Steric entanglements

In atomic force microscopy (AFM) indentation measurements, thin films of Ca " -PA gels displayed an apparent elastic modulus of 200 MPa, whereas HCl-PA gels had an elastic modulus of 100 MPa (Fig. 5d) [168]. The mesh size of Ca " -PA gels was calculated according to the MacKintosh model for sterically entangled semiflexible networks. The persistence length and the mesh size were estimated to be 102 and 20 nm, respectively [182]. 

The approach is based on a combination of the linear viscoelastic theory with elements of the elasticity theory developed by Erman, Floiy and Monnery in which the free energy of elasticity, AA i, is considered as a sum of the phantom component, AApj, and a component of steric entanglements determined by interlacing chains andjunctions. ... 

The superscript 0 on the diffusivities listed above refers to the fact that these are for dilute solutions. In a concentrated system the rate of rotation will be slowed down considerably because of steric hinderance from nearest neighbors. The nature of the entanglements from other rods onto a test rod is such that the translational motion perpendicular to the rod axis becomes highly constrained. The translation along the chain axis, on the other hand, is for the most part unaffected. The steric interactions imposed by the neighboring rods on a single test rod can be modeled by placing such a rod within a tube of radius ac... 

In the case of low-molecular-weight polar resins such as VE resins, relatively thin and dense adsorption layers can be assiuned. This should result in low viscosities due to low effective phase volumes of the dispersed phase and weak interparticulate interactions forces according to steric stabilization. However, addition of a solvent like styrene will influence the Hamaker constant of the liquid medium and of the adlayer and the structure of the adlayer in terms of swelling and/or multilayer formation. In particular, any multilayer formation could result in surface layer entanglement depending on the solvency of the liquid medium expressed in terms of the Flory-Huggins parameter % [11]. These effects should dramatically influence the viscosity and rest structure of the dispersion, as seen in the experiments. 

The formation of elastic networks from semiflexible cytoskele-tal filaments requires cross-linkers. As discussed below, filaments as stiff as F-actin or MTs do not form the same kinds of sterically trapped entanglements that can form in flexible polymer melts and, therefore, do not maintain shear stresses for times that are relevant for cell mechanics. Therefore, the viscoelastidty of the cell and of cytoskeletal preparations in vitro depends very strongly on the affinity and geometry of the bonds between filaments formed by various aoss-linkers, such as those listed in Table 1. 

According to the steric stmcture there can be three major configurations—a linear chain, a branched chain, or a cross-linked (network or 3-dimensional) chain, as shown in Figure 3-2. The linear chain has no branches or chemical links with neighboring chains (albeit with the existence of physical links, called entanglements). 

The Constrained Junction Fluctuation Model. The affine and phantom models are two limiting cases on the network properties and real network behavior is not perfectly described by them (recall Fig. 29.2). Intermolecular entanglements and other steric constraints on the fluctuations of junctions have been postulated as contributing to the elastic free energy. One widely used model proposed to explain deviations from ideal elastic behavior is that of Ronca and Allegra [34] and Hory [36]. They introduced the assumption of constrained fluctuations and of affine deformation of fluctuation domains. 

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