Recent developments in the kinetic theory of nucleation

A seminal perspective on the role of chondroitin sulfate in biomineralization

Chondroitin sulfate (CS) is an important extracellular matrix component of mineralized tissues. It participates in biomineralization, osteoblast differentiation and promotes bone tissue repair in vitro. However, the mechanism in which CS functions is unclear. Accordingly, an in-depth investigation of how CS participates in mineralization was conducted in the present study. Chondroitin sulfate was found to directly induce intrafibrillar mineralization of the collagen matrix. The mineralization outcome was dependent on whether CS remained free in the extracellular matrix or bound to core proteins; mineralization only occurred when CS existed in a free state. The efficacy of mineralization appeared to increase with ascending CS concentration. This discovery spurred the authors to identify the cause of heterotopic ossification in the Achilles tendon. Chondroitin sulfate appeared to be a therapeutic target for the management of diseases associated with heterotopic calcification. A broader perspective was presented on the applications of CS in tissue engineering.

"Sounding" out crystal nuclei-A mathematical-physical and experimental investigation

We outline techniques for the control and measurement of the nucleation of crystalline materials. Small angle x-ray scattering/wide angle x-ray scattering x-ray diffraction measurements are presented that demonstrate the impact of low power, continuous, non-cavitational ultrasound on the nucleation and crystallization of a wax-n-eicosane dissolved in a heptane/toluene solvent. A mathematical-physical approach based on the rectification of heat and mass transport by such a low power oscillating pressure field is outlined, and it is suggested that this approach be combined with dissipative particle dynamics computational modeling to develop a predictive method capable of modeling the impact of low power oscillating pressure fields (acoustics and ultrasonics) on a wide range of nucleating systems. Combining the ultrasound pitch and catch speed of sound measurements with low power harmonically oscillating pressure fields to monitor and control nucleation presents the prospect of entirely new industrially significant methods of process control in crystallization. It also offers new insights into nucleation processes in general. However, for the acoustic control technique to be widely applied , further theoretical and modeling work will be necessary since, at present, we are unable to predict the precise effect of low power ultrasound in any given situation.

Impact of Thermal Properties on Crystalline Structure, Polymorphism and Morphology of Polymer Matrices in Composites

Morphological analysis at different levels is fundamental to understand properties of materials, as these latter are dictated not only by the chemical composition but also by the shape. Solid structures arise from a balance between thermodynamic and kinetic factors, which, especially for polymer composites, depend also on interactions amongst components. In particular, morphology is strongly affected by the heat transfer pattern during crystallization and by the difference in thermal behavior between polymer matrix and filler. Polymers show a spherulitic structure, arising from the start of crystallization in several points of the liquid phase. Within a general rounded shape, spherulites show variability in growth patterns, morphology, and geometry of boundaries. The appearance and the number of spherulites, as well as their growth mechanism, may vary not only in dependence of the chemical composition and the crystalline structures but also, for a same polymer, in consequence of experimental conditions and incorporation of fillers. This article reviews the crystallization process of polymer matrices in the framework of crystal growth and heat transport theories, and explains microstructural differences between composites and neat matrices on the basis of the differences in thermal capacity and conductivity between polymers and additives.

Controllable Heterogeneous Nucleation for Patterning High-Quality Vertical and Horizontal ZnO Microstructures toward Photodetectors

High-quality crystalline micro- and nanostructures based on inorganic semiconductors including zinc oxide (ZnO) have attracted considerable interest in electronic and optoelectronic applications due to their outstanding properties. ZnO micro- and nanocrystals can be fabricated by the moderate and high throughput hydrothermal synthesis. Yet it is restricted by patterning large-area ZnO crystals with high-quality and programmable geometries through the hydrothermal process for the optoelectronic integration. Here, a capillary-bridge manipulation approach is demonstrated to control the dewetting process of ZnO precursor solution for patterning precursor arrays. Based on precursor arrays, vertically aligned high-quality ZnO microrod arrays with homogeneous morphology and pure crystallographic orientation are fabricated via a hydrothermal epitaxial method. Statistical results and crystallization theories guide the experimental optimization and discussion of the crystallization mechanism, dominated by the competition between homogeneous nucleation and heterogeneous nucleation. High-quality ZnO microbelt arrays are achieved through a surfactant-mediated hydrothermal method after ZnO microrod arrays are transferred to a polydimethylsiloxane substrate. Photodetectors based on ZnO microbelts exhibit a high responsivity of 2.3 × 10⁴ A W^-1 , a light on-off ratio exceeding 10⁵ , and stable recyclability. It is anticipated that this work provides new insights into patterning inorganic high-quality micro- and nanostructures for multi-functional integrated devices.

Kinetic equation of concurrent nucleation and chemical aging of an ensemble of aqueous organic aerosols

Using the formalism of classical nucleation theory, we derive a kinetic equation for the size and composition distribution of an ensemble of aqueous organic droplets evolving via nucleation and concomitant chemical aging. This distribution can be drastically affected by the enthalpy of heterogeneous chemical reactions and the depletion of organic trace gases absorbed by aerosols. A partial differential equation of second order for the temporal evolution of this distribution is obtained from the discrete equation of balance via Taylor series expansions. Once reduced to the canonical form of the multidimensional Fokker-Planck equation, this kinetic equation can be solved via the method of complete separation of variables. This kinetic equation opens a new direction in the development of the kinetic theory of first-order phase transitions, while its applications to the formation and evolution atmospheric organic aerosols via concurrent nucleation and chemical aging may drastically improve the accuracy of global climate models.

Numerical calculation of free-energy barriers for entangled polymer nucleation

The crystallization of entangled polymers from their melt is investigated using computer simulation with a coarse-grained model. Using hybrid Monte Carlo simulations enables us to probe the behavior of long polymer chains. We identify solid-like beads with a centrosymmetry local order parameter and compute the nucleation free-energy barrier at relatively high supercooling with adaptive-bias windowed umbrella sampling. Our results demonstrate that the critical nucleus sizes and the heights of free-energy barriers do not significantly depend on the molecular weight of the polymer; however, the nucleation rate decreases with the increase in molecular weight. Moreover, an analysis of the composition of the critical nucleus suggests that intra-molecular growth of the nucleated cluster does not contribute significantly to crystallization for this system.

Experimental Research on the Thermal Performance and Semi-Visualization of Rectangular Flat Micro-Grooved Gravity Heat Pipes

To strengthen the heat dissipating capacity of a heat pipe used for integrated insulated gate bipolar transistors, as an extension of our earlier work, the effect of micro-groove dimension on the thermal performance of flat micro-grooved gravity heat pipe was studied. Nine pipes with different depths (0.4 mm, 0.8 mm, 1.2 mm) and widths (0.4 mm, 0.8 mm, 1.2 mm) were fabricated and tested under a heating load range from 80 W to 180 W. The start-up time, temperature difference, relative thermal resistance and equivalent thermal conductivity were presented as performance indicators by comparison of flat gravity heat pipes with and without micro-grooves. Results reveal that the highest equivalent thermal conductivity of the flat micro-grooved gravity heat pipes is 2.55 times as that of the flat gravity heat pipe without micro-grooves. The flat gravity heat pipes with deeper and narrower micro-grooves show better thermal performance and the optimal rectangular micro-groove dimension among the selected options is determined to be 1.2 mm (depth) × 0.4 mm (width). Furthermore, the liquid–vapor phase behaviors were observed to verify the heat transfer effects and analyze the heat transfer mechanism of the flat micro-grooved heat pipes.

Solution-phase synthesis of transition metal oxide nanocrystals: Morphologies, formulae, and mechanisms

In this review, we provide a broad overview of solution-phase synthesis of transition metal oxide nanocrystals (NCs), including a substantial catalog of published methods, and a unifying classification and discussion. Prevalent subcategories of solution-phase synthesis are delineated and general features are summarized. The diverse morphologies achievable by solution-phase synthesis are defined and exemplified. This is followed by sequential consideration of the solution-phase synthesis of first-row transition metal oxides. The common oxides of Ti, V, Mn, Fe, Co, Ni, Cu, and Zn are introduced; major crystal lattices are presented and illustrated; representative examples are explained; and numerous synthesis formulae are tabulated. Following this presentation of experimental studies, we present an introduction to theories of NC nucleation and growth. Various models of NC nucleation and growth are addressed, and important concepts determining the growth and structure of colloidal NCs are explained. Overall, this review provides an entry into systematic understanding of solution-phase synthesis of nanocrystals, with a reasonably comprehensive survey of results for the important category of transition metal oxide NCs.

Structural characterization of MG and pre-MG states of proteins by MD simulations, NMR, and other techniques

Almost all proteins fold via a number of partially structured intermediates such as molten globule (MG) and pre-molten globule states. Understanding the structure of these intermediates at atomic level is often a challenge, as these states are observed under extreme conditions of pH, temperature, and chemical denaturants. Furthermore, several other processes such as chemical modification, site-directed mutagenesis (or point mutation), and cleavage of covalent bond of natural proteins often lead to MG like partially unfolded conformation. However, the dynamic nature of proteins in these states makes them unsuitable for most structure determination at atomic level. Intermediate states studied so far have been characterized mostly by circular dichroism, fluorescence, viscosity, dynamic light scattering measurements, dye binding, infrared techniques, molecular dynamics simulations, etc. There is a limited amount of structural data available on these intermediate states by nuclear magnetic resonance (NMR) and hence there is a need to characterize these states at the molecular level. In this review, we present characterization of equilibrium intermediates by biophysical techniques with special reference to NMR.

A novel approach to the theory of homogeneous and heterogeneous nucleation

A new approach to the theory of nucleation, formulated relatively recently by Ruckenstein, Narsimhan, and Nowakowski (see Refs. [7-16]) and developed further by Ruckenstein and other colleagues, is presented. In contrast to the classical nucleation theory, which is based on calculating the free energy of formation of a cluster of the new phase as a function of its size on the basis of macroscopic thermodynamics, the proposed theory uses the kinetic theory of fluids to calculate the condensation (W(+)) and dissociation (W(-)) rates on and from the surface of the cluster, respectively. The dissociation rate of a monomer from a cluster is evaluated from the average time spent by a surface monomer in the potential well as obtained from the solution of the Fokker-Planck equation in the phase space of position and momentum for liquid-to-solid transition and the phase space of energy for vapor-to-liquid transition. The condensation rates are calculated using traditional expressions. The knowledge of those two rates allows one to calculate the size of the critical cluster from the equality W(+)=W(-) as well as the rate of nucleation. The developed microscopic approach allows one to avoid the controversial application of classical thermodynamics to the description of nuclei which contain a few molecules. The new theory was applied to a number of cases, such as the liquid-to-solid and vapor-to-liquid phase transitions, binary nucleation, heterogeneous nucleation, nucleation on soluble particles and protein folding. The theory predicts higher nucleation rates at high saturation ratios (small critical clusters) than the classical nucleation theory for both solid-to-liquid as well as vapor-to-liquid transitions. As expected, at low saturation ratios for which the size of the critical cluster is large, the results of the new theory are consistent with those of the classical one. The present approach was combined with the density functional theory to account for the density profile in the cluster. This approach was also applied to protein folding, viewed as the evolution of a cluster of native residues of spherical shape within a protein molecule, which could explain protein folding/unfolding and their dependence on temperature.

Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives

Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions, with rather well-characterized pair interactions and minimized external influences. In complementary approaches experiment, analytic theory and simulation have been employed to study colloidal solidification in great detail. These studies were based on advanced optical methods, careful system characterization and sophisticated numerical methods. Over the last decade, both the effects of the type, strength and range of the pair-interaction between the colloidal particles and those of the colloid-specific polydispersity have been addressed in a quantitative way. Key parameters of crystallization have been derived and compared to those of metal systems. These systematic investigations significantly contributed to an enhanced understanding of the crystallization processes in general. Further, new fundamental questions have arisen and (partially) been solved over the last decade: including, for example, a two-step nucleation mechanism in homogeneous nucleation, choice of the crystallization pathway, or the subtle interplay of boundary conditions in heterogeneous nucleation. On the other hand, via the application of both gradients and external fields the competition between different nucleation and growth modes can be controlled and the resulting microstructure be influenced. The present review attempts to cover the interesting developments that have occurred since the turn of the millennium and to identify important novel trends, with particular focus on experimental aspects.

Synthesis and Characterization of Solid-State Phase Change Material Microcapsules for Thermal Management Applications

Polyalcohols such as neopentyl glycol (NPG) undergo solid-state crystal transformations that absorb/release significant latent heat. These solid–solid phase change materials (PCM) can be used in practical thermal management applications without concerns about liquid leakage and thermal expansion during phase transitions. In this paper, microcapsules of NPG encapsulated in silica shells were successfully synthesized with the use of emulsion techniques. The size of the microcapsules range from 0.2 to 4 μm, and the thickness of the silica shell is about 30 nm. It was found that the endothermic phase transition of these NPG-silica microcapsules was initiated at around 39 °C and the latent heat was about 96.0 J/g. A large supercooling of about 43.3 °C was observed in the pure NPG particles without shells, while the supercooling of the NPG microcapsules was reduced to about 14 °C due to the heterogeneous nucleation sites provided by the silica shell. These NPG microcapsules were added to the heat transfer fluid PAO to enhance its heat capacity and the effective heat capacity of the fluid was increased by 56% with the addition of 20 wt. % NPG-silica microcapsules.

Classical nucleation theory with a radius-dependent surface tension: a two-dimensional lattice-gas automata model

The constant surface tension assumption of the Classical Nucleation Theory (CNT) is known to be flawed. In order to probe beyond this limitation, we consider a microscopic, two-dimensional Lattice-Gas Automata (LGA) model of nucleation in a supersaturated system, with model input parameters E(ss) (solid particle-to-solid particle bonding energy), E(sw) (solid particle-to-water bonding energy), η (next-to-nearest-neighbor bonding coefficient in solid phase), and C(in) (initial solute concentration). The LGA method has the advantages of easy implementation, low memory requirements, and fast computation speed. Analytical results for the system's concentration and the crystal radius as functions of time are derived and the former is fit to the simulation data in order to determine the equilibrium concentration. The "Mean First-Passage Time" technique is used to obtain the nucleation rate and critical nucleus size from the simulation data. The nucleation rate and supersaturation data are evaluated using a modification to the CNT that incorporates a two-dimensional radius-dependent surface tension term. The Tolman parameter, δ, which controls the radius dependence of the surface tension, decreases (increases) as a function of the magnitude of E(ss) (E(sw)), at fixed values of η and E(sw) (E(ss)). On the other hand, δ increases as η increases while E(ss) and E(sw) are held constant. The constant surface tension term of the CNT, Σ(0), increases (decreases) with increasing magnitudes of E(ss) (E(sw)) at fixed values of E(sw) (E(ss)) and increases as η is increased. Σ(0) increases linearly as a function of the change in energy during an attachment or detachment reaction, |ΔE|, however, with a slope less than that predicted for a crystal that is uniformly packed at maximum density. These results indicate an increase in the radius-dependent surface tension, Σ, with respect to increasing magnitude of the difference between E(ss) and E(sw).

A perspective on the interfacial properties of nanoscopic liquid drops

The structural and interfacial properties of nanoscopic liquid drops are assessed by means of mechanical, thermodynamical, and statistical mechanical approaches that are discussed in detail, including original developments at both the macroscopic level and the microscopic level of density functional theory (DFT). With a novel analysis we show that a purely macroscopic (static) mechanical treatment can lead to a qualitatively reasonable description of the surface tension and the Tolman length of a liquid drop; the latter parameter, which characterizes the curvature dependence of the tension, is found to be negative and has a magnitude of about a half of the molecular dimension. A mechanical slant cannot, however, be considered satisfactory for small finite-size systems where fluctuation effects are significant. From the opposite perspective, a curvature expansion of the macroscopic thermodynamic properties (density and chemical potential) is then used to demonstrate that a purely thermodynamic approach of this type cannot in itself correctly account for the curvature correction of the surface tension of liquid drops. We emphasize that any approach, e.g., classical nucleation theory, which is based on a purely macroscopic viewpoint, does not lead to a reliable representation when the radius of the drop becomes microscopic. The description of the enhanced inhomogeneity exhibited by small drops (particularly in the dense interior) necessitates a treatment at the molecular level to account for finite-size and surface effects correctly. The so-called mechanical route, which corresponds to a molecular-level extension of the macroscopic theory of elasticity and is particularly popular in molecular dynamics simulation, also appears to be unreliable due to the inherent ambiguity in the definition of the microscopic pressure tensor, an observation which has been known for decades but is frequently ignored. The union of the theory of capillarity (developed in the nineteenth century by Gibbs and then promoted by Tolman) with a microscopic DFT treatment allows for a direct and unambiguous description of the interfacial properties of drops of arbitrary size; DFT provides all of the bulk and surface characteristics of the system that are required to uniquely define its thermodynamic properties. In this vein, we propose a non-local mean-field DFT for Lennard-Jones (LJ) fluids to examine drops of varying size. A comparison of the predictions of our DFT with recent simulation data based on a second-order fluctuation analysis (Sampayo et al 2010 J. Chem. Phys. 132 141101) reveals the consistency of the two treatments. This observation highlights the significance of fluctuation effects in small drops, which give rise to additional entropic (thermal non-mechanical) contributions, in contrast to what one observes in the case of planar interfaces which are governed by the laws of mechanical equilibrium. A small negative Tolman length (which is found to be about a tenth of the molecular diameter) and a non-monotonic behaviour of the surface tension with the drop radius are predicted for the LJ fluid. Finally, the limits of the validity of the Tolman approach, the effect of the range of the intermolecular potential, and the behaviour of bubbles are briefly discussed.

Nucleation of silica nanoparticles measured in situ during controlled supersaturation increase. Restructuring toward a monodisperse nonspherical shape

The first stages of the nucleation and growth of silica nanoparticles are followed in situ using both SAXS and Raman spectroscopy. Coupling these two techniques allows the determination of the fractions of soluble and solid silica as a function of the reaction time. SAXS also enables demonstrating that major modifications of the structure occur after the initial precipitation period, inducing an increase of the precipitate density. These structural modifications have important implications in the initial nucleation growth stages, which have never been introduced either in classical models or in more recent kinetic nucleation theories. Such restructuration stages could contribute to explain the monodispersity of the obtained silica nanoparticles that is not predicted by classical models.

Coarsening and accelerated equilibration in mass-conserving heterogeneous nucleation

We propose a model of mass-conserving heterogeneous nucleation to describe the dynamics of ligand-receptor binding in closed cellular compartments. When the ligand dissociation rate is small, competition among receptors for free ligands gives rise to two very different long-time ligand-receptor cluster-size distributions. Cluster sizes first plateau to a long-lived, initial-condition-dependent, "metastable" distribution, and coarsen only much later to a qualitatively different equilibrium one. Surprisingly, we also find parameters for which a very special subset of clusters have equal metastable and equilibrium sizes, appearing to equilibrate much faster than the rest. Our results provide a quantitative framework for ligand-binding kinetics and suggest a mechanism by which different clusters can approach their equilibrium sizes in unexpected ways.

Influence of process and formulation parameters on the formation of submicron particles by solvent displacement and emulsification-diffusion methods critical comparison

Solvent displacement and emulsification-diffusion are the methods used most often for preparing biodegradable submicron particles. The major difference between them is the procedure, which results from the total or partial water miscibility of the organic solvents used. This review is devoted to a critical and a comparative analysis based on the mechanistic aspects of particle formation and reported data on the influence of operating conditions, polymers, stabilizing agents and solvents on the size and zeta-potential of particles. In addition, a systematic study was carried out experimentally in order to obtain experimental data not previously reported and compare the data pertaining to the different methods. Thus the discussion of the behaviors reported in the light of the results obtained from the literature takes into account a wide range of theoretical and practical information. This leads to discussion on the formation mechanism of the particles and provides criteria for selecting the adequate method and raw materials for satisfying specific objectives in submicron particle design.

Effect of noise-induced nucleation on grain size distribution studied via the phase-field crystal method

We contribute to the more detailed understanding of the phase-field crystal model recently developed by Elder et al (2002 Phys. Rev. Lett. 88 245701), by focusing on its noise term and examining its impact on the nucleation rate in a homogeneously solidifying system as well as on successively developing grain size distributions. In this context we show that principally the grain size decreases with increasing noise amplitude, resulting in both a smaller average grain size and a decreased maximum grain size. Despite this general tendency, which we interpret based on Panfilis and Filiponi (2000 J. Appl. Phys. 88 562), we can identify two different regimes in which nucleation and successive initial growth are governed by quite different mechanisms.

Quantized liquid density-functional theory for hydrogen adsorption in nanoporous materials

We develop a finite-temperature quantized version of density-functional theory of atomic and molecular liquids (QLDFT). Following the Kohn-Sham partitioning of the free energy, we introduce a noninteracting reference fluid of particles obeying the Maxwell-Boltzmann statistics. The kinetic and potential energy of the reference fluid are evaluated exactly. All remaining contributions, including interactions between fluid particles and corrections due to the appropriate quantum statistics are subsumed by an excess (in electronic DFT called exchange-correlation) functional. Two variants to approximate the excess functional are presented: the simplest local-interaction expression (LIE-0) avoids the direct calculation of interparticle interactions and includes them in the excess functional, which is parametrized to reproduce experimental equation of state of normal hydrogen. The more sophisticated LIE-1 approximation is based on the weighted local-density approximation and includes the explicit interparticle interaction potential as well as the local approximation of the excess functional, the latter being weighted by the average over a spherical environment to include nonlocal effects in an approximate way. We apply LIE-0 and LIE-1 to two benchmark systems, bulk fluid hydrogen and hydrogen in a slit pore, and compare it with classical molecular-dynamics simulations employing the same potential. Both functionals produce similar results for direct quantum effects in adsorption free energy. At the same time, LIE-1 also yields a reasonable description of the fluid structure and classical packing effects, which are not reproduced by LIE-0. The source code of our implementation of the LIE-QLDFT is distributed under the GNU public license and is included as a supporting material.

Nucleation: what happens at the initial stage?

Crystallizing growth: The initial structure of crystal nuclei is supersaturation-dependent. At low degrees of supersaturation, liquid-like nuclei are formed initially, which undergo a continuous structure transition from liquid-like to crystal-like as the size N increases. This gradual structure evolution substantially lowers the nucleation barrier DeltaG* and facilitates the nucleation relative to the formation of crystal-like clusters from the beginning.

Radial density distribution of the metastable supersaturated vapor via restricted ensemble simulations

Extensive restricted canonical ensemble Monte Carlo simulations [D. S. Corti and P. Debenedetti, Chem. Eng. Sci. 49, 2717 (1994)] for the supersaturated Lennard--Jones (LJ) vapor were performed. These simulations were conducted at different densities and reduced temperatures from 0.7 to 1.0 and the radial density distribution functions were obtained, most of which are unavailable via integral equation theory due to phase separations. Among different constraints imposed on the system studied, the one with the local minimum of the excess free energy was taken to be the one that approximates the equilibrium state of the metastable LJ vapor. For the slightly saturated state points, where integral equation theory does have a solution, compared with our simulations, differences of the radial density distribution functions were found and they are attributed to ignoring density fluctuations in the integral equation theory.

The free energy of the metastable supersaturated vapor via restricted ensemble simulations. II. Effects of constraints and comparison with molecular dynamics simulations

Extensive restricted canonical ensemble Monte Carlo simulations [D. S. Corti and P. Debenedetti, Chem. Eng. Sci. 49, 2717 (1994)] were performed. Pressure, excess chemical potential, and excess free energy with respect to ideal gas data were obtained at different densities of the supersaturated Lennard-Jones (LJ) vapor at reduced temperatures from 0.7 to 1.0. Among different constraints imposed on the system studied, the one with the local minimum of the excess free energy was taken to be the approximated equilibrium state of the metastable LJ vapor. Also, a comparison of our results with molecular dynamic simulations [A. Linhart et al., J. Chem. Phys. 122, 144506 (2005)] was made.

Colloidal crystal growth at externally imposed nucleation clusters

We study the conditions under which and how an imposed cluster of fixed colloidal particles at prescribed positions triggers crystal nucleation from a metastable colloidal fluid. Dynamical density functional theory of freezing and Brownian dynamics simulations are applied to a two-dimensional colloidal system with dipolar interactions. The externally imposed nucleation clusters involve colloidal particles either on a rhombic lattice or along two linear arrays separated by a gap. Crystal growth occurs after the peaks of the nucleation cluster have first relaxed to a cutout of the stable bulk crystal.

On the Origin of Mesoscopic Inhomogeneity of Conducting Polymers

The mesoscopic inhomogeneity of conducting polymer films obtained by electropolymerization and spin-coating was studied using Kelvin probe force microscopy (KFM) and current-sensing atomic-force microscopy (CS-AFM). A well-pronounced correlation was established between the polymer morphology, on the one hand, and its local work function (which is related to the polymer oxidation degree) as well as polymer conductivity, on the other. The most conducting regions were associated with the tops of the polymer grains and showed Ohmic behavior. They were surrounded first by semiconducting and then by insulating polymer. The conductivity of the grain periphery could be lower by as much as 2 orders of magnitude. The grain cores also showed consistently higher values of the local work function as compared to the grain periphery. This fact suggested that the grain cores were more oxidized and/or more ordered as compared to the grain periphery, which is in good agreement with the local conductivity data. More uniform morphology corresponded to less variability in the other properties of the polymer. A model is proposed that relates the observed inhomogeneity to preferential deposition of polymer molecules with higher molecular weight at the early stages of the polymer phase formation. The polymer deposition in either electropolymerization or various solution-casting techniques involves the nucleation of a new phase from a solution containing polymer fractions of different molecular weights. The driving force of the nucleation process depends on the solubility of the polymer fractions, which decreases with an increase in the molecular weight. This gives rise to preferential deposition of more crystalline, higher molecular weight polymer at the early stages of the polymer deposition to form the cores of the polymer grains. The fractions with lower molecular weights are deposited later and form less ordered/less conducting grain periphery. On the basis of this model, we conclude that, to ensure the formation of materials with low inhomogeneity and high quality, one should use the starting polymer with as narrow molecular weight distribution as possible. Yet another possibility is to use solvents which would reduce the differences in the solubilities of polymer fractions with different molecular weight.

An off-lattice Wang-Landau study of the coil-globule and melting transitions of a flexible homopolymer

The Wang-Landau Monte Carlo approach is applied to the coil-globule and melting transitions of off-lattice flexible homopolymers. The solid-liquid melting point and coil-globule transition temperatures are identified by their respective peaks in the heat capacity as a function of temperature. The melting and theta points are well separated, indicating that the coil-globule transition occurs separately from melting even in the thermodynamic limit. We also observe a feature in the heat capacity between the coil-globule and melting transitions which we attribute to a transformation from a low-density liquid globule to a high-density liquid globule.