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A variation of the topological constraint theory is proposed where an atomic network is modeled as a collection of rigid polytopes, and which explicitly distinguishes the bond angle constraints as well as rigid bond angles from flexible ones. The proposed theory allows for direct quantitative estimation of the fraction f of zero-frequency or floppy modes of the network. A preliminary model is proposed to connect the theory to the two key experimental observables that characterize glass-forming liquids, i.e., the glass transition temperature Tg and fragility m. The predicted values are tested against the literature data available for binary and ternary chalcogenides in the Ge-As-Se system. The Tg is related to f in this model by the activation entropy associated with the bond scission-renewal dynamics that is at the heart of transport and relaxation in glass-forming liquids. On the other hand, the large and temperature-dependent conformational entropy contribution of the 1-polytopes, i.e., the selenium chain elements in these chalcogenide glass-forming liquids, plays a key role in controlling the variation of m with f.

A variation of the topological constraint theory is proposed where an atomic network is modeled as a collection of rigid polytopes, and which explicitly distinguishes the bond angle constraints as well as rigid bond angles from flexible ones. The proposed theory allows for direct quantitative estimation of the fraction f of zero-frequency or floppy modes of the network. A preliminary model is proposed to connect the theory to the two key experimental observables that characterize glass-forming liquids, i.e., the glass transition temperature Tg and fragility m. The predicted values are tested against the literature data available for binary and ternary chalcogenides in the Ge-As-Se system. The Tg is related to f in this model by the activation entropy associated with the bond scission-renewal dynamics that is at the heart of transport and relaxation in glass-forming liquids. On the other hand, the large and temperature-dependent conformational entropy contribution of the 1-polytopes, i.e., the selenium chain elements in these chalcogenide glass-forming liquids, plays a key role in controlling the variation of m with f.

Acidic zeolites are effective catalysts for the cracking of large hydrocarbon molecules into lower molecular weight products required for transportation fuels. However, the ways in which the zeolite structure affects the catalytic activity at Brønsted protons are not fully understood. One way to characterize the influence of the zeolite structure on the catalysis is to study alkane cracking and dehydrogenation at very low conversion, conditions for which the kinetics are well defined. To understand the effects of zeolite structure on the measured rate coefficient (kapp ), it is necessary to identify the equilibrium constant for adsorption into the reactant state (Kads-H+ ) and the intrinsic rate coefficient of the reaction (kint ) at reaction temperatures, since kapp is proportional to the product of Kads-H+ and kint . We show that Kads-H+ cannot be calculated from experimental adsorption data collected near ambient temperature, but can, however, be estimated accurately from configurational-bias Monte Carlo (CBMC) simulations. Using monomolecular cracking and dehydrogenation of C3 -C6 alkanes as an example, we review recent efforts aimed at elucidating the influence of the acid site location and the zeolite framework structure on the observed values of kapp and its components, Kads-H+ and kint .

Acidic zeolites are effective catalysts for the cracking of large hydrocarbon molecules into lower molecular weight products required for transportation fuels. However, the ways in which the zeolite structure affects the catalytic activity at Brønsted protons are not fully understood. One way to characterize the influence of the zeolite structure on the catalysis is to study alkane cracking and dehydrogenation at very low conversion, conditions for which the kinetics are well defined. To understand the effects of zeolite structure on the measured rate coefficient (kapp ), it is necessary to identify the equilibrium constant for adsorption into the reactant state (Kads-H+ ) and the intrinsic rate coefficient of the reaction (kint ) at reaction temperatures, since kapp is proportional to the product of Kads-H+ and kint . We show that Kads-H+ cannot be calculated from experimental adsorption data collected near ambient temperature, but can, however, be estimated accurately from configurational-bias Monte Carlo (CBMC) simulations. Using monomolecular cracking and dehydrogenation of C3 -C6 alkanes as an example, we review recent efforts aimed at elucidating the influence of the acid site location and the zeolite framework structure on the observed values of kapp and its components, Kads-H+ and kint .

Recent experimental work has shown that variations in the confinement of n-butane at Brønsted acid sites due to changes in zeolite framework structure strongly affect the apparent and intrinsic enthalpy and entropy of activation for cracking and dehydrogenation. Quantum chemical calculations have provided good estimates of the intrinsic enthalpies and entropies of activation extracted from experimental rate data for MFI, but extending these calculations to less confining zeolites has proven challenging, particularly for activation entropies. Herein, we report our efforts to develop a theoretical model for the cracking and dehydrogenation of n-butane occurring in a series of zeolites containing 10-ring channels and differing in cavity size (TON, FER, -SVR, MFI, MEL, STF, and MWW). We combine a QM/MM approach to calculate intrinsic and apparent activation parameters, with thermal corrections to the apparent barriers obtained from configurational-bias Monte Carlo simulations, to account for configurational contributions due to global motions of the transition state. We obtain good agreement between theory and experiment for all activation parameters for central cracking in all zeolites. For terminal cracking and dehydrogenation, good agreement between theory and experiment is found only at the highest confinements. Experimental activation parameters, especially those for dehydrogenation, tend to increase with decreasing confinement. This trend is not captured by the theoretical calculations, such that deviations between theory and experiment increase as confinement decreases. We propose that, because transition states for dehydrogenation are later than those for cracking, relative movements between the fragments produced in the reaction become increasingly important in the less confining zeolites. (Chemical Equation Presented).

Recent experimental work has shown that variations in the confinement of n-butane at Brønsted acid sites due to changes in zeolite framework structure strongly affect the apparent and intrinsic enthalpy and entropy of activation for cracking and dehydrogenation. Quantum chemical calculations have provided good estimates of the intrinsic enthalpies and entropies of activation extracted from experimental rate data for MFI, but extending these calculations to less confining zeolites has proven challenging, particularly for activation entropies. Herein, we report our efforts to develop a theoretical model for the cracking and dehydrogenation of n-butane occurring in a series of zeolites containing 10-ring channels and differing in cavity size (TON, FER, -SVR, MFI, MEL, STF, and MWW). We combine a QM/MM approach to calculate intrinsic and apparent activation parameters, with thermal corrections to the apparent barriers obtained from configurational-bias Monte Carlo simulations, to account for configurational contributions due to global motions of the transition state. We obtain good agreement between theory and experiment for all activation parameters for central cracking in all zeolites. For terminal cracking and dehydrogenation, good agreement between theory and experiment is found only at the highest confinements. Experimental activation parameters, especially those for dehydrogenation, tend to increase with decreasing confinement. This trend is not captured by the theoretical calculations, such that deviations between theory and experiment increase as confinement decreases. We propose that, because transition states for dehydrogenation are later than those for cracking, relative movements between the fragments produced in the reaction become increasingly important in the less confining zeolites. (Chemical Equation Presented).