A thermomechanical and photochemical description of the phase change process in roll-to-roll nanoimprinting lithography

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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.