Molecular Dynamic Simulation of Side-Chain Liquid Crystalline Elastomer

Summary: Molecular dynamic simulation of side chain liquid crystalline elastomer has been carried out. As an initial state a flexible polymer network in a low molecular liquid-crystal (LC) solvent was used. The LC solvent comprises of anisotropic rod-like semiflexible linear molecules (mesogens) composed of particles bonded into the chain by FENE potential. Rigidity of LC molecules was induced by a bending potential. All interactions between nonbonded particles are described by a repulsive Lennard-Jones potential. For the systems with different values of density and order parameter obtained after sufficiently long trajectory the attachment of ends of mesogens to the polymer network was simulated. The kinetic of the process of mesogens attachment to network was studied as well as morphology of attachment. The structural and dynamical behaviour of side chain LC elastomer was studied and compared with systems of polymer network in low molecular LC solvent.     

A density functional approach to retention in chromatography with chemically bonded phases

A density functional approach to the retention in a chromatography with chemically bonded phases is developed. The bonded phase is treated as brush built of grafted polymers. The chain molecules are modelled as freely jointed spheres. Segments of all components interact with the surface via the hard wall potential whereas interactions between the segments are described by Lennard-Jones (12-6) potential. The structure of the bonded phase is investigated. The distribution of different solutes in the stationary phases is determined. An influence of the following parameters on the retention is analyzed: the grafting density, the grafted chains length, the strength of molecular interactions, the solute sizes, temperature. The theoretical predictions are consisted with numerous experimental results.     

Blue phase stability of n-OCB homologue chiral nematic liquid crystal mixtures

Blue phase (BP) stability of a chiral nematic liquid crystal (LC) mixture is dependent upon chemical structure as well as physical properties. In this study, the blue phase temperature range dependent on alkyl chain length was investigated in order to evaluate the relationship between blue phase stability and the molecular structures of four kinds of 4-n-alkyloxy-4'-cyanobiphenyl (n-OCB) homologue chiral nematic LC mixtures composed of rod-like nematic LCs. It was confirmed that the blue phase temperature range was strongly dependent upon the molecular parity, K ₃₃/K ₁₁ and the helical twist power of the n-OCB homologues chiral nematic LC mixtures.     

Lyotropic liquid crystalline phase behavior of amphiphilic monomers and polymers having a rod-like hydrophobic moiety

Distinct changes in the lyotropic mesophase behaviour of nonionic polyethyleneglycol containing amphiphiles are observed, when rigid, rod-like molecular units are introduced into the hydrophobic part of these amphiphiles, or when the amphiphiles are added as side chains to poly(methylhydrogene siloxane), yielding amphiphilic side chain polymers. Low molar mass amphiphiles with a dominating rigid, rod-like hydrophobic unit form planar-like micelles which aggregate into lamellar mesophases. Compared with their corresponding low molar mass amphiphiles, amphiphilic side chain polymers show a distinct stabilization of mesophases composed of anisometric micelles, i.e. hexagonal H₁-phases (built up by rod shaped micelles), and lamellar L -phases (built up by planarshaped micelles). In addition, several of the polymeric amphiphiles exhibit the formation of a lyotropic nematic N_c-phase regime. Optically isotropic I₁-phases composed of approximately spherical-like micelles are, on the other hand, disfavoured by the polymerfixation. Investigations of monodisperse amphiphilic side chain oligomers reveal a linear relationship between the thermal stability of the individual mesophases and the logarithm of the degree of polymerization. Changes in mesophase behaviour, due to the introduction of rigid, rod-like molecular units into the hydrophobic part of the low molar mass amphiphiles, are ascribed to packing restraints of the amphiphiles in the micelles. Alterations in mesophase behaviour which occur as a consequence of polymerfixation are discussed in terms of changes in micellar kinetics, packing restraints, and changes in the interaction between adjacent hydrophobic layers of neighbouring micelles.     

Molecular Dynamic Simulation of Side-Chain Liquid Crystalline Elastomer Under Load

Summary: We present a molecular dynamic simulation of a side chain liquid crystalline elastomer (LCE) under load. The LCE is composed of a flexible tetrafunctional diamond like network with rod-like mesogens attached to the network. As a precursor of the LC elastomer a flexible polymer network in a low molecular liquid-crystal (LC) solvent was used. The phase behavior of the LCE under uniaxial stretching up to the deformations of λ = 1.5 and 2.0 at different densities was studied. As in the non-stretched case upon density increase an isotropic to nematic phase transition occurs. However, in contrast to thermotropic side chain LC elastomers the stress induced shift transition is not observed. The stretching slightly increases the anisotropy of translational diffusion of mesogens in the nematic state. The stress-strain dependence for LCE both in the isotropic and the nematic states is obtained. Elastic modulus increases at high values of order parameter.     

Theory of a helicoidal cholesteric phase induced by an external field

We present a mean field theory to describe a helicoidal cholesteric phase for mixtures of a chiral nematic liquid crystal (LC) and a polymer chain as well as for pure chiral nematic LC molecules in the presence of a longitudinal external field parallel to the pitch axis of a cholesteric (Ch) phase. The free energy of the helicoidal Ch phase (Ch_H) is derived as a function of a usual orientational order parameter and an order parameter of the Ch_H phase. On increasing the strength of the external field, we find that the Ch phase changes to the nematic (N) phase through the Ch_H phase. Depending on the temperature and the strength of the external field, we find the second-order N–Ch_H and Ch_H–Ch phase transitions and the first-order paranematic (pN)–N, pN–Ch_H and pN–Ch phase transitions. We also predict phase diagrams in mixtures of a flexible polymer and a Ch LC molecule under the external field.     

Phase behavior of polymer mixtures with nonadditive hard-sphere potential

The phase behavior of a binary mixture of homopolymers in which macromolecules are composed of tangent hard spheres was studied. The interaction of unlike units is characterized by the contact distance (1/2)(σ_A + σ_B)(1 + Δ), where σ _i is the diameter of the ith sphere (unit) and Δ is the nonadditivity parameter. The effect of nonadditivity was taken into account by means of the perturbation theory relative to the additive system (Δ = 0) considered earlier (Polymer Science, 47, 2146 (2005)) in terms of the Percus-Yevick approximation. The theoretical consideration presented is completely analytical. It was found that a polymer mixture experiences phase separation with an increase in pressure; the two-phase region extends with an increase in both the size ratio between the units α = σ_A/σ_B and the length of the chain per se. Closed phase diagrams were first predicted for athermal mixtures; such diagrams appear at Δ < 0 and certain values of α. It was shown that the thermodynamics of an incompressible mixture of hard-chain molecules at α = 1 follows the Flory-Huggins theory with the temperature-independent interaction parameter. Phase separation in polymer solutions with the nonadditive hard-sphere potential was also analyzed.     

Influence of meta-extended rigid-core,complementary hydrogen bonding and flexible chain on polymorphism in Schiff-base liquid crystals: (4)MeOBD(3)AmBA:nOBAs

ABSTRACT

Schiff-base complementary hydrogen-bonded liquid crystals (HBLC), viz., (4)_MeOBD(3)_AmBA:nOBAs with flexible chain length for n = 3,4,5,6,7,8,9,10,11 and 12 are reported. ¹H; ¹³C-NMR and Infra-Red spectroscopy used to confirm the formation of HBLCs. LC phases and transition temperatures (T_c) determined by polarised optical microscopy (POM) and differential scanning calorimetry (DSC). T_c and enthalpy (?H) determined by DSC also. Odd-Even effect observed at clearing and melting transitions. Influence of Schiff base and Oxygen as bridging atom promote smectic phase abundance. HBLCs exhibit tetra- or penta-phase variance. Maximum (penta) phase variance is exhibited by n = 8 and 12 with long flexible chain. Prevalent abundance of quasi-two-dimensional (2D) LC phases of SmF and SmI is observed. Nematic phase is quenched. Lower (n = 4) and intermediate (n = 6) members exhibited SmB_cryst phase. Predominant occurrence of enantiotropic LC phases is noticed. All members exhibited 3D tilted SmG phase. A-C transition exhibited by intermediate homologues (for n = 7, 8, 9 and 10) is found to be either second order or with very small enthalpy. Phase diagram reveals the abundance of multi-critical points with LC phasesinvolving exotic symmetries. Influence of meta-extended rigid core, complementary HB and flexibility is studied for the LC phase abundance with characteristic structural order. POM and DSC results are discussed in the wake of reports in other achiral calamitic LCs.     

Viscoelasticity of dilute chain-molecule solutions: Evaluation of hydrodynamic interaction

The viscoelastic properties of chain molecules varying in flexibility and length have been calculated by use of the bead-spring model theory of Zimm. In the evaluation of the hydrodynamic interaction parameter, the number of springs in the bead-spring model, N, has been selected from the range in which the properties predicted by the theory are insensitive to the value of N. The results for limiting viscosity number agree with those predicted by the Yamakawa–Fujii theory of the limiting viscosity number of wormlike chains. The theory also fits the experimental data of Johnson on a sample of polystyrene of molecular weight 860,000 in theta solvents at infinite dilution. The viscoelastic properties of some moderate molecular weight deoxyribonucleic acid solutions are predicted to deviate from the non-free-draining behavior toward the free-draining behavior.     

Rényi entropy of the U(3) vibron model

Rényi entropies and variances are determined in the vibron model. They provide a sharp detector for the quantum (shape) phase transition (from linear to bent) at the critical value ξ _c of a control parameter ξ. Numerical results are complemented and compared with a variational approximation in terms of parity-symmetry-adapted coherent (Schödinger’s catlike) states, which provide a good approximation to describe delocalization properties of the ground state of vibron models across the critical point for N-size molecules.     

Macromolecule-Induced Clustering of Hard Spheres

The connectivity Ornstein-Zernike formalism, together with the polymer reference interaction site model (PRISM), is employed to describe connectivity and network formation in mixtures of spheres and polymers. Results are presented for the percolation of spheres induced by both flexible coil-like and rigid rod-like linear polymers; the Percus-Yevick (PY) approximation is used throughout. Our results are compared with predictions based on the adhesive hard sphere (AHS) model, and correlations with the polymer-mediated second virial coefficient between spheres are discussed. Copyright 2001 Academic Press.     

Effect of persistent flexibility on the isotropic, nematic and columnar ordering in a self-assembling system

Concentrated solutions of reversibly assembling amphiphilic molecules often exhibit a variety of liquid-crystalline mesophases due to the asymmetry of their aggregates. For strongly elongated rod-like micelles flexibility may significantly influence the relative stability of these phases. This question is addressed for a simple model for a self-assembling system of monodisperse linear rod-like aggregates which are considered to be persistent flexible. Analogously to a recent calculation for a self-assembling system in which the rod-like aggregates are assumed to be perfectly rigid, persistent flexible aggregates may exhibit the same isotropic-nematic-columnar progression of phases. However, increasing the flexibility reduces the concentration range over which the nematic phase is stable. For sufficiently flexible aggregates the nematic phase is abandoned altogether and a direct isotropic-columnar transition occurs.     

Adsorption of short heteropolymers in slitlike pores

Adsorption of short linear heteropolymers in slitlike pores is studied using the density functional theory and Monte Carlo simulations. The molecules are assumed to be freely jointed tangent hard spheres. The segments have different affinity with regard to the walls. Each molecule contains one surface-binding segment that interacts with the walls via Lennard-Jones (3,9) potential and a number of segments interacting with surfaces via the hard-wall potentials. A position of the surface-binding segment in the chain can be arbitrarily chosen. We have studied the influence of the pore width, the chain length and the chemical structure of molecules on adsorption and the microscopic structure of the confined fluid. The theoretical predictions are compared with Monte Carlo simulations carried out for different 'isomeric' pentamers.     

Isotropic-cholesteric phase transition in colloidal suspensions of filamentous bacteriophage fd

The co-existence concentrations of the isotropic and cholesteric liquid crystalline phases of the semi-flexible rod-like virus fd in aqueous suspension were measured as a function of ionic strength at room temperature. At several ionic strengths the magnetic-field-induced birefringence, which is proportional to the number of particles in a correlation volume N_corr, was measured for fd concentrations spanning the entire isotropic region. From this data the limiting concentration of stability (spinodal) of the isotropic phase, ρ*, was obtained. The co-existence concentrations and ρ* versus ionic strength compare well with predictions based on the theory of Khokhlov and Semenov, modified to include the effects of charge. A theoretical expression for the magnetic birefringence of persistent polymers was derived and agreed well with the data with the exception that N_corr at the isotropic to liquid crystal transition was smaller than predicted.     

The trapezoidal cylinder phase: a new mode of self-assembly in liquid-crystalline soft matter

A new rectangular columnar liquid crystalline phase with p2gg lattice is reported, which represents a polygonal cylinder array composed of cylinders with trapezoidal cross section. In these polygonal cylinders, one of the sides has a different length and is composed of a different material than the others. This tiling pattern was obtained in two series of T-shaped facial amphiphilic triblock molecules in which a rigid rod-like p-terphenyl core is substituted laterally by a polar and flexible oligoethylene glycol chain, terminated either by a hydrogen-bonding COOH group or by a Li carboxylate group, and having identical or different alkyl groups in the terminal positions. The trapezoidal cylinder phase provides an improved packing for relatively long and rigid alkyl chains at lower temperature and more space inside the polygonal cylinders than triangular cylinders. This combination of conformational and space-filling effects leads to different phase sequences. The trapezoidal cylinder phases pave the way to a new level of complexity in LC engineering and show the huge potential of the general concept of polyphilic tectons for the design of new complex soft matter structures.     

Cholesteric pitch of rigid and semi-flexible chiral liquid crystals

We calculate using mean field theory, the cholesteric pitch in systems composed of chiral molecules, which we model as 'corkscrews'. We consider both the rigid and semi-flexible limits. Our result for the cholesteric pitch depends on the intrinsic molecular pitch length as well as the concentration of molecules, but does not depend on the flexibility of the molecule.     

Comb copolymer cylindrical brushes containing semiflexible side chains: a Monte Carlo study

The off‐lattice Monte Carlo method is applied to investigate the equilibrium conformations of isolated comb copolymer cylindrical brushes in an athermal solution. The molecules considered consist of a flexible backbone, which is densely grafted with semiflexible side chains. The study focuses on the influence of the degree of intrinsic stiffness, λ_side, of the side chains on the conformational behavior of the molecules. It is demonstrated that with a fixed side chain length, M, the local length scale conformational fluctuations of the backbone increase as a function of λ_side. However, the persistence length, λ, of the cylindrical brush increases considerably with the side chain stiffness, indicating that the backbone becomes more extended at the large length scale. Moreover, as a function of λ_side, there is an increase in the ratio λ/D of the persistence length and the diameter, D, of the brush. This behavior is in good agreement with recent theoretical predictions and provides important new insight in the latest experimental observations.     

λ-Shaped mesogens. Structure, phase formation and properties

This contribution is concerned with molecules composed of rigid linear segments which are connected in such a way that a λ-shape results. Such types of shape have been predicted to lead to an enhanced solubility in low molar mass solvents and in the melt state of flexible chain molecules. The theoretical treatment predicted additionally that such molecules should be able to form lyotropic and thermotropic liquid crystalline phases. Experimental data on the thermodynamic properties, the structure formation in the solid and fluid condensed state, the solubility in low molar mass solvents and selected optical and electro-optical properties are reported; these are in good agreement with the predictions.     

Monte Carlo simulation of phase separations of block copolymers and of corresponding blends

The Monte Carlo method has been used to simulate the phase separations of block copolymers and of corresponding blends with very high concentration (sum of volume fractions of blocks A and B: ϕ_A + ϕ_B = 0,9545). Our main findings are as follows: (1) The mixing is nonrandom even in the athermal limit. (2) The nonselective good solvent molecules (ϕ_V = 0,0455) are mostly located at the interface between A- and B-rich phases, thus, it is not true that solvent and monomeric units will remain mixed at all temperatures. (3) Even for the same microscopic A-B interaction energy, ε, and at the same temperature, the Flory-Huggins parameter χ of block copolymers is always higher than that of corresponding blends, and the χ values of block copolymers and corresponding blends have different ε-dependencies. (4) The critical values of χ both for block copolymer and corresponding blend are obtained and compared with the meanfield theoretical predictions. It is found that the ratio of χ_c (block)/χ_c (blend) is qualitatively compatible with the prediction of the Flory-Leibler theory.     

Monte Carlo studies of tethered chains

Monte Carlo computer simulations of end-tethered chains grafted onto a hard wall have been performed. The chains were modeled as self-avoiding chains on a cubic lattice at athermal solvent conditions. The simulations spanned a wide range of chain lengths, N (100–1000, i.e., up to molecular weights of a few hundred thousands), and anchoring densities, σ (2 × 10⁻⁴ to 0.4), to properly chart the relevant parameter space. It is shown that the reduced surface coverage σ* = σπR is the most appropriate variable that quantitatively determines the mushroom, overlapping mushroom and brush regimes, where R_g is the radius of gyration of a free chain in solution. The simulation data are analyzed to determine the conformational characteristics and shape of the anchored chains and to compare them with the predictions of the analytical self consistent field theory. The strong stretching limit of the theoretical predictions is obtained only for σ* > 8. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47:2449–2461, 2009