The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids

The ratio UT of all mechanical and electrical relaxation times at temperature T to their values at a reference temperature T. can be expressed, after suitable choice of T., by the equation log UT = -8.86 ( T - Ta)/( 101.6 + T - Ts). Over a T range of T, rt 50", this applies to a wide variety of polymers, polymer solutions, organic glass-forming liquids, and in- organic glasses. If, alternatively, the reference temperature is chosen as T,, then log UT - 17.44 ( T - Tg)/(51.6 + T - TE). Above T. + 50 (or T, + 100) the equa- tion fails because different systems show specific properties which are no longer dominated by the non-specific behavior associated with supercooling and vitrification. The apparent activation energy for relaxation processes, unlike UT, is not a universal function of T - T. or T - T,. Our empirical equations are shown to be consistent with earlier formulations of Fox and Flory, Tobolsky, Dienes and Bueche over limited temperature ranges. Comparison with a simplified version of Doolittle's free space equation for temperature dependence of viscosity shows that our empirical constants are determined by the increase in thermal expansion coefficient at the glass transition temperature and the fractional free volume at that point. deg.-], in rather good agreement with experimental measure- ments, and 0.025, a reasonable value. As chosen, T. lies about 50' above the glass transition temperature T,. The latter quantities are calculated to be 4.8 X The reaction between mesitylene and bromine in carbon tetrachloride solution is catalyzed by iodine bromide. At low concentrations of mesitylene the rate of disappearance of bromine is second order in iodine bromide, first order in bromine and fust order in mesitylene. At concentrations of mesitylene above 1 M the effect of increasing mesitylene concentration on the rate of reaction may be explained on the basis that both free and complexed iodine bromide act as a catalyst for the conversion of a 1-1 mesitylene-bromine complex to ring substituted bromomesitylene.