Phase Separation Kinetics of Rod/Coil Mixtures

Phase Separation and Nematic Order in Lyotropic Solutions: Two Types of Polymers with Different Stiffnesses in a Common Solvent

The interplay of the isotropic-nematic transition and phase separation in lyotropic solutions of two types of semiflexible macromolecules with pronounced difference in chain stiffness is studied by Density Functional Theory and Molecular Dynamics simulations. While the width of the isotropic-nematic two-phase coexistence region is narrow for solutions with a single type of semiflexible chain, the two-phase coexistence region widens for solutions containing two types of chains with rather disparate stiffness. In the nematic phase, both types of chains contribute to the nematic order, with intermediate values of the order parameter compared to the corresponding single component solutions. As the difference in bending stiffness is increased, the two chain types separate into two coexisting nematic phases. The phase behavior is rationalized by considering the chemical potentials of the two components and the Gibbs excess free energy. The geometric properties of the chain conformations under the various conditions are also discussed.

Entropic Unmixing in Nematic Blends of Semiflexible Polymers

Binary mixtures of semiflexible polymers with the same chain length, but different persistence lengths, separate into two coexisting different nematic phases when the osmotic pressure of the lyotropic solution is varied. Molecular Dynamics simulations and Density Functional Theory predict phase diagrams either with a triple point, where the isotropic phase coexists with two nematic phases or a critical point of unmixing within the nematic mixture. The difference in locally preferred bond angles between the constituents drives this unmixing without any attractive interactions between monomers.

Demixing by a Nematic Mean Field: Coarse-Grained Simulations of Liquid Crystalline Polymers

Liquid crystalline polymers exhibit a particular richness of behaviors that stems from their rigidity and their macromolecular nature. On the one hand, the orientational interaction between liquid-crystalline motifs promotes their alignment, thereby leading to the emergence of nematic phases. On the other hand, the large number of configurations associated with polymer chains favors formation of isotropic phases, with chain stiffness becoming the factor that tips the balance. In this work, a soft coarse-grained model is introduced to explore the interplay of chain stiffness, molecular weight and orientational coupling, and their role on the isotropic-nematic transition in homopolymer melts. We also study the structure of polymer mixtures composed of stiff and flexible polymeric molecules. We consider the effects of blend composition, persistence length, molecular weight and orientational coupling strength on the melt structure at the nano- and mesoscopic levels. Conditions are found where the systems separate into two phases, one isotropic and the other nematic. We confirm the existence of non-equilibrium states that exhibit sought-after percolating nematic domains, which are of interest for applications in organic photovoltaic and electronic devices.

Polydomain growth at isotropic-nematic transitions in liquid crystalline polymers

We studied the dynamics of isotropic-nematic transitions in liquid crystalline polymers by integrating time-dependent Ginzburg-Landau equations. In a concentrated solution of rodlike polymers, the rotational diffusion constant D(r) of the polymer is severely suppressed by the geometrical constraints of the surrounding polymers so that the rodlike molecules diffuse only along their rod directions. In the early stage of phase transition, the rodlike polymers with nearly parallel orientations assemble to form a nematic polydomain. This polydomain pattern, with characteristic length ℓ, grows with self-similarity in three dimensions over time with an ℓ~t(1/4) scaling law. In the late stage, the rotational diffusion becomes significant, leading to a crossover of the growth exponent from 1/4 to 1/2. This crossover time is estimated to be on the order of t~D(r)(-1). We also examined the time evolution of a pair of disclinations placed in a confined system by solving the same time-dependent Ginzburg-Landau equations in two dimensions. If the initial distance between the disclinations is shorter than some critical length, they approach and annihilate each other; however, at larger initial separations, they are stabilized.

Nematic-isotropic spinodal decomposition kinetics of rodlike viruses

We investigate spinodal decomposition kinetics of an initially nematic dispersion of rodlike viruses. Quench experiments are performed from a flow-stabilized homogeneous nematic state at a high shear rate into the two-phase isotropic-nematic coexistence region at a zero shear rate. We present experimental evidence that spinodal decomposition is driven by orientational diffusion, in accordance with a very recent theory.

Hydrodynamic theories for mixtures of polymers and rodlike liquid crystalline polymers

We develop a hydrodynamic theory for flows of incompressible blends of flexible polymers and rodlike nematic polymers (RNPs) or rodlike nematic liquid crystal polymers (RNLCPs) extending the thermodynamical theory of Muratov and E [J. Chem. Phys. 116, 4723 (2002)] for phase separation kinetics of the blend. We model the flexible polymer molecules in the polymer matrix as Rouse chains and assume the translational diffusion of the molecules is predominantly through the volume fraction of the flexible polymer and the molecules of rodlike nematic liquid crystal polymers. We then (i) derive the translational flux for the rodlike nematic liquid crystal polymers to ensure the incompressibility constraint; (ii) derive the elastic stress tensor, accounting for the contribution from both the rodlike nematic polymer and the flexible polymer matrix, as well as the extra elastic body force due to the nonlocal intermolecular potential for long range molecular interaction; (iii) show that the theory obeys positive entropy production and thereby satisfies the second law of thermodynamics. By applying the gradient expansion technique on the number density function of RNLCPs, we present an approximate, weakly nonlocal theory in differential form in which the intermolecular potential is given by gradients of the number density function of the RNLCP and the volume fraction of the flexible polymer. In the approximate theory, the elastic stress is augmented by an extra stress tensor due to the spatial convection of the macroscopic material point and long range interaction, whose divergence yields the analogous extra elastic body force with respect to the nonlocal intermolecular potential. Finally, we compare the model in steady simple shear with the Doi theory for bulk monodomains of rodlike nematic polymers.

Relaxation Processes in Semidilute Solutions of Polymers in Liquid Crystal Solvents

We investigate the relaxation phenomena in a polymer (polystyrene)/liquid crystal (4-cyano-4'-n-octyl-biphenyl) system, in its homogeneous isotropic phase near the isotropic-isotropic, isotropic-nematic, and isotropic-smectic coexistence curve, using both polarized and depolarized photon correlation spectroscopy (PCS). We study this system for different polystyrene molecular weights (4750, 12 500, and 65 000 g/mol), different compositions (50, 40, 30, and 10% polystyrene (PS) by weight), and different temperatures close to phase boundaries. First of all, we determine the phase diagrams of this system for the different molecular weights. The shape of the phase diagrams strongly depends on the molecular weight. However, in all cases, at low temperatures, these systems separate into an almost pure liquid crystalline (LC) phase and polystyrene-rich phase. PCS measurements show that the relaxation processes in the homogeneous phase are not affected by the proximity of the nematic, or smectic, boundaries (even at a temperature of 0.1 degrees C above the phase separation in two phases). In polarized PCS experiments, we always see three relaxation processes well separated in time: one, very fast, with a relaxation time of the order of 10(-5) s; a second one with a relaxation time within the range 10(-2)-10(-3) s; and a last one, very slow, with a relaxation time of the order of 1 s. Both the fast and slow modes are independent of the wave vector magnitude, while the intermediate relaxation process is diffusive. In depolarized PCS experiments, the intermediate mode disappears and only the fast and slow relaxation processes remain, and they are independent of the magnitude of the wave vector. The diffusive mode is the classical diffusive mode, which is associated with the diffusion of polymer chains in all polymer solutions. The fast mode is due to the rotational diffusion of 4-cyano-4'-n-octyl-biphenyl (8CB) molecules close to polystyrene chains (transient network). Finally, we assign the slowest mode to reorientational processes of small aggregates of PS chains that are not dissolved in 8CB.

Nematic-amorphous polymer interfaces in the presence of a compatibilizer

We introduce and apply a variant of a dynamic self-consistent field simulation in two dimensions to predict the structure of interfaces between a nematic and an amorphous polymer compatibilized by a diblock copolymer. First, we investigate the effect of the nematic order on the polymer polymer interface without compatibilizer. Then we include the compatibilizer and consider two interfacial setups previously used in experiments, i.e., the bilayer setup and the trilayer setup. In the bilayer setup the diblock copolymer is mixed into the amorphous homopolymer and migrates to the interface in the course of the simulation forming a layered structure. We compare the amount of copolymer at the interface for initial concentrations of the copolymer below and above the critical micelle concentration. In the trilayer setup the initial thickness of the diblock copolymer is varied. The resulting interfacial morphology evolves in the competition between the lamellar structure induced by the interface and a micellar structure, which is intrinsic to the copolymer.

Pattern formation driven by nematic ordering of assembling biopolymers

The biopolymers actin and microtubules are often in an ongoing assembling-disassembling state far from thermal equilibrium. Above a critical density this leads to spatially periodic patterns, as shown by a scaling argument and in terms of a phenomenological continuum model, which meets also Onsager's statistical theory of the nematic-to-isotropic transition in the absence of reaction kinetics. This pattern forming process depends much on nonlinear effects and a common linear stability analysis of the isotropic distribution of the filaments is often misleading. The wave number of the pattern decreases with the assembling-disassembling rate and there is an uncommon discontinuous transition between the nematic and periodic states.

Effect of ordering on spinodal decomposition of liquid-crystal/polymer mixtures

Partially phase-separated liquid-crystal/polymer dispersions display highly fibrillar domain morphologies that are dramatically different from the typical structures found in isotropic mixtures. To explain this, we numerically explore the coupling between phase ordering and phase-separation kinetics in model two-dimensional fluid mixtures phase separating into a nematic phase, rich in liquid crystal, coexisting with an isotropic phase, rich in polymer. We find that phase ordering can lead to fibrillar networks of the minority polymer-rich phase.