Ordering parameter, molecular glasses

A little work seems to have been carried out on the wavenumber-dependent orientational correlation functions C/m(, t). These correlation functions can provide valuable insight into the details of microscopic dynamics of the system. A molecular level understanding of C/m(, t) would first require the development of a molecular hydrodynamic theory that would have coupling between C/m(, t) and the dynamic structure factor S(k, t) of the liquid. A slowdown in C/m(, t) may drive a slowdown in the dynamic structure factor. This would then give rise to a two-order parameter theory of the type develops by Sjogren in the context of the glass transition and applied to liquid crystals by Li et al. [91]. However, a detailed microscopic derivation of the hydrodynamic equations and their manifestations have not been addressed yet. 

Liquid crystallinity is mainly exhibited in the following two temperature regions (1) from (glass transition temperature) to T, (isotropic transition temperature, also known as the clearing point ) (2) from (melting point) to T, where several mesophases can usually be observed. Like ordinary polymers, the transition behavior of liquid polymers is also dependent on their thermal history and relative molecular mass. Therefore, only the samples with sufficient molecular mass and the same thermal history are suitable for the purpose of comparison and study. The transition temperatures for these substances rise with increase in the relative molecular mass, but remain approximately constant when the latter is more than 10 000. The transition heat shows a similar tendency. In addition, the transition entropy from mesophase to isotropic, ASl, is related to the order parameters. 

In this situation, computer simulations have several prospects to offer. One can design simple models that reproduce the experimental phenomenology and can then be analyzed in far more microscopic detail. The models themselves can be simplified to such an extent that one can identify the molecular properties indispensable for defining a glass-forming substance. This and the complete microscopic information available allow for a guided search for possible order parameters needed to address the question of a possible underlying phase transition. Furthermore, a detailed simultaneous study of the temperature dependence of the structural and conformational relaxation in polymer melts is possible. 

Overall, the order parameter model provides both a simple physical interpretation of thermodynamic changes at Tg and a semiquantitative estimate of their magnitude. It does not, however, explain why segmental motion freezes in and in the absence of knowledge of the two-state parameters 8s and 8, it does not lead to predictions of Tg and therefore cannot explain how Tg will vary with molecular weight, composition, and chemical structure. The free-volume theory and the GM configurational entropy theory are the two most important attempts to explain why molecular motions eventually stop in a supercooled liquid and hence why the glass transition takes place. 

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