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Jinwu Jiang - One of the best experts on this subject based on the ideXlab platform.
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elastic Bending Modulus for single layer black phosphorus
Journal of Physics D, 2015Co-Authors: Haoyu Zhang, Jinwu JiangAbstract:We derive an analytic formula for the elastic Bending Modulus of single-layer black phosphorus (SLBP) based on the valence force field model. The obtained elastic Bending Modulus is 4.8028 eV and 7.9905 eV along the armchair and zigzag directions in the SLBP, respectively. These values are obviously larger than the Bending Modulus of 1.4 eV in graphene due to the intrinsic finite thickness for SLBP. Our derivation analytically illustrates that the elastic Bending Modulus of SLBP is proportional to the square of its intrinsic thickness.
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Elastic Bending Modulus for Single-Layer Black Phosphorus
Journal of Physics D: Applied Physics, 2015Co-Authors: Haoyu Zhang, Jinwu JiangAbstract:We derive an analytic formula for the elastic Bending Modulus of single-layer black phosphorus (SLBP) based on the valence force field model. The obtained elastic Bending Modulus is 4.8028 eV and 7.9905 eV along the armchair and zigzag directions in the SLBP, respectively. These values are obviously larger than the Bending Modulus of 1.4 eV in graphene due to the intrinsic finite thickness for SLBP. Our derivation analytically illustrates that the elastic Bending Modulus of the SLBP is proportional to the square of the intrinsic thickness of the SLBP.
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elastic Bending Modulus of single layer molybdenum disulfide mos2 finite thickness effect
Nanotechnology, 2013Co-Authors: Jinwu Jiang, Zenan Qi, H Park, Timon RabczukAbstract:We derive, from an empirical interaction potential, an analytic formula for the elastic Bending Modulus of single-layer MoS2 (SLMoS2). By using this approach, we do not need to define or estimate a thickness value for SLMoS2, which is important due to the substantial controversy in defining this value for two-dimensional or ultrathin nanostructures such as graphene and nanotubes. The obtained elastic Bending Modulus of 9.61 eV in SLMoS2 is significantly higher than the Bending Modulus of 1.4 eV in graphene, and is found to be within the range of values that are obtained using thin shell theory with experimentally obtained values for the elastic constants of SLMoS2. This increase in Bending Modulus as compared to monolayer graphene is attributed, through our analytic expression, to the finite thickness of SLMoS2. Specifically, while each monolayer of S atoms contributes 1.75 eV to the Bending Modulus, which is similar to the 1.4 eV Bending Modulus of monolayer graphene, the additional pairwise and angular interactions between out of plane Mo and S atoms contribute 5.84 eV to the Bending Modulus of SLMoS2.
Berend Smit - One of the best experts on this subject based on the ideXlab platform.
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Chain Length Dependencies of the Bending Modulus of Surfactant Monolayers
Physical review letters, 2004Co-Authors: Live Rekvig, Bjørn Hafskjold, Berend SmitAbstract:The effect of the surfactant chain length n on the Bending Modulus kappa of surfactant monolayers is simulated with a mesoscopic oil-water-surfactant model. We confirm a power law, kappa is proportional to np, as predicted by mean-field theory and found experimentally, and find p approximately 1.5 at a constant surface density and p approximately 1.0 at a constant interfacial tension. This agrees quite well with both mean-field theory (p=2-3, assuming constant surface density) and experiments (at constant surface tension). Our results suggest that the previously reported agreement between theory and experiment may be fortuitous and caused by the difference in surfactant types.
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Simulating the effect of surfactant structure on Bending moduli of monolayers
The Journal of chemical physics, 2004Co-Authors: Live Rekvig, Bjørn Hafskjold, Berend SmitAbstract:We have used dissipative particle dynamics to simulate amphiphilic monolayers on the interface between oil and water. An ultralow interfacial tension is imposed by means of Monte Carlo to resemble the amphiphilic films that separate oil and water regions in microemulsions. We calculate the Bending Modulus by analyzing the undulation spectrum. By varying the surfactant chain length and topology we investigate the effect of surfactant structure and composition of the monolayer on the Bending moduli. We find that increasing the thickness has a larger effect than increasing the density of the layer. This follows from the observations that at a given interfacial tension, the Bending Modulus increases with chain length and is larger for linear than branched surfactants. The increase with chain length is approximately linear, which is slower than the theoretical predictions at a fixed area. We also investigated a binary mixture of short and long surfactants compared to pure layers of the same average chain length. We find a roughly linear decrease in Bending Modulus with mole fraction of short surfactants. Furthermore, the mixed film has a lower Bending Modulus than the corresponding pure film for all mole fractions. Linking the Bending moduli to the structure of the surfactants is an important step in predicting the stability of microemulsions.
Markus Deserno - One of the best experts on this subject based on the ideXlab platform.
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Spontaneous curvature, differential stress, and Bending Modulus of asymmetric lipid membranes
Biophysical journal, 2019Co-Authors: Amirali Hossein, Markus DesernoAbstract:Abstract Lipid bilayers can exhibit asymmetric states, in which the physical characteristics of one leaflet differ from those of the other. This most visibly manifests in a different lipid composition, but it can also involve opposing lateral stresses in each leaflet that combine to an overall vanishing membrane tension. Here, we use theoretical modeling and coarse-grained simulation to explore the interplay between a compositional asymmetry and a nonvanishing differential stress. Minimizing the total elastic energy leads to a preferred spontaneous curvature that balances torques due to both Bending moments and differential stress, with sometimes unexpected consequences. For instance, asymmetric flat bilayers, whose specific areas in each leaflet are matched to those of corresponding tensionless symmetric flat membranes, still exhibit a residual differential stress because the conditions of vanishing area strain and vanishing Bending moment differ. We also measure the curvature rigidity of asymmetric bilayers and find that a sufficiently strong differential stress, but not compositional asymmetry alone, can increase the Bending Modulus. The likely cause is a stiffening of the compressed leaflet, which appears to be related to its gel transition but not identical with it. We finally show that the impact of cholesterol on differential stress depends on the relative strength of elastic and thermodynamic driving forces: if cholesterol solvates equally well in both leaflets, it will redistribute to cancel both leaflet tensions almost completely, but if its partitioning free energy prefers one leaflet over the other, the resulting distribution bias may even create differential stress. Because cells keep most of their lipid bilayers in an asymmetric nonequilibrium steady state, our findings suggest that biomembranes are elastically more complex than previously thought: besides a spontaneous curvature, they might also exhibit significant differential stress, which could strongly affect their curvature energetics.
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Do Gel Phase Lipid Bilayers Behave Like Euler Elastica
Biophysical Journal, 2015Co-Authors: Patrick M. Diggins, Zachary A. Mcdargh, Markus DesernoAbstract:The elasticity of fluid phase lipid membranes can be characterized using the Helfrich Hamiltonian, which depends only on the square of the total curvature and the Gaussian curvature and the corresponding curvature moduli: the mean Bending Modulus and the Gaussian curvature Modulus. Even at large curvatures approaching the inverse bilayer thickness, the effect of higher order terms of the elastic energy are minimal. Recently, a method has been developed to derive the Bending Modulus for fluid membranes from the stress-strain relationship of a buckled membrane [1,2]. The method also predicts the shape of the membrane, an Euler Elastica, and this serves as a check that the membrane indeed follows quadratic curvature elasticity. Using a coarse-grained lipid model, we analyze the shape of a buckled membrane in a gel phase and show that it does not behave like an Euler Elastica, even at low curvatures. The deviation from the theory suggests that higher order terms of the total curvature reduce the energy penalty for high curvatures. We present an extended version of the Helfrich Hamiltonian that captures this effect and show that it describes the shapes that we observe in simulations. We then calculate the Bending Modulus, as well as the Modulus describing higher order corrections.[1] Noguchi H., “Anisotropic surface tension of buckled fluid membranes”, Phys. Rev. E 83, 061919 (2011).[2] Hu M., Diggins P., and Deserno M., “Determining the Bending Modulus of a lipid membrane by simulating buckling”, J. Chem. Phys. 138, 214110 (2013).
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Buckling Gel-Phase Membranes is a Way to Measure their Mean Bending Regidity
Biophysical Journal, 2014Co-Authors: Patrick M. Diggins, Markus DesernoAbstract:The elasticity of lipid membranes can be characterized by two curvature moduli: the mean Bending Modulus and the Gaussian curvature Modulus. Due to the relevance of the mean Bending Modulus for countless biological processes, considerable effort has been devoted to determine it_both in experiment and in computational studies. The most common computational approach is to measure the power spectrum of shape undulation modes [1]. Unfortunately, this technique is challenging for gel-phase membranes, because their larger Modulus renders their fluctuations correspondingly smaller. In contrast, methods that infer a membrane's rigidity from actively Bending it yield a signal that becomes stronger as the membrane becomes stiffer. One recently proposed method derives the Modulus from the stress-strain relation of a buckled membrane, and it has been shown to provide accurate results for fluid membranes [2,3]. Using a coarse-grained lipid model, we show that this buckling method can also calculate the mean Bending Modulus of a gel phase membrane. We discuss the efficient implementation of the technique, paying special attention to difficulties that can arise while simulating a membrane in the gel phase. The method also provides insights into the contribution of entropy to the Bending Modulus, and hence its the temperature dependence.[1] Goetz R., Gompper G., and Lipowsky R., “Mobility and elasticity of self-assembled membranes”, Phys. Rev. Lett. 82, 221-224 (1999).[2] Noguchi H., “Anisotropic surface tension of buckled fluid membranes”, Phys. Rev. E 83, 061919 (2011).[3] Hu M., Diggins P., and Deserno M., “Determining the Bending Modulus of a lipid membrane by simulating buckling”, J. Chem. Phys. 138, 214110 (2013).
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Determining the Bending Modulus of a lipid membrane by simulating buckling
The Journal of chemical physics, 2013Co-Authors: Patrick M. Diggins, Markus DesernoAbstract:The force needed to buckle a thin elastic surface is proportional to its Bending rigidity. This fact suggests using a buckling setup to measure the Bending Modulus of lipid membranes. Extending the work of Noguchi [Phys. Rev. E 83, 061919 (2011)10.1103/PhysRevE.83.061919], we systematically derive highly accurate analytical expressions for the forces along and perpendicular to the buckle, and we elucidate some of their counterintuitive properties using the framework of a surface stress tensor. Furthermore, we estimate the corrections to buckling forces due to thermal fluctuations and find them significant only for stresses along the ridges. We then apply this buckling protocol to four different lipid membrane models, which widely differ in their level of resolution and the treatment of solvent, and show that in all cases buckling is a reliable and accurate means for measuring their rigidity. Finally, we show that monitoring both stresses and energies during a simulation offers additional insights into the...
Youhei Kawabata - One of the best experts on this subject based on the ideXlab platform.
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Pressure-dependence of the Bending Modulus of surfactant monolayers in ternary microemulsion systems observed by neutron spin echo
Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2005Co-Authors: Hideki Seto, Michihiro Nagao, Youhei KawabataAbstract:Pressure-dependence of dynamical fluctuations of surfactant monolayers of ternary microemulsion systems with an ionic surfactant and a non-ionic surfactant were investigated by neutron spin echo. The Bending Modulus of surfactant monolayers increased with increasing pressure both in the cases of the ionic surfactant and of the non-ionic surfactant. It is confirmed that the compression of hydrocarbon tails of surfactant is the main origin of pressure-induced phase transitions.
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Temperature‐ and Pressure‐dependences of a Bending Modulus of Surfactant Monolayers in a Ternary Microemulsion Composed of AOT / D2O / decane
AIP Conference Proceedings, 2004Co-Authors: Hideki Seto, Michihiro Nagao, Youhei Kawabata, Takayoshi TakedaAbstract:A Bending Modulus of surfactant monolayers in a microemulsion system composed of AOT, D2O and deuterated decane were investigated by means of neutron spin echo. In this system, a water‐in‐oil droplet structure at ambient temperature and pressure decomposes into two‐phases both with increasing temperature and pressure. However, the Bending Modulus slightly decreased with increasing temperature while it increased with increasing pressure. This behavior was explained in terms of a microscopic model proposed by Wurger (Phys. Rev. Lett. 85 (2000) 337). It was confirmed that an increase of an interaction between hydrocarbon tails of AOT molecules with increasing pressure could be an origin of the pressure‐induced phase transition.
Haoyu Zhang - One of the best experts on this subject based on the ideXlab platform.
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elastic Bending Modulus for single layer black phosphorus
Journal of Physics D, 2015Co-Authors: Haoyu Zhang, Jinwu JiangAbstract:We derive an analytic formula for the elastic Bending Modulus of single-layer black phosphorus (SLBP) based on the valence force field model. The obtained elastic Bending Modulus is 4.8028 eV and 7.9905 eV along the armchair and zigzag directions in the SLBP, respectively. These values are obviously larger than the Bending Modulus of 1.4 eV in graphene due to the intrinsic finite thickness for SLBP. Our derivation analytically illustrates that the elastic Bending Modulus of SLBP is proportional to the square of its intrinsic thickness.
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Elastic Bending Modulus for Single-Layer Black Phosphorus
Journal of Physics D: Applied Physics, 2015Co-Authors: Haoyu Zhang, Jinwu JiangAbstract:We derive an analytic formula for the elastic Bending Modulus of single-layer black phosphorus (SLBP) based on the valence force field model. The obtained elastic Bending Modulus is 4.8028 eV and 7.9905 eV along the armchair and zigzag directions in the SLBP, respectively. These values are obviously larger than the Bending Modulus of 1.4 eV in graphene due to the intrinsic finite thickness for SLBP. Our derivation analytically illustrates that the elastic Bending Modulus of the SLBP is proportional to the square of the intrinsic thickness of the SLBP.