A molecular theory of flow alignment and tumbling in sheared nematic liquid crystals

Rheology of oligomer melts in the nematic and isotropic states

Oligomers prepared by chain extension of liquid crystalline monomers are thermotropic. The alignment of liquid crystalline oligomers to shear flow via direct ink write printing is an increasingly popular approach to prepare aligned and 3-D printed liquid crystalline elastomers (LCEs). Here, we are concerned with the contribution of order and thermal history on the rheological properties of liquid crystalline. When the oligomers begin in a polydomain nematic state, the transition to an aligned nematic state occurs gradually over a wide range of shear rates. Conversely, when the oligomers begin in an isotropic state they behave as a Newtonian fluid until a critical shear rate is reached, at which point they align in a critical manner. It is shown that by either decreasing liquid crystalline content or increasing temperature, the viscosity of the oligomer melt decreases while this critical shear rate increases. In addition, the normal stress of oligomers is positive over all shear rates but decreases significantly in magnitude with increasing temperature. By combining the analysis of both temperature and liquid crystalline content, it is demonstrated that the temperature relative to the nematic-isotropic transition temperature is key to the oligomers' unique flow behaviors.

Rheology of liquid crystalline oligomers for 3-D printing of liquid crystalline elastomers

Liquid crystalline monomers can be oligomerized and subsequently 3-D printed to prepare liquid crystalline elastomers (LCEs) with spatial variation of the nematic director to create soft materials that undergo complex shape change when subject to stimulus. Here, we detail the correlation of alignment in 3-D printed LCE on the shear history of the oligomeric ink. This coupling is evident both in the polymerization of sheared LCE samples as well as steady-state rheological experiments that quantify the time-dependent flow behaviors of these complex fluids. Under a steady shear flow, oligomeric LC inks transition from a nematic state with unaligned (polydomain) orientation to a uniaxially aligned (monodomain) nematic phase over a large range of applied strain. After cessation of shear flow, the oligomeric LC inks return the polydomain orientation over approximately 30 minutes. The alignment of liquid crystalline segments in the LCE (and the associated stimuli-response of the materials) is ultimately correlated to the degree of strain applied to the ink.

Shear-Driven Mechanism of Temperature Gradient Formation in Microfluidic Nematic Devices: Theory and Numerical Studies

The purpose of this paper is to show some routes in describing the mechanism responsible for the formation of the temperature difference ΔT at the boundaries of the microfluidic hybrid aligned nematic (HAN) channel, initially equal to zero, if one sets up the stationary hydrodynamic flow vst or under the effect of an externally applied shear stress (SS) to the bounding surfaces. Calculations based on the nonlinear extension of the classical Ericksen–Leslie theory, supplemented by thermomechanical correction of the SS σzx and Rayleigh dissipation function while accounting for the entropy balance equation, show that the ΔT is proportional to the heat flux q across the HAN channel and grows by up to several degrees under the influence of the externally applied SS. The role of vst=ust(z)i^ with a sharp triangular profile ust(z) across the HAN in the production of the highest ΔT is also investigated.

Using Liquid Crystals for In Situ Optical Mapping of Interfacial Mobility and Surfactant Concentrations at Flowing Aqueous-Oil Interfaces

Flow-induced states of fluid interfaces decorated with amphiphiles underlie phenomena such as emulsification, foaming, and spreading. While past studies have shown that interfacial mass transfer, the kinetics of surfactant adsorption and desorption, interfacial mobility, and surfactant reorganization regulate the dynamic properties of surfactant-laden interfaces, few simple methods permit simultaneous monitoring of this interplay. Here, we explore the optical responses of micrometer-thick films of oils (4-cyano-4'-pentylbiphenyl, 5CB) with a liquid crystalline order in contact with flowing aqueous phases of soluble [e.g., sodium dodecyl sulfate (SDS)] or insoluble (e.g., 1,2-dilauroyl-sn-glycero-3-phosphocholine) amphiphiles. We observe the onset of flow of 0.5 mM SDS solutions within a millifluidic channel (area-average velocity of 200 mm/s) to transform a liquid crystal (LC) film with an alignment along the interface normal into a bright birefringent state (average LC tilt angle of 30°), consistent with an initially mobile interface that shears and thus tilts the LC along the flow direction. Subsequently, we observed the LC film to evolve to a steady state (over ∼10 s) with position-dependent optical retardance controlled by gradients in surfactant concentration and thus Marangoni stresses. For 0.5 mM SDS solutions, by using particle tracking and a simple hydrodynamic model, we reveal that the dominant role of the flow-induced interfacial surfactant concentration gradient is to change the mobility of the interface (and thus shear rate of LC) and not to change the easy axis (equilibrium orientation) or anchoring energy (orientation-dependent interfacial energy) of the LC. At lower surfactant concentrations (0.015 mM SDS), however, we show that the LC directly maps flow-induced interfacial surfactant concentration gradients via a change in the local easy axis of the LC. When combined with additional measurements obtained with simple salts and insoluble amphiphiles, these results hint that LC oils may offer the basis of general and facile methods that permit mapping of both interfacial mobilities and surfactant distributions at flowing interfaces.

Dynamics of defects around anisotropic particles in nematic liquid crystals under shear

Nematic multiparticle collision dynamics is used to simulate disclination ring defects around spherocylinders suspended in a liquid crystal. A solvent-solute interaction potential is integrated over a short-time scale by an auxiliary molecular dynamics procedure that updates the translational and angular coordinates of the spherocylinders. For suspended particles with length in the range ∼(60,160)nm and a fixed aspect ratio, this method is able to simulate static defects reported previously in the literature. It also simulates orientation fluctuations of the elongated colloids that exhibit a broad distribution and a slow relaxation rate. Finally, a nematic host driven from equilibrium by shear flow is simulated, and the consequent dynamic behavior of the colloid-defect pair is studied. Defects under shear present significant structural transformations from chairlike disclination rings to extended defects that cover most of the cylindrical surface of the colloid. This effect results from the hydrodynamic torque on the nematic field caused by the distorted flow around the spherocylinder, and it is present for small Reynolds and Ericksen numbers of order unity.

Two-shape-tensor model for tumbling in nematic polymers and liquid crystals

Most, but not all, liquid crystals tend to align when subject to shear flow, while most nematic polymeric liquid crystals undergo a tumbling instability, where the director rotates with the flow. The reasons of this instability remain elusive, as it is possible to find similar molecules exhibiting opposite behaviors. We propose a continuum theory suitable for describing a wide range of material behaviors, ranging form nematic elastomers to nematic polymers and nematic liquid crystals, where the material parameters have meaningful physical interpretations and the conditions for tumbling emerge clearly. There are two possible ways to relax the internal stress in a nematic material. The first is the reorganization of the polymer network, the second is the alignment of the network natural axis with respect to the principal direction of the effective strain. We show that tumbling occurs whenever the second mechanism is less efficient than the first. Furthermore, we provide a justification of the experimental fact that at high temperatures, in an isotropic phase, only flow alignment is observed and no tumbling is possible, even in polymers.

Multi-particle collision dynamics algorithm for nematic fluids

Research on transport, self-assembly and defect dynamics within confined, flowing liquid crystals requires versatile and computationally efficient mesoscopic algorithms to account for fluctuating nematohydrodynamic interactions. We present a multi-particle collision dynamics (MPCD) based algorithm to simulate liquid-crystal hydrodynamic and director fields in two and three dimensions. The nematic-MPCD method is shown to successfully reproduce the features of a nematic liquid crystal, including a nematic-isotropic phase transition with hysteresis in 3D, defect dynamics, isotropic Frank elastic coefficients, tumbling and shear alignment regimes and boundary condition-dependent order parameter fields.

Thermodynamic scaling of dynamic properties of liquid crystals: verifying the scaling parameters using a molecular model

The thermodynamic scaling of molecular dynamic properties of rotation and thermodynamic parameters in a nematic phase was investigated by a molecular dynamic simulation using the Gay-Berne potential. A master curve for the relaxation time of flip-flop motion was obtained using thermodynamic scaling, and the dynamic property could be solely expressed as a function of TV(γτ) , where T and V are the temperature and volume, respectively. The scaling parameter γτ was in excellent agreement with the thermodynamic parameter Γ, which is the logarithm of the slope of a line plotted for the temperature and volume at constant P2. This line was fairly linear, and as good as the line for p-azoxyanisole or using the highly ordered small cluster model. The equivalence relation between Γ and γ(τ) was compared with results obtained from the highly ordered small cluster model. The possibility of adapting the molecular model for the thermodynamic scaling of other dynamic rotational properties was also explored. The rotational diffusion constant and rotational viscosity coefficients, which were calculated using established theoretical and experimental expressions, were rescaled onto master curves with the same scaling parameters. The simulation illustrates the universal nature of the equivalence relation for liquid crystals.

Raman scattering study of phase biaxiality in a thermotropic bent-core nematic liquid crystal

Polarized Raman spectroscopy was used to investigate the development of orientational order and the degree of phase biaxiality in a bent-core mesogenic system. The values of the uniaxial order parameters <P200> and <P400>, and biaxial order parameters <P220>, <P420>, and <P440>, and their evolution with temperature were determined. The temperature dependence of almost all order parameters reveals a second order transition from the uniaxial to biaxial nematic phase with <P220> increasing to ∼0.22 before a first order transition to the smectic-C phase, upon cooling.

Statistical mechanics far from equilibrium: prediction and test for a sheared system

We report the application of a far-from-equilibrium statistical-mechanical theory to a nontrivial system with Newtonian interactions in continuous boundary-driven flow. By numerically time stepping the force-balance equations of a one-dimensional model fluid we measure occupancies and transition rates in simulation. The high-shear-rate simulation data reproduce the predicted invariant quantities, thus supporting the theory that a class of nonequilibrium steady states of matter, namely, sheared complex fluids, is amenable to statistical treatment from first principles.

Determination of rotary diffusivity of poly(n-propyl isocyanate) by molecular dynamics

The rotational dynamics of a nondilute solution of the rodlike polymer poly(n-propyl isocyanate) (PPIC) has been studied on an atomistic model by means of a large-scale classical molecular dynamics investigation. The rotary diffusivity of PPIC in toluene solution has been determined from the Einsteinian diffusion regime of the end-to-end vector on the surface of the unit sphere and has been found to be Dr=10.5x10(5)(+/-2.7) s-1, which falls in the range of the experimental data available. A comparison of molecular dynamics predictions with theoretical and perturbation expansion predictions has also been performed.

Periodic orientational motions of rigid liquid-crystalline polymers in shear flow

The collective periodic motions of liquid-crystalline polymers in a nematic phase in shear flow have, for the first time, been simulated at the particle level by Brownian dynamics simulations. A wide range of parameter space has been scanned by varying the aspect ratio L/D between 10 and 60 at three different scaled volume fractions Lphi/D and an extensive series of shear rates. The influence of the start configuration of the box on the final motion has also been studied. Depending on these parameters, the motion of the director is either characterized as tumbling, kayaking, log-rolling, wagging, or flow-aligning. The periods of kayaking and wagging motions are given by T=4.2(Lphi/D)gamma(-1) for high aspect ratios. Our simulation results are in agreement with theoretical predictions and recent shear experiments on fd viruses in solution. These calculations of elongated rigid rods have become feasible with a newly developed event-driven Brownian dynamics algorithm.

Agreements and disagreements between theories and experiments in nematoviscosity

In this work a set of viscosity data selected from the nematic liquid crystals literature is compared with the currently accepted microscopic (molecular) theories for the nematic viscosity. It is shown that the kinetic theory of Doi [N. Kuzuu and M. Doi, J. Phys. Soc. of Jpn. 52, 3486 (1983)] and the affine transformation theory of Hess [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)] equally predict that Miesowicz's coefficients of a given sample are not independent but, as it has been believed for many years [H. Kneppe, F. Scheneider, and N. K. Sharma, Ber. Bunsenges Phys. Chem. 85, 784 (1981)], they are connected by a linear relationship. Such conjecture gains a strong positive support when it is applied to a set of experimental data that we have collected. However, when these data are used to obtain the values of the parameters used to build these theories, it is found that the values assumed by them are in flagrant disagreement with the physical interpretation that they are supposed to have.

Mesoscopic model for the viscosities of nematic liquid crystals

Based on the definition of the mesoscopic concept by Blenk et al. [Physica A 174, 119 (1991); J. Noneq. Therm. 16, 67 (1991); Mol. Cryst. Liq. Cryst. 204, 133 (1991)] an approach to calculate the Leslie viscosity coefficients for nematic liquid crystals is presented. The approach rests upon the mesoscopic stress tensor, whose structure is assumed similar to the macroscopic Leslie viscous stress. The proposed form is also the main dissipation part of the mesoscopic Navier-Stokes equation. On the basis of the correspondence between microscopic and mesoscopic scales a mean-field mesoscopic potential is introduced. It allows us to obtain the stress tensor angular velocity of the free rotating molecules with the help of the orientational Fokker-Planck equation. The macroscopic stress tensor is calculated as an average of the mesoscopic counterpart. Appropriate relations among mesoscopic viscosities have been found. The mesoscopic analysis results are shown to be consistent with the diffusional model of Kuzuu-Doi and Osipov-Terentjev with the exception of the shear viscosity alpha(4). In the nematic phase alpha(4) is shown to have two contributions: isotropic and nematic. There exists an indication that the influence of the isotropic part is dominant over the nematic part. The so-called microscopic stress tensor used in the microscopic theories is shown to be the mean-field potential-dependent representation of the mesoscopic stress tensor. In the limiting case of total alignment the Leslie coefficients are estimated for the diffusional and mesoscopic models. They are compared to the results of the affine transformation model of the perfectly ordered systems. This comparison shows disagreement concerning the rotational viscosity, whereas the coefficients characteristic for the symmetric part of the viscous stress tensor remain the same. The difference is caused by the hindered diffusion in the affine model case.

Rotational viscosity in a nematic liquid crystal: a theoretical treatment and molecular dynamics simulation

The rotational viscosity coefficient gamma(1) of 4-n-pentyl-4(')-cyanobiphenyl in the nematic phase is investigated by combination of existing statistical-mechanical approaches (SMAs), based on a rotational diffusion model and computer simulation technique. The SMAs rest on a model in which it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMAs, gamma(1) is found to be a function of temperature, density, rotational diffusion coefficient, and a number of order parameters (OPs). The diffusion coefficient and the OPs were obtained from an analysis of a trajectory generated in a molecular dynamics simulation using realistic atom-atom interactions. In addition, a set of experimentally determined diffusion coefficients and OPs was used for evaluation of gamma(1). Reasonable agreement between calculated and experimental values of gamma(1) is obtained. It is shown that near the clearing point gamma(1) is proportional to (-)P22, where (-)P2 is the second-rank OP. This limiting value of gamma(1) is in agreement with mean-field theory.