On the definition of a Monte Carlo model for binary crystal growth

We show that consistency of the transition probabilities in a lattice Monte Carlo (MC) model for binary crystal growth with the thermodynamic properties of a system does not guarantee the MC simulations near equilibrium to be in agreement with the thermodynamic equilibrium phase diagram for that system. The deviations remain small for systems with small bond energies, but they can increase significantly for systems with large melting entropy, typical for molecular systems. These deviations are attributed to the surface kinetics, which is responsible for a metastable zone below the liquidus line where no growth occurs, even in the absence of a 2D nucleation barrier. Here we propose an extension of the MC model that introduces a freedom of choice in the transition probabilities while staying within the thermodynamic constraints. This freedom can be used to eliminate the discrepancy between the MC simulations and the thermodynamic equilibrium phase diagram. Agreement is achieved for that choice of the transition probabilities yielding the fastest decrease of the free energy (i.e., largest growth rate) of the system at a temperature slightly below the equilibrium temperature. An analytical model is developed, which reproduces quite well the MC results, enabling a straightforward determination of the optimal set of transition probabilities. Application of both the MC and analytical model to conditions well away from equilibrium, giving rise to kinetic phase diagrams, shows that the effect of kinetics on segregation is even stronger than that predicted by previous models.     

Model hysteresis dimer molecule II: deductions from probability profile due to system coordinates

The hysteresis dimer reaction of the first sequel is applied to test the Gibbs density-in-phase hypothesis for a canonical distribution at equilibrium. The probability distribution of variously defined internal and external variables is probed using the algorithms described, in particular the novel probing of the energy states of a labeled particle where it is found that there is compliance with the Gibbs’ hypothesis for the stated equilibrium condition and where the probability data strongly suggests that an extended equipartition principle may be formulated for some specific molecular coordinates, whose equipartition temperature does not equal the mean system temperature and a conjecture concerning which coordinates may be suitable is provided. Evidence of violations to the mesoscopic nonequilibrium thermodynamics (MNET) assumptions used without clear qualifications for a canonical distribution for internal variables are described, and possible reasons outlined, where it is found that the free dimer and atom particle kinetic energy distributions agree fully with Maxwell–Boltzmann statistics but the distribution for the relative kinetic energy of bonded atoms does not. The principle of local equilibrium (PLE) commonly used in nonequilibrium theories to model irreversible systems is investigated through NEMD simulation at extreme conditions of bond formation and breakup at the reservoir ends in the presence of a temperature gradient, where for this study a simple and novel difference equation algorithm to test the divergence theorem for mass conservation is utilized, where mass is found to be conserved from the algorithm in the presence of flux currents, in contradiction to at least one aspect of PLE in the linear domain. It is concluded therefore that this principle can be a good approximation at best, corroborating previous purely theoretical results derived from the generalized Clausius Inequality, which proved that the PLE cannot be an exact principle for nonequilibrium systems.      

Statistical mechanics of time independent nondissipative nonequilibrium states

We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent nondissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming that the phase space may be divided into time independent, locally ergodic domains, we argue that within such domains the relative probabilities of microstates are given by the standard Boltzmann weights. In contrast to previous energy landscape treatments that have been developed specifically for the glass transition, we do not impose an a priori knowledge of the interdomain population distribution. Assuming that these domains are robust with respect to small changes in thermodynamic state variables we derive a variety of fluctuation formulas for these systems. We verify our theoretical results using molecular dynamics simulations on a model glass forming system. Nonequilibrium transient fluctuation relations are derived for the fluctuations resulting from a sudden finite change to the system's temperature or pressure and these are shown to be consistent with the simulation results. The necessary and sufficient conditions for these relations to be valid are that the domains are internally populated by Boltzmann statistics and that the domains are robust. The transient fluctuation relations thus provide an independent quantitative justification for the assumptions used in our statistical mechanical treatment of these systems.     

A statistical model for instable thermodynamical systems

A generic model is presented for statistical systems which display thermodynamic features in contrast to our everyday experience, such as infinite and negative heat capacities. Such system are instable in terms of classical equilibrium thermodynamics. Using our statistical model, we are able to investigate states of instable systems which are undefined in the framework of equilibrium thermodynamics. We show that a region of negative heat capacity in the adiabatic environment, leads to a first order like phase transition when the system is coupled to a heat reservoir. This phase transition takes place without a phase coexistence. Nevertheless, all intermediate states are stable due to fluctuations. When two instable system are brought in thermal contact, the temperature of the composed system is lower than the minimum temperature of the individual systems. Generally, the equilibrium states of instable system cannot be simply decomposed into equilibrium states of the individual systems. The properties of instable system depend on the environment, ensemble equivalence is broken.     

Chemical reactions in microdroplets and microbubbles. Thermodynamic approach

In small dispersed systems, the standard chemical potential of the components present in the curved phases is different from the one in phases with a flat interface. Thermodynamic properties of reactions in such systems, at mechanical equilibrium, may be different from those for the same reactions at the same temperature, in a phase with zero curvature. Among these properties, we study here the dependence of the equilibrium constant on the curvature, on the surface tension and on the stoichiometry of the process. Reactions in an electric field are also discussed.     

Die erlangungsfähigkeit des gleichgewichtes in systemen,die aus flüssigkeit und wenigstens aus einer festen phase gebildet sind

The difficulties associated with the precise determination of the freezing temperature of different systems containing one, two, or several solid phases are discussed. The “thermal sensitivity test” is suggested for testing whether the precision with which the thermodynamic liquid-solid phase equilibrium, is restored is quite satisfactory.The static method makes it possible to introduce or to remove very small quantities of heat and to observe whether or not the restoration of the phase equilibrium takes place. If a kinetic method is applied, the “thermal sensitivity” of the system may be tested by comparing the solidification and the melting curves determined at different crystallization or melting velocities.     

Harmonic electron correlation operator

An appealing way to model electron correlation within the single determinant wave function formalism is through the expectation value of a linear two-electron operator. For practical reasons, it is desirable for such an operator to be universal, i.e., not depend on the positions and types of nuclei in a molecule. We show how a perturbation theory applied to a hookium atom provides for a particular form of a correlation operator, hence called the harmonic correlation operator. The correlation operator approach is compared and contrasted to the traditional ways to describe electron correlation. To investigate the two-electron approximation of this operator, we apply it to many-electron hookium systems. To investigate the harmonic approximation, we apply it to the small atomic systems. Directions of future research are also discussed.     

A simulation method for the calculation of chemical potentials in small, inhomogeneous, and dense systems

We present a modification of the gauge cell Monte Carlo simulation method [A. V. Neimark and A. Vishnyakov, Phys. Rev. E 62, 4611 (2000)] designed for chemical potential calculations in small confined inhomogeneous systems. To measure the chemical potential, the system under study is set in chemical equilibrium with the gauge cell, which represents a finite volume reservoir of ideal particles. The system and the gauge cell are immersed into the thermal bath of a given temperature. The size of the gauge cell controls the level of density fluctuations in the system. The chemical potential is rigorously calculated from the equilibrium distribution of particles between the system cell and the gauge cell and does not depend on the gauge cell size. This scheme, which we call a mesoscopic canonical ensemble, bridges the gap between the canonical and the grand canonical ensembles, which are known to be inconsistent for small systems. The ideal gas gauge cell method is illustrated with Monte Carlo simulations of Lennard-Jones fluid confined to spherical pores of different sizes. Special attention is paid to the case of extreme confinement of several molecular diameters in cross section where the inconsistency between the canonical ensemble and the grand canonical ensemble is most pronounced. For sufficiently large systems, the chemical potential can be reliably determined from the mean density in the gauge cell as it was implied in the original gauge cell method. The method is applied to study the transition from supercritical adsorption to subcritical capillary condensation, which is observed in nanoporous materials as the pore size increases.     

Temperature dependence of inhomogeneous broadening: on the meaning of isosbestic points

An isosbestic point in the temperature dependence of an absorption spectrum is commonly viewed as a sign of interconverting chemical or structural species. Here I explore an alternative microscopic origin of temperature-independent absorbance in inhomogeneously broadened spectra: While the equilibrium probability of observing a particular frequency generally changes with the magnitude of thermal fluctuations, the weight of at least one frequency is insensitive to small changes in temperature. The range of temperature accessible to aqueous solutions at ambient pressure is sufficiently small that such insensitivity would appear in experiments as an isosbestic point. This mechanism depends only on the continuity of equilibrium distributions, not on the presence of multiple components. Even the simplest model of a single solute species in a fluctuating environment exhibits isosbestic points, van't Hoff behavior, and, with appropriate dependence of transition frequency on configuration, multiple absorption peaks.     

Negative thermal expansion in single-component systems with isotropic interactions

We have devised an isotropic interaction potential that gives rise to negative thermal expansion (NTE) behavior in equilibrium many-particle systems in both two and three dimensions over a wide temperature and pressure range (including zero pressure). An optimization procedure is used in order to find a potential that yields a strong NTE effect. A key feature of the potential that gives rise to this behavior is the softened interior of its basin of attraction. Although such anomalous behavior is well-known in material systems with directional interactions (e.g., zirconium tungstate), to our knowledge, this is the first time that NTE behavior has been established to occur in single-component many-particle systems for isotropic interactions. Using constant-pressure Monte Carlo simulations, we show that as the temperature is increased, the system exhibits negative, zero, and then positive thermal expansion before melting (for both two- and three-dimensional systems). The behavior is explicitly compared to that of a Lennard-Jones system, which exhibits typical expansion upon heating for all temperatures and pressures.     

On the mechanism of photoinduced phase transitions in ternary liquid crystal systems near thermal equilibrium

According to their phase diagram, polyalkyl glycol ether dissolved in ternary solutions (water, alcane, and cyclohexane) lead to the formation of either liquid crystal phases or microemulsion phases. By photosensitization of the ternary system with laser dyes and choosing the adequate concentration and temperature conditions of these lyotropic systems, it is possible to photoinduce the phase transitions from the microemulsion phase to the liquid crystal phase (and vice versa). The phototransformation conditions were chosen in such a way that the system is in thermal equilibrium during the entire phase transition. The method of photo small angle x-ray scattering has been applied to investigate the mechanism of photoinduced phase transition. Spectroscopically, the mechanism of photoinduced phase transition has been characterized by optical absorption and emission techniques.     

Spatially Controlled Out‐of‐Equilibrium Host–Guest System under Electrochemical Control

Self‐assembly to create molecular and nanostructures is typically performed at the thermodynamic minimum. To achieve dynamic functionalities, such as adaptability, internal feedback, and self‐replication, there is a growing focus on out‐of‐equilibrium systems. This report presents the dynamic self‐assembly of an artificial host–guest system at an interface, under control by a dissipative electrochemical process using (electrical) energy, resulting in an out‐of‐equilibrium system exhibiting a supramolecular surface gradient. The gradient, its steepness, rate of formation, and complex surface composition after backfilling, as well as the surface compositions after switching between the different states of the system, are assessed and supported by modelling. Our method shows for the first time an artificial surface‐confined out‐of‐equilibrium system. The electrochemical process parameters provide not only control over the system in time, but also in space.     

Effect of chain stiffness on the morphology of diblock copolymer melts

The authors have studied the microphase separation of symmetric diblock copolymers with variable block stiffness and different block chain lengths using coarse-grained molecular dynamics simulations. The simulation results show that for symmetric diblock copolymers, a combination of chain length and relative stiffness between the blocks may play the major role in determining the equilibrium morphology of the system. When the variation in stiffness between blocks is small, the equilibrium morphology of the diblock system is found to be lamellar; this is also the case for systems with small chain lengths, regardless of the difference in block stiffness. However, in systems with longer chains with modest variation in stiffness between the blocks, an ordered cylindrical phase is formed in which the stiffer blocks form cylinders completely surrounded by the flexible components. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2556–2565, 2009     

New hybrid method for reactive systems from integrating molecular orbital or molecular mechanics methods with analytical potential energy surfaces

A computational approach to calculating potential energy surfaces for reactive systems is presented and tested. This hybrid approach is based on integrated methods where calculations for a small model system are performed by using analytical potential energy surfaces, and for the real system by using molecular orbital or molecular mechanics methods. The method is tested on a hydrogen abstraction reaction by using the variational transition-state theory with multidimensional tunneling corrections. The agreement between the calculated and experimental information depends on the quality of the method chosen for the real system. When the real system is treated by accurate quantum mechanics methods, the rate constants are in excellent agreement with the experimental measurements over a wide temperature range. When the real system is treated by molecular mechanics methods, the results are still good, which is very encouraging since molecular mechanics itself is not at all capable of describing this reactive system. Since no experimental information or additional fits are required to apply this method, it can be used to improve the accuracy of molecular orbital methods or to extend the molecular mechanics method to treat any reactive system with the single constraint of the availability of an analytical potential energy surface that describes the model system.     

Density functional approach to thermodynamics of self-assembly

A local density functional approximation for predicting the surface crystallization of a thermodynamically small system under gravity is described and tested. Using the model of the classical soft-sphere fluid, the state parameters for such systems are identified. A generalized phase diagram based upon the scaling variables is obtained; systems with the same reduced-state parameters exhibit identical profiles of thermodynamic properties such as density, pressure, and intrinsic chemical potential, measured in the direction of the applied field. The point-thermodynamic approximation of Rowlinson and the local density approximation of the density functional formalism are found to be remarkably accurate. A configurational temperature is defined and shown to agree with the corresponding kinetic temperature for inhomogeneous systems at equilibrium. The structural profiles at the crystal-fluid interface are indicative of a mesolayer of lower density crystal, not seen in the field-free isobaric crystal-liquid interface.     

Some new microchemical techniques used in the preparation and study of transplutonium elements and compounds

The design of experiments for the thermal reduction of actinidc trifluorides with lithium vapor and for the study of high-temperature phase relationships in transplutonium elements and compounds suggested the need for heating systems of low total heat capacity so that thermal equilibrium could be attained rapidly on both heating and cooling (quenching) of the system. Several such systems are described here that have been used successfully to prepare samples of Cm, Bk, and Cf metals and of Cm and Bk nitrides and that have allowed the study at room temperature of the high-temperature modifications of CfF₃ and metallic Cm. Although the techniques were designed to be compatible with the small size and radioactivity of the transplutonium element samples, they are seen as generally applicable techniques for other microscale investigations.     

Liquid–liquid phase equilibrium of methanol + ethylbenzene + isooctane + ethanol system at 303 K

The phase equilibrium data for methanol + ethanol + isooctane systems were obtained at 303.15 K. Data for methanol + ethylbenzene + isooctane system were taken from literature. The effect of ethanol addition on the system equilibrium was investigated at the same temperature. The distribution curves for ternary and quaternary system was analyzed. The experimental results for ternary systems were correlated with UNIQUAC and NRTL equations. For the ternary systems studied here, the NRTL equation is more accurate than the UNIQUAC. The equilibrium data for the three ternary systems were used to determine interactions parameters for the UNIQUAC equation. For the quaternary system, the experimental data can be fitted more accurately to UNIQUAC equation than by the UNIFAC method.