Aqueous solutions of salts of poly(vinylsulfonic acid)

JOURNAL OF POLYMER SCIENCE VOL. NLVII, PAGES 3-11 (1960)

Aqueous Solutions of Salts of Poly(vinylsu1fonic Acid) *

HESItYIi EISEXBEILGt and EDWAIZII F. CASASSA4, Mellon Institute, Pittsburgh, Pennsylvania

INTRODUCTION

A recent investigation1 showed that aqueous solutions of polyvinylsul- fonic acid (PVSA) and its salts with various univalent ions separate into two liquid phases a t high concentrations of added uni-univalent electrolytes. The phenomenon was found to be highly specific with respect to the mono- valent electrolytes investigated. Specific effects with alkali metal cations were shown to exist as well in dilute solutions of the polymer.

The present study is concerned with two matters: first, some further experiments with respect to phase separation; and second, some properties of dilute solutions of salts of PVSA and 1-1 electrolytes, in particular of the potassium salt (KPVS) in aqueous KCI and of the ammonium salt (?iH4- PVS) in aqueous SH4CI. Phase separation occurs under suitable conditions in the case of KPVS in KCI, but is never observed in the case of SH4PVS in ?iH4C1. It thus appears that aqueous KCI, a t suitable concentrations of KCI, constitutes a “poor” solvent for KPVS, whereas aqueous ?iH4Cl is a “good” solvent for XH4PVS. We have, therefore, under- taken light-scattering, viscosity, sedimentation, and membrane-distribution studies in order to compare thermodynamic behavior and configura- tional properties of the polymer chains in these two systems for I’VSA salts prepared from the same polymer fraction.

EXPERIMENTAL

Materials and Solutions

A sample of KaI’VS ( v sp = 0.954 in 1% aqueous solution) was fractionated in a 2% solution in 1.GM SaC1. The polymer was divided into three fractions by stepwise cooling below the cloud point (21.5”C.), first to 18 and then to 3‘C., the precipitated liquid phase being removed a t each temperature. The middle fraction obtained in this procedure was used in

* This study was supported in part by a grant (XSF-G7608) of the National Science Foundation. Some aspwts of the work were presented at the 137th national meeting of the American Chemiral Society, Cleveland, Ohio, April, 196G.

t Present address: The Weizmann Institute of Scicmce, Rehovot, Israel.

29

30 11. EISENBERG AND E. F. CASASSA

most experiments reported here. Solutions of salts of PVSA in various supporting electrolytes were obtained by dialysis against the respective electrolyte solutions. Visking seamless tubing was used for dialysis bags; the tubing was heated in air for 5 hr. a t 90°C. to reduce the pore size and thoroughly mashed in distilled water prior to use.

Methods Concentrations of polymer and supporting elec-

trolyte in solutions consisting of PVSA salts (Li, Na, K, Rb, Cs, NH4) with a 1-1 electrolyte having the cation in common with the polymer (the anions being F, C1, Br, I, and NO3) were determined by the following procedure.

Columns of a cationic sulfonic acid resin (Rohm & Haas Amberlite IR-120, analytical grade, hydrogen form) were treated with 10% HCl solution until no metallic cations could be detected in the effluent. This was assayed by evaporating an aliquot to dryness and testing for chloride, absence of which indicated complete regeneration of the resin. The regen- erated resin was then exhaustively washed with conductivity water, until the conductivity of the effluent approached that of the rinsing water (specific resistivity > lo6 ohm cm.) and stayed constant after contact with the column for periods of a few hours. The conductivity was measured by small electrodes sealed into the delivery tip of the ion exchange column. The regeneration procedure was repeated after each analysis.

For the analysis, 1 ml. samples (measured to *0.0005 ml. by a precision Pregl washout-type pipet) of polymer solution, containing between 0.03 to 0.25 equiv./l. of sulfonic acid groups and 0.05 to 0.5M supporting electrolyte, were passed through the ion exchange column (about 8 cm. in length containing 5 ml. wet resin, total exchange-capacity about 10 mequiv.) into 25 ml. volumetric flasks, and washed through with water until the effluent conductivity again fell to that of the conductivity water used. The exchanged samples were then made up to 25 ml. That there was no leakage of metallic cations through the column was ascertained by testing with a flame photometer. Aliquots (4 ml.) of the exchanged solutions were ti- trated potentiometrically against M/10 NaOH with a precision microm- eter syringe buret. The same 4 ml. pipet was used both for standardizing the NaOH solution and for dispensing the solutions for the titration. Thus total acidity, corresponding to total concentration of metallic cations in the solutions before exchange, was determined. Aliquots (again 4 ml.) of the exchanged solutions were transferred into polyethylene beakers and evaporated twice to dryness in vacuo a t room temperature in a desiccator over solid KOH. Thus all volatile acids (including HN03) were quan- titatively absorbed, and titration of the residue gave the equivalents of sulfonic acid groups in the solution. The evaporated solutions were tested to confirm absence of chloride after the titration with NaOH. Finally, the original concentration of supporting electrolyte was calculated by difference. By this procedure analyses accurate to 0.1% were obtained; and

Analytical Methods.

SAI,TS OF POLY(V1NYL SULFONIC ACID) 31

the direct determination of halogen ions, which is subject to inaccuracies in the presence of charged colloidal ions, was avoided.

It cannot be overemphasized that for membrane equilibrium studies, interpretation of which involves the exact knowledge of very small differences of concentrations of diffusible solutes across the membrane, one requires the highest accuracy obtainable in the analytical determination of the various ions.

Membrane Distribution. Membrane-distribution measurements were performed by equilibrating aliquots of the original NaPVS stock solution, against various supporting electrolyte solutions a t 23°C. The samples were shaken continuously for 4 days in sealed bags containing two or three glass beads, and the equilibrating electrolyte was changed a t 12-hr. inter- vals. Attainment of equilibrium was followed in a few selected cases by determining concentrations as a function of time; in no case could a signifi- cant change in salt concentration be detected in the polymer solution after two to three days of dialysis. In addition to the fractionated sample described above some other polymers covering a range of molecular weights were used in distribution measurements.

Density. Determinations of solution density were made in 4 ml. pyc- nometers a t 25°C. The polymer solutions contained about 0.1 equiv./l. of sulfonic acid groups and had been equilibrated by dialysis against supporting electrolyte in every case.

Viscosity. Viscosities of polymer solutions equilibrated by dialysis against and diluted with the supporting electrolyte solutions were measured a t 25°C. in Cannon-Ubbelohde semimicro dilution viscometers, size 50, requiring an initial sample of 1 ml. Efflux times for the solvents were about 250 sec., and kinetic energy corrections were negligible. It was ascertained that the solutions exhibited Newtonian behavior by comparison of viscosities measured in these viscometers and in a low-shear U-type instru- ment.

Refractive Index Increments. Refractive index increments were determined a t 25°C. a t a wavelength of 5461 A. in a Brice-Phoenix differential refractometer on solutions containing about 01. equiv./l. of polymer.

Light-scattering measurements were made in a Brice- Phoenix photometer a t 25°C. and 5461 A. The intensity scattered a t right angles sufficed for all calculations as the molecular weight of the polymer was low enough for angular dissymmetry of scattering to be negligible.

Velocity sedimentation was carried out in a Spinco model E ultracentrifuge a t 25°C. a t 60,000 rpm. The Schlieren optical system with the phase-plate modification was used.

Light Scattering.

Sedimentation.

THERMODYNAMIC TREATMENT OF MULTICOMPONENT SYSTEMS

Before discussing t,he experimental data, we shall find i t advantageous to consider the question of the definition of components in the thermody-

32 11. EISENBElZG AND E. F. CASASSA

namic treatment of multicompoiient systems. We have already treated this matter elsewhere;2 here we are concerned with applying the earlier rather general proposal to a specific case so as to establish a coherent set of experimental procedures and a consistent interpretation of light scattering and sedimentation measurements.

The solutions investigated are three-component systems containing water, nondiffusible polymer X,P (where 1’ is the polyanion of valence -2, and X is a univalent counterion) and diffusible uni-univalent supporting electrolyte XY. The number of charges 2 per macromolecule equals the degree of polymerization, and the polymer is assumed homogeneous. For any study of the equilibrium properties of such a system, the choice of independent components is largely a matter of convenience but recently we have shown that the definition obtained by equating “inner” and “outer” salt concentrations in a dialysis experiment offers considerable advantage in the interpretation of data from light scattering and equilibrium sedimentation.2 In developing this definition we designate the elec- trically neutral solute containing the macromolecular ionic species as component 2 , and the diffusible salt as component 3 Only small ions common with those of component 3 appear in the formulation of component 2 The activities u2, u3 of these solutes are given by3

l ~ i u2 = In mi + v 2 X In mk + vLY In my + p.!

In u3 = vdx In mx + v3y hi my + B j

with m denoting molal eoncentrations of compoiieiits and of species, and v2x, v 2 y , V ~ X , Y ~ Y , the number of moles of ion species X and Y included in one mole of components 2 and 3. For the uni-univalent supporting electrolyte V ~ X = v3y = 1, and

( 2 4

(2b)

(14

Oh)

mx = m:l + v?xm2

my = m3 + v,ymL

Turning now to the dialysis experiment, we define components by sctting m3 equal to my’ a t osmotic equilibrium (the prime referring to the outer, polymer-free, solution) and write

my’ = my’ = mJ (3a)

Also, electroneutrality requires

mx = my + Zm? = my + m, (31))

For the sake of uniformity with previous d i s ~ u s s i o n s , ~ ~ ~ we have in this section expressed all concentrations in molul units. For practical reasons, however, we have expressed experimental data in terms of concentrations per liter of solution. Since we are concerned with solutions dilutr in polymer, concentrations in the two systems of units generally differ sensibly only by a factor of the density of supporting electrolyte.

SAL’I’S Ok’ POLY(V1NYL SULE’ONIC ACID) 33

It is useful to express the equilibrium distribution of the co-ion in terms of a parameter given, by definition, as

r = (my’ - my)/mu

vLx* = (1 - r)z

(-1)

( 5 4

v2y* = -rz (5b)

It follows from eqs. ( a ) , (3), and (4) that

We use superscribed asterisks to denote quantities coiisistent M ith the definition of components from osmotic equilibrium and also to distinguish experimental values referring to dialyzed solution and dialysate. Com- ponent 2* is thus defined as X , , - ,,,PY-rZ or, equivalently, X,P(XY) - rz. Electroneutrality is preserved, and component 3 is still the salt XY. The molal and equivalent concentrations m X Z P = m, and mu of the polymer component 2* are unaffected by the definition of the components. The expressions for the activities in terms of these components are then obtained by substituting vZx* and vzy* from eqs. (5) into eqs. (1).

The physical consequences of this definition of compvnents are immediately obvious. With the salt XY at equal concentrations m3, on both sides of a semipermeable membrane, addition of one mole of component 2* to one side involves addition of one mole of XzP and removal of I’Z moles of XY; thus no net flow of XY occurs across the membrane and the original distribution of component 3 is not disturbed. The system may, therefore, be regarded formally as behaving like a two-component system, water and salt constituting the “solvent ”

The membrane-distribution parameter r may be interpreted in relation to an effective degree of ionization of the polyelectrolyte, a factor i by which the stoichiometric charge Z is apparently altered by interactions of un- specified character In terms of the effective charge iZ, the ideal Donnan equilibrium applies :

mx‘my‘ = (my + iZm,)my = (my + im,)my = mJ2

By solving this quadratic equation for my, expanding the square root in the result, and introducing the definition of r, eq. (4), we find

r = ( i / 2>( [I - (imu/4mj) + ~ [ ( i m , / m ~ ) ~ ] j

In the limit of vanishing mu, r reduces to i / 2 . Then, in the absence of interactions r is and i unity, and for “neutral” polymer both r and i are zero. In systems such as some protein solutions in which there is “binding” in excess of the stoichiometric macromolecular charge, r may be nega- tive, and the concentration of diffusible electrolyte is greater in the solution containing the macromolecular component.

For light-scattering experiments the polymer is dissolved and equilibrated by dialysis against a salt solution of concentration m3. The procedure is repeated for several polymer concentrations. (In practice, how-

34 II. EISENBERG AND E. F. CASASSA

ever, as r is found to be independent of mu for mu << ma, the dialyzed solution may simply be diluted with more salt solution of concentration m3). The refractive index and turbidity differences An* and AT* between the equilibrated polymer solution and the equilibrium salt solution are measured. In terms of the experimental quantities defined by these operations, the light-scattering equation (cf. eq. (8) of reference 2) is

(dn*/dm,)2(H’Vmm,/RTAT*) = (1/Z) + 2A,m, (6) where H’ = 32n3n2kT/3X4, and V , is the volume of the system containing 1 kg. of solvent. From eq. (8) of reference 2 it is evident that the second virial coefficient A,, in units of (m,Z)-l, is given by A , = ( 1 / 2 ~ 2 ) { (1 - r)2~2/[m3 + (1 - r ) ~ m , ]

where Pz2* = b&*/bm,. always much smaller than m3, eq. (7) may be simplified to

+ [r2Z2/(m3 - rzm,) + A,*) (7) Since (1 - r)Zm, in the present instances is

2A, = (1 - 2r + 2r2)/ma + (&,*/Z2)

It is to be noted from eq. (6) that, with the above definition of components, a knowledge of r and, therefore, of the composition of component 2* is not needed for the evaluation of the degree of polymerization Z of the charged macromolecule; furthermore, under the experimental conditions specified, the value of A , is identical with that obtained from an osmotic pressure measurement (at least, if component 2* is homogeneous with regard to molecular weight). Of course, the separation of A , into two contributions according to eq. (7) or (8) does require knowledge of I?.

Similar considerations hold for sedimentation and the same definition of components proves useful. The experimental procedure involves equili- bration of the polymer against a supporting electrolyte solution as before ; and evaluation of the polymer concentration mu and the quantity A*p/m,, where A*p is the density difference between the polymer solution and the supporting electrolyte in dialysis equilibrium with it. Similarly the refractive-index increment of component 2* is evaluated with reference to dialysate. Component 2* sediments in the equilibrium “solvent” without redistribution of ions: in particular, when a solution containing polymer and salt a t original concentrations mu and my sediments, the polymer-free salt solution above the boundary always has the composition my‘ = my + rmu, if compressibility effects may be ignored. Of course, should r not be independent of polyelectrolyte concentration, interpretation of a sedimentation experiment requires separate evaluation of the polyelectrolyte and simple electrolyte gradients.

(8)

DISCUSSION OF RESULTS

Phase Separation

Phase-separation temperature measurements previously reported have Figure 1 shows a been extended to explore the influence of several anions.

SALTS OF POLY(V1NYL SULFONIC ACID)

80

60

0 0 . ,,40

20

0-

‘ 0 ° 1

-

-

-

-

I

I I I I 1 0 I 2 3 4

rn3 ,equiv /P

Fig. 1. Influence of anions on phase-separation temperatures T,.

35

Fig. 2. Phase-separation temperatures T , in a mixed simple electrolyte system.

plot of precipitation temperatures T , against salt concentration, a t constant polymer concentration with Na as the counterion in each case. It is seen that the T , increases for the coanions in the order KO3, F, C1, Br, I. Figure 2 describes T , for a mixed electrolyte system (NaCl + RbC1)

36 11. ISISENBERG AND E. 1'. CASASSA

together with the curves for KaC1 and RbCl for comparison. We recall that in the alkali chloride series the order of the alkali cations with respect to T , is (LiCl) < XaC1 < KCI > RbCl > (CsCI), no phase separation occurring in the two extreme cases down to the freezing point of the colu- tions.1 If it is supposed that the increasing insolubilization from LiCl to KCI and the increasing solubilization from KC1 to CsCl are due to two different antagonistic mechanisms, a mixed solution of LiCl and CsCl might be expected to show an observable phase separation. In fact, no phase separation was observed in mixtures of LiCl and CsCI, but an equi- molar mixture of NaCl and RbCl did give a phase-separation curve (Fig. 2 ) which was distinctly above the individual curves for KaCl and for RbC1. A plausible explanation of this phenomenon is not available now, but the effect is of interest for further investigations.

Membrane Distribution Studies

The results of the membrane-equilibrium studies are summarized in Table I. The experimental accuracy in determinations of t,he distribution parameter r is estimated to be of the order of 55%. Within this experimental error, 'no systematic dependence on either polymer concentration mu or degree of polymerization 2 (300 < 2 < 1200) could be observed.

TABLE I Membrane Distribution Coefficients 1' in Solutions of

Salts of PVSA in Various Electrolytes a t 23°C.

r a t various m3

0.05M 0.1M 0.25M 0.5M

KPVS in KC1 NHaPVS in NH&l

NaPVS in NaC1 NaPVS in NaNOl NaPVS in NaBr NaPVS in NaI

LiPVS in LiCl NaPVS in NaCl KPVS in KCl RbPVS in RbCl CsPVS in CsCl NHaPVS in NHICl

0.118 0.125 0.130 0.150 0.141 0.160 0.180 0.205

0.161 0.183 0.186 0.216

0.242 0.161 0.150 0.154 0.188 0.205

Measurements were made in the range 0.1 < mu/my' < 1 and the uncertainty in r is due to the fact that although my' and my can be determined to *O.l%, the quantity my' - my is small compared to my and my' and, therefore, subject to greater error. Thus, for instance, for KPVS a t 0.1 equiv./l. in 0.514 KCI, my' - my is 0.015 with an experimental uncertainty of 2ko.001.

SALTS OF POLY(V1NYL SULFONIC ACID) 37

As Table I indicates, I’ increases with increase of my‘ = m3 both for KPVS in KCl and NH4PVS in NH4Cl. It is noteworthy that this behavior is altogether unlike a manifestation of equilibrium “binding” of small ions by specific sites on the polymer chain in that the amount of salt “bound” decreases as m3 is increased. A similar effect has been observed by Strauss and Ander4 for various salts of long chain polyphosphates.

Fig. 3. Membrane-distribution measurements a t 23°C.

Our work constitutes a test of the interpretation of the Donnan equilibrium proposed by Strauss and Ander. They assume that the polyelectrolyte molecule may be represented by a series of rodlike segments, each surrounded by a cylindrical volume element from which the salt solution of concentration m3 is excluded. The radius of the cylinder is further assumed to be given hy

r = d + ( s / K )

where s is a constant of the order of unity, K is the reciprocal Debye- Huckel length, which is proportional to (m3)’/’, and d is, therefore, the radius of the shell a t infinite ionic strength. The ratio (J?/mJ’’’ is a linear function of (ms)-’/‘ with positive slope. The plots in Figure 3 do indeed exhibit the predicted linear character for both KPVS in KC1 and XH4PVS in NH,Cl. From the intercepts we find d to be 1.44 A. for KPVS in KC1 and 2.16 A. for KH4PVS in SH4Cl; from the slopes we find s to be 1.50 and 1.G3, respectively. The theory of Strauss and Ander correctly predicts the increase of I’ with m3 and the fact that d is significantly smaller for the

38 €1. EISENBERG AND E. F. CASASSA

system with higher specific interaction also appears intuitively correct. The usefulness of this model in interpreting intrinsic viscosity or the second virial coefficient has not been established.

The dependence of r on the cations Li, Na, K, Rb, Cs, and XH, is shown in Table I for 0.5M concentration of the chlorides. The values exhibit a pattern complementary to the phase-separation data in that r goes through a minimum in the alkali chloride series whereas T , in the same series ex- hibits a maximum. When the anions are changed with the cation Ka re- tained, the order of increasing values of r parallels the increase in the T , values (NaCl < NaBr < NaI). In both cases the variations in r are not large and their significance should not be overestimated in view of the large experimental error.

Light Scattering, Viscosity, and Sedimentation

We now consider in somewhat greater detail the properties of the systems KPVS in 0.5M KC1 and NH4PVS in 0.5M NHbC1. The relevant data are summarized in Table 11. Figure 4 represents the light-scattering behavior of dilute solutions. Both light-scattering curves were obtained from polymer solutions dialyzed against 0.5M KC1 and 0.5M NH4C1, respectively, and then diluted with the same solvents; refractive-index increments were obtained similarly from the difference in refractive index between the polymer solutions and the equilibrium salt solution. It is seen that, in agreement with eq. (6) both curves extrapolate (within experimental uncertainty) to the same intercept l / Z to give 2 as 355 for this polymer. The experimental values of the second virial coefficient from light scattering for the two systems are given in Table 11. The indication from the much smaller A , in the KC1 solution that this is the poorer solvent agrees with the observed phase equilibrium. The critical temperature for liquid-liquid separation in 0.5M KC1 is 17°C. for this

TABLE I1 Properties of Solutions of KPVS and NHaPVS (2 = 355) at 25°C.

KPVS in NHlPVS in 0.5M KC1 0.5M NHaCl

r = (my' - my)/m,, Equiv. weight of component 2* (XzP -

rzxy) / z

(bn*/dm,,) X lo3, X = 5461 A. Az X lo3, 1. mole/equiv.2

Experimental Calculated [eq. (9)]

(~ ,* /m, ) x 103 so X 10': see.-' [ q ] , I./equiv. %'/ap-l X 10-6

0.150

146.2 - 1-74.56 = 135.0

16.41

2.91 2.78

5.87 2.07 1.30

78.0 '

0.205

125.2 - r53.50

17.48 . = 114.5

16.6 14.7 54.7 3.55 3.48 1.05


I 1

I I 2 4

mu x lo', equiv/e

Fig. 4. Light-scattering measurements at 25°C.

polymer fraction, but for NH4PVS in NH&l no phase separation occurs down to the freezing point, of the solution.

In the evaluation of intrinsic viscosities from flow times in the capillary viscometers, the following density correction was found to be important. From Poiseuille's equation we have, for the ratio q*/vs of solution viscosity q* to the viscosity qs of the solvent:

r],,l* = r l * / ? S = P*t*/PStS

where p* and ps and t* and t, are the densities and the flow times for equilibrated solution and solvent, respectively. Combining this expression with the definition of the specific viscosity, qsp* = qrel* - 1, we obtain:

%P*/mu = [ ( t * / t 8 ) - ll(l/mu> + (A*Pt*/Psmuk)

in which, as above, A*p = p* - ps. The first term on the right-hand side of this equation is the quantity

usually evaluated in capillary-viscosity studies of polymer solutions, but the second term is appreciable when qsp/mu is small or A*p/mu is not negligible. For KPVS in 0.5M KCl a t 25"C., for example, A*p/psmu = 0.0765. For the polymer fraction with 2 = 355, the limit of [ ( t / t s ) - l](l/mu) at mu = 0 is 1.99 l./equiv., and so application of the correction leads to an intrinsic viscosity [v] = limmu--rO(qsp*/mu) of 2.07 I./equiv. All the viscosity values reported here have been corrected in this way. It should

40 H. EISENBERG AND E. F. CASASSA

7 . I

I

NH,PVS, 0.5M NH,CI I

3l KPVS, 0.5M KCI

mu XIO', equiv/ l

Fig. 5. Viscosity measurements at 25°C.

be mentioned that whereas, in general, (qsP*/mu) is not equal to (~sp/m, ) , [ q ] * is the same as [ q ] .

Figure 5 represents the viscous behavior of KPVS and NH4PVS in 0.05 and 0.5M KCI and NH4C1. It is seen that in 0.5M salt, [v] is much lower for KPVS in KC1 than for NH4PVS in NHbC1, but is nearly identical for the two systems in 0.05M salt. It appears, then, that at the lower value of the ionic strength, the conformation of the macromolecules is not very sensitive to specific interactions, but that in 0.521.1 salt the proximity of the KPVS- KC1 system to the theta temperature5 0 (indicated by the small value of A?) leads to a lower value of [ q ] .

By combining theoretical treatments relating thermodynamic properties6 and viscosity7 to chain dimensions, it is possible to calculate the second virial coefficient from values of [ q ] . We can proceed by making the tenta- tive assumption, the validity of which is currently being investigated, that [71s is the same in both sytems and equal to the value (1.62 l.,/equiv.) in the theta solvent (0.65M KC1 a t 25OC.).* We consider, first, the approximate analytic expression for A , [in units of (rnll2)-l] derived by Orofino and

A , = (1G?rN(R2)3'/'/3s'/' X 103Z2) In [ l + ( ~ " ~ , / 2 ) ( ( r ~ - l ) ] (9)

F I O ~ Y ~


together with the relations5

[sl = P ~ ( R ~ / z )

and

& 4 3 = [7ll/[?ls (10)

where @ = 1.5 X 1020, consistent with the value derived (see below) from a combination of sedimentation and viscosity measurements, (R2) is the mean-square molecular radius of gyration, and N is Avogadro’s number. Equation (10) is a modified of the familiar Flory-Fox7 relation. The values of A, calculated in this may from eq. (9) are shown in Table I1 and are evidently in qualitative agreement with experiment. A more detailed discussion of the second virial coefficient in polyelectrolyte solutions will be given elsewhere.

E

5

P m v)

“7

- 0 4 x v)

I I I I I

21 I I I I I 0 2 4 6 8 10

rn,xio2, equ iv / l

Fig. 6. Sedimentstion measurements at 25’C.

Figure 6 represents the sedimentation behavior of KPVS in 0.551 KC1 and of NHJ‘VS in 0.5M iYH4C1 as a function of polymer concentration; s* x l O I 3 is the sedimentation constant in Svrdberg units. The product s*r],,l*, as shown by the dotted lines in Figure 6, is nearly independent of concentration. Qualitatively, it is immediately apparent that the sedimentation constant in the “good” solvent, (0.5M XH,Cl) is significantly lower than in the “poor” solvent (0.5JC KCI).

42 H. ELSENBERG AND E. F. CASSASA

To obtain a direct relation between [ q ] and so = so*, the value of s* in the limit of zero polymer concentration, we combine Svedberg’s equation for sedimentation in the ultracentrifuge with a suitable expression for [ q ] in order to eliminate the frictional coefficient.12 In terms of the degree of polymerization, the equivalent weight Mu* of the polymer component, the partial volume P*, and the intrinsic viscosity as defined here, the relation in question is

@’/”-’ = [ [q]’/”osoN/Z2~~Mu*(1 - P*p,)] (11)

From many studies of uncharged polymers, the currently accepted value5 of the theoretically universal constant @.‘/‘P-’ is, in our units, 1.16 X 106. From density measurements we can calculate an apparent specific volume 4* defined byI3

4* = ( 1 / d [1 - (lo3A*p/Jf~*mu)l (12)

If Mu* is defined consistently with the experimental procedure, as explained above, 4* converges to the thermodynamically correct partial volume P* as mu vanishes. For our present purpose, however, we do not need to introduce r and calculate Mu*, since by equating +* and P* and combining eqs. (11) and (12), we eliminate Mu*, obtaining finally:

@‘/3Pp-’ = [q]1’SqosoN/Z2/a(A*p/m,) X lo3 (13)

Using our data and eq. (13), we find a value of 1.03 X 106 for @‘/3P-l for the system KPVS in 0.5M KC1 and 1.05 X lo6 for the system NHIPVS in 0.5M NHIC1. Introducing5 P = (3s)”/’/2”/” = 5.11, we arrive a t an average value of @ = 1.5 X 1OZo, a result somewhat lower than the accepted value of 2.1 x lozo (with volume in liters) for nonionic polymers.

CONCLUSION

In various ways, the measurements described above add to information concerning specific ion effects in solutions of salts of PVSA and a supporting electrolyte. Although the basis of these phenomena has yet to be under- stood, the present results show clearly their marked influence on solution properties and serve as a basis for more detailed studies now in progress.

The analysis of data for these three-domponent systems demonstrates in a concrete instance the utility of employing experimental procedures that cause the thermodynamic formalism to reduce to that for two-component systems. Well-established interrelations among thermodynamic and hydrodynamic properties of nonionic polymers are seen to apply as well to these polyelectrolytes, a t least in the presence of moderate concentrations of supporting electrolyte.

We are grateful to Ih. D. Breslow of the Hercules Powder Company for the polymer Miss Patricia E. Brown, Mr. Robert E. Kerwin, and Mr. sample used in this work.

Harvey J. Notariris aided by performing many of the experimental measurements.


References 1. Eisenberg, H., and G. Ram Mohan, J . Phys. Chem., 63,671 (1959). 2. Casassa, E. F., and H. Eisenberg, J . Phys. Chem., 64, 753 (1960). 3. Scatchard, G., J . Am. Chem. SOC., 68, 2315 (1946). 4. Strauss, U. P., and P. Ander, J . Am. Chem. Soc., 80,6434 (1958). 5. Flory, P. J., Prinriples of Polymer Chemistry, Cornell Univ. Press, Ithaca, N. Y.,

6. Flory, P. J., and W. R. Krigbaum, J . Chem. Phys., 18, 1086 (1950). 7. Flory, P. J. and T. G. Fox, J . Am. Chem. SOC., 73, 1904 (1951). 8. Eisenberg, H., and D. Woodside, paper presented a t 138th National Meeting of

9. Orofino, T. A,, and P. J. Flory, J . Phys Chem., 63, 283 (1959).

1953 Chap. 14.

the American Chemical Society, New York, N. Y., September 1960.

10. Kurata, M., H. Yamakawa, and H. Utiyama, Macromol. Chem., 34,139 (1959). 11. Ptitsyn, 0. B., and Yu. E. Ebner, Zhur. Fiz. Khim., 32, 2464 (1958). 12. Mandelkern, L., and P. J. Flory, J . Chem. Phys., 20,212 (1952). 13. Casassa, E. F., and H. Eisenberg, J . Phys. Chem., in press.

Synopsis

Specific ion effects in solutions of salts of poly(viuy1 sulfonic acid) in aqueous univalent supporting electrolyte are described in regard to observations of phase separation, dialysis equilibrium, light scattering, viscosity, and sedimentation. The most complete data have been obtained on two systems, ammonium poly(viny1 sulfonate) in 0.5M NH&l and potassium poly(viny1 sulfonate) in 0.5M KCI. Although the distribution of small ions across a semipermeable membrane is not markedly different in the two cases, other thermodynamic properties, the occurrence of phase separation in the KC1 solution and its absence with NHaC1, together with a larger second virial coefficient in the latter case, indicate that NHnCl is a much better solvent for the corresponding polymer than is KCI. The hydrodynamic measurements concur in showing that the polymer chain configuration is more expanded in the NH4CI solution. The interrelations among thermodynamic and hydrodynamic properties developed and generally substantiated for solutions of unionized polymers are found to be valid, at least qualitatively, for both these systems. This study also illustrates how the thermodynamic formalism for a two-component system is applicable to three components, two diffusible and one nondiffusible, provided solutions are equilibrated by dialysis against the solvent mixture.

R6sum6 Les eff ets d’ions spkcifiques dans les solutions de sels d’acide polyvinyl-sulfonique, en

milieu Clectrolytique uni-univalente, sont dkcrits tenant compte des mesures de skpara- tion de phases, d’kquilibre de dialyse, de diffusion lumineuse, de viscosith e t de skdi- mentation.

Les donnkes les plus compliites ont k tk obtenues pour deux systiimes: le polyvinylsulfonate d’ammonium en solution NH&l 0,5 M. et le polyvinylsulfonate de potassium en solution KCl 0,5 M. Quoique la rkpartition de petits ions B travers une membrane semi-permkable ne soit pas trbs diffkrente dans les deux cas, d’autres propriktks thermodynamiques, B savoir: la shparation de phases en solution KC1 et son absence en solution NH4Cl et d’autre part un second coefficient de viriel plus grand dans le 2bme cas, montre que NH&I est un bien meilleur solvant pour le polymbre correspondant que KCl. Des mesures hydrodynamiques concourent B montrer que la configuration de la chaine polymerique est plus ktendue en solution NH4Cl. Des corrklations entre les propriktks thermodynamiques et hydrodynamiques gCnCralement justifikes pour des solutions de polymbres non ionisks, se sont montrks valables, tout au moins quantitative- ment pour ces deux systkmes. Cette ktude montre aussi que le formalisme thermo- dynamique pour un systkme B deux composants est applicable B un systEme B trois

44 13. EISENBERG AND E. F. CASASSA

composants, dcux diffusibles et un non-diffusible, porirvu que les solutions soient Bquil- ibr6es par dialyse ?i 1’6gard du melange des solvants.

Zusammenfassung Spezifische Ioneneffekte in Losungen von Salzen der Polyvinylsulfonsiiure in wassri-

gem, einwertigen Grundelektrolyt werden im Zusammenhang mit Beobachtungen uber Phasentrennung, Dialysegleichgewicht, Lichtstreuung, Viskositat und Sedimentation beschrieben. Die vollstandigsten Ergebnisse wurden an den beiden Systemen Ammo- niumpolyvinylsulfonat in 0,5M NH&1 und Kaliumpolyvinylsulfonat in 0,5M KC1 erhalten. Obwohl die Verteilung der kleinen Ionen durch eine semipermeable Membran in den beiden Fallen nicht merklich verschieden ist, zeigen andere thermodynamische Eigenschaften, wie das Auftreten einer Phasentrennung in der KC1-Losung und ihr Fehlen mit NH4C1, zusammen mit einem grosseren zweiten Virialkoeffizienten im letz- teren Fall, dass NH&l ein vie1 besseres Losungsmittel fur das entsprechende Polymere ist als KC1. Die hydrodynamischen Messungen ergeben damit ubereinstimmend fur die NHdC1-Losung eine starker aufgelockerte Konfiguration der Polymerkette. Die fur Losungen nichtionisierter Polymerer entwickelten und weitgehend bestatigten Beziehungen zwischen thermodynamischen und hydrodynamischen Eigenschaften erwei- sen sich, zumindest qualitativ, fur diese beiden Systeme gultig. Die vorliegende Unter- suchung zeigt auch, wie der thermodynamische Formalismus fur ein Zwei-Komponenten- system auf drei Komponenten, zwei diff usionsfahige und eine nicht-diff usionsfahige, angewendet werden kann, vorausgesetzt, dass die Losungen durch Dialyse mit dem Losungsmittelgemisch ins Gleichgewicht gesetzt sind.

Received July 25, 1960 Revised October 17,1960

Documents

Aqueous solutions of salts of poly(vinylsulfonic acid)