External field-induced switching in nematic elastomers: A Monte Carlo study

We present a Monte Carlo study of external field-induced switching in nematic elastomers, employing a coarse-grained shearable lattice model. In large enough systems a full-wavelength Fréedericksz effect is observed --as opposed to the half-wavelength effect seen in ordinary nematics-- that clearly reflects in simulated polarized light textures, as well as in deuterium magnetic resonance spectra. The reorientation of mesogenic units is accompanied by pronounced shear deformations.     

Linear hydrodynamics and viscoelasticity of nematic elastomers

We develop a continuum theory of linear viscoelastic response in oriented monodomain nematic elastomers. The expression for the dissipation function is analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we propose the relations between the anisotropic rubber moduli and new viscous coefficients. A new dimensionless number is introduced, which describes the relative magnitude of viscous and rubber-elastic torques. In an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics, the model shows a dramatic decrease in the dynamic modulus in certain deformation geometries. The degree to which the storage modulus does not altogether drop to zero is shown to be both dependent on frequency and to be proportional to the semi-softness, the non-ideality of a nematic network. We consider the most interesting geometry for the implementation of the theory, calculating the dynamic response to an imposed simple shear and making predictions for effective moduli and (exceptionally high) loss factors. Received 16 October 2000 and Received in final form 10 December 2000     

Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model

We present a new model of rubber elasticity where linear forces act to constrain the fluctuations of the eigenmodes of the phantom model. The model allows us to treat the constrained junction and the tube model within the same, transparent formalism, does not require any further approximations, and is particularly suited for the analysis of simulation data for (strained) model polymer networks. As an interesting side result we show that in order for the model to be consistent, the constraints (but not the mean polymer conformations!) have to deform affinely, a severe restriction that might also apply to other models. Complementary, we prove in analogy to the derivation of the virial theorem that introducing constraints into the phantom network Hamiltonian leads to extra terms in addition to the usual Doi-Edwards formulas for the polymer contribution to the stress tensor which vanish only for affinely deforming constraints. Received: 28 November 1997 / Received in final form and accepted: 31 March 1998     

Critical voltages and blocking stresses in nematic gels

We present a model of the dynamics of director rotation in nematic gels under combined electro-mechanical loading. Focusing on a model specimen, we describe the critical voltages that must be exceeded to achieve director reorientation, and the blocking stresses that prevent alignment of the nematic director with the applied electric field. The corresponding phase diagram shows that the dynamic thresholds defined above are different from those predicted on the sole basis of energetics. Multistep loading programs are used to explore the energy landscape of our model specimen, showing the existence of multiple local minima under the same voltage and applied stress. This leads us to conclude that hysteresis should be expected in the electro-mechanical response of nematic gels.     

Biaxial liquid-crystal elastomers: A lattice model

We present a simple coarse-grained lattice model for monodomain biaxial liquid-crystal elastomers and perform large-scale Monte Carlo simulations in the proposed model system. Orientational ordering --uniaxial or biaxial-- reflects in sample deformations on cooling the system. The simulation output is used to predict calorimetry data and deuterium magnetic resonance spectra.     

Spontaneous thermal expansion of nematic elastomers

We study the monodomain (single-crystal) nematic elastomer materials, all side-chain siloxane polymers with the same mesogenic groups and crosslinking density, but differing in the type of crosslinking. Increasing the proportion of long di-functional segments of main-chain nematic polymer, acting as network crosslinking, results in dramatic changes in the uniaxial equilibrium thermal expansion on cooling from the isotropic phase. At higher concentration of main chains their behaviour dominates the elastomer properties. At low concentration of main-chain material, we detect two distinct transitions at different temperatures, one attributed to the main-chain, the other to the side-chain component. The effective uniaxial anisotropy of nematic rubber, r(T) = / proportional to the effective nematic order parameter Q(T), is given by an average of the two components and thus reflects the two-transition nature of thermal expansion. The experimental data is compared with the theoretical model of ideal nematic elastomers; applications in high-amplitude thermal actuators are discussed in the end. Received 25 June 2001 and Received in final form 29 September 2001     

Dynamics of reorientation of a constrained nematic elastomer

A model is proposed for the reorientation dynamics of a confined nematic liquid crystal elastomer, where the effect of crosslinks is to couple the director to deformations of the elastic matrix. The model combines the (equilibrium) `neo-classical' theory of liquid crystal rubber elasticity with the simplest time evolution equations for a system described by two coupled, non-conserved order parameters. Relaxation from an orientation imposed by an electric field is studied as a function of elastic softness, starting angle, surface pretilt, and the relative mobilities of director and strain. Most importantly, the absence of a `semi-soft' elastic threshold changes the long-time behaviour of the effective refractive index of the medium from exponential to inverse power law decay. Predictions are compatible with recent experimental results by Chang, Chien and Meyer [Phys. Rev. E 56, 595 (1997)]. Received 22 June 1998     

Elastic rod model of a supercoiled DNA molecule

We study the elastic behaviour of a supercoiled DNA molecule. The simplest model is that of a rod-like chain, involving two elastic constants, the bending and the twist rigidities. Writing this model in terms of Euler angles, we show that the corresponding Hamiltonian is singular and needs a small distance cut-off, which is a natural length scale giving the limit of validity of the model, of the order of the double-helix pitch. The rod-like chain in the presence of the cut-off is able to reproduce quantitatively the experimentally observed effects of supercoiling on the elongation-force characteristics, in the small supercoiling regime. An exact solution of the model, using both transfer matrix techniques and its mapping to a quantum mechanics problem, allows to extract, from the experimental data, the value of the twist rigidity. We also analyse the variation of the torque and the writhe-to-twist ratio versus supercoiling, showing analytically the existence of a rather sharp crossover regime which can be related to the excitation of plectoneme-like structures. Finally we study the extension fluctuations of a stretched and supercoiled DNA molecule, both at fixed torque and at fixed supercoiling angle, and we compare the theoretical predictions to some preliminary experimental data. Received 1 April 1999 and Received in final form 4 January 2000     

Density functional theory for nonuniform polymer melts: Based on the universality of the free energy density functional

A density functional theory is proposed for nonuniform freely jointed tangential hard sphere polymer melts in which the bonding interaction is treated on the basis of the properties of the Dirac δ-function, thus avoiding the use of the single chain simulation in the theory. The excess free energy is treated by making use of the universality of the free energy density functional and the Verlet-modified (VM) bridge function. To proceed numerically, one of the input parameters, the second-order direct correlation function of a uniform polymer melt is obtained by solving numerically the Polymer-RISM integral equation with the Percus-Yevick (PY) closure. The predictions of the present theory for the site density distribution, the partition coefficient and the adsorption isotherm, near a hard wall or between two hard walls are compared with computer simulation results and with those of previous theories. Comparison indicates that the present approach is more accurate than the previous integral equation theory and the most accurate Monte Carlo density functional theories. The predicted oscillations of the medium-induced force between two hard walls immersed in polymer melts are consistent with the experimental results available in the literature. Received 18 April 2000     

Confinement of columnar diblock copolymers: Simulations, theory and applications

The inherent nanoscale morphologies of self-organizing diblock copolymer melts are now being investigated for a variety of technological applications. To obtain global, well-oriented, regular patterns requires suitably confining and aligning the melt between two flat plates. Here we consider such confinement for an asymmetrical diblock melt, which forms columns of the minority phase in a matrix of the majority phase. We investigate this system with a combination of numerical simulations and strong segregation theory and make suggestions as to when perpendicular orientation should prevail over parallel orientation of the columns. Received 22 May 2001 and Received in final form 14 February 2002     

Piezoelectricity of chiral nematic elastomers

A molecular model of freely jointed chains of chiral monomers is developed to describe the piezoelectric effect in chiral nematic elastomers. The model, an extension of the neo-classical theory of nematic polymer networks, takes into account a chiral biasing of molecular alignment under shear which leads to induced polarisation if the monomers contain a transverse dipole moment. The resulting theory is fully non-linear in elastic deformations, in the spirit of ordinary rubber elasticity. The expansion to the highest order in small strains gives the three linear piezoelectric coefficients predicted by phenomenological models. Received 7 September 1998 and Received in final form 19 October 1998     

Influence of polydispersity on the phase behavior of statistical multiblock copolymers with Schultz-Zimm block molecular weight distributions

In this paper we investigate in a systematic way the influence of polydispersity in the block lengths on the phase behavior of AB-multiblock copolymer melts. As model system we take a polydisperse multiblock copolymer for which both the A-blocks and the B-blocks satisfy a Schultz-Zimm distribution. In the limit of low polydispersity the expressions for the vertex functions are clarified by using simple physical arguments. For various values of the polydispersity the phase diagram is presented, which shows that the region of stability of the bcc phase increases considerably with increasing polydispersity. The strong dependence of the periodicity of the microstructure on the polydispersity and on the interaction strength is presented. Received 2 July 1998     

Kinetics of reversible surface crystallization and melting in poly(ethylene oxide): Effect of crystal thickness observed in the dynamic heat capacity

Poly(ethylene oxide) (PEO) in the semi-crystalline state shows a reversible surface crystallization and melting; a temperature decrease leads to a certain crystal thickening, a temperature increase reversely to an expansion of the amorphous intercrystallite layers. Dynamic calorimetry provides a means to investigate the kinetics of the process. The structural rearrangement in the region of the crystalline-amorphous interface can only be accomplished if the chains can slide through the crystallites. One therefore expects the associated time to change with the crystallite thickness. Variations of the crystal thickness of PEO can be achieved by choosing different crystallization temperatures. We studied the effect of the crystal thickness employing temperature-modulated differential scanning calorimetry and heat wave spectroscopy, and by carrying out small-angle X-ray scattering experiments for the structural characterization. The effect of the crystal thickness is clearly observed. Results indicate that the sliding diffusion through the crystallites takes place by helical jumps of whole stems. Data yield the activation energy per unit length of the stems. Received 20 April 2001 and Received in final form 13 August 2001     

What can polymer crystal structure tell about polymer crystallization processes?

Contrary to most or all other materials, crystallization of chiral but racemic polymers such as isotactic polypropylene is accompanied by a conformational rearrangement which leads to helical geometries: the building units of the crystal are helical stems, -20nm long, which can be either right-handed or left-handed. Helical hand cannot be reversed within the crystal structure: it is therefore a permanent marker and an indicator of molecular processes (in particular segregation/selection of helical hands) which take place during crystal growth, and more precisely during the crucial step of “efficient” helical stem deposition. The issue of proper helical hand selection during polymer crystal growth is mainly illustrated with isotactic polypropylene. Its various crystalline polymorphs (, , and smectic) display virtually all possible combinations of helical hands, azimuthal settings and even non-parallel orientation of helix axes in space. Furthermore, a specific homoepitaxy which generates a lamellar branching in the phase “quadrites” and composite structures makes it possible a) to determine the helical hand and associated azimuthal setting of every stem in the crystalline entities and b) to determine the impact on the crystal structure and morphology of “mistakes” in helical hand of the depositing stem. Analysis of these morphologies demonstrates that the crystallization of isotactic polypropylene (and by implication of other achiral, helical polymers) is a highly sequential and “substrate-determined” process, i.e. that the depositing stem probes the topography of the growth face prior to attachment. These observations appear difficult to reconcile with crystallization schemes in which molecules (helical segments) are prearranged in a kind of pseudo-crystalline bundle (and as such, are not subjected to the high constraints of crystal symmetry) before deposition as a preassembled entity on the substrate. Received: 5 May 2000     

Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T _g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T _g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T _g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation. Received 21 March 2000 and Received in final form 4 December 2000     

Heterogeneous dynamics at the glass transition in van der Waals liquids: Determination of the characteristic scale

Recent experiments have demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous. The characteristic size of these heterogeneities has been measured to be a few nanometers at T _g. We extend here a recent model for describing the heterogeneous nature of the dynamics which allows both to derive this length scale and the right orders of magnitude of the heterogeneities of the dynamics close to the glass transition. Our model allows then to interpret quantitatively small probes diffusion experiments. Received 29 March 2002 and Received in final form 11 November 2002 RID="a" ID="a"e-mail: long@lps.u-psud.fr     

Dielectric properties of side chain liquid crystalline elastomers: influence of crosslinking on side chain dynamics

Dielectric response, from 1 Hz to 10 MHz, of liquid crystalline side chain elastomers has been compared to the one of analogous uncrosslinked materials. Results are discussed in terms of mobility of the mesogens. Two different systems have been investigated: smectic A elastomers allow to determine the influence of crosslinking on the relaxation (i.e. the reorientation of the whole mesogen around the chain), a S _C ^* elastomer shows the drastic influence of the polymer network on the Goldstone mode. Received 12 October 1998     

Solvable lattice gas models of random hetero-polymers at finite density: I. Statics

We introduce -dimensional lattice gas versions of three common models of random hetero-polymers, in which both the polymer density and the density of the polymer-solvent mixture are finite. These solvable models give valuable insight into the problems related to the (quenched) average over the randomness in statistical mechanical models of proteins, without having to deal with the hard geometrical constraints occurring in finite-dimensional models. Our exact solution, which is specific to the -dimensional case, is compared to the results obtained by a saddle-point analysis and by the grand ensemble approach, both of which can also be applied to models of finite dimension. We find, somewhat surprisingly, that the saddle-point analysis can lead to qualitatively incorrect results. Received 15 June 1999 and Received in final form 14 October 1999     

Anomalous elasticity of an ordered lamellar liquid foam

We investigate experimentally the linear viscoelastic properties of a lamellar liquid foam as a function of the cell size and spatial organisation. The system consists of multilamellar vesicles generated by a simple shear flow on a lyotropic lamellar phase. The vesicles can be prepared either in an amorphous or a spatially ordered state. Their size is easily tunable in the range R = 0.5-15 μm. Whereas the shear modulus of the amorphous lamellar foam is alike that of usual liquid foams or concentrated emulsions and scales linearly with 1/R, the elastic modulus of the ordered foam is almost independent of the cell size. This result --probably the first describing the elasticity of an ordered foam-like system-- remains unexplained. Received 7 August 2000