Elastic Free Energy Research Articles

Study the coupling effect of shear and electric field on rheological behaviors of liquid crystals

The rheological behaviors of 5CB liquid crystal under the coupling effect of shear and electric field are investigated by theoretical and experimental study. Establish calculating equation of the system Gibbs free energy by adopting the continuum theory of liquid crystals which contains anchoring energy, elastic free energy, dielectric free energy and flow energy. Then the molecular orientation angle distribution and apparent viscosity of liquid crystal under the coupling effect are obtained by minimizing the Gibbs free energy, revealing the microscopic mechanism of rheological behaviors and influence rules of coupling effect from the molecular model. Meanwhile the calculated results are verified by rheological test. Comparative Analysis of the errors and reasons of theoretical and experimental results, which demonstrates that anchoring effect plays an important role in the molecular orientation and viscosity of liquid crystal. Both the theoretical and experimental results indicate that liquid crystals have electroviscous effect and behavior like non-Newtonian liquids under electric field. The viscosities of liquid crystals are determined by the coupling and competition action of shear and electric field, which can reach 4 times of its original value under electric field. This property of controllable viscosity is important in tribology, which can self-adaptively satisfy the requirement of viscosities for different working conditions as a "smart lubrication" under certain condition.

Opening Barrier Renormalization by Membrane Local Curvature Fluctuations around the Mechanosensitive Channel: Analytical Expression

We calculate renormalization of the opening energy barrier of mechanosensitive channel by local curvature fluctuations: U= U0 +Ufl, Eq. (1), P0(z) and P1(z,H) are lateral pressure profiles in the flat and curved bilayer respectively, H and A(z) are local mean curvature and the difference between open/closed channel cross-section profiles. Function P1(z,H) was derived in [1] analytically using flexible strings model of lipid chains [2]. The average over fluctuations of the membrane's shape h(x,y) in the Monge representation [3] uses Boltzmann factor of a curved conformation exp(-F(H)/T) with elastic free energy functional F(H) taken in the Helfrich form, Eq. (3); k and r are bending rigidity and surface tension. Comparing our results with molecular dynamics data [4] for curved bilayers, we estimate relative importance of the contributions of the lipid tails and phospholipid headgroups to the energy barrier U.

Stability analysis of kinked DNA with generalized rod model

The stability of short DNA ring is phenomenologically analyzed by discussing the second variation of its elastic free energy. Through expanding the perturbation functions as Fourier series, the DNA ring's stability condition is obtained in a general case. This result is also suitable for other structures which can be taken as one-dimensional (1D) curvature elastomers, such as ribbons and filaments. Stability analysis in a typical model provides some useful results which are consistent with the experimental observations in a wide parameter range.

Generalized Berreman's model of the elastic surface free energy of a nematic liquid crystal on a sawtoothed substrate

In this paper we present a generalization of Berreman's model for the elastic contribution to the surface free-energy density of a nematic liquid crystal in presence of a sawtooth substrate which favors homeotropic anchoring as a function of the wave number of the surface structure q, the tilt angle α, and the surface anchoring strength w. In addition to the previously reported nonanalytic contribution proportional to -q ln q, due to the nucleation of disclination lines at the wedge bottoms and apexes of the substrate, the next-to-leading contribution is proportional to q for a given substrate roughness, in agreement with Berreman's predictions. We characterize this term, finding that it has two contributions: the deviations of the nematic director field with respect to a reference field corresponding to the isolated disclination lines and their associated core free energies. Comparison with the results obtained from the Landau-de Gennes model shows that our model is quite accurate in the limit wL>1, when strong anchoring conditions are effectively achieved.

Effect of elastic energy on the folding of an RNA hairpin

We analyse the folding and unfolding of an RNA hairpin using a conventional zipping model that includes both the free energy for RNA binding and the elastic free energy of the system. Unfolding under isotonic conditions (where we control the applied load) is known to occur at a well-defined critical load. In marked contrast, we find that unfolding under isometric conditions (where we control the extension of the hairpin) produces a series of sharp peaks in the average load as the stem of the hairpin starts to unzip base by base. A peak occurs when the elastic energy stored in the unzipped arms of the hairpin becomes so large that it is energetically favourable for the next base pair to unzip: the consequent increase in the contour length of the unzipped arms reduces their elastic energy and causes the average load to fall abruptly. However, as the contour length of the unzipped arms increases, the peaks become less distinct. Moreover, when we include the long DNA/RNA handles that have been used in single-molecule experiments, the unzipping of individual base pairs cannot be resolved at all. Instead, with the hairpin in the folded state, the average load increases with extension until the elastic energy stored in the handles makes it energetically favourable for the hairpin to unzip over a narrow range of extensions. The resultant yield point produces a mechanical hysteresis loop with a negative slope, as observed experimentally. Unfolding of the hairpin is also affected by the elastic energy stored in a compliant force transducer. We find that short, stiff handles and a stiff force transducer could improve the resolution of mechanical experiments on single molecules.

A multiplicative approach for nonlinear electro-elasticity

The recent interest in dielectric elastomers has given rise to a pressing need for predictive non-linear electromechanical coupling models. Since elastomers behave elastically and can sustain large deformations, the constitutive laws are naturally based on the formulation of adequate free energy functions. Due to the coupling, such functions include terms which combine the strain tensor and the electric field. In contrast to existing frameworks, this paper proposes to establish the electromechanical coupling by the multiplicative split of the deformation gradient into a part related to the elastic behavior of the material and further one which describes the deformation induced by the electric field. Already available and well tested functions of elastic free energy functions can be immediately deployed without any modifications provided the argument of the function is the strain tensor alone which in turn is defined by the elastic part of the deformation gradient only. An appropriate constitutive relation is formulated for the electrically induced part of the deformation gradient. The paper discusses in depth such a formulation. The approach is elegant, straightforward and above all, provides clear physical insight. The paper presents also a numerical formulation of the theoretical framework based on a meshfree method. Various numerical examples of highly non-linear coupled deformations demonstrate the potential and strength of the theory.

Stabilization of bilayer structure of raft due to elastic deformations of membrane

Line tension of the boundary of specific domains (rafts) rich in sphingomyelin was calculated. The line tension was calculated based on macroscopic theory of elasticity under assumption that the bilayer in raft is thicker than in the surrounding membrane. The calculations took into account the possibility of lateral shift of the domain boundaries located in different monolayers of the membrane. The line tension was associated with the energy of elastic deformations appearing in the vicinity of the boundary in order to compensate for the difference in the thickness of the monolayers. Spatial distribution of deformations and the line tension was calculated by minimization of elastic free energy of the system. Dependence of the line tension on the distance between the domains boundaries located in different monolayers was obtained. It was shown that the line tension is minimal if the distance is about 4 nm. Thus, membrane deformations stabilize the bilayer structure of rafts observed experimentally. The calculated value of line tension is about 0.6 pN for the difference between the monolayer thickness of raft and surrounding membrane of about 0.5 nm, which is in agreement with the experimental data available.

Electro‐tuning of surface state in two‐dimensional photonic crystals

AbstractIn this paper, we have investigated the electro‐tuning of surface states in two‐dimensional square lattice photonic crystal (PC) of circular air holes in alumina background in which one row of the outermost air holes is infiltrated by a nematic liquid crystal (NLC). By minimizing the total (elastic plus electromagnetic) free energy, the configuration of the NLC directors, as a function of radial distance can be obtained. This configuration determines the dielectric tensor as function of radial distance. Therefore, by use of supercell method, dependence of surface states on applied electrical field has been studied. Numerical results show that position of surface modes can be effectively controlled by applying an external field on liquid crystal rods.

An Elastoplastic-anisotropic Damage Model for Concrete

An elastoplastic-anisotropic damage constitutive model for the description of nonlinear behavior of concrete is presented. The yield surface is developed in effective stress spaces, which takes into account the hardening effect and better match the experimental data. The stiffness degradation and softening effect are considered in the framework of continuum damage mechanics formulation. The second-order damage tensor is used to characterize the anisotropy induced by the orientation of microcracks. In order to simulate the unilateral effect, the elastic Helmholtz free energy is decomposed into a volumetric part and a deviatoric part. The different behavior under tensile and compressive loadings is modeled by using different variables in effective stress and damage tensor. Numerical results of the model accord well with experimental results at the material and structural levels.

Character of the structural and magnetic phase transitions in the parent and electron-doped BaFe2As2compounds

We present a combined high-resolution x-ray diffraction and x-ray resonant magnetic scattering (XRMS) study of as-grown BaFe2As2. The structural/magnetic transitions must be described as a two-step process. At T_S = 134.5 K we observe the onset of a second-order structural transition from the high-temperature paramagnetic tetragonal structure to a paramagnetic orthorhombic phase, followed by a discontinuous step in the structural order parameter that is coincident with a first-order antiferromagnetic (AFM) transition at T_N = 133.75 K. These data, together with detailed high-resolution x-ray studies of the structural transition in lightly doped Ba(Fe{1-x}Co{x})2As2 and Ba(Fe{1-x}Rh{x})2As2 compounds, show that the structural and AFM transitions do, in fact, occur at slightly different temperatures in the parent BaFe2As2 compound, and evolve towards split secondorder transitions as the doping concentration is increased. We estimate the composition for the tricritical point for Co-doping and employ a mean-field approach to show that our measurements can be explained by the inclusion of an anharmonic term in the elastic free energy and magneto-elastic coupling in the form of an emergent Ising-nematic degree of freedom.

Stress Accumulation Originating from Mechanical Asymmetry Promotes Actin Filament Severing at Boundaries of Bare and Cofilin-Decorated Segments

The regulatory protein, cofilin, severs actin filaments and increases the number of ends from which subunits add and dissociate. Structural and biochemical analyses demonstrate that cofilin binding alters the conformation and mechanics of actin filaments such that cofilin-decorated filaments are ∼20-fold more compliant in bend and twist than native actin filaments. Equilibrium and kinetic binding models as well as direct visualization of cofilin binding to filaments favor a mechanism in which severing occurs at or near boundaries of bare and cofilin-decorated segments. It is hypothesized that shear stress associated with conformational fluctuations accumulates locally at boundaries of mechanical asymmetry, thereby leading to preferential severing at junctions of bare and cofilin-decorated segments. In this work, we evaluate if mechanical and conformational periodicity in filaments promotes stress accumulation at junctions of asymmetry (i.e. boundaries). We have derived mathematical expressions of the actin filament elastic free energy, accounting for contributions from bending, twisting and twist-bend coupling, and used a computational modeling approach to evaluate the distribution of energy and stress of model filaments strained by external mechanical (buckling or torque) loads applied to filament ends. Our results indicate that mechanical asymmetry introduced by cofilin binding promotes the accumulation of shear stress at boundaries between bare and cofilin-decorated segments that likely increases the probability of failure (i.e. severing) under active or passive, thermal deformation, analogous to the fracture of some non-protein materials. Elastic coupling between twisting and bending is critical for stress accumulation at boundaries.

The Non-Equilibrium Thermodynamics and Kinetics Governing Focal Adhesion and Cytoskeletal Dynamics: Application to Cancer Cell Motility

We consider the chemo-mechanical growth dynamics of actin stress fibers (SFs) and focal adhesions (FAs). Free energy changes drive the binding and unbinding of proteins to SFs and FAs, thereby controlling their dynamic modes of growth, treadmilling and disassembly via four mechanisms (Ref. 1) : (a) work done during addition of protein molecules, (b) the chemical free energy change associated with the addition of protein molecules, (c) the elastic free energy change of deforming SFs, FAs, cell wall and substrates (d) the work done by molecular conformational changes. We treat these dynamics as nonlinear kinetic processes driven by out-of-equilibrium thermodynamic driving forces. The above four mechanisms admit the full range of experimentally-observed behavior. The model has been coupled with cellular structure to explain the observed modes of motility in highly metastatic breast cancer cells of the MDA-MB-231 cell line, as well as in genetically-modified versions of this line. The graphc shows a grey FA with elastic elements and binding/unbinding proteins. Reference [1] Olberding JE, Thouless MD, Arruda EM, Garikipati K (2010) The Non-Equilibrium Thermodynamics and Kinetics of Focal Adhesion Dynamics. PLoSONE 5(8): e12043. doi:10.1371/journal.pone.0012043

Origin of Twist-Bend Coupling in Actin Filaments

Actin filaments are semiflexible polymers that display large-scale conformational twisting and bending motions. Modulation of filament bending and twisting dynamics has been linked to regulatory actin-binding protein function, filament assembly and fragmentation, and overall cell motility. The relationship between actin filament bending and twisting dynamics has not been evaluated. The numerical and analytical experiments presented here reveal that actin filaments have a strong intrinsic twist-bend coupling that obligates the reciprocal interconversion of bending energy and twisting stress. We developed a mesoscopic model of actin filaments that captures key documented features, including the subunit dimensions, interaction energies, helicity, and geometrical constraints coming from the double-stranded structure. The filament bending and torsional rigidities predicted by the model are comparable to experimental values, demonstrating the capacity of the model to assess the mechanical properties of actin filaments, including the coupling between twisting and bending motions. The predicted actin filament twist-bend coupling is strong, with a persistence length of 0.15–0.4 μm depending on the actin-bound nucleotide. Twist-bend coupling is an emergent property that introduces local asymmetry to actin filaments and contributes to their overall elasticity. Up to 60% of the filament subunit elastic free energy originates from twist-bend coupling, with the largest contributions resulting under relatively small deformations. A comparison of filaments with different architectures indicates that twist-bend coupling in actin filaments originates from their double protofilament and helical structure.

The Non-Equilibrium Thermodynamics and Kinetics of Focal Adhesion Dynamics

BackgroundWe consider a focal adhesion to be made up of molecular complexes, each consisting of a ligand, an integrin molecule, and associated plaque proteins. Free energy changes drive the binding and unbinding of these complexes and thereby controls the focal adhesion's dynamic modes of growth, treadmilling and resorption.Principal FindingsWe have identified a competition among four thermodynamic driving forces for focal adhesion dynamics: (i) the work done during the addition of a single molecular complex of a certain size, (ii) the chemical free energy change associated with the addition of a molecular complex, (iii) the elastic free energy change associated with deformation of focal adhesions and the cell membrane, and (iv) the work done on a molecular conformational change. We have developed a theoretical treatment of focal adhesion dynamics as a nonlinear rate process governed by a classical kinetic model. We also express the rates as being driven by out-of-equilibrium thermodynamic driving forces, and modulated by kinetics. The mechanisms governed by the above four effects allow focal adhesions to exhibit a rich variety of behavior without the need to introduce special constitutive assumptions for their response. For the reaction-limited case growth, treadmilling and resorption are all predicted by a very simple chemo-mechanical model. Treadmilling requires symmetry breaking between the ends of the focal adhesion, and is achieved by driving force (i) above. In contrast, depending on its numerical value (ii) causes symmetric growth, resorption or is neutral, (iii) causes symmetric resorption, and (iv) causes symmetric growth. These findings hold for a range of conditions: temporally-constant force or stress, and for spatially-uniform and non-uniform stress distribution over the FA. The symmetric growth mode dominates for temporally-constant stress, with a reduced treadmilling regime.SignificanceIn addition to explaining focal adhesion dynamics, this treatment can be coupled with models of cytoskeleton dynamics and contribute to the understanding of cell motility.

Bistable switching of twist direction in a twisted-nematic liquid crystal cell

We propose a bistable liquid crystal mode based on switching of the twist direction in a conventional π/2-twisted nematic cell. Switching between the −π/2 and +π/2 twist states can be performed by applying vertical and/or in-plane electric fields. The proposed bistable mode has an infinite memory time because the two stable twist states have the same elastic free energy.

Confined nematic polymers: Order and packing in a nematic drop

We investigate the tight packing of nematic polymers inside a confining hard sphere. We model the polymer via the continuum Frank elastic free energy augmented by a simple density dependent part as well as by taking proper care of the connectivity of the polymer chains when compared with simple nematics. The free energy ansatz is capable of describing an orientational ordering transition within the sample between an isotropic polymer solution and a polymer nematic phase. We solve the Euler-Lagrange equations numerically with the appropriate boundary conditions for the director and density field and investigate the orientation and density profile within a sphere. Two important parameters of the solution are the exact locations of the beginning and the end of the polymer chain. Pending on their spatial distribution and the actual size of the hard sphere enclosure we can get a plethora of various configurations of the chain exhibiting different defect geometry.

Ab initio calculation of band edges modified by (001) biaxial strain in group IIIA–VA and group IIB–VIA semiconductors: Application to quasiparticle energy levels of strained InAs/InP quantum dot

Results of first-principles full potential calculations of absolute position of valence and conduction energy bands as a function of (001) biaxial strain are reported for group IIIA–VA (InAs, GaAs, InP) and group IIB–VIA (CdTe, ZnTe) semiconductors. Our computational procedure is based on the Kohn–Sham form of density functional theory (KS DFT), local spin density approximation (LSDA), variational treatment of spin-orbital coupling, and augmented plane wave plus local orbitals method (APW+lo). The band energies are evaluated at lattice constants obtained from KS DFT total energy as well as from elastic free energy. The conduction band energies are corrected with a rigid shift to account for the LSDA band gap error. The dependence of band energies on strain is fitted to polynomial of third degree and results are available for parameterization of biaxial strain coupling in empirical tight-binding models of IIIA–VA and IIB–VIA self-assembled quantum dots (SAQDs). The strain effects on the quasiparticle energy levels of InAs/InP SAQD are illustrated with empirical atomistic tight-binding calculations.

Free energy wells for small gas bubbles in soft deformable materials

Thermodynamic expressions are derived for the system relative Gibbs free energy, and the relative Gibbs free energy per bubble, for all possible equilibrium bubble states that can form in a soft slightly rigid material, initially supersaturated with a dissolved inert gas (N(2)). While the thermodynamic manipulations are exact, the final expressions are approximate, due to an approximation made in deriving the expression for the elastic free energy of a soft material containing more than a single bubble. The expressions predict that provided the shear modulus of the soft material is not negligibly small, free energy wells which stabilize small gas bubbles for finite periods of time exist in such materials. This is consistent with a previous calculation, based solely on the bubble pressure equation, which resulted in the conjecture that bubbles found in soft materials with some rigidity (or shear resistance) are likely to be small. The possible relevance of this to the field of decompression sickness is outlined.

Phospholipid demixing and the birth of a lipid droplet

The biogenesis of lipid droplets (LD) in the yeast Saccharomyces cerevisiae was theoretically investigated on basis of a biophysical model. In accordance with the prevailing model of LD formation, we assumed that neutral lipids oil-out between the membrane leaflets of the endoplasmic reticulum (ER), resulting in LD that bud-off when a critical size is reached. Mathematically, LD were modeled as spherical protuberances in an otherwise planar ER membrane. We estimated the local phospholipid composition, and calculated the change in elastic free energy of the membrane caused by nascent LD. Based on this model calculation, we found a gradual demixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation. During demixing, the phospholipid monolayer was able to gain energy during LD growth, which suggested that the formation of curved interfaces was supported by or even driven by lipid demixing. In addition, we show that demixing is thermodynamically necessary as LD cannot bud-off otherwise. In the case of Saccharomyces cerevisiae our model predicts a LD bud-off diameter of about 12 nm. This diameter is far below the experimentally determined size of typical yeast LD. Thus, we concluded that if the standard model of LD formation is valid, LD biogenesis is a two step process. Small LD are produced from the ER, which subsequently ripe within the cytosol through a series of fusions.

Atomistic details of the associative phosphodiester cleavage in human ribonuclease H

During translation of the genetic information of DNA into proteins, mRNA is synthesized by RNA polymerase and after the transcription process degraded by RNase H. The endoribonuclease RNase H is a member of the nucleotidyl-transferase (NT) superfamily and is known to hydrolyze the phosphodiester bonds of RNA which is hybridized to DNA. Retroviral RNase H is part of the viral reverse transcriptase enzyme that is indispensable for the proliferation of retroviruses, such as HIV. Inhibitors of this enzyme could therefore provide new drugs against diseases like AIDS. In our study we investigated the molecular mechanism of RNA cleavage by human RNase H using a comprehensive high level DFT/B3LYP QM/MM theoretical method for the calculation of the stationary points and nudged elastic band (NEB) and free energy calculations to identify the transition state structures, the rate limiting step and the reaction barrier. Our calculations reveal that the catalytic mechanism proceeds in two steps and that the nature of the nucleophile is a water molecule. In the first step, the water attack on the scissile phosphorous is followed by a proton transfer from the water to the O2P oxygen and a trigonal bipyramidal pentacoordinated phosphorane is formed. Subsequently, in the second step the proton is shuttled to the O3' oxygen to generate the product state. During the reaction mechanism two Mg(2+) ions support the formation of a stable associated in-line S(N)2-type phosphorane intermediate. Our calculated energy barrier of 19.3 kcal mol(-1) is in excellent agreement with experimental findings (20.5 kcal mol(-1)). These results may contribute to the clarification and understanding of the RNase H reaction mechanism and of further enzymes from the RNase family.