Thermodynamics of long-chain molecules

Monte Carlo methods offer a useful alternative to Molecular Dynamics techniques for the study of the equilibrium structure and properties, including phase behavior, of complex fluids. This is especially true of systems that exhibit a broad spectrum of characteristic relaxation times in such systems, the computational demands required to generate a long trajectory using Molecular Dynamics methods can be prohibitively large. In a fluid consisting of long chain molecules, for example, Monte Carlo techniques can now be used with confidence to determine thermodynamic properties, provided appropriate techniques are employed. 

The melting, or dissolution, of long chain molecules at high dilution is a natural consequence of phase equilibrium. The dissolution process results in the separation of the solute molecules and is usually accompanied by a change in the molecular conformation of the chain from an ordered structure to a statistical coil. However, it is also possible for the individual polymer molecules to maintain the conformation in solution that is typical of the crystalline state. This is particularly true if the steric requirements that favor the perpetuation of a preferred bond orientation or the ordered crystalline structure can be maintained by intramolecular bonding, such as hydrogen bonds. Further alterations in the thermodynamic environment can cause a structural transformation in the individual molecules. Each molecule is then... 

In this chapter, we review the basic mechanisms underlying adsorption of long-chain molecules on solid surfaces such as oxides. We concentrate on the physical aspects of adsorption and summarize the main theories which have been proposed. This chapter should be viewed as a general introduction to the problem of polymer adsorption at thermodynamical equilibrium. For a selection of previous review articles see Refs 1—4, while more detailed treatments are presented in two books on this subject [5,6]. We do not attempt to explain any specific polymer/oxide system and do not emphasize experimental results and techniques. Rather, we detail how concepts taken from statistical thermodynamics and interfacial science can explain general and universal feamres of polymer adsorption. The present chapter deals with equilibrium properties whereas Chapter 3 by Cohen Stuart and de Keizer is about kinetics. 

The crystallization process of flexible long-chain molecules is rarely if ever complete. The transition from the entangled liquid-like state where individual chains adopt the random coil conformation, to the crystalline or ordered state, is mainly driven by kinetic rather than thermodynamic factors. During the course of this transition the molecules are unable to fully disentangle, and in the final state liquid-like regions coexist with well-ordered crystalline ones. The fact that solid- (crystalline) and liquid-like (amorphous) regions coexist at temperatures below equilibrium is a violation of Gibb s phase rule. Consequently, a metastable polycrystalline, partially ordered system is the one that actually develops. Semicrystalline polymers are crystalline systems well removed from equilibrium. 

Finally, it should be mentioned that a combination of COSMO-RS with tools such as MESODYN [127] or DPD [128] (dissipative particle dynamics) may lead to further progress in the area of the mesoscale modeling of inhomogeneous systems. Such tools are used in academia and industry in order to explore the complexity of the phase behavior of surfactant systems and amphiphilic block-co-polymers. In their coarse-grained 3D description of the long-chain molecules the tools require a thermodynamic kernel... 

Nonideal thermodynamic behavior has been observed with polymer solutions in which A Hm is practically zero. Such deviations must be due to the occurrence ofa nonideal entropy, and the first attempts to calculate the entropy change when a long chain molecule is mixed with small molecules were due to Flory [8] and Huggins [9]. Modifications and improvements have been made to the original theory, but none of these variations has made enough impact on practical problems of polymer compatibility to occupy us here. 

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