Elastic interaction numerical estimations

Parameter used in predicting the solubility of nonelectrolytes (including amorphous polymers) in a given solvent. The Hildebrand solubility parameter provides a numerical estimate of the degree of interaction between materials and solvents. The Hildebrand solubility parameter is the square root of the cohesive energy density Resistance of an elastic body to deformation by an applied force... 

The simplified-kinetic-theory treatment of reaction rates must be regarded as relatively crude for several reasons. Numerical calculations are usually made in terms of either elastic hard spheres or hard spheres with superposed central attractions or repulsions, although such models of molecular interaction are better known for their mathematical tractability than for their realism. No account is taken of the internal motions of the reactants. The fact that every combination of initial and final states must be characterized by a different reaction cross section is not considered. In fact, the simplified-kinetic-theory treatment is based entirely on classical mechanics. Finally, although reaction cross sections are complicated averages of many inelastic cross sections associated with all possible processes by which reactants in a wide variety of initial states are converted to products in a wide variety of final states, the simplified kinetic theory approximates such cross sections by elastic cross sections appropriate to various transport properties, by cross sections deduced from crystal spacings or thermodynamic properties, or by order-of-magnitude estimates based on scientific experience and intuition. It is apparent, therefore, that the usual collision theory of reaction rates must be considered at best an order-of-magnitude approximation at worst it is an oversimplification that may be in error in principle as well as in detail. 

Monomers which produce polymers with the desired polymer interaction parameter are now selected for possible testing as lens materials. Formulations of those monomers with the appropriate amount of ctosslinker and ctosslinking are identified by estimating modulus of elasticity that a reaction product would possess using a Monte Carlo method developed by Xu and Mark (28). Potential formulations to make the lens are further refined by comparison of reactivity ratios between prospective monomers. The potential for a mixture of monomers to form a desired copolymer is estimated fiom the AUrey-Price, Q-e scheme (29) for radical-monomer reactivity. If the reactivity ratios ofthe monomers in a formulation are close in numerical value, the polymer is projected to be truly random and it may form a functional lens. These formulations are accepted. If the reactivity ratios are very different the monomers will react in block fashion. A block copolymer is prone to be hazy because the blocks in the copolymer can aggregate and create sharp changes in index of refraction in a lens. These formulations are rejected. 

---