arXiv subjects

E. M. Terentjev

Publications and source records attributed to E. M. Terentjev.

48 records · Page 3Linked to original sources

arXiv2000

Dynamic mechanical response of polymer networks

The dynamic-mechanical response of flexible polymer networks is studied in the framework of tube model, in the limit of small affine deformations, using the approach based on Rayleighian dissipation function. The dynamic complex modulus G* is calculated from the analysis of a network strand relaxation to the new equilibrium conformation around the distorted primitive path. Chain equilibration is achieved via a sliding motion of polymer segments along the tube, eliminating the inhomogeneity of the polymer density caused by the deformation. The characteristic relaxation time of this motion separates the low-frequency limit of the complex modulus from the high-frequency one, where the main role is played by chain entanglements, analogous to the rubber plateau in melts. The dependence of storage and loss moduli, G' and G'', on crosslink and entanglement densities gives an interpolation between polymer melts and crosslinked networks. We discuss the experimental implications of the rather short relaxation time and the slow square-root variation of the moduli and the loss factor tan at higher frequencies.

cond-mat.soft↗

arXiv2000

Ageing of Natural Rubber under Stress

We report a dynamical-mechanical study of stress relaxation at small deformation in a natural (polyisoprene) rubber well above its glass transition temperature Tg. We find that an almost complete relaxation of stress takes place over very long periods of time, even though the elastic network integrity is fully retained. The relaxation rate and the long-time equilibrium modulus are sensitive functions of temperature which do not follow time-temperature superposition. Many characteristic features of non-ergodic ageing response are apparent at both short and very long times. We interpret the observed behaviour in terms of the properties of rubber crosslinks, capable of isomerisation under stress, and relate the results to recent models of soft glassy rheology.

cond-mat.soft↗

arXiv2000

Cellular solid behaviour of liquid crystal colloids. 1. Phase separation and morphology

We study the phase ordering colloids suspended in a thermotropic nematic liquid crystal below the clearing point Tni and the resulting aggregated structure. Small (150nm) PMMA particles are dispersed in a classical liquid crystal matrix, 5CB or MBBA. With the help of confocal microscopy we show that small colloid particles densely aggregate on thin interfaces surrounding large volumes of clean nematic liquid, thus forming an open cellular structure, with the characteristic size of 10-100 micron inversely proportional to the colloid concentration. A simple theoretical model, based on the Landau mean-field treatment, is developed to describe the continuous phase separation and the mechanism of cellular structure formation.

cond-mat.soft↗

arXiv2000

Cellular solid behaviour of liquid crystal colloids. 2. Mechanical properties

This paper presents the results of a rheological study of thermotropic nematic colloids aggregated into cellular structures. Small sterically stabilised PMMA particles dispersed in a liquid crystal matrix densely pack on cell interfaces, but reversibly mix with the matrix when the system is heated above Tni. We obtain a remarkably high elastic modulus, G'~10^5 Pa, which is a nearly linear function of particle concentration. A characteristic yield stress is required to disrupt the continuity of cellular structure and liquify the response. The colloid aggregation in a ``poor nematic'' MBBA has the same cellular morphology as in the ``good nematic'' 5CB, but the elastic strength is at least an order of magnitude lower. These findings are supported by theoretical arguments based on the high surface tension interfaces of a foam-like cellular system, taking into account the local melting of nematic liquid and the depletion locking of packed particles on interfaces.

cond-mat.soft↗

arXiv2000

Untwisting of a cholesteric elastomer by a mechanical field

A mechanical strain field applied to a monodomain cholesteric elastomer will unwind the helical director distribution. There is an analogy with the classical problem of an electric field applied to a cholesteric liquid crystal, but with important differences. Frank elasticity is of minor importance unless the gel is very weak. The interplay is between director anchoring to the rubber elastic matrix and the external mechanical field. Stretching perpendicular to the helix axis induces the uniform unwound state via the elimination of sharp, pinned twist walls above a critical strain. Unwinding through conical director states occurs when the elastomer is stretched along the helical axis.

cond-mat.soft↗

arXiv1998

Electro-Mechanical Fredericks Effects in Nematic Gels

The solid nematic equivalent of the Fredericks transition is found to depend on a critical field rather than a critical voltage as in the classical case. This arises because director anchoring is principally to the solid rubbery matrix of the nematic gel rather than to the sample surfaces. Moreover, above the threshold field, we find a competition between quartic (soft) and conventional harmonic elasticity which dictates the director response. By including a small degree of initial director misorientation, the calculated field variation of optical anisotropy agrees well with the conoscopy measurements of Chang et al (Phys.Rev.E56, 595, 1997) of the electro-optical response of nematic gels.

cond-mat.soft↗

arXiv1998

Exponential Decay of Correlations in a Model for Strongly Disordered 2D Nematic Elastomers

Lattice Monte-Carlo simulations were performed to study the equilibrium ordering in a two-dimensional nematic system with quenched random disorder. When the disordering field, which competes against the aligning effect of the Frank elasticity, is sufficiently strong, the long-range correlation of the director orientation is found to decay as a simple exponential, Exp[-r/x]. The correlation length {x} itself also decays exponentially with increasing strength of the disordering field. This result represents a new type of behavior, distinct from the Gaussian and power-law decays predicted by some theories.

cond-mat.dis-nn↗

arXiv1998

Slow stress relaxation in randomly disordered nematic elastomers and gels

Randomly disordered (polydomain) liquid crystalline elastomers align under stress. We study the dynamics of stress relaxation before, during and after the Polydomain-Monodomain transition. The results for different materials show the universal ultra-slow logarithmic behaviour, especially pronounced in the region of the transition. The data is approximated very well by an equation Sigma(t) ~ Sigma_{eq} + A/(1+ Alpha Log[t]). We propose a theoretical model based on the concept of cooperative mechanical resistance for the re-orientation of each domain, attempting to follow the soft-deformation pathway. The exact model solution can be approximated by compact analytical expressions valid at short and at long times of relaxation, with two model parameters determined from the data.

cond-mat.soft↗

arXiv1996

Friction Drag on a Particle Moving in a Nematic Liquid Crystal

The flow of a liquid crystal around a particle does not only depend on its shape and the viscosity coefficients but also on the direction of the molecules. We studied the resulting drag force on a sphere moving in a nematic liquid crystal (MBBA) in a low Reynold's number approach for a fixed director field (low Ericksen number regime) using the computational artificial compressibility method. Taking the necessary disclination loop around the sphere into account, the value of the drag force anisotropy (F_\perp/F_\parallel=1.50) for an exactly computed field is in good agreement with experiments (~1.5) done by conductivity diffusion measurements. We also present data for weak anchoring of the molecules on the particle surface and of trial fields, which show to be sufficiently good for most applications. Furthermore, the behaviour of the friction close to the transition point nematic <-> isotropic and for a rod-like and a disc-like liquid crystal will be given.

cond-mat↗

arXiv1995

Non-uniform deformations in liquid crystalline elastomers

We develop a molecular model of non-uniform deformations within the framework of liquid crystal rubber elasticity. We show that, similarly to the uniform case, the theory is not sensitive to the molecular details of polymer liquid crystal involved and the resulting elastic free energy is quite universal. The result of this work is the general expression for the free energy of deformations, which combines the effects of large non-symmetric affine strains in the rubbery network and gradients of curvature deformations of the director field, $F = λ^T (\nabla {n})^2 λ$. We derive the molecular expressions for the elastic constants governing non uniform deformations in the presence of elastic strains. They also depend on the polymer step length anisotropy and - most strikingly - have an overall {negative} sense. We therefore predict that in some circumstances, especially at large elastic deformations $λ$, these new terms may overpower the usual, positive Frank elastic moduli of the underlying nematic structure, as well as the coupling in nematic elastomers of uniform relative rotations of the director and the elastic matrix. In this event highly distorted polydomain textures n(r) would be favoured.

cond-mat↗

arXiv1995

Stability of Liquid Crystalline Macroemulsions

The thermodynamic stability of emulsions of liquid crystal in water (glycerol) matrices is demonstrated for a wide range of materials and concentrations. Coalescence is prevented by an energy barrier for a topological ring defect formation in a neck between the two merging droplets. There is a characteristic size of emulsion droplets, typically tens of microns or more, controlled by the balance of elastic and anchoring energies of the liquid crystal. On removal of liquid crystallinity (by raising the temperature above $T_{ni}$ in thermotropic nematic materials, for example) the energy barriers for coalescence disappear and emulsion droplets can merge quickly, controlled only by the traditional kinetic effects. Practical applications of this effect, as well as some wider theoretical implications are discussed in the end.

mtrl-th↗

arXiv1995

GRAMA. A Mathematica program for analytical calculations in 10-dimensional supergravity. Version 1.0

"GRAMA" is a Mathematica package for doing symbolic tensor computations and complicated algebraic manipulations in 10-dimensional (D=10) simple (N=1) supergravity. The main new ingredients of this package inside the general Mathematica environment are the computation of complicated products of Dirac matrices and the treatment of covariant derivatives: spinorial and vectorial. In principle, with small modifications, GRAMA can also be used for calculations in 4-dimensional supergravity. With the help of this package we were able to obtain the equations of motion and the Lagrangian for the 10-D supergravity including superstring corrections (see hep-th/9507033) - a calculation that would be otherwise impossible to perform. "GRAMA" is designed as a community- and user-friendly program.

hep-th↗