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.

中文翻译：

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定向聚合物结晶物理

有人提出，由移动水槽驱动的聚合物的非等温定向结晶与等效的等温结晶方案具有精确的相似性。我们证明这基本上是正确的，因为聚合物是不良的热导体。因此，聚合物结晶发生在相对狭窄的空间范围内，而由这种冻结产生的热梯度发生在更广泛的范围内。这种尺度分离使我们能够用等效的步骤替换空间分布的结晶过程。此步骤的温度对应于所需的等效等温结晶温度，与下沉速度成线性关系。然而，在这两种情况下，一些指标，例如表征结晶动力学的 Avrami 指数是非常不同的。