agreement with experiments. The
crossover to positive slope takes place at a higher binding level in the theoretically calculated
isotherms for the two lowest salt concentrations than in the experiments. This is directly an effect
of setting f=1 for β+¿≤ 1¿ in the PDM model, an approximation introduced to simplify the
calculations. Recall also that in the present model the crossover is a consequence of the entropic
penalty of binding surfactant counterions when the net charge of the PDM becomes positive (
β+¿>1¿). The mechanism is thus different from that in the site binding model39 often used to
analyze binding isotherms.
We conclude that according to the theoretical model calculations the data in Fig. 5 do not
represent true binding isotherms for MKM. The in-model explanation is that they are constructed
with the assumption that the measured electrode potential is a function of the activity of the
protonated form of MKM only, when it is in fact a function of both the protonated and
deprotonated forms. The largest consequence of that is that the reduction of the signal above the
CAC is interpreted as a lowering of the free concentration of (protonated) MKM, whereas it is
only the free concentration of the deprotonated form that is reduced. This is the origin of the
negative slope of the binding isotherms. In contrast, the protonated fraction, which is much larger
in magnitude, continues to increase above the CAC. The explanation is strongly supported by the
overall good qualitative agreement between the theoretically calculated electrode response
functions and experiments, both in the present and absences of the polyelectrolyte.
Conclusions
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The micellization of a recently synthesized biocompatible lysine-based surfactant MKM having
a C12 hydrocarbon chain and its interaction with the sodium salt of hyaluronic acid (NaHA) were
studied in aqueous solutions at different NaCl concentrations by the surfactant-selective electrode
(SSE)-based potentiometric titrations and by pyrene-based fluorescence measurements. The
surfactant showed several anomalies. First, its CMC values did not fit the usual double
logarithmic relationship in dependence on the ionic strength as known for conventional
surfactants but followed a semi-logarithmic relation of the form CMC=−a−b logI (I is the ionic
strength). Second, the slopes of the SSE response curves decreased with increasing I below the
CMC and turned to negative above the CMC, which resulted in pronounced negative slopes of
the experimental binding isotherms in the region of cooperative binding. The ‘back swing’ of the
isotherms even increased with increasing salt concentration. These observations were explained
by proposing equilibrium between the protonated (charged) and deprotonated (uncharged) form
of MKM in solution. All important features of the experimental isotherms were captured by a
theoretical model that considered the possibility of competitive binding of the two forms to the
electrode membrane. In particular, it was shown that the measured electrode potential is a
function of the activity of both the protonated and deprotonated MKM, which brings around the
anomalous behavior as detected by SSE.
One important implication of the result in the present study is that determination of binding
isotherms for pH sensitive surfactants by means of surfactant selective electrodes may be
difficult. The same should apply to mixtures of ionic and non-ionic amphiphiles in general. Such
example may be an anomalous binding isotherm obtained from the electrode measurements in
mixtures of a cationic surfactant and a non-ionic lipid as reported by Kadi et al.40 Additional
examples of electrode measurements that resulted in negative slopes of binding isotherms were
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reported also for mixtures of anionic surfactants and neutral polymers41 or cationic surfactant and
an anionic polyelectrolyte.42
Acknowledgements
This work was partially supported by the Slovenian Research Agency, ARRS, through the
Physical Chemistry program P1-0201, program P2 0118, and project L2-4060. LP generously
thanks the Spanish Plan National I+D+I MAT2012-38047-C02-02.
Supporting Information. Structures of MKM and HA, additional information about the PDM
model and a simple model of the SSE response, examples of pyrene emission spectra,
experimentally determined CMC and CAC values, dependence of CMC on ionic strength, SSE
potentiometric titration curves, and discussion about CMC values obtained by NMR. This
material is available free of charge as Supporting Information on the ACS Publications website.
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Table of contents graphics for the paper
Interaction of hyaluronic acid with a biocompatible cationic surfactant from lysine: a binding study
by Matej Bračič, Per Hansson, Lourdes Perez, Lidija F. Zemljič, and Ksenija Kogej
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Supporting information for the paper
Interaction of sodium hyaluronate with a
biocompatible cationic surfactant from lysine: a
binding study
Matej Bračič a Per Hansson,b Lourdes Pérez,c Lidija Fras Zemljič,a* and Ksenija Kogejd*
a Institute for the Engineering and Design of Materials, University of Maribor, Smetanova 17,
2000 Maribor, Slovenia.
b Department of Pharmacy, Biomedical Centre, Uppsala University, SE-75123 Uppsala, Sweden
c Department of Chemical and Surfactant technology, Instituto de Química Avanzada de
Cataluña, CSIC, Jordi Girona 18-26, 08034 Barcelona, Spain
d Department of Chemistry and Biochemistry, Faculty of Chemistry and Chemical Technology,
University of Ljubljana, 1000 Ljubljana, Slovenia.
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S1. Materials
Scheme S1. Chemical structures of a) MKM1 and b) NaHA2.
S1.1. Additional characterization of MKM
HPLC analysisof MKM were carried out using an analytical HPLC instrument, model Elite
LaChrom, using a UV-VIS detector at 215 nm. A Lichrospher 100 CN (propylciano) 5 μm, 250 x
4 mm, column was used. A gradient elution profile was employed from the initial solvent
composition of A/B 75:25 (by volume), changing during 24 min to a final composition of 5:95.
Solvent A was 0.1% (v/v) trifluoroacetic acid (TFA) in H2O and solvent B was 0.085% TFA in
H2O/CH3CN 1:4. The flow rate through the column was 1.0 mL min -1. The 1H NMR spectra were
recorded on a Varian spectrometer at 400 MHz using the deuterium signal of the solvent as the
lock. All measurements were performed in deuterated methanol using 5 mm tubes.
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Figure S1. The HPLC chromatograms (UV signal as a function of the retension time) taken at t = 0 and 20 hours, as indicated in the panels.
Table S1. Retention time, area, and height of the main peak in the HPLC chromatogram of MKM in water
after t = 0, 2, 4, and 20 hours of stirring the solution.
t / hours retention time (min) area (a.u.) height (a.u.)
0 13.490 9812177 404641
2 13.493 10748325 422992
4 13.520 11030196 428674
20 13.567 9856165 401192
41
Minutes0 5 10 15
mA
U
0
20
40
60
80
100
120
140
160
180
200
mA
U
0
20
40
60
80
100
120
140
160
180
200
13,4
90
UVmkmT0
Retention Time
Minutes0 5 10 15
mA
U
0
20
40
60
80
100
120
140
160
180
200
mA
U
0
20
40
60
80
100
120
140
160
180
200
13,5
67
UVmkmT20
Retention Timet = 0 hours t = 20 hours
811812813814815
816
817
818
819
820
821
8182
Figure S2. The 1H NMR spectra of MKM in deuterated methanol taken at t = 0 and 20 hours, as indicated in the panels.
42
t = 0 hours
t = 20 hours
822
823
824
825826827
8384
S2. Additional information about the model of polyion-dressed micelle (PDM)
Electrostatic free energy. The free energy expression underlying the PDM model derives from a
recent model of complexes between surfactant micelles and oppositely charged flexible polyion
chains.3, 4, 5, 6 The aggregation number N of a micelle with a spherical hydrocarbon core is related
to the core radius r, the volume per surfactant tail v, and the area per surfactant in the head group
region a:
N= 4 π r3
3v=4 π r2
a=36 π v2
a3 (S:1)
When v is the same for all components, (S:1) is valid also for mixed micelles. The polyion and
small ions are solubilized in the aqueous regions between the micelles (see Figure S1). To
describe the interactions in concentrated solutions each micelle is positioned in a spherical cell of
radius R=L+r, where L is the thickness of the aqueous layer surrounding the micelle in the cell.
R is directly related to the molar concentration of micelles Cmic:
NvCmic N A=( rR )
3
(S:2)
with NA being the Avogadro number.
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Figure S3. Schematic picture of micelle – polyion complex phase indicating how the radius of the bare micelle (r), the effective double layer thickness (d), the thickness of the aqueous layer (L), and the radius of the cell (R) are defined in the electrostatic model. The electrostatic free energy is expressed as a function of L and the number of micelles Nmic
(equal to the number of cells):
Gel=2 πNmic σ2 r3
ε0 εr( d (L)r+d (L) ) (S:3)
d (L)=Lc (1−e−L/Lc) (S:4)
Lc=hr√Z
(S:5)
Eq. (S:3) has the form of the energy of a spherical capacitor. The same type of expression or
similar has been used to model complex formation between micelles and polyelectrolytes with
results in good agreement with experiments.3, 4, 5, 6 The theoretical basis for it rests on a
comparison with an analogous expression for the electrostatic energy between planar surfaces
separated by counterions.7 In the strong electrostatic coupling regime the electrostatic force
between the surfaces is independent of the valence of the counterions and their position in the gap
between the planes. The behavior is described well by the strong coupling (SC) theory by
Moreira and Netz,8 in which the energy expression has the form of the energy of a capacitor.7 The
SC theory works fairly good also at considerably lower coupling strength as long as the
separation between planes is smaller than the average distance between the counterions. This is
attributed to the correlation between the counterions: In order to avoid each other the counterions
to both surfaces tend to form one correlated layer in the gap between the planes (rather than one
at each surface).9 As a result, the average distance between counterions does not change much
when the distance between the planes changes, and therefore the coulomb energy due to
counterion-counterion interactions is nearly constant. This means that the variation of the energy
only depends on the plate – plate and plate – counterion interactions. The net effect is an
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electrostatic energy increasing linearly with increasing plate-plate distance,9 similar to a
capacitor. This is the origin of the electrostatic ion-ion correlation attraction between like charged
surfaces. The applicability range of the SC theory can be extended to lower electrostatic coupling
strengths by replacing the constant force with an exponential force law.7 Comparison with Monte
Carlo simulations shows that the decay length of the interaction (defined as 2Lc) is of order the
average distance between the counterions in the compressed monolayer.7, 9 For monovalent
counterions this means 2 Lc∝√a, where a is the area per surface charge. The interpretation placed
on this is that upon increasing the distance between the planes the attraction vanishes when the
monolayer of counterions separates into two layers (one at each surface), i.e. when the electric
double layers at each surface no longer overlap. Lc can thus be interpreted as an effective
thickness of the electric double layer at a single surface. In agreement with that, the energy (per
plate) in the modified SC theory approaches that of a capacitor with separation Lc in the limit of
infinite separation.7 More specifically, the model assumes that the energy between two planes at a
distance 2L is twice that that of a capacitor with separation d, where d is a function of L given by
eq. (S:4). The form of the function is mainly intuitive but comparison with MC simulations
shows that it works fairly well in a wide range of coupling strengths.7 Eqs. (S:3) – (S:4) are based
on the assumption that the capacitor analogy is transferrable to systems of charged spheres.6 The
energy (per sphere) is equal to that of a spherical capacitor (eq. S:3) with separation d as shown
in Figure S1, where d is a function (eq. S:4) of the thickness L of the aqueous layer surrounding
each sphere. In further analogy with the case of planes separated by monovalent counterions, Lc
is related to the area a+¿¿ per charge on the (positively charged) sphere, but since for spheres
√a+¿∝r√Z
¿, we use eq. (S:5) with h being a constant.
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The usefulness of the model is that it allows us to quantify both the correlation induced attraction
between like charged micelles in the concentrated regime and the energy of the electric double
layer surrounding single micelles in the dilute regime. The last aspect is the central one in the
present work. Upon dilution the dense complex phase disintegrates into single PDM:s or single
PDM:S and free polyelectrolytes depending on the polyion/surfactant ratio; see Figure S2. Eq.
(S:3) assumes that small ions are evenly distributed in the aqueous regions (i.e., no counterion
‘condensation’ at the polyion and the micelle), which is a reasonable approximation in the
concentrated regime. In the dilute regime counterion binding is treated on the Poisson-Boltzmann
(PB) level. The electrostatic free energy expression (S:3) is replaced by
Gel=G polel +Gmic
el ,ext+Gmicel ,∫¿¿ (S:6)
The first term in (S:6) is the electrostatic free energy of the free polyion chains and the second
term is the electrostatic free energy due to the net charge of PDM ( f ≠ 1). Both are evaluated by
means of the PB-equation as described in the paper. The last term is the “internal” electrostatic
(free) energy of the PDM:s which is the limiting form of eq. (S:3) as L goes to infinity:
Gmic
el ,∫¿=2 πNmicσ
2 r3
ε 0 εr( Lc
r+Lc)¿ (S:7)
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900
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903
904
905
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Figure S4. Schematic picture of a single PDM (left) and a polyion chain (right) surrounded by simple ions in the dilute regime. Dashed line has the same meaning as in Figure S1. In the PB-cell model the PDM and the polyion is described as a uniformly charged sphere and cylinder, respectively. In the dilute solutions considered in the present work the spheres and cylinders are treated as in contact with a common bulk electrolyte solution, meaning that the radii of the cells (solid red lines) are infinitely large.
For mixed micelles of a cationic and a nonionic surfactant
Nmic=N+ ¿mic+N0
mic
N ¿ (S:8)
σ=Nx+¿e
4 π r2 ¿ (S:9)
Lc=hr
√N x+¿¿ (S:10)
with N imic being the number of i molecules in the micellar sub-phase and h a model parameter
related to distribution of charges on the micelle. With eqs. (S:8) – (S:10), the definition of the
Bjerrum length and the equalities Z=N x+¿ ¿, and Nmic N=N +¿mic+N0mic ¿, (S:7) can be rewritten as:
Gmicel ,∫¿=kBT ¿¿ (S:11)
Surface free energy. The surface free energy of the micelles due to the contact between the
hydrocarbon core and water is:10
Gmicsurf=a¿ (S:12)
Chemical potential of surfactant in PDM. The electrostatic contribution to the chemical potential
of the two surfactants in the PDM is obtained in the usual way by taking the derivatives of eq.
(S:6) with respect to N+¿mic¿ and N 0mic, respectively. The contribution from Gmic
el , ext is the expressions
obtained within the PB-theory for ionic and non-ionic surfactants in mixed micelles of a given net
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charge.10 For S+ there is a contribution also from Gpolel since, for each micelle formed, f free
polyion charges are removed from the solution per charged surfactant. This is also evaluated
using the PB-theory for a cylindrical polyion.10 However, we include only the entropic part
associated with the release of the counterion bound to the free polyion. Thus, in eq. (8) and (9)
we put ∆ μp=− f μp−TS; see section 2.3.3. The argument comes from a previous study6 suggesting
that the energetic part is nearly equal to a standard free energy of a polyion charged group
positioned in the PDM double layer (an excess energy due to the interaction between neighboring
charges on the polyion). Since we have chosen not
1
2
3
4
5
6
7
0 20 40 60 80 100 120
(Gm
ic /
k BT) /
(Nm
icN
)
N
tot
surf
el
a
0
50
100
150
200
250
1 1.5 2 2.5 3 3.5 4
Nop
t
h
b
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937
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940
941
942
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Figure S5. (a) Total free energy (Gmicel ,∫¿+Gmic
surf ¿) per surfactant in PDM (tot) and individual contributions from the surface (surf) and electrostatic free energy (el) as a function of N calculated from theory with h=2.5; x+=1. (b) Optimal aggregation number (Nopt) as a function of h (x+=1).
to include the latter in Gmicel ,∫¿¿ it is most correct not to include the energetic part in G pol
el when
taking the derivative with respect to N imic. The contribution from Gmic
el ,∫¿¿ to the chemical potential
is given by eq. (7), and the contribution from Gmicsurf is just μi
surf=a γi.
Optimal aggregation number and determination of h. The optimal aggregation number is
obtained by minimizing the sum Gmicel ,∫¿+Gmic
surf ¿ with respect to N keeping N+¿mic¿ and N0mic fixed. The
result for pure micelles of a cationic ionic surfactant (x+¿=1¿) with 12 carbons in the hydrocarbon
chain (v = 351 Å3)9 in aqueous solution at 298 K (lB = 7.14 Å) is shown in Figure S3. For the
surface free energy we have used γ+¿¿=0.018 J/m2 a value often used in models of ionic
surfactants.10, 11 Fig. S3a shows the individual and total free energy contributions as a function of
N for h = 2.5, for which the optimal aggregation number is 62; Fig. S3b shows optimized N-
values as a function of h. Aggregation numbers for C12-tailed ionic surfactants in dilute solution
reported in the literature are typically around 60. For example, for dodecyltrimethylammonium
bromide values between 55 and 65 have been reported both for the pure surfactant12 and in
complexes with hydrophilic polyelectrolytes,3 motivating setting h = 2.5 in the model calculations
for the surfactant under study. As a check, insertion of this value in (S:5) gives Lc = 5.5 Å. Since
2Lc is of the order of the distance between the charged head groups at the micelle surface (
8 Å) and 5.5 Å is a reasonable value of the thickness of the polyion layer surrounding
a micelle (see, e.g., MC simulations on sphere + polyion13) the h-value used is consistent with the
conditions underlying the model. The maximum aggregation number for a C12 surfactant
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consistent with a spherical hydrocarbon core is 56. However, in practice the micelle radius is
allowed to exceed the length of a fully stretched tail by ca. 10%,10 and so the pure micelles (x+=1)
should still have an average spherical shape. For the mixed micelles the optimal value provided
by the model increases as the fraction of the non-ionic component increases, and exceeds that
conceivable for a sphere already for x+≈0.9, as shown in Figure S3. This is not unexpected
considering that the non-ionic component lowers the net repulsion between the head groups.
60
70
80
90
100
110
0.75 0.8 0.85 0.9 0.95 1 1.05
Nop
t
x+
Figure S6. Optimal aggregation number (Nopt) as a function of x+; h =2.5.
S3. Simple model of surfactant selective electrode response
In this section we derive an electrode response function based on a simple model of how the
charged and uncharged forms of MKM interact in the electrode membrane. The selectivity of the
electrode for cationic surfactants over inorganic ions indicates that the surfactant has the highest
permeability through the membrane. This can be explained in part by the hydrophobic tail of the
surfactant and in part by the presence of (fixed) anionic groups in the plastic membrane
(explaining why the performance of the present type of electrode is usually excellent for cationic
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but poor for anionic surfactants). The membrane is assumed to contain a concentration c−¿ ¿ of
negative charges fixed to the polymer matrix. S+ and Na+ dissolved in the membrane are restricted
to the regions immediately surrounding the negative charges, the latter functioning as sites always
associated with exactly one cation. S0 is allowed to reside at a site together with Na+ but not with
S+ due to steric hindrance. S0 at these sites are in equilibrium with those distributed elsewhere in
the membrane (and in the solution). Sites occupied by S+, Na+, and simultaneously by Na+ and S0
are denoted S+¿¿, Na+¿¿, and Na+¿S 0
¿, respectively. The correspondning concentrations of site are
denoted c+¿¿, c Na, and c Na0, respectively. For the ion exchange between cations in the solution and
the membrane we have:
S+¿+Na+¿⇆Na+¿+S+¿¿¿ ¿¿ (S:13)
K Na=K Na
'
K+¿=c+¿ cNa
cNa c+¿¿¿¿
(S:14)
where K Na is the equilibrium constant and K+¿=exp¿¿ and K Na' =exp {−(μNa
0 −μNa0 , w )/RT }. For the
binding of S0 to a site we have:
S0+Na+¿⇆Na+¿ S0
¿¿ (S:15)
K 0' =
cNa0
c Na c0 (S:16)
where the equilibrium constant K 0' =exp {−( μNa 0
0 −μNa0 −μ0
0 ,w ) /RT }. Provided that the equilibrium
distruibution of S+ between the membrane and the solution is given by the relationship
μ+¿0,w+RTln c+¿=μ+¿0+RTln
c+¿c−¿+F ∆∅ ¿¿ ¿
¿ ¿ (S:17)
51
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985
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987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
101102
where c−¿=c+¿+cNa+cNa0 ¿¿, the electrostatic potential difference between the membrane and the solution
∆∅ can be written
∆∅= RTF
lnK+¿+
RTF ln c
+¿ c−¿
c+¿=RTF
lnK+¿+ RT
F ln¿ ¿¿¿¿ ¿ (S:18)
After using (S:14) and (S:16) we arrive at an expression resembling eq. (13):
∆∅=const .+ RTF
ln¿ (S:19)
where K 0' '=K Na cNa K0
' . Double prime is used to signify that K0' ' is a conditional equilibrium
constant dependent on the salt concentration. The net result of the mechanism is that S0 helps Na+
in replacing S+ in the membrane, which can also be seen by adding together (S:13) and (S:15):
S+¿+Na+¿ +S0⇆ Na+¿S0
+S+¿¿¿ ¿¿. The salt dependence of K0' ' appears not to be in agreement with
experiments.
S4.1 Experimentally determined CMC and CAC values
52
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
103104
Figure S7. Examples of fluorescence spectra of pyrene in aqueous MKM solutions without (H2O) and with added NaCl (csalt = 0.05 M). Numbers 1-6 correspond to increasing MKM concentration from below (1-3) to above the CMC (4-6).
Table S2. CMC values in pure MKM and CAC values in mixed NaHA-MKM solutions
determined by the SSE based potentiometric titrations (CMC(SSE) and CAC(SSE)) and by
fluorescence measurements (CMC(FM)) at various salt (NaCl) concentrations, csalt.
csalt (mol/L) CMC(SSE) (mol/L) CMC(FM) (mol/L) CAC (SSE) (mol/L)
0 4.9 10-4 4.9 10-4 3.9 10-5
0.01 3.1 10-4 2.5 10-4 7.6 10-5
0.05 1.6 10-4 8.3 10-5 1.1 10-4
0.1 1.1 10-4 7.4 10-5 1.1 10-4
53
1021
102210231024
1025
1026
1027
1028
105106
0
5
10
CM
C (m
M)
MKM: SSE MKM: fluorescence SDS: Rosen CPC: Kogej
10-3 10-2 10-1
0.1
1
10
CM
C (m
M)
I (M)
Figure S8. The dependence of the critical micelle concentration, CMC, on the ionic strength, I (= csalt + CMC) in aqueous MKM solutions. For comparison, CMC data for SDS 14 and CPC15 are included. Above: linear axis for CMC and logarithmic axis for I. Below: a double logarithmic plot.
54
1029
1030
1031103210331034
107108
S5.
Figure S9. Left panel: SSE potentiometric titration curves for pure MKM (full squares) and for MKM in the presence of NaHA (cp = 5 10-4 mol/L; open circles) in aqueous NaCl solutions: the NaCl concentration (csalt) is indicated in the Figures. Right panel: Theoretical titration curves calculated as described in Section 3.2. The curves have been adjusted in the vertical direction by adding a constant to the calculated E to coincide with the experimental data at the lowest surfactant concentration. E*/mV: 236 (0.1 M), 248 (0.05 M), 257 (0.01 M), 283 (0.0005 M).
55
1035
1036
103710381039104010411042
109110
S6. Discussion about CMC values determined by NMR
The results from the theoretical calculations show that the fraction of surfactant in micelles
decreases with decreasing salt concentration and with that the extent to which C+ is affected by
the micellar equilibrium. To check the consequences of that for the possibility to determine the
CMC using the NMR self-diffusion method we used the data in Fig. 6 (at 0.1 M salt) and the
corresponding data for 0.0005 M salt case to calculate the expected observable self-diffusion
coefficients (Dobs). The result showed that an accurate estimate should be possible at the higher
salt concentration but not at the lower salt concentration where the variation of Dobs in the
vicinity of CMC is too small on an absolute scale. In the calculations we used the relationship
Dobs= p Dmic+(1− p)D1 11 where p, Dmic (= 1×10-10 m2/s) and D1 (= 4×10-10 m2/s) represent the
fraction of surfactant in micelles, and the self-diffusion coefficient for micelles and monomers,
respectively.
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