From The Multi-tensor Model Of Liquid Crystals Based On Molecular Theory To The Frame Dynamics Model Of General Symmetr

Liquid crystal is a non-Newtonian fluid characterized by local anisotropy.The same kind of molecules can form a variety of di?erent liquid crystal phases,including isotropic,nematic,sematic,and cholesteric.Has C_2vsymmetry of liquid crystal molecular structure is relatively complex,can form the C_2v,C_1v,D_2ddi?erent symmetric structure,such as the nematic phase.In this paper,a multi-tensor model based on molecular theory is established and the frame dynamics models of the three nematic phases are derived from the model.Firstly,four order parameters are used to describe the local anisotropy of nematic liquid crystals with C_2vsymmetry.In this paper,based on the Onsager molecular the-ory of liquid crystal,a multi-tensor model is established by the variational method of free energy and the closed approximation with quasi-entropy.This model can be used to describe the phase transition between di?erent liquid crystal phases,which satisfies the energy dissipation of the system,and the coe cient is derived from the molecular parameters,which can reflect the characteristics of liquid crystal molecules to a certain extent.Secondly,the stability points of volume energy in nematic phases with di?erent symmetries are obtained from the minimum volume energy.In this paper,the orientation elasticity of these nematic phases is calculated,and the frame dynamics model is derived from the multi-tensor model based on molecular theory by using the Hilbert expansion method.The model can describe nematic liquid crystals with di?erent symmetries.The frame dynamics model of C_1vsymmetrical nematic phase is obtained by reducing the frame model of C_2vsymmetrical nematic phase.These models also satisfy energy dissi-pation,and the coe cients are derived from molecular-based multi-tensor models,thus having definite physical significance.The quasi-entropy is used to replace the original entropy in the modeling process.They all have the properties of rotation invariance,positive quality,strict convexity,and so on.These properties ensure that the modeling method is reasonable and close to unique,and ensure the energy dissipation of the model.In addition,quasi-entropy largely solves the computational di culties generated by the original entropy form.Since the coe cients of these models are associated with molecular parameters,these models can well reflect the molecular structure and the structure of the liquid crystal phase,and then the relationship between molecules and phase structure can be studied by using these models.