Statistical thermodynamics of associating polymers

On the other hand, Hirschfelder et al. [6] pointed out that the lower critical solution temperature appears as a result of heteromolecular association in solutions of water or alcohol with ammonia derivatives. The problem posed by them has been smdied in relation to reentrant phase separation in liquid mixtures. 

Consider a binary mixture of linear polymers R A/ and R Bg carrying associative groups A and B. The number of statistical repeat units on a chain (for simplicity referred to as the degree of polymerization, DP) is assumed to be ha for R Ay chains and b for R Bg chains. Although we use the word polymer for the primary molecules before they form associated complexes, we may apply our theory to low-molecular weight molecules equally well by simply fixing ma and b at small values. 

These polymers are assumed to carry a fixed number / of reactive groups A and g of reactive B groups, both of which are capable of forming reversible bonds that can thermally break and recombine. Hydrogen bonds, hydrophobic interaction, electrostatic interaction, etc., are important examples of such associative forces. The type of associative interaction does not need to be specified at this stage, but it will be given in each of the following applications. We symbolically indicate this binary model system as R A/ /R Bg.  

In the extreme limit of strong bonds, such as covalent ones, the formation of associated clusters is thermally irreversible and should be regarded as a chemical reaction. The molecular weight distribution of such irreversible reactions is studied in detail in Section 3.2. 

In the experiments, various types of solvents are commonly used, so that we should consider a mixture R A/ /R Bg /S, where S denotes the solvent. Extension of the following theoretical consideration to such ternary systems is straightforward as long as the solvent is inactive. Therefore, for simplicity, we will mainly confine the discussion to binary systems. 

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C-C bonds in the actual molecules. The LCT is an analytical molecular-based theory for the statistical thermodynamics of molten polymers, associated with recognizing the degree to which the distinct chemical structures of the individual monomers are relevant. LCT also incorporates free volume and uses the nonrandom... 

Construction of theoretical phase diagrams similar to the diagram in Fig. 2.17 should facilitate the search for major proaches to the analysis of polymer-solvent systems in which equilibria involving isotropic, liquid-crystalline, crystal solvate, and truly crystalline phases are complexly associated. This is valid, since, as indicated in the classic course of statistical thermodynamics of van der Waals and Konstamm [45], physicists and chemists do not need the precise quantitative dependence for the concrete case as much as to establish general types and then to study whether the qualitative differences of these types coincide with the experimentally found types. ... 

This chapter will describe how we can apply an understanding of thermodynamic behavior to the processes associated with polymers. We will begin with a general description of the field, the laws of thermodynamics, the role of intermolecular forces, and the thermodynamics of polymerization reactions. We will then explore how statistical thermodynamics can be used to describe the molecules that make up polymers. Finally, we will learn the basics of heat transfer phenomena, which will allow us to understand the rate of heat movement during processing. 

In order to understand the thermodynamic issues associated with the nanocomposite formation, Vaia et al. have applied the mean-field statistical lattice model and found that conclusions based on the mean field theory agreed nicely with the experimental results [12,13]. The entropy loss associated with confinement of a polymer melt is not prohibited to nanocomposite formation because an entropy gain associated with the layer separation balances the entropy loss of polymer intercalation, resulting in a net entropy change near to zero. Thus, from the theoretical model, the outcome of nanocomposite formation via polymer melt intercalation depends on energetic factors, which may be determined from the surface energies of the polymer and OMLF. 

Although one might imagine that at USC Simha s interests were focused solely on solution viscosity and statistical thermodynamics, he found time to be involved in such diverse topics as computation of DNA sequences (with Jovan Moacanin from the Jet Propulsion Laboratory), in glass transition phenomena and thermal expansion of polymers (with Moacanin and Ray Boyer of the Dow Chemical Co.), observation of multiple subglass transitions in polymers (with a research associate, Robert Haldon), and thermal degradation (another collaboration with Leo Wall from NBS). 

The present volume was suggested and stimulated by the aforementioned thoughts. We shall be concerned here with the phenomena and problems associated with the participation of macromolecules in phase transitions. The term crystallization arises from the fact that ordered structures are involved in at least one of the phases. The book is composed of three major portions which, however, are of unequal length. After a deliberately brief introduction into the nature of high polymers, the equilibrium aspects of the subject are treated from the point of view of thermodynamics and statistical mechanics, with recourse to a large amount of experimental observation. The second major topic discussed is the kinetics of crystallization. The treatment is intentionally very formal and allows for the deduction... 

Most people associate polymers with solid materials—from rubber bands to car tires to Tupperware — but what about acrylic and latex paints or ketchup and salad dressing or oil-drilling fluids The thermodynamics and statistics of polymer solutions is an interesting and important branch of physical chemistry, and is the subject of many good books and large sections of books in itself. It is far beyond the scope of this chapter to attempt to cover the subject in detail. Instead, we will concentrate on topics of practical interest and try to indicate, at least qualitatively, their fundamental bases. Three factors are of general interest ... 

The SCLF method was developed by Koopal and coworkers [46-50] to describe adsorption of surfactant molecules at the solution-solid interface. The method derives from two earlier statistical thermodynamic lattice theories (1) the Flory and Fluggins [51 ] model describing properties of polymers in solution, and (2) the methods of Scheutjens and coworkers [52-55] developed to describe the properties of polymer molecules adsorbed at the solution-solid interface and in associated mesomorphic solution structures such as micelles and vesicles. 

An important factor that is not taken into account in the DLVO theory is adsorption, on the particle s surface, of long polymeric chains. The adsorption of a non-ionic polymer or a polyelectrolyte on the solid surface can cause, not only a modification of the zeta potential, but also a critical difference between the value of the zeta potential and the state of dispersion. Steric repulsion is associated with the obstmction effect of these polymers that are capable to form a sufficiently thick layer to prevent the particles from approaching one another in the distanee of influence of the Van der Waals attractive forces. Steric stabihzation will therefore depend on the adsorption of the polymeric dispersant and the thickness of the layer developed. Several interpretation models for stabilization by steric effect have been put forward. They rely either on a statistical approach, or on the thermodynamics of solutions. Steric stabilization is particularly useful in organic, fairly non-polar or non-polar environments, as in the case of tape casting (see section 5.4.3). 

When all lengths associated with polymers are measured in units of the Kuhn statistical segment length 2q, the thermodynamic functions AF, II, and g, given by Eqs. (19)-(21), contain two molecular parameters N = L/2q and d s d/2q and two state variables c = (2q)3 c and a. Thus, numerical solution to Eqs. (23) and (31) provides ci, cA, and a as functions of N and d. The results for the phase boundary concentrations have been found to be represented to a good approximation by the following empirical expressions ... 

The contribution "Application of Meso-Scale Field-based Models to Predict Stability of Particle Dispersions in Polymer Melts" by Prasanna Jog, Valeriy Ginzburg, Rakesh Srivastava, Jeffrey Weinhold, Shekhar Jain, and Walter Chapman examines and compares Self Consistent Field Theory and interfacial Statistical Associating Fluid Theory for use in predicting the thermodynamic phase behavior of dispersions in polymer melts. Such dispersions are of quite some technological importance in the... 

The occurrence of a secondary phase separation inside dispersed phase particles, associated with the low conversion level of the p-phase when compared to the overall conversion, explains the experimental observation that phase separation is still going on in the system even after gelation or vitrification of the a-phase [26-31]. A similar thermodynamic analysis was performed by Clarke et al. [105], who analyzed the phase behaviour of a linear monodisperse polymer with a branched polydisperse polymer, within the framework of the Flory-Huggins lattice model. The polydispersity of the branched polymer was treated with a power law statistics, cut off at some upper degree of polymerization dependent on conversion and functionality of the starting monomer. Cloud-point and coexistence curves were calculated numerically for various conversions. Spinodal curves were calculated analytically up to the gel point. It was shown that secondary phase separation was not only possible but highly probable, as previously discussed. 

Long-chain molecules can exist in either one of two states. These are characterized by the conformation of the individual molecular chains and their organization relative to one another. The liquid state is the state of molecular disorder. In this state, the individual chains adopt a statistical conformation, commonly called the random coil. The centers of mass of the molecules are arranged randomly relative to one another in this situation. All the thermodynamic and stmctural properties observed in this state are those which are commonly associated with a liquid, although usually a very viscous one. This state exhibits the characteristic long-range elasticity. The liquid state in polymers is also commonly called the amorphous state. 

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