NORIOISE AND TSUNEO OKUBO
1930
Mean Activity Coefficient of Polyelectrolytes.
11. Measurements of Sodium
Salts of Polyvinyl Alcohols Partially Acetalized with Glyoxylic Acid’
by Norio Ise and Tsuneo Okubo Department of Polymer Chemistry, Kyoto University, Kyoto, Japan
(Received December 81, 1966)
The mean activity coefficients of sodium salts of polyvinyl alcohols partially acetalized with glyoxylic acid were measured electrochemically. The single-ion activity coefficient of the sodium ions and the transference number of the macroion were also determined. It was found that the mean activity coefficient decreased with increasing concentration, whereas the single-ion activity coefficient was almost independent of concentration. On the assumption that the single-ion activity coefficient has a clear meaning, this difference was interpretated as implying that the contribution of macroions is very influential in determining the thermodynamic solution properties. This result agrees with the one previously reported with sodium polyacrylate. The logarithm of the mean activity coefficient was found to decrease linearly with the cube root of concentration, as was the case for dilute solutions of simple electrolytes. The magnitude of the slope increased with increasing charge density and decreased with increasing degree of polymerization of the polyelectrolytes. The cube root rule is qualitatively interpreted by the local regularity of ionic distribution proposed earlier, and it is suggested that the formation of the regularity may be facilitated in polyelectrolyte solutions by the fact that the ionizable groups of macroions are linked to each other by polymer chain and furthermore by “linkages” between macroions through the intermediary of gegenions.
Introduction I n a previous paper, the first direct measurements of mean activity coefficient have been reported on polyelectrolytes using sodium polyacrylate.2 I n the present paper, experimental data are reported on the sodium salts of polyvinyl alcohols partially acetalized with glyoxylic acid (PVAG). NaPVAG is of interest for three reasons. First the degree of polymerization and the total number of charges on a polymer molecule can be adjusted independently. Second, PVAG is a fairly strong acid so that the pH of the sodium salt solution is near 7, even when the charge density is low. Accordingly, the hydrogen ion activity is suppressed to a value about 4 decades below the sodium level experimentally used. This is a requirement for the Naglass electrode to respond exclusively to sodium ion activity. By using PVAG, therefore, we can apply the Na-glass electrode method to the determination of the mean activity coefficient of polyelectrolytes with low charge (COO-) densities. Third, various other The Journal of Physical Chemistry
properties of this polyelectrolyte have already been studied in our l a b ~ r a t o r y . ~
Experimental Section The details of the measurements of mean activity coefficient, single-ion activity coefficient, and transference data were reported in previous paper^.^,^ A concentration cell with transference was set up with Na-glass electrodes as
1
Na-glass NaPVAG NaPVAG Na-glass electrode solution 2 I solution 1 1 electrode
(1)
(1) Presented a t the 14th Symposium of Polymer Sciences, Kyoto, Japan, Oct 1965. (2) N. Ise and T. Okubo, J. Phys. Chem., 69, 4102 (1965). ( 3 ) A. Nakajima, S. Ishida, and I. Sakurada, Chem. High Polymers (Tokyo), 14,259 (1957); I. Sakurada, M.Hosono, and N. Ise, ibid., 15, 175 (1958); N.Ise, M.Hosono, and I. Sakurada, ibid., 15, 339 (1958); I. Sakurada and N. Ise, Makromo2. Chem., 40, 126 (1960); N. Ise and M. Hosono, J . Polymer Sci., 39, 389 (1959). (4) T. Okubo, Y . Nishizaki, and N. Ise, J . Phya. Chem., 69, 3690 (1965).
MEANACTIVITYCOEFFICIENT OF POLYELECTROLYTES
The emf ( E )of the cell is given by
1
Na-glass NaPVAG calomel electrode j solution electrode
Ez,
=
+ (RT In F
Elgo
-
(11)
aNa+
where Ezg,is the standard emf of the above cell, and aNa+the single-ion activity of Na+. From this equation, we determined a N a + , and hence the single-ion activity coefficient of gegenions, y*zg. As is well known, the physical meaning of the single-ion activities was questioned by Guggenheim.6 The present authors share his strictest interpretation, but, in the field of polyelectrolytes, emphasis had not been put on the mean activity or activity coefficient before our study was initiatede2 (The reason for this situation was discussed in the previous paper.2) Actually, in a great number of papers in this field, the single-ion activity, or activity coefficient of gegenions, was claimed to be measurable and gave interesting information of thennodynamic properties of polyelectrolyte solutions. Whether the information may be correct or not, it would be necessary to pay attention to the single-ion activity coefficient of gegenions as well as the mean activity coefficient at the present stage. The starred activity coefficient, mean or single-ion, is a “stoichiometric” quantity, which was defined in the previous paper.2 Transference experiments were based on the methods developed earlier by Wall and his associates.’ PVAG’s were prepared by acetalization of polyvinyl alcohol with glyoxylic acid. Glyoxylic acid was prepared by reaction of 1-tartaric acid with paraperiodic
1931
acid.8 Glyoxylic acid was added to mixed aqueous solutions of fractionated polyvinyl alcohol and sulfuric acid (-1-2 M ) . Then the mixture was kept at 60’ for 4 days, neutralized with NaOH, dialyzed against distilled water until sulfate ions could not be detected by Ba(OH)2, passed through a column containing cationand anion-exchange resins, and neutralized with sodium hydroxide with the aid of conductometric titration. The polymer solution thus obtained was then concentrated and poured into a methanol-acetone mixture, and the polymer (sodium salt of PVAG) thus separated was dried under reduced pressure. The content of carboxyl groups in the PVAG was determined by conductivity measurements, and the degree of polymerization was estimated by viscometry of the parent polyvinyl alcoh01.~ I n Table I, the characteristics of PVAG samples are shown. The degree of acetalization is defined as the fraction of OH groups acetalized. The stoichiometric number of charges on a macroion ( z ) is then given by one-half of the product of the degree of polymerization and the degree of acetalization. All fractions of polyvinyl alcohol except the ones of the lowest and the highest degrees of polymerization were obtained by fractionation of a PVA sample furnished by the Denki Kagaku Co., Tokyo. The fractionation was effected at 30” using 1-propanol as a precipitant and water as a solvent. PVA having a degree of poly-
Table I : Characteristics of NaPVAG
Sample
Degree of polymeriration
Degree of acetaliration, mole %
86 1,050 2,490 10,500 1,700 1,700 I , 700
33.9 31.3 26.7 29.3 5.99
NaPVAG-21 NaPVAG-23 NaPVAG-24 NaPVAG-27 NaPVAG-N1 NaPVAG-N2 NaPVAG-N3
10.1
21.0
(5) By printer’s mistake, eq 5 in the ref 2 is in error. It should read
log (yzlyi)
FE/(4.606ta(RT) log
(ntzlnti)
LE
+ (F/4.606<)
bdE
(6) E. A. Guggenheim, J. Phgs. Chem., 33, 842 (1929). (7) J. R. Huizenga, P. F. Grieger, and F. T. Wall, J . Am. Chem. SOC.,72, 2636 (1950). (8) A. A. Eisenbraun and C. B. Purves, Can. J . Chem., 38, 622 (1960). (9) Control experiments show that no appreciable degradation of polymer molecule during the acetalization process took place.
Volume 70, Number 6
June 1966
1932
merization of 10,500 was prepared by a -pray-induced bulk polymerization of vinyl acetate at -78", and the sample with a degree of polymerization of 86 was obtained by solution polymerization of vinyl acetate in butylaldehyde at 60" using benzoyl peroxide as a catalyst.
Results and Discussion The important data of single-ion activity coefficient, transference number, and mean activity coefficient are gathered in Table 11. I n the first column, the number of effective charges of each sample (assumed to be equal to a),as determined by the transference experiment, is given with the stoichiometric value x. I n the second column, the polymer concentration in equiv/ 1000 g is given. The emf value of the concentration cell shown by (I) is given in the third column. The transference number is in the fourth column. The mean activity coefficient (y*) obtained from the emf and transference data is listed in the fifth column, and the single-ion activity coefficient of gegenions (y*zg) determined by emf measurement of the cell shown by (11) is in the sixth column. The y* values were expediently determined with the convention that y* is equal to y*zgat nz = 0.01, as was described in the previous paper.2 The accuracy of the emf measurement of the concentration cell was * O . l mv in this present work, and the reproducibility was & 2%. The accuracy of transference number data is estimated to be & 3%. Taking these factors into consideration, the limit of error associated with the y* value was found to increase with decreasing concentration and t 2 p value; the highest limit of error obtained for the y* value was about 10% for NaPVAG-24 at v z = 0.0256. Except for this extreme case, * 5 % was the limit of experimental error. The accuracy of the emf measurement of cell I1 was AO.1 mv, and the limit of error associated with y*zgwas 2%. The experimental results show that the single-ion activity coefficient of the gegenion ( Y * ~ ~is) almost independent of concentration in the range covered, and y*Zg is independent of molecular weight except for a sample of low molecular weight, NaPVAG-21, which gives higher values than other samples (compare 21, 23, 24, and 27). The first observation is in agreement with the previous data on sodium p~lyacrylate,~ and the second one agrees with the usually accepted tendency. The y*2g values of NaPVAG are much higher than those of sodium polyacrylate (about 0.3) previously r e p ~ r t e d . ~Evidently, this can be attributed to the low charge density of NaPVAG. The y * z g value appears to decrease with increasing charge density
NORIO ISE AND TSUNEO OKUBO
Table I1 : Transference and Activity Coefficient Data of NaPVAG (25') 102m,
equiv/
Eta
Sample
1000 g
mv
t2P
Y*
Y*%
NaPVAG-21 z = 15 a = 14
0.145 0.278 0.668 1.53 2.39 3.06
27.4 23.1 12.7 5.8 2.2 0
0.59 0.57 0.53 0.45 0.36 0.31
1.53 1.06 0.91 0.69 0.63 0.64
0.73 0.79 0.79 0.80 0.77 0.75
NaPVAG-23 z = 164 a = 148
0.159 0,302 0.727 1.66 2.59 2.85 3.34
22.7 17.8 11.2 4.6 1.7 0.9 0
0.46 0.44 0 40 0.38 0.36 0.35 0.35
1.23 0.99 0.76 0.64 0.56 0.56 0.53
0.65 0.67 0.67
0.271 0.653 0.995 1.49 2.34 2.56 3.00
18.0 10.9 7.9 5.0 1.4 0.7 0
0.47 0.45 0.44 0.43 0.42 0.42 0.41
1.14 0.86 0.74 0.64 0.57 0.55 0.51
0.404 0.615 0.923 1.44 1.59 1.86
13.1 10.3 6.3 2.3 1.7 0
0.43 0.43 0.43 0.43 0.43 0.43
0.82 0.69 0.66 0.61 0.59 0.59
NaPS'AG-N1 z = 51 a = 48
0.136 0.316 0.482 0.723 1.14 1.47
11.2 6.1 3.8 2.8 1.3 0
0.25 0.24 0.23 0.23 0.21 0.19
1.76 1.46 1,39 1.10 0.93 0.93
0.95 0.95 0.97 0.99 0.95 0.90
NaPVAG-N2 z = 86 a = 82
0.170 0.396 0,603 0.905 1.41 1.82
12.3 7.2 5.3 2.8 0.7
0.34 0.33 0.31 0.30 0.27 0.26
1.85 1.39 1.14 1.05 0.90 0.77
0.99 0.99 0.99 0.99 0.97 0.95
0.225 0,525 0.800 1.20 1.88 2.41
14.7 9.7 6.9 4.6 1.8 0
0.42 0.39 0.37 0.34 0.30 0.30
1.75 1,17 1.02 0.88 0.79 0.77
0.98 0.97 0.94 0.94 0.94 0.83
NaPVAG-24 z = 332 a = 283
NaPS'AG-27 z = 1540 a = 1260
*
The Journal of Physical Chemistry
NaPVAG-N3 z = 179 a = 170
0
. I .
0.67 0.68 0.66 0.60 0.63
... 0.64 0.64 0.65 0.65 , . .
... 0.64
... 0.65 0.63
I n the emf measurements, the reference concentration was the highest one for each sample.
(compare N1, N2, N3, and 24 or 23). This is understandable in the light of the gegenion association which becomes important with increasing charge density.
MEANACTIVITYCOEFFICIENT OF POLYELECTROLYTES
It should be noted that, for the sake of brevity, other data such as conductivity, pH, fraction of bound gegenions, etc., which are pertinent to the transference experiments, are omitted in this paper since they are not relevant to the present discussion. They will be published at a later date. Table I1 shows that the mean activity coefficient (y*) decreases sharply with increasing concentration. The same tendency mas observed for sodium polyacrylate.2 y* is almost independent of the degree of polymerization, unless the latter is very low. Furthermore, y* appears to decrease with increasing charge density (see N1, K2, S3, and 24 or 23). A meaningful discussion, however, cannot be given on the dependences with degree of polymerization and charge density, since the y* value was determined by a rather arbitrary convention mentioned in the previous paper.2 Thus our discussion will be limited to the concentration dependence of y* and related problems. As mentioned above, the single-ion activity coefficient of gegenions ( Y * ~ ~ is ) almost independent of concentration for all samples, whereas the mean activity coefficient (y *) sharply decreases with increasing concentration. I n other words, y* is not always equal to y*zg. This conclusion is the same as the one previously reported for sodium polyacrylate.2 On the other hand, in the case of a 1-1 type electrolyte, Le., potassium chloride, its mean activity coefficient is equal to single-ion activity coefficient of potassium ion or of chloride ion by JfacInnes’ convention.’O Thus, the situation in this case is in contrast with that in polyelectrolytes. According to our interpretation, the discrepancy between y* and y*2gis due to the singleion activity coefficient of macroions being extremely large or small, since the definition of y* is given by ,,*‘+a
=
*2g Y*2P
7
(3)
where CY, the number of free gegenions produced by dissociation of one polyelectrolyte molecule, is usually very large compared to unity. I n other words, the contribution of macroions in the thermodynamic solution properties is very influential, though hitherto largely overlooked. It should be noted here that excellent agreement was obtained between the y* values determined by the electrochemical method mentioned in this paper and those obtained from isopiestic measurements of vapor pressure of solvent by means of the Gibbs-Duhem equation. The details of these comparisons will be the subject of a future paper.“ The next problem is the concentration dependence of y*. As is well known, the logarithm of y* for elec-
1933
trolytes of low valency can be represented as a linear function of the square root of concentration in very m for 1-1 type electrodilute solution, say below lytes. This relation is in accordance with the DebyeHuckel limiting law.I2 At higher concentration, it has been pointed out by several a u t h o r ~ ’ ~ -that l ~ log y* decreases linearly with the cube root of concentration. On the other hand, no discussion, theoretical or empirical, has been presented on the concentration dependence of y* for polyelectrolytes. Using the y* values experimentally found, the square root and cube root plots mere carried out. The former plot deviated from linearity. Figures 1 and 2 show the latter plots. As is readily seen from these figures, the cube root rule holds approximately for KaPVAG, though a slight departure can be noticed at higher concentrations. The slopes of the straight line are -2.3, -2.8, and -3.2 for N1, X2, and N3, respectively, the magnitude increasing with increasing number of charges. This variation of the slope seems quite plausible judging from the experimental data of simple electrolytes, which are presented by broken curves in Figure 3. From this figure, the slopes for NaC1, CaC12, and L a c & are -0.30, -0.64, and -1.0, respectively.16 The slopes of NaPVAG-21, -23, -24, and -27 are -3.0, -2.6, -2.5, and -1.6, respectively, the magnitude decreasing with increasing degree of polymerization in the range covered. This variation of the slope can be accepted by recalling the experimental fact that, in dilute solutions of simple electrolytes, the larger the excluded volume of ions, the less steep is the 7’-concentration curve.” (10) R. G. Bates, “Determination of pH, Theory and Practice,” 1st ed, John U‘iley and Sons, Inc., New York, X. Y . , 1964, Chapter 3. (11) N.Ise and T. Okubo, in preparation. (12) P. Debye and E. Hockel, Physik. Z., 24, 185 (1923). (13) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworth and Co. Ltd., London, 1959, Chapter 9. (14) H. S. Frank and P. T. Thompson, J . Chem. Phys., 31, 1086 (1959). (15) J. E. Desnoyers and B. E. Conway, J . Phys. Chem., 68, 2305 (1964). (16) The activity coefficient data were taken from the following literature. NaCl: G. Scatchard and S. S. Prentiss, J . Am. Chem. Soc., 5 5 , 4355 (1933); Appendix 8.10, Table 10 in ref 13. CaClz: T . Shedlovsky, J . Am. Chem. Soc., 72, 3680 (1950); R. H. Stokes, Trans. Faradau Soc., 41, 637 (1945). LaC13: T . Shedlovsky, J . Am. Chem. Soc., 72, 3680 (1950): H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd ed, Reinhold Publishing Carp., New York, N. Y., 1958, Appendix A, Table 13-7-1A, p 746. (17) In comparing NaPVAG-21, -23, -24, and -27, attention should be paid t o the increase in number of charges with increasing degree of polymerization. Owing to the preceeding observation that the magnitude of slope increases with increasing number of charges, the observed variation of the slope with increasing degree of polymerization (or exclusion volume factor of macroions) indicates that the volume effect is much more dominating than the charge effect.
Volume 70, Number 6
June 1966
NORIOISE AND TSUNEO OKUBO
1934
1
‘1
‘I; 21
I
I
I
I 1 4
-0.2 I
I
\ I
1
0
*
I
-0.21
t I
0
I
I
I
1
0.1
L o.2
-y
t
I
0.3
I
I
0.4
0.5
0.6
I
I
I
I
0.3
I
I
0.2
0.3
1
I
0,I
.
mi Figure 2. Concentration dependence of the mean activity coefficients of NaPVAG having various degrees of polymerization (25’). The vertical bars represent an uncertainty of f 5 % .
The square and cube root rules have also been examined using the previously reported y* values of sodium polyacrylat,e.2 For this polyelectrolyte, the square root rule was not successful. The cube root plot is shown in Figure 3. The linearity holds in a wide range of concentration, the slope being -0.74. The Journal of Physical Chemistry
Figure 3. “Cube root” plots of the mean activity coefficients of NaCl, CaC12, Lacla, and NaPAA a t 25’: (1) NaC1, (2) CaC12, (3) Lacla, (I) NaPAA. The vertical bars represent an uncertainty of f57,.
I
m3
0
I
0.2
mT
Figure 1. Concentration dependence of the mean activity coefficients of NaPVAG having various numbers of charges (25’). The vertical bars represent an uncertainty of =t5%.
I
I
0.1
Robinson and StokesI3 have explained the linearity in the cube root rule by taking into consideration the local regularity of ionic distribution in solutions. Although qualitative, it would be interesting to apply this explanation to polyelectrolyte systems. Since ionized groups on macroions are linked to each other by a polymer chain, we may approximately regard the charge distribution inside the polymer domain to be more regular than would be expected for simple electrolyte ions. It is conceivable that this intramacroion regularity remains in existence even at high concentrations, where the “regularity” disappears in simple electrolyte solutions because of the shortrange interactions between ions which would become predominant in such a concentration range. Thus, we may expect that in polyelectrolyte solutions, the local regular structure can be formed, and hence the cube root rule holds, in a much wider concentration range than in simple electrolyte solutions. Actually, the upper limits of concentration, a t which the cube root rule begins to fail, are found to be 0.125, 0.040, and 0.020 for NaC1, CaC12, and LaC13, respectively, whereas the upper limit is above 0.2 equiv/1000 g for NaPAA, not appearing in the concentration range studied (Figure 3). An objection to this argument may immediately be raised pertaining to the cases of NaPVAG, CaCL, and LaCl3. However, it can be rejected by the high valency of these electrolytes, as follows. As the number of charges of an ionic species increases, the repulsive force between the ionic species becomes large enough to break the local regular structure which would have been present for electrolytes having a small number of charges. This is the reason why the concentration range, where the cube root rule holds, shifts to lower concentrations and becomes narrower for NaPVAG, CaC12, and LaC13than for NaCl. Then the next question is why the cube root rule
1935
APPARENT CATALYSIS OF GRAPHITIZATION
holds in a narrower range of concentration for NaPVAG than for sodium polyacrylate. I n short, this is ultimately due to the difference in the charge densities of these polyelectrolytes. As expected, a good fraction of gegenions clusters around macroions, and the fraction goes up with increasing charge density of the macroion. The electrostatic attractive force between gegenions and macroion is so strong that there might be created “linkages” between the macroion and other macroions through the intermediary of the gegenions, as was earlier suggested by Wall and Drenan. la This linkage would contribute to the enhancement of local regularity in the distribution of macroions. The strength of the linkage would increase with increasing charge density, so that NaPVAG has lower orders of regularity in the distribution of macroion than sodium polya~ry1ate.l~Thus the cube root rule holds at lower
concentrations and in a narrower range of concentra tion for NaPVAG than for sodium polyacrylate. Acknowledgments. The authors acknowledge gratefully the criticisms and encouragements received from Professor Ichiro Sakurada. The transference experiments were partly carried out by Miss Y. Nishizaki. PVA samples of the highest and lowest degrees of polymerization were prepared by Dr. H. hiatsuzawa.
Apparent Catalysis of Graphitization. I.
Possible Mechanisms
(18) F. T. Wall and J. W. Drenan, J. Polymer Sci., 7, 83 (1951). (19) The existence of the linkage is supported by the experimental fact that single-ion activities of polyacrylate or PVAG ions decrease very steeply with increasing polymer concentration. The activity of neutral polymers, however, increases with increasing concentration according to the Flory theory (P. J. Flory, “Principles of Polymer Chemistry,” Cornel1 University Press, Ithaca, N. Y., 1953, Chapter 12), and the (single-ion) activity of small ions in simple electrolytes also increases with increasing concentration. Though the details will be published separately, it is interesting to note that the tendency for the activity t o decrease with increasing concentration was found only for macroions.
by M. L. Pearce and E. A. Heintz Speer Carbon Company, Division of Air Reduction Company, I n c . , ‘Viagara Falls, New York I@O$ (Received December $1, 1966)
The effect of ambient oxygen-bearing atmospheres on the graphitization process has been theoretically examined from the viewpoint of mechanism. It is concluded that the presence of oxygen cannot enhance the process by virtue of supplying a faster route for the reorientation of carbon atoms. However, it would appear that oxygen may be beneficial because it supplies a more facile energetic route for the graphitization process or because it removes atoms or groups of atoms which hinder the process. Reports of beneficial effects for other gaseous and nongaseous materials have also been considered, and generally the same conclusions appear to be valid. The limited quantitative data available essentially support this reasoning.
Introduction
oxygen are reported to “accelerate” graphitization2s3 implying a Purely kinetic “Am-Iism whereas it has There have been reports of small but significant been suggested that the advantages of silicon carbide beneficial effects on the graphitization process for several additives or gaseous environments. 1-9 However, the (1) T. Noda and H. Matsuoka, KoOUo Kaoaku Zasshi, 64, 2083 mechanisms by which the ~ ~ ~ ~ are teffective ~ 1 has~ ~ (1961). t ~ i ~ been the subject of speculation rather than detailed (2) T. Noda, XI. Inagaki, and T . Sekiya, Carbon, 3, 175 (1965). analysis.2-6 For example, small partial pressures of (3) T. Noda and M. Inagaki, ibid., 2, 127 (1964). Volume 70, Number 6 J u n e 1966
