Theoretical analysis of reaction kinetics with singlet oxygen molecules

A comparative analysis of predictive ability of three approaches to estimate the rate constants of reactions of H(2), H, H(2)O and CH(4) with electronically excited O(2)(a(1)Δ(g)) and O(2)(b(1)Σ(g)(+)) molecules is conducted. The first approach is based on a detailed ab initio study of potential energy surfaces. The second one is known as the "bond energy-bond order" method, and the third approach is a modification of the updated method of vibronic terms that makes it possible to evaluate the activation energy of reactions involving electronically excited species. The comparison showed that the estimates of the energy barrier by the updated method of vibronic terms for some reactions can be in good agreement with ab initio calculations and available experimental data. It was revealed that reactions of O(2)(b(1)Σ(g)(+)) molecules with H(2), H(2)O and CH(4) molecules and with the H atom result in the formation of electronically excited species. The reactivity of O(2)(b(1)Σ(g)(+)) molecules is smaller than that of O(2)(a(1)Δ(g)) ones, but much higher as compared to the reactivity of ground state O(2) molecules. For each reaction under study involving oxygen molecules in the excited electronic states O(2)(a(1)Δ(g)) and O(2)(b(1)Σ(g)(+)) the recommended temperature-dependent rate constants are presented.     

Diffusion coefficients of small molecules at the gas-solid interface as measured by the nuclear magnetic resonance pulsed field gradient method

The nuclear magnetic resonance pulsed field gradient method has been used to measure the diffusion coefficients for some low molecular weight compounds adsorbed at the gas-solid interface. The systems studied are ammonia adsorbed upon graphite, methane adsorbed upon graphite, neopentane adsorbed upon graphite and neopentane adsorbed upon titanium dioxide. Results are compared with values obtained from quasi-elastic neutron scattering where available.     

Diffusion coefficients of tungsten heteropolyacids

Controlled hydrodynamics at rotating platinum and amalgamated copper electrodes were used to measure diffusion coefficients for 12-phosphotungstic and polyphosphotungstic acids in 1 M phosphoric acid, D_112-PTA=2.48 · 10^-6; D_polymer= 2.68 · 10^-7 cm²/sec, assuming only 1 tungsten atom in 12 is reduced at each diffusing entity. The phosphotungstic acids in phosphoric acid probably exist as polymers on initial formation, not greater than tetramers, rearranging to give monomers from calculations based on one reduced tungsten atom to each complex ion. Diffusion parameters of the phosphotungstic acids are compared with diffusion results of tungsten compounds from the literature obtained with dropping mercury electrodes. In all instances, low diffusion values are obtained indicating large diffusing entities.     

Diffusion coefficients and complex equilibria in solution-I theory: Diffusion coefficients of complex species

It is shown that in principle it is possible to obtain values of the formation constants of metal complexes in solution from values of diffusion coefficients. It is also confirmed that, in a system of successively formed complexes, there is a linear relationship between the square root of the diffusion coefficients and the co-ordination numbers of the complexes formed. In some instances such analysis has shown that revision of some previously reported formation constant data is required.     

Diffusion anomaly as a function of molecular length of linear molecules: levitation effect

Previous work on monatomic spherical sorbates has shown the existence of an anomalous peak in self-diffusivity (D) when plotted as a function of size of the diffusant. Molecular dynamics studies on linear molecules of different lengths l in zeolite NaY at 140 and 200 K are reported. It is seen that there is a peak in D as a function of l, suggesting that the levitation effect exists for linear molecules, the simplest member of polyatomics. This is confirmed by the lowering of the activation energy for the molecule whose length l exhibits highest D. Related quantities of interest such as the guest-host interaction energy and preexponential factor are discussed.     

Diffusion coefficients of small gas molecules in amorphous cis-1,4-polybutadiene estimated by molecular dynamics simulations

Molecular dynamics (MD) simulations were employed to estimate the diffusion coefficients of small gas molecules (Ar, O2, N2, CO2, and CH4) in amorphous cis-1,4-polybutadiene in the temperature range of 250-400 K. The VT diagram and solubility parameter of the amorphous polymer have been successfully reproduced using a full atomistic potential. Diffusion coefficients were calculated from long NPT MD runs (up to 3 ns) at temperature ranging from 250 up to 400 K. Calculated diffusion coefficients compare well with experimental data as well as previous published work, though a systematic overestimation is found due to the finite-size effect of the model. The influence of various physical and computational parameters on the results is discussed. The diffusion mechanism is examined at the different temperatures of study.     

Diffusion of small molecules inside a peptide hydrogel

A set of four phenylalanine analogues experiences diffusion retardation when transferred from phosphate-buffered saline into a peptide hydrogel of the same pH and ionic strength. The extent of retardation increases linearly with logP(oct), their lipophilicity.     

Diffusion coefficients of the ternary system water-tetrabutylammonium bromide-potassium bromide as a function of tetrabutylammonium bromide concentration

Sets of four diffusion coefficients were obtained for the water-tetrabutylammonium bromide-potassium bromide system at 25°C as a function of tetrabutylammonium bromide concentration with the mean concentration of potassiumbromide fixed at 0.1 mole-liter^?1. The experiments were performed at tetrabutylammonium bromide concentrations of 0.075, 0.15, 0.3, and 0.45 mole-liter^?1. The results are compared with the binary diffusion coefficients of these components and also with the calculated diffusion coefficients using the first approximation theory.     

Diffusion coefficients in a halocarbon–polybutene system

The diffusion coefficient of 1,1,2-trichlorotrifluoroethane (TTE) in a liquid polybutene was determined at 25°C. as a function of concentration over the range 1.0–19.5 g. TTE/100 cc. The diffusion coefficient increase with increasing TTE concentration, rising continuously from 3 × 10^?8 cm.²/sec. at the lowest concentration to 15 × 10^?8 cm.²/sec. at the highest. The magnitudes of the diffusion coefficients indicate that the diffusion mechanism for small molecules in polymeric media must afford vastly greater opportunities for diffusion than the Stokes-Einstein relation allows. Similarly, self-diffusion coefficients for the liquid polymer are much lower than the observed mutual diffusion coefficients. An explanation for this behavior is presented.     

Application of luminescent nanocrystals as labels for biological molecules

Luminescent semiconductor nanocrystals, so called quantum dots (QD), have attracted increasing interest for bioanalytical labeling applications in recent years. This review describes the major optical and (bio)chemical features of this class of label, compared with organic dyes. Different conjugation methods are also discussed and the most important recent applications are presented. An overview over the current state-of-the-art is given, as also is an outlook on possibilities and limitations.     

Diffusion of optically pumped molecules as a tool for probing the interaction of excited species

We have developed a theory to describe the diffusion of molecules whose internal-state populations are being perturbed by the application of intense pumping radiation. We show how to extract ground -and excited-state diffusion coefficients from experimental measurements carried out at several pumping intensities. Order-of-magnitude estimates of excited-state diffusion coefficients are presented, and the relation to the potential energy of interaction of excited species is discussed briefly.     

Diffusion of vibrationally excited molecules

A treatment is presented for the effect of intermolecular vibrational energy transfer on the diffusion coefficient of vibrationally excited molecules. An analytic treatment based on random walk statistics and a Monte Carlo type calculation have been performed. Both methods yield very similar results which correlate well with existing experimental studies. A hard sphere collision model is treated extensively with comparisons made to other internmolecular potentials. The results support the involvement of long range energy transfer in V → V interactions. The effect of temeprature on the diffusion coefficient of vibrationally excited molecules is calculated, with applications to the CO^*₂CO₂ system.     

Pulling direction as a reaction coordinate for the mechanical unfolding of single molecules

The folding and unfolding kinetics of single molecules, such as proteins or nucleic acids, can be explored by mechanical pulling experiments. Determining intrinsic kinetic information, at zero stretching force, usually requires an extrapolation by fitting a theoretical model. Here, we apply a recent theoretical approach describing molecular rupture in the presence of force to unfolding kinetic data obtained from coarse-grained simulations of ubiquitin. Unfolding rates calculated from simulations over a broad range of stretching forces, for different pulling directions, reveal a remarkable "turnover" from a force-independent process at low force to a force-dependent process at high force, akin to the "roll-over" in unfolding rates sometimes seen in studies using chemical denaturant. While such a turnover in rates is unexpected in one dimension, we demonstrate that it can occur for dynamics in just two dimensions. We relate the turnover to the quality of the pulling direction as a reaction coordinate for the intrinsic folding mechanism. A novel pulling direction, designed to be the most relevant to the intrinsic folding pathway, results in the smallest turnover. Our results are in accord with protein engineering experiments and simulations which indicate that the unfolding mechanism at high force can differ from the intrinsic mechanism. The apparent similarity between extrapolated and intrinsic rates in experiments, unexpected for different unfolding barriers, can be explained if the turnover occurs at low forces.     

Diffusion and kinetics of solvent-free reaction between molecular crystals by time-resolved powder UV-Vis reflection spectrum

Traditionally, chemical reaction between solids has been considered to typically occur on a geological time scale without the benefit of high temperature, due to diffusion block in the solids. However, recent advancements have revealed that many solvent-free reactions between molecular crystals can quickly occur at room or near-room temperature. These reactions have raised a novel scientific question as to how the reactive species can overcome the diffusion-controlled kinetic limitations under such moderate conditions. From time-resolved powder UV-vis reflection spectra and optical micrographs with the reaction between dimethylglyoxime and Ni(Ac) 2.4H 2O and the reaction between hexamethylenetetramine and CoCl 2.6H 2O as models, we found that the solvent-free reaction really occurs at an intermediate state between the solid state and the liquid state. Formation of the liquid phase provides a convenient approach to diffusion of reactive species, whereas formation of a solid product layer hampered the transfer of reactive species. Both factors led to a broad reactive rate band in the long reaction region. The results have explained the diffusion mechanism of the fast reaction between the molecular crystals under moderate conditions.     

Second virial coefficients of asymmetric top molecules

A short self-contained derivation is given for the second virial coefficient B2(T) of a gas consisting of identical interacting asymmetric rigid rotors. The resulting expression is correct through variant Planck's over h2. First, the canonical partition function is derived by means of an variant Planck's over h expansion of exp[-H/(k(B)T)] due to Friedmann [Adv. Chem. Phys. 4, 225 (1962)]. The present work applies angular momentum operators and known facts from angular momentum theory. It is considerably more accessible than Friedmann's exposition, which is not based on angular momentum operators, but instead on explicit derivatives with respect to Euler angles. The partition function obtained from the variant Planck's over h expansion is applied to the derivation of an expression for B2(T) that is identical in appearance to the expression for symmetric rotors of T Pack [J. Chem. Phys. 78, 7217 (1983)]. The final equation in this work is valid for rigid rotors of any symmetry.     

Diffusion of small molecules in glassy polymers

Small molecules in glassy polymers are considered to occupy sites with a distribution of free energies of dissolution. Then their diffusivity depends on concentration and temperature in the same way as it has been derived for hydrogen atoms in metallic glasses. For hydrogen it was shown that the tracer diffusion coefficient is proportional to the activity coefficient of the solute atoms. The latter can be evaluated from measured data of sorption of the small molecules in the polymer. Knowing this quantity, the thermodynamic factor can be calculated and the concentration dependence of the mutual diffusion coefficient is obtained in excellent agreement with published experimental results. New experimental results are presented for the diffusion coefficient of CO₂ in Kapton and four polycarbonates (BPA-PC, BPZ-PC, TMBPA-PC, and TMC-PC) in the low CO₂ pressure range of a few mbar up to 1 bar. The results are in agreement with the model developed for hydrogen. The reference diffusion coefficient, which is a fitting parameter of the model that is independent of the distribution of free energies is smallest for the polycarbonate BPZ-PC having a high γ-relaxation temperature. This correlation between the diffusion coefficient and the dynamics of the polymer can be found for other substituted polycarbonates as well. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2397–2408, 1997