Order vs. Disorder

Whereas Z omb decreases with disorientation, increases. For sufficiently small axial ratios (x) and/or concentrations, the product of these factors, i.e., the partition function Zm (see Eq. (7)) for the mixture of rods and diluent, is dominated by Zo,je ,. Then Z increases monotonically with y and the state of complete disorder with y = X is the one of maximum stability (see Eq. (C-1) in Appendix-C). As the axial ratio and/or concentration are increased, the decrease in Zco b with y becomes more marked. Eventually, Z exhibits a maximum followed by a minimum with increase in y, i.e., with increasing disorder. The maximum marks either a metastable or a stable state with respect to orientation. It is stable only if Z, at the maximum exceeds Zm for complete disorder (y = x). This requires a somewhat greater concentration, or axial ratio, than that at the critical point where the extrema first appear. 

The character of the transition from disorder to (partial) order may be better understood through analysis of relevant characteristics of the partition function. By 

3 Equation (9) differs from previous renditionsaccording to which w y through choice of the randomly disoriented rods (y = x) as the state of reference, instead of adopting the state of perfect aligment (y = 1) for this purpose. The difference is of no signiflcance in applications of the theory here discussed. 

A useful semi-empirical approximation for the critical volume fraction v for incipience of metastable order (see Fig. 2) that follows from analysis of Eq. (1) is 

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A semiempirical/theoretical ionic model was derived to cor-relate and interrelate the ultrastructure morphology, surface charge, surface chemistry, and surface molecular motions of a model semicrystalline hydrophobic triblock copolymer to thrombogenesis. This chapter addresses the aspects of ultra-structure order vs. disorder, primary and secondary molecular motions, surface and side chain chemistry, thrombogenesis, and the resultant ionic model. This model can be extrapolated to predict the relative thrombogenic responses of various crystalline and semicrystalline hydrophobic polymeric substrates. 

Order vs. disorder is thus seen to be inescapably subjective, unless the rules are clear (Denbigh and Denbigh, 1985). To most people, the concept of a well-ordered room has a fairly clear meaning, and there are limitless ways of disordering the room. But if Mr. X likes to keep his shoes on top of the dresser and the rug on the bed, this constitutes perfect order for him. However even for him, there is only one way of achieving perfect order and limitless ways of disordering the room. In either case, the disordered state of the room is more probable. 

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