Polymers entropic ordering

Entropic ordering also appears in nonbiological settings, especially in the ways polymer molecules clump together. For example, polymers added to. paint to improve the flow characteristics of the paint actually caused it to coagulate because of depletion forces. 

The formation of a polymer from monomers is not entropically favorable. This is because we convert many monomer molecules into a few polymer molecules. This greatly reduces the disorder and motion of the system. The ordering effect observed in polymerization is mitigated somewhat in condensation polymerization processes, by the evolution of low molecular weight species, which contribute to the entropy of the system. 

Water-soluble polymers in general, and especially polyelectrolytes, are often difficult due to their specific and long range electrostatic interactions, which complicate all analytical techniques that rely on single particle properties that are usually realized by high dilution. In most cases the ionic strength of the solution must be increased by the addition of salt in order to screen electrostatic forces. Ideally, SEC separation is predominantly governed by entropic interactions,... 

Homopolymers such as poly[(V)-3,7-dimethyloctyl-2-methylpropylsilylene], 117, were initially studied, and the helix-helix transition was discussed in terms of an entropically driven phenomenon in which at temperatures below Tc the side chains of the helical polymer are in a very ordered state and enforce a particular screw sense, whereas above Tc, the side chains become disordered such that the main chain can relax into the opposite screw sense.314 This concept is expressed in Figure 47. 

Each submolecule will experience a frictional drag with the solvent represented by the frictional coefficient /0. This drag is related to the frictional coefficient of the monomer unit (0- If there are x monomer units per link then the frictional coefficient of a link is x(0- If we aPply a step strain to the polymer chain it will deform and its entropy will fall. In order to attain its equilibrium conformation and maximum entropy the chain will rearrange itself by diffusion. The instantaneous elastic response can be thought of as being due to an entropic spring . The drag on each submolecule can be treated in terms of the motion of the N+ 1 ends of the submolecules. We can think of these as beads linked... 

The structure of this interface determines fhe sfabilify of PEMs, the state of water, the strength of interactions in the polymer/water/ion system, the vibration modes of side chains, and the mobilities of wafer molecules and protons. The charged polymer side chains contribute elastic ("entropic") and electrostatic terms to the free energy. This complicated inferfacial region thereby largely contributes to differences in performance of membranes wifh different chemical architectures. Indeed, the picture of a "polyelectro-lyfe brush" could be more insighttul than the picture of a well-separated hydrophobic or hydrophilic domain structure in order to rationalize such differences. ... 

Nano-Confinement. There are limited, but interesting studies, regarding the confinement in ordered mesoporous materials. First observations were made on nematic liquids within mesoporous SBA-15 host materials which showed a change in the phase transition, when confined within the mesoporous cavities. To evidence also that there are many studies of confinement in mesoporous materials in the polymer diffusion and membrane literature, but they refer essentially to entropic effects due to restricted motion of these materials inside the ordered mesoporous materials which in enhanced by more hydrophobic and less polar surfaces. This is especially true as the molecules become larger, because the number of conformations the molecule can adopt in a confined space is limited. We refer here, on the contrary, to aspects relevant for catalysis and in which thus the dimensions of the molecules (of the order of 0.1 nm) is far below the dimensions of the cavities (around 5 nm for SBA-15, for example). 

The fundamental driving force behind the remarkable elastic properties of the elastin polymer is believed to be entropic, where stretching decreases the entropy of the system and elastic recoil is driven by a spontaneous return to maximum entropy. The precise molecular basis for elasticity has not been fully elucidated and a number of models exist. Two main categories of structure-function models have been proposed those in which elastin is considered to be isotropic and devoid of structure, and those which consider elastin to be anisotropic with regions of order (Vrhovski and Weiss, 1998). 

At temperatures well below Tg, when entropic motions are frozen and only elastic bond deformations are possible, polymers exhibit a relatively high modulus, called the glassy modulus (Eg) which is on the order of 3 Gpa. As the temperature is increased through Tg the stiffness drops dramatically, by perhaps two orders of magnitude, to a value called rubbery modulus Er. In elastomers that have been permanently crosslinked by sulphur vulcanization or other means, the values of Er, is determined primarily by the crosslink density the kinetics theory of rubber elasticity gives the relation as... 

Rubber materials are soft, elastic solids, made of mobile, flexible polymer chains (with a glass transition temperature (Tg) typically lower than 0 °C) which are linked together to form a three-dimensional network. They are characterised by a low, frequency independent elastic modulus (of the order 105 to 106 Pa) and usually by a large maximum reversible deformation (up to a few hundred per cent). Rubber elasticity is based on the properties of crosslinked polymer chains at large spatial scales, the presence of crosslinks ensures the reversibility of the deformation, while at short scales, mobile polymer chains behave as molecular, entropic springs. 

The other kind of systems largely studied, consists of polymethylmethacrylate (PMMA) or silica spherical particles, suspended in organic solvents [23,24]. In these solvents Q 0 and uy(r) 0. The particles are coated by a layer of polymer adsorbed on their surface. This layer of polymer, usually of the order of 10-50 A, provides an entropic bumper that keeps the particles far from the van der Waals minimum, and therefore, from aggregating. Thus, for practical purposes uw(r) can be ignored. In this case the systems are said to be sterically stabilized and they are properly considered as suspensions of colloidal particles with hard-sphere interaction [the pair potential is of the form given by Eq. (5)]. 

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