Bending tensions and the bending rigidity of fluid membranes

1993 ◽  
Vol 3 (3) ◽  
pp. 287-292 ◽  
Author(s):  
W. Helfrich ◽  
M. M. Kozlov
2000 ◽  
Vol 11 (08) ◽  
pp. 1509-1518 ◽  
Author(s):  
HIROSHI KOIBUCHI ◽  
MITSURU YAMADA

We study two-dimensional triangulated surfaces of sphere topology by the canonical Monte Carlo simulation. The coordination number of surfaces is made as uniform as possible. The triangulation is fixed in MC so that only the positions X of vertices may be considered as the dynamical variable. The well-known Helfrich energy function S = S1 + bS2 is used for the definition of the model where S1 and S2 are the area and bending energy functions respectively and b is the bending rigidity. The discretizations of S1 and S2 are identical with that of our previous MC study for a model of fluid membranes. We find that the specific heats have peaks at finite bending rigidities and obtain the critical exponents of the phase transition by the finite-size scaling technique. It is found that our model of crystalline membranes undergoes an expected second order phase transition.


1991 ◽  
Vol 1 (9) ◽  
pp. 1121-1132 ◽  
Author(s):  
M. Skouri ◽  
J. Marignan ◽  
J. Appell ◽  
G. Porte

1990 ◽  
Vol 51 (21) ◽  
pp. 2395-2398 ◽  
Author(s):  
Shigeyuki Komura ◽  
Artur Baumgärtner

Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley

This chapter contains the essential statistical mechanics required to understand the inner workings of, and interpretation of results from, computer simulations. The microcanonical, canonical, isothermal–isobaric, semigrand and grand canonical ensembles are defined. Thermodynamic, structural, and dynamical properties of simple and complex liquids are related to appropriate functions of molecular positions and velocities. A number of important thermodynamic properties are defined in terms of fluctuations in these ensembles. The effect of the inclusion of hard constraints in the underlying potential model on the calculated properties is considered, and the addition of long-range and quantum corrections to classical simulations is presented. The extension of statistical mechanics to describe inhomogeneous systems such as the planar gas–liquid interface, fluid membranes, and liquid crystals, and its application in the simulation of these systems, are discussed.


2019 ◽  
Vol 116 (10) ◽  
pp. 4012-4017 ◽  
Author(s):  
Yiping Cao ◽  
Sreenath Bolisetty ◽  
Gianna Wolfisberg ◽  
Jozef Adamcik ◽  
Raffaele Mezzenga

Amyloid fibrils have evolved from purely pathological materials implicated in neurodegenerative diseases to efficient templates for last-generation functional materials and nanotechnologies. Due to their high intrinsic stiffness and extreme aspect ratio, amyloid fibril hydrogels can serve as ideal building blocks for material design and synthesis. Yet, in these gels, stiffness is generally not paired by toughness, and their fragile nature hinders significantly their widespread application. Here we introduce an amyloid-assisted biosilicification process, which leads to the formation of silicified nanofibrils (fibril–silica core–shell nanofilaments) with stiffness up to and beyond ∼20 GPa, approaching the Young’s moduli of many metal alloys and inorganic materials. The silica shell endows the silicified fibrils with large bending rigidity, reflected in hydrogels with elasticity three orders of magnitude beyond conventional amyloid fibril hydrogels. A constitutive theoretical model is proposed that, despite its simplicity, quantitatively interprets the nonmonotonic dependence of the gel elasticity upon the filaments bundling promoted by shear stresses. The application of these hybrid silica–amyloid hydrogels is demonstrated on the fabrication of mechanically stable aerogels generated via sequential solvent exchange, supercriticalCO2removal, and calcination of the amyloid core, leading to aerogels of specific surface area as high as 993m2/g, among the highest values ever reported for aerogels. We finally show that the scope of amyloid hydrogels can be expanded considerably by generating double networks of amyloid and hydrophilic polymers, which combine excellent stiffness and toughness beyond those of each of the constitutive individual networks.


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