Atomistic theory of amyloid fibril nucleation

We consider the nucleation of amyloid fibrils at the molecular level when the process takes place by a direct polymerization of peptides or protein segments into β-sheets. Employing the atomistic nucleation theory (ANT), we derive a general expression for the work to form a nanosized amyloid fibril (protofilament) composed of successively layered β-sheets. The application of this expression to a recently studied peptide system allows us to determine the size of the fibril nucleus, the fibril nucleation work, and the fibril nucleation rate as functions of the supersaturation of the protein solution. Our analysis illustrates the unique feature of ANT that the size of the fibril nucleus is a constant integer in a given supersaturation range. We obtain the ANT nucleation rate and compare it with the rates determined previously in the scope of the classical nucleation theory (CNT) and the corrected classical nucleation theory (CCNT). We find that while the CNT nucleation rate is orders of magnitude greater than the ANT one, the CCNT and ANT nucleation rates are in very good quantitative agreement. The results obtained are applicable to homogeneous nucleation, which occurs when the protein solution is sufficiently pure and/or strongly supersaturated.     

Bubble nucleation in polymeric liquids. II. theoretical considerations

A theory based on classical nucleation theory is developed for bubble nucleation in polymer solutions. The theory requires information on solubility, diffusivity, concentration, surface tension, temperature, and degree of supersaturation. The effects of supersaturation and of the presence of large molecules in a liquid mixture on the free energy of bubble formation are included in the theoretical development. A semiempirical equation for the determination of bubble nucleation rate is developed, with the aid of experimental results reported in part I of this series. Using the experimental data, computer simulations of bubble nucleation in polymer solutions are performed. The consumptions of the volatile component in a liquid mixture, due to bubble nucleation and subsequent growth, and the variation of bubble nucleation rate during the expansion process are included in the simulation of the bubble nucleation process.     

Generalized Kelvin equation and pseudospinodal in nucleation theory

The classical Kelvin equation, relating the size of the critical cluster to the supersaturation, is inadequate for very small, molecular-sized clusters emerging at deep quenches observed in recent nucleation experiments. Using statistical mechanical considerations, we propose a generalization of the Kelvin equation applicable up to the vicinity of the pseudospinodal, where the nucleation barrier is approximately k(B)T. The supersaturation at the pseudospinodal is expressed in terms of the second virial coefficient. It is shown that near the pseudospinodal the critical cluster size is close to the coordination number in the liquid phase. Comparisons with computer simulations are presented.     

Crossover model for the work of critical cluster formation in nucleation theory

We propose a relation for the work of critical cluster formation in nucleation theory W for the systems with long-range interparticle interactions. The method of bridge functions is used to combine the system behavior at sufficiently small quenches, adequately predicted by the classical nucleation theory, with nonclassical effects at deep quenches in the vicinity of the thermodynamic spinodal, described within the framework of the field theoretical approach with an appropriate Ginzburg-Landau functional. The crossover between the two types of nucleation behavior takes place in the vicinity of the kinetic spinodal where the lifetime of a metastable state is of the order of the relaxation time to local equilibrium. We argue that the kinetic spinodal corresponds to the minimum of the excess number of molecules in the critical cluster. This conjecture leads to the form of W containing no adjustable parameters. The barrier scaling function Gamma = W/W(cl), where W(cl) is the classical nucleation barrier, depends parametrically on temperature through the dimensionless combination of material properties. The results for argon nucleation are presented.     

Determining the nucleation rate from the dimer growth probability

A new method is proposed for the determination of the stationary one-component nucleation rate J with the help of data for the growth probability P2 of a dimer which is the smallest cluster of the nucleating phase. The method is based on an exact formula relating J and P2, and is readily applicable to computer simulations of nucleation. Using the method, the dependence of J on the supersaturation s is determined by kinetic Monte Carlo simulations of two-dimensional (2D) nucleation of monolayers on the (100) face of Kossel crystal. The change of J over nearly 11 orders of magnitude is followed and it is found that the classical nucleation theory overestimates the simulation J values by an s-dependent factor. The 2D nucleus size evaluated via the nucleation theorem is described satisfactorily by the classical Gibbs-Thomson equation and its corrected version accounting for the spinodal limit of 2D nucleation.     

Nucleation rates of water and heavy water using equations of state

The original formula of Gibbs for the reversible work of critical nucleus formation is evaluated in three approximate ways for ordinary and heavy water. The least approximate way employs an equation of state to evaluate the pressure difference between the new and old phases. This form of the theory yields a temperature dependence for the nucleation rate close to that observed experimentally. This is a substantial improvement over the most commonly used (and most approximate) form of classical theory.     

A study of nucleation in supersaturated ibuprofen vapor in a flow diffusion chamber

Isothermal nucleation of supersaturated ibuprofen racemate vapor has been experimentally studied in a flow diffusion chamber at 293.3 and 301.2 K. Nucleation rates have been measured in the range of 10⁴?10⁴ cm^?3 s^?1 as functions of supersaturation. According to the first nucleation theorem, the numbers of molecules in critical nuclei have been found and used to determine the nucleation rate and supersaturation values as depending on the sizes of critical nuclei. The comparison of the experimental data with theoretical predictions has shown that the nucleation rates measured as functions of the numbers of molecules in critical nuclei are higher than the rates predicted by the classical theory by six to seven decimal orders of magnitude but, within one order of magnitude, coincide with the rates predicted by a theory previously proposed in a work by one of the authors, in which nucleation clusters were considered to be microscopic objects.     

Nucleation from supersaturated water vapors onn-dodecane substrate: A reverse Wilson chamber (RWC) method study

The reverse Wilson chamber method (RWC), developed for heterogencous nucleation investigation is applied to critical supersaturation measurements and determination of the surface concentration of nuclei (droplets) vs. supersaturation dependence in the case of nucleation from supersaturated water vapors onn-dodecane substrate. The experimental results obtained are interpreted in terms of the classical (Volmer) theory of heterogeneous nucleation as well as in the framework of the theory of barrierless nucleation. The several times lower critical supersaturations measured at four different temperatures, covering the range between 20° and 35° C, are explained by taking into account the effect of the negative line tension of three-phase contact. The temperature dependence of line tension for the three-phase systemn-dodecane/water/water vapor is extracted from the data to fir the theory. The results obtained are in complete disagreement with those ones obtained by Wu and Maa for the same system using jet-tensimeter technique, however, in another temperature interval. This discrepancy is discussed in detail in the text.     

Homogeneous nucleation of water between 200 and 240 K: new wave tube data and estimation of the Tolman length

We have measured homogeneous nucleation rates of water at 200-240 K in the carrier gas helium, in the range of 10(13) - 10(17) m(-3) s(-1) using an expansion wave tube. The rates agree well with the results of Wolk and Strey [J. Phys. Chem. B 105, 11683 (2001)] in the range of overlap (220-240 K), and are summarized by the empirical fit J = S exp[4.6 + 0.244T-(906.8 - 2.914T)(ln S)(2)], with J the nucleation rate in m(-3) s(-1), S the supersaturation, and T the temperature in K. We find that the supersaturation dependence of both our rates and those of Wolk and Strey is lower than classical theory predicts, and that the critical cluster is smaller than the classical critical size. These deviations are explained in the framework of the Tolman theory for surface tension, and the "Tolman length" is estimated from our experimental results. We find a positive Tolman length that increases with decreasing temperature, from about 0.1 Angstrom at 260 K to (0.6 +/- 0.4) Angstroms at 200 K. We present a nucleation rate expression that takes the Tolman length into account and show that both the supersaturation and temperature dependence are improved, compared to the classical theory.     

Nucleation in cylindrical capillaries

We use a local density functional theory in the square gradient approximation to explore the properties of critical nuclei for the liquid-vapor transition of van der Waals fluids in cylindrical capillaries. The proposed model allows us to investigate the effect of pore size, surface field, and supersaturation on the behavior of the system. Our calculations predict the existence of at least three different pathways for the nucleation of droplets and bubbles in these confined fluids: axisymmetric annular bumps and lenses, and asymmetric droplets. The morphological transition between these different structures is driven by the existence of states of zero compressibility in the capillary. We show that the classical capillarity theory provides surprisingly accurate predictions for the work of formation of critical nuclei in cylindrical pores when line tension contributions to the free energy are taken into account.     

Anharmonic nuclear dynamics in the mixed quantum-classical limit

This study employs mixed quantum-classical dynamics (MQCD) formalism to evaluate the linear electronic dipole moment time correlation function (DMTCF) in which a Morse oscillator serves to model the associated vibrations in a mixed quantum-classical (MQC) environment. While the main purpose of this work is to study the applicability of MQCD formalism to anharmonic systems in condensed phase, approximate schemes to physically evaluate the mathematically divergent integrals have been developed in order to deal with the essential singularities that arise while evaluating the Morse oscillator canonical partition function and the DMTCF in MQC systems in the classical limit. The motivation for numerically and analytically evaluating these divergent integrals is that a partition function of any system should lead to a finite value at any temperature and therefore this divergence is unphysical. Additionally, since a partition function is to signify the number of accessible states to the system at hand, divergent results are not physically acceptable. As such, straightforward approximate analytic expressions, at different levels of rigor, for both the classical Morse oscillator partition function and the DMTCF in MQC systems are derived, for the first time. Calculations of Morse oscillator partition function values using different approaches at various temperatures for CO, HCl, and I(2) molecules, showing good results, are presented to test the expressions derived herein. It is found that this divergence, due to singularity, diminishes upon lowering the temperature and only arises at high temperatures. The gradual diminishing of the singularity upon lowering the temperature is sensible since the Morse potential fits the parabolic potential at low temperatures. Model calculations and discussion of the DMTCF and linear absorption spectra in MQC systems using the molecular constants of CO molecule are provided. The linear absorption lineshape is derived by two methods, one of which is asymptotic expansion.     

Nucleation and growth of bubbles in elastomers

The theory of homogeneous nucleation of bubbles is combined with an expression, for their rate of growth in elastomers to obtain approximate expressions for calculating the number of bubbles formed under a high degree of supersaturation. Experimental results are given for several elastomers with argon as the dissolved gas under a variety of foaming conditions. The theory adequately describes the manner in which the number of bubbles formed depends on the temperature, surface tension of the polymer, and permeability of the dissolved gas.     

Experimental study of homogeneous nucleation from the bismuth supersaturated vapor: evaluation of the surface tension of critical nucleus

The homogeneous nucleation of bismuth supersaturated vapor is studied in a laminar flow quartz tube nucleation chamber. The concentration, size, and morphology of outcoming aerosol particles are analyzed by a transmission electron microscope (TEM) and an automatic diffusion battery (ADB). The wall deposit morphology is studied by scanning electron microscopy. The rate of wall deposition is measured by the light absorption technique and direct weighting of the wall deposits. The confines of the nucleation region are determined in the "supersaturation cut-off" measurements inserting a metal grid into the nucleation zone and monitoring the outlet aerosol concentration response. Using the above experimental techniques, the nucleation rate, supersaturation, and nucleation temperature are measured. The surface tension of the critical nucleus and the radius of the surface of tension are determined from the measured nucleation parameters. To this aim an analytical formula for the nucleation rate is used, derived from author's previous papers based on the Gibbs formula for the work of formation of critical nucleus and the translation-rotation correction. A more accurate approach is also applied to determine the surface tension of critical drop from the experimentally measured bismuth mass flow, temperature profiles, ADB, and TEM data solving an inverse problem by numerical simulation. The simulation of the vapor to particles conversion is carried out in the framework of the explicit finite difference scheme accounting the nucleation, vapor to particles and vapor to wall deposition, and particle to wall deposition, coagulation. The nucleation rate is determined from simulations to be in the range of 10(9)-10(11) cm(-3) s(-1) for the supersaturation of Bi(2) dimers being 10(17)-10(7) and the nucleation temperature 330-570 K, respectively. The surface tension σ(S) of the bismuth critical nucleus is found to be in the range of 455-487 mN/m for the radius of the surface of tension from 0.36 to 0.48 nm. The function σ(S) changes weakly with the radius of critical nucleus. The value of σ(S) is from 14% to 24% higher than the surface tension of a flat surface.     

Secondary nucleation and growth of ZnO

Recently we discovered that under certain conditions new crystal growth (branch) can be induced on specific crystalline planes of the same material. This is a new phenomenon and is in sharp contrast to typical nucleation and growth in which a crystal will simply grow larger in preferred directions depending on the surface energy of the specific crystalline planes. Based on our observation, we developed a sequential nucleation and growth technique offering the power to assemble complex hierarchical crystals step-by-step. However, the key questions of when and how the secondary nucleation takes place have not been answered. Here we systematically study secondary ZnO crystal growth using organic diamine additives with a range of chain lengths and concentration. We found that ZnO branches form for a narrow diamine concentration range with a critical lower and upper critical nucleation concentration limit, which increases by about a factor of 5 for each additional carbon in the diaminoalkane chain. Our results suggest that the narrow window for secondary growth is dictated by the solubility of the ZnO crystals, where the low critical nucleation concentration is determined by slight etching of the surface to produce new nucleation sites, and the upper critical concentration is determined by the supersaturation concentration. Kinetic measurements show that the induction time and growth rate increase with increasing diamine concentration and follow classical nucleation and growth theory. Observations of branch morphological evolution reveal the mechanisms guiding the tunable crystal size and morphology.     

Kinetics of nucleation in highly polar substances in the presence of ions

Based on of a previously proposed model for describing the effect of the electric field of the ion on the vapor-liquid phase transition, expressions for the work of formation of the critical nucleus in highly polar substances were derived. Analytical expressions for the nucleation frequency were obtained and used to calculate the heterogeneous nucleation frequency in a supersaturated water vapor.     

Density functional theory of inhomogeneous liquids. IV. Squared-gradient approximation and classical nucleation theory

The squared-gradient approximation to the modified-core Van der Waals density functional theory model is developed. A simple, explicit expression for the SGA coefficient involving only the bulk equation of state and the interaction potential is given. The model is solved for planar interfaces and spherical clusters and is shown to be quantitatively accurate in comparison to computer simulations. An approximate technique for solving the SGA based on piecewise-linear density profiles is introduced and is shown to give reasonable zeroth-order approximations to the numerical solution of the model. The piecewise-linear models of spherical clusters are shown to be a natural extension of classical nucleation theory and serve to clarify some of the nonclassical effects previously observed in liquid-vapor nucleation. Nucleation pathways are investigated using both constrained energy-minimization and steepest-descent techniques.     

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.