Physics of Directional Polymer Crystallization

Abstract

It has been proposed that the nonisothermal directional crystallization of a polymer driven by a moving sink has an exact analogy to an equivalent isothermal crystallization protocol. We show that this is substantially true because polymers are poor thermal conductors; thus, polymer crystallization occurs over a relatively narrow spatial regime, while the thermal gradients created by this freezing occur over a much broader scale. This separation of scales allows us to replace the crystallization process, which is spatially distributed, with an equivalent step. The temperature at this step, which corresponds to the desired equivalent isothermal crystallization temperature, scales linearly with sink velocity. However, a few metrics, such as the Avrami exponent characterizing the kinetics of crystallization are very different in the two cases. These findings provide new insights into the physics of these spatially varying crystallization protocols and should inspire new experiments to probe the underlying equivalences more deeply.

Directional polymer crystallisation with a fast-moving sink

“…2a illustrates a representative case for small sink velocity behavior which was studied in detail in our previous works. [6][7][8] It can be seen from Fig. 2 that the crystallinity is fully developed, and the temperature to the left of the sink plateaus to the sink temperature.…”

“…From the above discussion, it is clear that the transition happens when z i – z s and δ bl are of the same order. Mathematically, using the scales for z i – z s and δ bl developed earlier, 8 we can writeThus, the transition from complete to incomplete crystallisation happens when .…”

“…In this work, we extend our recent analytical–numerical modeling of directional polymer crystallisation under a slowly moving heat sink, 8 to instead focus on the high sink velocity regime. Numerical simulations show that polymer crystallisation changes from a complete to a partial crystallisation behavior as we go from low to high sink velocities, i.e.…”

“…In this work, we extend our recent analytical-numerical modeling of directional polymer crystallisation under a slowly moving heat sink, 8 to instead focus on the high sink velocity regime.…”

“…This equivalence in the two disparate protocols was seen not only in the equal crystal growth rates from the two methods, but also in crystal structural parameters such as the long period and the degree of crystallinity. To understand this surprising equivalence, in our recent works, [6][7][8] we considered the directional crystallisation of a polymer melt under a moving sink (analogous problem to ZA protocol) and explored the crystallisation behavior by combining theory and numerical simulations. The results from these studies showed the existence of a steady state characterized by a constant distance between the sink and the solid-melt interface and a linear relationship in the steady state between the sink velocity and the local temperature in the sample where crystallisation primarily occurs.…”