Polymers Potential energy function

In the previous section, the adaptation of the RIS model was based on the distance between next-nearest neighbor beads. This approach is obviously inadequate for CH3-CHX-CH2-CHX-CH3, because it necessarily abandons the ability to attribute different conformational characteristics to the meso and racemo stereoisomers. Therefore a more robust adaption of the RIS model to the 2nnd lattice is necessary if one wants to investigate the influence of stereochemical composition and stereochemical sequence on vinyl polymers [156]. Here we describe a method that has this capability. Of course, this method retains the ability to treat chains such as PE in which the bonds are subject to symmetric torsion potential energy functions. 

Calculations of the MM type have long been popular in the fields of polymers (12) and biochemistry (proteins) (13), where the huge size of the molecules demands drastic simplification of potential energy functions. These applications are not discussed here. 

It should make sense then, that as we attempt to pull atoms apart or force them further together through an applied stress, we can, at least in principle, relate how relatively difficult or easy this is to the potential energy function. We can develop a quantitative description of this process of pulling atoms apart, provided that we do so over small deformations, in which the deformation is wholly recoverable that is, the atoms can return back to their original, undeformed positions with no permanent displacement relative to one another. This is called an elastic response. The term elastic here does not imply anything specific to polymers in the same way that the more everyday use of the term does. It is used in the same sense that it is in physics and chemistry—a completely recoverable deformation. 

The conformational entropies of copolymer chains are calculated through utilization of semiempirical potential energy functions and adoption of the RIS model of polymers. It is assumed that the glass transition temperature, Tg, is inversely related to the intramolecular, equilibrium flexibility of a copolymer chain as manifested by its conformational entropy. This approach is applied to the vinyl copolymers of vinyl chloride and vinylidene chloride with methyl acrylate, where the stereoregularity of each copolymer is explicitly considered, and correctly predicts the observed deviations from the Fox relation when they occur. It therefore appears that the sequence distribution - Tg effects observed in many copolymers may have an intramolecular origin in the form of specific molecular interactions between adjacent monomer units, which can be characterized by estimating the resultant conformational entropy. 

R. L. Jaffe, D. Y. Yoon, and A. D. McLean, in Computer Simulation of Polymers, R. J. Roe, Ed., Prentice Hall, New York, 1991, pp. 1-13. Calculation of Ab-Initio Intrasegmental Potential-Energy Functions for use in Modeling Polymer Properties. 

Forces between polymer-covered surfaces are a subset of the general subject of intermolecular forces, which are more fully discussed elsewhere (Maitland etal. 1981, Israelachvili 1991). Before the SFA and the results obtained from it are discussed, a brief consideration of intersurface forces is needed. If the intermolecular potential energy function between two individual molecules is generated solely by van der Waals forces it is purely attractive and of the form... 

The relationships given in subsection 2.4.3 for critical opalescence of solutions hold good for polymer solutions as well with a modification of the quantities jj and Q as wj should be the volume of a monomeric unit and the potential energy functions y(r) concern interactions among the monomeric units and LMWL molecules. When z monomeric units are Gaussianly distributed about their centre of gravity (Debye, 19.59),... 

KJ/mol and a gauche-trms energy difference of 2.5 kJ/mol). The constants D, and y [see Eq. (2)] represent the usual Morse oscillator parameters. The nonbonded terms e and a [Eq. (3a)] represent the Lennard-Jones parameters, b and C [Eq. 3b)] are related to the overlap and dispersion of the atoms i and j, and A is a parameter related to the position and well-depth of the interaction. The bending force constant is, and 6o [Eq. (4)] indicates the equilibrium value of the angle formed by the three atoms of interest. The above potential energy functions [Eqs. (2-5)] have been demonstrated to yield good spectroscopic, thermodynamic, and kinetic data, as well as to provide the atomistic details of temperature-dependent phase transitions for crystalline polymers. 

The reduced variables are employed as in the theory of the corresponding states therefore a universal form of potential-energy function has to be assumed by all components of the mixture. The validity of this hypothesis is doubtful even in the case of small molecules, and even more so in the case of polymer solutions. 

In molecular systems, the potential energy function V(r) includes bonded interactions between atoms connected by chemical bonds, and nonbonded interactions between atoms of different molecules, or between atoms of the same molecule which are not chemically bonded, for example between the atoms of nonadjacent monomers of the same polymer chain. 

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