In this paper, a model for the phase change process due to irradiation with an Ultraviolet (UV) light in a mold filled with a viscoelastic fluid in roll-to-roll nanoimprinting lithography is developed. Employing a thermomechanical approach, constitutive equations for the phase change of a mixture of viscoelastic fluid and solid constituents of the polymer are derived. A general model describing phase change that relates both thermomechanics and photochemistry is presented. A function defining the mass fractions of fluid and solid in the mixture is utilized in the thermomechanical description, and the governing equations for the evolution of the fluid and solid mixtures are obtained based on photochemical reactions under UV light. General properties and kinematic equations that impact phase change in terms of material properties and process parameters are obtained. A simplification of the model without sacrificing the underlying physics to make the problem amenable to analysis is put into place. The general model of phase transition is simplified by assuming that the gradient of the displacement, the strain and its time rate, are small; this results in an integro-differential quasilinear system of equations. A numerical scheme is proposed to solve the problem and results from the numerical simulations are presented and discussed.

在本文中，开发了在卷对卷纳米压印光刻中由于在充满粘弹性流体的模具中用紫外线 (UV) 光照射而引起的相变过程模型。采用热机械方法，推导出粘弹性流体和聚合物固体成分混合物相变的本构方程。介绍了一个描述相变的通用模型，该模型涉及热力学和光化学。在热力学描述中利用了定义混合物中流体和固体质量分数的函数，并基于紫外光下的光化学反应获得了流体和固体混合物演化的控制方程。获得了在材料特性和工艺参数方面影响相变的一般特性和运动学方程。在不牺牲基础物理学以使问题易于分析的情况下简化模型。通过假设位移梯度、应变及其时间速率很小，简化了相变的一般模型；这导致了一个积分微分拟线性方程组。提出了一个数值方案来解决这个问题，并提出并讨论了数值模拟的结果。通过假设位移梯度、应变及其时间速率很小，简化了相变的一般模型；这导致了一个积分微分拟线性方程组。提出了一个数值方案来解决这个问题，并提出并讨论了数值模拟的结果。通过假设位移梯度、应变及其时间速率很小，简化了相变的一般模型；这导致了一个积分微分拟线性方程组。提出了一个数值方案来解决这个问题，并提出并讨论了数值模拟的结果。