NOTES
344
Discussion of the Available Experimental Data. The experimental data on ion-exchange equilibria in mixed solvents are not very extensive and no single study covers all of the aspects discussed here. In particular, no one has determined selectivity coefficients as a function of resin composition in mixed solvents. However, the following general features for ion-exchange equilibria in mixed solvents have been recognized (i) h general increase in KD on addition of the orA- maximum ganic solvent has been 0 b s e r v e d . ~ ~ ” ~ ~ ~ ’8 has been obtained by SakakiI6 as well as Strobel” in alkali metal ion-hydrogen ion exchange on PSStype exchangers in alcohol-water systems, when the mole fraction of alcohol is increased to 0.7 or greater. (ii) A linear dependence of log KD on 1 / D (where D is the dielectric constant of the medium) in the ascending part of the log K D us. 1 / D curve has been obtained. The explanations of these phenomena range from the differences in the hypothetical desolvation energy lnvolved in ion exchange15 to the changes in solution and exchanger phase activity coefficients. 11.12 Recently, Athavale rtnd co-workers” have studied alkali metal ion-?;H4+ or H + exchange systems in mixed solvents on PSS-type exchangers. They have compared the equilibrium constants determined a t one resin composition and seemingly this resin composition is not even the same for all the systems being compared. As such, conclusions drawn by them on the basis of this comparison are highly questionable. Sakaki’s and Strobfll’s data on uni-univalent exchange systems in alcohol- mater media have been obtained a t various alcohol concentrations but unfortunately only a t one resin composition. As the exchanger composition has , is some justification been maintained a t O . ~ N B Rthere in equating the equilibrium constant to the selectivity coefficient a t this composition. l 9 These studies also lack the solvent uptake data for the different forms of exchangers. h s such, no quantitative application of eq. 10 or 12 is possible. Therefore, an explanation of the above-mentioned general features, on the basis of these equations, perforce will have to be qualitative ; rather, it will be shown that these equations can lead to these observed features. The main points to be explained are a linear dependence of log KD on 1/D at low alcohol concentrations and the maximum in the log KD ZJS. 1 D curve. Referring t o the approximate eq. 12 and recalling that majol’ contributions come from the Yo terms (the last two integrals making opposite contributions of the same order of magnitude), let us consider the situation when the organic solvent is present in low concentraThe Journal of Physical Chemistry
tions. The last two integrals of eq. 12, taken together, will make approximately a constant contribution to log K . Then the actual variations in log K’Dwill be due to log yo terms, which have a linear dependence on 1 / D . As alcohol concentration is increased, the last two integrals will make varying and lower contributions, and log K’D will exhibit a maximum and then decrease. Strobe1 has attributed the variations in K (obtained when KD is corrected for the yo terms) to the changes in resin phase activity coefficients. (Other authors6 have used the concept of increased ionpair formation in resin phase to explain the increase in K D in mixed solvents, but the resin phase activity coefficients incorporate all such effects.) These variations in K , most probably, are partly due to the approximation used in equating the equilibrium constant to the value of KD a t O.~NBR and partly to the neglect of solvent absorption terms. I n eq. 10 or 12 above, the resin phase activity coefficients as well as the sorption terms are implicitly included. Experiments on some simple exchange systems in mixed solvents, where the solvent sorption data will also be determined, are in progress so that the above equations can be verified.
Acknowledgment. The author expresses his sincere thanks to Dr. J. Shankar for his encouragement and keen interest during the course of this investigation. (14) G. M. Panchenkov, V. T. Gorshkov, and M. V. Kuklanova, Zh. Fiz. K h i m . , 32, 361, 616 (1958). (15) T. Sakaki, Bull. Chem. SOC.Japan, 28, 217, 219 (1955). (16) E. A. Materova, 2. L. Vert, and G. P. Grinberg, J . Gen. Chem. USSR, 24, 959 (1954). (17) V. T. Athavale, C. 1’. Krishnan, and C . T‘enkateswarlu, Inorg. Chem., 3, 533 (1964). (18) M. R. Ghate, Ph.D. Thesis, Bombay University, Oct. 1963. (19) E. Hogfield, Acta Chem. Scand., 9, 151 (1955).
The Vapor Pressure of Copper Phthalocyanine
by James Curry and Robert W. Shaw, Jr. Department of Chemistry, Williams College, Walliamstown; Massachusetts (Received J u l y 24, 1964)
There are many references in the literature to the sublimation of copper phthalocyanine in the temperature interval 400-5000. Lawton’ investigated the remarkable thermal stability of this substance. For he found that the infrared spectra of copper (1) E. A. Lawton, J . m y s . Chem., 6 2 , 3 8 4 (1958).
NOTES
345
phthalocyanine did not change if the compound was heated under vacuum for 1hr. a t 800'. We have been interested in growing single crystals of copper phthalocyanine to use in studying the semiconducting properties of this substance. In order to select suitable conditions for the growth of crystals, we have found it expedient to measure the vapor pressure of solid copper phthalocyanine as a function of temperature. From such measurements, one may also calculate thermodynamic data useful in characterizing the intermolecular forces holding the molecules together in the crystal.
Experimental The Knudsen rate-of-effusion method was used for the measurements. The cell consisted of a 1.5 X 1.3 cni. platinum crucible which was closed with a piece of aluminum foil containing a small orifice. The foil was firmly bound to the crucible by a chrome1 wire. The diameter of the hole was measured by means of a microscope with a calibrated eyepiece, and the thickness of the foil was measured with a micrometer. The data for the cells are given in Table I. Table I : Dimensions of Orifice Cell
Diametar, cm.
Length, cm.
1 2a
0.290 0.242 0,0792 0.0440 0.04OO
0.0080 0,0030
3 4
5
5 This cell had a square hole. round hole of equivalent area.
calibrated chromel-alumel thermocouple. Calibration runs were made to determine the temperature a t the crucible relative to the temperature of the air in the furnace. In measuring vapor pressures by the Iinudsen rateof-effusion method, the start and the end of a run are always associated with some uncertainty. This situation was compensated for by making two runs-a short one of 1 hr. and a longer one of 3 to 6 hr.-at the same temperature. It was assumed that the conditions a t the beginning and end of both runs were the same, so in order to get data for calculating the vapor pressure, the weight loss and time of the first run were subtracted from the second.
Results Vapor pressures were measured in the range 384 to 449'. The Knudsen equation for ideal conditions is
where P is the vapor pressure, w is the loss in weight in grams, a is the area of the orifice in cm.*,t is the effusing time in seconds, M is the molecular weight of the effusing species, R is the gas constant, and T is the absolute temperature. For various reasons this equation is usually not directly applicable. Clausing2 has shown that the orifice area must be multiplied by a correction factor in order to take into account the finite length of the hole. Thus the Knudsen equation becomes
nRT
0.0020 0.0040 0,0040
The diameter given is that of a
Copper phthalocyanine, procured from the Du Pont Co., was sublimed in a stream of nitrogen and single crystals of the p form were obtained. These were thoroughly ground in a Wig-L-Bug. The powder was mixed with some crushed Pyrex glass before it was put into the crucible. This was done to avoid caking, although there was no evidence that this precaution was necessary. The cell was placed a t the closed end of a quartz tube of 18-mm. i.d., the other end of which formed one section of a 35/25 ball-and-socket joint. This tube in turn could be connected to a movable vacuum system which reduced the pressure to mm. During a run, the tube containing the cell was placed in a Temco Model 1.515 electric furnace through a specially constructed door. Temperatures were measured with a
act
where PSis the steady-state pressure in the cell and c is the Clausing correction factor. Often the pressure in the effusion cell, as calculated from eq. 2, is less than the vapor pressure because the condensation coefficient of the substance is less than unity and because of the geometry of the cell. These matters have been discussed by Whitman,3a R f ~ t z f e l d t ,and ~ ~ Speiser and S ~ r e t n a k . Stern ~~ and Gregory3d as well as Hildenbrand and Hall3" have evaluated their data by using the Motzfeldt equation and we have done likewise. This involves using the equation
P. Clausing, Ann. Phys., 12, 961 (1932). (3) (a) C. I. Whitman, J . Chem. Phys.. 20, 161 (1952); (b) K . Motsfeldt, J . Phys. Chem., 59, 139 (1955); (c) R. Speiser and J. W . Spretnak, Vacuum Metallurgy Electrothermics and lletallurgy Division of the Electrochemical Society, 1955, pp. 155-160, 186--187; (d) J. H. Stern and N. W. Gregory, J . Phys. Chem.. 61, 1226 (1957); (e) D. L. Hildenbrand and W. F. Hall, ibid., 68, 989 (1964). (2)
Volume 69,Number 1
January 1966
346
NOTES
where a is the condensation coefficient, WA is the Clausing factor for the interior of the cell, and A is the area of the surface of the effusing material. For the cell used in this work WA = 0.5, so eq. 3 reduces to Ps
=
P -
(4)
(&)CUPs
The steady-state pressures and the vapor pressures are given in Table 11. The steady-state pressures were
Table 11: Summary of Pressure Data"
a
T ,OK.
Cell
Pa X 101. mm.
P X 108, mrn.
687 687 685 68 1 717 722 711 702 661 675 661 657 706 698 697 690 700 693
2 2 2 2 5 5 5 5 1 1 1 1
0.602 0.557 0.521 0.354 14.38 16.75 9.70 4.82 0,0860 0.206 0.0940 0.0664 7.81 4.09 3.82 1,708 3.41 2.35
2.09 1.95 1,82 1.23 15.50 17,80 10.46 5.12 0.380 0.910 0.416 0.295 8.30 4.36 4.07 2.14 4.27 2.95
4 4 4 3 3 3
The runs are listed in the order they were made.
calculated using eq. 2, assuming that the copper phthalocyanine was not associated in the vapor phase. The magnitude of 1 / A a was found by plotting PS against caps for the various cells a t one temperature. The points fell on a reasonably good straight line, and thus it seems that a does not change appreciably in the temperature range studied. From the slope of the line the value of 1 / A a was found to be 54 cm.-2. Using this and eq. 4, the values of P were calculated. A plot of log P against 1/T gave a good straight line. A least-squares treatment of the data gives the equation log P,,, = 17.575 - 13900/T with the standard deviation of the slope being 260. Thus for copper phthalocyanine in the range 384-449", the heat of sublimation is 63.6 i 1.2 kcal./niole and the entropy of sublimation (to P = 1 atm.) is 67.2 cal./deg./mole. From 1,lAa it is possible to calculate the condensation coefficient if the area of the solid phase of the effusing material is known, but it is difficult to estimate this when a powder is used. I n this work the nominal T h e Journal of Physical Chemistru
area of the surface was 1.77 If this area is used, a comes out to be about 0.01. Since the true ares is undoubtedly larger than the nominal area, the true value of a is probably less than 0.01. When the crystal structure of copper phthalocyanine is considered, it is not surprising that the condensation coefficient is so low. The molecule is large and flat, and Robertson4 has shown that the planes in adjoining rows of molecules are almost a t right angles to each other. Thus one would expect that in only a small fraction of the collisions the molecule makes with the crystal is the molecular orientation favorable for condensation. (4) J. M. Robertson, J . Chem. Soc., 1195 (1936)
Dynamic Mechanical Properties of Dilute Solutions of Poly-a-methylstyrene
by J . E. Frederick and John D. Ferry Department of Chemistry, University of Wisconsin, Madison, Wisconsin (Received J u l y 25? 1964)
An extensive study of dynamic mechanical properties of dilute polystyrene solutions has been recently reported.' I n this work, viscous solvents were used so the viscoelastic dispersion could be observed in the low audiofrequency range, and measurements a t different molecular weights and concentrations were interpreted by the theories of Zimm,2 R o u s ~ ,and ~ Tschoegl. We now report some additional measurements on poly-a-methylstyrene, undertaken to determine whether the additional steric hindrance of the methyl group would influence the behavior significantly.
Experimental Two samples of poly-a-methylstyrene were generously given us by Dr. P. Rempp of the Centre de Recherches sur les ;\1acromol6culesl Strasbourg. They had been prepared by anionic polymerization and presumably had sharp molecular weight distributions; their weight-average molecular weights, determined a t Strasbourg by light scattering, were 349,000 and 630,000. They were dried in vacuo a t 60" for several (1) J. E. Frederick, N. W. Tschoegl, and J. D. Ferry, J . Phys. Chem., 68, 1974 (1964). (2) B. H. Zimm, J . Chem. Phys., 24, 269 (1956). (3) P. E. Rouse, Jr., i b i d . , 21, 1272 (1953). (4) N. W. Tschoegl, ibid., 40, 473 (1964).
