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 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

Consideration is given to phenomena which we believe to be controlled by the fluctuations in the poorly understood intermediate range order in liquids and glasses. These include structural relaxation, crystal nucleation and incipient liquid-liquid phase separation. Techniques which show promise for investigating the intermediate range order are considered, and predictable or conceivable developments in these techniques which may, by the year 2004 (N.J. Kreidl's 100th), greatly increase or even revolutionize our knowledge of the intermediate range order, are discussed. These include difference spectroscopy, difference scattering, and computer simulation techniques. Finally, we consider possible developments in system preparation or system manipulation techniques which may lead to new insights into relations between physical properties and intermediate range order. An example of special interest is the preparation of noncommunicating microsystems of the same size as the clusters which many believe are the building blocks of the glassy state.

Spectroscopy simulation and scattering, and the medium range order problem in glass

We have studied the temperature dependence of dielectric relaxation times in terms of the peak frequency fmax(T) of dielectric loss e″(ω) and the dc‐conductivity σdc(T) of several glass‐forming liquids, covering 12 decades in the peak frequency fmax and 9 decades in σdc. Although dc‐conductivity samples the mobility of ionic tracers, its variation with temperature is similar to that of fmax(T). The fmax(T) and σdc(T) are analyzed using the temperature‐derivative method and compared to the viscosity data η−1(T). While most liquids reveal a common Vogel–Fulcher–Tammann (VFT) behavior for fmax, σdc and η−1 in an extended temperature range T≥Tm, some liquids deviate from this behavior by displaying a crossover at T=TA to an Arrhenius regime. In these cases the quantity fmax(T) decouples from the common curves for σdc(T) and η−1(T) and attains activation energies in excess (∼40% for alcohols) of those related to translational processes. For many samples a departure from the VFT behavior occurs at lower tempera...

Dynamics of glass-forming liquids. II. Detailed comparison of dielectric relaxation, dc-conductivity, and viscosity data

‘Tunnelling’ is the metaphorical name given to the process, possible in quantum mechanics, but not in classical mechanics, whereby a particle can disappear from one side of a potential-energy barrier and appear on the other side without having enough kinetic energy to mount the barrier. One can think of this as a manifestation of the wave-nature of particles. The wavelength is larger if a particle is lighter. In particular electrons, being very light compared to atoms, have wavelengths as large or larger than atoms at energies found in the valence shells of molecules. Thus, they easily ooze through and around atoms and molecules. We are also concerned with the tunnelling of heavy particles: nuclei, atoms, molecules.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S003358350000175X

Quantum mechanical tunnelling in biological systems

Viscosities of some organic glasses used as trapping matrixes

Effects of matrix polarity on the optical and electron spin resonance spectra of trapped electrons in organic glasses

Further studies on the properties of electrons trapped in glassy hydrocarbons.

The experimental observations dealing with trapped electrons in organic glasses which are most revealing as to the nature of the trapping process are discussed, and a model of trapping which they suggest is outlined. Data from optical and ESR spectrometry, differential thermal analysis, bleaching, decay, and scavenger studies are cited. It appears that after mobile electrons produced by $gamma$ irradiation or photoionization of solutes are thermalized they first become stabilized in weak traps through polarization and dipole interactions and then deepen these traps by molecular orientation at rates dependent on the polarity of the matrix molecules and the temperature. The data suggest that the stabilized condition at any temperature involves a continuum of trap depths in which the electrons give optical spectra of different lambda/sub max/ which add up to give the broad observed spectrum. The energy of a photon absorbed by an electron in excess of the detrapping threshold for that electron determines whether the electron can migrate far enough to encounter a capturing entity. If the energy is too low the electron is retrapped rather than being bleached. Evidence for capture of epithermal subexcitation electrons by some scavengers and on the heats of solvation of electrons and cationsmore » in organic glasses is also noted. (auth)« less

John E. Willard

Papers

Viscosities of some organic glasses used as trapping matrixes

Effects of matrix polarity on the optical and electron spin resonance spectra of trapped electrons in organic glasses

Further studies on the properties of electrons trapped in glassy hydrocarbons.

Trapped electrons in organic glasses

Absence of hydrogen atom production in radiolysis of solid hydrocarbons.