arXiv subjects

E. M. Terentjev

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

At least 19 recordsLinked to original sources

arXiv2017

Oscillations and damping in the fractional Maxwell materials

This paper examines the oscillatory behaviour of complex viscoelastic systems with power law-like relaxation behaviour. Specifically, we use the fractional Maxwell model, consisting of a spring and fractional dashpot in series, which produces a power-law creep behaviour and a relaxation law following the Mittag-Leffler function. The fractional dashpot is characterised by a parameter beta, continuously moving from the pure viscous behaviour when beta=1 to the purely elastic response when beta=0. In this work, we study the general response function and focus on the oscillatory behaviour of a fractional Maxwell system in four regimes: stress impulse, strain impulse, step stress, and driven oscillations. The solutions are presented in a format analogous to the classical oscillator, showing how the fractional nature of relaxation changes the long-time equilibrium behaviour and the short-time transient solutions. We specifically test the critical damping conditions in the fractional regime, since these have a particular relevance in biomechanics.

cond-mat.soft↗

arXiv2016

Kinetics of fragmentation and dissociation of two-strand protein filaments: Coarse-grained simulations and experiments

While a significant body of investigations have been focused on the process of protein self-assembly, much less is understood about the reverse process of a filament breaking due to thermal motion into smaller fragments, or depolymerization of subunits from the filament ends. Indirect evidence for actin and amyloid filament fragmentation has been reported, although the phenomenon has never been directly observed either experimentally or in simulations. Here we report the direct observation of filament depolymerization and breakup in a minimal, calibrated model of coarse-grained molecular simulation. We quantify the orders of magnitude by which the depolymerization rate from the filament ends $k_\mathrm{off}$ is larger than fragmentation rate $k_{-}$ and establish the law $k_\mathrm{off}/k_- = \exp [( \varepsilon_\| - \varepsilon_\bot) / k_\mathrm{B}T ] = \exp [0.5 \varepsilon / k_\mathrm{B}T ]$, which accounts for the topology and energy of bonds holding the filament together. This mechanism and the order-of-magnitude predictions are well supported by direct experimental measurements of depolymerization of insulin amyloid filaments.

cond-mat.soft↗

arXiv2016

F1 rotary motor of ATP synthase is driven by the torsionally-asymmetric drive shaft

F1F0 ATP synthase (ATPase) either facilitates the synthesis of ATP in the mitochondrial membranes and bacterial inner membranes in a process driven by the proton moving force (pmf), or uses the energy from ATP hydrolysis to pump protons against the concentration gradient across the membrane. ATPase is composed of two rotary motors, F0 and F1, which generate the opposing rotation and compete for control of their shared central gamma-shaft. Here we present a self-consistent physical model of the F1 motor as a simplified two-state Brownian ratchet based on the asymmetry of torsional elastic energy of the coiled-coil gamma-shaft. This stochastic model unifies the physical description of linear and rotary motors and explains the stepped unidirectional rotation of the $γ$-shaft, in agreement with the `binding-change' ideas of Boyer. Substituting the model parameters, all independently known from recent experiments, our model quantitatively reproduces the ATPase operation, e.g. the `no-load' angular velocity is ca. 400~rad/s anticlockwise at 4 mM ATP, in close agreement with experiment. Increasing the pmf torque exerted by F0 can slow, stop and overcome the torque generated by F1, switching from ATP hydrolysis to synthesis at a very low value of `stall torque'. We discuss the matters of the motor efficiency, which is very low if calculated from the useful mechanical work it produces - but is quite high when the `useful outcome' is measured in the number of H+ pushed against the chemical gradient in the F1 ATP-driven operation.

q-bio.SC↗

arXiv2016

Local structure controls shear and bulk moduli in disordered solids

Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices, all of these models assume central-force interactions between particles/atoms. Each of these models differs in the spatial arrangement and the correlations among particles. In turn, this is reflected in the widely different behaviours of the shear (G) and compression (K) elastic moduli. The relation between the macroscopic elasticity as encoded in G, K and their ratio, and the microscopic lattice structure/order, is not understood. We provide a quantitative analytical connection between the local orientational order and the elasticity in model amorphous solids with different internal microstructure, focusing on the two opposite limits of packings (strong excluded-volume) and networks (no excluded-volume). The theory predicts that, in packings, the local orientational order due to excluded-volume causes less nonaffinity (less softness or larger stiffness) under compression than under shear. This leads to lower values of G/K, a well-documented phenomenon which was lacking a microscopic explanation. The theory also provides an excellent one-parameter description of the elasticity of compressed emulsions in comparison with experimental data over a broad range of packing fractions.

cond-mat.soft↗

arXiv2015

Fragmentation and depolymerization of non-covalently bonded filaments

Protein molecules often self-assemble by means of non-covalent physical bonds to form extended filaments, such as amyloids, F-actin, intermediate filaments, and many others. The kinetics of filament growth is limited by the disassembly rate, at which inter-protein bonds break due to the thermal motion. Existing models often assume that the thermal dissociation of subunits occurs uniformly along the filament, or even preferentially in the middle, while the well-known propensity of F-actin to depolymerize from one end is mediated by biochemical factors. Here, we show for a very general (and generic) model, using Brownian dynamics simulations and theory, that the breakup location along the filament is strongly controlled by the asymmetry of the binding force about the minimum, as well as by the bending stiffness of the filament. We provide the basic connection between the features of the interaction potential between subunits and the breakup topology. With central-force (that is, fully flexible) bonds, the breakup rate is always maximum in the middle of the chain, whereas for semiflexible or stiff filaments this rate is either a minimum in the middle or flat. The emerging framework provides a unifying understanding of biopolymer fragmentation and depolymerization and recovers earlier results in its different limits.

cond-mat.soft↗

arXiv2014

Microscopic origin of nonlinear non-affine deformation and stress overshoot in bulk metallic glasses

The atomic theory of elasticity of amorphous solids, based on the nonaffine response formalism, is extended into the nonlinear stress-strain regime by coupling with the underlying irreversible many-body dynamics. The latter is implemented in compact analytical form using a qualitative method for the many-body Smoluchowski equation. The resulting nonlinear stress-strain (constitutive) relation is very simple, with few fitting parameters, yet contains all the microscopic physics. The theory is successfully tested against experimental data on metallic glasses, and it is able to reproduce the ubiquitous feature of stress-strain overshoot upon varying temperature and shear rate. A clear atomic-level interpretation is provided for the stress overshoot, in terms of the competition between the elastic instability caused by nonaffine deformation of the glassy cage and the stress buildup due to viscous dissipation.

cond-mat.soft↗

arXiv2014

Role of the potential landscape on the single-file diffusion through channels

Transport of colloid particles through narrow channels is ubiquitous in cell biology as well as becoming increasingly important for microfluidic applications or targeted drug delivery. Membrane channels in cells are useful models for artificial designs because of their high efficiency, selectivity and robustness to external fluctuations. Here we model the passive channels that let cargo simply diffuse through them, affected by a potential profile along the way. Passive transporters achieve high levels of efficiency and specificity from binding interactions with the cargo inside the channel. This however leads to a paradox: why should channels which are so narrow that they are blocked by their cargo evolve to have binding regions for their cargo if that will effectively block them? Using Brownian dynamics simulations, we show that different potentials, notably symmetric, increase the flux through narrow passive channels -- and investigate how shape and depth of potentials influence the flux. We find that there exist optimal depths for certain potential shapes and that it is most efficient to apply a small force over an extended region of the channel. On the other hand, having several spatially discrete binding pockets will not alter the flux significantly. We also explore the role of many-particle effects arising from pairwise particle interactions with their neighbours and demonstrate that the relative changes in flux can be accounted for by the kinetics of the absorption reaction at the end of the channel.

cond-mat.soft↗

arXiv2011

Thermodynamically Stable Blue Phases

We show theoretically that flexoelectricity stabilizes blue phases in chiral liquid crystals. Induced internal polarization reduces the elastic energy cost of splay and bend deformations surrounding singular lines in the director field. The energy of regions of double twist is unchanged. This in turn reduces the free energy of the blue phase with respect to that of the chiral nematic phase, leading to stability over a wider temperature range. The theory explains the discovery of large temperature range blue phases in highly flexoelectric "bimesogenic" and "bent-core" materials, and predicts how this range may be increased further.

cond-mat.soft↗

arXiv2009

Polysiloxane surfactants for the dispersion of carbon nanotubes in non-polar organic solvents

We develop two new amphiphilic molecules that are shown to act as efficient surfactants for carbon nanotubes in non-polar organic solvents. The active conjugated groups, which are highly attracted to graphene nanotube surface, are based on pyrene and porphyrin. We show that relatively short (C18) carbon tails are insufficient to provide stabilization. As our ultimate aim is to disperse and stabilize nanotubes in siloxane matrix (polymer and crosslinked elastomer), both surfactant molecules were made with long siloxane tails to facilitate solubility and steric stabilization. We show that pyrene-siloxane surfactant is very effective in dispersing multi-wall nanotubes, while the porphyrin-siloxane is making single-wall nanotubes soluble, both in petroleum ether and in siloxane matrix.

cond-mat.mtrl-sci↗

arXiv2009

Strength of nanotubes, filaments and nanowires from sonication-induced scission

We propose a simple model to describe the cavitation-induced breakage of mesoscale filaments during their sonication in solution. The model predicts a limiting length below which scission no longer occurs. This characteristic length is a function of the tensile strength and diameter of the filament, as well as the solvent viscosity and cavitation parameters. We show that the model predicts accurately experimental results for materials ranging from carbon nanotubes to protein fibrils, and discuss the use of sonication-induced breakage as a probe for the strength of nanostructures.

cond-mat.mtrl-sci↗

arXiv2009

Buckling of semiflexible filaments under compression

A model for filament buckling at finite temperatures is presented. Starting from the classical worm-like chain model under constant compression, we use a mean-field approach for filament inextensibility to find the complete partition function. We find that there is a simple interpolation formula that describes the free energy of chains or filaments as a function of end-to-end separation, which spans the whole range of filament stiffnesses. Using this formula we study the buckling transition of semiflexible filaments and find that kinetics plays an important role. We propose that the filament buckling is essentially the first order transition governed by the kinetics of escaping a local free energy minimum. A simple model for the kinetics is put forward, which shows the critical buckling force for a filament is reduced by a fraction that has a universal scaling with temperature with an exponent 0.56.

cond-mat.soft↗

arXiv2008

Affine model of stress stiffening in semiflexible filament networks

We present a revised theoretical study of the affine assumption applied to semiflexible networks. Drawing on simple models of semiflexible worm-like chains we derive an expression for the probability distribution of crosslink separations valid at all separations. This accounts for both entropic and mechanical filament stretching. From this we obtain the free energy density of such networks explicitly as a function of applied strain. We are therefore able to calculate the elastic moduli of such networks for any imposed strain or stress. We find that accounting for the distribution of cross-link separations destroys the simple scaling of modulus with stress that is well known in single chains, and that such scaling is sensitive to the mechanical stretch modulus of individual filaments. We compare this model to three experimental data sets, for networks of different types of filaments, and find that a properly treated affine model can successfully account for the data. We find that for networks of stiffer filaments, such as F-actin, to fit data we require a much smaller effective persistence length than usually assumed to be characteristic of this filament type. We propose that such an effectively reduced rigidity of filaments might be a consequence of network formation.

cond-mat.soft↗

arXiv2008

Phase behavior of C18 monoglyceride in hydrophobic solutions

We apply a set of different techniques to analyze the physical properties and phase transitions of monoglycerides (MG) in oil. In contrast to many studies of MG in water or aqueous systems, we find a significant difference in the phase structure at different concentrations and temperatures. By adding small quantities of water to our base MG/oil systems we test the effect of hydration of surfactant head-groups, and its effect on the phase behavior. The phase diagrams are determined by calorimetry and their universal features are recorded under different conditions. Two ordered phases are reported: the inverse lamellar gel phase and the sub-alpha crystalline gel phase. This sequence is very different from the structures in MG/water; its most striking feature is the establishing of a 2D densely packed hexagonal order of glycerol heads in the middle of inverse lamellar bilayers. Rheology was examined through temperature scans to demonstrate the gelation phenomenon, which starts from the onset of the lamellar phase during the cooling/ordering process.

cond-mat.soft↗

arXiv2008

Aging and metastability of monoglycerides in hydrophobic solutions

The aging of aggregated structures of monoglycerides in hydrophobic medium is described by a set of different techniques. Polarized microscopy was used to study the mesomorphic behavior as a function of time. Differential scanning calorimetry was utilized to quantitatively monitor changes in the latent heat in different phase transformations that take place in the aging system. Infrared spectroscopy was applied to detect the formation of hydrogen bonding between surfactants. The X-ray diffraction patterns fingerprinted the molecular arrangement in different emerging phases. Infra-red spectroscopy was used to monitor the state of hydrogen bonding in the system. We conclude that in both inverted-lamellar and sub-alpha crystalline phases, monoglyceride molecules inevitably lose their emulsified ability in the hydrophobic solutions through the gradual change in hydrogen bonding patterns. On aging, the formation of intermolecular hydrogen bonding between glycerol groups causes the segregation of chiral (D and L) isomers within the bilayers. Therefore all structures were eventually forced to reorder into the beta-crystalline state, distinguishing between the D and L layers. Accordingly, the highly ordered packing of aged structures weakened the emulsifying ability and finally leaded the collapse of the percolating gel network.

cond-mat.soft↗

arXiv2008

Critical fluctuations and random-anisotropy glass transition in nematic elastomers

We carry out a detailed deuterium NMR study of local nematic ordering in polydomain nematic elastomers. This system has a close analogy to the random-anisotropy spin glass. We find that, in spite of the quadrupolar nematic symmetry in 3-dimensions requiring a first-order transition, the order parameter in the quenched ``nematic glass'' emerges via a continuous phase transition. In addition, by a careful analysis of the NMR line shape, we deduce that the local director fluctuations grow in a critical manner around the transition point. This could be the experimental evidence for the Aizenman-Wehr theorem about the quenched impurities changing the order of discontinuous transition.

cond-mat.dis-nn↗

arXiv2007

Thermal diffusion and bending kinetics in nematic elastomer cantilever

Vertically aligned mono-domain nematic liquid crystal elastomers contract when heated. If a temperature gradient is applied across the width of such a cantilever, inhomogeneous strain distribution leads to bending motion. We modelled the kinetics of thermally-induced bending in the limit of a long thin strip and the predicted time-variation of curvature agreed quantitatively with experimental data from samples with a range of critical indices and nematic-isotropic transition temperatures. We also deduced a value for the thermal diffusion coefficient of the elastomer.

cond-mat.soft↗

arXiv2006

Nematic-Isotropic Transition with Quenched Disorder

Nematic elastomers do not show the discontinuous, first-order, phase transition that the Landau-De Gennes mean field theory predicts for a quadrupolar ordering in 3D. We attribute this behavior to the presence of network crosslinks, which act as sources of quenched orientational disorder. We show that the addition of weak random anisotropy results in a singular renormalization of the Landau-De Gennes expression, adding an energy term proportional to the inverse quartic power of order parameter Q. This reduces the first-order discontinuity in Q. For sufficiently high disorder strength the jump disappears altogether and the phase transition becomes continuous, in some ways resembling the supercritical transitions in external field.

cond-mat.soft↗

arXiv2006

Quenched disorder and spin-glass correlations in XY nematics

We present a theoretical study of the equilibrium ordering in a 3D XY nematic system with quenched random disorder. Within this model, treated with the replica trick and Gaussian variational method, the correlation length is obtained as a function of the local nematic order parameter and the effective disorder strength. These results clarify what happens in the limiting cases of diminishing order parameter and disorder strength, that is near a phase transition of a pure system. In particular, it is found that quenched disorder is irrelevant as the order parameter tends to zero and hence does not change the character of the continuous XY nematic to isotropic phase transition. We discuss how these results compare with experiments and simulations

cond-mat.soft↗