Polymers, kinetic modeling statistical approach

Numerous reports are available [19,229-248] on the development and analysis of the different procedures of estimating the reactivity ratio from the experimental data obtained over a wide range of conversions. These procedures employ different modifications of the integrated form of the copolymerization equation. For example, intersection [19,229,231,235], (KT) [236,240], (YBR) [235], and other [242] linear least-squares procedures have been developed for the treatment of initial polymer composition data. Naturally, the application of the non-linear procedures allows one to obtain more accurate estimates of the reactivity ratios. However, majority of the calculation procedures suffers from the fact that the measurement errors of the independent variable (the monomer feed composition) are not considered. This simplification can lead in certain cases to significant errors in the estimated kinetic parameters [239]. Special methods [238, 239, 241, 247] were developed to avoid these difficulties. One of them called error-in-variables method (EVM) [239, 241, 247] seems to be the best. EVM implies a statistical approach to the general problem of estimating parameters in mathematical models when the errors in all measured variables are taken into account. Though this method requires more information than do ordinary non-linear least-squares procedures, it provides more reliable estimates of rt and r2 as well as their confidence limits. 

A considerable advantage of the axiomatic approach is its universality (for instance, the author previously succeeded in developing the kinetic statistic theory of molecular weight distributions of polymers formulated according to the model for the axiomatic theory [6]). Moreover, in the initial stage of the... 

The model of the ideal gas ignores intermolecular interactions. Given some intermolecular interactions, statistical mechanics must be employed to obtain the equation of state of the real fluid. For fluids of high density, approximations are necessary, but these naturally evolve from the formal, general statistical mechanical framework. For polymers in bulk, the present theories are of the kinetic theory variety since they do not, in principle, relate all macroscopic properties to the constituent molecular properties. In approaching a statistical mechanical theory of polymers in bulk, we can first ask if we can learn from these successes in the statistical mechanics of gases. One way to accomplish this is to consider a bulk polymer situation whicli simulates as closely as possible ideal gas situations. This model illustrates the following ... 

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