Importance of heat capacity determination in homogeneous nucleation: application to progesterone

Progesterone is known to exist under different crystallographic forms in the solid state. The thermodynamic stable form (I), melts at 129.2 °C (402.35 K) under atmospheric pressure. After melting and cooling a metastable form (II) can be obtained which melts at 122 °C (395.15 K). This uncommon behaviour can be explained with the theory of nucleation, only if heat capacity of the different forms are known.     

A kinetic approach to the theory of heterogeneous nucleation on soluble particles during the deliquescence stage

Deliquescence is the dissolution of a solid nucleus in a liquid film formed on the nucleus due to vapor condensation. Previously, the kinetics of deliquescence was examined in the framework of the capillarity approximation which involves the thermodynamic interfacial tensions for a thin film and the approximation of uniform density therein. In the present paper we propose a kinetic approach to the theory of deliquescence which avoids the use of the above macroscopic quantities for thin films. The rates of emission of molecules from the liquid film into the vapor and from the solid core into the liquid film are determined through a first passage time analysis whereas the respective rates of absorption are calculated through the gas kinetic theory. The first passage time is obtained by solving the single-molecule master equation for the probability distribution of a "surface" molecule moving in a potential field created by the cluster. Furthermore, the time evolution of the liquid film around the solid core is described by means of two mass balance equations which involve the rates of absorption and emission of molecules by the film at its two interfaces. When the deliquescence of an ensemble of solid particles occurs by means of large fluctuations, the time evolution of the distribution of composite droplets (liquid film+solid core) with respect to the independent variables of state is governed by a Fokker-Planck kinetic equation. When both the vapor and the solid soluble particles are single component, this equation has the form of the kinetic equation of binary nucleation. A steady-state solution for this equation is obtained by the method of separation of variables. The theory is illustrated with numerical calculation regarding the deliquescence of spherical particles in a water vapor with intermolecular interactions of the Lennard-Jones kind. The new approach allows one to qualitatively explain an important feature of experimental data on deliquescence, namely the occurrence of nonsharp deliquescence, a feature that the previous deliquescence theory based on classical thermodynamics could not account for.     

Simple correction to the classical theory of homogeneous nucleation

Formation of the new disperse phase via homogeneous nucleation plays a fundamental role wherever the first-order phase transitions occur. Inconsistent temperature dependence of the nucleation rates and poor agreement of theoretical critical supersaturations with experimental data for a number of substances are fundamental problems of the classical nucleation theory (CNT). Here we show that these problems can be solved with a simple empirical correction to CNT. Despite its simplicity, the corrected CNT (CCNT) accurately predicts temperature dependences and absolute values of the critical supersaturations for both organic and inorganic substances with widely varying properties at different ambient conditions and it works surprisingly well in a wide size range down to few molecules. The difference in predictions of CCNT and other versions of the classical nucleation theory commonly used in analyzing experimental data is discussed. It has been found that CCNT consistently gives better agreement with experimental data than other versions of classical nucleation theory.     

Communication: A dynamical theory of homogeneous nucleation for colloids and macromolecules

Homogeneous nucleation is formulated within the context of fluctuating hydrodynamics. It is shown that for a colloidal system in the strong damping limit the most likely path for nucleation can be determined by gradient descent in density space governed by a nontrivial metric. This is illustrated by application to low-density/high-density liquid transition of globular proteins in solution where it is shown that nucleation process involves two stages: the formation of an extended region with enhanced density followed by the formation of a cluster within this region.     

A novel approach to ring A analogues of the marine pyridoacridine alkaloid ascididemin

A novel approach to ring A analogues of the marine pyridoacridine alkaloid ascididemin starting from readily available 4-bromobenzo[c][2,7]naphthyridine (10) comprises a high-yield Minisci-type homolytic methoxycarbonylation at C-5, followed by introduction of the ring A scaffold via Suzuki cross-coupling reaction, and a trifluoromethanesulfonic acid-aided Friedel–Crafts-type intramolecular acylation. This protocol allows for the introduction of various electron-rich carbocyclic and heterocyclic ring A substitutes.     

Fractal approach of nucleation in liquid and gas phases

Summary The authors present a generalised fractal treatment of the nucleation from the liquid solution or gas-phase reactant.     

A novel approach to modelling counter-current chromatography

Literature lists a number of counter-current chromatography (CCC) models that can predict the retention time and to a certain extent the peak width of a solute eluting from a CCC column. The approach described in this paper distinguishes itself from previous reports by relating all model parameters directly to column dimensions and experimental settings. Most importantly, this model can predict a chromatogram from scratch without resorting to traditional calibration using empirical values. The model validation with experimental results obtained across a range of CCC instruments demonstrated that the solute retention time, peak width, and peak resolution could be predicted within reasonable accuracy. Additionally, the effect of several process parameters, such as mobile phase flow rate, rotational speed of the column or β-value, showed that the model is robust and applicable to a wide range of CCC instruments. Overall, this model proved to be a useful tool for parameter estimation and, most significantly, separation optimisation.     

Unsolved problems in the theory of dynamics in homogeneous and heterogeneous polymer networks

A brief review related to some unsolved problems of the dynamic theory of polymer networks and to possible ways of solving them is presented. The comparative role of small‐scale intrachain and long‐scale collective interchain relaxation processes, the influence of long‐range hydrodynamic interactions between the network elements and the effective viscous medium, and the problem of the structure heterogeneity of polymer networks are considered. New approaches for theoretical treatment of these problems are proposed and discussed.     

A novel approach to Lab-In-Syringe Head-Space Single-Drop Microextraction and on-drop sensing of ammonia

A novel approach to the automation technique Lab-In-Syringe, also known as In-Syringe Analysis, is proposed which utilizes a secondary inlet into the syringe void, used as a size-adaptable reaction chamber, via a channel passing through the syringe piston. This innovative approach allows straightforward automation of head-space single-drop microextraction, involving accurately controlled drop formation and handling, and the possibility of on-drop analyte quantification.     

A structural comparative approach to identifying novel antimalarial inhibitors

Malaria continues to affect millions of people annually. With the rise of drug resistant strains, the need for alternative treatments has become increasingly urgent. Recently, PfUCHL3 was identified as an essential deubiquitinating enzyme. The increasing number of drug target structures being solved has increased the feasibility of utilizing a structural comparative approach to identifying novel inhibitors. Using AutoDock Vina, we recently screened the NCI library of about 320,000 compounds against the crystal structure of PfUCHL3. The top hits were subsequently screened against its human ortholog UCHL3 as to identify compounds that could specifically target the PfUCHL3 over its human counterpart. This method was used to identify small molecule inhibitors that can preferentially inhibit the parasitic enzyme. Several compounds were identified that demonstrated significant binding affinity preference for the malaria target over the human enzyme. Two of these compounds demonstrated ng/mL activity.     

New approach to the kinetics of heterogeneous unary nucleation on liquid aerosols of a binary solution

The formation of a droplet on a hygroscopic center may occur either in a barrierless way via Kohler activation or via nucleation by overcoming a free energy barrier. Unlike the former, the latter mechanism of this process has been studied very little and only in the framework of the classical nucleation theory based on the capillarity approximation whereby a nucleating droplet behaves like a bulk liquid. In this paper the authors apply another approach to the kinetics of heterogeneous nucleation on liquid binary aerosols, based on a first passage time analysis which avoids the concept of surface tension for tiny droplets involved in nucleation. Liquid aerosols of a binary solution containing a nonvolatile solute are considered. In addition to modeling aerosols formed through the deliquescence of solid soluble particles, the considered aerosols constitute a rough model of "processed" marine aerosols. The theoretical results are illustrated by numerical calculations for the condensation of water vapor on binary aqueous aerosols with nonvolatile nondissociating solute molecules using Lennard-Jones potentials for the molecular interactions.     

Weight distribution approach to the theory of random depolymerization of heterogeneous chains

The random depolymerization model of Montroll and Simha for originally homogeneous polymers is derived analytically by utilizing a weight distribution function approach not requiring the use of any approximations. The model is then extended to consider heterogeneous initial chains having an arbitrary chain length distribution. The probabilities for breakage are assumed to be identical for all bonds joining monomeric elements in the system and to be independent of chain length and position in the chain, assumptions also used in the model of Montroll and Simha. An expression is found for estimating the probability of bond breakage.     

Complete thermodynamically consistent kinetic model of particle nucleation and growth: numerical study of the applicability of the classical theory of homogeneous nucleation

A complete thermodynamically consistent elementary reaction kinetic model of particle nucleation and growth from supersaturated vapor was developed and numerically evaluated to determine the conditions for the steady-state regime. The model treats all processes recognized in the aerosol science (such as nucleation, condensation, evaporation, agglomerationcoagulation, etc.) as reversible elementary reactions. It includes all possible forward reactions (i.e., of monomers, dimers, trimers, etc.) together with the thermodynamically consistent reverse processes. The model is built based on the Kelvin approximation, and has two dimensionless parameters: S0-the initial supersaturation and Theta-the dimensionless surface tension. The time evolution of the size distribution function was obtained over the ranges of parameters S0 and Theta. At low initial supersaturations, S0, the steady state is established after a delay, and the steady-state distribution function corresponds to the predictions of the classical nucleation theory. At high initial supersaturations, the depletion of monomers due to condensation on large clusters starts before the establishing of the steady state. The steady state is never reached, and the classical nucleation theory is not applicable. The boundary that separates these two regimes in the two dimensionless parameter space, S0 and Theta, was determined. The model was applied to several experiments on water nucleation in an expansion chamber [J. Wolk and R. Strey, J. Phys. Chem. B 105, 11683 (2001)] and in Laval nozzle [Y. J. Kim et al., J. Phys. Chem. A 108, 4365 (2004)]. The conditions of the experiments performed using Laval nozzle (S0=40-120) were found to be close to the boundary of the non-steady-state regime. Additional calculations have shown that in the non-steady-state regime the nucleation rate is sensitive to the rate constants of the initial steps of the nucleation process, such as the monomer-monomer, monomer-dimer, etc., reactions. This conclusion is particularly important for nucleation from supersaturated water vapor, since these processes for water molecules at and below the atmospheric pressure are in the low pressure limit, and the rate constants can be several orders of magnitude lower than the gas kinetic. In addition, the impact of the thermodynamic inconsistency of the previously developed partially reversible kinetic numerical models was assessed. At typical experimental conditions for water nucleation, S0=10 and Theta=10 (T=250 K), the error in the particle nucleation rate introduced by the thermodynamic inconsistency exceeds one order of magnitude.     

Comparison between the classical theory predictions and molecular simulation results for heterogeneous nucleation of argon

We have performed Monte Carlo simulations of homogeneous and heterogeneous nucleations of Lennard-Jones argon clusters. The simulation results were interpreted using the major concept posing a difference between the homogeneous and heterogeneous classical nucleation theories-the contact parameter. Our results show that the multiplication concept of the classical heterogeneous nucleation theory describes the cluster-substrate interaction surprisingly well even for small molecular clusters. However, in the case of argon nucleating on a rigid monolayer of fcc(111) substrate at T=60 K, the argon-substrate atom interaction being approximately one-third as strong as the argon-argon interaction, the use of the classical theory concept results in an underestimation of the heterogeneous nucleation rate by two to three orders of magnitude even for large clusters. The main contribution to this discrepancy is induced by the failure of the classical theory of homogeneous nucleation to predict the energy involved in bringing one molecule from the vapor to the cluster for clusters containing less than approximately 15 molecules.     

Design on head-to-tail directly linked homogeneous and heterogeneous cyclodextrin dimers and their evaluation of hydrophobic cavity

Covalent directly head-to-tail linked homogeneous and heterogeneous cyclodextrin (CD) dimers were synthesized, and that the reaction of 6-tosylated α-, β-, or γ-CD with a β-CD mono-oxyanion linked the second CD to the secondary hydroxyl side of β-CD was demonstrated. Moreover, deprotonation of α- and γ-CD using NaOH gave corresponding mono-oxyanions, which reacted with the 6-tosylated CDs to produce the CD dimers. The binding of the dimers to sodium 6-(4-tert-butylaniline)-2-naphthalenesulfonate (BNS) was investigated. The binding constant of the ⁶β–²β-CD dimer with BNS was estimated as 3.2 × 10⁶ M⁻¹, about 10² times larger than that of β-CD monomer.     

Method of moments approach and coupled cluster theory

Summary The single reference coupled cluster (CC) approach to the many-electron correlation problem is examined from the viewpoint of the method of moments (MM). This yields generally an inconsistent (overcomplete) set of equations for cluster amplitudes, which can be solved either in the least squares sense or by selective projection process restricting the number of equations to that of the unknowns. These resulting generalized MM-CC equations always contain the standard CC equations as a special case. Since, in the MM-CC formalism, the Schrödinger equation will be approximately satisfied on a subspace spanned by non-canonical configurations, this procedure may be helpful in extending the standard single reference CC theory to quasi-degenerate situations. To examine the potential usefulness of this idea, we explore the linear version of the CC approach for systems with a quasi-degenerate reference, in which case the standard linear theory is plagued with singularities due to the intruder states. Implications of this analysis for the structure of the wavefunction are also briefly discussed.Killam Research Fellow 1987–89     

A novel method to determine the molecular weight of the oligomers of biodegradable polymer

The biodegradable polymers used in controlled release applications are primarily insoluble polymers which undergo chemical or enzymatic hydrolysis to form soluble monomeric or oligomeric units. To determine the endurance of the polymer after implantation or injection into the body it is important to determine the rate of elimination of the intermediates formed upon the hydrolysis of the polymer. It is essential to identify these intermediates before its elimination rate can be determined. Identification of these intermediates is a problem because they are difficult to isolate, and are thermally and hydrolytically unstable. A new technique is proposed, taking advantage of the neighboring group effect on the hydrolysis of ionic and non-ionic oligomers, to determine the molecular weight of unknown species that are formed upon hydrolysis of the polymer. The technique involves the determination of the specific acid and base catalytic rate constants. To demonstrate the technique, a time sequence synthesis was carried out to synthesize several oligomers that would be forming upon the hydrolysis of poly(butylene tartrate). Hydrolysis studies were conducted with these oligomers and the samples were analyzed by liquid chromtography. The observed rate constant for the hydrolysis under acidic and alkaline pH medium were calculated from the terminal slopes of the first order plot. The observed rate constants were further utilized to calculate the specific acid and base catalytic rate constants. These specific rate constants, along with the micro-hydrogen and -hydroxyl ion catalytic rate constants, were used to determine the molecular weight of the intermediate species. The molecular weight obtained from the kinetic parameters was in excellent agreement with the results obtained from fast atom bombardment mass spectrometry. The same type of analysis can be extended to any multifunctional group compound which has repeat units and can undergo a specific reaction which can be accurately measured.     

Kinetic model for binary homogeneous nucleation in the H2O-H2SO4 system: comparison with experiments and classical theory of nucleation

A kinetic model to predict nucleation rates in the sulfuric acid-water system is presented. It allows calculating steady-state nucleation rates and the corresponding time lag, using a direct solution of a system of kinetic equations that describe the populations of sub- and near-critical clusters. This kinetic model takes into account cluster-cluster collisions and decay of clusters into smaller clusters. The model results are compared with some predictions obtained with the classical nucleation theory (CNT) and also with available measurement data obtained in smog chambers or flow tubes. It is shown that in the case of slow nucleation processes, the kinetic model and the CNT as used by Shugard et al. [J. Chem. Phys. 75, 5298 (1974)] give the same results. However, in the case of intensive nucleation, a large part of the nucleation flux is due to cluster-cluster collisions and the CNT underestimates the nucleation rates.