Application of the statistical rate theory of interfacial transport to interpret the relaxation time of proton adsorption from solution onto oxides

A new way to analyze the rate of hydrogen ion adsorption from solution onto oxides was described. The statistical rate theory of interfacial transport (SRT) was applied to interpret relaxation time of ion adsorption. The new procedure for determination of rate constants of surface reaction was compared with the classical theory of activated adsorption and desorption (TAAD). It was found that for adsorption of uncharged species, both models give the same result, but for ion adsorption, their predictions differ considerably. Influence of surface potential and total concentration of adsorption sites on calculated rate constants was also discussed.     

Nonideal statistical rate theory formulation to predict evaporation rates from equations of state

A method of including nonideal effects in the statistical rate theory (SRT) formulation is presented and a generic equation-of-state based SRT model was developed for predicting evaporation rates. Further, taking the Peng-Robinson equation of state as an example, vapor phase pressures at which particular evaporation rates are expected were calculated, and the predictions were found to be in excellent agreement with the experimental observations for water and octane. A high temperature range (near the critical region) where the previously existing ideal SRT model is expected to yield inaccurate results was identified and predictions (for ethane and butane) were instead made with the Peng-Robinson based SRT model to correct for fluid nonidealities at high temperatures and pressures.     

Interference theory: Moment solution for two component adsorption chromatography

Summary Moment analysis is used to study two component perturbation chromatography with linear non-equilibrium adsorption. The interference between components is included through the adsorption equilibrium. In this work, the expressions for the first and second moments of two component pertubations have been obtained for the first time. They are just the vectorization of those for the single component system, and they clearly show the interference between components. These results could be applied to establish an experimental procedure to measure adsorption equilibrium and kinetic data.     

Continuum states from time-dependent density functional theory

Linear response time-dependent density functional theory is used to study low-lying electronic continuum states of targets that can bind an extra electron. Exact formulas to extract scattering amplitudes from the susceptibility are derived in one dimension. A single-pole approximation for scattering phase shifts in three dimensions is shown to be more accurate than static exchange for singlet electron-He(+) scattering.     

Predicting adsorption isotherms using a two-dimensional statistical associating fluid theory

A molecular thermodynamics approach is developed in order to describe the adsorption of fluids on solid surfaces. The new theory is based on the statistical associating fluid theory for potentials of variable range [A. Gil-Villegas et al., J. Chem. Phys. 106, 4168 (1997)] and uses a quasi-two-dimensional approximation to describe the properties of adsorbed fluids. The theory is tested against Gibbs ensemble Monte Carlo simulations and excellent agreement with the theoretical predictions is achieved. Additionally the authors use the new approach to describe the adsorption isotherms for nitrogen and methane on dry activated carbon.     

Adsorption kinetics at the solid/solution interface: statistical rate theory at initial times of adsorption and close to equilibrium

The kinetics of solute adsorption at the solid/solution interface has been studied by statistical rate theory (SRT) at two limiting conditions, one at initial times of adsorption and the other close to equilibrium. A new kinetic equation has been derived for initial times of adsorption on the basis of SRT. For the first time a theoretical interpretation based on SRT has been provided for the modified pseudo-first-order (MPFO) kinetic equation which was proposed empirically by Yang and Al-Duri. It has been shown that the MPFO kinetic equation can be derived from the SRT equation when the system is close to equilibrium. On the basis of numerically generated points ( t, q) by the SRT equation, it has been shown that we can apply the new equation for initial times of adsorption in a larger time range in comparison to the previous q vs radical t linear equation. Also by numerical analysis of the generated kinetic data points, it is shown that application of the MPFO equation for modeling of whole kinetic data causes a large error for the data at initial times of adsorption. The results of numerical analysis are in perfect agreement with our theoretical derivation of the MPFO kinetic equation from the SRT equation. Finally, the results of the present theoretical study were confirmed by analysis of an experimental system.     

Kinetics of metal ions adsorption at heterogeneous solid/solution interfaces: A theoretical treatment based on statistical rate theory

The statistical rate theory combined with a two-component competitive adsorption model is applied to describe the effect of pH on the kinetics of metal ions adsorption at energetically heterogeneous solid/solution interfaces. The surface heterogeneity has been represented by both Gaussian-like and rectangular functions of the adsorption energy distribution. A concept of effective heterogeneity parameters is found to represent very well the combined effects of surface energetic heterogeneity and of the electrostatic lateral interactions in the adsorbed phase, described by using the mean field approximation. The applicability of our approach is demonstrated by a quantitative analysis of two sets of experimental data reported in literature. Our theoretical expressions have been able to successfully correlate kinetic and equilibrium data in both these cases.     

Application of the Polanyi potential theory to phthalates adsorption from aqueous solution with hyper-cross-linked polymer resins

The adsorption equilibria of dimethyl phthalate (DMP) and diethyl phthalate (DEP) on two hyper-cross-linked polymer resins (NDA-99 and NDA-150) in aqueous solution were investigated at 298 K. And a coal-based granular activated carbon (AC-750) was chosen for comparison. All the adsorption equilibrium data of DMP were well fitted by the Polanyi-based isotherm modeling (Polanyi-Manes (PM) equation), and the characteristic curves of the three adsorbents were obtained. It is noteworthy that a reasonably good agreement was obtained between the combined micropore and mesopore volume of adsorbents and the corresponding adsorption volume capacity for phthalates. Compared to the granular activated carbon (AC-750), the greater adsorption performances of the two resins (NDA-99 and NDA-150) were assumed to result from their more abundant micro- and mesopore structure, where phthalates can be intensively adsorbed by pore-filling mechanism. According to the exponent b value of the PM equation, NDA-99 and NDA-150 show the more micro- and mesopore heterogeneity than AC-750. On the other hand, the functional groups on the adsorbent surfaces did not take a notable effect on the adsorption equilibria of phthalates. The theory equilibrium adsorption amounts of DEP, predicted by the specific characteristic curve of each adsorbent, agree well with the experimental ones, respectively. The characteristic curve of hyper-cross-linked polymer resins and its prediction of phthalates adsorption calculated by Polanyi-based isotherm modeling have a potential applicability for field applications.     

Continuum theory of polymer crystallization

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with G approximately exp(1/TDeltaT), where G is the growth rate and DeltaT is the supercooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with G approximately DeltaT, for small DeltaT. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.     

Nonempirical statistical theory for molecular evaporation from nonrigid clusters

We propose a nonempirical statistical theory to give the reaction rate and the kinetic energy distribution of fragments for molecular evaporation from highly nonrigid atomic and van der Waals clusters. To quantify the theory, an efficient and accurate method to evaluate the absolute value of classical density of states (the Thomas-Fermi density in phase space) and the flux at the so-called dividing surface is critically important, and we have devised such an efficient method. The theory and associated methods are verified by numerical comparison with the corresponding molecular dynamics simulation through the study of Ar(2) evaporation from Ar(8) cluster, in which evaporation is strongly coupled with structural isomerization dynamics. It turns out that the nonempirical statistical theory gives quite an accurate reaction rate. We also study the kinetic energy release (KER) arising from these evaporations and its Boltzmann-like distribution both for atomic and diatomic evaporations. This provides a general relation between the KER and temperature of the fragments.     

Interfacial properties of statistical copolymer brushes in contact with homopolymer melts

We use polymer self-consistent field theory to quantify the interfacial properties of random copolymer brushes (AB) in contact with a homopolymer melt chemically identical to one of the blocks (A). We calculate the interfacial widths and interfacial energies between the melt and the brush as a function of the relative chain sizes, grafting densities, compositions of the random copolymer in the brush, and degree of chemical incompatibility between the A and B species. Our results indicate that the interfacial energies between the melt and the brush increase (signifying expulsion of the free chains from the brush) with increasing grafting density, chemical incompatibility between A and B components, and size of the free chains relative to the grafted chains. We also compare the interfacial energies of random copolymers of different sequence characteristics and find that, except for the case of very blocky or proteinlike chains, blockiness of the copolymer has only little effect on interfacial properties. Our results for interfacial energies are rationalized based on the concept of an "effective volume fraction" of the brush copolymers, f(eff), which quantifies the chemical composition of the brush segments in the interfacial zone between the brush and melt copolymers. Using this concept, we modify the strong-stretching theory of brush-melt interfaces to arrive at a simple model whose results qualitatively agree with our results from self-consistent field theory. We discuss the ramifications of our results for the design of neutral surfaces.     

Dynamical theory of proton tunneling transfer rates in solution: general formulation

A general dynamical theory is presented for the rate constant of weak coupling, nonadiabatic proton-tunneling reactions in solution. The theory incorporates the critical role of the solvent and the vibration of the separation of the heavy particles between which the proton transfers, including their dynamics. The formulation which allows the computation of the quantum rate constant k via classical molecular dynamics simulation techniques is presented, as are a number of approximate analytic results for k in a variety of different important regimes. The frequent appearance of (nearly) classical Arrhenius behavior for k — even though the intrinsic reactive event is quantum proton tunneling — is discussed, together with the solvent and vibrational contributions to the apparent activation energy. In certain weak solvation limits, however, non-Arrhenius behavior for k is found and is related to vibrational Franck-Condon features in the reaction.     

Comparison of random-walk density functional theory to simulation for bead-spring homopolymer melts

Density profiles for a homopolymer melt near a surface are calculated using a random-walk polymeric density functional theory, and compared to results from molecular dynamics simulations. All interactions are of a Lennard-Jones form, for both monomer-monomer interactions and surface-monomer interactions, rather than the hard core interactions which have been most investigated in the literature. For repulsive systems, the theory somewhat overpredicts the density oscillations near a surface. Nevertheless, near quantitative agreement with simulation can be obtained with an empirical scaling of the direct correlation function. Use of the random phase approximation to treat attractive interactions between polymer chains gives reasonable agreement with simulation of dense liquids near neutral and attractive surfaces.     

Application of the vacancy solution theory to describe the enthalpic effects accompanying mixed-gas adsorption

The possibility of utilizing vacancy solution theory (VST) to study the enthalpic effects accompanying mixed-gas adsorption equilibria is presented. Besides heterogeneity, the interaction effects by using the regular adsorbed solution, Flory-Huggins, and Wilson models of nonideality in the adsorbed phase are taken into account. To predict adsorption phase diagrams and calorimetric effects in the mixed-gas adsorption system, only a knowledge of the single-gas adsorption isotherms and accompanying calorimetric effects is required. The possibility of simplification of the obtained theoretical expressions is shown. The obtained agreement between theory and experiment is very satisfactory.     

Exact statistical mechanical lattice model and classical Lindemann theory of melting of inert gas solids

A modified form of Lindemann’s model shows that the melting points of the heavy inert gases and other effectively spherical molecular species are proportional to the depths of their diatomic potential wells. The success of the model when compared with experiment seems to rely on the almost constant value of the ratio of the fractional volume and entropy changes during fusion. The Lindemann proposal can be incorporated into an exactly treated statistical mechanical lattice model utilising expandable clusters which reproduces the solid–liquid melting phenomenon for argon with a realistic volume change and melting line.     

A direct method for measuring adsorption from solution onto solids

A direct method of measuring solution adsorption onto a solid has been developed. The results are exactly the same as those given by the conventional method of measuring the change in composition of the solution upon contacting the adsorbent. The development is cast in the terms of Gibbsian surface concepts, from which the correct thermodynamic significance of adsorption measurements made by directly analyzing material adsorbed on the solid can be understood. The method was tested for the adsorption of Na-Laurate and n-hexanol from aqueous and n-decane solutions, and typical isotherms are presented. The various realized and potential advantages of the method are discussed. The most important of these are the ability to measure adsorption in complex systems with a negligible change in solution composition, and the possibility of ameliorating in certain situations some of the difficulties in measuring adsorption at high concentrations or on low surface area solids.