Kinetic changes, weight-average molecular

Kinetic Changes in Weight-Average Molecular Weight... 

Equations 4a,b provide means for evaluating the kinetic parameters by combined measurements of the rate and the number average molecular weight. Conversely, if the kinetic parameters have been determined, for example, by measurements of the initial rate as a function of molecular weight, the molecular weight change may be estimated from the more readily measured rate of volatilization. It must be noted in this connection that the coefficients e and a are only approximately constant and independent of C, since they are both functions of the radical concentration R. For the case corresponding to Equation 4a we find (21,26) ... 

A mathematical model for styrene polymerization, based on free-radical kinetics, accounts for changes in termination coefficient with increasing conversion by an empirical function of viscosity at the polymerization temperature. Solution of the differential equations results in an expression that calculates the weight fraction of polymer of selected chain lengths. Conversions, and number, weight, and Z molecular-weight averages are also predicted as a function of time. The model was tested on peroxide-initiated suspension polymerizations and also on batch and continuous thermally initiated bulk polymerizations. 

Since the forcing terms in equation (34) all vanish in this problem, we obtain equation (39), in which for simplicity we shall introduce the further assumption that C = 1—that is, p/t = [see equation (30)]. This assumption (that pp does not vary across the boundary layer) often is reasonable for gases if changes in the average molecular weight are negligible, then— because of the constancy of the pressure—the ideal-gas law implies that p 1/T, in which case constancy of pp corresponds to p T, a dependence close to the kinetic-theory predictions discussed in Appendix E. With C = 1, equation (39) is the Blasius equation [4], F " -F FF" = 0, and in view of equation (28), the boundary conditions implied by equations (48) and (49) are F co) = 1 and F (0) = 0. Use may be made of the present formula for p, C = 1, F (0) = 0, and equations (27) and (29) to ascertain the boundary condition implied by equation (50) the calculation results in... 

Enzyme Kinetics. The change in the number-average molecular weight of gelatin with time was determined as follows. Measurements of viscosity at known concentrations were extrapolated to infinite dilution to obtain the intrinsic viscosity r from Huggins and Kramer s equations,... 

The parallel change of conversion and average molecular weight with increasing energy input is not clear at a glance as it apparently contradicts the normal expectation of radical kinetics. However, an explanation is possible considering the peculiarities of both the pulsed thermal polymerization procedure and the heterophase conditions. 

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