Glass free volume theory

It would be an advantage to have a detailed understanding of the glass transition in order to get an idea of the structural and dynamic features that are important for photophysical deactivation pathways or solid-state photochemical reactions in molecular glasses. Unfortunately, the formation of a glass is one of the least understood problems in solid-state science. At least three different theories have been developed for a description of the glass transition that we can sketch only briefly in this context the free volume theory, a thermodynamic approach, and the mode coupling theory. 

It was found that Afi Tg and Aa Tg are not constant and therefore the SB equation has limited applicability. Hie results indicate an increase in Aa Te with increasing Tg. Therefore it is inadmissible to use the product A a Tg as a universal value in any theoretical discussion of the glass-transition phenomenon. At the same time, this conclusion in no way excludes the free-volume theory and the role of free-volume in the transition from the glassy to the liquid or rubberlike state. 

We believe the difficulty is that the free-volume theory as applied to the glass-transition does not take account of the essential role of intra- and intermolecular interaction in the system and the flexibility of the polymer chains, all of which factors play an important role in the glass-transition phenomena. 

We therefore believe one of the most pressing problems in the field of free-volume theory and glass-transition theory to be the development of new concepts and obtaining of new parameters for the corresponding states. Miller37 as early as 1968 introduced the idea that the glass transition corresponds to the iso-relaxation state, which at molecular weights of polymers below the critical ones may be replaced by an iso-viscous state. 

Styrene-Divinylbenzene Networks. Using ionic polymerization methods, Rietsch et al. (1976) prepared polystyrene (PS) networks with a well-controlled length of elastically active chains and crosslinks of variable functionality. In a given series, the glass transition temperature obeys the classical free volume theory ... 

Using the classical hypotheses of the free volume theory, the glass transition temperature for a polymer (p) and solvent (s) solution, with a volume fraction of solvent, v, is given by (Kelley and Bueche, 1960) ... 

Free Volume Theory. Free volume theory suggests that the glass transition temperature is observed for polymers when their viscosity approaches that of their liquid state. Following a derivation based on the Doolittle expression for polymer viscosity (r ) as a function of free volume (Eisenberg, 1984)... 

Similarly to Fig. 5-4 for other glassy polymer-solvent systems also the predictions of this free-volume theory are in general agreement with experimental data on the temperature dependence of D in the vicinity of Tg2. In particular, the theory predicts a step change in Ed at Tg2, and this is consistent with most experimental investigations of polymer-solvent diffusion at temperatures just above and below the glass transition temperature (6,11,15). 

The authors of the cluster theory draw the conclusion that the theory affords a sufficiently rigorous theoretical derivation of Doolittle s equation (72). Verification of the free volume theory advanced by Cohen and Grest was carried out by Hiwatari using computer simulation [97], showed that glass transition in liquids can really be described in terms of the percolation theory, the value of Pcr in this case being close to 0.2. Unlike Cohen and Grest s assumptions, however, this transition is not accompanied by a drastic change in the fluidity of the liquid near Per-... 

Kawamura, J. and Shimoji, M. Ionic conductivity and glass transition in superionic conducting glasses II. Structural relaxation and excess free volume theory. J. Non-Cryst. Solids 88 295, 1986. 

The free volume theory of glass transition is based on Doolittle s empirical assumption (29), which states that the viscosity, q, at T > Tg is related to the free volume fraction by the equation... 

Most previous work has been reviewed by Grace (G13) and Schiigerlet al. (in D5). Botterill (B12) and Hetzler and Williams (H8) correlated the apparent viscosity of liquid- and gas-fluidized systems, applying a free-volume theory which may be used successfully for glass-forming (polymeric) liquids. Saxton et al. (S3) proposed another approach to a free-volume theory. They compared theoretical expectations with the experimental data obtained in liquid-fluidized systems. Their extension to gas-fluidized systems (in cgs units) became, for sand. 

---