A general linear-viscoelastic theory for nearly monodisperse flexible linear polymer melts and concentrated solutions and comparison of theory and experiment

A Semi‐Microscopic Modeling for Polymer Flow Reactors

“…Note that the effects of such a subtle disparity in the description of polymerization cannot be revealed in a traditional type of modeling that concerns only average molecular weights, and the following discussion should provide a simple explanation of the results of comparison. With the same M n and M w , the GEX distribution function, in general, leads to a slightly higher polymer viscosity than does its Gauss counterpart on the basis of Equation (12)- (16). According to the correlation relationship discussed earlier, a higher polymer viscosity would lead to a lower heat transfer coefficient and thus a higher local fluid temperature.…”

“…To account for the contributions from various relaxation modes of an individual chain as well as from a polydispersity in the weight distribution for a polymer melt, the following formulation has been established: [16][17][18][19][20][21] GðtÞ ¼ G A ðtÞ þ G B ðtÞ þ G c ðtÞ ð 13Þ…”

“…Figure 6. Comparison of the predicted temperature profile between Monte Carlo-based simulation and the ones utilizing moment equations together with two different weight distributions; in all cases, polymer viscosity is computed self-consistently using Equation (12)- (16). Experimental data for LDPE and the prediction based on moment equations together with the empirical equations for evaluating polymer viscosity are also shown for comparison.…”

“…That is, for the latter cases, the moment equations were first solved to obtain the required average molecular weights, and then a specific distribution function was assumed to obtain a detailed weight distribution. In all cases, the polymer viscosity necessary for solving both the momentum and thermal-energy equations is self-consistently evaluated on the basis of Equation (12)- (16). In this comparison, one sees that the prediction is rather sensitive to the way by which the reaction is solved or the weight distribution is modeled.…”

“…For such a purpose, the nonisothermal polymer kinetic theories established by Curtiss and Bird [27] may serve as a useful starting point for molecularly modeling the thermal transport. The constitutive equations, Equation (12)- (16), employed here may also be replaced by stochastic simulation models that bear no closed-form solutions, examples being the models recently developed for simulating the rheologies of both linear [28] and pom-pom branched [29] polymer melts. At such a level of modeling, in fact, the coupling between reaction and various transport mechanisms should become even clearer.…”