Modeling of polymer crystallization in plates, pipes, and rods during cooling

Abstract

ABSTRACT:We modeled crystallization of isotactic polypropylene inside plates, rods, and pipes during cooling. The modeling was based on the solution of the heat conduction equation, which takes into account the liberation of the heat of crystallization. The predictions of polymer crystallization kinetics was based on differential scanning calorimetry data and on spherulite growth rate measurements. The influence of size on the crystallization process was determined.

Modeling of polymer crystallization in a temperature gradient

“…Therefore, the conversion degree at a certain time t is expressed by the classic equation, α( t ) = 1 − exp[− E ( t )], with E denoting the extended volume or expectancy. An earlier treatment of the problem by Kolmogoroff7 is based on an inaccurate approach: the errors made in his derivation accidentally cancel one another, leading to the correct result 8…”

New Possibilities in the Description of Overall Crystallization of Polymers

“…[22] , we apply the heat conduction equation for the plate of thickness d, quenched from initial temperature T 0 to temperature T e , with heat production inside described by a function A(x,t), dependent on the x coordinate (0 , x , d) and time t. We assume that the temperatures of plate surfaces are changed rapidly from T 0 to T e , i.e., no thermal resistance at the boundary is taken into account. It is necessary to take into account the cooling conditions and also the liberation of heat of crystallization, dependent on the conversion rate, latent heat of fusion, and crystallinity level of spherulites.…”

“…In a rod of radius equal to the wall thickness of the pipe, the temperature decrease is faster than within the pipe. [22] . 13.…”

“…13. [22] . An increase of the thickness leads to a markedly higher crystallization temperature, as demonstrated in Fig.…”

“…Moreover, the model allows not only the conversion of melt into spherulites to be predicted but also the development of interspherulitic boundaries, thus giving some insight into microstructure. [21] We also propose an approach to solidification in thick-walled products [22] based on a combination of the solution of the heat conduction equation, in a form appropriate for the considered article geometry, with modeling of nonisothermal crystallization based on the analytical conversion rate equation and the experimental data. [21] We also propose an approach to solidification in thick-walled products [22] based on a combination of the solution of the heat conduction equation, in a form appropriate for the considered article geometry, with modeling of nonisothermal crystallization based on the analytical conversion rate equation and the experimental data.…”