Transformations without change in molecular conformation

The solid curves in the hgure represent the best fit between experiment and theory for the three different molecular weight samples. Good agreement is obtained and the increased sharpness of the transihon with increasing molecular weight is apparent. The best fit is obtained with a = 2 x 10 and AH = 900 cal mol .  

The helix-coil transition is unique in that the coordinated action of many molecules is not required. It is by necessity restricted to the very dilute portion of the phase diagram. As the concentration of polymer molecules in the helical conformation increases, intermolecular interactions begin to manifest themselves. The cooperative character of the transihon will be further enhanced. The dimensional interdependence will increase from one in the case of a dilute soluhon to three in the more concentrated system. The transition will then become formally idenhcal to the melting of the dense crystalline phase that has been discussed previously. 

Asymmetry of molecular shape is a feature that is common to all substances that exhibit liquid crystalUnity. The smdy of Uquid crystals involving macromolecules is a major subject in itself. It has been discussed in several reviews (80-83) and books.(84-88) It is not the purpose here to discuss liquid crystals involving polymers in any detail. Rather, efforts will be directed to place the behavior of such highly asymmetric molecules, and the transitions that they undergo without any conformational change, in perspective in terms of polymer crystallization. Thus, the effort will be in outUning the theoretical basis for the behavior and highlighting the unique features that result. 

There are several different theoretical approaches to the problem. The Landau molecular field theory was applied by de Gennes to liquid-crystal phase transitions. (89) The Maier-Saupe theory focuses attention on the role of intermolecular attractive forces.(90) Onsager s classical theory is based on the analysis of the second virial coefficient of very long rodlike particles.(91) This theory was the first to show that a solution of rigid, asymmetric molecules should separate into two phases above a critical concentration that depends on the axial ratio of the solute. One of these phases is isotropic, the other anisotropic. The phase separation is, according to this theory, solely a consequence of shape asymmetry. There is no need to involve the intervention of intermolecular attractive forces. Lattice methods are also well suited for treating solutions, and phase behavior, of asymmetric shaped molecules.(80,92,93) 

The lattice method is used to enumerate the number of conhgurations available to 2 rigid, rodlike polymer molecules, with an asymmetry x (the ratio of molecular length to its breadth) and partial orientation about an axis, and monomeric solvent molecules. When the usual Van Laar heat of mixing term is employed, the free energy of mixing can be expressed as (80,92) 

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Among the infinite number of ways of transforming the set of canonical m.o.s without changing the eigenfunction some would conform better to the classical structural formula of the molecule, namely those unitary transformations that lead to Xt functions which are practically localized in each formal bond (or in individual atoms, as electron lone pairs). For example,, by replacing the canonical oi and ctj molecular orbitals of H2O by... 

Up to this point, we have emphasized the stereochemical properties of molecules as objects, without concern for processes which affect the molecular shape. The term dynamic stereochemistry applies to die topology of processes which effect a structural change. The cases that are most important in organic chemistry are chemical reactions, conformational changes, and noncovalent complex formation. In order to understand the stereochemical aspects of a dynamic process, it is essential not only that the stereochemical relationship between starting and product states be established, but also that the spatial features of proposed intermediates and transition states must account for the observed stereochemical transformations. 

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