Kinetic Phase Diagrams Research Articles

Glassy colloidal systems

This review focuses on recent developments in the theoretical, numerical and experimental study of slow dynamics in colloidal systems, with a particular emphasis on the glass transition phenomenon. Colloidal systems appear to be particularly suited for tackling the general problem of dynamic arrest, since they show a larger flexibility compared to atomic and molecular glasses because of their size and the possibility of manipulating the physical and chemical properties of the samples. Indeed, a wealth of new effects, not easily observable in molecular liquids, have been predicted and measured in colloidal systems. The slow dynamic behavior of three classes of colloidal suspension is reviewed – hard colloids, short-range attractive colloids and soft colloidal systems – selecting the model systems among the most prominent candidates for grasping the essential features of dynamic arrest. Emphasis is on the possibility of performing a detailed comparison between experimental data and theoretical predictions based on the mode coupling theory of the glass transition. Finally, the importance of understanding the system's kinetic arrest phase diagram, i.e. the regions in phase space where disordered arrested states can be expected, is stressed. When and how these states are kinetically stabilized with respect to the ordered lowest free energy phases is then examined in order to provide a framework for interpreting and developing new ideas in the study of new materials. Glassy colloidal systemsAll authorsF. Sciortino & P. Tartagliahttps://doi.org/10.1080/00018730500414570Published online:19 February 2007Table Download CSVDisplay Table

Effective Kinetic Phase Diagrams

The composition of a solid solution that is growing at conditions well away from equilibrium is not prescribed by equilibrium thermodynamics, but is determined kinetically. It depends both on the surface kinetics and on the transport of mass and heat to and away from the solidification front. In previous work, we have formulated a model for the kinetic or nonequilibrium segregation taking place at the solidification front enabling the construction of kinetic phase diagrams, which gives the growth composition of a solid solution as a function of the liquid composition and undercooling at the surface. In the present work, we extend this model to include both mass and heat transport, giving rise to effective kinetic phase diagrams. An overview of the tendencies in the calculated effective kinetic phase diagrams is given by scanning a large part of the parameter space, covering different types of materials, including metals, semiconductors, and molecular systems. We find striking and characteric differences in the relative contribution of the various processes to the effective segregation. For molecular mixtures, interfacial undercooling and heat transport limitation can be expected to be much more important than for metal and semiconductor mixtures where mass transport limitation is dominant.

Evolution kinetics and phase transitions of complex adaptive systems

Motivated by the fact that a population of competing agents never set up a true stationary distribution, we propose a theory of evolution kinetics for complex adaptive systems. The formula derived for the survival probability is used to describe different phases in the population evolution when the prize-to-fine ratio as well as time changes. A kinetic phase diagram is obtained to show the phase boundaries for the self-segregating region, the intermediate region, and the clustering region. The kinetic evolutionary equations of strategy distribution are also established and used to give the root-mean-square separation of strategy distribution. It is revealed that the rootstock of the phase transitions is ascribed to the cooperation and competition among agents with different gene values for a limited resource.

Structural arrest transitions in fluids described by two Yukawa potentials

We study a model colloidal system where particles interact via short-range attractive and long-range repulsive Yukawa potentials. Using the structure factor calculated from the mean-spherical approximation as the input, the kinetic phase diagrams as functions of the attraction depth and the volume fraction are obtained by calculating the Debye-Waller factors in the framework of the mode-coupling theory for three different heights of the repulsive barrier. The glass-glass reentrance phenomenon in the attractive colloidal case is also observed in the presence of the long-range repulsive barrier, which results in the lower and upper glass regimes. Competition between the short-range attraction and the long-range repulsion gives rise to new regimes associated with clusters such as "static cluster glass" and "dynamic cluster glass," which appear in the lower glass regime. Along the liquid-glass transition line between the liquid regime and the lower glass regime, crossover points separating different glass states are identified.

Nucleation in binary polymer blends: effects of foreign mesoscopic spherical particles.

We study nucleation in binary polymer blends in the presence of mesoscopic spherical particles using self-consistent field theory, considering both heterogeneous and homogeneous nucleation mechanisms. Heterogeneous nucleation is found to be highly sensitive to surface selectivity and particle size, with rather subtle dependence on the particle size. Particles that preferentially adsorb the nucleating species generally favor heterogeneous nucleation. For sufficiently strong adsorption, barrierless nucleation is possible. By comparing the free energy barrier for homogeneous and heterogeneous nucleation, we construct a kinetic phase diagram.

Compositional ordering kinetics of epitaxial growth of fcc alloy systems

The kinetics of ordering in fcc alloys during the epitaxial growth is investigated by the kinetic mean field method. There are various evolution behaviors during the growth of the system. The kinetic phase diagrams for the epitaxial alloy of an fcc multilayer are calculated. We have found that there is a kinetic induced oscillatory ordered phase in addition to the equilibrium ordered phase in the kinetic phase diagrams.

Kinetically induced ordering oscillation during epitaxial growth of a fcc multilayer alloy

The kinetics of ordering in fcc multilayer alloys during the epitaxial growth is investigated by the kinetic mean-field method. The kinetic phase diagrams for the epitaxial alloy of a fcc multilayer are calculated. We have found that there is a kinetically induced oscillatory ordered phase in addition to the equilibrium ordered phase in the kinetic phase diagrams. This ordering oscillation is caused by the kinetic correlation of different growth processes. It occurs with growth condition of higher deposition rate and in materials with high jumping barrier energies.

Controlled Iron-Doping of Macrotextured Nanocrystalline Titania

Titanium dioxide, despite its rather simple summation formula, is a material with widespread applications. Fe-doped TiO2, because of its photocatalytic properties, is employed in devices for water detoxification, water splitting, and air purification, as well as for solar cells. For each application, its functionality can be optimized by adjusting the crystal modification by the degree of Fe doping and by structuring on atomic to macroscopic length scales. We have developed a flexible and inexpensive butanediol sol−gel synthesis for Fe-doped titania which allows us to control the material properties on atomic, mesoscopic, and macroscopic scales with respect to structure−morphology property relationships, i.e., to generate a tailor-made functional material. A kinetic phase diagram of TiO2:Fe based on this synthesis pathway, in particular with respect to Fe incorporation, has evolved as a result of the application of a large set of complementary means of investigation.

The weak shear kinetic phase diagram for nematic polymers

We study the shear problem for nematic polymers as modeled by the molecular kinetic theory of Doi (1981), focusing on the anomalous slow flow regime. We provide the kinetic phase diagram of monodomain (MD) attractors and phase transitions vs normalized nematic concentration (N) and weak normalized shear rate (Peclet number, Pe). We then overlay all rheological features typically reported in experiments: alignment properties, normal stress differences and shear stress. These features play a critical role in the synthesis between theory and experiment for nematic polymers (Larson 1999; Doi and Edwards 1986). MD type is routinely used for rheological shear characterization: cf., flow-aligning 5CB (Mather et al. 1996a), tumbling PBT (Srinivasarao and Berry 1991), and 8CB (Mather et al. 1996b), evidence for a wagging regime (Mewis et al. 1997), out-of-plane kayaking modes (Larson and Ottinger 1991), and evidence for chaotic major director dynamics (Bandyopadhyay et al. 2000). MD transitions correlate with sign changes in normal stresses (Larson and Ottinger 1991; Magda et al. 1991; Kiss and Porter 1978, 1980). Furthermore, structure formation in shear devices appears to be correlated with monodomain precursor dynamics (Tan and Berry 2003; Forest et al. 2002a). In this paper we combine seminal kinetic theory results (Kuzuu and Doi 1983, 1984; Larson 1990; Larson and Ottinger 1991; Faraoni et al. 1999; Grosso et al. 2001), symmetry observations (Forest et al. 2002b), and mesoscopic results on the fate of orientational degeneracy in weak shear (Forest and Wang 2003; Forest et al. 2003a), together with our resolved numerical simulations, to provide the kinetic flow-phase diagram of Doi theory in the weak shear regime, 0<Pe<1, for infinitely thin rods. We report the "birth" of key rheological features at the onset of flow: sign changes and local maxima and minima in normal stress differences (N 1 and N 2 ) associated with MD transitions. These results serve as the basis for continuation of the kinetic phase diagram to Pe>1 ; as the definitive benchmark for any mesoscopic or continuum model; and experimental data can be compared in order to determine accuracy and limitations of the Doi theory in weak shear.

Kinetic phase diagram for terrace and step nucleation of CaF/Si(1 1 1)

Competing processes during the growth on vicinal surfaces are the nucleation on terraces and the nucleation at steps. From kinetic Monte Carlo (KMC) simulations which are performed on vicinal surfaces of various terrace widths, a kinetic phase diagram (parameters: terrace width and deposition temperature) has been deduced. The boundary between both phases of terrace and step nucleation is described by w∝ D(T c ) . In addition, the nucleation of CaF on Si(1 1 1) has been investigated by means of scanning tunneling microscopy (STM). A comparison of the experimental data with the kinetic Monte Carlo simulations shows that the diffusion barrier of CaF molecules on Si(1 1 1) is 1.8 eV.

Electrochemically assisted deposition of thin calcium phosphate coatings at near-physiological pH and temperature.

An electrochemical method for the deposition of calcium phosphate phases on titanium surfaces using the galvanostatic mode is presented. Deposition was performed in a (Ca(2+) / H(x)PO(4) ((3-x)-))-containing electrolyte near physiological conditions with regard to pH (6.4) and temperature (36 degrees C). Cathodic alkalization leads first to the formation of a thin homogeneous layer that shows a nanoscale surface topography of alternating wall-like elevations and channels. It is thought that these channels in the calcium phosphate prelayer are formed as pathways for hydroxyl ions and hydrogen. Upon this layer, spheres of amorphous calcium phosphate (ACP) are formed as indicated by Fourier transform infrared spectroscopy (FTIR) and transmission electron microscopy. According to transmission electron microscopy images, these spheres consist of small clusters of calcium phosphate (approximately 30 nm) and can grow up to 300 nm in diameter. Characteristic for this ACP is a high water content as seen by FTIR. As a function of current density, the ACP is then transformed into crystalline hydroxyapatite (HAP), which was identified using FTIR and X-ray diffraction. The morphology of the HAP crystals can be described as needles with dimensions of <500-nm length and <60-nm width. By choice of different electrochemical parameters, a homogeneous coating of either ACP, HAP, or the intermediate phase can be achieved, as shown in a kinetic phase diagram, thus allowing the formation of coatings with different properties in solubility and morphology.

Microstructural changes of a binary polymer blend in simple shear flow across the phase boundary

We explore the dynamic response of a marginally entangled poly(dimethyl siloxane)/poly(ethyl methyl siloxane) blend in simple shear flow using rheology and small angle light scattering in situ. Data are collected in both the flow/gradient and flow/vorticity planes. We find that for this model binary blend, exhibiting upper critical solution temperature behavior, shear suppresses the large pretransitional concentration fluctuations and eventually yields homogenization. The simple modified Cahn–Hilliard–Cook phenomenological model of Lai and Fuller [J. Polym. Sci. Part B: Polym. Phys. 32, 2461–2474 (1994)] describes semiquantitatively the time evolution of the structure factor and orientation angle well, supporting the experimental observations of enhanced orientation with flow. In the phase separated region, when the late stages of spinodal decomposition are reached, the shear-induced anisotropic distortion of the spinodal ring, orienting in the flow direction, and its relaxation upon flow cessation are probed and found to depend on the distance from the spinodal point. At intermediate times the spinodal ring gives rise to unstable butterfly patterns, as a consequence of the coupling of fluctuations with the flow, yielding clongated droplets at later times. The latter turn into streaks at higher rates, suggesting that the mechanism of shear-induced homogenization from the spinodal region, is analogous to that observed in blend solutions. A kinetic phase diagram indicating different microstructures at different temperatures and shear rates, is constructed. These results underline important similarities between binary polymer blends and polymer blend solutions and mark the important parameter ranges for controlling their rheology.

Kinetic Phase Diagram of Fractal and Euclidean Nonequilibrium Growth Patterns of Ice I h in Supercooled Water

Kinetic Phase Diagram of Fractal and Euclidean Nonequilibrium Growth Patterns of Ice I h in Supercooled Water

Interplay between the structure and properties of new metastable carbon phases obtained under high pressures from fullerite C60 and carbyne

A brief review of structural, electrotransport, optical, elastic, and mechanical properties of carbon phases synthesized under pressure by heating fullerite C60 and carbynoid materials is given. A large variety of carbon modifications with a variable bonding type, a variable mean coordination number, a variable molecular or atomic structural type, a variable characteristic dimensionality (from zero-to three-dimensional structures), a variable degree of covalence, etc., were prepared. Emphasis in the review is given to the elucidation of the interplay between the structural and topological characteristics of carbon phases and their key electronic and mechanical properties. A version of the kinetic phase diagram of fullerite C60 transformations on heating under pressure is also suggested. This version is modified with respect to the interpretations known in the literature.

Kinetic arrest of crowded soft spheres in solvents of varying quality.

Crowded solutions of multiarm star polymers, representing model colloidal spheres with ultrasoft repulsive interactions, undergo a reversible gelation transition upon heating in solvents of intermediate quality (between good and Theta). This unusual phenomenon is due to the kinetic arrest of the swollen interpenetrating spheres at high temperatures, forming clusters, in analogy to the colloidal glass transition. In this work we demonstrate that the choice of the solvent has a dramatic effect on the gelation transition, because of the different degree of star swelling (at the same temperature) associated with the solvent quality. We construct a generic kinetic phase diagram for the gelation of different stars in different solvents (gelation temperature against effective volume fraction, phi) and propose a critical "soft sphere close packing" volume fraction phi(c) distinguishing the temperature-induced (for phi<phi(c)) from the concentration-induced (for phi>phi(c)) glass-like gelation. We conclude that appropriate selection of the solvent allows for manipulation of the sol-gel transition in such ultrasoft colloids.

Epitaxial Growth of CaF2 Films on Si(111) Studied by Scanning Tunneling Microscopy

Using ultrahigh vacuum scanning tunneling microscopy, we have studied the early stages of the epitaxial growth of CaF2 films on Si(111) at 630°C at a slow deposition rate of 0.2 monolayer (ML) per minute. After formation of CaF interface layer, we observe the film grows in the sequence of step edge decoration, one-dimensional islands growth on the terrace, formation of clusters of the islands, coalescence of the island cluster and filling of gaps between the one-dimensional islands in the cluster and between the island clusters to complete a layer. By such a sequence, epitaxial CaF2 films with atomically flat surface could be grown in layer-by-layer fashion up to 3 ML. The growth mode is discussed in relation to kinetic phase diagram [M. A. Olmstead: Thin Films: Heteroepitaxial Systems, eds. W. K. Liu and M. B. Santos (World Scientific, Singapore, 1999) Chap. 5].

Kinetic phase diagram for crystallization of bimodal mixtures of oligomers as predicted by computer simulations

We analyze the crystallization process of mixtures of long and short oligomers such as n-alkanes using a Sadler–Gilmer-type growth algorithm. The short chains are assumed to crystallize only in a fully stretched conformation, while the long chains take a pathway over a folded state. Increasing the concentration of long chains from zero to unity, the zero-growth temperature, which separates the stable growing phase from the non-growing phase, first decreases for low concentrations of long chains, reaching a minimum value at intermediate concentrations, and increases again for higher concentrations, as a result a growth-gap appears. Here, mixing long chains into the short chain liquid stops the growth process completely until it resumes at higher concentrations of long chains. This effect is explained by the particular kinetic pathway, the long chains take into the crystalline state. Since the folded state has to be passed at first, long chains are more likely to be desorbed again. At low concentrations, the long chains thus effectively dilute the short chain liquid leading to a decrease of the zero-growth temperature. At higher concentrations, the transition into the stretched state of the long chains leads more frequently to bonded pairs, which stabilizes the growth again due to the higher binding energy among fully stretched long chains.

Diffusion-influenced reversible energy transfer reactions between polymers

Diffusion-influenced reversible reactions of polymers are investigated by using the hierarchical reaction–diffusion equations for end-functionalized Rouse chains. It is found that distinct dynamic characteristics of reactive groups over different time scales lead to rich time-dependent behaviors in the reactant number densities, which are totally absent in the small molecular reactions. On time scales smaller than the Rouse relaxation time, the number densities of excited reactants are described by a scaling function, whereas for larger times, they approach the equilibrium values exponentially. A kinetic phase diagram locating regions of distinct behaviors of Stern–Volmer coefficients is presented which can be directly confirmed by experiments.

Uniform island height selection in the low temperature growth of Pb/Si([formula omitted])-(7×7)

Self-organized, uniform-height, Pb islands with flat tops and steep edges form on Si(111)-(7×7) at low temperatures 120<T<250 K. Islands of heights differing by bilayer height increments are observed depending on growth conditions. The formation of these structures is highly unusual since at low temperatures thermal diffusion is suppressed. The origin of the regular structures is believed to be quantum size effects (i.e. effects related to the quantization of the electron energy levels in the islands). We have studied with two complementary techniques (i.e. high resolution spot profile analysis low energy electron diffraction and variable temperature scanning tunneling microscopy) how the preferred island heights depend on the growth parameters (i.e. temperature, coverage, kinetic pathway etc.). We have constructed a kinetic phase diagram in the coverage–temperature plane which indicates the type of islands formed under different growth conditions. The phase diagram can be used as a guide so the island height can be easily controlled.

Equilibria and kinetics of polydisperse mixture adsorption

We study the equilibrium and kinetic properties of a model for polydisperse mixture adsorption. The system consists of a bulk phase of hard disks with a given size distribution and overall concentration that adsorb and desorb on a continuous planar surface. The disks adsorb at a rate proportional to their bulk concentration and desorb at a rate that may depend on the particle size. The model is characterized by α, the dimensionless binding energy of a solute per unit area, and K which is proportional to the total bulk concentration. The properties of the model are determined with scaled particle theory (SPT) and with numerical simulation. If the desorption rate is independent of particle size, an equilibrium is rapidly established between the bulk and adsorbed phases. The resulting adsorption isotherms predicted by SPT agree well with the numerical simulations. If the desorption rate depends exponentially on the binding energy of the adsorbed particle, the approach to equilibrium is dramatically slowed. At high bulk concentrations and low values of α the adsorbed density increases monotonically with time, while the coverage displays an overshoot. At low K and high α, it is the coverage that increases monotonically, while the density passes through a maximim. For a given bulk phase distribution, one can construct an (α,K) kinetic phase diagram delineating this behavior.