Modelling of glasses

Mathematical modelling, in biochemical engineering, 77 41 Mathematical models of glass melting, 72 605 process-control, 20 687-691 Mathematical optimization approach, in computer- aided molecular design, 26 1037... 

Process measurements, 20 678-684 Process metallurgy, 16 127 Process modeling, in synthetic latex manufacture, 14 722 Process models, of glass melting, 12 605-606... 

J. P. Garrahan and D. Chandler, Coarse-grained microscopic models of glass formers. Proc. Natl. Acad. Sci. USA 100, 9710-9714 (2003). 

Our discussion has so far been restricted to the schematic model of glass formation, which focuses on the relative flexibility of the chain backbone and side groups. The side groups in this schematic model are short linear chains (see Fig. 3b) with three united atom units, a structure inspired by many synthetic polymers in which the size of the side groups is on the order of a few... 

This work is supported, in part, by NSF grant CHE 0416017. We are grateful to Arun Yethiraj for performing MD simulations for chains of our schematic model of glass formation and thank Alexei Sokolov and Ken Schweizer for helpful discussions and comments. 

Interaction frustration has also been found to be a control parameter for fragility in a spin model of glass formation. 

There are a number of mechanisms that pose potential problems to predicting dissolution rate kinetics as the system approaches saturation. Part of this conundrum originates from current models of glass corrosion kinetics that cannot yet incorporate these unanticipated phenomena into a mathematical equation that is consistent with the constraints of thermodynamics or kinetics. These phenomena include (1) alkali-hydrogen exchange (2) dissimilar reactivity of... 

Although the operation of parallel reactions explains why B and Na rates are different, there is no immediate explanation for why B rates become independent of solution saturation state as Si builds up in solution. Models of glass dissolution fashioned from TST arguments do not anticipate these results. According to TST-based models, the glass dissolution rate should depend solely on the solution saturation state... 

Figure 15-5. a) Schematic structure of solid Na20-Si02, crystal and glass. Si4+ Al3+ O 02 Na+. b) Cluster tissue model of glass. areas of increased stresses. 

Snyder, L. C., G. E. Peterson, and C. R. Kurkjian (1976). Molecular orbital calculations of quadrupolar coupling of "B in molecular models of glasses. J. 

One important point we should stress, in conjunction with our current interest, is that similar slow relaxation as liquid water is observed in much simpler model systems The binary mixture of Lennard-Jones liquids, which consist of two species of particles, is now studied extensively as a toy model of glass-forming liquids. It is simulated after careful preparation of simulation conditions to avoid crystallization. Also, the modified Lennard-Jones model glass, in which a many-body interaction potential is added to the standard pairwise Lennard-Jones potential, is also studied as a model system satisfying desired features. 

Although glass transition is conventionally defined by the thermodynamics and kinetic properties of the structural a-relaxation, a fundamental role is played by its precursor, the Johari-Goldstein (JG) secondary relaxation. The JG relaxation time, xjg, like the dispersion of the a-relaxation, is invariant to changes in the temperature and pressure combinations while keeping xa constant in the equilibrium liquid state of a glass-former. For any fixed xa, the ratio, T/G/Ta, is exclusively determined by the dispersion of the a-relaxation or by the fractional exponent, 1 — n, of the Kohlrausch function that fits the dispersion. There is remarkable similarity in properties between the JG relaxation time and the a-relaxation time. Conventional theories and models of glass transition do not account for these nontrivial connections between the JG relaxation and the a-relaxation. For completeness, these theories and models have to be extended to address the JG relaxation and its remarkable properties. 

Figure 14.12 Two structural models of glass-like carbon heated to high temperature (a) network of ribbon stacking model (After Jenkins and Kawamura, 1971) (b) alternate model. (After, Shiraishi, 1984 ).

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