Finite size scaling for a first order phase transition, where a continuous symmetry is broken, is tested using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor. Predictions are compared to the data from Monte Carlo simulations of the Lebwohl-Lasher model on L x L x L simple cubic lattices. The data show that the intersection of the fourth-order cumulant of the order parameter for different lattice sizes can be expressed in terms of the relative degeneracy q = 4 pi of the ordered and disordered phases. This result further supports the concept of universality at first order transitions developed recently.

Phase transitions of water and its mixtures are of fundamental importance in physical chemistry, the pharmaceutical industry, materials sciences, and atmospheric sciences. However, current understanding remains elusive to explain relevant observations, especially at the nanoscale. Here, by using molecular dynamics simulations, we investigate the dissolution of sodium chloride (NaCl) nanocrystals with volume-equivalent diameters from 0.51 to 1.75 nm. Our results show that the dissolution of NaCl in aqueous nanodroplets show a strong size dependence, and its solubility can be predicted by the Ostwald-Freundlich equation and Gibbs-Duhem equation after considering a size-dependent solid-liquid surface tension. We find that the structure of dissolved ions in the saturated aqueous nanodropplet resembles the structure of a molten NaCl nanoparticle. With decreasing nanodroplet size, this similarity grows and the average potential energy of NaCl in solution, the molten phase and the crystal phase converges.

A tutorial survey of theoretical methods for the study of polymeric coatings on surfaces is given. Both analytic methods (self-consistent field theory, density functional theory, etc.) as well as simulation techniques (Monte Carlo and molecular dynamics methods) are treated. The introductory description of each method is illustrated by application examples, considering both thin adsorbed polymeric films on planar solid surfaces and polymer brushes. These examples include phase transition behavior (competition between parallel or perpendicular orientation of block copolymer lamellae as a result of the conflict between thin film thickness and the preference of the surface for one component), local partitioning between solvent molecules and the monomeric units of grafted chains along the density profile of a polymer brush for varying solvent quality, prediction of the surface tension of polymer solutions at walls and the discussion of wetting/dewetting behavior of the films, effects of chemical architecture (rings versus linear polymers) on polymer brush properties, and last but not least dynamical properties, such as the effect of adsorption/desorption kinetics of monomeric units in dense films near the glass transition, shear effects on thin films, or regarding lubrication properties of brushes, sheared against each other.

Investigating biomarkers and potential therapies in animal models is essential to determine which target mechanisms could prevent posttraumatic epilepsy (PTE). In theory, an ideal candidate biomarker should be easily measurable (noninvasive) and specific for PTE (distinct from traumatic brain injury (TBI) and epilepsy biomarkers) while an ideal therapeutic agent would be efficacious at preventing the development of seizures and secondary injuries associated with brain injury. In this chapter, we will discuss biomarkers and therapeutic interventions that reduce seizure susceptibility examined in animal models of PTE.

From studies via molecular dynamics simulations, we report results on structure and dynamics in mixtures of active colloids and passive polymers that are confined inside a spherical container with a repulsive boundary. All interactions in the fully passive limit are chosen in such a way that in equilibrium coexistence between colloid-rich and polymer-rich phases occurs. For most part of the studies the chosen compositions give rise to Janus-like structure: nearly one side of the sphere is occupied by the colloids and the rest by the polymers. This partially wet situation mimics approximately a neutral wall in the fully passive scenario. Following the introduction of a velocity-aligning activity to the colloids, the shape of the polymer-rich domain changes to that of an ellipsoid, around the long axis of which the colloid-rich domain attains a macroscopic angular momentum. In the steady state, the orientation of this axis evolves via diffusion, magnitude of which depends upon the strength of activity, but only weakly.

A model for a mixture of two kinds of semiflexible polymers (A and B) with the same chain length (N-A = N-B = 32), but different persistence lengths, confined between parallel planar repulsive walls in a common good solvent is studied by molecular dynamics simulations. In the isotropic phase at low polymer concentrations, both polymers are repelled by the walls, and the system is anisotropic near the walls over a range controlled by the polymer linear dimensions. Close to the concentrations where in the bulk nematic order sets in, precursors of thick nematic layers at the walls are observed, strongly enriched by a stiffer component, which hence is depleted in the center of the slit pore. At larger concentrations, where in the bulk a uniformly mixed nematic phase occurs, the enrichment of B-chains at the walls is rather minor, extending over the scale of the transverse correlation length of concentration fluctuations, which is of the order of a few monomeric diameters only for the present model. In this ordered phase, both self-diffusion and interdiffusion of chains (in the direction perpendicular to the director) are found to be significantly slowed down in comparison to dilute solutions. Since equilibration times scale with the square of the slit thickness, incomplete equilibration is predicted when polymeric coatings on substrate containing polymers differing in stiffness are produced.

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.

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.

The combination of improved experimental capability, great advances in computer performance, and the development of new algorithms from computer science have led to quite sophisticated methods for the study of certain biomolecules, in particular of folded protein structures. One such technique, called ‘threading’, picks out small pieces of the primary structure of a protein whose structure is unknown and examines extensive databases of known protein structures to find similar pieces of primary structure. One then guesses that this piece will have the same folded structure as that in the known structure. Since pieces do not all fit together perfectly, an effective force field is used to ‘optimize’ the resultant structure, and Monte Carlo methods have already begun to play a role in this approach. (There are substantial similarities to ‘homology modeling’ approaches to the same, or similar, problems.) Of course, the certainty that the structure is correct comes primarily from comparison with experimental structure determination of crystallized proteins. One limitation is thus that not all proteins can be crystallized, and, even if they can, there is no assurance that the structure will be the same in vivo. Threading algorithms have, in some cases, been extraordinarily successful, but since they do not make use of the interactions between atoms it would be useful to complement this approach by atomistic simulations. (For an introductory overview of protein structure prediction, see Wooley and Ye (2007).) Biological molecules are extremely large and complex; moreover, they are usually surrounded by a large number of water molecules. Thus, realistic simulations that include water explicitly and take into account polarization effects are inordinately difficult. There have also been many attempts to handle this task by means of molecular dynamics simulations, but the necessity of performing very long runs of very large systems makes it very difficult to reach equilibrium. A possible advance is the use of so-called accelerated molecular dynamics (Miao et al., ), and it has been suggested that this may help to understand ‘genetic engineering’ mechanisms (Palermo et al., ). However, there are many phenomena that involve large spatial and temporal scales so that the use of coarse-grained models may often be necessary (Hyeon and Thirumalai, ).

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.

Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a phase separated structure with cylindrical symmetry occurs, with the isotropic phase located around the cylinder axis. For melt densities the mixed nematic phase forms at the wall a layer with a screw-like structure of a tilted smectic phase. The observed behavior is tentatively interpreted in terms of the competition of the chain orientational entropy with entropy of mixing and excluded volume due to the wall.

Lyotropic solutions containing two types of semiflexible macromolecules in spherical confinement are studied by molecular dynamics simulations and density functional theory, using a coarse-grained model. The case of strong stiffness disparity between both types of polymers is treated, and for simplicity, we take the contour lengths of both types of polymers to be equal. Only sphere radii larger than this contour length are considered, so that many chains can be packed inside the sphere, even when the chains are stretched out in a nematic state. For the chosen polymer solution, in the bulk one finds with increasing monomer concentration a transition from an isotropic phase through an isotropic-nematic two-phase region to a homogeneous nematic phase to which both constituents contribute. In the corresponding confined systems, there is an interplay between these phase transitions and surface enrichment of one component (typically, but not always, the stiffer one). In rather dilute confined solutions, the main effect of the surfaces is that the random orientation of the end-to-end vectors of the stiff chains is perturbed in a surface shell whose thickness is roughly the contour length. In more concentrated systems, a thin layer of wall-attached stiff chains is observed in addition, while (for equal mole fractions of both constituents) the stiffer component can also form an almost cylindrical domain with a bipolar orientational order, surrounded in the remainder of the sphere by the less stiff component. Topological defects in the nematic order can be identified, similar to the case where a single type of semiflexible polymer is confined in a sphere. The radial profiles of monomer concentrations and of various order parameters are compared to analogous data near planar and cylindrical repulsive walls, to provide a comprehensive picture of confinement effects on such polymer solutions.

The examination of the equation of state of a two-dimensional model fluid (the hard disk system) was the very first application of the importance sampling Monte Carlo method in statistical mechanics (Metropolis et al., 1953), and since then the study of both atomic and molecular fluids by Monte Carlo simulation has been a very active area of research. Remember that statistical mechanics can deal well analytically with very dilute fluids (ideal gases), and it can also deal well with crystalline solids (making use of the harmonic approximation and perfect crystal lattice periodicity and symmetry), but the treatment of strongly correlated dense fluids (and their solid counterparts, amorphous glasses) is much more difficult. Even the description of short range order in fluids in a thermodynamic state far away from any phase transition is a non-trivial matter (unlike the lattice models discussed in Chapter 5, where far away from phase transitions the molecular field approximation, or a variant thereof, is usually both good enough and easily worked out, and the real interest is generally in phase transition problems).

Der diesjährige Physik-Nobelpreis für bahnbrechende Beiträge zum Verständnis komplexer Systeme geht zu einer Hälfte an die Klimaforscher Syukuro Manabe und Klaus Hasselmann, zur anderen Hälfte an den Theoretiker Giorgio Parisi.

From studies via Molecular Dynamics simulations, we report results on structure and dynamics in mixtures of active colloids and passive polymers that are confined inside a spherical container with a repulsive boundary. Such systems mimic the presence of bacteria in the background of bio-polymers. All interactions in the fully passive case are chosen in such a way that in equilibrium coexistence between colloid-rich and polymer-rich phases occurs. For most part of the studies the chosen compositions give rise to Janus structure; one side of the sphere is occupied by the colloids and the rest by the polymers. This partially wet situation mimics nearly a neutral wall in the fully passive scenario. Following the introduction of a velocity-aligning activity to the colloids, the shape of the polymer-rich domain changes to that of an ellipsoid, around the long axis of which the colloid-rich domain attains a macroscopic angular momentum. In the steady state, the orientation of this axis evolves via diffusion, implying that the passive domain is set into motion as well by the active particles.

Conformations of wormlike chains in cylindrical pores with attractive walls are explored for varying pore radius and strength of the attractive wall potential by molecular dynamics simulations of a coarse-grained model. Local quantities such as the fraction of monomeric units bound to the surface and the bond-orientational order parameter as well as the radial density distribution are studied, as well as the global chain extensions parallel to the cylinder axis and perpendicular to the cylinder surface. A nonmonotonic convergence of these properties to their counterparts for adsorption on a planar substrate is observed due to the conflict between pore surface curvature and chain stiffness. Also the interpretation of partially adsorbed chains in terms of trains, loops, and tails is discussed.

Temporal lobe epilepsy (TLE) is the most common form of focal epilepsy. Dysregulation of glutamate transporters has been a common finding across animal models of epilepsy and in patients with TLE. In this study, we investigate NRG-1/ErbB4 signaling in epileptogenesis and the neuroprotective effects of NRG-1 treatment in a mouse model of temporal lobe epilepsy. Using immunohistochemistry, we report the first evidence for NRG-1/ErbB4-dependent selective upregulation of glutamate transporter EAAC1 and bihemispheric neuroprotection by exogeneous NRG-1 in the intrahippocampal kainic acid (IHKA) model of TLE. Our findings provide evidence that dysregulation of glutamate transporter EAAC1 contributes to the development of epilepsy and can be therapeutically targeted to reduce neuronal death following IHKA-induced status epilepticus (SE).

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.

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 externally driven systems, such as unmixing of sheared binary fluid mixtures, the driven lattice gas model, and the onset of Rayleigh-Benard convection. Then, some models for phase separation in models for active systems, where particles possess internal motility, are discussed, emphasizing what one can learn by extending analysis methods to study phase transitions in equilibrium systems by computer simulations to active systems. Specific examples will include colloid-polymer mixtures where the colloids are assumed to be active particles, and active Brownian particles. The extent to which concepts familiar from the study of equilibrium systems are still useful will be critically discussed.