https://onlinelibrary.wiley.com/doi/pdf/10.1021/js9601896

Characteristics and Significance of the Amorphous State in Pharmaceutical Systems

Recent attempts have been made to assess the relative merits of the free volume and entropy theories of viscous flow in glass‐forming liquids by accurate measurement of viscosity over wide temperature ranges, and subsequent comparison with the equations derived from these theories. In the author's view, this effort is misguided. The theories are crude and qualitative, and such tests are too stringent. It is better to make qualitative or semiquantitative comparison of a wide variety of physical phenomena; judged by this criterion, the entropy theory appears more successful. It is conjectured that further progress can be made by accepting the crude, naive character of any model we are likely to find tractable for the foreseeable future, and recognizing both the values and limitations of such models. A picture of the flow process in viscous liquids is proposed, in an attempt to answer certain questions about the molecular steps in flow either answered unsuccessfully or ignored by present theories, in the hop...

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Viscous Liquids and the Glass Transition: A Potential Energy Barrier Picture

The elastic properties, elastic models and elastic perspectives of metallic glasses

The field of enthalpy relaxation is reviewed. Current phenomenologies for dealing with the non-linear and non-exponential character of enthalpy relaxation are presented, and their successes and shortcomings are discussed. Qualitative experimental data and quantitative parameterizations are summarized, and some directions for future research are suggested.

Enthalpy relaxation and recovery in amorphous materials

The free-volume model, which has been useful for describing the behavior of the viscosity $\ensuremath{\eta}$ of dense liquids and glasses, is extended to account for their thermodynamic behavior as well. Experimental results for the heat capacity ${C}_{p}$ and the volume $\overline{v}$ show that the system falls out of complete, metastable thermodynamic equilibrium at the glass transition temperature ${T}_{g}$. As a first step in understanding these universal phenomena, a theory of the underlying metastable phase, the amorphous phase, is developed. Recent molecular-dynamic calculations demonstrating the existence of a cellular structure in liquids and the properties of the local free energy of the molecular cells permit us to formulate more precisely and justify in more detail the standard free-volume model. In particular, it is possible to define the free volume and distinguish solid-like and liquidlike cells. This leads to the introduction of percolation theory, which is used to describe the gradual development of the communal entropy of the amorphous phase. We then determine the probability distribution of the cellular volume as a function of the fraction of liquidlike cells, $p$. The equilibrium liquid-glass transition is associated with the increase of $p$ with temperature. This occurs via a phase transition which is most probably first order. The results of our theory give a generalized equation for the viscosity which agrees accurately with experimental results at all temperatures. Results for ${C}_{p}$ and $\overline{v}$ are also obtained. This equilibrium theory can provide the basis for a relaxation theory of the kinetic effects observed around and below ${T}_{g}$. The relationship between the entropy theory and the free-volume model is also clarified.

Liquid-glass transition, a free-volume approach

The rate‐theory approach of Eyring and the free‐volume theory of Cohen and Turnbull for liquid viscosities have been reconsidered. The rate theory has been reformulated using the Cohen and Turnbull expression for the probability of finding a vacant site and yields an equation of the form η=A0exp[Ev*/RT+γV0/Vf]. This result has been applied to many liquids ranging from fused silica to liquid argon and including polyatomic van der Waals as well as hydrogen‐bonded liquids.Consistent fits to both temperature and pressure dependence of viscosity were obtained. A significant conclusion is that the free volume of liquids is considerably higher than that suggested by the WLF and Cohen and Turnbull equations.

T. A. Litovitz

Papers

On the Relative Roles of Free Volume and Activation Energy in the Viscosity of Liquids