Pressure polymer thermodynamics

Tsujita, Y. Nose, T. Hata, T., "Thermodynamic Properties of Polylethylene glycol) and Poly(tetrahydrofuran). I. P-V-T Relations and Internal Pressure," Polym. J., 5, 201 (1973). 

Over the years, many versions of the EoS theories have been proposed. Several comprehensive reviews of the EoS s used in the polymer thermodynamics have been published. For example, Curro [1974] discussed applications of EoS within a full range of materials and variables, viz. to crystals, glasses, molten polymers and monoatomic liquids. The review discusses fundamentals of the theories as well as it provides a list of available experimental data. The comparison between different EoS was made on two levels, first by comparing the derived expressions for physical quantities (e.g., the characteristic reducing parameters, cohesive energy density, or internal pressure), then comparing how well the EoS describes the observed PVT dependencies for polymers. 

Equation 2.2 shows that D is determined by the interplay of the thermodynamic factor dH/dc and the friction factor /. In general, the friction factor is expected to increase monotonically with increasing c rind decrease with rising temperature. On the other hand, as can be deduced from the known information about osmotic pressure, the thermodynamic factor as a function of c varies in complex ways with solvent quality and temperature. Thus, the concentration dependence of D for a given polymer should exhibit a variety of features depending on solvent conditions. 

The possibilities of pressure, shear and supercritical solvents will be included in the technologies for the production of such advanced products. Current polymer thermodynamics, on the other hand, mainly deals with bulk properties of phases. Although modem microscopic techniques give detailed information about local molecular arrangements and interface composition, it is doubtful whether thermodynamics scientists will be prepared to deal with such macromolecular arrangements and very complex nanostructures when these technologies are developed in the near future. 

Most of the thermodynamic studies reported in literature deal with molecules of a molar mass < 100. Even polymer thermodynamics at present fails to adequately deal with simple molecules like hyperbranched chains, star-shaped macromolecules or with sequence length (distribution) and the resulting morphology in blocky co- and terpolymers. Commercialization of nanostructure-based materials most probably will take place without essential contributions from thermodynamics scientists. One may hope that these polymer thermodynamic scientists will soon get more interested in such molecules and thus become able to achieve major advances in this area and contribute to the next step, the optimization of the production processes for such nanomolecules, via supercritical separations or - modifications and high pressure processing steps. 

The same as classic thermodynamics, polymer thermodynamics is function of pressure, temperature and composite. But in many cases, pressure effects on polymer thermodynamics was neglected, because polymer thermodynamics were often studied under atmosphere. The classic theory of polymer thermodynamics is Flory-Huggins hard lattice theory. In this theory, the hard lattice is incompressible. A rigorously incompressible system should be unaffected by pressure. However, since experimental results show that the critical temperature for polymer demixing system is strongly affected by pressure, it is clear that polymer containing systems show significant departures from this ideal limit. We wish... 

Beiner et al. 1998, Pressure-induced compatibility in a model polymer blend. Physical Review Letters, Vol. 81, No. 3, PP. 594-597 2002, Strong isotopic labeling effects on the pressure dependent thermodynamics of... 

KLE Kleintjens, L.A.L., Effects of chain branching and pressure on thermodynamic properties of polymer solutions, Ph.D. Thesis, Univ. Essex, 1979. 

In Chap. 8 we discuss the thermodynamics of polymer solutions, specifically with respect to phase separation and osmotic pressure. We shall devote considerable attention to statistical models to describe both the entropy and the enthalpy of mixtures. Of particular interest is the idea that the thermodynamic... 

The title of this chapter is somewhat misleading. In one sense it is too broad, in another sense too restrictive. We shall really discuss in detail only the phase separation and osmostic pressure of polymer solutions a variety of other thermodynamic phenomena are ignored. In this regard the chapter title would better read Some aspects of. . . . Throughout this volume only a small part of what might be said about any topic is actually presented, so this modifying phrase is taken to be understood and is omitted. 

Polymorphism. Many crystalline polyolefins, particularly polymers of a-olefins with linear alkyl groups, can exist in several polymorphic modifications. The type of polymorph depends on crystallisa tion conditions. Isotactic PB can exist in five crystal forms form I (twinned hexagonal), form II (tetragonal), form III (orthorhombic), form P (untwinned hexagonal), and form IP (37—39). The crystal stmctures and thermal parameters of the first three forms are given in Table 3. Form II is formed when a PB resin crystallises from the melt. Over time, it is spontaneously transformed into the thermodynamically stable form I at room temperature, the transition takes about one week to complete. Forms P, IP, and III of PB are rare they can be formed when the polymer crystallises from solution at low temperature or under pressure (38). Syndiotactic PB exists in two crystalline forms, I and II (35). Form I comes into shape during crystallisation from the melt (very slow process) and form II is produced by stretching form-1 crystalline specimens (35). 

The parameters which characterize the thermodynamic equilibrium of the gel, viz. the swelling degree, swelling pressure, as well as other characteristics of the gel like the elastic modulus, can be substantially changed due to changes in external conditions, i.e., temperature, composition of the solution, pressure and some other factors. The changes in the state of the gel which are visually observed as volume changes can be both continuous and discontinuous [96], In principle, the latter is a transition between the phases of different concentration of the network polymer one of which corresponds to the swollen gel and the other to the collapsed one. 

The difficulties engendered by a hypothetical liquid standard state can be eliminated by the use of unsymmetrically normalized activity coefficients. These have been used for many years in other areas of solution thermodynamics (e.g., for solutions of electrolytes or polymers in liquid solvents) but they have only recently been employed in high-pressure vapor-liquid equilibria (P7). 

Theta temperature is one of the most important thermodynamic parameters of polymer solutions. At theta temperature, the long-range interactions vanish, segmental interactions become more effective and the polymer chains assume their unperturbed dimensions. It can be determined by light scattering and osmotic pressure measurements. These techniques are based on the fact that the second virial coefficient, A2, becomes zero at the theta conditions. 

Microdomain stmcture is a consequence of microphase separation. It is associated with processability and performance of block copolymer as TPE, pressure sensitive adhesive, etc. The size of the domain decreases as temperature increases [184,185]. At processing temperature they are in a disordered state, melt viscosity becomes low with great advantage in processability. At service temperamre, they are in ordered state and the dispersed domain of plastic blocks acts as reinforcing filler for the matrix polymer [186]. This transition is a thermodynamic transition and is controlled by counterbalanced physical factors, e.g., energetics and entropy. 

Since we are interested in this chapter in analyzing the T- and P-dependences of polymer viscoelasticity, our emphasis is on dielectric relaxation results. We focus on the means to extrapolate data measured at low strain rates and ambient pressures to higher rates and pressures. The usual practice is to invoke the time-temperature superposition principle with a similar approach for extrapolation to elevated pressures [22]. The limitations of conventional t-T superpositioning will be discussed. A newly developed thermodynamic scaling procedure, based on consideration of the intermolecular repulsive potential, is presented. Applications and limitations of this scaling procedure are described. 

The industrial process for which this methodology was developed comprised polymerizing a monomer in the presence of a mixed solvent, the catalyst and other Ingredients. Once the batch polymerization is complete, the product requires removal of the solvents to a specified level. The solvents, an aromatic Cy and aliphatic Cy compounds, are removed by a two-step process schematically shown in Figure 1. As shown, the polymer slurry is initially flashed to a lower pressure (Pj ) in the presence of steam and water. The freely available solvent in the polymer-solvent mixture is removed by the shift in thermodynamic equilibrium. Solvent attached to the surface of the polymer particle is removed by the steam. In this first step, 90% of the total solvents are recovered. The remaining solvents are recovered in the second flash, where the effluent is almost all water with very low concentrations of the solvents. 

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

The vapor pressure of a polymer is, of course, far too small to measure We may, nevertheless, insist that such a vapor pressure exists, however small it may be. Or we may resort to the use of the escaping tendency, or fugacity, in place of the partial vapor pressure in the development given above, in accordance with usual thermodynamic procedures applied to the treatment of solutions. The treatment given here is in no way restricted to volatile solutes. 

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