Chain-of-effects models

In summary, it is more common to examine pairs of variables from a profit chain-of-effects model rather than the profit chain in its entirety. A scatter plot or correlation analysis of a pair of profit-chain variables (e.g. satisfaction and loyalty) almost always indicates a weak correlation. The weak correlation is typically interpreted as suggesting a crisis whereby the implied profit chain-of-effects or cascading model is not supported. 

An exception to difficult-to-model filled systems is provided by the norbomene-POSS pol5miers studied by Bharadwaj and co-workers (278). POSS is polyhedral oligomeric silseqiuoxane—groups that are pendant from the poly(norbornene) chains of the model. This can be viewed as a filled system, but one in which the filler is nanoscopic and chemically bonded to the chains. The simulations were done to determine Tg, density, thermal expansion, solubility parameter, POSS mobilities, and elastic moduli in a wide-ranging study. They conclude that the ponderous nature of the POSS moieties is largely responsible for the reinforcing effect. 

In the limit that the number of effective particles along the polymer diverges but the contour length and chain dimensions are held constant, one obtains the Edwards model of a polymer solution [9, 30]. Polymers are represented by random walks that interact via zero-ranged binary interactions of strength v. The partition frmction of an isolated chain is given by... 

In the foregoing discussions of theoretical models and experimental results, we have focused on linear polymers. We have seen the effect of chain substituents on viscosity. All other things being equal, bulky substituents tend to decrease f and thereby lower 17. The effect is primarily due to the opening up of the liquid because of the steric interference with efficient packing arising from the substituents. With side chains of truly polymeric character, the picture is quite different. 

Whether the beads representing subchains are imbedded in an array of small molecules or one of other polymer chains changes the friction factor in Eq. (2.47), but otherwise makes no difference in the model. This excludes chain entanglement effects and limits applicability to M < M., the threshold molecular weight for entanglements. 

One of the most sensitive tests of the dependence of chemical reactivity on the size of the reacting molecules is the comparison of the rates of reaction for compounds which are members of a homologous series with different chain lengths. Studies by Flory and others on the rates of esterification and saponification of esters were the first investigations conducted to clarify the dependence of reactivity on molecular size. The rate constants for these reactions are observed to converge quite rapidly to a constant value which is independent of molecular size, after an initial dependence on molecular size for small molecules. The effect is reminiscent of the discussion on the uniqueness of end groups in connection with Example 1.1. In the esterification of carboxylic acids, for example, the rate constants are different for acetic, propionic, and butyric acids, but constant for carboxyUc acids with 4-18 carbon atoms. This observation on nonpolymeric compounds has been generalized to apply to polymerization reactions as well. The latter are subject to several complications which are not involved in the study of simple model compounds, but when these complications are properly considered, the independence of reactivity on molecular size has been repeatedly verified. 

In summary the results of our 2H NMR investigation illustrate the spacer model for liquid crystalline polymers, indicating, however, that the decoupling of the mesogenic groups from the main chain, while effective, is not complete. 

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