Molecular Aspect Ratio Research Articles

Symmetries of the Doi kinetic theory for nematic polymers of arbitrary aspect ratio: at rest and in linear flows.

The Doi theory has successfully modeled the monodomain shear flow problem for rigid, rodlike nematic polymers. Numerical simulations of the Smoluchowski equation for the orientational probability distribution function (PDF) predict monodomain attractors in regions of nematic concentration N and shear rate gamma. Theoretical work has focused on approximate constructions of PDF solutions in linear flow regimes. Here we develop a collection of simple observations, expressed by symmetries of the Smoluchowski equation, which imply global properties that all PDF solutions must obey. The well-known orientational degeneracy of quiescent nematics is a continuous O(3) symmetry. In simple shear, a discrete reflection symmetry survives that is evident in recent numerical simulations and implies bistability of out-of-plane attractors; and rodlike and discotic nematic liquids of reciprocal aspect ratio respond identically up to a fixed rotation of the PDF. Finally, we show the orientational effects due to varying molecular aspect ratio in any linear flow are equivalent to varying the straining component of the flow field.

Monodomain response of finite-aspect-ratio macromolecules in shear and related linear flows

Recent extensions of the Doi kinetic theory for monodisperse nematic liquids describe rigid, axisymmetric, ellipsoidal macromolecules with finite aspect ratio. Averaging and presumed linear flow fields provide tensor dynamical systems for mesoscopic, bulk orientation response, parameterized by molecular aspect ratio. In this paper we explore phenomena associated with finite vs infinite aspect ratios, which alter the most basic features of monodomain attractors: steady vs unsteady, in-plane vs out-of-plane, multiplicity of attracting states, and shear-induced transitions. For example, the Doi moment-closure model predicts a period-doubling cascade in simple shear to a chaotic monodomain attractor for aspect ratios around 3:1 or 1:3, similar to full kinetic simulations by Grosso et al. [Grosso M, Keunings R, Crescitelli S, Maffettone PL (2001), Prediction of chaotic dynamics in sheared liquid crystalline polymers. Preprint (2001) and lecture, Society of Rheology Annual Meeting, Hilton Head, SC, February 2001] for infinite aspect ratios. We develop symmetries of mesoscopic tensor models robust to closure approximations but specific to linear flow fields, and analytical methods to determine: Simulations highlight the degree to which scaling properties of Leslie-Ericksen theory are violated. By varying molecular aspect ratio, any shear-induced monodomain is reproducible among the well-known closure approximations, yet no single closure rule suffices to capture all known attractors and transition scenarios.

A hydrodynamic theory for solutions of nonhomogeneous nematic liquid crystalline polymers of different configurations

A hydrodynamic theory is developed for solutions of nonhomogeneous nematic liquid crystalline polymers (LCPs) of a variety of molecular configurations in proximity of spheroids, extending the Doi kinetic theory for rodlike molecules. The new theory accounts for the molecular aspect ratio as well as the finite range molecular interaction so that it is applicable to liquid crystals ranging from the rodlike liquid crystal at large aspect ratios to the discotic one at small aspect ratios. It also exhibits enhanced shape effects in the viscous stress and warrants a positive entropy production, thereby, the second law of thermodynamics. When restricted to uniaxial symmetry in the weak flow limit, the theory recovers the director equation of the Leslie–Eriksen (LE) theory, but the stress tensor contains excessive gradient terms in addition to the LE stress tensor. The theory predicts that the elastic moduli K1, K2, and K3 obey the ordering K3<K1<K2 for stable, discotic (oblate spheroidal) LCPs in the weak flow limit. The ordering is reversed for rodlike (prolate spheroidal) LCPs. It yields a positive Leslie viscosity α2 (α3) in the flow-aligning (tumbling) regime for oblate (prolate) spheroidal LCPs. Moment averaged, approximate, mesoscopic theories for complex flow simulations are obtained via closure approximations.

Closure approximations for the Doi theory: Which to use in simulating complex flows of liquid-crystalline polymers?

The goal of this article is to determine which closure model should be used in simulating complex flows of liquid-crystalline polymers (LCPs). We examine the performance of six closure models: the quadratic closure, a quadratic closure with finite molecular aspect ratio, the two Hinch–Leal closures, a hybrid between the quadratic and the first Hinch–Leal closures and a recently proposed Bingham closure. The first part of the article studies the predictions of the models in homogeneous flows. We generate their bifurcation diagrams in the (U,Pe) plane, where U is the nematic strength and Pe is the Peclet number, and place special emphasis on the effects of the flow type. These solutions are then compared with the “exact solutions” of the unapproximated Doi theory. Results show the Bingham closure to give the best approximation to the Doi theory in terms of reproducing transitions between the director aligning, wagging and tumbling regimes at the correct values of U and Pe and predicting the arrest of period...

External field induced paranematic–nematic phase transitions in rod-like systems

The external field induced paranematic–nematic phase separation of hard spherocylinder systems is studied using the Onsager and Parsons free-energy functionals. A bifurcation analysis is carried out in the context of the Onsager theory at an infinitesimal external field. The bifurcation concentration is found to decrease with increasing field strength. Below the critical field strength, van der Waals-like loops are found. The molecular aspect ratio dependence of the phase coexistence curves of hard spherocylinders also is investigated. The critical field strength is found to decrease with decreasing aspect ratio. The external field dependence of the order parameter along the paranematic–nematic phase equilibrium curve is also studied.

Computer Simulation of Steady Shear Flow of Liquid Crystals with the Gay-Berne Potential

Computer simulations of steady shear flow of nematic phases are performed using a non-equilibrium molecular dynamics. The SLLOD-type algorithm is applied to the shear flows of Gay-Berne fluids which are nematic in the equilibrium states. Two Gay-Berne potentials with μ = 1, v = 2 and μ = 2, v = 1 are used and both molecular aspect ratios are set equal to 3. In the initial stage of shearing various patterns of the transient behavior are found in the order parameter and orientation angle, according to the initial conditions and shear rate. In the steady state the director is inclined to the flow at a constant angle regardless of the shear rate and the system becomes more highly oriented state. The fluids exhibit shear-thinning in viscosity and non-zero first and second normal stress differences.

Extensional viscosity measurements of dilute solutions of various polymers

Four constant and equal viscosity polymer solutions (Boger fluids) were constructed for comparable elongational property measurements. The common constant viscosity of the solutions was 0.20 Pa s while four polymers were chosen to range from rigid and slender to flexible coiled and enlarged molecules in solution. Comparative elongational measurements on the four solutions in the Newtonian (inelastic) solvents were made with a Rheometrics RFX opposed jet viscometer. The Trouton ratios observed for the polymer solvents and various water—glycerol solutions agreed to within ±30% of the expected Trouton ratio of 3, while the results for the rigid molecules in solution agreed with the Batchelor prediction based on the molecular aspect ratio determined independently for the polymer from light scattering measurements. This paper presents a direct comparison of extensional flow resistance of the several types of polymers: a rod-like polymer, a semi-rigid chain, a compact random coil, and a highly expanded random coil.

A deformation tensor model of liquid crystalline polymers

A new approach is described to obtain dynamical equations for the conformation of a liquid crystalline polymer (LCP). The starting point is kinetic theory, which yields an unwieldy evolution equation for the orientation distribution of molecules associated with a material point of the liquid crystal. The usual approach is to average this integro‐partial‐differential evolution equation for the distribution function and to make use of moment closure approximations in order to obtain a direct moment tensor evolution equation. In the approach proposed herein, the evolution equation for the orientation distribution function is specialized to a particular class of deformations of the LCP. The resulting ordinary differential equation for the remaining degrees of freedom of the deformation is self consistent, in the sense that deformations remain in the designated class. This deformation tensor model is carefully constructed to yield physically sensible dynamics in any flow; however, in tests of the model particular emphasis is placed on the behavior in shear flow. The model displays the complex dynamics of flow aligning, tumbling, log rolling, wagging, etc. that are observed in experiments. Moreover, the model captures the subtle distinctions between flow aligning and tumbling dynamics based on molecular aspect ratio.