Makromol. Chem. 183,2273 -2283 (1982) 2213

Electrolytic Conductivity of Polyelectrolyte Solutions

Hans Vink

Institute of Physical Chemistry, University of Uppsala, P.O. Box 532, S-751 21 Uppsala, Sweden

(Date of receipt: December 14, 1981)

SUMMARY: The electrolytic conductivity of the polyelectrolytes poly(methacry1ic acid), carboxymethyl-

cellulose, poly(vinylsulfonates), and poly(styrenesu1fonates) was investigated. The concentra- tion dependence of the equivalent conductivity was studied in detail and the limiting equivalent conductivity Ao was determined. The rapid increase of the equivalent conductivity in dilute polyelectrolyte solutions, which is characteristic for most polyelectrolyte systems, was found to be due to decreased counterion binding in very dilute solutions. In this respect the behaviour of the poly(styrenesu1fonate)s was exceptional, as their equivalent conductivities were practically constant down to limiting concentrations. Also, the poly(styrenesu1fonic acid) clearly displayed specific hydrogen ion-polyion interactions.

Introduction

The phenomenological characterization as well as the theoretical interpretation of the electrolytic conductivity of polyelectrolyte solutions has been hampered by the lack of data concerning the conductivity behaviour in the limit of infinite dilution. In an earlier work l ) it was shown that conventional extrapolation of the equivalent conductivity to infinite dilution is in general not possible because of uncertainties about the solvent correction. The extrapolation is usually carried out with the help of the equation

where K and K~ are the electrolytic conductivities of solution and solvent, respectively, C is the equivalent concentration, A is the equivalent conductivity, and A o is the equivalent conductivity at infinite dilution.

The function @ (C) represents the effect of interionic interactions on the conductiv- ity. For polyelectrolytes this effect is much more pronounced than for simple salts, which makes it mandatory to extend the extrapolation to very dilute solutions. In such solutions, where K and x0 are of the same order of magnitude, any uncertainty in K~ renders A undefined and Eq. (1) becomes inapplicable for the determination of Ao.

A more appropriate procedure is to rewrite Eq. (1) in the form

and to determine Ao from the slope of the linear part of the K vs. C plot. In this case K; is obtained as the intercept at C = 0, and reflects the actual value of

solvent conductivity in very dilute solutions. For an accurate determination of A o by

0025-1 16X/82/09 2273-1 1/$03.00

2274 H. Vink

this procedure it is necessary that the curve representing K is linear over a sufficiently wide range of concentrations.

The limiting equivalent conductivity of the polyelectrolyte may be related to the limiting equivalent conductivities of the individual ions by the equation’ - J,

where fo < I is an interaction parameter (which includes ionic association effects) and the indices i and p refer to the counter-ion and polyion, respectively.

Eq. (3) may be extended to higher concentrations and is then written in the form

A complete determination of the parameters in Eqs. (3) and (4) requires the determination of transport numbers for the ions, which is experimentally extremely difficult in dilute polyelectrolyte solutions. However, there exists an alternative procedure, which may be used if two counter-ion species j and k can be found which interact identically with the polyion. Then

Akp - Ajp LO, - A? f =

and

n i p

P f A =--A!, f o r i = j , k

We have further1)

where F is the Faraday constant, Z, = (DS - DP) is the stoichiometric charge number of the polyion, and fdw is the stoichiometric friction coefficient of the polyion.

We have good reasons to believe that the alkali ions K+ and Na+ fulfill the require- ment of identical interactions with the polyion6*”. An a posteriori justification of this assumption may also be found in the consistency of the following results.

Experimental Part

Conductioity measurements : The conductivity measurements were carried out with a Leeds and Northrup conductivity bridge*), using acoustic detection. The conductivity cells were of immersion-type. For dilute solutions a cell with bright platinum electrodes, and a cell constant of 1,114 m-’ was used. The cell used for more concentrated solutions had black-platinized electrodes, and a cell constant of 170,6 m-’. The conductivity water was freshly distilled in a large commercial still from water demineralized by ion exchange. It was further purified by letting a stream of C02-free air pass through the water for 12 h. It had an electrolytic conductivity in the range (0,5 to 0,7). Sa-’ . m-’ . All measurements were carried out in a water thermostat at 25T, at a frequency of 1 kHz.

Electrolytic Conductivity of Polyelectrolyte Solutions 2275

Materials : The polyelectrolytes used were poly(styrenesu1fonate)s (XPSS, X = H, K, Na), poly(vinylsu1fonate)s (XPVS), polymethacrylate (XPMA) and carboxymethylcellulose (XCMC), the latter having different degrees of substitution (DS).

HPSS was prepared according to ref.') from narrow molecular weight polystyrene'(MW = 860000, from Pressure Chem. Comp., Pittsburgh).

NaPVS was prepared by polymerizing sodium vinylsulfonate (from Fluka, Buchs) in an approximately 60% solution by UV-light. The intrinsic viscosity of the product in 0,5 M NaCI- solution was 0,22 dl . g-', which according to ref.") corresponds to the molecular weight M, = 43000.

The HPMA sample was from Bofors, Nobelkrut. The original NaCMC sample (sample 13d in ref.")) was further carboxymethylated with

sodium chloroacetate and concentrated alkali, in a medium of 2-propanol. The reaction was carried out at room temperature, in nitrogen atmosphere to prevent degradation. Sample CMC2 was carboxymethylated once, sample CMC3 three times. A caracterization of all the polyelectrolyte samples used is given in Tab. 1.

Tab. 1. Data for the polyelectrolyte samples a)

Sample DP DS r PSS PVS CMCl CMC2 CMC3 PMA

8 300 1 330 1 750 0,94 750 1,43 750 2,14

1300 1

2,85 2,85 1,30 1,98 2,96 235

a) < = B/I where B = e2 / ( ekT) is the Bjerrum length and I is the average distance between charged groups on the fully extended polyelectrolyte molecules; DP = degree of polymeriza- tion; DS = degree of substitution.

The solutions used in the conductivity measurements were prepared by the following procedure. A fairly concentrated polyelectrolyte solution was dialyzed first against a dilute HCI solution and subsequently against distilled water, until all simple electrolytes were removed (which was checked by conductivity measurements). The concentration of the polyacid solution was then determined by titration with a standard NaOH solution. Stock solutions of sodium and potassium salts were prepared by neutralizing aliquots of the acid solution with equivalent amounts of NaOH and KOH solutions.

Results and Discussion

Measurements on the carboxylic polyelectrolytes

The alkali salts of PMA were found to be extensively hydrolyzed at all concentra- tions and conductivity measurements for PMA are, therefore, recorded only for HPMA.

For CMC some typical conductivity curves for very dilute solutions of KCMC are shown in Fig. 1, the curves being representative also for NaCMC. We find that for

2276 H. Vink

Fig. 1 . Dilute-solution con- ductivity curves for KCMCl (0) and KCMC3 (+) ( K , electrolytic conductivity of solution; C, equivalent concentration)

low charge densities the curves are linear over a wide concentration range, and thus allow an accurate determination of Ao to be made. With increasing change density the linear part of the curve shrinks and the determined AO-values become accordingly more uncertain. At high charge densities the curves exhibit a characteristic bilinear form, indicating a rather sharp change, or transition, in the conductivity behaviour of the polyelectrolyte. For all samples the extrapolated &values lie below K~ for pure conductivity water. The results of the measurements are listed in Tab. 2.

Complete phoreograrnsl2) for the KCMC samples are shown in Fig. 2. With in- creasing concentration the equivalent conductivity A decreases, the decrease being steeper the higher the charge density of the sample. From the smoothed data in the phoreograms the parameters f and A, were evaluated using Eqs. (5 ) and (6) , and are represented in diagram form in Fig. 3. It is interesting to note that the steep decrease of A at low concentrations is parallelled by a decrease of the parameter f. This indicates that counter-ion binding (condensation) is not independent of the polyelec- trolyte concentration, but decreases with decreasing concentration in the range of very low concentrations (C < 1 equiv. m-3). At higher concentrations the parameter f is nearly constant, although a small increase with concentration is observed for the samples having high charge densities.

For Ap a moderate decrease with increasing concentration is observed, which probably reflects the increasing frictional interaction between the polyions. In this respect the behaviour is similar to what is found in other transport processes, e. g. the sedimentation of uncharged macromolecules.

Measurements on the carboxylic polyacides

The dilute-solution conductivity curves for the carboxylic polyacids are shown in Fig. 4. They are linear over a wide concentration range and the solvent conductivity is practically unaffected by the polyelectrolyte. The determined limiting equivalent conductivities are listed in Tab. 2.

Complete phoreograms for the polyacids are shown in Fig. 5 . In contrast to the alkali salts, the equivalent conductivities of the polyacids decrease steadily with in-

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Fig. 3

Fig. 2. Phoreogram for KCMCI ( o ) , KCMC2 (o), and KCMC3 (+) (A: equivalent conductivity)

Fig. 3. Concentration dependence of the parametersfand Ap for CMCl (0), CMC2 ( o ) , and CMC3 ( + )

Fig. 4. Dilute-solution conductivity curves for HCMCI (o), HCMC2 (o), HCMC3 (+), and HPMA (A)

creasing concentration, reflecting the decreasing dissociation of the carboxy groups. The data clearly demonstrate the very low acid strenght of HPMA, its &value being only half of that for poly(acry1ic acid)').

Electrolytic Conductivity of Polyelectrolyte Solutions 2219

Fig. 5 . HCMC2 ( o ) , HCMC3 (+), and HPMA (A)

Phoreogram for HCMCl (o),

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(C/(equiv: m-3))1'2

Measurements on the polysu[fonates

The dilute-solution conductivity curves for KPVS and KPSS are shown in Fig. 6, and their complete phoreograms are displaced in Fig. 7. We find that PVS in its conductivity behaviour resembles CMC of high DS: the K vs. C plot is linear over a

"6 ' ' ' ' 0,05 ' ' ' ' ' 0,1 ' ' '

C/(equiv: m-3)

Fig. 6. Dilute-solution conductivity curve for KPVS (0) and KPSS (+)

narrow concentration range and in the phoreogram A decreases steeply with increasing concentration to a nearly constant value at high concentrations. For PSS a completely different behaviour is observed. Here, the K vs. C curve is linear over a wide concentration range and the determined AO-value is only marginally higher than

2280 H. Vink

the A-value at higher concentrations. It should be noted that for polysulfonates the solvent conductivity is practically unaffected by the polyelectrolyte.

The limiting conductivity parameters are listed in Tab. 3, and the concentration dependence of the parametersfand I, is represented in Fig. 8. They are seen to follow the expected trend from the phoreograms. The I,-values for PVS are exceptionally high, which may depend on the low molecular weight of the sample used.

70 t h

Fig. 7 Fig. 8

Fig. 7. Phoreogram for KPVS (0) and KPSS (+)

Fig. 8. Concentration dependence of the parametersfand A, for PVS (0) and P:S (+)

Measurements on the polysulfonic acids

The dilute-solution conductivity curves and the phoreograms for HPVS and HPSS are shown in Figs. 9 and 10, respectively, and the limiting conductivity parameter are listed in Tab. 3. From the phoreograms it follows that the two polyacids exhibits a similar behaviour at high concentrations, where the equivalent conductivity increases with concentration. However, in dilute solutions the two polyacids behave quite differently. For HPVS A increases on dilution, which resembles the behaviour of its alkali salts. The opposite is true for HPSS, for which A decreases on dilution. In scrutinizing the phoreogram, one can discern a tendency for A to increase even for HPSS, but a transition seems to occur near the concentration C = 1 equiv. m-’, and A decreases steeply to the limiting A’-value. The peculiar behaviour of the poly(su1fonic acid)s indicates the existence of specific interactions between hydrogen ions and the polyions, especially in HPSS.

Electrolytic Conductivity of Polyelectrolyte Solutions 2281

0,05 001 C/(equiv: rn-3) Fig. 9 Fig. 10

Fig. 9.

Fig. 10. Phoreograrn for HPVS (0) and HPSS (+)

Dilute-solution conductivity curves for HPVS (0) and HPSS (+)

Conclusions

The main results of the conductivity measurements may be summarized in the following conclusions.

The observed decrease of the solvent conductivity in carboxylic polyelectrolytes is due to partial hydrolysis of the carboxy groups, the effect being enhanced by the attraction of hydrogen ions into the counter-ion atmosphere around the polyion. The effect is absent in the carboxylic polyacid solutions and in the polysulfonate solu- tions, where no hydrolysis can take place.

The steep increase of the equivalent conductivity with decreasing concentration, which is characteristic for most polyelectrolyte systems, is mainly due to decreased counter-ion binding in very dilute solutions. Frictional effects seem to play a secondary role in this connection. This view is supported by the strong dependence of the effect on charge density. Thus, the general assumption, that counter-ion binding is concentration independent, seems not to hold in very dilute solutions (the effect is difficult to observe in equilibrium experiments, which in general are far less sensitive than conductivity).

The experiments with PSS demonstrate that local environmental effects, such as variations in the local dielectric constant, hydrophobic interactions etc. may play a prominent part in the behaviour of some polyelectrolytes.

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Electrolytic Conductivity of Polyelectrolyte Solutions 2283

Finally, it should be noted that the numerical values of the parameters f and Ap critically depend on the assumption that the K+ and Na+ ions interact identically with the polyions. The determined f-values are too low if the K+ ions interact more strongly with the polyion than the Na+ ions, and vice versa. Since preferential inter- action would strongly depend on the DS and the concentration of the polyelectrolyte, the consistency of the data for CMC seems to indicate the absence of such effects in this system. However, the conclusions concerning the variation of ion binding with concentration would still hold if such effects existed.

’) H. Vink, J. Chem. SOC., Faraday Trans. 1 , 77, 2439 (1981) *) J. R. Huizenga, P. G. Greiger, F. T. Wall, J. Am. Chem. Soc. 72, 2636 (1950) 3, G. S. Manning, J. Chem. Phys. 51, 924 and 934 (1969) 4, G. S. Manning, Biopolymers 9, 1534 (1970)

6, H. Eisenberg, J. Polym. Sci. 30, 47 (1958) ’) W. J . H. M. Moiler, G. A. J. van Os, J. Th. U. G. Overbeek, Trans. Faraday SOC. 57, 325

A. Schmitt, R. Varoqui, J. Chem. SOC., Faraday Trans. 2, 69, 1087 (1973)

(1961) P. H. Dike, Rev. Sci. Instrum. 2, 379 (1931)

’) H. Vink, Makromol. Chem. 182, 279 (1981) lo) K. Dialer, R. Kerber, Makromol. Chem. 17, 56 (1955)

’’) R. M. Fuoss, J. Chem. Educ. 32, 527 (1955) W. Brown, D. Henley, J. Ohman, Makromol. Chem. 62, 164 (1963)