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As the liquid scintillation counting technique has greatly improved the accuracy of C14 ana.lysis in the past decade, we decided to check a few sucrose intradiffusion coefficients to see if the above effect was real. The difFusion and counting techniques used have been adequately described e l s e ~ h e r e . ~The , ~ intradiffusion coefficients 60 measured are given in Table I. For comparison with other diffusion data, these (Dt)v values are graphed in Figure 1. The Gouy data from which the D , curve has been derived have been reported in separate concentration regions by Gosting and Morris,6 Gladden and Dole,Band E1lerton.l Table I : Intradiffusion Coefficients of Sucrose in Aqueous Solution a t 25" C, mole/l.
( D t h x 106 cma/sec
mole/l.
cmg/sec
0.00002 0.00285 0.1518
0.524 0.525 0.468
0.4086 0.7717 0.9272
0.398 0.299 0.267
C,
(Dt),X
5.0
7'
105
Clearly, the values of the intradiff usion coefficients measured in this work differ considerably from those of Irani and Adamson14 the discrepancy a t 1 M being -20%. Further, our intradiffusion data all lie below the mutual diffusion data in a manner consistent with the other systems so far studied. No special diffusive process a t high concentration needs now to be postulated. For the present, we have not extended our experiments beyond a concentration of 1 M because the normal stirring techniques are becoming inadequate here because of the rapidly increasing viscosity. Tests using colored liquid have been carried out to show that a stirring rate of 75 rpm gives barely adequate mixing at 1 M (comparable to 54 rpm for 0.5 M KC1 solution). In the 2 M region, the former speed was quite inadequate; complete mixing required about 10 min. We intend to extend these measurements when a new type of diaphragm cell, in which the compartment solutions are circulated by pumping, has been developed and tested. As these further measurements may not be completed for a year or more, we are reporting the present data now, as they serve to remove the anomalies discussed above. The trace sucrose intradiff usion values agree with the corresponding extrapolated Gouy value to within *0.2%, indicating the general accuracy of our method. We would estimate our overall precision a t this stage to be about f 1%. (5) L. J. Gosting and M. 9. Morris, J. Am. Chem. Soc., 71, 1998 (1949). (6) J. K.Gladden and M. Dole, ibid., 75, 3900 (1953). (7) H.D. Ellerton, Ph.D. Thesis, University of Adelaide, Australia, 1966.
4.0
P
3
DIFFUSIONRESEARCH UNIT RESEARCH SCHOOL OF PHYSICAL SCIENCES AUSTRALIAN NATIONAL UNIVERSITY CANBERRA, AUSTRALIA
.o-
2
X 4
J. F. TILLEY R. MILLS
RECEIVED APRIL20, 1967 3.0
Hydrophobic Hypercoiling i n Copolymers of Maleic Acid and Alkyl Vinyl Ethers 2.0 0
0.5 C, mole 1. -1.
1.0
Figure 1. Comparison of diffusion data in aqueous sucrose solutions a t 25': 0, intradiffusion (Dt), data, this work; , intradiffusion (Dt),data, Irani and Adamson; - - - _, mutual-diffusion D , Gouy data.
-
Sir: Potentiometric titrations of a hydrolyzed alternating copolymer of maleic anhydride and n-butyl vinyl ether indicate that there occurs a conformational transition which is not exhibited by a copolymer of maleic anhydride and ethyl vinyl ether. These results are presented in Figure 1, where pK,, defined by the relation listed as eq 1 Volume 71, Number 8 July 1967
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is given as a function of a. The degree of neutralization, a, is defined so that a = 1 a t the equivalence point of the first acid group of the dicarboxylic acid constituent. The difference in potentiometric behavior of the two copolymers resembles that observed between polymethacrylic and polyacrylic acid. 1-6 However, whereas the titration curves for the latter polyacids differ from each other over the whole titration range14 the titration curves for the alkyl vinyl ether copolymers coincide when a exceeds 0.7. While most investigators believe now that the transition in polymethacrylic acid is caused by hydrophobic bonding6 between the methyl groups, there also exists some disagreement with this vie^.^^^ One source of the difficulty lies in the fact that, in view of the closeness of the methyl group to the polymer backbone, interactions other than hydrophobic bonding may be involved.8 On the other hand, the two copolymers described here differ from each other only in the number of methylene groups in their alkyl side chains. Thus the hump in the titration curve for the butyl copolymer may be attributed with confidence to hydrophobic forces among the butyl groups. At low charge (a < 0.25), these forces hold the polymer in a compact coil. As a increases beyond 0.25, a transition to the more extended random coil form takes place which is complete when a reaches 0.7. It has been shown that titration data of the type obtained here may be used to calculate AGO,,, the free energy for the process: (uncharged compact form) + [(hypothetical) uncharged random coil Normally, one obtains AGO,, from the area bounded by the actual pK, against a curve and a curve extrapolated from the curve a t high a,where the polymer is in the random coil form, to a = 0.10-12I n the present case, we have assumed that the extrapolated curve of the butyl copolymer coincides with the actual curve for the ethyl copolymer and obtained AGO,, from the area between the two curves in Figure l. This procedure is predicated on the supposition that the copolymers behave as monoprotic acids in the region of interest (0 < a < 0.7). This supposition is justified by the large difference between the two pKo values of the maleic acid units: from our titration data we estimate pKol as 3.8 and pKozas 7.0 for both polyacids. The value found for AGO,, was -0.28 kcal/mole of dibasic acid unit, a value remarkably close to that theoretically estimated by NBmethy and Scheraga for the formation of hydrophobic bonds of minimum strength (0.3 kcal/ mole). l 3 The copolymers were prepared by polymerizing The Journal of Physical Chemistry
I l l I 2 3
l
l
I
4
5
6d7
I
I I 8 9
I 1.0
I
Figure 1. Dependence of the apparent pK on the degree of neutralization (of the first acid group) for: 0,ethyl copolymer; and A, butyl copolymer.
maleic anhydride and the alkyl vinyl ether in benzene with azobisisobutyronitrile as an initiator. The polymers were purified by several precipitations from tetrahydrofuran into ethyl ether. They both had an intrinsic viscosity of 1.0 in tetrahydrofuran, indicating similar degrees of polymerization of about 1500 as esti(1) R. Arnold and J. Overbeek, Rec. Trav. Chim., 69, 192 (1950). (2) A. Katchalsky, J. Polymer Sci., 7 , 393 (1951). (3) M. Mandel and J. C. Leyte, ibid.,, 56, 825 (1962). (4) H . Morawetr, “Macromolecules in Solution,” Interscience Publishers, Inc., New York, N . Y., 1965, p 353. (5) A. M. Liquori, et al., J. Macromol. Chem., 1 , 291 (1966). (6) W. Kauzmann, Advan. Protein Chem., 14, 1 (1959). (7) M. Nagasawa, T. Murase, and K. Kondo, J . Phys. Chem., 69, 11 (1965). (8) M. Mandel, J. C. Leyte, and M. G. Stadhouder. ibid.. 71, 603 (1967). (9) B. H. Zimm and 8. A. Rice, Mol. Phys., 3, 391 (1960). (10) M. Nagasawa and A. Holtzer, J . Am. Chem. SOC.,86, 538 (1964). (11) J. C. Leyte and M. Mandel, J. Polymer Sci., A2, 1879 (1964). (12) J. Hermans, Jr., J. phy8. Chem., 70, 510 (1966). (13) G. NBmethy and H . A. Scheraga, ibid., 66, 1773 (1962).
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mated from the relation of Ito, Ono, and Yarna~hita.’~ The polymers were hydrolyzed in water a t 60” for 24 hr. Titrations were performed in the absence of salt on aliquots containing 50 mg of polymer in 50 ml of water with 0.19 N NaOH, using a Radiometer Model 25 pH meter with glass and calomel electrodes. The hypercoiling phenomenon of the butyl copolymer a t low charge is essentially identical with the behavior previously found for highly charged poly~oaps.’~-’~ It is not difficult to predict that as we increase the alkyl chain length of the maleic acid-alkyl vinyl ether copolymers, the compact form will be increasingly stabilized and the transition to the random coil form correspondingly displaced to higher values of a. That the dodecyl copolymer behaves as a typical polysoap when cr = 1 has already been dernon~trated.’~A comprehensive study of such polyelectrolyte to polysoap transitions as a function of alkyl chain length, degree of ionization, added electrolyte, and temperature is in progress.
The yoreported by Shafrin and Zisman should be compared with the nonequilibrium yoof Johnson and Dettre (Figure 2 in ref 2) which is 20.7 dynes/cm a t 24 5”. If we assume a temperature correction of 0.4 dyne/cm, yo a t 20” would be about 21.1 dynes/cm, which is in better agreement with Shafrin and Zisman. The data of Aveyard and Haydon (Figure 1 in ref 1) (which also do not include adsorption from the vapor) give a yo of about 21.3 dynes/cm.
Acknowledgment. This work was supported by Grant GM-12307 from the National Institutes of Health, United States Public Health Service.
Concentrated Electrolyte Solution Transport
(1) E. G. Shafrin and W. A. Zisman, J . Phys. Chem., 71, 1309 (1967). (2) R. E. Johnson, Jr., and R. H. Dettre, J. Colloid Interface Sci., 21, 610 (1966).
E. I. DU PONTDE NEMOURS & COMPANY, INC. WILMINGTON, DELAWARE19898
R. E. JOHNSON, JR. R. 11. DETTRE
RECEIVED APRIL26, 1967
Theory : Directly Measured Glass Temperatures and Vitreous Ice
(14) K. Ito, H. Ono, and Y. Yamashita, J . Colloid Sci., 19, 28 (1964). (15) U. P. Strauss and E. G. Jackson, J . Polymer Sci., 6 , 649 (1951). (16) U. P. Strauss and N. L. Gershfeld, J . Phys. Chem., 58, 747 (1954). (17) U. P. Strauss and B. L. Williams, ibid., 65, 1390 (1961).
Sir: I n recent articles,’J the longstanding problem of interpreting the isothermal transport behavior of electrolyte solutions a t high concentrations has been discussed in terms of the dilution of the high concentration SCHOOLOF CHEMISTRY PAULDUBIN limiting “solution” which, in the case of ambient temRUTGERS, THESTATEUNIVERSITY ULRICH P. STRAUSS perature solutions of salts of multivalent ions, is asNEWBRUNSWICK, NEWJERSEY 08903 serted to be an ideal glassn3 The approach is thus the reverse of the traditional development which takes the RECEIVED APRIL24, 1967 infinitely dilute solution as starting point. Since a central feature of the approach is the thermodynamic significance attached to the ideal glass transition, a Comments on “Critical Surface Tension for matter which presents conceptual difficulties and is still controversial, some direct experimental support for the Spreading on a Liquid Substrate,” by approach is desirable to establish its plausibility. E. G. Shafrin and W. A. Zisman To provide such support we present here some independent measurements which bear out predictions of Sir: Shafrin and Zisman’ report the critical surface the transport model and a t the same time relate the tension of water (as measured with n-alkanes) as 21.7 basis of the concentrated solutions treatment to the dynes/cm. They state (on p 1314) that “Johnson and properties of pure water. Dettre’s significantly lower value of yo = 19.1 dynes/cm The interpretation of the concentration dependence a t 24.5” is difficult to explain since one would not expect of conductance‘ has been based on the explanation of the 4.5” temperature difference to cause such a change the temperature dependence of the process, the equain yo.” We would like to point out that the two yc)s do not (1) C. A. Angell, J . Phvs. Chem., 7 0 , 3988 (1966). refer to the same system. Johnson and Dettre’s2 (2) C. A. Angell, J . Chem. Phys., in press. value refers to systems in complete equilibrium. ( 3 ) An “ideal glass” is defined as a glass from which the configurational entropy content characteristic of the liquid state has comShafrin and Zisman’s value refers to systems not in pletely vanished; i.e., there is no “frozen in” entropy. See, e.g., adsorption equilibrium with the vapors of the alkanes. J. H. Gibbs and E. A. Dimarsio, J . Chem. Phys., 2 8 , 373 (1958). Volume 71, Number 8 July 1967
