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T. P. YIN, S. E. LOVELL AND J. D. FERRY
greater than that by C1,. T ~ =z u4,(N02) and
Consequently, -log
where the small correction factor 6 can be evaluated with acceptable accuracy from the initial reaction conditions. Equation 6 may be finally solved by iteration, using the initial reactant concentrations, the experimentalvalues of (NO2)and (kl,), eq. 7, and a preliminary value of k l / k z . A preliminary value can be determined from eq. 6 by ignoring the exponential term. In this way kl/lc2 was obtained for each set of reaction conditions at the various selected values of reaction time. E o systematic variation in kl/k2 with time was observed. The ratio ICllkz, obtained as described, was found to be 3 f for all experimental variables in the ranges cited earlier. In particular, the temperature variation of kl/kz in the temperature range 500 to 540°K. is less than the limits of error given above. A temperature coefficient for k l / k z was obtained by using only the results of experiments in which the initial rakio (C12)l/(N02)i was about 3, and (XOz), 5 X moles/cc. These concentrations resulted in comparable rates of disappearance of NO, and Clz, and were chosen with the intention of minimizing experimental error. The results of experiments which satisfied the above restrictions are shown in Fig. 2. The estimated limits of error are shown by the symbols used in the figure. The data were fitled visually by a straight line which corresponds to the Arrhenius equation
-
ki
= 2.63
ki
X e3130/RT
(8)
Vol. 65
The individual rate constants kl and kz may be represented by eq. 9 and 10 kl = Ale-QliRT kp = A,e-QziRT
(9) (10)
Then eq. 8 implies that AJA2 = 2.63 and QZ - Q1= 3130 cal. It is known6that Qz lies between 2 and 3 kcal., consequently one obtains Q1 = 0 kcal. and A1/A2 = 2.6. An explicit expression for IC2 has been reported7 which in conjunction with eq. 8 leads to the value IC, = 1013Jcc./mole sec. in the temperature range 500 to 540°K. This value for ICl corresponds to a collision efficiency of about 1 in 20. The results are consistent with the fact that reaction 1involves two free radicals and may be expected to proceed at a rate comparable to the collision rate. The procedure used in deriving klikz is critically dependent on the assumption that the reaction chains are long. For the two-component system HZ--Cl2such a condition undoubtedly obtains. In the case of the system HZ-NO2 the reaction chains are probably shorter than in the case of the system H2--Cl2. The ternary system H ~ C ~ Z - N Owould Z be expected to involve chain lengths intermediate between the values for the individual binary systems. Very long chain lengths for H2-Cl2 will consequently tend to validate the method used in our calculations of Jc1/k2. (6) A. F. Trotman-Dickenson, "Gas Kinetics," Butterworths, London, 1955, p. 185. (7) M. Bodenstein and W. Joat, "Katalyse bei Homogenen Gas Reaktionen," Handbuch der Katalyses (ed. G. M. Schwab) SpringerVerlag, Vienna, Vol. I. 1941, p. 301.
VISCOELASTIC PROPERTIES OF POLYETHYLENE OXIDE IN THE RUBBER-LIKE STATE* BY THEODORE P. YIN, STUART E. LOVELLAND JOHN D. FERRY Department of Chemistry, University of Wisconsin, Madison, Wisconsin Received October 10, 1.960
The viscoelastic properties of a sample of polyethylene oxide, molecular weight 1.15 X lo4, have been studied in the rubber-like state above the melting point. The real and imaginary parts of the complex compliance were measured between 0.04 and 1000 cycles/sec. in the temperature range from 68 t o 120'; the creep compliance was measured at 80 t o loo", including creep recovery a t 100'. The method of reduced variables gave superposed curves for all the data with shift factors which followed the Arrhenius equation with an activation energy of 11.7 kcal./mole. The creep was represented by the Andrade equation with an additional term for steady-state flow, from which the steady flow visc0sit.y was calculated. The relaxation and retardation spectra comprised the plateau and terminal zones. The average spacing between coupling entanglement points was estimated in two ways t o be about 200 chain atoms, of normal magnitude. However, the extremely wide plateau of the relaxation spectrum indicates that the entanglements are unusually tight. Since t.he transition zone lies a t shorter times than those covered in the present experiments, the logarithm of the monomeric friction coefficient a t 100" must be less than - 6.4.
Introduction Most investigations of time-dependent mechanical properties of amorphous polymers have been confined to polyvinyl derivatives whose chain backbones consist solely of carbon atoms and carry pendant side groups. The present study is concerned with polyethylene oxide, whose repeating * Part XXXIV of a series on hbohaniod Prepsrtiea of SubPtaneer et Xl#h BlufoCru~dP\)TPlgh€,
unit is -CHt-CHz-O-. The expectation of a high degree of mobility in configurational rearrangements, due to the oxygen chain atoms and the absence of side groups, has been confirmed. Measurements on the amorphous polymer were limited to a temperature range between 65 (the melting point) and 120" (where degradation set in if the experiments continued more than a day). At the lowest temperature and highest frequency of rneaeire-
March, 1961
VISCOELASTIC PROPERTIES OF POLYETHYLENE OXIDEI N
ment (1000 cycles/sec.) , the transition zone between rubber-like and glass-like consistency was not reached. However, the measurements served to define the viscoelastic properties in the rubber-like plateau and terminal zones. Material and Methods The polymer was kindly furnished by Dr. F. E. Bailey of Union Carbide Chemicals Company.' It was a specially selected sample (138,541-6307) with a viscosity-average molecular weight of 1.15 X lo5 as estimated from the intrinsic viscosity in water a t 30", [?] = 1.11, using the equation of Bailey, Kucera and Imhof .z The melting point was determined by observation under a microscope to be 65O, the density of the amorphous polymer at 70" was 1.077 g./ml., and the thermal expansion coefficient was 6.2 X lo-' deg.-'. The granular polymer was dried in vucuo for 5 weeks a t room temperature. Samples for mechanical measurements were molded a t 78" and annealed for about 3 hours a t 70". To avoid oxidative degradation, which can be rapid a t higher temperatures, all measurements were made in a continuous stream of nitrogen. In the Fitzgerald-Ferry transducer a p p a r a t ~ sthe , ~ level of oxygen was thusreducedto
