Entropic constraints

These transverse entanglements, separated by a typical length ta govern the elastic response of solutions, in a way first outlined by Isambert and Maggs. A more complete discussion of the rheology of such solutions can be found in Morse and Hiimer et al.The basic result for the mbber-like plateau shear modulus for such solutions can be obtained by noting that the mrmber density of entropic constraints (entanglements) is thus where n = fl[a ) is... 

The blending of polymers offers the opportunity to create materials with modified properties such as impact strength or rigidity without the necessity to synthesize a new polymer. However, because of entropic constraints, most polymer combinations are immiscible. A polymer blend can be produced by a non-reactive or reactive route. 

The preceding study is extended [37] by replacing solvent partides with polymer chains. A set of typical snapshots at the end of simulations is presented in Figures 2.8 and 2.9 with attractive and repulsive interactions between the polymers and the sheets with the polymer matrix density ( ) = 0.2. Let us examine these figures to probe the effect of interaction between the sheets and the polymer chains and their molecular weight. Because of the entropic constraints on the conformations, shorter chains can move and intercalate more easily than the chains with higher molecular weights. 

In the case of the retro Diels-Alder reaction, the nature of the activated complex plays a key role. In the activation process of this transformation, the reaction centre undergoes changes, mainly in the electron distributions, that cause a lowering of the chemical potential of the surrounding water molecules. Most likely, the latter is a consequence of an increased interaction between the reaction centre and the water molecules. Since the enforced hydrophobic effect is entropic in origin, this implies that the orientational constraints of the water molecules in the hydrophobic hydration shell are relieved in the activation process. Hence, it almost seems as if in the activated complex, the hydrocarbon part of the reaction centre is involved in hydrogen bonding interactions. Note that the... 

Miscibility or compatibility provided by the compatibilizer or TLCP itself can affect the dimensional stability of in situ composites. The feature of ultra-high modulus and low viscosity melt of a nematic liquid crystalline polymer is suitable to induce greater dimensional stability in the composites. For drawn amorphous polymers, if the formed articles are exposed to sufficiently high temperatures, the extended chains are retracted by the entropic driving force of the stretched backbone, similar to the contraction of the stretched rubber network [61,62]. The presence of filler in the extruded articles significantly reduces the total extent of recoil. This can be attributed to the orientation of the fibers in the direction of drawing, which may act as a constraint for a certain amount of polymeric material surrounding them. 

The elastic contribution to Eq. (5) is a restraining force which opposes tendencies to swell. This constraint is entropic in nature the number of configurations which can accommodate a given extension are reduced as the extension is increased the minimum entropy state would be a fully extended chain, which has only a single configuration. While this picture of rubber elasticity is well established, the best model for use with swollen gels is not. Perhaps the most familiar model is still Flory s model for a network of freely jointed, random-walk chains, cross-linked in the bulk state by connecting four chains at a point [47] ... 

The earliest and simplest approach in this direction starts from Langevin equations with solutions comprising a spectrum of relaxation modes [1-4], Special features are the incorporation of entropic forces (Rouse model, [6]) which relax fluctuations of reduced entropy, and of hydrodynamic interactions (Zimm model, [7]) which couple segmental motions via long-range backflow fields in polymer solutions, and the inclusion of topological constraints or entanglements (reptation or tube model, [8-10]) which are mutually imposed within a dense ensemble of chains. 

Entropic trap A strategy aimed at improving the efficiency of catalytic antibodies, via the incorporation of a molecular constraint into the transition state analogue that gives the hapten a higher energy conformation than that of the reaction product. 

The efiect is thus not related to geometrical constraints induced on complexes anchored in mesoporous charmels (sometimes also called as confinement efiect, even if this definition is not properly correct), neither to shape-selectivity effects as possible in zeolites, since the size of mesoporous charmels is much larger than those of micro-porous materials. Instead, an effective modification on the characteristics of the fluids is observed due to the electrostatic field generated by the charmel walls. This is an enthalpic effect versus an entropic effect as observed when the modification is instead related to limitations in the translation modes of molecules. Recently, it was also demonstrated that wall curvature influence the molecular orientation of the... 

J>j = fij-. For chemical interactions and entropic effects with no other constraint (e.g., interstitial diffusion). Section 3.1.4. 

The resulting physical picture of a rubber-like system as a close-packed collection of mers is radically different from the two-phase image introduced by James and Guth [10]. The latter represents mbber as a network of chains, which act as entropic springs in tension, embedded in a bath of simple liquid. The bath gives rise to an isotropic pressure, whereas the network is responsible for the deviatoric stress. More recent physical pictures consider as well the distribution of network junctions in the liquid and the action of these junctions as constraints on the free motion of a generic chain of the network. The current description is on the mer or atomic level and treats the full stress tensor, both the mean and deviatoric portions, in terms of atomic interactions. 

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