COMMUNICATIONS TO THE EDITOR
2759
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
COMMUNICATIONS TO THE EDITOR
2760
1
tion for which contains, as a central parameter, the theoretical (or ideal) glass transition temperature, To. A = AA exp
-
250
- 20
231)
- 40
210
-60
190
- 80
170
- 100
kA
(T
- To)
The equation is distinguished from the ordinary Arrhenius rate equation by the presence of To in the denominator. To is the temperature a t which the configurational entropy content of the supercooled liquid would vanish in a cooling process of infinite time scale.3 It therefore falls a t a somewhat lower temperature than the (closely related) experimental glass transition temperature, T,,which is a rate-dependent quantity. I n simple ionic liquids T,/To is found to be ~ 1 . 0 5 1.15.4 , 5 I n electrolyte solutions, TOincreases with increasing electrolyte concentration, N . The high concentration limit referred to above is set by the concentration a t which Toreaches the temperature of the isotherm and is referred to as No (equiv le-'). The equation proposed' to describe in the first a p proximation the isothermal composition dependence of conductance is
-
The slope k' of the linear plot log A os. l/(No N) contains the concentration dependence of TO,which we give the symbol Q , through the relation Q = k/k'. Using the measured conductances of Ca(NO&-HzO solutions a t 0" and the value of k of 680" obtained from a temperature study of the conductance of liquid Ca(N03)2.4H20,we obtained' Q = 8.8" equiv-' 1. The value of k of 626" obtained recently by Moynihan4 for the same liquid is probably more accurate, suggesting Q = 8.1" equiv-'1. If this approach is correct, then a direct determination of the concentration dependence of the experimental glass transition temperature measured a t a constant heating rate for those solutions which can be supercooled to the glassy state should yield a Q, (Q, = dT,/dN) which compares very closely with the above value of Q derived from the isothermal conductance data. We have therefore measured T , for a series of Ca(N03)rHzO solutions, using a simple differential thermal analysis technique. The temperature differential between a sample contained in a 2-mm diameter Pyrex glass sample tube and a corresponding sample of inert material (benzene6) was recorded during warm-up from liquid nitrogen temperature. A break in the differential emf vs. time plot (Figure 1 inset), due The Journal of Physical Chemistru
270
9
&' 150
-120
- 140
130
9 8 G
- 160 - 180
90
70
'
, -Tinu min
N
01 0.C
m
-L
R-
30
I 2
4
6
8
10
12
14
8 10 12 14 N , equiv. I.-' a t Tg.
17
i
IS
16
18
Figure 1. Dependence of glass transition temperature on concentration in calcium nitrate solutions. Inset: differential emf ua. time trace showing location of T,.
to a change of heat capacity from crystallike to liquidlike values a t T,, allows T , to be determined (as indicated in Figure 1) with a reproducibility of j ~ 0 . 5 "a t constant heating rate. Tochanges by -1" for a doubling of heating rate from 5 to 10" min-'. Solutions in the concentration range 7.5-17 equiv l,-I, corresponding to a water: salt molar ratio ( R ) range of R = 3 to R = 12, may be quenched to the glassy state. I n solutions of lower concentration, partial crystallization could not be avoided. The values of T , found for the glass-forming solutions are plotted against N in Figure 1. The corresponding, predicted dependence of Toon N , ie., Q , of 8.1" equiv-' 1. is shown as a dashed line, with which the experimental plot corresponds a t high concentrations (significantly, for R < 6). (The slope of the experimental plot is actually 8.7" equiv-l 1.) Now a departure from the linear dependence of To on N, assumed (in the absence of any better information) in the derivation of eq 2, had to be expected as otherwise Tofor water would fall at too low a temperature. Accordingly, we noted' that for the linear log A (4) C. T. Moynihan, J . Phys. Chem., 7 0 , 3399 (1966). (5) C. A. Angell, ibid., 68, 218 (1964). (6) J. A. McMillan, J . Chem. Phys., 42, 3497 (1965).
COMMUNICATIONS TO THE EDITOR
2761
us. l/(No - N) plot to be maintained as observed k and
argon (Ar/XCCl3 = 200-500) were simultaneously condensed with an atomic beam of lithium (Li/ XCCl3 = '/z, 1, or 2) on a cesium iodide window a t 15"K, as described by Andrews and Pimentel.6 Infrared spectra were recorded in the 200-4000-~m-~spectral region. I n the carbon tetrachloride experiments using 'Li, intense bands a t 579 cm-', which shifted to 617 cm-' with 6Li, were recorded. The former absorption agrees with 580 cm-l reported by Schlick and Schnepp7 for lLiCl while the latter is higher than the 608 cm-' assigned by these workers to 6LiC1. However, the 617cm-' absorption is intense (0.28 OD) and its assignment to 6LiCl appears to be certain. When bromotrichloromethane is used as a precursor with "i, the 617cm-' band and one at 541 cm-' corresponding to Schlick and Schnepp's assignment of 540 cm-' to 6LiBr were recorded. Obviously, lithium reacts with the halomethanes to produce lithium halides under the conditions of the experiment. I n every carbon tetrachloride experiment an intense band (1.1 OD, vlI2 = 2 cm-l) a t 898 cm-l was recorded. I n a separate experiment using a 51% 13C-enrichedcc14 sample, an intense (1.2 OD) well-resolved doublet with components of equal intensity a t 898 and 869 cm-' was (7) J. A. McMillan and S. C. Los, Nature, 206, 806 (1965). observed. Spectra for the BrCC4 experiments showed (8) K. E. Larsson, V. Dahlborg, and 5. Holmryd, Arkiv Fysik, 17, an intense (1.1 OD) doublet a t 898 and 888 cm-l. 369 (1960) : discussed in "Thermal Neutron Scattering," P. A. Egelstaff, Ed., Academic Press, New York, N. Y., 1965, Chapter by These absorptions show no detectible lithium isotope K. E. Larsson. effect and they decrease in intensity with respect to an DEPARTMENT OF CHEMISTRY C. A. ANGELL absorption due to a species containing lithium when the PURDUE UNIVERSITY E. J. SARE Li/CCI4 ratio is increased. LAFAYETTE, INDIANA 47907 R. D. BRESSEL Spectra of samples of C2C16and C2C14in argon were RECEIVED MAY5, 1967 recorded. The absorptions a t 898 cm-' are not due to a known stable chlorocarbon species. After sample warming to 47"K, the 898-cm-' absorption intensity decreased while the C2C&band appeared a t 684 cm-'. Infrared Detection of Trichloromethyl The well-resolved doublet near 900 cm-' in the 51% Radical i n Solid Argon 13C-enriched CC14 experiment suggests that a single carbon atom is present in the molecular species responsiSir: The trichloromethyl radical is suggested to be a ble for the absorptions, where the resolved components photolytic decomposition product of carbon tetraat 898 and 869 cm-I are due, respectively, to the 12Cand chloride' and bromotrichloromethane2 and an interl3C species. Unfortunately, chlorine isotope shifts are mediate in the reaction of bromine with bromotrichlorotoo small (2-3 cm-') to resolve. CC1 absorbsa near methane. We are not aware of any previous direct spectroscopic (1) B. C. Roguitte and M. H. J. Wijnen, J . Am. Chem. SOC.,85, evidence for the trichloromethyl radical. Since the 2053 (1963). matrix reaction between lithium atoms and methyl (2) J. M. Tedder and R. A. Watson, Trans. FaTaday SOC.,6 2 , 1215 (1966). halides has produced sufficient methyl radicals for infra(3) N. Davison and J. H. Sullivan, J . Chem. Phys., 17, 176 (1949); red spectral s t ~ d y ,we ~ ,have ~ applied this technique to A. A. Miller and J. E. Willard, ibid., 17, 168 (1949). XCCl, molecules in an attempt to study the trichloro(4) W. L. S. Andrews and G. C. Pimentel, ibid., 44, 2527 (1966). methyl radical. (5) L. Andrews and G. C. Pimentel, ibid., submitted for publication. Samples of carbon tetrachloride, 51% 13C-enriched (6) W. L. S. Andrews and G. C. Pimentel, ibid., 44, 2361 (1966). carbon tetrachloride, or bromotrichloromethane in (7) S. Schlick and 0. Schnepp, ibid., 41, 463 (1964).
Q probably remained proportional rather than constant. However, the slope of the linear plot was determined mainly by the high concentration points, where k was measured experimentally, so dT,/dN should correspond with Q in this region. Figure 1 shows this is gratifyingly close to correct. Of even greater interest is the temperature to which the curvilinear plot extrapolates a t zero concentration. This temperature, 140 f 5"K, is in excellent agreement with the value of T, of 139°K observed by McMillan and LOS' in the warm-up of vapor-deposited vitreous ice. Noting that T$T0 a t R = 4 is 1.09 we arrive a t an estimate of Tofor water of 128 f 5°K. The neutron scattering data of Larsson, et aE.,8have been interpreted to yield an effective Debye temperature for the collective vibratory motions in water of -130°K. While the coincidence with the value of To may prove fortuitous, the implication that the glass transition is related in some way to a rapid increase in the importance of multiphonon scattering processes in the glassy solid deserves serious examination in view of its potential importance to the understanding of liquid-solid relations.
Volume 71, Number 8 July 1967
