Statistical mechanical approach, polymer

Recent developments in the theory of polymer solutions have been reviewed by Berry and Casassa (32), and by Casassa (71). Casassa, who has contributed very largely to these developments, has adopted a statistical mechanical approach using molecular distribution functions, as first outlined by Zimm (72), rather than using a lattice model like that used by Flory, Huggins, and many later workers. 

Many authors7-21 have theoretically investigated the conformation of an isolated adsorbed polymer as a function of adsorption energy, using statistical mechanical approaches. Some important conclusions are as follows ... 

Our simulations are based on well-established mixed quantum-classical methods in which the electron is described by a fully quantum-statistical mechanical approach whereas the solvent degrees of freedom are treated classically. Details of the method are described elsewhere [27,28], The extent of the electron localization in different supercritical environments can be conveniently probed by analyzing the behavior of the correlation length R(fih/2) of the electron, represented as polymer of pseudoparticles in the Feynman path integral representation of quantum mechanics. Using the simulation trajectories, R is computed from the mean squared displacement along the polymer path, R2(t - t ) = ( r(f) - r(t )l2), where r(t) represents the electron position at imaginary time t and 1/(3 is Boltzmann constant times the temperature. 

In this section, we review the statistical mechanical approach to the problem of the folding of long polymer chains. From the standpoint of physics, considerable efforts have been made to extract simple and universal laws of biopolymers behavior regardless of their complexity and diversity. This leads... 

A similar equation to Eq. (11) was derived by Joos (1969) using the statistical mechanical approach of Frisch and Simha (1957) for linear flexible polymer chains. In the equation of Joos, A = v cr0 where <70 is the limiting area of one amino acid residue and v is the number of resi-... 

The statistical mechanical approach, in which the polymer configuration is treated as being composed of three types of stracture - trains, loops, and tails - with each having a different energy state. 

Interactions between soluble polymer and either colloidal particles, surfactant micelles, or proteins control the behavior and viability of a large number of chemical and biochemical products and processes. Considerable scientific interest also centers on these interactions because of their profound and, sometimes, unexpected effects on the thermodynamics and dynamics of the dispersions or solutions, known collectively as complex fluids. Syntheses of novel block copolymers, improved scattering and optical techniques for characterization, and predictions emerging from sophisticated statistical mechanical approaches provide additional stimulus. Thus, the area is vigorous academically and industrially as evidenced by the broad and international participation in this volume. 

An elegant statistical mechanical approach to the dimensions of flexible polymers was developed by Landau and Lifschitz [4], who considered a long, flexible thread of contour length L and positive bending energy (Jxm in SI units). The lowest energy state is when the thread is straight, but thermal fluctuations allow it to bend and wobble in a complex way that tends to shrink below the full... 

Several theories exist that describe the process of polymer adsorption, which have been developed either using a statistical mechanical approach or quasi-lattice models. In the statistical mechanical approach, the polymer is considered to consist of three... 

AUegra G. Chain folding and polymer crystallization A statistical-mechanical approach. J Chem Phys 1977 66 5453-5463. 

Polymer networks are conveniently characterized in the elastomeric state, which is exhibited at temperatures above the glass-to-rubber transition temperature T. In this state, the large ensemble of configurations accessible to flexible chain molecules by Brownian motion is very amenable to statistical mechanical analysis. Polymers with relatively high values of such as polystyrene or elastin are generally studied in the swollen state to lower their values of to below the temperature of investigation. It is also advantageous to study network behavior in the swollen state since this facilitates the approach to elastic equilibrium, which is required for application of rubber elasticity theories based on statistical thermodynamics. ... 

A successful theoretical description of polymer brushes has now been established, explaining the morphology and most of the brush behavior, based on scaling laws as developed by Alexander [180] and de Gennes [181]. More sophisticated theoretical models (self-consistent field methods [182], statistical mechanical models [183], numerical simulations [184] and recently developed approaches [185]) refined the view of brush-type systems and broadened the application of the theoretical models to more complex systems, although basically confirming the original predictions [186]. A comprehensive overview of theoretical models and experimental evidence of polymer bmshes was recently compiled by Zhao and Brittain [187] and a more detailed survey by Netz and Adehnann [188]. 

Hunter, R. J., Foundations of Colloid Science, Vol. 2, Clarendon Press, Oxford, England, 1989. (Undergraduate and graduate levels. Along with Volume 1, these two volumes cover almost all the topics covered in the present chapter at a more advanced level. Volume 1 discusses DLVO theory and thermodynamic approaches to polymer-induced stability or instability and is at the undergraduate level. Volume 2 presents advanced topics (e.g., statistical mechanics of concentrated dispersions, rheology of dispersions, etc.).)... 

Two theoretical approaches for calculating NMR chemical shift of polymers and its application to structural characterization have been described. One is that model molecules such as dimer, trimer, etc., as a local structure of polymer chains, are in the calculation by combining quantum chemistry and statistical mechanics. This approach has been applied to polymer systems in the solution, amorphous and solid states. Another approach is to employ the tight-binding molecular orbital theory to describe the NMR chemical shift and electronic structure of infinite polymer chains with periodic structure. This approach has been applied to polymer systems in the solid state. These approaches have been successfully applied to structural characterization of polymers... 

In this review, we introduce another approach to study the multiscale structures of polymer materials based on a lattice model. We first show the development of a Helmholtz energy model of mixing for polymers based on close-packed lattice model by combining molecular simulation with statistical mechanics. Then, holes are introduced to account for the effect of pressure. Combined with WDA, this model of Helmholtz energy is further applied to develop a new lattice DFT to calculate the adsorption of polymers at solid-liquid interface. Finally, we develop a framework based on the strong segregation limit (SSL) theory to predict the morphologies of micro-phase separation of diblock copolymers confined in curved surfaces. 

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