Free Energy Of Crystal Research Articles

Solid–solid transitions induced by repulsive interactions revisited

We revisit a problem already studied 15 years ago by us in collaboration with Stell and Hemmer: the isostructural solid–solid transitions induced by repulsive particle interactions exhibited by classical systems interacting via the Stell–Hemmer potentials. The full phase diagram in the crystal region is obtained by applying a perturbation theory for classical solids used during our collaboration with Stell. Also, the performance of such a theory is now tested by comparing the perturbative phase diagram with that obtained from computer simulations. The latter was calculated using a recently refined method to obtain the free-energy of crystals by means of Monte Carlo simulations. The perturbation theory captures the correct topology and correctly identifies the stable, fcc and bcc, phases. In addition, the theory predicts the occurrence of special points: a point where the two stable structures coexist at the same density, and two critical points terminating the corresponding isostructural phase transitions for fcc and bcc phases. The location of some of these features in the phase diagram is predicted almost quantitatively. However, phase boundaries involving the non-compact bcc phase are much less accurate, a problem that can be traced to the poor representation used for the bcc phase of the reference, hard-sphere, system.

Shape change in crystallization of biological macromolecules

Abstract

Liquid crystal free energy relaxation by a theoretically informed Monte Carlo method using a finite element quadrature approach.

A theoretically informed Monte Carlo method is proposed for Monte Carlo simulation of liquid crystals on the basis of theoretical representations in terms of coarse-grained free energy functionals. The free energy functional is described in the framework of the Landau-de Gennes formalism. A piecewise finite element discretization is used to approximate the alignment field, thereby providing an excellent geometrical representation of curved interfaces and accurate integration of the free energy. The method is suitable for situations where the free energy functional includes highly non-linear terms, including chirality or high-order deformation modes. The validity of the method is established by comparing the results of Monte Carlo simulations to traditional Ginzburg-Landau minimizations of the free energy using a finite difference scheme, and its usefulness is demonstrated in the context of simulations of chiral liquid crystal droplets with and without nanoparticle inclusions.

A Self-Assembling Octahedral Aggregate of Poly(methyl methacrylate) Nanospheres on a Silver Substrate.

A large-area, self-assembling, octahedral aggregate composed of poly(methyl methacrylate) nanospheres (PMMA-NS) was constructed by using a one-step electrodeposition approach from an aqueous solution containing AgNO3 and PMMA-NS as sacrificial electrolytes. The surface chain geometry of the product was revealed by Raman spectroscopy. The results revealed that the orientation of chains of the PMMA-NS octahedron is different from that of the nonaggregated PMMA-NS because of the interfacial interactions between the polymer chain and Ag metal. This can be explained by the crystal surface free energy of the octahedral Ag substrate, which gives rise to diverse conformations of the PMMA molecular chain at different surface regions of the silver substrate. In addition, the adsorptive properties of PMMA-NS octahedra are such that the adsorbent-adsorbate system is cost-effective, efficient and fast for the removal of dyes from contaminated wastewater.

Crystal nuclei in melts: a Monte Carlo simulation of a model for attractive colloids

As a model for a suspension of hard-sphere-like colloidal particles where small non-adsorbing dissolved polymers create a depletion attraction, we introduce an effective colloid–colloid potential closely related to the Asakura–Oosawa model, but that does not have any discontinuities. In simulations, this model straightforwardly allows the calculation of the pressure from the virial formula, and the phase transition in the bulk from the liquid to crystalline solid can be accurately located from a study where a stable coexistence of a crystalline slab with a surrounding liquid phase occurs. For this model, crystalline nuclei surrounded by fluid are studied both by identifying the crystal–fluid interface on the particle level (using suitable bond orientational order parameters to distinguish the phases) and by ‘thermodynamic’ means, i.e. the latter method amounts to compute the enhancement of chemical potential and pressure relative to their coexistence values. We show that the chemical potential can be obtained from simulating thick films, where one wall with a rather long-range repulsion is present, since near this wall, the Widom particle insertion method works, exploiting the fact that the chemical potential in the system is homogeneous. Finally, the surface excess free energy of the nucleus is obtained, for a wide range of nuclei volumes. From this method, it is established that classical nucleation theory works, showing that for the present model, the anisotropy of the interface excess free energy of crystals and their resulting non-spherical shape has only a very small effect on the barrier.

Crystal structure and free energy of Ti2Ni3 precipitates in Ti–Ni alloys from first principles

First-principles calculations are presented for stable and metastable intermetallic phases of TiNi shape memory alloys. Density functional theory (DFT) is applied to predict the electronically preferred structures of the Ti2Ni3 phases. In the DFT analysis, two modifications of Ti2Ni3 phase are distinguished, the low-temperature orthorhombic and the high-temperature tetragonal structure. Enthalpies of formation at 0K and atomic coordinates of the unit cells of Ti2Ni3 modifications are reported. Based on refined atom positions, the enthalpy of formation at 0K of cubic TiNi (B2), hexagonal TiNi3 (D024) and rhombohedral Ti3Ni4 (R-3 phase) are optimized and compared to existing data from literature. Lattice constants of the investigated phases are consistent with experimental measurements.

Thermal vacancies in close-packing solids

We derive an approximate expression for the equilibrium concentration of thermal monovacancies in solids which allows for a transparent interpretation of the vacancy volume and the energetic/entropic part in the corresponding Gibbs energy of vacancy formation . For the close-packing crystals of the hard-sphere and Lennard-Jones model systems, very good agreement with simulation data is found. Application to metals through the embedded-atom method (EAM) reveals a strong sensitivity of the variation of with temperature to details of the EAM potential. Our result allows for an approximate, but direct measurement of crystal free energies and vacancy concentration in colloidal model systems using laser tweezers.

Redox process catalysed by growing crystal—strengite, FePO4,2H2O, crystallizing from solution with iron(II) and hydroxylamine

In an attempt to grow pure crystals of the iron(II) phosphate vivianite, Fe3(PO4)2,8H2O, from a solution of Mohr's salt, Fe(NH4)2(SO4)2,6H2O, added to a solution of ammonium phosphate, hydroxylammonium chloride, NH3OHCl, was added to the iron(II) stock solution to eliminate oxidation of iron(II) by oxygen from the air. However, the effect turned out to be the opposite of the expected: whereas hydroxylamine reduces iron(III) in bulk solution, it acted as a strong oxidant in the presence of growing iron phosphate crystals, causing the crystallization of the iron(III) phosphate strengite, FePO4,2H2O, as the only solid phase. Evidently the crystal surface catalyses oxidation of iron(II) by hydroxylamine. The usual composite kinetics of spiral growth and surface nucleation was found. The surface-nucleation part yielded edge free energy λ in the range 12–45pJ/m, virtually independent of temperature and in the range typical for phosphates of divalent metals. The scatter of values for λ presumably arises from contributions from different crystal forms to the overall growth rate. The low mean value points to strong adsorption of iron(II), which is subsequently oxidized at the crystal surface, forming strengite. The state of the system did not tend to thermodynamic equilibrium, but to a metastable state, presumably controlled by the iron(II) rich surface layer of the crystal. In addition to crystal growth, it was possible to measure nucleation kinetics by light scattering (turbidimetry). A point of transition from heterogeneous to homogeneous nucleation was found, and from the results for the homogeneous domain a rather precise value of crystal surface free energy γ=55mJ/m2 was found. This is a relatively low value as well, indicating that the redox process plays a role already at the nucleation stage.

Understanding the Formation of Pentagonal Cyclic Twinned Crystal from the Solvent Dependent Assembly of Au Nanocrystals into Their Colloidal Crystals

Due to the presence of high-density twinned-defects and diffuse elastic strain, pentagonal cyclic twinning (PCT) structures may have more fascinating properties than the corresponding single crystalline structure. Although there are a lot of reports concerning the PCT nanocrystals of many monometals and bimetal alloys, the established growth mechanisms of PCT structures are still not straightforward and usually inconsistent with each other. In this Letter, using dodecanethiol-capped Au nanocrystals (NCs) as building blocks, taking self-assembly of Au NCs into their colloidal crystals as the crystallization model, we found the competition of crystal cohesive energy and surface free energy plays an important role in the formation of PCT colloidal crystal. By rationally selecting the solvent to tailor the crystal cohesive energy, the structure of the colloidal crystals can be tuned. PCT structures are more likely to form when the interaction between building blocks is weak, while the single crystal structure is formed when the interaction is strong. The results demonstrate that the thermodynamic factors are the origin of pentagonal cyclic twinning.

Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres

We propose an Einstein-solid, self-consistent phonon theory for the crystal phase of hard spheres that interact via short-range attractions. The approach is first tested against the known behavior of hard spheres, and then applied to homogeneous particles that interact via short-range square well attractions and the Baxter adhesive hard sphere model. Given the crystal symmetry, packing fraction, and strength and range of attractive interactions, an effective harmonic potential experienced by a particle confined to its Wigner-Seitz cell and corresponding mean square vibrational amplitude are self-consistently calculated. The crystal free energy is then computed and, using separate information about the fluid phase free energy, phase diagrams constructed, including a first-order solid-solid phase transition and its associated critical point. The simple theory qualitatively captures all the many distinctive features of the phase diagram (critical and triple point, crystal-fluid re-entrancy, low-density coexistence curve) as a function of attraction range, and overall is in good semi-quantitative agreement with simulation. Knowledge of the particle localization length allows the crystal shear modulus to be estimated based on elementary ideas. Excellent predictions are obtained for the hard sphere crystal. Expanded and condensed face-centered cubic crystals are found to have qualitatively different elastic responses to varying attraction strength or temperature. As temperature increases, the expanded entropic solid stiffens, while the energy-controlled, fully-bonded dense solid softens.

First-Principles Calculation of the Intrinsic Aqueous Solubility of Crystalline Druglike Molecules

We demonstrate that the intrinsic aqueous solubility of crystalline druglike molecules can be estimated with reasonable accuracy from sublimation free energies calculated using crystal lattice simulations and hydration free energies calculated using the 3D Reference Interaction Site Model (3D-RISM) of the Integral Equation Theory of Molecular Liquids (IET). The solubilities of 25 crystalline druglike molecules taken from different chemical classes are predicted by the model with a correlation coefficient of R = 0.85 and a root mean square error (RMSE) equal to 1.45 log10S units, which is significantly more accurate than results obtained using implicit continuum solvent models. The method is not directly parametrized against experimental solubility data, and it offers a full computational characterization of the thermodynamics of transfer of the drug molecule from crystal phase to gas phase to dilute aqueous solution.

A theory of polymer crystallization kinetics influenced by magnetic field

The mechanism of the magnetic field influence on polymer bulk crystallization has been discussed, which included nucleation and crystal growth. We have constructed relative equations of crystallization kinetics based on the classic thermodynamic theory. The equations show that the “magnetocrystallization effect” (MCE) caused by the difference of magnetic energy between crystal and amorphous phases. It came from the difference of magnetic susceptibilities between crystal and amorphous phases. The “like-liquid-crystal phase” induced by magnetic field in some polymer is another possible reason of MCE, which have low entropy and change the free energy in crystallization. They could affect the process of nucleation, crystal growth, the entire formula of crystal kinetics. We used “Matlab” software to figure the function of nucleation critical parameters and crystal free energy, the pictures indicated that small free energy changed by the temperature or magnetic field could greatly impact on the values of nucleation critical parameter with low degree of supercooling.

The Effect of Inorganic Nanoadditives on the Thermal, Mechanical and UV Radiation Barrier Properties of Polypropylene Fibres

The objective of this study of modified polypropylene (PP) fibres using nanoadditives (nano-CaCO3 and Cloisite 30B) was to determine the influence of these additives on thermal and mechanical properties, but especially on the barrier properties of the nanocomposite fibres against UV radiation. The DSC data obtained from measurements of PP/CaCO3 or PP/C30B nanocomposite fibres were used for determination of the constants n and K of the Avrami equation and in the estimation of other thermal properties of the fibres, such as their crystallization half-time t1/2, rate of crystallization t1/2, the necessary time for maximum crystallization tmax and free energy per unit area of surface in the lamella perpen-dicular to the axis of a high-molecular chain se. The nano-CaCO3 or Closite 30B fillers (pre-treated separately in three different solvents: glycerine, acetone and water) did not influence the melting temperatures but caused an increase in PP crystallization temperatures in comparison with the pure PP fibres. The pre-treatments of nanoadditives resulted in increase of n, K, t1/2 values and decrease of t1/2, tmax as well as the values of free surface energies per unit area of the modified PP fibres. There was also observed a decrease in the mechanical properties, however, there was an increase of barrier properties against UV radiation of nanocomposite PP fibres in comparison with neat PP fibres, which was one of the main objectives of the study.

Morphology engineering of ZnO nanostructures

Nanosized ZnO structures were grown by atmospheric pressure metalorganic chemical vapor deposition (APMOCVD) in the temperature range 200–500°C at variable precursor pressure. Temperature induced evolution of the ZnO microstructure was observed, resulting in regular transformation of the material from conventional polycrystalline layers to hierarchically arranged sheaves of ZnO nanowires. The structures obtained were uniformly planarly located over the substrate and possessed as low nanowires diameter as 30–45nm at the tips. The observed growth evolution is explained in terms of ZnO crystal planes free energy difference and growth kinetics. For comparison, the convenient growth at constant precursor pressure on Si and SiC substrates has been performed, resulting in island-type grown ZnO nanostructures. The demonstrated nanosized ZnO structures may have unique possible areas of application, which are listed here.

Modeling Multiple Time Scales during Glass Formation with Phase-Field Crystals

The dynamics of glass formation in monatomic and binary liquids are studied numerically using a microscopic field theory for the evolution of the time-averaged atomic number density. A stochastic framework combining phase-field crystal free energies and dynamic density functional theory is shown to successfully describe several aspects of glass formation over multiple time scales. Agreement with mode coupling theory is demonstrated for underdamped liquids at moderate supercoolings, and a rapidly growing dynamic correlation length is found to be associated with fragile behavior.

Metastable zone width for secondary nucleation and secondary nucleation inside the metastable zone

AbstractThis study presents an evaluation of a new method, called zero growth activation free energy, used to determine the metastable zone width for the secondary nucleation case. It predicts the metastable zone width with a maximum error of 5‐10%. Estimation of the metastable zone width for different isothermal crystallization conditions can be modeled according to a chosen reference set of growth experiments carried out in the volume diffusion regime at different initial supersaturations, using seed crystals of a certain characteristic size. Moreover, the activation free energy of the secondary nucleation was estimated. The role of the enthalpy of immersion in the formation of secondary nucleation events inside the metastable zone was pointed out, as well as its effect in causing extra‐fast growth rate. Furthermore, sucrose crystal surface free energy was estimated. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Structure prediction, disorder and dynamics in a DMSO solvate of carbamazepine

We have applied crystal structure prediction methods to understand and predict the formation of a DMSO solvate of the anti-convulsant drug carbamazepine (CBZ), in which the DMSO molecules are disordered. Crystal structure prediction calculations on the 1:1 CBZ:DMSO solvate revealed the generation of two similar low energy structures which differ only in the orientation of the DMSO molecules. Analysis of crystal energy landscapes generated at 0 K suggests the possibility of solvent disorder. A combined computational and experimental study of the changes in the orientation of the DMSO within the crystal structure revealed that the nature of the disorder changes with temperature. At low temperature, the DMSO disorder is static whilst at high temperature the DMSO configurations can interconvert by a 180° rotation of the DMSO molecules within the lattice. This 180° rotation of the DMSO molecules drives a phase change from a high temperature dynamically disordered phase to a low temperature phase with static disorder. Crystallisation of a DMSO solvate of the related molecule epoxycarbamazepine resulted in a different degree of DMSO disorder in the crystal structure, despite the similarity of the carbamazepine and epoxycarbamazepine molecules. We believe consideration of disorder and its contribution to entropy and crystal free energies at temperature other than 0 K is fundamental for the accuracy of future energy rankings in crystal structure prediction calculations of similar solvated structures.

Analysis of Influencing Factors on the Structure and Surface Properties of Palygorskite

The relationship between surface properties and water vapor absorption performance was studied according to crystal structure and surface free energy of purified palygorskite. The results show that the unit cell volume of samples increases along with the increase of temperature ranging from 0 to 200 °C, leading to the increase of water vapor absorption. The intensity of diffraction peak, crystal plane spacing and unit cell volume decrease with the increase of the heat temperature ranging from 200 to 800°C, leading to the decrease of water vapor absorption. The intensity of diffraction peak almost disappears when the temperature is over 800°C. The palygorskite turns into non-crystallization, and the new phase of diopside appears. The surface free energy and polarity component increase along with the increase of heat-treatment temperature, and the dispersion component is obviously relevant to water vapor absorption performance.

Free energies, vacancy concentrations, and density distribution anisotropies in hard-sphere crystals: A combined density functional and simulation study

We perform a comparative study of the free energies and the density distributions in hard-sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique [T. Schilling and F. Schmid, J. Chem. Phys. 131, 231102 (2009)] we obtain crystal free energies to a high precision. The free energies from fundamental measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between fundamental measure theory and simulations on the level of the free energies is also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it is found that fundamental measure theory gives slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of fundamental measure functionals studied, only the White Bear II functional [H. Hansen-Goos and R. Roth, J. Phys.: Condens. Matter 18, 8413 (2006)] exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.

Nematic Order in Small Systems: Measuring the Elastic and Wall-Anchoring Constants in Vibrofluidized Granular Rods

We investigate nematic order in vibrated granular rods confined to a small quasi-2D container less than 10 rod lengths in diameter. As rod density ρ increases, patterning shifts from bipolar to uniform alignment. We find that a continuum liquid crystal free energy functional captures key patterning features down to almost the particle size. By fitting theory to experiments, we estimate the relative values of bend and splay elastic constants and wall anchoring. We find that splay is softer than bend for all ρ and rod lengths tested, while the ratio of the average elastic constant to wall anchoring increases with ρ.