June, 1955
NOTE^
term, and a t the middle of the membrane the amplitude becomes go which is a characteristic of the internal pressure provided k and a are held constant. Hence it is possible to measure the effect of change in the internal pressure by ad‘usting L for self-excited instability and measuring t e new amplitude at 2 = L / 2 . The amplitude or displacement is a function of pkessure. Therefore, it is possible to calibrate a stretched membrane for initial reactant pressure and as the flow reaction progresses resulting in the increase or decrease of pressure, the new displacement can be measured and hence the pressure. Once the pressure is known, the reactiofl velocity can be estimated. Consider the general unimolecular reaction a t constant volume A +rb (15) where y is the number of moles of products formed from the reaction of one mole of A. Ideal gas laws are assumed. Let nAOmoles of A continutously enter the reaction zone per uhit time, n A , the number of moles unreacted after time 0 and passing any given point in the zone per unit time and V , the total volume. Under isothermal cohditions, the rate equation
Studies of relaxation of stress a t constant extension coupled with simultaneous measurements of birefringence provides some interesting insights into polycrystalline polymers and their gels. Very frequently the relaxation of stress at constant extension for such systems (e.g., plasticized polyvinyl chloride) is very slow and the change in birefringence is also very slight.l The crystallites appear to be acting as cross-links which are quite stable with respect to time, Le., they do not break and remake. As the temperature is increased the modulus of the sample decreases, indicating fewer crystallites (hence fewer cross-links). The relative rate of decay of stress is unaffected, however, by the increase in temperature. Very often the decay in stress in polycrystalline polymers or their gels is accompanied by an increase in birefringence, as noted by Stein and Tobolsky,l indicating that the stress decay was caused by a growth and/or orientation of crystallites. I n extreme cases, such as natural rubber held at constant length at -25’ the growth of oriental crystalline material might cause a relatively rapid decay of stress to zero stress followed by an actual lengthening of the sample beyond its stretched length. This phenomenon is called spontaneous el~ngation.~ The birefringence in these cases obviously increases enormously. The behavior of polycrystalline polymers with respect t o simultaneous measurements of stress decay and birefringence is to be sharply contrasted with the behavior of linear amorphous polymers. For linear amorphous polymers in the temperature interval of “rubbery flow,” or in the temperature interval of chemical stress relaxation the decay of stress t o zero stress is paralleled by the decay of birefringence, so that the ratio of stress to birefringence remains constant during the relaxation. Studies have been made of the stress decay of gelatin gels maintained at constant extension.’ It was postulated that this decay was due to a breaking and remaking of bonds between collagen chains acting as temporary cross-links.’ If such were the case, however, it would be expected that the stress decay and birefringence decay would be strictly parallel. However, it has been noted that, even when stress decay in a strained gelatin gel was complete, some double refraction persisted.8 It appears to me that the mechanism postulated for relaxation of gelatin gels, ie., the breaking and remaking of temporary cross-linkages, may not be entirely correct. If crystallites are acting as crosslinkages, they would not make and remake very readily. Part of the stress decay in the gelatin gels may well be due to the further growth of oriented crystalline material, perhaps around already existing nuclei, which would account for the persistence of birefringence after stress decay was complete.
h
1
[-%
=
krna]
Integrating between limits
*I
[h = 2.303 7log nA
Equation 18 can be rewritten in terms of initial and final pressure after a time lapse of e Evaluating pl. by the method outliiied in the beginning, kl can be determined from eq. 19 conveniently, by introducing the flerible membtane at different intervals in the line. The author is indebted to Dr. T. Baron of Shell Developrhent Go., California, for the suggestion of the problem. STRESS RELAXATION, BIREFRINGENCE ,4ND THE STRUCTURE O F GELATIN AND OTHER POLYMERIC GELS BYARTHURV. TOBOLSHY Fraclc Chemrcal Laboratory, Princeton Universafy, P Ianeelon, N . J . Recezved Januaiy 88, 1866
Whenever concentrated or dilute solutions of polycrystalline polymers form gels, there is a strong likelihood that such gels are held together hy crystallites acting as cross-links. This has been shown to be true for polyvinyl chloride, polyacrylonitrile2 and for gelatin.3s4 (1) R. 5. Stein and A. V. Tobolsky, Terlzle Research J . , 18, 302 (1948); abad., 19, 8 (1949). (21 J. B~sschops,J . Polumer Scz., 12, 583 (1054). (3) IC. Heimann and 0. Gerngross, Kautschuk, 8 , 181 (1932). (4) H. Ropdtker and P. Doty, THIR JOURNAL,58, 908 (1054).
575
ls6
( 5 ) C. Park, Rubber Chem. Tech., 12, 278 (1939); G. M. Blown, Ph.D. Thesis, Princeton University, 1948. (6) R . S. Stein, F. H. Holmes and A . V. Tobolsky, J . Polymer Scz., 1 4 , 443 (1954).
(7) M. Miller, J. D. Feiry, F. W. Sclueini>and J. E. Eldtidge, THIS 1387 (1951). ( 8 ) J. D. Ferry, “Advances In Pioteln Cliemistlv,” Vol. I V , Academic Prssa, Inr., New Yolk, N. P.,1048, p. 45.
JOURNAL, 6 6 ,
