Kinetics of binary condensation on the droplet growing in diffusion regime

A relaxation equation determining the regular tendency of the concentration of binary solution in the growing droplet to the stationary value, at which there is a self-similar solution to the problem of the condensation in a binary mixture, is derived. An analytical solution of the relaxation equation is obtained and it is demonstrated that the stationary value of concentration is achieved via the power law. The time interval that elapses from the emergence of the droplet until the diffusion regime of droplet growth and derived relaxation equation become effective is revealed. The stationary value of concentration is found for the model of ideal solution.     

Self-similar theory of nonisothermal vapor condensation on a droplet growing in a vapor-gas medium

Rigorous self-similar solutions to the joint problems of vapor diffusion toward a droplet growing in a vapor-gas medium and the removal of heat released during vapor condensation are found. An equation for the temperature of a droplet ensuring the existence of a self-similar solution is derived. This equation sets the constancy of the temperature of a droplet throughout the time of its growth and unambiguously determines this temperature. In the case of the strong heat effects, when the rate of droplet growth decreases substantially, the analytical solution to this equation is obtained. This temperature coincides precisely with the temperature, which is established in the droplet at the diffusion regime of its growth. At the found droplet temperature, interconnected fields of vapor concentration and temperature of vapor-gas medium around the droplet are expressed through the initial (prior to the droplet nucleation) parameters of a vapor-gas medium. These parameters are used to express the dependence of the radius of a droplet on the time at the diffusion regime of its growth and the time required to establish the diffusion regime of droplet growth. The case of weak heat effects is also studied.     

Kinetics of nonstationary condensation of methane on a perovskite catalyst

The interaction of methane with the oxidized surface of the KNaSrCoO_3−x is first order in methane with respect to formation of higher hydrocarbons and zero order with respect to formation of CO₂. At the initial stage the rate of formation of the reaction products is independent of the amount of oxygen from the catalyst consumed (up to 5–7 monolayers of oxygen), after which the rate of the reaction falls linearly. The overall amount of oxygen consumed in the reaction reaches 30 monolayers. L. V. Pisarzhevskii Institute of Physical Chemistry, National Academy of Sciences of Ukraine, 31 Prospekt Nauki, Kiev 03039, Ukraine. Translated from Teoreticheskaya i éksperimental'naya Khimiya, Vol. 36, No. 3, pp. 182–187, May–June, 2000.     

Measuring free-energy difference between crystal polymorphs through eutectic melting

We describe a method to measure the free-energy difference, DeltaG, between crystal polymorphs from their calorimetric data of eutectic melting with a common additive. The use of different additives yields DeltaG as a function of temperature. The method is suitable for crystals that chemically decompose or physically transform before melting. It applies to not only true polymorphs but also pairs of racemate and conglomerate of resolvable enantiomers. We illustrate the method with the polymorphs of glycine, d-mannitol, and tazofelone and report a new value (123 degrees C) for the enantiotropic transition temperature of alpha and gamma glycine. We show how different additives (including a liquid additive, water) can be used for different compounds. The DeltaG data thus obtained are important for structure-stability studies and controlling crystallization in polymorphic systems.     

Effect of the coil-globule transition on the free-energy barrier for intrachain crystal nucleation

The rate of crystal nucleation of colloids and globular proteins can be enhanced by critical density fluctuations. It has been argued that a closely related phenomenon influences the rate of intramolecular "crystallization" of single-chain polymers. We report Monte Carlo simulations of the free-energy barrier that separates the crystalline state of a homopolymer chain from the disordered state. The simulations show that the barrier for nucleation of the ordered state is drastically lowered as the disordered state changes from a coil to a globule. We discuss the relation of the present findings to intramolecular nucleation of heteropolymers, such as proteins.     

Thermal effects accompanying stationary binary condensation of vapors into overcritical droplet

A set of equations is derived to calculate the stationary temperature and concentration of a solution in a overcritical droplet with regard to the heat release accompanying the condensation of a binary mixture of vapors in a diffusion or free-molecular regime. In the approximation of an ideal solution, relations are found for the stationary temperature of droplet growing under the conditions of strong and weak thermal effects. For the general case and the cases of strong and weak thermal effects, the temperature and concentration of the droplet and the coefficient of the thermal deceleration of the droplet growth are calculated as functions of the density of a passive gas. The influence of the condensation heat values of the first and second components of the mixture on the stationary temperature and concentration of the solution in the growing droplet is investigated separately.     

Kinetics of the thiazolium ion-catalyzed benzoin condensation.

The formation of benzoin (Ph-CHOH-CO-Ph) from two molecules of benzaldehyde, catalyzed by 3-benzyl-5-(2-hydroxyethyl)-4-methylthiazolium bromide in methanol buffered with Et(3)N/Et(3)NH(+)Cl(-) has been studied. Initial-rate studies at various concentrations of PhCHO (0.1-1.7 M) showed that the reaction is close to being first order in PhCHO. Following the reaction in deuteriomethanol, (1)H NMR spectroscopy allowed rate constants for all three kinetically significant steps to be determined. These show that all three steps are partially rate-determining. A normal deuterium kinetic isotope effect for the overall reaction (k(H)/k(D) approximately 3.4) is observed using PhCDO, and a large inverse solvent isotope effect (k(D)/k(H) approximately 5.9) is observed using deuteriomethanol, consistent with the kinetic scheme presented here.     

Kinetics of polymer translocation through a pore

We theoretically study kinetics of a polymer threading through a pore embedded in a flat membrane. We numerically solve three coupled kinetic equations for the number n(1) of polymer segments in one side of the membrane and expansion factors of the polymer chain in each side of the membrane. We find the time evolution n(1) proportional to t(1/(1+nu)) at late stages and the translocation time tau(t) is scaled as tau(t) proportional to 1+nu) for large number n of the polymer segments, where nu is the effective size exponent of the radius of gyration of the polymer. When the polymer is translocated into a region with a good solvent condition (nu=3/5), we obtain n(1) proportional to t(5/8) and tau(t) proportional to n(8/5).     

Estimating free-energy barrier heights for an ultrafast folding protein from calorimetric and kinetic data

Differential scanning calorimetry was used to measure the temperature dependence of the absolute heat capacity of the 35-residue subdomain of the villin headpiece, a protein that folds in 5 mus and is therefore assumed to have a small free-energy barrier separating folded and unfolded states. To obtain an estimate of the barrier height from the calorimetric data, two models, a variable-barrier model and an Ising-like model, were used to fit the heat capacity in excess of the folded state over the temperature range 15-125 degrees C. The variable-barrier model is based on an empirical mathematical form for the density of states, with four adjustable parameters and the enthalpy (H) as a reaction coordinate. The Ising-like model is based on the inter-residue contact map of the X-ray structure with exact enumeration of approximately 10(5) possible conformations, with two adjustable parameters in the partition function, and either the fraction of native contacts (Q) or the number of ordered residues (P) as reaction coordinates. The variable-barrier model provides an excellent fit to the data and yields a barrier height at the folding temperature ranging from 0.4 to 1.1 kcal mol(-1), while the Ising-like model provides a less good fit and yields barrier heights of 2.3 +/- 0.1 kcal mol(-1) and 2.1 +/- 0.1 kcal mol(-1) for the Q and P reaction coordinates, respectively. In both models, the barrier to folding increases with increasing temperature. Assuming a sufficiently large activation energy for diffusion on the free-energy surfaces, both models are consistent with the observation of a temperature-independent folding rate in previously published laser temperature-jump experiments. Analysis of this kinetic data, using an approximate form for the pre-exponential factor of Kramers theory and the 70 ns relaxation time for the fast phase that precedes the unfolding/refolding relaxation to determine the diffusion coefficient, results in a barrier height of 1.6 +/- 0.3 kcal mol-1 for an unspecified reaction coordinate. Although no independent test of the validity of the H, Q, or P reaction coordinates is given, the barrier-height estimates obtained with the three reaction coordinates are in quite good agreement with the value derived from a Kramers analysis of the kinetics that makes no assumptions about the reaction coordinate. However, the higher estimates obtained using Q or P appear more consistent with the finding of barrier-crossing kinetics of a villin mutant that folds in 700 ns, corresponding to a 1.3 kcal mol-1 reduction in the folding barrier relative to wild-type. All of the results suggest that the free-energy barrier to folding is sufficiently low that it should be possible to engineer this protein or find solution conditions that would eliminate the barrier to create the "downhill" folding scenario of Wolynes and Onuchic.     

Kinetics of supersaturated vapor nucleation on molecular condensation nuclei

The kinetics of nucleation is calculated for a supersaturated vapor containing molecular condensation nuclei, that is, foreign molecules able to induce the formation of viable nuclei of a condensed phase by themselves. In contrast to the previous calculation, the possibility of the escape of molecular condensation nuclei from very small clusters containing a few condensed vapor molecules is taken into account. More exact equations are derived for the rate of steady-state nucleation and the concentration of aerosol particles in a quasisteady-state regime of nucleation. The calculation demonstrates that, at a high probability of the escape of a molecular condensation nucleus, the predominating mechanism of cluster formation is the attachment of a molecular condensation nucleus to a cluster formed from vapor molecules rather than their condensation on the nucleus. At the same time, allowances for the possible escape of molecular condensation nuclei from clusters slightly affect the rate of nucleation and the concentration of aerosol particles being formed.     

Dynamics of variations in size and composition of supercritical droplet at binary condensation

A general analytical solution is found in quadratures for the radius and concentration of a solution droplet, which isothermally grows or evaporates in a diffusion or free-molecular regime in a binary mixture of vapors. The obtained solution describes the dynamics of variations in the size and composition of a super-critical droplet during the binary condensation in mixed vapors at an arbitrary initial droplet composition. It is shown that, at small (linear) deviations of the growth regime and droplet composition from the stationarity, these quadratures lead to the results that were recently obtained for the composition relaxation in a growing droplet. Moreover, it is demonstrated that, in terms of the nonlinear theory, when the deviation of solution concentration in a droplet from its stationary value is not small, it is invalid to use the law of stationary variations in the size of a droplet with time to describe the relaxation process for its chemical composition.     

Intramolecular condensation of nitro group with olefinic double bond

Conclusions A new reaction of nitro compounds was discovered on the example of the thermal isomerization of unsaturated nitrocarbinols and nitrodihydropyrans, consisting in the intramolecular addition of the nitro group to the olefinic double bond with the formation of the heterolytic 1,3,2-dioxazoline system.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 2, pp. 370–378, February, 1968.     

Kinetics of condensation of adenine at the mercury electrolyte interface

The kinetics of phase transitions of adenine adsorbed on mercury are studied by chronocoulometry and chronoamperometry from aqueous 0.1 M KClO₄ and 0.5 M NaF solutions. Experimental conditions have been selected to minimise, in the overall kinetic response, the contribution of the initial current decay, due to double-layer charging and the adsorption step. The transients corrected for these fast initial contributions present a peaked shape and can be described by the classical theory for nucleation and growth. The potential dependences of the rate constants of nucleation and growth have been obtained from double potential step experiments. The analysis of the condensation kinetics according to the classical nucleation theory leads to the evaluation of the line tension, and the Gibbs energy of formation of a critical cluster and its size.     

Non-Isothermal Crystallization Kinetics of PET Under Solid State Poly condensation

An equation of non-isothermal crystallization kinetics was derived according to a new model and the crystallizations of both the PET samples under solid state polycon-densation and the pre-orientation yarn of high speeding spinning PET were studied with this equation. The results show that there is a good linear relationship between In {-In[1-X(T)]} and lnΦ. The index m in the equation approximately equals to 3 for PET chips and 1. 3 for pre-orientated yarn. At the same temperature, Q(T) decreases with the increase of PET M. W. and the kinetics parameters obtained by Jeziorny' s method indicate that G also decreases with the increase of PET M. W.. Q(T) and Gc show the same varying tendency in the non-isothermal crystallization process.     

Aldol condensation of furfural and acetone on layered double hydroxides

The Aldol condensation of furfural (Fur) with acetone (Ac) to 4-(2-Furyl)-3-buten-2-one (FAc) is one of the most important processes in the aqueous-reforming of oxygen-containing biomass derivatives and has been carried out in the presence of solid-base catalysts, calcined-rehydrated Layered Double Hydroxides (LDH). The Mg-Al Layered Double Hydroxides has been prepared by the coprecipitation, calcination and regeneration from mixed oxides by rehydration. The catalyst prepared with different Mg/Al molar ratios showed different catalytic performance and the best catalyst was with the Mg/Al molar ratio of 2.5. Phenol adsorption showed that the best catalyst had the largest numbers of accessible basic sites. The appropriate rehydration temperature and time for mixed oxides obtained by calcination were also investigated. The Mg-Al LDH catalysts can be regenerated by calcination at 773 K and rehydration in decarbonate water, but the regeneration is complex and incomplete. In addition, the catalyst calcined at high temperature also had activity, which was attributed to the formation of the Mg-Al spinels.     

Dielectric behavior of double emulsions with "core-shell droplet" morphology

The dielectric behavior of double emulsions with "core-shell droplet" morphology is investigated over a broad range of frequency. A new modified Pauly-Schwan model is proposed for the complex permittivity of double emulsions. The proposed model takes into consideration the morphology and packing limit of droplets. The dielectric behaviors of oil-in-water-in-oil (O/W/O) and water-in-oil-in-water (W/O/W) types of double emulsions, as predicted by the proposed model, are discussed.     

A new droplet breakup phenomenon in electrokinetic flow through a microchannel constriction

A completely new droplet breakup phenomenon is reported for droplets passing through a constriction in an electrokinetic flow. The breakup occurs during the droplet shape recovery process past the constriction throat by the interplay of the dielectrophoretic stress release and the interface energy for droplets with smaller permittivity than that of the ambient fluid. There are conditions for constriction ratios and droplet size that the droplet breakup occurs. The numerical predictions provided here require experimental verification, and then can give rise to a novel microfluidic device design with novel droplet manipulations.     

1,5-Benzoheteroazepines through eco-friendly general condensation reactions

Condensation reactions of o-phenylenediamine and 2 equiv of acetone produce biaryl-substituted 1,5-benzodiazepines. The synthetic protocol shows general applicability since similar reaction of o-phenylenediamines, o-aminophenol, and o-aminothiophenol with ketones or chalcones leads to formation of functionalized 1,5-benzoheteroazepines in good to excellent yields. The synthetic protocol fulfills many green-chemical requirements using simple MW-assistance to promote the activation of ketones and the eco-compatible Er(III) triflate as activator of chalcones.     

Excluded volume driven counterion condensation inside nanotubes in a concave electrical double layer model

The physical properties of organic nanotubes attract increasing attention due to their potential benefit in technology, biology and medicine. We study the effect of ion size on the electrical properties of cylindrical nanotubes filled with electrolyte solution within a modified Poisson-Boltzmann (PB) approach. For comparison purposes, small hollow nanospheres filled with electrolyte solution are considered. The finite size of the particles in the inner electrolyte solution is described by the excluded volume effect within a lattice statistics approach. We found that an increased ion size reduces the number of counterions near the charged inner surface of the nanotube, leading to an enlarged electrostatic surface potential. The concentration of counterions close to the inner surface saturates for higher surface charge densities and larger ions. In the case of saturation, the closest counterion packing is achieved, all lattice sites near the surface are occupied and an actual counterion condensation is observed. By contrast, the counterion concentration at the axis of the nanotube steadily increases with increasing surface charge density. This growth is more pronounced for smaller nanotube radii and larger ions. At larger nanotube radii for small ion size counterion condensation may also be observed according to the Tsao criterion, i.e. the counterion concentration at the centre is independent of the number of counterions in the system. With decreasing radius the Tsao condensation effect is shifted towards physiologically unrealistic surface charge densities.