Thermodynamics, orientational order and elasticity of strained liquid crystalline melts and elastomers

A microscopic polymer liquid-state theory has been developed for the structure, thermodynamics and mechanical properties of strained liquid crystalline elastomers. The theory captures the experimentally observed phenomenon of spontaneous distortion and establishes a direct correlation between it and the nematic order parameter. Strain induced softening of the elastic modulus is predicted to emerge due to coupling of the induced orientational order and anisotropic interchain excluded volume interactions. Comparison of our results with limited experiments shows good qualitative and sometimes quantitative agreement. The theory predicts that deformation in the liquid crystalline state results in an increase of the amplitude of density fluctuations (compressibility) which becomes more pronounced as chain degree of polymerization and/or segmental density are decreased.     

Microscopic theory of rubber elasticity

A microscopic integral equation theory of elasticity in polymer liquids and networks is developed which addresses the nonclassical problem of the consequences of interchain repulsive interactions and packing correlations on mechanical response. The theory predicts strain induced softening, and a nonclassical intermolecular contribution to the linear modulus. The latter is of the same magnitude as the classical single chain entropy contribution at low polymer concentrations, but becomes much more important in the melt state, and dominant as the isotropic-nematic liquid crystal phase transition is approached. Comparison of the calculated stress-strain curve and induced nematic order parameter with computer simulations show good agreement. A nearly quadratic dependence of the linear elastic modulus on segmental concentration is found, as well as a novel fractional power law dependence on degree of polymerization. Quantitative comparison of the theory with experiments on polydimethylsiloxane networks are presented and good agreement is found. However, a nonzero modulus in the long chain limit is not predicted since quenched chemical crosslinks and trapped entanglements are not explicitly taken into account. The theory is generalizable to treat the structure, thermodynamics and mechanical response of nematic elastomers.     

X-ray diffraction by liquid-crystalline elastomers

A new series of mesomorphic side chain polysiloxane networks has been recently synthesized in which the chemical nature of the linkage and the mesogenic group have been varied and the gelation conditions during the chemical reaction have been studied. This paper presents an X-ray diffraction study of the mesogenic group orientation in stretched samples of these networks. The angular extension of the so-called wide angle diffuse ring is used to estimate the orientational order of the mesogenic group versus strain. To perform these experiments, a special stretching device was developed and a new two-dimensional X-ray detector was used which allowed us to collect the data in a few minutes. On stretching, it was observed that the mesogenic groups orient themselves perpendicular to the stress direction for all of the samples but for one for which the parallel orientation prevailed. This prevents the establishment of a simple general law. From another point of view, the polymer concentration during the chemical reaction, which controls the gelation, is shown to be an important parameter with which to understand the physical properties: the networks synthesized below the gel point do not display reproducible and reversible behaviour, rather they flow when they are stretched. Conversely, all of the networks synthesized above the gel point really show the same well-defined behaviour independent of the sample history. Their orientational order increases regularly with the strain, first quickly, then moderately until it eventually saturates. This saturation value of the mesogenic group orientational order does not reach the nematic order parameter of the same (uncross-linked) mesomorphic side chain polymers. This suggests that the cross-links may create local tensions which disturb the nematic field.     

MOLECULAR FIELD THEORY FOR NEMATIC LIQUID CRYSTAL POLYMER COMPRISING FLEXIBLE SPACER

Basea on the new model and concept of mtramolecular orientational order parameter, a molecular field theory was built up for main chain liquid crystalline polymer (MC-LCPs) with flexible spacers. The theory takes account of orientational correlation among all mesogens in a polymer chain and the relationship between the intramolecular orientation and spatial orientation of the mesogens. The free energy, temperature and entropy of the nematic-isotropic transition were determined with the theory and compared with experiments in current work. It was found that many unique transition properties of the MC-LCPs comprising flexible spacer are correctly predicted by the theory and the agreement of the theory with the experiments is impressive.     

Dynamic uniaxiality in strained networks: A deuterium NMR investigation

The orientational order generated in a polymer network by a uniaxial stress is probed using deuterium NMR. The experiments are performed on end-linked polydimethylsiloxane networks. When a uniaxial force is applied, the observed NMR spectra show that the chain segments reorient uniaxially around the external force direction. This experimental fact appears as new evidence for cooperative orientational interactions between chain segments in the deformed networks.     

Chain segment ordering in uniaxially strained networks: A deuterium NMR investigation

The deuterium NMR (²H-NMR) is used for probing the chain segment orientation in polymer networks under uniaxial stress. The method is based on the observation of an incomplete time averaging of quadrupolar interactions affixed to deuterated segments. The samples are end-linked polydimethylsiloxane networks. The ²H-NMR experiments are performed either on labelled network chains or an labelled probe polymer chains dissolved in the network. The basic results are the following: — The induced uniaxial order is related to a uniaxial dynamics of chain segments around the direction of the applied constraint. — A permanent orientation is observed on free polymer chains dissolved in the deformed networks. — The mean degrees of orientational order induced along short and long chains in bimodal networks are the same. These experimental facts appear as evidences for cooperative orientational couplings between chain segments in the deformed networks.     

Segmental orientation and chain relaxation of polymers by fourier transform infrared dichroism

Fourier transform infrared dichroism has been used to investigate molecular orientation in polymeric materials. It is first applied to characterize network behavior in some elastomeric systems such as model networks of poly(dimethylsiloxane). The strain dependence of segmental orientation is analyzed through networks of known degree of cross-linking and experimental results are compared with calculation predictions based on the rotational isomeric state formalism. Infrared dichroism spectroscopy has also been used to analyze orientational relaxation in binary blends of long and short polystyrene chains. The effect of short deuterated chains (M_w = 3000 to 72000) on the orientational relaxation of long entangled chains (Mw = 2 000 000) is examined in the bidisperse melts uniaxially deformed above the glass transition temperature. While the long chain relaxation is found to be dependent on the short-chain concentration, the local orientational order of the latter is molecular weight dependent in agreement with the classical relaxation theories.     

THEORY OF INTRAMOLECULAR ORIENTATIONAL ORDER OF MESOGENIC UNITS IN MC-LCPS AND ITS APPLICATION

New concepts such as intramolecular orientational order parameter and corresponding model as well as theory were proposed to describe the intramolecular orientation of mesogenic units in the liquid crystalline polymer chains. The relationship between the intramolecular orientational order parameter and the molecular geometrical parameters such as the bond angle, the bond rotational angle and the rotational potential energy of chemical bonds was deduced. A significant even-odd oscillation of the intramolecular orientational order parameter of LCPs with different length of flexible spacer was found and rationally related to even-odd zig-zag manner of transition properties The verification and application of the theory are also discussed. The isotropic transition temperature predicted by the theory is shown to be in favourable agreement with the experiments.     

Diffusion of spheres in isotropic and nematic networks of rods: electrostatic interactions and hydrodynamic screening

Translational diffusion of a small charged tracer sphere in isotropic and nematic suspensions of long and thin charged rods is investigated as a function of ionic strength and rod concentration. A theory for the diffusive properties of a small sphere is developed, where both (screened) hydrodynamic interactions and charge interactions between the tracer sphere and the rod network are analyzed. Hydrodynamic interactions are formulated in terms of the hydrodynamic screening length. As yet, there are no independent theoretical predictions for the hydrodynamic screening length for rod networks. Experimental tracer-diffusion data are presented for various ionic strengths as a function of the rod concentration, both in the isotropic and nematic states. Orientational order parameters are measured for the same ionic strengths as a function of the rod concentration. The hydrodynamic screening length is determined from these experimental data and scaling relations obtained from the above mentioned theory. For the isotropic networks, a master curve is found for the hydrodynamic screening length as a function of the rod concentration. For the nematic networks the screening length turns out to be a very sensitive function of the orientational order parameter.     

Orientational behaviour of a liquid crystalline side chain polymer in applied electric and magnetic fields as detected by NMR

The molecular orientational order of a side chain thermotropic nematic polymer has been measured by proton NMR. The alignment of the side chains is reflected in the splitting of the NMR signal into a doublet. Simultaneous orientational effects of magnetic and electric fields on the mesogenic groups were studied in magnetically preoriented layers. Temperature, twist angle and thickness dependences of the spectra were measured. The order parameter S and the parameter of orientational order S' of the samples were estimated.     

Testing assumptions about solute concentration dependence in liquid crystal NMR

The NMR spectra of four solutes, used as probes of liquid crystal orientational order, were analyzed. For each solute, samples were prepared at different solute concentrations, and the concentration dependence was used to extrapolate zero-concentration properties. The mean-field (Maier-Saupe) model when applied to solutes neglects solute-solute interactions and assumes all solutes in a mixed-solute sample see the same average environment. The first assumption is only valid as one approaches zero concentration, while experiments are typically carried out at concentrations between 0 and 10 mol %. The solute concentration dependence has in the past been "scaled out" using an internal solute reference as an orientational standard. We measured the concentration dependence of the orientational order parameter and calculate the corresponding interaction energies based on a mean-field interaction potential for a solute. We find agreement at the 3% level between experiments for different solutes while using (i) the zero-concentration values as solute-dependent orientational references and (ii) scaling to either order parameters or interaction energies; these two scalings gave equivalent but not identical results. We find, too, that errors inherent in the experiment and the calculations will limit attempts to refine the theory to push the comparisons beyond the 2% level.     

Theory of glassy dynamics in conformationally anisotropic polymer systems

A mode coupling theory for the ideal glass transition temperature, or crossover temperature to highly activated dynamics in the deeply supercooled regime, T(c), has been developed for anisotropic polymer liquids. A generalization of a simplified mode coupling approach at the coarse-grained segment level is employed which utilizes structural and thermodynamic information from the anisotropic polymer reference interaction site model theory. Conformational alignment or/and coil deformation modifies equilibrium properties and constraining interchain forces thereby inducing anisotropic segmental dynamics. For liquid-crystalline polymers a small suppression of T(c) with increasing nematic or discotic orientational order is predicted. The underlying mechanism is reduction of the degree of coil interpenetration and intermolecular repulsive contacts due to segmental alignment. For rubber networks chain deformation results in an enhanced bulk modulus and a modest elevation of T(c) is predicted. The theory can also be qualitatively applied to systems that undergo nonuniversal local deformation and alignment, such as polymer thin films and grafted brush layers, and large elevations or depressions of T(c) are possible. Extension to treat directionally dependent collective barrier formation and activated hopping is possible.     

Effects of Nematic Ordering on the Relaxation Spectrum of a Polymer Network with Included rod‐like Particles: Mean‐Field Approximation

Summary: Equilibrium and local dynamic properties of ordered polymer networks with included rod‐like particles are considered using a simplified network model. Lagrange multipliers in the equations of motion of rigid rods are replaced by their averaged values. This approximation corresponds to modelling rod‐like particles by elastic Gaussian springs with mean‐square lengths independent of the orientational order. Nematic‐like interactions between network segments and rods are taken into account in terms of the Maier‐Saupe mean‐field approximation. Nematic ordering of rods induces network segments ordering and changes the relaxation spectrum of the network. The relaxation spectrum of the ordered network splits into two main branches for parallel and perpendicular components of chain segments with respect to the director. Relaxation times of a polymer network are calculated as functions of the wave number for the corresponding normal mode and of the order parameter taking into account both the dynamic factor (determined by friction effects) and the statistical factor (related to mean‐square fluctuations of segment projections). We compare the relaxation spectra of ordered unstretched polymer networks with fixed boundaries with those for polymer networks at free boundaries. A polymer network with free boundaries is stretched along the director. This produces additional fine structure of the two main branches in the relaxation spectrum.

Cell of a three‐chain network model with included rods.     

Orientational ordering of polymer chains near the surface and asymmetry of the statistical segment of macromolecules

The parameter of the orientational order of polymer chain fragments near the substrate (film) surface in relation to the degree of asymmetry of the statistical segment of the macromolecule was discussed in terms of the model of adsorption of rigid cylinders on the substrate surface. The theoretical parameters of the orientational order were analyzed and compared with the experimental data for films of polysaccharides, sulfated phenyl-containing polymers, and polytrimethylsilylpropynes.     

Short-range orientational order and thermodynamic properties of polymer solutions

The concept of short-range orientational order was applied to the calculation of thermodynamic characteristics of polymer solutions in terms of the lattice model. It was shown that allowance for short-range order makes it possible to explain negative values of the entropy of mixing and the existence of a lower critical solution temperature in both polymer solutions and solutions of low-molecular-mass compounds. It was found that systems with lower critical solution temperature can exist even when the degree of orientational order in solutions slightly increases as compared with the corresponding values of this parameter in their components.     

The structure and spontaneous orientational order in surface layers of water-soluble methyl- and hydroxypropylmethyl cellulose films

The structure of the surface layers of thin films cast from water-soluble derivatives of cellulose—methyl cellulose and hydroxypropyl methylcellulose—has been studied by the methods of an oblique polarized beam and molecular hydrodynamics. It has been demonstrated that the molecular chains of the polymers under study are characterized by a high degree of order in surface film layers. The orientational order of molecular chains demonstrates a strong molecular mass dependence. This effect is associated with the concentration of terminal segments whose orientational order parameter relative to the film surface differs from the corresponding value of internal segments composing the molecular chain. The quantitative estimates of the orientational order parameter of terminal and internal segments have been performed.     

Phase and orientational ordering of low molecular weight rod molecules in a quenched liquid crystalline polymer matrix with mobile side chains

We study the phase diagram and orientational ordering of guest liquid crystalline (LC) rods immersed in a quenched host made of a liquid crystalline polymer (LCP) matrix with mobile side chains. The LCP matrix lies below the glass transition of the polymer backbone. The side chains are mobile and can align to the guest rod molecules in a plane normal to the local LCP chain contour. A field theoretic formulation for this system is proposed and the effects of the LCP matrix on LC ordering are determined numerically. We obtain simple analytical equations for the nematic/isotropic phase diagram boundaries. Our calculation show a nematic-nematic (N/N) first order transition from a guest stabilized to a guest-host stabilized region and the possibility of a reentrant transition from a guest stabilized nematic region to a host only stabilized regime separated by an isotropic phase. A detailed study of thermodynamic variables and interactions on orientational ordering and phases is carried out and the relevance of our predictions to experiments and computer simulations is presented.     

Mechanistic model for deformation of polymer nanocomposite melts under large amplitude shear

We report the mechanical response of a model nanocomposite system of poly(styrene) (PS)-silica to large-amplitude oscillatory shear deformations. Nonlinear behavior of PS nanocomposites is discussed with the changes in particle dispersion upon deformation to provide a complete physical picture of their mechanical properties. The elastic stresses for the particle and polymer are resolved by decomposing the total stress into its purely elastic and viscous components for composites at different strain levels within a cycle of deformation. We propose a mechanistic model which captures the deformation of particles and polymer networks at small and large strains, respectively. We show, for the first time, that chain stretching in a polymer nanocomposite obtained in large amplitude oscillatory deformation is in good agreement with the nonlinear chain deformation theory of polymeric networks. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Chain retraction,length fluctuations,and small-angle neutron scattering in strained polymer melts

We propose a possible explanation for an apparent contradiction between the Doi–Edwards (DE) theory and time-resolved small-angle neutron scattering experiments. The original DE theory predicts that a chain in a melt subjected to a step-elongation undergoes a reduction of its dimensions in both the parallel and perpendicular directions to the strain axis, before returning to an isotropic conformation by reptation. In the present paper, we propose a crude model to compare the relative effect of retraction and of the chain length fluctuations, introduced later by Doi to explain the M power law of viscosity of polymer melts. We show that length fluctuations are able to screen retraction in most experimental situations available to small-angle neutron scattering, whereas that is not the case for viscoelasticity. Quantitative predictions are consistent with the experimental data presently available.