Phase states, classical polymer

The thermodynamic behavior of fluids near critical points is drastically different from the critical behavior implied by classical equations of state. This difference is caused by long-range fluctuations of the order parameter associated with the critical phase transition. In one-component fluids near the vapor-liquid critical point the order parameter may be identified with the density or in incompressible liquid mixtures near the consolute point with the concentration. To account for the effects of the critical fluctuations in practice, a crossover theory has been developed to bridge the gap between nonclassical critical behavior asymptotically close to the critical point and classical behavior further away from the critical point. We shall demonstrate how this theory can be used to incorporate the effects of critical fluctuations into classical cubic equations of state like the van der Waals equation. Furthermore, we shall show how the crossover theory can be applied to represent the thermodynamic properties of one-component fluids as well as phase-equilibria properties of liquid mixtures including closed solubility loops. We shall also consider crossover critical phenomena in complex fluids, such as solutions of electrolytes and polymer solutions. When the structure of a complex fluid is characterized by a nanoscopic or mesoscopic length scale which is comparable to the size of the critical fluctuations, a specific sharp and even nonmonotonic crossover from classical behavior to asymptotic critical behavior is observed. In polymer solutions the crossover temperature corresponds to a state where the correlation length is equal to the radius of gyration of the polymer molecules. A... 

In polymer science, the 1980s were marked by the birth and turbulent development of a new field the chemistry and physics of liquid-crystal polymers. This field, which includes synthesists, theoretical physicists, classic physical chemists, polymer chemists, and production engineers, has grown in an intensely developed new direction which has very rapidly led to practical successes in the creation of high-strength chemical fibers and is now drawing the attention of optical scientists and specialists in microelectronics. However, the main point is that the liquid-crystalline state in polymers and polymer systems is not only extremely common (many hundreds of polymeric liquids crystals have now been described) but is also a stable equilibrium phase state of polymeric substances. 

The chains that make up a polymer can adopt several distinct physical phases the principal ones are rubbery amorphous, glassy amorphous, and crystalline. Polymers do not crystallize in the classic sense portions of adjacent chains organize to form small crystalline phases surrounded by an amorphous matrix. Thus, in many polymers the crystalline and amorphous phases co-exist in a semicrystalline state. 

Now again, a state of inhomogeneity in polymers, so especially interesting in films and interfaces, occur when discontinuities are built into the main valence chains and networks. Block polymers are the classic embodiments of this. Many periodic distances separating domains in such alternating or rhymthic copolymers have been reported. These indicate existence of phases in laminar domains and, in other cases, of spherical domains.(51) Cases are shown experimentally for styrene/isoprene copolymers and also for styrene/butadiene.(52,53,54)... 

A Statistical-Mechanics based Lattice-Model Equation of state (EOS) for modelling the phase behaviour of polymer-supercritical fluid mixtures is presented. The EOS can reproduce qualitatively all experimental trends observed, using a single, adjustable mixture parameter and in this aspect is better than classical cubic EOS. Simple mixtures of small molecules can also be quantitatively modelled, in most cases, with the use of a single, temperature independent adjustable parameter. 

This general scheme of events, although valid for all materials, does not predict the same effects under the same conditions for all species. It depends quite critically on the complexity of the molecule. Large biomolecules or polymers have no gas-phase existence and even in solution, or the liquid state, may have a well-defined molecular shape, while small molecules like ammonia settle into a classical structure only at very low temperatures. 

The intention of this brief survey has been to demonstrate that besides the "classical" aspects of isotropic polymer solutions and the amorphous or partially crystalline state of polymers, a broad variety of anisotropic structures exist, which can be induced by definable primary structures of the macromolecules. Rigid rod-like macromolecules give rise to nematic or smectic organization, while amphiphilic monomer units or amphiphilic and incompatible chain segments cause ordered micellar-like aggregation in solution or bulk. The outstanding features of these systems are determined by their super-molecular structure rather than by the chemistry of the macromolecules. The anisotropic phase structures or ordered incompatible microphases offer new properties and aspects for application. 

For mixtures of low-molecular-weight compounds only, it can be stated that mixing is the rule and the presence of two liquid phases is the exception. The contrary typically occurs for polymer solutions, for which the presence of two liquid phases is evidenced very often. Figure 16.2 presents a classical example, the extensively studied acetone/polystyrene system at three different polymer molecular weights. The most important features of polymer-solvent LLE can be discussed based on this graph ... 

For example, simple fluorescence intensity measurements on dispersed hydrocarbon probes such as anthracene [17], perylene [18], pyrene [6,17,22], 9,10-dimethylanthracene (DMA) [60], and coumarin dyes [62] have confirmed that PMAA displays pH-dependent solution behavior. A marked decrease in the intensity of the probe occurs between pH 5 and 6, which coincides with the conformational transition of PMAA as determined by classical methods [2-4,47-50]. Two interrelated effects account for this behavior the solubilizing capacity of the polymer promotes an increase in the concentration of the probe in the solution [6,17,18,60,62] and because the intensity of the fluorescence observed is proportional to the excited state population the resulting emission is enhanced. The hydrocarbons may also be considered to be preferentially solubilized within the hydrophobic domains or structures of the hypercoiled state [6,22]. This results in a degree of protection from the deactivating effects of the aqueous phase and a concomitant increase in the fluorescence observed [6,17,18,22,60,62]. 

In its classic form, ECL is regarded as a solution-phase process, on the basis of both direct evidence (Problem 18.4) and the expectation that metal electrodes quench excited states (18, 19). The band structure of semiconductor electrodes sometimes removes the latter difficulty (see Section 18.2), and emission from excited states produced directly in heterogeneous charge transfer at semiconductors can occur (20-22). More recently, even surface films, such as monolayer assemblies and polymer-modified electrodes (Chapter... 

PFS block co-polymers in which the blocks are immiscible (which is generally the case) would be expected to self-assemble to form phase-separated organometallic domains in the solid state. Based on the classical behavior of organic block co-polymers, thin films of polyferrocene diblock co-polymers would be expected to form domains such as spheres, cylinders (or their anti-structures), double diamonds (or gyroids), or lamellae (Section 1.2.5). The preferred domain structure would be expected to be controlled by the ratio of the blocks, their degree of immiscibility (as defined by the Flory-Huggins interaction parameter y), and the overall molecular weight of the block co-polymer. 

The purpose of this chapter is to review the kinetics and mechanisms of photochemical reactions in amorphous polymer solids. The classical view for describing the kinetics of reactions of small molecules in the gas phase or in solution, which involves thermally activated collisions between molecules of approximately equivalent size, can no longer be applied when one or more of the molecules involved is a polymer, which may be thousands of times more massive. Furthermore, the completely random motion of the spherical molecules illustrated in Fig. la, which is characteristic of chemically reactive species in both gas and liquid phase, must be replaced by more coordinated motion when a macromolecule is dissolved or swollen in solvent (Fig. b). Furthermore, a much greater reduction in independent motions must occur when one considers a solid polymer matrix illustrated in Fig. Ic. According to the classical theory of thermal reactions the collisional energy available in the encounter must be suificient to transfer at least one of the reacting species to some excited-state complex from which the reaction products are derived. The random thermal motion thus acts as an energy source to drive chemical reactions. 

Among the observable facts it was found that there is no significant effect of the concentration of emulsifier on this system. Therefore, the implication is that the polymerization initially takes place exclusively in the aqueous phase [136]. The resulting polymer particle precipitates as it forms [134]. In this case we may assume, that only a microscopic phase-separation takes place. The polymer particles which form adsorb emulsifier fiom the aqueous environment and remain dispersed. Then the particles may absorb more monomer somewhat in the manner called for by the Smith-Ewart theory. Of course, other dissolved vinyl acetate monomer molecules may continue to be polymerized in aqueous solution, thus accounting for the increase in the number of particles as the polymerization proceeds to high conversion. The classical Smith-Ewart treatment states that the number of particles is determined by the surfactant to monomer ratio and, in effect remains constant throughout the process. 

In the NET-GP analysis, the glassy polymer-penetrant phases are considered homogeneous, isotropic, and amorphous, and their state is characterized by the classical thermodynamic variables (i.e. composition, temperature, and pressure) with the addition of a single-order parameter, accounting for the departure from equilibrium. The specific volume of the polymer network, or, equivalently, the polymer density Pp, is chosen as the proper order parameter. In other words, the hindered mobility of the glassy polymer chains freezes the material into a non-equilibrium state that can be labeled by the... 

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