Dynamics Of Liquid Crystalline Polymers Research Articles

Coarse Brownian dynamics for nematic liquid crystals: Bifurcation, projective integration, and control via stochastic simulation

We demonstrate how time integration of stochastic differential equations (i.e., Brownian dynamics simulations) can be combined with continuum numerical analysis techniques to analyze the dynamics of liquid crystalline polymers (LCPs). Sidestepping the necessity of obtaining explicit closures, the approach analyzes the (unavailable in closed form) “coarse” macroscopic equations, estimating the necessary quantities through appropriately initialized, short “bursts” of Brownian dynamics simulation. Through this approach, both stable and unstable branches of the equilibrium bifurcation diagram are obtained for the Doi model of LCPs and their “coarse stability” is estimated. Additional macroscopic computational tasks enabled through this approach, such as coarse projective integration and coarse stabilizing controller design, are also demonstrated.

Smoothed particle hydrodynamics techniques for the solution of kinetic theory problems Part 1: Method

The smoothed particle hydrodynamics (SPH) technique has been applied to a problem in kinetic theory, namely, the dynamics of liquid crystalline polymers (LCPs). It is a Lagrangian solution method developed for fluid flow calculations; its adaption to kinetic theory is outlined. The Lagrangian formulation of the Doi theory for LCPs is first described, and the problem is presented in the general framework of nonparametric density estimation. The implementation of the SPH technique in this specific problem is given, highlighting particular aspects of our implementation of SPH, including the form of the kernel function and use of an adaptive kernel. We then present results which demonstrate convergence and other details of the solution method, and also make comparisons with other solution techniques and discuss other potential applications.

Relaxation spectroscopy of LC main chain polymers: Experimental and theoretical investigations

AbstractA series of thermotropic main chain polymers with extended dimethylsiloxane segments was investigated. The study of dielectric properties of polymers revealed the relationship between their ability to form a mesophase and their molecular mobility. The peculiar behaviour of dielectric α‐relaxation parameters during the transition from mesomorphic to isotropic members of this polymeric series was shown. The theoretical approaches were developed for understanding macrochain dynamics of liquid crystalline polymers. The theoretical and experimental results are in good agreement.

Structure and Dynamics of Liquid Crystalline Polymers from Deuteron NMR

AbstractThe molecular structures of thermotropic liquid crystalline polymers, which have been synthesized systematically in recent years, are described according to the model of decoupling the molecular motions of the mesogenic groups and the polymer chain by inserting a flexible spacer. The molecular structure is related to the properties of these systems, e.g., phase transition temperatures, mesophases formed, etc. The structure and mobility of a specific side chain, liquid crystalline polyacrylate with phenyl benzoate as a mesogenic group is investigated by deuteron NMR and compared with the behaviour of low molecular weight analogues selectively deuterated at equivalent positions, i.e., at the mesogenic group and at the spacer. The temperature dependence of the order parameter of the mesogenic group indicates significant differences between the intermolecular potential in polymeric liquid crystals and their low molecular weight analogues. The order parameter of the spacer (methylene group adjacent to the polymer chain) is reduced to 50% of the value of the mesogenic group, whereas the equivalent methylene group in the low molecular weight system exhibits a reduction by only 25%. This indicates a substantially higher fraction of gauche‐conformers in the spacer of the polymeric liquid crystal than in the alkyl chains of low molecular weight liquid crystals. In the glassy state the order parameter of the mesogenic group is high, 0.85 and 0.65 for a frozen smectic‐A and a frozen nematic system, respectively. In the glassy state rapid rotational jumps by 180° are observed. This process can be followed by 2H NMR line‐shape analysis down to temperatures 100K below the glass transition.