Abstract: We have performed exact classical rate calculations to compute adsorption and desorption rate constants with a model representative of a real system. We compute the desorption rate using transition-state theory by taking the dividing-surface far from the surface of the solid. We find that using a mean-field assumption, i.e., applying potential of mean force to transition state theory, could lead to two orders-of-magnitude errors in the rate constant owing to large fluctuations in the desorption barrier. Furthermore, we compute the adsorption rate by including a dynamical factor which reflects the probability of sticking to the solid surface. We find that the sticking probability is highly sensitive to the coverage. Also, we find that the adsorption rate computed from the mean-field assumption is not very different from the exact adsorption rate. We also compute entropic contribution to desorption rates and compare it to that obtained from two limiting models of adsorption—2D ideal gas and 2D ideal lattice gas. We show that at high temperatures (700 K), the entropic contribution to desorption rates computed from the exact calculations is very close to that obtained from the 2D ideal gas model. However, for lower to intermediate temperatures from 200 K to 500 K, the entropic contributions cover a wide range which lies in between the two limiting models and could lead to over two-orders-of-magnitude errors in the rate coefficient.
Abstract: We review here some aspects of computational work on the catalytic chemistry of oxides. The difficulties of using density functional theory in calculations are explained. Different ways of structural or chemical modifications aimed at improving catalytic activity are reviewed. The reaction mechanism of partial oxidation reaction catalyzed by oxides is discussed. The focus is on qualitative design rules rather than on obtaining highly accurate computational results.
Abstract: Metals that are active catalysts for methane (Ni, Pt, Pd), when dissolved in inactive low–melting temperature metals (In, Ga, Sn, Pb), produce stable molten metal alloy catalysts for pyrolysis of methane into hydrogen and carbon. All solid catalysts previously used for this reaction have been deactivated by carbon deposition. In the molten alloy system, the insoluble carbon floats to the surface where it can be skimmed off. A 27% Ni–73% Bi alloy achieved 95% methane conversion at 1065°C in a 1.1-meter bubble column and produced pure hydrogen without CO2 or other by-products. Calculations show that the active metals in the molten alloys are atomically dispersed and negatively charged. There is a correlation between the amount of charge on the atoms and their catalytic activity.
Abstract:MoO3 is a versatile catalyst for oxidation reactions that consists of bilayers connected by van der Waals interaction. In principle, a MoO3 nanocrystal can be exfoliated to create two-dimensional ribbons. For this article, we study the difference between the chemistry of slabs having a variety of crystal faces and that of the edges of ribbons cut from a two-dimensional bilayer. As a descriptor of chemical reactivity we use the energy of oxygen-vacancy formation: the easier it is to form an oxygen vacancy, the better oxidant the face of a slab or the edge of a two-dimensional ribbon is. We find that the properties of ribbon edges are different from those of the corresponding slab surfaces. The surface energies of slabs are in the order (010)s < (100)s < (101)s < (001)s, whereas the edge energies of ribbons are in the order ⟨100⟩r ≈ ⟨101⟩r < ⟨001⟩r (the subscript s indicates a slab, and r, a ribbon). Among the surfaces studied, we have found that (001)s and (101)s faces have the lowest oxygen-vacancy formation energies, and (010)s has the highest. In contrast, among the edges studied, ⟨101⟩r has the lowest vacancy formation energies. Our calculations suggest that no benefit is obtained by creating ⟨100⟩r or ⟨001⟩r ribbon edges. However, a significant decrease of oxygen-vacancy formation energies is observed on formation of ⟨101⟩r edge by exfoliating (101)s slabs. Also, among the structures studied, we found ⟨101⟩r edges to be the most reactive and (010)s surfaces to be the least reactive.
Abstract:Oxygen vacancy formation energies are often used as a descriptor of the catalytic activity of metal oxides for oxidation reactions having the Mars–van Krevelen mechanism. When these energies are calculated, it is often assumed that they depend only on the concentration of the vacancies in the top oxygen layer. Previous work has shown that in the case of TiO2 and V2O5, the energy of vacancy formation depends not only on their concentration but also on the manner in which they are distributed on the surface. However, the energy change due to the change of configuration in these systems is very small. Here, we find that in the case of α-MoO3(010) the dependence on the energy of vacancy formation of the distribution of vacancies is very large: if the lattice made by the vacancies consists of parallelograms, the energy of vacancy formation is 0.4 eV smaller than when the lattice consists of rectangles (the two systems having the same vacancy concentration).
Abstract: Density functional theory is used to determine differences in hydrogen abstraction and ammonia binding energies between two zeolites (BEA and MFI-type) and two α-quartz surfaces doped with Al, B, Sc, or Ga. One of the questions we wanted to answer is whether the fact that zeolite cages are made of a silica monolayer plays any role in their catalytic activity. We find no important difference. Doped α-quartz has acid hydroxyls such as those in zeolites; however, their density is very low, and doped quartz is not a shape selective catalyst. Therefore, the doped silica examined here is an inferior acid catalyst when compared to BEA or MFI.
Abstract:We use the Potts-lattice gas model to study nucleation at and near the eutectic composition. We use rare-event methods to compute the free energy landscape for the competing nucleation products, and short trajectories at the barrier top to obtain prefactors. We introduce a procedure to tune the frequency of semigrand Monte Carlo moves so that the dynamics of a small closed system roughly resemble those of an infinite system. The non- dimensionalized nucleation rates follow trends as predicted by the classical nucleation theory. Finally, we develop corrections that convert free energy surfaces from closed (canonical) simulations into free energy surfaces from open (semigrand) simulations. The new corrections extend earlier corrections to now address situations like nucleation at the eutectic point where two products nucleate competitively.
Abstract: This chapter focuses on a frontier for molecular simulation: nucleation of solute precipitates from solution. The chapter refers to simulations of solute precipitate nucleation with a fixed number of solute and solvent molecules simulations of “closed systems”. Two simple cases of heterogeneous nucleation are considered: (i) a spherical cap model for nucleation on a hard flat surface and (ii) a lens model for nucleation at fluid–fluid interfaces. Over the decade following the discovery of two'step nucleation, several computational studies have pointed to two'step nucleation as a more general phenomena occurring even at points where there is no metastable fluid–fluid critical point. Rare events simulation methods can relax many of the assumptions made by classical nucleation theory (CNT). The chapter concludes with case studies on laser'induced nucleation, and on nucleation of methane hydrates and calcium carbonate.
Abstract:We modeled nascent decomposition processes in cellulose pyrolysis at 327 and 600 °C using Car–Parrinello molecular dynamics (CPMD) simulations with rare events accelerated with the metadynamics method. We used a simulation cell comprised of two unit cells of cellulose Iβ periodically repeated in three dimensions to mimic the solid cellulose. To obtain initial conditions at reasonable densities, we extracted coordinates from larger classical NPT simulations at the target temperatures. CPMD-metadynamics implemented with various sets of collective variables, such as coordination numbers of the glycosidic oxygen, yielded a variety of chemical reactions such as depolymerization, fragmentation, ring opening, and ring contraction. These reactions yielded precursors to levoglucosan (LGA)—the major product of pyrolysis—and also to minor products such as 5-hydroxy-methylfurfural (HMF) and formic acid. At 327 °C, we found that depolymerization via ring contraction of the glucopyranose ring to the glucofuranose ring occurs with the lowest free-energy barrier (20 kcal/mol). We suggest that this process is key for formation of liquid intermediate cellulose, observed experimentally above 260 °C. At 600 °C, we found that a precursor to LGA (pre-LGA) forms with a free-energy barrier of 36 kcal/mol via an intermediate/transition state stabilized by anchimeric assistance and hydrogen bonding. Conformational freedom provided by expansion of the cellulose matrix at 600 °C was found to be crucial for formation of pre-LGA. We performed several comparison calculations to gauge the accuracy of CPMD-metadynamics barriers with respect to basis set and level of theory. We found that free-energy barriers at 600 °C are in the order pre-LGA < pre-HMF < formic acid, explaining why LGA is the kinetically favored product of fast cellulose pyrolysis.
Abstract:We have modeled the transformation of cellulose Iβ to a high temperature (550 K) structure, which is considered to be the first step in cellulose pyrolysis. We have performed molecular dynamics simulations at constant pressure using the GROMOS 45a4 united atom forcefield. To test the forcefield, we computed the density, thermal expansion coefficient, total dipole moment, and dielectric constant of cellulose Iβ, finding broad agreement with experimental results. We computed infrared (IR) spectra of cellulose Iβ over the range 300–550 K as a probe of hydrogen bonding. Computed IR spectra were found to agree semi-quantitatively with experiment, especially in the O–H stretching region. We assigned O–H stretches using a novel synthesis of normal mode analysis and power spectrum methods. Simulated IR spectra at elevated temperatures suggest a structural transformation above 450 K, a result in agreement with experimental IR results. The low-temperature (300–400 K) structure of cellulose Iβ is dominated by intrachain hydrogen bonds, whereas in the high-temperature structure (450–550 K), many of these transform to longer, weaker interchain hydrogen bonds. A three-dimensional hydrogen bonding network emerges at high temperatures due to formation of new interchain hydrogen bonds, which may explain the stability of the cellulose structure at such high temperatures.
Abstract:We have studied base strengths of nitrogen-substituted (nitrided) zeolites with faujasite (FAU) structure by calculating sorption energies of probe molecules (BF3 and BH3) using density functional theory with mixed basis sets applied to embedded clusters. BH3 was found to be a better probe of base strength because it does not introduce competing metal−fluorine interactions that obfuscate trends. In all cases, the base strengths of nitrided zeolites (denoted M−N−Y) were found to exceed those of the corresponding standard M−Y zeolites, where M = Li, Na, K, Rb, or Cs charge-compensating cations. We have found that for a particular Si:Al ratio, BH3 sorption energies vary in the order Li < Na < K ∼ Rb ∼ Cs. Sorption energy and hence base strength was found to decrease with increasing Si:Al ratio from 1 to 3 beyond which the base strength was found to increase again. The initial regime (1 < Si:Al < 3) is consistent with the prevailing understanding that the base strength increases with Al content, while the latter regime (Si:Al > 3) involves the surprising prediction that the base strength can be relatively high for the more stable, high-silica zeolites. In particular, we found the sorption energy in Na−N−Y (Si:Al = 11) to be nearly equal to that in (Si:Al = 1). Taken together, these results suggest that K−N−Y (Si:Al = 11) optimizes the balance of activity, stability, and cost.
Abstract: We have modeled the formation kinetics of nitrogen-substituted (nitrided) zeolites HY and silicalite; we have also modeled the stability of nitrided sites to heat and humidity. These kinetic calculations are based on mechanisms computed from DFT-computed pathways reported in our previous work. Reactant ammonia and product water concentrations were fixed at various levels to mimic continuous nitridation reactors. We have found that zeolite nitridation — replacing Si–O–Si and Si–OH–Al linkages with Si–NH–Si and Si–NH2–Al, respectively — proceeds only at high temperatures (> for silicalite and > for HY) due to the presence of large overall barriers. These threshold temperatures are in good agreement with experiments. Nitridation yields were found to be sensitive to water concentration, especially for silicalite where nitridation is more strongly endothermic. As a result, overall nitridation yields in silicalite are predicted to be much lower than those in HY. The stability of nitrided sites was investigated by modeling the kinetics of nitridation in reverse, going back to untreated zeolite plus ammonia. Using 10 h as a benchmark catalyst lifetime, nitrided silicalite and HY half-lives exceeded 10 h for temperatures below 275 and 500 °C, respectively, even at saturation water loadings. As such, our calculations suggest that nitrided silicalite and HY zeolites require high temperatures to form, but once formed, they remain relatively stable, auguring well for their use as shape-selective base catalysts.
Abstract: We have performed embedded-cluster calculations using density functional theory to investigate mechanisms of nitrogen substitution (nitridation) in HY and silicalite zeolites. We consider nitridation as replacing Si–O–Si and Si–OH–Al linkages with Si–NH–Si and Si–NH2–Al, respectively. We predict that nitridation is much less endothermic in HY (29 kJ/mol) than in silicalite (132 kJ/mol), indicating the possibility of higher nitridation yields in HY. To reveal mechanistic details, we have combined for the first time the nudged elastic band method of finding elusive transition states, with the ONIOM method of treating embedded quantum clusters. We predict that nitridation of silicalite proceeds via a planar intermediate involving a ring with pentavalent Si, whereas nitridation of HY is found to proceed via an intermediate similar to physisorbed ammonia. B3LYP/6-311G(d,p) calculations give an overall barrier for silicalite nitridation of 343 kJ/mol, while that in HY is 359 kJ/mol. Although the overall nitridation barriers are relatively high, requiring high temperatures for substitution, the overall barriers for the reverse processes are also high. As such, we predict that once these catalysts are made, they remain relatively stable.
Abstract: Nanoporous acid catalysts such as zeolites form the backbone of catalytic technologies for refining petroleum. With the promise of a biomass economy, new catalyst systems will have to be discovered, making shape-selective base catalysts especially important because of the high oxygen content in biomass-derived feedstocks. Strongly basic zeolites are attractive candidates, but such materials are notoriously difficult to make due to the strong inherent acidity of aluminosilicates. Several research groups have endeavored to produce strongly basic zeolites by treating zeolites with amines, but to date there is no compelling evidence that nitrogen is incorporated into zeolite frameworks. In this communication, we detail synthesis, NMR spectroscopy, and quantum mechanical calculations showing that nitrogen adds onto both surface and interior sites while preserving the framework structure of zeolites. This finding is crucial for the rational design of new biomass-refinement catalysts, allowing 50 years of zeolite science to be brought to bear on the catalytic synthesis of biofuels.
Abstract: In reactive distillation (RD) one can conveniently manipulate the concentration profiles on the reactive stages by exploiting the difference in volatility of the various components. This property of RD can be advantageously used to improve the selectivity toward the desired product in case of series or series parallel reactions, and obtain a performance superior to the network of conventional reactors. In the previous work [Agarwal, V., et al., 2008. Attainable regions of reactive distillation—Part I. Single reactant non-azeotropic systems. Chemical Engineering Science, submitted for publication], we introduced representative unit models of RD to obtain the attainable regions of RD for non-azeotropic systems. In this work, we extend the approach to a system involving single binary azeotrope. Design guidelines have been formulated based on the residue curve maps, to obtain the improved attainable region with the help of these representative RD models either alone or in the form of their network.
Abstract:Reactive distillation (RD), a promising multifunctional reactor, can be used to improve the selectivity of the desired product by manipulating the concentration profiles in the reactive zone of the column. In this work, a new approach has been proposed to obtain the feasible regions of RD for the reactive systems involving single reactants, e.g. dimerization, aldol condensation, etc. Two new models namely the reactive condenser and the reactive re-boiler have been proposed. These models indicate the best location of the reactive zone in a column. Multistage versions of these models namely, reactive rectification and reactive stripping further expand the feasible region and are capable of representing the performance offered by a conventional RD unit. Several hypothetical non-azeotropic ideal systems have been extensively studied using these models and it has been shown that selectivity close to 100% is attainable over the entire range of conversion for a series as well as a combination of series and parallel reactions with positive reaction orders. Two industrially important cases of aldol condensation of acetone and dimerization of isobutylene have also been addressed using this approach. For porous catalysts, the presence of intra-particle diffusion resistance may limit the feasible region and even in the case of ideal non-azeotropic systems it may not be possible to obtain 100% selectivity. A methodology to incorporate pore diffusion effects is also illustrated.
Abstract: Aldol condensation of acetone in the presence of acid catalyst gives diacetone alcohol (DAA) as an intermediate product, which further dehydrates to give mesityl oxide (MO). By using reactive distillation (RD), one can improve selectivity toward DAA, by continuously removing it from the reactive zone and thereby suppressing the dehydration reaction. The presence of water in the reaction mixture has a predominant effect on the intrinsic reaction rates of the individual reactions. This rate-inhibiting effect of water can be advantageously used to improve the selectivity toward the desired intermediate products. The present study, through experiments and simulation, shows that introduction of water in RD can further increase the selectivity toward DAA. Batch kinetics of the reaction in the presence of water is studied, and a suitable kinetic expression is proposed. Further, the batch and continuous reactive distillation experiments are performed to assess the feasibility. The experimental results are explained with the help of an equilibrium-stage model, and the operating parameters for the desired performance are suggested based on the validated model.
Abstract: Dimerization of acetone (Ac) yields diacetone alcohol (DAA), which on further dehydration gives mesityl oxide (MO) along with various side-products. The reacting system is a combination of various series and parallel reactions. In the present work, the reaction is studied using a cation exchange resin (Amberlyst 15®) as catalyst. The effect of catalyst loading and temperature on reaction kinetics was evaluated and three models based on simplified Langmuir–Hinselwood mechanism are proposed. Aim of the work is to minimize undesired side-products and understand the effect of different parameters and operating modes on DAA:MO product ratio in reactive distillation (RD). It has been shown that the reaction when operated in a reactive rectification mode offers flexibility in the relative production rates of DAA and MO. The experimental results obtained are explained by simulation.
Abstract: Reactive distillation (RD), a combination of reaction and separation, holds the potential of giving selectivity/yield much above that offered by the conventional reactors or combination of them. It can be effectively used to improve selectivity of a reaction especially when an intermediate product is desired in series or parallel reactions. In this work, some representative model systems are introduced to obtain attainable region. A series as well as a combination of series parallel reactions (irreversible and mixture of reversible and irreversible reaction systems) were studied with the proposed models and it was found that for the single reactant ideal systems one can obtain almost 100% selectivity for a near quantitative conversion, which is much greater than that obtained in the conventional reactors like PFR and CSTR. These models were also studied for the non-ideal azeotropic systems and it was found that there is a limit to feasible region. The results obtained in the theoretical analysis are supported by experiments on aldol condensation of acetone.