Polymer statistical mechanics

H. Yamakawa, Polymer statistical mechanics, Ann. Rev. Phys. Chem. 25, 179(1974). 

H. Yamakawa, Modern Theory of Polymer Solutions, Harper and Row, New York, 1971. H. Yamakawa, Polymer statistical mechanics, Ann. Rev. Phys. Chem. 25, 179 (1974). 

Conformational Analysis.— The major effort in this area has been directed towards empirical correlations of chemical shift and conformation. Tonelli and co-workers have examined the stereosequence dependence of C chemical shifts in polypropylene (PP) poly(vinyl chloride) (PVC), and polystyrene (PS) using the rotational isomeric-state scheme of polymer statistical mechanics. The structural variation of C shifts was shown to correlate well with the occurrence of three-bond gauche (y) interactions between carbon atoms together with y interactions between carbon and chlorine atoms in PVC and ring-current shifts in PS. It has been... 

Conformation and Chemical Shifts.—Chemical shifts have been correlated with conformation for H shifts in polystyrene and poly(vinyl chloride) and C shifts in model compounds of polypropylene. In all these papers, the chemical shift is related empirically to the occurrence of three- and four-bond steric interactions, similar to those used in the rotational isomeric state treatment of polymer statistical mechanics, " and the shift is expressed as a sum of compositional and conformational increments. The origin of the shielding contributions (magnetic anisotropy, electric field effects, etc.) is not stated, except for polystyrene in which the magnetic anistropy of the aromatic rings are incorporated... 

Fixman M 1974 Classical statistical mechanics of constraints a theorem and application to polymers Proc. Natl Acad. Sc/. 71 3050-3... 

Due to the noncrystalline, nonequilibrium nature of polymers, a statistical mechanical description is rigorously most correct. Thus, simply hnding a minimum-energy conformation and computing properties is not generally suf-hcient. It is usually necessary to compute ensemble averages, even of molecular properties. The additional work needed on the part of both the researcher to set up the simulation and the computer to run the simulation must be considered. When possible, it is advisable to use group additivity or analytic estimation methods. 

As Eq. (3) sh vs, the critical composition (ticn can be controlled by the asymmetry of chain lengths. Particularly interesting is the limit Na = N, Nb = I (which physically is realized by polymer solutions, B representing a solvent of variable quality). Checking the deviations from the mean field predictions, Eq. (3), further contributes to the understanding of the statistical mechanics of mixtures. 

Spin orbitals, 258, 277, 279 Square well potential, in calculation of thermodynamic quantities of clathrates, 33 Stability of clathrates, 18 Stark effect, 378 Stark patterns, 377 Statistical mechanics base, clathrates, 5 Statistical model of solutions, 134 Statistical theory for clathrates, 10 Steam + quartz system, 99 Stereoregular polymers, 165 Stereospecificity, 166, 169 Steric hindrance, 376, 391 Steric repulsion, 75, 389, 390 Styrene methyl methacrylate polymer, 150... 

The entropic elasticity of a single polymer chain is treated similarly to the statistical mechanical property of gas molecules. Now, let us compare gas molecules to children moving around freely... 

The large deformability as shown in Figure 21.2, one of the main features of rubber, can be discussed in the category of continuum mechanics, which itself is complete theoretical framework. However, in the textbooks on rubber, we have to explain this feature with molecular theory. This would be the statistical mechanics of network structure where we encounter another serious pitfall and this is what we are concerned with in this chapter the assumption of affine deformation. The assumption is the core idea that appeared both in Gaussian network that treats infinitesimal deformation and in Mooney-Rivlin equation that treats large deformation. The microscopic deformation of a single polymer chain must be proportional to the macroscopic rubber deformation. However, the assumption is merely hypothesis and there is no experimental support. In summary, the theory of rubbery materials is built like a two-storied house of cards, without any experimental evidence on a single polymer chain entropic elasticity and affine deformation. 

Statistical Mechanics of Unfilled and Filled Polymer Networks.608... 

STATISTICAL MECHANICS OF UNFILLED AND FILLED POLYMER NETWORKS... 

It is beyond our control how the cross-links are spaced along the polymer chains during the vulcanization process. This extraordinary important fact demands a generalization of the Gibbs formula in statistical mechanics for amorphous materials that have fixed constraints of which the exact topology is unknown. Details of a modified Gibbs formula of polymer networks can be found in the pioneering paper of Deam and Edwards [13]. 

Krigbaum, W. R. and Flory, P. J., Statistical mechanics of dilute polymer solutions. IV. Variation of the osmotic second coefficient with molecular weight, /. Am. Chem. Soc., 75, 1775, 1953. 

There are several attractive features of such a mesoscopic description. Because the dynamics is simple, it is both easy and efficient to simulate. The equations of motion are easily written and the techniques of nonequilibriun statistical mechanics can be used to derive macroscopic laws and correlation function expressions for the transport properties. Accurate analytical expressions for the transport coefficient can be derived. The mesoscopic description can be combined with full molecular dynamics in order to describe the properties of solute species, such as polymers or colloids, in solution. Because all of the conservation laws are satisfied, hydrodynamic interactions, which play an important role in the dynamical properties of such systems, are automatically taken into account. 

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

RJ Pace, A Datyner. Statistical mechanical model of diffusion of complex penetrants in polymers. I. Theory. J Polym Sci, Polym Phys Ed 17 1675-1692, 1979. 

PJ Flory, R Rehner Jr. Statistical mechanics of cross-linked polymer networks. J ChemPhys 11 521-525, 1943. 

Suspension Model of Interaction of Asphaltene and Oil This model is based upon the concept that asphaltenes exist as particles suspended in oil. Their suspension is assisted by resins (heavy and mostly aromatic molecules) adsorbed to the surface of asphaltenes and keeping them afloat because of the repulsive forces between resin molecules in the solution and the adsorbed resins on the asphaltene surface (see Figure 4). Stability of such a suspension is considered to be a function of the concentration of resins in solution, the fraction of asphaltene surface sites occupied by resin molecules, and the equilibrium conditions between the resins in solution and on the asphaltene surface. Utilization of this model requires the following (12) 1. Resin chemical potential calculation based on the statistical mechanical theory of polymer solutions. 2. Studies regarding resin adsorption on asphaltene particle surface and... 

---