Dependence of the fragility of a glass former on the softness of interparticle interactions

We study the influence of the softness of the interparticle interactions on the fragility of a glass former by considering three model binary mixture glass formers. The interaction potential between particles is a modified Lennard-Jones type potential, with the repulsive part of the potential varying with an inverse power q of the interparticle distance, and the attractive part varying with an inverse power p. We consider the combinations (12,11) (model I), (12,6) (model II), and (8,5) (model III) for (q,p) such that the interaction potential becomes softer from model I to III. We evaluate the kinetic fragilities from the temperature variation of diffusion coefficients and relaxation times, and a thermodynamic fragility from the temperature variation of the configurational entropy. We find that the kinetic fragility increases with increasing softness of the potential, consistent with previous results for these model systems, but at variance with the thermodynamic fragility, which decreases with increasing softness of the interactions, as well as expectations from earlier results. We rationalize our results by considering the full form of the Adam-Gibbs relation, which requires, in addition to the temperature dependence of the configurational entropy, knowledge of the high temperature activation energies in order to determine fragility. We show that consideration of the scaling of the high temperature activation energy with the liquid density, analyzed in recent studies, provides a partial rationalization of the observed behavior.     

Critical dynamics of dimers: implications for the glass transition

The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy-vanishing phase transition and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments, and numerical diagonalizations of the master equation, we find nonexponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics.     

Spatially heterogeneous dynamics and the Adam-Gibbs relation in the Dzugutov liquid

We perform molecular dynamics simulations of a one-component glass-forming liquid and use the inherent structure formalism to test the predictions of the Adam-Gibbs (AG) theory and to explore the possible connection between these predictions and spatially heterogeneous dynamics. We calculate the temperature dependence of the average potential energy of the equilibrium liquid and show that it obeys the Rosenfeld-Tarazona T(3/5) law for low temperature T, while the average inherent structure energy is found to be inversely proportional to temperature at low T, consistent with a Gaussian distribution of potential energy minima. We investigate the shape of the basins around the local minima in configuration space via the average basin vibrational frequency and show that the basins become slightly broader upon cooling. We evaluate the configurational entropy S(conf), a measure of the multiplicity of potential energy minima sampled by the system, and test the validity of the AG relation between S(conf) and the bulk dynamics. We quantify the dynamically heterogeneous motion by analyzing the motion of particles that are mobile on short and intermediate time scales relative to the characteristic bulk relaxation time. These mobile particles move in one-dimensional "strings", and these strings form clusters with a well-defined average cluster size. The AG approach predicts that the minimum size of cooperatively rearranging regions (CRR) of molecules is inversely proportional to S(conf), and recently (Phys. Rev. Lett. 2003, 90, 085506) it has been shown that the mobile-particle clusters are consistent with the CRR envisaged by Adam and Gibbs. We test the possibility that the mobile-particle strings, rather than clusters, may describe the CRR of the Adam-Gibbs approach. We find that the strings also follow a nearly inverse relation with S(conf). We further show that the logarithm of the time when the strings and clusters are maximum, which occurs in the late-beta-relaxation regime of the intermediate scattering function, follows a linear relationship with 1/TS(conf), in agreement with the AG prediction for the relationship between the configurational entropy and the characteristic time for the liquid to undergo a transition to a new configuration. Since strings are the basic elements of the clusters, we propose that strings are a more appropriate measure of the minimum size of a CRR that leads to configurational transitions. That the cluster size also has an inverse relationship with S(conf) may be a consequence of the fact that the clusters are composed of strings.     

Study of viscometric properties of L-ascorbic acid in binary aqueous mixtures of D-glucose and D-fructose

The relative viscosities and activation parameters of L-ascorbic acid have been determined in water and binary aqueous mixtures of D-glucose and D-fructose at different temperatures. A and B-coefficients of Jones–Dole equation are determined using density and viscosity data. Gibbs energy of activation of viscous flow per mole of solvent as well as per mole of solute along with activation enthalpy and entropy is also determined using Feakin’s transition-state theory. The obtained results are explained in terms of intermolecular interactions and in this study L-ascorbic acid has been found as structure breaker in binary aqueous mixtures of D-glucose and D-fructose.     

Comparison of kinetic Monte Carlo and molecular dynamics simulations of diffusion in a model glass former

We present results from kinetic Monte Carlo (KMC) simulations of diffusion in a model glass former. We find that the diffusion constants obtained from KMC simulations have Arrhenius temperature dependence, while the correct behavior, obtained from molecular dynamics simulations, can be super-Arrhenius. We conclude that the discrepancy is due to undersampling of higher-lying local minima in the KMC runs. We suggest that the relevant connectivity of minima on the potential energy surface is proportional to the energy density of the local minima, which determines the "inherent structure entropy." The changing connectivity with potential energy may produce a correlation between dynamics and thermodynamics.     

Configurational entropy of interacting particles adsorbed on one-dimensional channels arranged in a triangular structure

The configurational entropy of interacting particles adsorbed on one-dimensional channels arranged in a triangular cross-sectional structure is studied by combining Monte Carlo simulation and thermodynamic integration method. Three different energies have been considered in the adsorption process: (1) epsilono, constant interaction energy between a monomer and an adsorption site; (2) wL, interaction energy between nearest-neighbor particles adsorbed along a single channel, and (3) wT, interaction energy between particles adsorbed across nearest-neighbor channels. Special attention is devoted to the case of repulsive transversal interactions (wT>0), for which a rich variety of ordered phases are observed in the adlayer, depending on the value of the parameters kBT/wT (being kB the Boltzmann constant) and wL/wT. The influence of each ordered structure on the configurational entropy of the adlayer has been analyzed and discussed in the context of the lattice-gas model.     

Configurational entropy of binary hard-disk glasses: nonexistence of an ideal glass transition

We study the thermodynamics of a binary hard-disk mixture in which the ratio of disk diameters is kappa=1.4. We use a recently developed molecular dynamics algorithm to calculate the free-volume entropy of glassy configurations and obtain the configurational entropy (degeneracy) of the supercompressed liquid as a function of density. We find that the configurational entropy of the glasses near the kinetic glass transition is very close to the mixing entropy, suggesting that the degeneracy is zero only for the phase-separated crystal. We explicitly construct an exponential number of jammed packings with densities spanning the spectrum from the accepted "amorphous" glassy state to the phase-separated crystal, thus showing that there is no ideal glass transition in binary hard-disk mixtures. This construction also demonstrates that the ideal glass, defined as having zero configurational entropy, is not amorphous, but instead is nothing more than a phase-separated crystal. This critique of the presumed existence of an ideal glass parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000)]. We also perform free-energy calculations to determine the equilibrium phase behavior of the system. The calculations predict a first-order freezing transition at a density below the kinetic glass transition. However, this transition appears to be strongly kinetically suppressed and is not observed directly. New simulation techniques are needed in order to gain a more complete understanding of the thermodynamic and kinetic behavior of the binary disk mixture and, in particular, of the demixing process during crystallization.     

Dynamically correlated regions and configurational entropy in supercooled liquids

When a liquid is cooled below its melting temperature, if crystallization is avoided, it forms a glass. This phenomenon, called glass transition, is characterized by a marked increase of viscosity, about 14 orders of magnitude, in a narrow temperature interval. The microscopic mechanism behind the glass transition is still poorly understood. However, recently, great advances have been made in the identification of cooperative rearranging regions, or dynamical heterogeneities, i.e., domains of the liquid whose relaxation is highly correlated. The growth of the size of these domains is now believed to be the driving mechanism for the increase of the viscosity. Recently a tool to quantify the size of these domains has been proposed. We apply this tool to a wide class of materials to investigate the correlation between the size of the heterogeneities and their configurational entropy, i.e., the number of states accessible to a correlated domain. We find that the relaxation time of a given system, apart from a material dependent prefactor, is a universal function of the configurational entropy of a correlated domain. As a consequence, we find that, at the glass transition temperature, the size of the domains and the configurational entropy per unit volume are anticorrelated, as originally predicted by the Adam-Gibbs theory. Finally, we use our data to extract some exponents defined in the framework of the random first-order theory, a recent quantitative theory of the glass transition.     

Solvent response of mixed polymer brushes

We have performed classical density functional theory calculations to study the behavior of mixed polymer brushes tethered to a planar surface. We assume no lateral segregation of the polymer at the grafting density studied and consider an implicit solvent. For a binary mixture of short and long athermal polymer chains, the short chain is compressed while the long chain is stretched compared with corresponding pure polymer chains at the same grafting density, which is consistent with simulation. This results from configurational entropy effects. Furthermore, we add a mean-field interaction for each polymer brush to simulate their different response towards a solvent. The long chain is forced to dislike the solvent more than the short chain. Through the interplay between the solvent effects and configurational entropy effects, a switch of the polymer brush surface (or outer) layer is found with increasing chain length of the long chain. The transition chain length (long chain) increases with increasing the solvent selectivity, and decreases with increasing the grafting density of the long chain. These results can provide guidance for the design of smart materials based on mixed polymer brushes.     

Free energy, entropy, and induced fit in host-guest recognition: calculations with the second-generation mining minima algorithm

This study applies a novel computational method to study molecular recognition for three sets of synthetic hosts: molecular clips, molecular tweezers, and a synthetic barbiturate receptor. The computed standard free energies of binding for the 12 binding reactions agree closely with experiment and provide insight into the roles of configurational entropy, preorganization, and induced fit in the systems studied. The computed changes in configurational entropy are comparable in magnitude to the changes in mean potential plus solvation energy, and they result primarily from changes in the average width of the energy wells upon binding. A strong correlation is observed between the changes in configurational energy and configurational entropy upon binding, resulting in near-linear compensation analogous to classical entropy-enthalpy compensation.     

Phase separation of a binary two-dimensional core-softened fluid

Using molecular dynamics simulations, we study the phase separation in a binary two-dimensional core-softened fluid with different size ratios and concentrations. The correlation functions for both components are analyzed to show the dependence of the configurational structure of the binary fluid on size ratio and concentration. A phase separation diagram is obtained and the structural features of the phase separation are further investigated using the direct imaging method.     

含无规共聚物三元共混体系SMMA-PMMA-SAN相行为

含无规共聚物共混体系的相容性研究正在成为近年来的研究热点 ,因为相容的驱动力来自共聚物分子内不同单体链段间的排斥性相互作用 [1～ 3] .目前研究这类体系还主要采用过份简化的 F- H平均场理论 ,用旨在克服平均场理论缺陷的 Flory状态方程 ( EOS)理论仅局限于研究二元共聚物共混体系[4～ 8] .与三元共混体系相比 ,用 EOS理论预测含两个无规共聚物三元体系相行为尚需确定共聚物 -共聚物间的二元参数 sj/si,Xij和 Qij.若用 Ax B1- x和 Cy D1- y分别代表共聚物 1和 2 ,则 A,B,C,D代表相应共聚物中的单体单元 ,x,y分别是 1和 2的共…     

Designing generalized statistical ensembles for numerical simulations of biopolymers

Conformational properties of polymers, such as average dihedral angles or molecular alpha-helicity, display a rather weak dependence on the detailed arrangement of the elementary constituents (atoms). We propose a computer simulation method to explore the polymer phase space using a variant of the standard multicanonical method, in which the density of states associated to suitably chosen configurational variables is considered in place of the standard energy density of states. This configurational density of states is used in the Metropolis acceptance/rejection test when configurations are generated with the help of a hybrid Monte Carlo algorithm. The resulting configurational probability distribution is then modulated by exponential factors derived from the general principle of the maximal constrained entropy by requiring that certain average configurational quantities take preassigned (possibly temperature dependent) values. Thermal averages of other configurational quantities can be computed by using the probability distributions obtained in this way. Moments of the energy distribution require an extra canonical sampling of the system phase space at the desired temperature, in order to locally thermalize the configurational degrees of freedom. As an application of these ideas we present the study of the structural properties of two simple models: a bead-and-spring model of polyethylene with independent hindered torsions and an all-atom model of alanine and glycine oligomers with 12 amino acids in vacuum.     

Determining landscape-based criteria for freezing of liquids

The correlation between statistical properties of the energy landscape and the number of accessible configurational states, as measured by the exponential of the excess entropy (e(Se)), are studied in the case of a simple Lennard-Jones-type liquid in the neighborhood of the thermodynamic freezing transition. The excess entropy Se is defined as the difference between the entropy of the liquid and that of the ideal gas under identical temperature and pressure conditions and is estimated using the pair correlation contribution, S2. Landscape properties associated with three categories of configurations are considered: instantaneous configurations, inherent saddles, and inherent minima. Landscape properties studied include the energy and the key parameters of the Hessian eigenvalue distribution as well as the mean distances between instantaneous configurations and the corresponding inherent saddles and minima. The signatures of the thermodynamic freezing transition are clearest in the case of inherent structure properties which show, as a function of e(S2), a pronounced change in slope in the vicinity of the solid-liquid coexistence. The mean distance between instantaneous and saddle configurations also shows a similar change in slope when the system crosses from the stable to the supercooled regime. In the case of inherent saddles, the minimum eigenvalue acts as a similar indicator of the thermodynamic freezing transition but the average and maximum eigenvalues do not carry similar signatures. In the case of instantaneous configurations, a weak indicator of the thermodynamic freezing transition is seen in the behavior of the fraction of negative curvature directions as a function of the exponential of the excess entropy.     

Molecular dynamics simulation of discontinuous volume phase transitions in highly-charged crosslinked polyelectrolyte networks with explicit counterions in good solvent

The volumetric properties of highly-charged defect-free polyelectrolyte networks with tetrafunctional crosslinks are studied through molecular dynamics simulations in the canonical ensemble. The network backbone monomers, which are monovalent, and the counterions, which are mono-, di-, or trivalent, are modeled explicitly in the simulations, but the solvent is treated implicitly as a dielectric medium of good solvation quality. The osmotic pressure of the network-solvent system is found to depend greatly on the strength of electrostatic interactions. Discontinuous volume phase transitions are observed when the electrostatic interactions are strong, and the onset of these transitions shifts to higher solvent dielectricity as the counterion valency increases. The roles of the various virial contributions to the osmotic pressure are examined. The network elasticity entropy is found to behave nearly classically. As the network contracts and collapses with increasing strength of electrostatic interactions, the loss of counterion entropy leads to increased counterion osmotic pressure contributions via two mechanisms. The reduction in available configurational space increases the counterion translational entropy contribution to the ideal part of the osmotic pressure, and the greater number of counterion-monomer contacts formed due to counterion condensation and confinement increases the counterion excluded-volume entropy contribution to the excess part of the osmotic pressure. These observations contrast the decrease in the single ideal-gas-like counterion translational entropy contribution to the osmotic pressure predicted by the counterion condensation-charge renormalization theory. An accompanying decrease in the total electrostatic energy balances the loss of counterion excluded-volume entropy as the polyelectrolyte networks collapse in low-dielectric solvents. This interplay between the electrostatic energy and the counterion excluded-volume entropy appears to be responsible for the discontinuous volume phase transitions that are observed in polyelectrolyte networks. The structure of the polyelectrolyte network is also found to be affine in the swollen state, with constituent chains nearly fully extended, and nonaffine in the collapsed state, with the chains adopting a Gaussian conformation.     

Cylindrical inclusions in a copolymer membrane

The membrane-mediated interaction between two parallel, cylindrical inclusions is investigated by using the self-consistent field theory (SCFT). The rodlike inclusions are located within the interior of the bilayer and are enveloped by two monolayers. They may exhibit one of the two basic types of behaviors involving pinching two monolayers together and swelling them outward. For different parameters, we calculate the density profile of the deformation membrane, the associated interaction free energy, as well as the conformational entropy of polymer chains. The similarity of the two types of interaction potentials is the qualitative characteristics. An energy barrier separates an attractive from a repulsive region; the repulsive region is preceded by a weak attraction at a large distance. The difference between them, which is due to the different contact environments around the rods, lies in the appearance of a small barrier at a short distance in the pinching structure. Particular emphasis is put on the closely energetic and entropic analyses of the interaction potential. We show that the chemical potential energy has provided a qualitative trend and roughly dominated the basic shape of the interaction potential; the amphiphile entropy in the swelling structure and the solvent entropy in the pinching structure, combined with the corresponding chemical potential energy, are responsible for the repulsive barrier at an intermediate distance and for the weak attraction at a large distance, respectively. The influence of inclusion hydrophobicity on the interaction potential is taken into account. In particular, the pinching and swelling structures can appear and can transform into each other in a system at intermediate hydrophobicity.     

Blind prediction of SAMPL4 cucurbit[7]uril binding affinities with the mining minima method

Accurate methods for predicting protein–ligand binding affinities are of central interest to computer-aided drug design for hit identification and lead optimization. Here, we used the mining minima (M2) method to predict cucurbit[7]uril binding affinities from the SAMPL4 blind prediction challenge. We tested two different energy models, an empirical classical force field, CHARMm with VCharge charges, and the Poisson–Boltzmann surface area solvation model; and a semiempirical quantum mechanical (QM) Hamiltonian, PM6-DH+, coupled with the COSMO solvation model and a surface area term for nonpolar solvation free energy. Binding affinities based on the classical force field correlated strongly with the experiments with a correlation coefficient (R²) of 0.74. On the other hand, binding affinities based on the QM energy model correlated poorly with experiments (R² = 0.24), due largely to two major outliers. As we used extensive conformational search methods, these results point to possible inaccuracies in the PM6-DH+ energy model or the COSMO solvation model. Furthermore, the different binding free energy components, solute energy, solvation free energy, and configurational entropy showed significant deviations between the classical M2 and quantum M2 calculations. Comparison of different classical M2 free energy components to experiments show that the change in the total energy, i.e. the solute energy plus the solvation free energy, is the key driving force for binding, with a reasonable correlation to experiment (R² = 0.56); however, accounting for configurational entropy further improves the correlation.     

基于液态合金短程序的混合构型熵新模型

基于液态合金化学短程序与拓扑短程序发展了一个新的混合构型熵计算模型, 从这个模型可以导出用来描述等原子直径随机混合物的理想混合熵. 通过将该模型应用于一些理想的和真实的液态二元合金, 可以看到化学短程序减小了混合构型熵, 而原子尺寸差异的影响则较为复杂. 当大原子进入小原子基体时, 混合构型熵增大; 而当小原子进入大原子基体时, 混合构型熵减小. 在这些合金中, 共晶成分处并没有出现混合构型熵极大值.     

Polymorphism in AB(13) nanoparticle superlattices: an example of semiconductor-metal metamaterials

Colloidal crystallization of nanoparticles with different functionalities into multicomponent assemblies provides a route to new classes of ordered nanocomposites with novel properties tunable by the choice of the constituent building blocks. While theories based on hard sphere approximation predict crystallization of only a few stable binary phases (NaCl-, AlB(2)- and NaZn(13)-type), we find that additional polymorphs of lower packing density are possible. We demonstrate that PbSe and Pd nanoparticles can be reproducibly crystallized into two polymorphs with AB(13) stoichiometry. One polymorph is isostructural with the intermetallic compound NaZn(13) and is consistent with dense packing of hard spheres driven by entropy. The second unanticipated polymorph is of lower packing density. This observation underscores the shortcomings of applying simple space-filling principles to the crystallization of organically passivated nanocrystals and further motivates the development of models that incorporate combinations of hard-sphere, van der Waals, dipolar, and hydrophobic forces. This work demonstrates that ordered periodic structures with lower packing density are achievable and provides the first example of a binary semiconductor-metal superlattice using a combination of PbSe-Pd nanocrystals.