Thermodynamics polymer systems

C. M. Marques, M. E. Cates. Nonlinear thermodynamic relaxation in living polymer systems. J Phys II (France) 7 489-492, 1991. 

In many process design applications like polymerization and plasticization, specific knowledge of the thermodynamics of polymer systems can be very useful. For example, non-ideal solution behavior strongly governs the diffusion phenomena observed for polymer melts and concentrated solutions. Hence, accurate modeling of... 

If the polymer system was able to exist in an equilibrium state only, then a strictly defined correlation between (a, ph) and (a, ph) would exist in particular conditions, according to minimum of free energy of system formation. Consequently, there would occur only one temperature at which process initiation is thermodynamically probable. In rare ca.ses there may occur different correlations between ( ph, a) and ( ph, a ), which display one and the same value of free energy minimum of system formation. 

A surface is that part of an object which is in direct contact with its environment and hence, is most affected by it. The surface properties of solid organic polymers have a strong impact on many, if not most, of their apphcations. The properties and structure of these surfaces are, therefore, of utmost importance. The chemical stmcture and thermodynamic state of polymer surfaces are important factors that determine many of their practical characteristics. Examples of properties affected by polymer surface stmcture include adhesion, wettability, friction, coatability, permeability, dyeabil-ity, gloss, corrosion, surface electrostatic charging, cellular recognition, and biocompatibility. Interfacial characteristics of polymer systems control the domain size and the stability of polymer-polymer dispersions, adhesive strength of laminates and composites, cohesive strength of polymer blends, mechanical properties of adhesive joints, etc. 

There are two major experimental techniques that can be used to analyze hydrogen bonding in noncrystalline polymer systems. The first is based on thermodynamic measurements which can be related to molecular properties by using statistical mechanics. The second, and much more powerful, way to elucidate the presence and nature of hydrogen bonds in amorphous polymers is by using spectroscopy (Coleman et al., 1991). From the present repertoire of spectroscopic techniques which includes IR, Raman, electronic absorption, fluorescence, and magnetic resonance spectroscopy, the IR is by far the most sensitive to the presence of hydrogen bonds (Coleman et al., 1991). 

Klenin VJ (1999) Thermodynamics of systems containing flexible chain polymers. 

In summary, it is clear that water absorbs into amorphous polymers to a significant extent. Interaction of water molecules with available sorption sites likely occurs via hydrogen bonding such that the mobility of the sorbed water is reduced and the thermodynamic state of this water is significantly altered relative to bulk water. Yet accessibility of the water to all potential sorption sites appears to be dependent on the previous history and physical-chemical properties of the solid. In this regard, the water-solid interaction in amorphous polymer systems is a dynamic relationship depending quite strongly on water activity and temperature. 

Higaki, Y Otsuka, H. Takahara, A. A thermodynamic polymer cross-linking system based on radically exchangeable covalent bonds. Macromolecules 2006, 39, 2121-2125. 

Polymers don t behave like the atoms or compounds that have been described in the previous sections. We saw in Chapter 1 that their crystalline structure is different from that of metals and ceramics, and we know that they can, in many cases, form amorphous structures just as easily as they crystallize. In addition, unlike metals and ceramics, whose thermodynamics can be adequately described in most cases with theories of mixing and compound formation, the thermodynamics of polymers involves solution thermodynamics—that is, the behavior of the polymer molecules in a liquid solvent. These factors contribute to a thermodynamic approach to describing polymer systems that is necessarily different from that for simple mixtures of metals and compounds. Rest assured that free energy will play an important role in these discussions, just as it has in previous sections, but we are now dealing with highly inhomogeneous systems that will require some new parameters. 

Polymer-polymer systems exhibit phase behavior similar to other mixtures, such that an initially uniform system separates into two or more phases as a result of small change in thermodynamic variable. Two mechanisms can be envisioned to explain this phenomenon nucleation and growth (NG), and spinodal decomposition (SD). 

From a thermodynamic and mechanical point of view, the glass transition, Tg, is one of the most important parameters for characterizing a polymer system [1-3,24,29,32,33]. Consequently, the determination of the Tg is usually one of the first analyses performed on a polymer system. 

In Fiery s theory of the excluded volume (27), the chains in undiluted polymer systems assume their unperturbed dimensions. The expansion factor in solutions is governed by the parameter (J — x)/v, v being the molar volume of solvent and x the segment-solvent interaction (regular solution) parameter. In undiluted polymers, the solvent for any molecule is simply other polymer molecules. If it is assumed that the excluded volume term in the thermodynamic theory of concentrated systems can be applied directly to the determination of coil dimensions, then x is automatically zero but v is very large, reducing the expansion to zero. 

The miscibility behaviour of polymer systems has been studied extensively, and experimental data and thermodynamic models have been generated for (co)polymer solutions and for polymer blends. 

Current thermodynamic theories for polymer systems are combinations of the Flory -Huggins, Guggenheim, and Equations-of-State approaches. All of these theories make use of empirical parameters and are based on assumptions about the underlying molecular model. 

Thermodynamic descriptions of polymer systems are usually based on a rigid-lattice model published in 1941 independently by Staverman and Van Santen, Huggins and Flory where the symbol x(T) is used to express the binary interaction function [16]. Once the interaction parameter is known we can calculate the liquid liquid phase behaviour. 

Polymer systems containing copolymers call for a further extension of the thermodynamic model. The interaction function for statistical copolymers was originally derived by Simha and Branson [34], discussed by Stockmayer [35] et al., and experimentally verified by Glbckner and Lohmann [36]. 

Klenin, V. J. Thermodynamics of Systems Containing Flexible-Chain Polymers. Elsevier Amsterdam, 1999. 

LATTICE BASED MOLECULAR THERMODYNAMIC MODEL OF POLYMER SYSTEMS... 

The above molecular thermodynamic model for polymer systems has been widely tested by comparing with simulation results (Yang et al., 2006a Xin et al., 2008a). Figure 8 shows the comparisons between predicted critical temperature and critical volume fraction for binary polymer solutions at different chain lengths of with the... 

Many polymer blends or block polymer melts separate microscopically into complex meso-scale structures. It is a challenge to predict the multiscale structure of polymer systems including phase diagram, morphology evolution of micro-phase separation, density and composition profiles, and molecular conformations in the interfacial region between different phases. The formation mechanism of micro-phase structures for polymer blends or block copolymers essentially roots in a delicate balance between entropic and enthalpic contributions to the Helmholtz energy. Therefore, it is the key to establish a molecular thermodynamic model of the Helmholtz energy considered for those complex meso-scale structures. In this paper, we introduced a theoretical method based on a lattice model developed in this laboratory to study the multi-scale structure of polymer systems. First, a molecular thermodynamic model for uniform polymer system is presented. This model can... 

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