Constitutive modeling of concentrated solutions of main-chain liquid crystalline polymers

Abstract

Processing of concentrated semi-flexible LCP (liquid-crystalline polymer) solutions is very important from an industrial point of view. In particular, concentrated semiflexible LCP solutions are used in the production of fibers with outstanding mechanical properties. Understanding of the relation between the processing of LCP solutions and the ultimate properties of the fibers requires the development of constitutive models for LCP solutions. Despite the fact that processing of LCP solutions started more than 50 years ago and a lot of research was devoted to the constitutive modeling of these systems, there are still questions to be answered. Some aspects, such as the formation of hairpins and their connection with entanglements in concentrated semi-flexible LCP solutions are still of great interest. However, the introduction of these concepts increases the complexity of the constitutive model and increases the difficulty of studying the rheological properties of LCP solutions. The present thesis deals with the development of the constitutive model for concentrated semi-flexible LCP solutions containing hairpins. Themodel also accounts for the fact that the formation of the hairpins increases the number of entanglements between the chains. The present work combines both, numerical and analytical techniques. We start by formulating the coarse-grained mechanical model for semi-flexible polymer molecule. Then we employ the methods of phase-space kinetic theory for deriving the evolution equation (the Smoluchowski equation) for a single-chain distribution function representing a single polymer chain immersed into the LCP solution. We also involve the concept of the mean-field approximation for the nematic interaction (Maier-Saupe potential) to eliminate the two-chain distribution function. Though the methods of phase space theory are extensively studied, we describe this derivation in detail in order to show explicitly the assumptions involved in this derivation. Next, we reformulate the obtained Smoluchowski equation in terms of the corresponding system of stochastic differential equations (SDEs) in the Stratonovich interpretation. This system of SDEs is used for the analytical study of the unentangled highlyordered concentrated semi-flexible LCP solution containing hairpins in elongational flow. Our results for this limit indicate that for unentangled LCP solutions the presence of hairpins reduces the response functions. We have further developed a numerical code for solving the system of SDEs for the entangled concentrated semi-flexible LCP solutions containing hairpins. Firstly, this code is tested by reproducing the equilibrium properties of the LCP solutions. Secondly, the results of simulations for the elongation flow are compared with the theoretical prediction for unentangled LCP solution. It turns out that results of simulations for unentangled LCP solutions reproduce the theoretical predictions correctly. However, from the simulations for entangled LCPs it follows that the entanglements increase the response functions and become important when the average number of hairpins per chain becomes greater than 1. In addition, we perform simulations of the behavior of the LCP solution under shear. Our model is capable of reproducing the well known dynamical transition and a peculiar dynamics of the director: kayaking, wagging and flow-aligning. From these simulations we also obtain the steady-state shear viscosity, which demonstrates the plateau for intermediate shear rates and the shear-thinning behavior for high shear rates. This is qualitatively in agreement with Asada-Onogi plot for typical LCP solutions. Besides that, our results of simulations for high and medium shear-rates agree with the experimental data by order of magnitude.