Search

Glass as a material was already known in ancient Egypt. Now its use for windows, bottles, etc. is very common; thus, it may sound surprising that the glassy state of matter and the transition from an undercooled melt to this state are grand challenge problems of physics. This article describes the basic concepts; then it points out how the discovery of “spin glasses” and the theory by Giorgio Parisi has given a new boost to the interest in these problems. The status of a theory of the glass transition will be critically discussed.

Lignin is the second most abundant biopolymer on earth and accrues in large amounts in the pulp- and paper industry. While currently lignins are mainly used for low-value applications such as energy production, recently the potential of laccases for upgrading lignins has been demonstrated. In this study, two laccases of fungal and bacterial origin were characterized regarding their potential to polymerize lignosulfonate. The laccases MaL1 from Melanocarpus albomyces, and SrLA from Streptomyces rochei were heterologously expressed and showed typical characteristics of laccases, like acidic pH optima for ABTS at pH 4 and 5, respectively, and temperature optima at 50 °C and 80 °C. Polymerization of lignosulfonate with MaL1 led to an almost two-fold increase of the molecular weight, according to size exclusion (SEC) multiangle laser light scattering (MALLS) analysis. In contrast, SrLA showed considerably less activity on lignosulfonates, as measured based on oxygen consumption and SEC-MALLS.

A tutorial introduction to the statistical mechanics of phase transitions and phase coexistence is presented, starting out from equilibrium systems and nonequilibrium steady-state situations in ext...

Binary mixtures of semiflexible polymers with the same chain length, but different persistence lengths, separate into two coexisting different nematic phases when the osmotic pressure of the lyotropic solution is varied. Molecular Dynamics simulations and Density Functional Theory predict phase diagrams either with a triple point, where the isotropic phase coexists with two nematic phases or a critical point of unmixing within the nematic mixture. The difference in locally preferred bond angles between the constituents drives this unmixing without any attractive interactions between monomers.

The interplay of the isotropic-nematic transition and phase separation in lyotropic solutions of two types of semiflexible macromolecules with pronounced difference in chain stiffness is studied by Density Functional Theory and Molecular Dynamics simulations. While the width of the isotropic-nematic two-phase coexistence region is narrow for solutions with a single type of semiflexible chain, the two-phase coexistence region widens for solutions containing two types of chains with rather disparate stiffness. In the nematic phase, both types of chains contribute to the nematic order, with intermediate values of the order parameter compared to the corresponding single component solutions. As the difference in bending stiffness is increased, the two chain types separate into two coexisting nematic phases. The phase behavior is rationalized by considering the chemical potentials of the two components and the Gibbs excess free energy. The geometric properties of the chain conformations under the various conditions are also discussed.

Mixtures of semiflexible polymers with a mismatch in either their persistence lengths or their contour lengths are studied by Density Functional Theory and Molecular Dynamics simulation. Considering lyotropic solutions under good solvent conditions, the mole fraction and pressure is systematically varied for several cases of bending stiffness κ (the normalized persistence length) and chain length N. For binary mixtures with different chain length (i.e., NA=16, NB=32 or 64) but the same stiffness, isotropic-nematic phase coexistence is studied. For mixtures with the same chain length (N=32) and large stiffness disparity (κB/κA=4.9 to 8), both isotropic-nematic and nematic-nematic unmixing occur. It is found that the phase diagrams may exhibit a triple point or a nematic-nematic critical point, and that coexisting phases differ appreciably in their monomer densities. The properties of the two types of chains (nematic order parameters, chain radii, etc.) in the various phases are studied in detail, and predictions on the (anisotropic) critical behavior near the critical point of nematic-nematic unmixing are made.

Sodium chloride (NaCl) is one of the key components of atmospheric aerosols. The surface tension of aqueous NaCl solution (σNaCl,sol) and its concentration dependence are essential to determine the equilibrium water vapor pressure of aqueous NaCl droplets. Supersaturated NaCl solution droplets are observed in laboratory experiments and under atmospheric conditions, but the experimental data for σNaCl,sol are mostly limited up to subsaturated solutions. In this study, the surface tension of aqueous NaCl is investigated by molecular dynamics (MD) simulations and the pressure tensor method from dilute to highly supersaturated solutions. We show that the linear approximation of concentration dependence of σNaCl,sol at molality scale can be extended to the supersaturated NaCl solution until a molality of ∼10.7 mol kg−1 (i.e., solute mass fraction (xNaCl) of ∼0.39). Energetic analyses show that this monotonic increase in surface tension is driven by the increase in excess surface enthalpy (ΔH) as the solution becomes concentrated. After that, the simulated σNaCl,sol remains almost unchanged until xNaCl of ∼0.47 (near the concentration upon efflorescence). The existence of the “inflection point” at xNaCl of ∼0.39 and the stable surface tension of xNaCl between ∼0.39 and ∼0.47 can be attributed to the nearly unchanged excess surface entropy term (T⋅ΔS) and the excess surface enthalpy term (ΔH). After a “second inflection point” at xNaCl of ∼0.47, the simulated σNaCl,sol gradually regains the growing momentum with a tendency to approach the surface tension of molten NaCl (∼175.58 mN m−1 at 298.15 K, MD simulation-based extrapolation). This fast increase in σNaCl,sol at xNaCl>0.47 is a process driven by excess surface enthalpy and excess surface entropy. Our results reveal different regimes of concentration dependence of the surface tension of aqueous NaCl at 298.15 K: a water-dominated regime (xNaCl from 0 to ∼0.39), a transition regime (xNaCl from ∼0.39 to ∼0.47) and a molten NaCl-dominated regime (xNaCl from ∼0.47 to 1).

he contact angle of a liquid droplet on a surface under partial wetting conditions differs for a nanoscopically rough or periodically corrugated surface from its value for a perfectly flat surface. Wenzel's relation attributes this difference simply to the geometric magnification of the surface area (by a factor $r_{\rm w}$), but the validity of this idea is controversial. We elucidate this problem by model calculations for a sinusoidal corrugation of the form $z_{\rm wall}(y) = \Delta\cos(2\pi y/\lambda)$ , for a potential of short range $\sigma_{\rm w}$ acting from the wall on the fluid particles. When the vapor phase is an ideal gas, the change of the wall-vapor surface tension can be computed exactly, and corrections to Wenzel's equation are typically of order $\sigma_{\rm w}\Delta/\lambda^2$. For fixed $r_{\rm w}$ and fixed $\sigma_{\rm w}$ the approach to Wenzel's result with increasing $\lambda$ may be nonmonotonic and this limit often is only reached for $\lambda/\sigma_{\rm w}>30$. For a non-additive binary mixture, density functional theory is used to work out the density profiles of both coexisting phases both for planar and corrugated walls, as well as the corresponding surface tensions. Again, deviations from Wenzel's results of similar magnitude as in the above ideal gas case are predicted. Finally, a crudely simplified description based on the interface Hamiltonian concept is used to interpret corresponding simulation results along similar lines. Wenzel's approach is found to generally hold when $\lambda/\sigma_{\rm w}\gg 1$, $\Delta/\lambda

Size-dependent solubility is prevalent in atmospheric nanoparticles, but a molecular level understanding is still insufficient, especially for organic compounds. Here, we performed molecular dynamics simulations to investigate the size dependence of succinic acid solvation on the scale of ~1-4 nm with the potential of mean forces method. Our analyses reveal that the surface preference of succinic acid is stronger for a droplet than the slab of the same size, and the surface propensity is enhanced due to the curvature effect as the droplet becomes smaller. Energetic analyses show that such surface preference is primarily an enthalpic effect in both systems, while the entropic effect further enhances the surface propensity in droplets. On the other hand, with decreasing droplet size, the solubility of succinic acid in the internal bulk volume may decrease, imposing an opposite effect on the size dependence of solubility as compared with the enhanced surface propensity. Meanwhile, structural analyses, however, show that the surface to internal bulk volume ratio increases drastically, especially when considering the surface in respect to succinic acid, e.g., for droplet with radius of 1 nm, the internal bulk volume would be already close to zero for the succinic acid molecule.

When physicians are asked to determine the positive predictive value from the a priori probability of a disease and the sensitivity and false positive rate of a medical test (Bayesian reasoning), it often comes to misjudgments with serious consequences. In daily clinical practice, however, it is not only important that doctors receive a tool with which they can correctly judge—the speed of these judgments is also a crucial factor. In this study, we analyzed accuracy and efficiency in medical Bayesian inferences. In an empirical study we varied information format (probabilities vs. natural frequencies) and visualization (text only vs. tree only) for four contexts. 111 medical students participated in this study by working on four Bayesian tasks with common medical problems. The correctness of their answers was coded and the time spent on task was recorded. The median time for a correct Bayesian inference is fastest in the version with a frequency tree (2:55 min) compared to the version with a probability tree (5:47 min) or to the text only versions based on natural frequencies (4:13 min) or probabilities (9:59 min).The score diagnostic efficiency (calculated by: median time divided by percentage of correct inferences) is best in the version with a frequency tree (4:53 min). Frequency trees allow more accurate and faster judgments. Improving correctness and efficiency in Bayesian tasks might help to decrease overdiagnosis in daily clinical practice, which on the one hand cause cost and on the other hand might endanger patients’ safety.

When systems that can undergo phase separation between two coexisting phases in the bulk are confined in thin film geometry between parallel walls, the phase behavior can be profoundly modified. These phenomena shall be described and exemplified by computer simulations of the Asakura-Oosawa model for colloid-polymer mixtures, but applications to other soft matter systems (e.g. confined polymer blends) will also be mentioned. Typically a wall will prefer one of the phases, and hence the composition of the system in the direction perpendicular to the walls will not be homogeneous. If both walls are of the same kind, this effect leads to a distortion of the phase diagram of the system in thin film geometry, in comparison with the bulk, analogous to the phenomenon of "capillary condensation" of simple fluids in thin capillaries. In the case of "competing walls", where both walls prefer different phases of the two phases coexisting in the bulk, a state with an interface parallel to the walls gets stabilized. The transition from the disordered phase to this "soft mode phase" is rounded by the finite thickness of the film and not a sharp phase transition. However, a sharp transition can occur where this interface gets localized at (one of) the walls. The relation of this interface localization transition to wetting phenomena is discussed. Finally, an outlook to related phenomena is given, such as the effects of confinement in cylindrical pores on the phase behavior, and more complicated ordering phenomena (lamellar mesophases of block copolymers or nematic phases of liquid crystals under confinement)., Comment: 25 pages, 17 figures, to be published in Soft Matter

In the present paper we empirically investigate the psychometric properties of some of the most famous statistical and logical cognitive illusions from the “heuristics and biases” research program by Daniel Kahneman and Amos Tversky, who nearly 50 years ago introduced fascinating brain teasers such as the famous Linda problem, the Wason card selection task, and so-called Bayesian reasoning problems (e.g., the mammography task). In the meantime, a great number of articles has been published that empirically examine single cognitive illusions, theoretically explaining people’s faulty thinking, or proposing and experimentally implementing measures to foster insight and to make these problems accessible to the human mind. Yet these problems have thus far usually been empirically analyzed on an individual-item level only (e.g., by experimentally comparing participants’ performance on various versions of one of these problems). In this paper, by contrast, we examine these illusions as a group and look at the ability to solve them as a psychological construct. Based on an sample ofN= 2,643 Luxembourgian school students of age 16–18 we investigate the internal psychometric structure of these illusions (i.e., Are they substantially correlated? Do they form a reflexive or a formative construct?), their connection to related constructs (e.g., Are they distinguishable from intelligence or mathematical competence in a confirmatory factor analysis?), and the question of which of a person’s abilities can predict the correct solution of these brain teasers (by means of a regression analysis).

Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness &kappa, as well as the strength of the adsorption potential ϵ w a l l are varied over a wide range. The excluded-volume (EV) interactions inherent in this model can also be &ldquo, switched off&rdquo, to provide a discretized version of the Kratky&ndash, Porod wormlike chain model. We study both local order parameters (fraction f of monomers within the range of the potential, bond-orientational order parameter &eta, ) and the mean square gyration radius parallel, &lang, R g 2 &rang, | , and perpendicular, &lang, &perp, to the wall. While for strongly adsorbed chains EV has negligible effect on f and &eta, we find that &lang, | is strongly affected when the chain contour length exceeds the persistence length. Monomer coordinates in perpendicular (&perp, ) direction are correlated over the scale of the deflection length which is estimated. It is found that f , &eta, and &lang, converge to their asymptotic values with 1 / N corrections. For both weakly and strongly adsorbed chains, the distribution functions of &ldquo, loops&rdquo, &ldquo, trains&rdquo, and &ldquo, tails&rdquo, are analyzed. Some consequences pertaining to the analysis of experiments on adsorbed semiflexible polymers are pointed out.

Wetting and drying phenomena are studied for flexible and semiflexible polymer solutions via coarse-grained molecular dynamics simulations and density functional theory calculations. The study is based on the use of Young's equation for the contact angle, determining all relevant surface tensions from the anisotropy of the pressure tensor. The solvent quality (or effective temperature, equivalently) is varied systematically, while all other interactions remain unaltered. For flexible polymers, the wetting transition temperature $T_{\rm w}$ increases monotonically with chain length $N$, while the contact angle at temperatures far below $T_{\rm w}$ is independent of $N$. For semiflexible polymer solutions, $T_{\rm w}$ varies non-monotonically with the persistence length: Initially, $T_{\rm w}$ increases with increasing chain stiffness and reaches a maximum, but then a sudden drop of $T_{\rm w}$ is observed, which is associated with the isotropic-nematic transition of the system.

In a theoretical description of homogeneous nucleation one frequently assumes an "equilibrium" coexistence of a liquid droplet with surrounding vapor of a density exceeding that of a saturated vapor at bulk vapor-liquid two-phase coexistence. Thereby one ignores the caveat that in the thermodynamic limit, for which the vapor would be called supersaturated, such states will at best be metastable with finite lifetime, and thus not be well-defined within equilibrium statistical mechanics. In contrast, in a system of finite volume stable equilibrium coexistence of droplet and supersaturated vapor at constant total density is perfectly possible, and numerical analysis of equilibrium free energies of finite systems allows to obtain physically relevant results. In particular, such an analysis can be used to derive the dependence of the droplet surface tension γ( R) on the droplet radius R by computer simulations. Unfortunately, however, the precision of the results produced by this approach turns out to be seriously affected by a hitherto unexplained spurious dependence of γ( R) on the total volume V of the simulation box. These finite size effects are studied here for the standard Ising/lattice gas model in d = 2 dimensions and an Ising model on the face-centered cubic lattice with 3-spin interaction, lacking symmetry between vapor and liquid phases. There also the analogous case of bubbles surrounded by undersaturated liquid is treated. It is argued that (at least a large part of) the finite size effects result from the translation entropy of the droplet or bubble in the system. This effect has been shown earlier to occur also for planar interfaces for simulations in the slab geometry. Consequences for the estimation of the Tolman length are briefly discussed. In particular, we find clear evidence that in d = 2 the leading correction of the curvature-dependent interface tension is a logarithmic term, compatible with theoretical expectations, and we show that then the standard Tolman-style analysis is inapplicable.

Conformations of partially or fully adsorbed semiflexible polymer chains are studied varying both contour length $L$, chain stiffness, $\ensuremath{\kappa}$, and the strength of the adsorption potential over a wide range. Molecular dynamics simulations show that partially adsorbed chains (with ``tails,'' surface attached ``trains,'' and ``loops'') are not described by the Kratky-Porod wormlike chain model. The crossover of the persistence length from its three-dimensional value (${\ensuremath{\ell}}_{p}$) to the enhanced value in two dimensions ($2{\ensuremath{\ell}}_{p}$) is analyzed, and excluded volume effects are identified for $L\ensuremath{\gg}{\ensuremath{\ell}}_{p}$. Consequences for the interpretation of experiments are suggested. We verify the prediction that the adsorption threshold scales as ${\ensuremath{\ell}}_{p}^{\ensuremath{-}1/3}$.

The interplay of nematic order and phase separation in solutions of semiflexible polymers in solvents of variable quality is investigated by density functional theory (DFT) and molecular dynamics (MD) simulations. We studied coarse-grained models, with a bond-angle potential to control chain stiffness, for chain lengths comparable to the persistence length of the chains. We varied both the density of the monomeric units and the effective temperature that controls the quality of the implicit solvent. For very stiff chains, only a single transition from an isotropic fluid to a nematic is found, with a phase diagram of "swan-neck" topology. For less stiff chains, however, also unmixing between isotropic fluids of different concentration, ending in a critical point, occurs for temperatures above a triple point. The associated critical behavior is examined in the MD simulations and found compatible with Ising universality. Apart from this critical behavior, DFT calculations agree qualitatively with the MD simulations.

Changing the information format from probabilities into frequencies as well as employing appropriate visualizations such as tree diagrams or 2 × 2 tables are important tools that can facilitate people’s statistical reasoning. Previous studies have shown that despite their widespread use in statistical textbooks, both of those visualization types are only of restricted help when they are provided with probabilities, but that they can foster insight when presented with frequencies instead. In the present study, we attempt to replicate this effect and also examine, by the method of eye tracking, why probabilistic 2 × 2 tables and tree diagrams do not facilitate reasoning with regard to Bayesian inferences (i.e., determining what errors occur and whether they can be explained by scan paths), and why the same visualizations are of great help to an individual when they are combined with frequencies. All ten inferences of N = 24 participants were based solely on tree diagrams or 2 × 2 tables that presented either the famous “mammography context” or an “economics context” (without additional textual wording). We first asked participants for marginal, conjoint, and (non-inverted) conditional probabilities (or frequencies), followed by related Bayesian tasks. While solution rates were higher for natural frequency questions as compared to probability versions, eye-tracking analyses indeed yielded noticeable differences regarding eye movements between correct and incorrect solutions. For instance, heat maps (aggregated scan paths) of distinct results differed remarkably, thereby making correct and faulty strategies visible in the line of theoretical classifications. Moreover, the inherent structure of 2 × 2 tables seems to help participants avoid certain Bayesian mistakes (e.g., “Fisherian” error) while tree diagrams seem to help steer them away from others (e.g., “joint occurrence”). We will discuss resulting educational consequences at the end of the paper.

Finite-size scaling for a first-order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological ``degeneracy'' factor included. Predictions are compared with data from Monte Carlo simulations of the three-dimensional, $XXZ$ Heisenberg antiferromagnet in a field in order to study the finite-size behavior on a $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ simple cubic lattice for the first-order ``spin-flop'' transition between the Ising-like antiferromagnetic state and the canted, $XY$-like state. Our theory predicts that for large linear dimension $L$ the field dependence of all moments of the order parameters as well as the fourth-order cumulants exhibit universal intersections. Corrections to leading order should scale as the inverse volume. The values of these intersections at the spin-flop transition point can be expressed in terms of a factor $q$ that characterizes the relative degeneracy of the ordered phases. Our theory yields $q=\ensuremath{\pi}$, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality can be invoked for first-order phase transitions.

Semiflexible polymers in concentrated lyotropic solution are studied within a bead-spring model by molecular dynamics simulations, focusing on the emergence of a smectic A phase and its properties. We systematically vary the density of the monomeric units for several contour lengths that are taken smaller than the chain persistence length. The difficulties concerning the equilibration of such systems and the choice of appropriate ensemble (constant volume versus constant pressure, where all three linear dimensions of the simulation box can fluctuate independently) are carefully discussed. Using HOOMD-blue on graphics processing units, systems containing more than a million monomeric units are accessible, making it possible to distinguish the order of the phase transitions that occur. While in this model the nematic-smectic transition is continuous, the transition from the smectic phase to a related crystalline structure with true three-dimensional long-range order is clearly of first order. Further, both orientational and positional correlations of monomeric units are studied as well as the order parameters characterizing the nematic, smectic A, and crystalline phases. The analogy between smectic order and one-dimensional harmonic crystals with respect to the behavior of the structure factor is also explored. Finally, the results are put in perspective with pertinent theoretical predictions and possible experiments.

A topical review of recent theoretical work on the properties of lyotropic solutions and melts containing semiflexible polymers in thermal equilibrium is given, with a focus on the liquid-crystalline and smectic order of these systems in the bulk and under confinement. Starting with a discussion of single chain properties in terms of the Kratky-Porod worm-like chain model and its limitations, extensions along the lines of Onsager’s theory for the isotropic-nematic transition of solutions of hard rods are briefly reviewed. This discussion is followed by a review of recent Molecular Dynamics simulations and classical Density Functional Theory calculations. It is argued that, even in the simplest case of athermal solutions, coarse-grained polymer models must include three lengths: the contour length L, the persistence length ℓ p , and the effective chain thickness D. The discussion is then extended to semiflexible polymers in solutions with thermally driven transitions, where the isotropic-isotropic phase separation competes with the isotropic-nematic transition. Basic physical phenomena due to confinement of these systems in thin films with either repulsive or attractive walls are briefly reviewed, and conditions for the formation of strongly ordered surface layers are identified.

A great triumph of statistical physics in the latter part of the 20th century was the understanding of critical behavior and universality at second-order phase transitions. In contrast, first-order transitions were believed to have no common features. However, we argue that the classic, first-order “spin-flop” transition (between the antiferromagnetic and the rotationally degenerate, canted state) in an anisotropic antiferromagnet in a magnetic field exhibits a new kind of universality. We present a finite-size scaling theory for a first-order phase transition where a continuous symmetry is broken using an approximation of Gaussian probability distributions with a phenomenological degeneracy factor “q” included, where “q” characterizes the relative degeneracy of the ordered phases. Predictions are compared with high resolution Monte Carlo simulations of the three-dimensional, XXZ Heisenberg antiferromagnet in a field to study the finite-size behavior for L×L×L simple cubic lattices. The field dependence of all moments of the order parameters exhibit universal intersections at the spin-flop transition. Our Monte Carlo data agree with theoretical predictions for asymptotic large L behavior. Our theory yields q = π, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality.

Results from Monte Carlo simulations of wall-attached droplets in the three-dimensional Ising lattice gas model and in a symmetric binary Lennard-Jones fluid, confined by antisymmetric walls, are analyzed, with the aim to estimate the dependence of the contact angle $(\Theta)$ on the droplet radius $(R)$ of curvature. Sphere-cap shape of the wall-attached droplets is assumed throughout. An approach, based purely on "thermodynamic" observables, e.g., chemical potential, excess density due to the droplet, etc., is used, to avoid ambiguities in the decision which particles belong (or do not belong, respectively) to the droplet. It is found that the results are compatible with a variation $[\Theta(R)-\Theta_{\infty}] \propto 1/R$, $\Theta_{\infty}$ being the contact angle in the thermodynamic limit ($R=\infty$). The possibility to use such results to estimate the excess free energy related to the contact line of the droplet, namely the line tension, at the wall, is discussed. Various problems that hamper this approach and were not fully recognized in previous attempts to extract the line tension are identified. It is also found that the dependence of wall tensions on the difference of chemical potential of the droplet from that at the bulk coexistence provides effectively a change of the contact angle of similar magnitude. The simulation approach yields precise estimates for the excess density due to wall-attached droplets and the corresponding free energy excess, relative to a system without a droplet at the same chemical potential. It is shown that this information suffices to estimate nucleation barriers, not affected by ambiguities on droplet shape, contact angle and line tension., Comment: 18 pages, 11 figures

We study active Brownian particles as a paradigm for a genuine nonequilibrium phase transition requiring steady driving. Access to the critical point in computer simulations is obstructed by the fact that the density is conserved. We propose a method based on arguments from finite-size scaling to determine critical points and successfully test it for the two-dimensional (2D) Ising model. Using this method allows us to accurately determine the critical point of two-dimensional active Brownian particles at ${\mathrm{Pe}}_{\text{cr}}=40(2), {\ensuremath{\phi}}_{\text{cr}}=0.597(3)$. Based on this estimate, we study the corresponding critical exponents $\ensuremath{\beta}, \ensuremath{\gamma}/\ensuremath{\nu}$, and $\ensuremath{\nu}$. Our results are incompatible with the 2D-Ising exponents, thus raising the question whether there exists a corresponding nonequilibrium universality class.

Monte Carlo simulations of crystal nuclei coexisting with the fluid phase in thermal equilibrium in finite volumes are presented and analyzed, for fluid densities from dense melts to the vapor. Generalizing the lever-rule for two-phase coexistence in the canonical ensemble to finite volume, "measurements" of the nucleus volume together with the pressure and chemical potential of the surrounding fluid allows to extract the surface free energy of the nucleus. Neither the knowledge of the (in general non-spherical) nucleus shape nor of the angle-dependent interface tension is required for this task. The feasibility of the approach is demonstrated for a variant of the Asakura-Oosawa model for colloid-polymer mixtures, which form face-centered cubic colloidal crystals. For a polymer to colloid size ratio of $0.15$, the colloid packing fraction in the fluid phase can be varied from melt values to zero by the variation of an effective attractive potential between the colloids. It is found that the approximation of spherical crystal nuclei often underestimates actual nucleation barriers significantly. Nucleation barriers are found to scale as $\Delta F^*=(4\pi/3)^{1/3}\bar{\gamma}(V^*)^{2/3}+const.$ with the nucleus volume $V^*$, and the effective surface tension $\bar{\gamma}$ that accounts implicitly for the nonspherical shape can be precisely estimated., Comment: 17 pages, 17 figures

Densely packed semiflexible polymers with contour length L confined in spheres with radius R of the same order as L cannot exhibit uniform nematic order. Depending on the chain stiffness (which we vary over a wide range), highly distorted structures form with topological defects on the sphere surface. These structures are completely different from previously observed ones of very long chains winding around the inner surface of spheres and from nematic droplets. At high densities, a thin shell of polymers close to the sphere surface exhibits a tennis ball texture due to the confinement-induced gradual bending of polymer bonds. In contrast, when the contour length of the chains is significantly smaller than the radius of the confining sphere, a few bent smectic layers form in the sphere. Molecular dynamics simulations demonstrate these complex structures, and suitable order parameters characterizing them are proposed. Fil: Nikoubashman, Arash. Johannes Gutenberg Universitat Mainz; Alemania Fil: Vega, Daniel Alberto. Johannes Gutenberg Universitat Mainz; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina Fil: Binder, Kurt. Johannes Gutenberg Universitat Mainz; Alemania Fil: Milchev, Andrey. Bulgarian Academy Of Sciences; Bulgaria. Johannes Gutenberg Universitat Mainz; Alemania

Semiflexible polymers in lyotropic solution confined inside spherical nanoscopic “containers” with repulsive walls are studied by molecular dynamics simulations and density functional theory, as a first step to model confinement effects on stiff polymers inside of miniemulsions, vesicles, and cells. It is shown that the depletion effects caused by the monomer-wall repulsion depend distinctly on the radius R of the sphere. Further, nontrivial orientational effects occur when R, the persistence length ℓp, and the contour length L of the polymers are of similar magnitude. At intermediate densities, a “shell” of wall-attached chains is forming, such that the monomers belonging to those chains are in a layer at about the distance of one monomer from the container wall. At the same time, the density of the centers of mass of these chains is peaked somewhat further inside, but still near the wall. However, the arrangement of chains is such that the total monomer density is almost uniform in the sphere, apart from a small layering peak at the wall. It is shown that excluded volume effects among the monomers are crucial to account for this behavior, although they are negligible for comparable isolated single semiflexible chains of the same length.

We performed extensive simulations of the random-bond Ising model confined between walls where competitive surface fields act. By properly taking the thermodynamic limit we unambiguously determined wetting transition points of the system, as extrapolation of localization-delocalization transitions of the interface between domains of different orientation driven by the respective fields. The finite-size scaling theory for wetting with short-range fields establishes that the average magnetization of the sample, with critical exponent β, is the proper order parameter for the study of wetting. While the hyperscaling relationship given by γ+2β=ν +ν requires β=1/2 (γ=4, ν =3, and ν =2), the thermodynamic scaling establishes that Δs=γ+β, which in contrast requires β=0 (Δs=4), where γ, ν, ν, and Δs are the critical exponents of the susceptibility, the correlation lengths parallel and perpendicular to the interface, and the gap exponent, respectively. So, we formulate a finite-size scaling theory for wetting without hyperscaling and perform numerical simulations that provide strong evidence of hyperscaling violation (i.e., β=0) and a direct measurement of the susceptibility critical exponent γ/ν =2.0±0.2, in agreement with theoretical results for the strong fluctuation regime of wetting transitions with quenched noise., Instituto de Física de Líquidos y Sistemas Biológicos

Purely entropic systems such as suspensions of hard rods, platelets and spheres show rich phase behavior. Rods and platelets have successfully been used as models to predict the equilibrium properties of liquid crystals for several decades. Over the past years hard particle models have also been studied in the context of non-equilibrium statistical mechanics, in particular regarding the glass transition, jamming, sedimentation and crystallization. Recently suspensions of hard anisotropic particles also moved into the focus of materials scientists who work on conducting soft matter composites. An insulating polymer resin that is mixed with conductive filler particles becomes conductive when the filler percolates. In this context the mathematical topic of connectivity percolation finds an application in modern nano-technology. In this article, we briefly review recent work on the phase behavior, confinement effects, percolation transition and phase transition kinetics in hard particle models. In the first part, we discuss the effects that particle anisotropy and depletion have on the percolation transition. In the second part, we present results on the kinetics of the liquid-to-crystal transition in suspensions of spheres and of ellipsoids.

As a rule, mean-field theories applied to a fluid that can undergo a transition from saturated vapor at density ρυ to a liquid at density ρl yield a van der Waals loop. For example, isotherms of the chemical potential μ(T,ρ) as a function of the density ρ at a fixed temperature T less than the critical temperature Tc exhibit a maximum and a minimum. Metastable and unstable parts of the van der Waals loop can be eliminated by the Maxwell construction. Van der Waals loops and the corresponding double minimum potentials are mean-field artifacts. Simulations at fixed μ=μcoex for ρυ

As a simplified model of a liquid nanostripe adsorbed on a chemically structured substrate surface, a two-dimensional Ising system with two boundaries at which surface fields act is studied. At the upper boundary, the surface field is uniformly negative, while at the lower boundary (a distance L apart), the surface field is negative only outside a range of extension b, where a positive surface stabilizes a droplet of the phase with positive magnetization for temperatures T exceeding the critical temperature Tw of the wetting transition of this model. We investigate the local order parameter profiles across the droplet, both in the directions parallel and perpendicular to the substrate, varying both b and T. Also, precursor effects to droplet formation as T approaches Tw from below are studied. In accord with theoretical predictions, for T>Tw the droplet is found to have the shape of a semiellipse, where the width (distance of the interface from the substrate) scale is proportional to b (b1/2). So, the area of the droplet is proportional to b3/2, and the temperature dependence of the corresponding prefactor, which also involves the interfacial stiffness, is studied. Fil: Trobo, Marta Liliana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina. Universidad Nacional de la Plata. Facultad de Ingeniería. Departamento de Fisicomatemática; Argentina Fil: Albano, Ezequiel Vicente. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina Fil: Binder, Kurt. Johannes Gutenberg Universitat Mainz; Alemania

The nematic ordering in semiflexible polymers with contour length $L$ exceeding their persistence length $\ell_p$ is described by a confinement of the polymers in a cylinder of radius $r_{eff}$ much larger than the radius $r_\rho$, expected from the respective concentration of the solution. Large scale Molecular Dynamics simulations combined with Density Functional Theory are used to locate the Isotropic-Nematic ($I-N$)-transition and to validate this cylindrical confinement. Anomalous fluctuations, due to chain deflections from neighboring chains in the nematic phase are proposed. Considering deflections as collective excitations in the nematically ordered phase of semiflexible polymers elucidates the origins of shortcomings in the description of the $I-N$ transition by existing theories., Comment: 5 pages, 5 figures

We study numerically the critical behavior of a modified, active Asakura-Oosawa model for colloid-polymer mixtures. The colloids are modeled as self-propelled particles with Vicsek-like interactions. This system undergoes phase separation between a colloid-rich and a polymer-rich phase, whereby the phase diagram depends on the strength of the Vicsek-like interactions. Employing a subsystem-block-density distribution analysis, we determine the critical point and make an attempt to estimate the critical exponents. In contrast to the passive model, we find that the critical point is not located on the rectilinear diameter. A first estimate of the critical exponents $\beta$ and $\nu$ is consistent with the underlying 3d-Ising universality class observed for the passive model., Comment: 9 pages, 8 figures

The finite size scaling analysis of Monte Carlo data is discussed for two models for which hyperscaling is violated: (i) the random field Ising model (using a model for a colloid-polymer mixture in a random matrix as a representative) (ii) The Ising bi-pyramid in computing surface fields.

The properties of a single semiflexible chain tethered to a planar surface with a long-ranged attractive potential are studied by means of Monte Carlo simulations. We employ the bond fluctuation lattice model and the Wang-Landau sampling technique. We present the diagram of states for semiflexible chains consisting of N = 64 and 128 monomer units as a function of temperature T and strength of the adsorption potential, epsilon(w), and also compare this with the diagram of states for flexible chains of these two lengths. The diagram of states consists of the regions of a coil, liquid globule, solid isotropic globule, adsorbed coil, and quasi-two-dimensional solid globule with nematic bond order (or quasi-two-dimensional isotropic crystal in the case of a flexible chain). The diagram of states for the flexible case agrees with a result for the same model and a short-ranged attraction to the wall for small values of the attraction strength. For larger values, the transition to the two-dimensional behavior is more gradual in the long-ranged attractive potential. For the range of chain stiffness that we studied, the low-temperature phase in the bulk is an isotropic globule (i.e., a globule without bond order). At the attractive surface, a nematic-type bond order is induced upon adsorption, leading to ordered structures, which can be considered a precursor to the crystalline lamellae forming in real polymers. Other than that, the diagram of states in general is not changed by introducing stiffness of the chains.

We present an efficient method for direct determination of the excess free energy Δ F of a nanoparticle inserted into a polymer brush. In contrast to Widom's insertion method, the present approach can be efficiently implemented by Monte Carlo or Molecular Dynamics methods also in a dense environment. In the present investigation the method is used to determine the free energy penalty Δ F ( R , D ) for placing a spherical particle with an arbitrary radius R at different positions D between the grafting plane and the brush surface. Deep inside the brush, or for dense brushes, one finds Δ F ∝ R 3 whereas for shallow nanoclusions Δ F ∝ R 2 , regardless of the particle interaction (attractive/repulsive) with the polymer. The pressure and density fields around spherical nanoinclusions in a polymer brush are also investigated. Extensive Monte Carlo simulations show that the force, exerted on the particle by the surrounding brush, depends essentially on the proximity of the nanocolloid particle to the brush surface not only in strength but also with respect to its angular distribution. For shallow nanoinclusions close to the brush surface this angular distribution is shown to result in a growing buoyant force while deep inside the brush this effect is negligible.

This review discusses Monte Carlo simulations of simple models for fluids and binary mixtures (lattice gas, lattice models for binary polymer blends, Asakura-Oosawa model of colloid-polymer mixtures) in confined geometries. The geometries considered are thin films confined by either symmetric or competing walls, as well as wedges and pyramid-shaped cones, including “closed” geometries such as double wedges and bipyramids. Testing of theoretical concepts on the phase behavior in these geometries is emphasized: There is a delicate interplay between wetting phenomena and phase separation into vapor and liquid (or two fluids of different composition, respectively). Capillary condensation phenomena occur in thin films with symmetric walls, and interface localization transitions occur in cases with competing walls. Concepts on wedge filling and cone filling are also examined.

We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method. The nanotube is a long channel opened at one end and its diameter $D$ is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position $x$ inside the tube: the free energy of confinement, the average end-to-end distance, the average number of imprisoned monomers, and the average stretching of the confined part of the chain for various values of $D$ and for the number of monomers in the chain, $N$. We show that when the chain end is dragged by a certain critical distance $x^*$ into the tube, the polymer undergoes a first-order phase transition whereby the remaining free tail is abruptly sucked into the tube. This is accompanied by jumps in the average size, the number of imprisoned segments, and in the average stretching parameter. The critical distance scales as $x^*\sim ND^{1-1/\nu}$. The transition takes place when approximately 3/4 of the chain units are dragged into the tube. The theory presented is based on constructing the Landau free energy as a function of an order parameter that provides a complete description of equilibrium and metastable states. We argue that if the trapped chain is released with all monomers allowed to fluctuate, the reverse process in which the chain leaves the confinement occurs smoothly without any jumps. Finally, we apply the theory to estimate the lifetime of confined DNA in metastable states in nanotubes., Comment: 13pages, 14figures

solids to complex multi-component materials and even biological matter, are governed by well understood laws of physics: on the relevant scales of length and time; the appropriate description would be just the Schrodinger equation for the quantum-many-body problem of the nuclei and electrons interacting with Coulomb forces. Statistical mechanics would then provide the framework to extend this quantum theory of condensed matter towards a statistical description in terms of averages taken at nonzero temperature. However, this program cannot be carried out straightforwardly: even dealing only with the associated electrons is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the manybody problem can be effectively reduced to a problem of independent particles or quasi-particles. Such problems are, for instance, ideal gases, paramagnets, or the multidimensional harmonic oscillator describing phonons in harmonic crystals. While all these problems are useful and educative (we hence teach them all to students to illustrate the spirit of the general theoretical framework) they do not encompass most of the problems of interest in condensed matter physics: the interactions among the considered degrees of freedom introduce nontrivial correlations between them. Systematic perturbation-theory type methods usually do not lead very far, and uncontrolled closed form approximations often fail utterly. A well-known example is the study of the liquid gas transition in fluids: simple theories such as the van der Waals equation and its extensions (e.g. the "perturbed chain" statistical associating fluid theory [PC-SAFT] intended to model the equation of state of polymer melts [1]) give rise to spurious loops in the isotherms, fail to describe the critical behavior correctly, and may even predict completely unphysical phase equilibria that do not correspond to any physical behavior of the system but are mere artefacts of the inappropriate approximations [1]. The theory of condensed matter systems contains a never-ending list of such failures! Hence, until about 50 years ago, condensed matter theory suffered from the basic problem that only a formal framework for the theoretical description in terms of quantum theory and statistical mechanics did exist, while a reliable set of tools that would allow accurate explicit predictions to be made for the static and dynamic properties of these systems from first principles was simply missing! This unsatisfactory situation has changed fundamentally through the invention of computer simulation, which provides a much more promising approach to these problems. Computer simulation is a novel methodic route allowing the Condensed matter theory by computer simulation: from materials to chemical biology [DOI: 10.1051/EPN:2007009]

As a model for a suspension of hard-sphere like colloidal particles where small nonadsorbing 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 nonspherical shape has only a very small effect on the barrier.

Confining a binary mixture, one can profoundly alter its miscibility behavior. The qualitative features of miscibility in confined geometry are ratheruniversal and shared by polymer mixtures as well as small molecules, but the unmixing transition in the bulk and the wetting transition are typically well separated in polymer blends. The interplay between wetting and miscibility of a symmetric polymer mixture via large-scale Monte Carlo simulations in the framework of the bond fluctuation model and via numerical self–consistent field calculations is studied. The film surfaces interact with the monomers via short ranged potentials, and the wetting transition of the semi–infinite system is of first order. It can be accurately located in the simulations by measuring the surface and interface tensions and using Young’s equation. If both surfaces in a film attract the same component, capillary condensation occurs and the critical point is close to the critical point of the bulk. If surfaces attract different components, an interface localization/delocalization occurs which gives rise to phase diagrams with two critical points in the vicinity of the pre-wetting critical point of the semi–infinite system. The crossover between these two types of phase diagrams as a function of the surface field asymmetry is studied. The dependence of the phase diagram on the film thickness Δ for antisymmetric surface fields is investigated. Upon decreasing the film thickness, the two critical points approach the symmetry axis of the phase diagram, and below a certain thickness Δtri, there remains only a single critical point at the symmetric composition. This corresponds to a second-order interface localization/delocalization transition even though the wetting transition is of first order. At a specific film thickness, Δtri, tricritical behavior is found. The behavior of antisymmetric films is compared with the phase behavior in an antisymmetric double wedge. While the former is the analog of the wetting transition of a planar surface, the latter is related to the filling behavior of a single wedge. Evidence for a second-order interface localization/delocalization transition in an antisymmetric double wedge is presented, and its unconventional critical behavior is related to the predictions of Parry et al. (Phys. Rev. Lett. 83:5535 (1999)) for wedge filling. The critical behavior differs from the Ising universality class and is characterized by strong anisotropic fluctuations.

We study the problem ofsurfacedirected spinodal decomposition, viz., the dynamical interplay of wetting and phase separation at surfaces. In particular, we focus on the kinetics of wetting-layer growth in a semi-infinite geometry for arbitrary surface potentials and mixture compositions. We also present representative results for phase separation in confined geometries, e.g., cylindrical pores, thin films, etc.

The interplay between chain conformations and phase separation in binary symmetric polymer mixtures confined into thin films by "neutral" hard walls (i.e., walls that do not preferentially attract or repel one of the two components of the mixture) is studied by Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice in the semi grand canonical ensemble, we locate the critical temperature of demixing via finite size scaling methods for a wide range of chain lengths (16/= N/= 256 effective monomers per chain) and film thicknesses (2/= D/= 19 lattice spacings). Simultaneously, we investigate the geometrical structure of the chains, showing that despite using melt densities there are pronounced "correlation hole effects", in particular for the smaller values of D. Also the components of the radius of gyration and end-to-end distance parallel and perpendicular to the confining walls are analyzed and their scaling behavior is studied. Evidence is presented that for strictly two-dimensional polymers (as occur for D = 2) the average number of intermolecular contacts scales with chain length N as z(c) proportional, variant N(-3/8) and therefore the critical temperature scales as T(c) proportional, variant N(5/8), whereas for values of D that exceed the excluded volume screening length, z(c) remains nonzero for N --infinity, and hence T(c) proportional, variant N. However, strong deviations from the Flory-Huggins theory occur as long as the unperturbed chain dimension exceeds D, and the critical behavior falls in the universality class of the two-dimensional Ising model for any finite value of D.

Structural and dynamic properties of silicate melts and glasses (SiO 2 and its mixtures with Na 2 O and Al 2 O 3 ) are derived from Molecular Dynamics simulations and compared to pertinent experimental data. It is shown that these mixtures exhibit additional intermediate order as compared to pure silica, where the characteristic length scales stem from the tetrahedral network structure. While sodium ions show much faster diffusion through percolating channels than the silicon and oxygen ions forming the surrounding network, aluminium ions are incorporated into the network (leading to tricluster formation) and do not show such an enhanced mobility.

Dynamic Monte Carlo simulation of a bead-spring model of flexible macromolecules threading through a very narrow pore in a very thin rigid membrane are presented, assuming at the cis side of the membrane a purely repulsive monomer-wall interaction, while the trans side is attractive. Two choices of monomer-wall attraction epsilon are considered, one choice is slightly below and the other slightly above the "mushroom to pancake" adsorption threshold epsilon(c) for an infinitely long chain. Studying chain lengths N=32, 64, 128, and 256 and varying the number of monomers N(trans) (time t=0) that have already passed the pore when the simulation started, over a wide range, we find for epsilonepsilon(c) (nonadsorbing case) that the translocation probability varies proportional to c(trans)=N(trans)(t=0)/N for small c(trans), while for epsilonepsilon(c) a finite number N(trans)(t=0) suffices that the translocation probability is close to unity. In the case epsilonepsilon(c), however, the time it takes for those chains to get through the pore to complete the translocation process scales as tau proportional, variant N(2.23+/-0.04). This result agrees with the suggestion of Chuang, Kantor, and Kardar [Phys. Rev. E 65, 011802 (2001)] that the translocation time is proportional to the Rouse time, that scales under good solvent condition as tau(Rouse) proportional, variant N(2nu+1), with the excluded-volume exponent nu approximately 0.59 in d=3 dimensions. Our results hence disagree with the suggestions that the translocation time should scale as either N(2) or N(3). For epsilonepsilon(c), we find that the translocation time scales as tau proportional, variant N(1.65+/-0.08). We suggest a tentative scaling explanation for this result. Also the distribution of translocation times is obtained and discussed.

A Lennard–Jones model of a binary (AB) dense liquid with a symmetrical miscibility gap is investigated by means of computer simulation methods. Semigrand-canonical Monte Carlo simulations yield the phase diagram in the T–x plane (T: temperature, x: concentration of A or B particles), as well as equilibrated configurations at coexistence. Then, we undertake molecular dynamics simulations which use these configurations to determine static properties (isothermal compressibility κ T , and concentration susceptibility χ), as well as the shear and bulk viscosities ηs and ηB, respectively. The latter quantities are calculated along a path approaching the coexistence line from high temperatures in the one-phase region and ending at a state at the coexistence line about 15% below the critical point. We find that κ T and χ increase significantly near the coexistence line, reflecting the vicinity of the critical point. Whereas η s exhibits a weak temperature-dependence, ηB increases significantly near the coexistenc...