407 1
MEANACTIVITY COEFFICIENT OF POLYELECTROLYTES
Mean Activity Coefficient of Polyelectrolytes. XI.
Activity Coefficients of
Various Salts of Polyacrylic Acid and Carboxymethylcellulose1
by Kiyotsugu Asai, Katsuhiko Takaya, and Norio Ise Department of Polymer Chemiatry, Kyoto Univeraity, Kyoto, Japan
(Received February 19, 1969)
The osmotic and (mean) activity coefficients of propionates, polyacrylates (PAA), and carboxymethylcellulose (CMC) salts of various gegenions in aqueous media have been determined a t 25’ by means of the isopiestic vapor pressure measurement. As had been found in previous works, a marked specificity of gegenions was noted. For propionates, the osmotic and activity coefficients decreased in the order N(n-C4H9)4 > N(CH3)4 > K > Na > Li. For polyacrylates a t high degrees of neutralization, the order was N(n-C4H9)4 > N(n-CaH?)d > N(C2H5)4 > N(CH& > Li > K > Na. I n the case of a CMC sample of a higher degree of substitution (DS = 0.95) the order was N(n-C4H9)4 > N(CK& > Na. Lowering of the DS value changed the order. At DS = 0.78, NR4(R = alkyl) cs K > Na > Li and a t DS = 0.68 N(CH8)d > Na > N(n-C4H9)4. The order Na > N(n-C4H9)4 was also found for polyacrylates a t a degree of neutraliaation of 0.2. These results could be accounted for in terms of the structural influence of ions on water by taking into consideration balancing of two “counteracting” effects of hydrophobic and ionic groups. The electrostrictional structure formation effect, which was predominant a t a highly charged state, could be screened off by the cage-like structure formation of hydrophobic parts a t low degrees of neutralization or substitution. Comparison of the PAA and CMC ions suggested that the former is more hydrophobic than the latter.
Introduction In previous papers from this laboratory,2 the mean activity coefficients of a variety of synthetic polyelectrolytes having various gegenions have been measured. The results have shown that the mean activity coefficients are largely influenced not only by the character of macroions but also by that of gegenions; the specificity of macroions and gegenions was successfully, though qualitatively, accounted for in terms of the structural influence of ions on water. Furthermore, it was concluded that the solvent-solute interaction is more important than the gegenion association, though the reverse was often believed to be true. While we intend to extend the measurements to biologically important polyelectrolytes, we want to report here the mean activity coefficient data of various salts of polyacrylic acid (PAA) and carboxymethylcellulose (CMC) . No other types of salts than the sodium salt of PAA3l4have been measured previously. The salts of CMC were thought interesting because the CMC molecule contains a number of polar groups and is believed to be comparatively stiff.
polyacid solution thus obtained was neutralized with the aid of conductometric titration with an aqueous solution of reagent grade LiOH, NaOH, KOH, (CH&NOH, (C2Hs).SOH, (n-C3H7)4NOH, or (n-C4H9)4NOH. The polymer concentration was determined by the titration data. The isopiestic measurements were carried out at 25 f 0.005” by using an apparatus and experimental procedures described previously.6
Results and Discussion The measured concentrations of the solutions of PAA salts and potassium chloride (refeyence electrolyte) in isopiestic equilibria are listed in Table I. The corresponding data for propionates and CMC salts are given in Tables I1 and 111,respectively. The practical osmotic coefficient of the electrolyte wm calculated by the condition of equal solvent vapor pressure, as previously d e ~ c r i b e d . ~The osmotic coefficients of potassium chloride solutions were taken from the literature.B The osmotic coefficients of pro-
Experimental Section
(1) Presented at the 21st Annual Meeting of the Chemical Society
The NaPAA was a gift from the Toa Gosei Chemicals Co., Nagoya. Its weight-average degree of polymerization was 640. T h e NaCMC was kindly furnished from the Daiichi Kogyo. The degree of polymerization was estimated by the supplier to be about 400. The NaPAA and NaCMC solutions were purified by passing through cation- and anion-exchange resins. Propionic acid was twice distilled at reduced pressure in a nitrogen atmosphere (42 mm, 65.1’). The
of Japan, Tokyo, Japan, April 1968, and a t the 17th”AnnualMeeting of the Society of High Polymers, Japan, May 1968. (2) (a) N. Ise and T. Okubo, J . Phys. Chem., 71, 1886 (1967); (b) N. Ise and T. Okubo, ibid., 72, 1361 (1968); ( 0 ) N. Ise and K. Asai, {bid., 72, 1366 (1968); (d) N. Ise and T. Okubo, ibid., 72, 1370 (1068). (3) N. Ise and T. Okubo, ibid., 69, 4102 (1965). (4) N. Ise and T. Okubo, ibid., 71, 1287 (1967). ( 5 ) T. Okubo, N. Ise, and E’. Matsui, J . Amer. Chem. Soc., 89, 3697 (1967). (6) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworth and Co., Ltd., London, 1959, pp 476, 481.
Volume 73, Number 12 December 1969
4072
K. ASAI,K. TAKAYA, AND K, ISE
Table I : Concentrations of Isopiestic Solutions of Potassium Chloride and Polyacrylates a t 25"" 1. PAA Salts at a Degree of Neutralization = 1 mKCl
Li
K
N(CH3)r
N(CzHs)r
K(n-CaH7)4
N(n-CaHs)a
0.0962 0.123 0.151 0.164 0.200 0.241 0.332
0.504 0.667 0.809 0.869 1.03 1.18 1.56
0.550 0.731 0.872 0.933 1.10 1.26 1.65
0.352 0.448 0.542 0.669 0.754 0.945 1.23
0.326 0.408 0.491 0.612 0.685 0.858 1.11
0.300 0.375 0.450 0.564 0.623 0.773 0.986
0.266 0.325 0.392 0.496 0.562 0.707 0.922
2. NaPAA and N(n-C4Hg)4PAA at Degrees of Neutralization of 0.2, 0.4, 0.6, and 0.8
-NaPAA
7
0.248 0.331 0.503 0.628 0.819 1.03 1.14 1.31 1.63 1.95 2.75 3.00 3.62
0.105 0,139 0.216 0.268 0.342 0.428 0.475 0.543 0,695 0.851 1.36 1.53 2.01 a mKc1
0.4
0.2
nwci
0.320 0.414 0.606 0.733 0.923 1.13 1.23 1.42 1.72 2.07 2.93 3.19 3.86
0.6
--
0.430 0.550 0.792 0.958 1.19 1.45 1.55 1.73 2.10 2.46 3.40 3.69 4.36
,-.----
0.8
N (n-CaHe)aPAA-----------. 0.4 0.6
0.2
0.523 0.668 0.969 1.17 1.43 1.73 1.84 2.03 2.41 2.76 3.64 3.87 4.47
0.267 0.338 0.471 0.560 0.683 0 828 0.891 0.995 1.24 1.47
0.377 0.626 0.825 1.11 1.46 1.62 1.86
0.8
0.356 0.481 0.560 0.660 0.778 0.824 0.901 1.07 1.23 1.72 1.92
0.377 0.503 0.578 0.671 0.779 0.821 0.892 1.05 1.17 1.56 1.71
is in molality; polymer concentration is in equiv/1000 g of water.
Table I1 : Concentrations of Isopiestic Solutions of Potassium Chloride and Propionates a t 25" mIm
0.144 0,188 0.420 0.880
Na
0,143 0.185 0.386 0.800
Li
K
0.145 0.187 0.405 0.836
0,142 0.185 0.381 0.777
N(CHs)4 N(n-C4H9)4
0.131 0.169 0.364 0.729
0.128 0.165 0.347 0.660
1.2
-8 10 .
pionates (+) are given in Figure 1, together with the + values of the sodium salt reported previously (given by the filled circles).' The osmotic coefficients of polyacrylates (4J*are given in Figure 2. The +E values for NaPAA were obtained from the results previously published by using the observed value of the polymer charge f r a ~ t i o n . ~Figure 3 gives the t # ~as ~ a function of polyelectrolyte concentrations for salts of CMC of a degree of substitution (DX) of 0.95 (carboxymethyl groups per glucose unit). From Figures 1, 2, and 3, it is seen that alkali metal salts of electrolytes have lower osmotic coefficient values than tetraalkylammonium salts. For CMC salts having lower DX values, however, the situation is different; as shown in Figure 4,a t DX = 0.78, the values of the tetraalkylammonium salts fell on a curve and were as large as those of KCMC. It is seen from Figure 5 that at DX = 0.68 N(n-ChHa)r CMC showed smaller values than N(CH3)&MC,
+
C#J~
The Journal of Physical Chemistry
0
0
Na Li
.
8
U
0.2
-
-
0.4
l
m
0.6
0.8
I.o
Figure 1. Osmotic coefficients of aqueous solutions of N(n-C4&)*-, N(CH3)4-, K-, Na-, and Li propionates (25'). a: data for the sodium salt taken from the work cited in ref 6.
whereas the reverse was the case in Figures 1 , 2 , and 3. Figure 6 gives the +* values of sodium salts of the poly(7) Taken from ref 6,p 484,Appendix 8.10. (8) The $a valucs were calculated on the assumption that the electrolyte is fully dissociated. For polyelectrolytes, it is possible to define another osmotic coefficient on the basis of the number of free gegenions, which has been denoted by 4 without suffix in a series of our work. We note that it is not necessary to distinguish between 6 and 4. for simple electrolytes, since the so-called gegenion associac tion does not so markedly occur for this kind of electrolytes as for polyelectrolytes. We further note that the mean activity coemcient y* to be discussed in the present paper corresponds to 4s by the fundamental thermodynamic relation, but not to 4.
4073
MEANACTIVITY COEFFICIENT OF POLYELECTROLYTES ~ ~~
~
Table I11 : Concentrations of the Isopiestic Solutions of Potassium Chloride and Salts of Carboxymethylcelluloses at 25"" 1. CMC (DS = 0.78)
2. CMC (DS = 0.78)
mKCl
Na
K
0.143 0.176 0.219 0.305 0.424 0.623 0.956
0.333 0,456 0.598 0.741 0.964 1.38 1.99
0.239 0.329 0.425 0.524 0.676 0.924 1.30
Li
0.391 0.493 0.636 0.783 1.03 1.47 2.15
mxc I
N (CHs)4
N (Ca&)c
0.155 0.195 0.255 0.336 0.459 0.665
0.260 0.328 0.400 0.535 0.740 0.964
0.276 0.345 0.419 0.553 0.762 0.997
3. CMC (DS = 0.95 and 0.68)
0.243 0.288 0.406 0.466 0.520 0.601 0.703 0.794 0.972
0.271 0.325 0.472 0.546 0.616 0.722 0.855 0.987 1.21
0.364 0.430 0.637 0.749 0.840 1.01 1.24 1.43 1.80
0.108 0.128 0.209 0.244 0.268 0.338 0.427 0.493 0,672
0.258 0.308 0.477 0.566
0.228 0.268 0.386 0.446
0.767 0.927 1.07 1.35
0.581 0.689 0.747 0.914
0.293 0.340 0.479 0.550 0.621 0.716 0.854 0.979 1.21
'mxcl is in molality; CMC concentration is in equiv/1000 g of water.
I
1.4c
I
I
Bu
Figure 2. Osmotic coefficients of aqueous solutions of N(n-C4H~)4-, N(n-CsH&, N(CzH&, N(CH&-, Li-, K-, and Na polyacrylates (25').
0
I
0
" I
I
0.5
os=o.'7*
m
1.0
Figure 3. Osmotic coefficients of aqueous solutions of N(n-C4H&, N(CH&, and NaCMC at a degree of substitution of 0.95 (25").
I
Figure 4. Osmotic coefficients of aqueous solutions of N(n-C4Ho)4-,N(CHs)4-, K-, Na-, and LiCMC at a degree of substitution of 0.78 (25').
acrylic acid a t degrees of neutralization of 0.2, 0.4, 0.6, and 1.0 and of carboxymethylcellulose samples a t approximate degrees of substitution of 0.7, 0.8, and 1.0. For both PAA and CMC, the & becomes larger as the charge density on the polymer chain decreases. The mean activity coefficient was calculated using the Gibbs-Duhem relation, as reported previously.4 The assumptions involved in the calculation of the coefficient of the polyelectrolytes were, again, that (1) the cube-root rule holds down to infinite dilution and (2) the polyelectrolytes have the same activity coefficient a t infinite dilution (TO*), irrespective of the gegenion, the degree of substitution, or the degree of neutralizaVoZume 78, Number 18 December 1960
4074
K. ASAI,K. TAKAYA, AND N. ISE DS = 0.68
g-I l -
0
1.0
0.5
-I 3-
a
Figure 5. Osmotic coefficients of aqueous solutions of N(CH&-, N(n-C4Hg),-, and NaCMC a t a degree of substitution of 0.68 (25').
-1.5
06
07
08
09
II
1.0
m
I
No-Salt
I
!
-0.2 -x-x-x
*xo x
-x4-
-
Bu xc*
Pr
....*
-cn --1.0 O , ~
Figure 6. Osmotic coefficients of sodium salts of carboxymethylcellulose and polyacrylic acid a t various degrees of neutralization and of substitution (25'). CMC, 0.7,0.8, and 1.0 denote the samples a t degrees of substitution of 0.68, 0.78, and 0.95,respectively. 0.2,0.4, 0.6, and 1.0PAA denote the degrees of neutralization of 0.2, 0.4, 0.6, and 1.0,respectively,
06
I.o
0.8
I.2
13'
Figure 8. The cube-root plot of the activity coefficients of polyacrylates at a degree of neutralization of 1.0 (25').
the concentration range studied. Furthermore, the activity coefficient decreased in the order
K = Na
> Li
(A)
and
N(n-CdHa)r
1
0.4
I
I
0.8
0.6
I
1.0
I
1.2
m 1 ' 3
Figure 7. The cube-root plot of the activity coefficients of propionates (25 ').
tion. Obviously the second assumption is questionable and will be considered in the latter part of this paper. Figure 7 gives the activity coefficients of propionates as a function of the cube root of electrolyte concentration. It is seen that the cube-root rule is not valid in The JOUTnd of Physical Chemistry
> N(CHa)4
(B)
The order (A) is the same as found for acetates,loand is the reverse of that observed for polyvinyl sulfates, polystyrenesulfonates, polyethylenesulfonates, and polyphosphates.2 The order (B) was also found for all these polyelectrolytes examined so far2 and for tetraalkylammonium halides in a dilute region." Figures 8a and 8b give the mean activity coefficients of alkali metal salts and tetraalkylammonium salts of the polyacrylic acid, respectively. The cube-root rule is seen to hold a t low concentrations. The upper bound of the range of fit (9! For earlier references on the cube-root rule of the activity coefficient of electrolytes and for the related problem, see H. S. Frank and P. T. Thompson, "The Structure of Electrolytic Solutions," W. J. Hamer, Ed., John Wiley and Sons, Inc., New York, N. Y., 1969,Chapter 8. (10) Reference 7,pp 492,494. (11) (a) S. Lindenbaum and G. E. Boyd, J. Phys. Chem., 68, 911 (1964); (b) W. Y. Wen, S. Saito, and C. M. Lee, ibid., 70, 1244 (1966) I
4075
MEANACTIVITY COEFFICIENT OF POLYELECTROLYTES of the rule is about 1 equiv/1000 g of water for the inorganic salts and about 0.5 equiv/1000 g of water for the organic salts. The slopes are -0.82, -1.00, -1.30, -0.40, -0.60, -0.80, and -0.95 for Li-, K-, Na-, N(n-C4H9)4-r N(n-C3H7)r, N(CSH~)~-,and M(CH3)4-PAA, respectively. The activity coefficients of polyacrylates decreased in the order Li
> K > Na
(C)
1
- 1.0
and N(n-C4H9)4 > N(n-C3H,)4
> N(CzHs)4 > N(CHB)Q (D)
While the order (D) was already found for polyelectrolytes studied so far,2 for tetraalkylammonium halides” and for the propionates, the order (C) is new in two respects: it differs from the order (A) found for propionates or acetates, and also from the order Li > Na > K observed for polyelectrolytes studied in this laboratory.2 According to the existing theories of structural influences of ions on ~ a t e r , l l b , l 2 -the ~ ~ structural saltingout and salting-in effects result in the high-lying and low-lying activity coefficient concentration curves, respectively. The observed order for propionates (E( > Na > Li) indicates that the propionate ion is a structure-former in the same sense as for L i + ion. As was earlier suggested by Gurney,16 the acetate ion is a structure-former. Therefore, the propionate ion would be structure-forming also, though probably even less so than the acetate ion because of the presence of an ethyl group which is a structure former of a mode incompatible with the carboxylate group.’6 The order (C) for the polyacrylates (Li > K > Na) suggests that the polyacrylate ion is a weaker structure former than the propionate ion. This would be understood as follows. The -CHs-CH groups present in the polymer chain could
I
show a stronger cage-like structure-forming tendency than the CH3-CH2 groups in the corresponding monomer unit, Le., the propionate ion. I n other words, we can expect a cooperative influence by the repeating units in the polymer chain on the water structure. As a consequence, the electrostrictional influence of the carboxylate group would be weakened more strongly for the polyacrylates than for the propionates. Thus, the order (C) differs from the order (A). As for the orders (B) and (D), which agree to each other, it is useful to point out that the organic ions are strong cage-like structure formers. The incompatibleness of the modes of the water structure around the organic ions and the propionate or polyacrylate ions gave rise to the observed order. The foregoing discussion was clearly based on two “counteracting” structural influences on water structure, namely the cage-like structure formation by the hydrophobic part (methyl and ethyl groups for acetates and propionates) and the electrostrictional structure formation by the ionic part (carboxylate ion for
Figure 9. T h e cube-root plot of the activity coefficients of N(R-C*HB),and Na polyacrylate at degrees of neutralization of
0.4 and 0.2.
acetates and propionates). The relative magnitudes of these two effects determine the position of the activity (or osmotic) coefficient-concentration curves. l7 Thus, the CNIC salts of DS = 0.95 (Figure 3) showed in the order N(n-C4H9)4 > N(CH&
> Na
(E)
which agrees with the finding for the polyacrylates. When the charge density (or the degree of substitution) is lowered, the contribution of the electrostrictional factor becomes smaller and the hydrophobic influence becomes more important. I n other words, the structure-forming character of the CMC ions becomes closer to that of the organic gegenions with decreasing DS. Therefore N(n-C4H9)4-CMC a t DS = 0.68 has smaller osmotic coefficients than N(CH3)4CMC, as shown in Figure 5 N(CH,),
> Ma = N(n-C4H9)4
(F)
The CMC salts a t DS = 0.78 represent an intermediate feature, as seen from Figure 4. At this degree of substitution, the osmotic coefficients of the tetraalkylammonium salts fell on the same curve; no observable difference was observed between N ( Y L - C ~ Hand ~)~ N(CHS)~ salts. It would be interesting to examine the order of the (12) H. S. Frank and W.-Y. Wen, Discussions Faraday SOC.,24, 133 (1957). (13) H. S. Frank, J . Phys. Chem., 67, 1554 (1963). (14) H. S.Frank, 2. Phys. Chern. (Leipzig), 228,364 (1965). (15) R. W. Gurney, “Ionic Processes in Solution,” McGraw-Hill Book Co., Inc., New York, N. Y., 1953,Chapter 16. (16) The reasoning that the structureforming tendency of the propionate ion is weaker than that of the acetate ion is substantiated by the fact that sodium propionate has larger activity coefficients than sodium acetate. See ref 6, p 484,Appendix 8.10. (17) The structural influences can be discussed in terms of the osmotic coefficient,instead of the activity coefficient. When comparison of various polyelectrolytes is sought, the use of the osmotic coefficient is convenient because the activity coefficient at infinite dilution varies from sample to sample. The activity coefficients of CMC samples are not given in the present paper, because the isopiestic data were not reliable enough a t higher dilutions to allow the cube-root extrapolation. Volume 73, Number 12 December 1969
4076
0. B. VERBEKE,V. JANSOONE, R. GIELEN,and J. DE BOELPAEP
activity coefficientsof PAA salts at lower degrees of neutralization. Figure 9 shows that a t a degree of neutralization = 0.4 we have the order N(n-CeHe) > Na (GI which is the same as found a t a degree of neutralization = 1 (see Figures 8a and 8b). However, when we go down to 0.2, we have Na > N(n-CkH9) (H) I n words, the inversion of the order of the activity (or osmotic) coefficients can occur not only for CMC salts but also for PAA salts. This fact strongly supports the validity of the above-mentioned explanation in terms of the shift of balance between the structural influences of ionic and hydrophobic groups with varying charge density.
Finally, we compare the ipz values of the PAA and CMC. As was mentioned before, the linear charge density of a CMC having a DS = 1.0 is about the same as that of a PAA of a degree of neutralization of 0.3. Figure 6 shows that the ipz of this PAA sample is larger than that of the corresponding CMC salt. This result indicates that the PAA anions are more hydrophobic than the CMC anions. This is consistent with the information derived from the solubility measurements of naphthalene and biphenyl in solutions of watersoluble polymers.18
Acknowledgments. The sodium polyacrylate and sodium salts of carboxymethylcellulose were gifts of the Toa Gosei Chemicals Co., Nagoya, and the Daiichi Kogyo Seiyaku Co., Kyoto, respectively. (18) T . Okubo and N. Ise, J. Phys. C h m . , 73, 1488 (1969).
The Equation of State of Fluid Argon and Calculation of the Scaling Exponents by Olav B. Verbeke, Institute for Molecular Physics, University o j Maryland, College Park, Maryland
Vik Jansoone, Rik Gielen, and Jan De Boelpaep Fysisch Instituut, Universiteit van Leuven, Leuven, Belgium (Received February 19, 1869)
Experimental P-V-T data of fluid argon are presented. Most of the data cover the volume range from 28 to 132 cm8 in the range from 90 to 200’K and below 150 atm. Special attention is paid to the critical region. One isochore, however, is measured up to 2000 atm and in the high-density range. In the high-density range with molar volumes below 38 cms a Tait-like equation of state is fitted to the data. I n the range from 40 to 132 cma/mol, a new type of equation of state is proposed which fits the data through the critical point. It is shown that the latter equation is compatible with the power laws, and the exponents are derived. From these equations different thermodynamic properties are calculated.
Apparatus and Method The apparatus used for this experiment is a modification of the equipment used with liquid hydrogen by Van Itterbeelr, el al.’ (See Figure 1.) The 99,99G% purity gas is liquefied in a formerly evacuated highpressure volume HP in a cryostat K. By means of thermal compression the experimental volume VM is filled through I
