Viscosity of polyelectrolyte solutions

Die Makromolekulare Chemie 131 (1970) 133-145 (Nr . 3113)

From the Institute of Physical Chemistry, University of Uppsala, Uppsala, Sweden

Viscosity of Polyelectrolyte Solutions

By HANS VINK

(Eingegangen am 28. April 1969)

SUMMARY:

The viscosity behaviour of polyelectrolytes in solutions of low ionic strength has been investigated. The dependence of the viscosity on the degree of substitution, the molecular weight and the velocity gradient was studied in detail. The measurements were carried out in solutions of different ionic strength and the limiting intrinsic viscosity a t zero ionic strength was determined by extrapolation. It was found that at zero ionic strength the exponent in the KUHN-MARK-HOUWINK equation has the value a = 1.1. It was further found that the intrinsic viscosities in the low and medium molecular weight region were considerably higher than those expected for rigid rodlike molecules of comparable size. The exceptionally high values of the intrinsic viscosity in solutions of low ionic strength indicate the presence of a pronounced “electroviscous effect” in these solutions.

ZUSAMMENFASSUNG: Das Viskositatsverhalten von Polyelektrolyten in Losungen kleiner Ionenstarken wurde

untersucht. Die Abhangigkeit der Viskositat von Substitutionsgrad, Molekulargewicht und Geschwindigkeitsgradienten wurde eingehend untersucht. Die Messungen wurden in Lo- sungen verschiedener Ionenstarken durchgefiihrt und der STAUDINGER-Index in Losungen mit der Ionenstarke Null durch Extrapolation ermittelt. Man fand, daB fur die extra- polierten Werte des STAUDINGER-Index der Exponent in der KuHN-MARK-HouwINK-Glei- chung gleich 1,1 ist. Es wurde weiter festgestellt, daB der STAUDJNGER-Index im Bereich kleiner und mittlerer Molekulargewichte vie1 grol3er ist, als man es fur gleichgrofle stab- chenformige Molekiile erwarten wiirde. Diese sehr hohen Werte des STAUDINGER-Index in Losungen kleiner Ionenstarken weisen auf das Vorhandensein eines ,,elektroviskosen“ Effektes hin.

The viscosity behaviour of flexible polyelectrolytes in solutions of low ionic strength is dominated by the electrostatic interactions of the charged groups on the polyelectrolyte molecules. For polyelectrolytes with charged groups of equal sign the forces are repulsive, which gives rise to an expansion of the polymer chain. This effect, commonly known as the “polyelectrolyte effect” is in general characterized by a rapid increase of the reduced viscosity with decreasing polyelectrolyte concentration. In the present work this effect has been studied as a function of the degree of substitution with respect to ionizing groups and the molecular weight of

133

H. VINK

the polyelectrolyte. The polyelectrolytes used in these investigations were sodium salts of carboxymethyl cellulose (CMC) and carboxymethylated cellulose ethers of widely differing degrees of substitution.

Experimental Materials

The carboxymethylated cellulose ethers were prepared by carboxymethylating hydroxy- ethyl cellulose. A more detailed description of the procedure has been presented in an earlier articlel). To obtain samples of different molecular weight, portions of one of the sample (H4) were degraded in 0.15 M hydrochloric acid a t 6OoC for different periods of time. The samples were recovered by neutralizing the solutions with a sodium hydroxide solution to the phenolphthalein end point and precipitating the polymer with acetone. Remaining traces of sodium chloride were removed by repeated extraction with 95% ethanol.

For comparison purposes two samples of CMC were also used in the experiments. One of them (Cl) had a very high rnol. wt. (sample 13a in ref.2)). The other (Cz) was obtained from the former by degradation, which was carried out in a similar fashion as in the case of samples H4a-H4C. For the estimation of the mol. wt. of the degraded sample the following KUHN-MARK-HOUWINK equation, determined for CMC in 0.2 M NaCl-solutions3), was used

[q] = 4 . 3 . 1 0 ~ 4 . M : ~ ~ (1)

In the case of samples H4a-H4c a similar equation, calibrated with sample H4, was used

[q] = 3.63.10-4.MY4

The data of the different samples are listed in Table 1.

Sample

Table 1. Data of the polyelectrolyte samples

DS (carboxyl)

0.051 0.183 0.57 1.15 1.15 1.15 1.15 0.96 0.96

m

240.1 250.6 281.6 328.0 328.0 328.0 328.0 238.8 238.8

P

1900 1900 1900 1900 674 272 172

4420 341

M . l o 4

456 476 535 623 221 89.1 56.3

81.4 1056

[q10 dllg (in 0.5 M NaCI)

8.72 8.56 7.40 7.04 3.28 1.67 1.19

1.85 13.1

Throughout the experiments double-distd. water of very high purity (with the specific conductance lower than 1.10-6 R-1 cm-1) was used for the preparation of solutions.

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Viscosity determination

Most of the preliminary measurements were carried out with a modified OSTWALD visco- meter4), which yielded a shearing stress of 12.5 dyne cm-2 at the capillary wall for water a t 25'C.

To determine the gradient dependence of the viscosity a capillary viscometer was used, which was similar to those described by CHANG and MORAWETZ~) and by CLAESSON and LOHMANDER~), although a modified procedure was employed for performing the measurements and evaluating the data. Thus, the viscometer consisted of a pair of wide measuring tubes connected by a long capillary and had the form shown in Fig. 1. The measuring

Fig. 1. Schematic drawing of the viscometer for measurement at different velocity gradients

tubes were of precision bore and had a diameter of 8 mm. The capillary had a diameter of 0.56 mm and a length of 59.3 cm. The positions of the liquid menisci in the measuring tubes were determined with the help of a cathetometer, which had a reading accuracy of 0.01 mm. Viewed against a bright background of diffuse light the meniscus appeared as a dark band with a sharp boundary, which could be accurately located with the cathetometer. As a rule readings were taken for only one limb of the viscometer, and from the position of the meniscus at different times and from its equilibrium position the corresponding height differences between the menisci in the two limbs of the viscometer were calculated.

Denoting the height difference by h, we have

k - h - dh

d t 3 (3)

where k is a constant, characteristic of the viscometer, and 3 is the viscosity of the solution.

135

H. VINK

Eq. (3) may also be written

k - d log h -_ - - dt 2.303 -q (4)

Approximating the derivative in Eq. (4) by the corresponding quotient of differences, we get for the average viscosity in the interval Ah

k A t ? = - - - 2.303 Alogh

The corresponding mean shearing stress at the wall of the capillary has the value

(5’

where E is the mean height difference (h = h + l/zAh), p the density of the solution, g the acceleration due to gravity and L and R are the length and the radius of the capillary, respectively.

This method of determining the gradient dependence of viscosity is very simple and thus well suited for routine measurements. It has about the same accuracy as attainable by a multibulb UBBELOHDE viscometer (SCHURZ and IMMERGUT7)), but with the present instrument a much wider range of shearing stress can be covered. In the present experiments the height difference varied between 1-30 cm, corresponding to a shearing stress between 0.23-6.93 dyne cm-2. The instrument has the further advantage of being insensi- tive to surface tension variations in the solutions.

Results and Discussion Degradation

I n solutions of very low ionic strength a slow degradation of the polyelectrolyte was observed. This gave rise to some complications in the viscosity determinations, especially in solutions with pure water as solvent. It made necessary the extrapolation of the viscosity data to zero time and called for a rapid performance of the measurements. I n general the degradation rate increased with decreasing concentration of the polyelectrolyte. It was also markedly dependent on the degree of substitution with respect t o the ionizing groups, the degradation rate decreasing with decreasing degree of substitution. Thus, for sample Hq the decrease of the specific viscosity amounted to a few per cent per hour in very dilute solutions, whereas for sample HI it was barely detectable.

The probable reason for the degradation is the tendency of the charged polyelectrolyte molecules to attract protons into the region occupied by the molecule. All protons are obviously not attached to the carboxyl

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groups, but can move around and attack the glycoside bonds of the cellulosic chains. Evidence for this interpretation of the degradation is found in the fact tha t the addition of minute amounts of alkali t o the solutions inhibits the degradation reaction. Thus, in solutions which were made 10-5 M with respect to sodium hydroxide the degradation was barely detectable.

Concentration dependence of the reduced viscosity

It has long been a wellknown fact that the reduced viscosity of polyelectrolytes in solutions of very low ionic strength increases on dilution. The general pattern of concentration dependence was first established by KERNS), whose results have latcr been confirmed in numerous investigations. The concentration dependence may be represented by the following empirical relation of FUOSS~)

where a and b are constants. Eq. ( 7 ) yields a straight line when c/-qsp is plotted against 1;: Eq. (7) is sometimes modified by adding a constant term to the right member of the equationlo), which then covers a wider range of concentrations.

It can be anticipated that Eq. (7) is not valid down to zero concentration. The polyelectrolyte molecules will probably reach their final state of expansion in a finite concentration range and the reduced viscosity will then decrease according to HUGGINS' equation. The reduced viscosity must therefore decrease with concentration a t sufficiently low concentrations. Experimental evidence for the existence of the downward bend in the -qsp/c us. c curve was first found in solutions of DNA11712) and the existence of the effect has later been demonstrated also for flexible poly- electrolytesl3-15).

In the present investigations the downward bend in the -qSp/c us. c curve for solutions in pure water was clearly displayed by all polyelectrolyte samples, except those having very low molecular weights or very low degrees of substitution. At higher concentrations the experimental data conformed rather well with Eq. (7) over wide ranges of concentration. This is shown in Fig. 2, where c/-qsp is plotted against 1.. The decrease of the reduced viscosity a t low concentrations is in this plot manifested by an upturn of the curves.

137

H. VINK

It should be noted that the slopes of the lines are strongly dependent on the molecular weight of the polyelectrolyte, the slope decreasing with increasing molecular weight. This behaviour may be qualitatively under-

0.05

0.04

0.03

0.02

0.01

C I 01 0.2 0.3 0.1 0.2 0.3

vr VT Fig. 2a Fig. 2b

Fig. 2 a. Viscosity data for solutions in pure water (T = 12.5 dyne cm-2) plotted according to Eq. (7). 0 for C1, o for H3, + for Ha, 0 for Hz, and A for Hi

Fig. 2 b. 0 for Haar o for H4b, and + for HqC

stood when it is realized that in the concentration dependence two counter- acting effects are superimposed, namely the electrostatic interaction and the ordinary concentration dependence, represented by HUGGINS' formula

The former effect is probably only slightly dependent on the molecular weight of the polyelectrolyte, whereas the factor k~[# in Eq. (8) increases rapidly with molecular weight. Thus, the ordinary concentration dependence, represented by HUGGINS' formula, becomes increasingly more im- portant as the molecular weight increases, and finally dominates over the electrostatic expansion.

It is also of great interest to consider the influence of the degree of substitution with respect to the ionizing groups on the viscosity behav-

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iour of the polyelectrolyte. This can be seen in Fig. 2 and we find tha t all samples exhibit a typical polyelectrolyte behaviour, although the effect is less pronounced for the samples of low degrees of substitution. With increasing degrees of substitution the curve converge rapidly to a com- mon limit and for samples Hs and Hq, having the degrees of substitution 0.57 and 1.15, respectively, the resultant curves are practically identical. It should also be noted that the slopes of the lines increase with decreasing degree of substitution.

Gradient dependence of viscosity

For a complete characterization of the viscosity behaviour of polymers, the gradient dependence of the viscosity must be investigated and the intrinsic viscosity a t zero velocity gradient has to be determined. I n the present investigation a complicating factor was the degradation of the polymer, which was especially troublesome in connection with the determination of the gradient dependence, since the measurements involved were comparatively time-consuming. Accurate measurements which solutions in pure water were therefore hardly possible. However, since the degradation could be eliminated by adding minute amounts of sodium hydroxide to the solutions, the measurements were carried out in sodium hydroxide solutions of varying ionic strength and the intrinsic viscosity a t zero ionic strength was determined by extrapolation. Apart from eliminating the degradation this procedure has the further advantage tha t i t allows a more secure extrapolation of the reduced viscosity to zero concentration to be made. I n pure water the downward bend in the qsp/c us. c curve occurs in general a t too low a concentration and the form of the curve is too uncertain to permit the performance of a satisfactory extrapolation. I n solutions of higher ionic strength the extrapolation follows are more normal course and a satisfactory determination of the intrinsic viscosity is in general possible.

It was found tha t the gradient dependence of viscosity followed the general pattern found in earlier investigations on cellulosic polymers6916). Thus, using the shearing stress as independent variable, the dependence of the specific viscosity on the shearing stress could be expressed by the formula

1

Y)SP - Y -- - a + p r (9)

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Sample

Hi

H2

H3

H4

H4a

H4b

H4c

c1

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H. VINK

Table 2. Viscosity data a t different ionic strength

I

2.5.10-5 10-4

2.10-4

10-5 2.5.10-5

10-4 2.10-4

10-5 2.5.10-5

10-4

10-5

0.5

0.5

0.5

2.5.10-5 5.10-5

10-4 2.10-4

2.5.10-5 10-4

2.10-4

0.5

5.10-4 0.5

10-4

5.10-4 8.10-4

10-4 2.10-4

3.10-4

0.5

3.10-4 6.10-4

0.5

10-5

10-4 2.10-4 5.10-4

3.10-5 5.10-5

0.5

41 21 14.3

8.72

210 170

80 52

8.56

320 250 132

7.40

310 255 190 136

91 7.04

87 50.5 32.0 20.4

3.28

18.7 10.4 8.2 6.8 L67

13.0 9.3 7.5 5.5 1.19

780 665 486 305 223 134

13.1

B cmZ/dyne

0.10 0.03 0.02 -

0.33 0.24 0.10 0.05 -

0.40 0.34 0.20 -

0.37 0.31 0.27 0.18 0.09 0.005

0.05 0.05 0.03 0.01 -

0 0 0 0 0

0 0 0 0 0

0.90 0.80 0.72 0.42 0.31 0.14 0.015

2.43 1.43 1.40 -

1.57 1.41 1.25 0.96 -

1.25 1.36 1.52 -

1.19 1.22 1.42 1.32 0.99 0.71

0.57 0.99 0.94 0.49 -

0 0 0 0 0

0 0 0 0 0

1.15 1.20 1.48 1.38 1.39 1.04 1.15


B cmz/dyne

0 0 0 0 0

Table 2. Continued

B/[-q]'J .lo3

0 0 0 0 0

Sample

c2 10-4 3.10-4 5.10-4 8.10-4

0.5

20.7 11.6

9.1 7.4 1.85

where 'x, p, and y are constan 5 . With thc help of this formula a linear extrapolation of the viscosity data to zero shearing stress could be ef- fected. The parameter y, the limiting specific viscosity a t infinite shearing stress, was usually rather small, and its value could be estimated by trial, choosing the best straight line.

In the region of very low shearing stress Eq. (9) can be approximated by the following linear formula

where rip is the specific viscosity a t zero shearing stress and the constant B is related to the parameters in Eq. (9) by the following equation

It can therefore be determined directly from the data obtained from a linear plot according to Eq. (9). Within experimental error B was found to be independent of the concentration of the solution and therefore it provides a convenient measure of the gradient dependence of viscosity. The intrinsic viscosities a t zero shearing stress [ q ] O and the corresponding values of the parameter B are listed in Table 2.

Considering the gradient dependence of the specific viscosity we find that i t varies considerably with the molecular weight of the sample and the ionic strength of the solutions. At low ionic strength and high molecular weight the gradient dependence is extremely high. An interesting feature is that for different solutions the parameter B is roughly pro- portional to the intrinsic viscosity [q]O, which may be seen by examining the B/[q]O-values in Table2. This is in accordance with the empirical relation of STRAUSS and Fuoss17)

14 1

H. VINK

Dependence of the intrinsic viscosity on ionic strength

The dependence of the intrinsic viscosity on ionic strength seems not t o follow a simple relation over the entire range of ionic strength investigated. In solutions of very low ionic strength i t may be represented by a relation similar t o Eq. (9), namely

where MI, PI, and yl are constants and I is the ionic strength. This formula differs from the one proposed by PALS and HER MANS^^)

which, however, was established in a region of much higher ionic strength.

Fig. 3a Fig. 3b

Fig. 3a. Extrapolation of the intrinsic viscosity to zero ionic strength according to Eq. (13). 0 for C1 and o for H4

Fig. 3 b. 0 for H4&, o for H4b, and + for Hlc

The experimental data, plotted according to Eq. (13) are shown in Fig. 3, and in Table 3 the values of the intrinsic viscosity extrapolated to zero ionic strength [?I& and the parameter yl are listed. The values of the latter were determined by trial, choosing the best straight line. They are seen to be larger than the corresponding intrinsic viscosities in 0.5 M NaCl solutions, which demonstrates the limitation of Eq. (13).

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Sample HI Hz H3 H4 H4a H4b H4c ci C2

We are now in the position to discuss the viscosity behaviour of polyelectrolytes a t very low ionic strength in the light of pertinent hydro- dynamic theories. First we determine the exponent in the KUHN-MARK- HOUWINK equation. We may do this by comparing directly the viscosity data a t zero ionic strength with those in 0.5 M sodium chloride solutions. For the two cases we have, respectively,

and

If we plot log [q]: us. log we should get a straight line with the slope

The plot is shown in Fig. 4 and i t yields the slope al/az = 1.5. From earlier investigations we know3) that for CMC in 0.2 M NaCl solutions a = 0.74, and this may be taken as a reasonable approximation for ag. Thus

a1 = 1.1 (18)

This result is of great importance as it shows tha t the molecular weight dependence of the intrinsic viscosity a t zero ionic strength does not follow the relation expected for rigid rodlike molecules, in which case the exponent has a value close to 2. This would indicate tha t the polyelectrolyte molecule a t zero ionic strength is far from its fully extended state, or else that the data are affected by some other, hitherto unknown, effect. To get more insight into the nature of such an effect we compare the magnitudes of the experimental intrinsic viscosities with those calculated for rigid rodlike molecules of comparable size. We use the formula of KIRKWOOD and A u E R ~ ~ )

TC Nb3 P2

2250 m In P - -

x Nb 12

= 2250 m In l /b (19)

143

H. VINK

where N is the AVOGADRO’s number, b the length of the monomer unit (here b = 5.15 .lo-* cm), m the molecular weight of the unit, 1 the total length of the polymer molecule and P the degree of polymerization. I n applying Eq. (19) we have to take into account the polydispersity of the samples used. Since the samples were obtained by random degradation of higher molecular weight samples, they may be considered to have random molecular weight distributions (this in only approximately true for the highest molecular weight sample). For such a distribution the ratio between viscosity and weight average molecular weights is

M,:M, = [(l + a)I’(l + a)]l/”:2 (20)

I n Eq. (19) we have very nearly a = 2 and hence

My:Mw = 1.225

As the degrees of polymerization in Table 1 are close to the weight average values, they have to be multiplied by the factor 1.225 before using them in Eq. (19). The data are shown in Fig. 4 and we find that the theoretical and experimental curves intersect each other in the high molecular weight region. Even when accepting large systematic errors in the experimental and computed data we may consider i t as established tha t in the low molecular weight region the intrinsic viscosity of the poly-

Fig. 4. Double-logarithmic plot of [q]: vs. [q]:,;. Experi- mental data are represented by circles and computed data by triangles. Filled and unfilled circles and triangles repre- sent samples C1 and C2 and samples H ~ - H Q ~ , respectively

1 0 0 0.5

log Id& electrolyte is much higher than the intrinsic viscosity of neutral rodlike molecules of equal size. Consequently, this discrepancy has to be attri- buted t o an “electroviscous effect”, brought about by interactions between the electric charges in the system. One conceivable mechanism would imply a coupling between the polyions and the counterions, the latter being forced to take part in the motion of the polyions, thus giving rise to an extra dissipation of energy.

144


It is also of interest to consider the gradient dependence of the electroviscous effect. It was found that the viscosities of the solutions of the lowest molecular weight samples (H4b, Hlc and C2) did not show any detectable gradient dependence. On the other hand the viscosities of solutions of neutral polymers, having intrinsic viscosities of comparable size, would exhibit a pronounced gradient dependence. We may therefore conclude that the electroviscous effect is essentially independent of the velocity gradient.

It should be mentioned that the existence of an electroviscous effect of a similar kind was predicted already in 1916 by VoN SMOLUCHOWSKY~~) , who considered the viscosity behaviour of solutions of charged spherical particles and presented a formula relating the specific viscosity to the electrokinetic potential. A number of improvements of the VON SMOLU- CHOWSKY formula have been made in more recent years21>22). However, the assumptions under which these formulae have been derived do not permit their application to the present experimental data. It is further doubtful if the concepts of the electrical double layer and the electrokinetic potential are relevant in the description of threadlike polyelectrolyte molecules.

1) H. VINK, Makromolekulare Chem. 122 (1969) 271. 2) W. BROWN, D. HENLEY, and J. OHMAN, Makromolekulare Chem. 62 (1963) 164. 3) W. BROWN and D. HENLEY, Makromolekulare Chem. 79 (1964) 68. 4) H. VINK, Makromolekulare Chem. 67 (1963) 105. 5 ) L. S. CHANG and H. MORAWETZ, J. Polymer Sci. 13 (1954) 414. 6) S. CLAESSON and U. LOHIUNDER, Makromolekulare Chem. 44-44i (1961) 461. 7) J. SCHURZ and E. H. IMMERGUT, J. Polymer Sci. 9 (1952) 279. 8 ) W. KERN, Z. physik. Chem. A 181 (1938) 283. 9 ) R. M. Fuoss, Discuss. Faraday SOC. 11 (1951) 125. 10) R. M. Fuoss, J. Polymer Sci. 3 (1948) 603. 11) J. POUYET, C. R. hebd. SBances Acad. Sci. 234 (1952) 152. 12) B. E. CONWAY and J. A. V. BUTLER, J. Polymer Sci. 12 (1954) 199. 13) H. EISENBERG and J. POUYET, J. Polymer Sci. 13 (1954) 85. 14) J. A. V. BUTLER and B. E. CONWAY, Nature [London] 172 (1953) 153. 15) B. E. CONWAY, J. Polymer Sci. 18 (1955) 257. 16) U. LOHMANDER and R. STROMBERG, Makromolekulare Chem. 72 (1964) 143. 17) U. P. STRAUSS and R. M. FUOSS, J. Polymer Sci. 8 (1952) 593. 18) D. T. F. PALS and J. J. HERMANS, Recueil Trav. chim. Pays-Bas 71 (1952) 433. 19) J. G. KIRKWOOD and P. L. AUER, J. chem. Physics 19 (1951) 281. 20) M. VON SMOLUCHOWSKY, Kolloid-Z. 18 (1916) 190. 21) W. KRASNY-ERGEN, Kolloid-2. 74 (1936) 172. 22) F. BOOTH, Proc. Roy. SOC. [London], Ser. A 203 (1950) 533.

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Viscosity of polyelectrolyte solutions