Bending/rigidity modulus

What are typical values for the parameters k and kl The bending rigidity of surfactant films is typically of the order of 1-20 kBT at room temperature. Factors that reduce k are short alkyl chains, cosurfactants, double-chain surfactants with unequal chains, and cis-unsaturated bonds. For the saddle-splay modulus only few measurements have been done. It tends to be negative with an amount much smaller than the bending rigidity for the same system. 

I J l K k k Lo M m N Electric current (A) Nucleation rate (s 1 m 3) Length of one chain link (m) in a polymer chain Spring constant (Nm-1), equilibrium constant (e.g. mol/L) Bending rigidity (J) Saddle-splay modulus (J) Thickness of a polymer brush (m) Molar mass (kg mol-1), torque in Ch. 11 (Nm) Mass (kg), molecular mass (kg per molecule) Number of molecules (dimensionless or mol), number of segments in a linear polymer chain... 

Note that the product of the foundation modulus and the plate rigidity controls the stiffness. Increasing the plate bending rigidity or the foundation modulus will increase the stiffness, but the two methods will have opposite effects on the characteristic length. 

The existence of a cortical tension suggests that there is a cortex — a relatively thick layer of F-actin filaments and myosin — that is capable of exerting a finite tension at the surface. If such a layer exists, it would have a finite thickness and bending rigidity. Zhelev et al. [1994] aspirated the surface of neutrophils into pipettes with increasingly smaller diameters and determined that the surface had a bending modulus of about 1 to 2 X 10 J, which is 5 to 50 times the bending moduli for erythrocyte or lipid bilayer membranes. The thickness of the cortex should be smaller than the radius of smallest pipette used in this study, which was 0.24 fjtra. 

We have already mentioned in the Introduction that microemulsions containing long-chain amphiphiles can be described by interfacial models. These models are based on the curvature elasticity of the amphiphilic monolayer and thus contain as material parameters the bending rigidity and the saddle-splay modulus. These parameters have to be calculated from a more microscopic model. A somewhat similar problem occurs in the... 

Fiber Density (g/cm j Tenacity cN/denier (MPa) Breaking strain (%) Initial modulus N/tex (GPa) Relative bending rigidity ... 

Electrical/optical conductivity Resistivity (of insulating layer) Act as an elastic circuit board Attenuation of signal Bending rigidity Flexural endurance Elongation and creep Tensile strength and modulus Weight... 

Only a simplified version of the fluid plate model is presented here to establish a crude relationship between the stretching modulus and the bending rigidity of fluid monolayers. The resulting formulas, frequently used in the literature, permit some estimates and serve to illustrate the role of the reference surface. 

The phase diagram of such curved surfaces in the amphiphilic system has been studied by Huse and Liebler [8] on the basis of the elastic energy of the surface. The phase behavior is determined by the balance of the surface tension, the bending rigidity and the saddle-splay modulus of the curved interface and the IPMS structure appears when the saddle-splay modulus increased to a some critical value. Mathematically, more than 30 species of curved surfaces have been reported as IPMS [9] and, experimentally, several types of IPMS structures have been found in cubic phases of lipid-water systems [10]. Concerning the formation mechanism of the cubic network, Ranpon and Charvolin [6] found the epitaxial relationships between reticular planes of these three phases in the... 

C < 1- The smallest eigenvalue of M is a convenient way to measure h ) for an open membrane. The scale-dependent bending rigidity k in the flat phase scales as with tj = 2 - 2, while the scale-dependent shear modulus scales as with % = 4C - Nelson and Peliti car-... 

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