Isonicotinamide self-association: the link between solvent and polymorph nucleation.

We show that, in a controlled and reproducible way, specific solvents lead to specific polymorphic forms of isonicotinamide. We argue on the basis of Raman and FTIR spectroscopy that the hydrogen bonding in solution kinetically drives the nucleation towards a specific form. This generally may lead to good understanding and control of polymorphism and crystal nucleation.

Fluids density functional theory studies of supramolecular polymers at a hard surface.

We have applied a fluids density functional theory based on that of Yu and Wu [J. Chem. Phys. 116, 7094 (2002)] to treat reversible supramolecular polymers near a hard surface. This approach combines a hard-sphere fluids density functional theory with the first-order thermodynamic perturbation theory of Wertheim. The supramolecular polymers are represented in the theory by hard-spheres with two associating sites. We explore the effects of the bonding scheme, monomer concentration, and association energy upon the equilibrium chain sizes and the depletion lengths. This study is performed on simple systems containing two-site monomers and binary mixtures of two-site monomers combined with end stopper monomers which have only a single association site. Our model has correct behavior in the dilute and overlap regimes and the bulk results can be easily connected to simpler random-flight models. We find that there is a nonmonotonic behavior of the depletion length of the polymers as a function of concentration and that this depletion length can be controlled through the concentration of end stoppers. These results are applicable to the study of colloidal dispersions in supramolecular polymer solutions.

Phase behavior of polymer/nanoparticle blends near a substrate.

We use the recent fluids density functional theory of Tripathi and Chapman [Phys. Rev. Lett. 94, 087801 (2005); J. Chem. Phys. 122, 094506 (2005)] to investigate the phase behavior of athermal polymer/nanoparticle blends near a substrate. The blends are modeled as a mixture of hard spheres and freely jointed hard chains, near a hard wall. There is a first order phase transition present in these blends in which the nanoparticles expel the polymer from the surface to form a monolayer at a certain nanoparticle concentration. The nanoparticle transition density depends on the length of the polymer, the nanoparticle diameter, and the overall bulk density of the system. The phase transition is due to both packing entropy effects related to size asymmetry between the components and to the polymer configurational entropy, justifying the so-called "entropic push" observed in experiments. In addition, a layered state is found at higher densities which resembles that in colloidal crystals, in which the polymer and nanoparticles form alternating discrete layers. We show that this laminar state has nearly the same free energy as the homogeneously mixed fluid in the bulk and is nucleated by the surface.

Surface-induced first-order transition in athermal polymer-nanoparticle blends.

We investigate the phase behavior of athermal polymer-nanoparticle blends near a substrate. We apply a recent fluids density functional theory of Tripathi and Chapman to a simple model of the blend as a mixture of hard spheres and freely jointed hard chains, near a hard wall. We find that there is a first-order phase transition in which the nanoparticles expel the polymer from the surface to form a monolayer. The nanoparticle transition density depends on the length of the polymer and the overall bulk density of the system. The effect is due both to packing entropy effects related to size asymmetry between the components and to the polymer configurational entropy. The simplicity of the system allows us to understand the so-called "entropic-push" observed in experiments.

Statistical physics of grain-boundary engineering.

Percolation theory is now standard in the analysis of polycrystalline materials where the grain boundaries can be divided into two distinct classes, namely "good" boundaries that have favorable properties and "bad" boundaries that seriously degrade the material performance. Grain-boundary engineering (GBE) strives to improve material behavior by engineering the volume fraction c and arrangement of good grain boundaries. Two key percolative processes in GBE materials are the onset of percolation of a strongly connected aggregate of grains, and the onset of a connected path of weak grain boundaries. Using realistic polycrystalline microstructures, we find that in two dimensions the threshold for strong aggregate percolation c(SAP) and the threshold for weak boundary percolation c(WBP) are equivalent and have the value c(SAP) = c(WBP) =0.38 (1) , which is slightly higher than the threshold found for regular hexagonal grain structures, c(RH) =2 sin (pi/18) =0.347... . In three dimensions strong aggregate percolation and weak boundary percolation occur at different locations and we find c(SAP) =0.12 (3) and c(WBP) =0.77 (3) . The critical current in high T(c) materials and the cohesive energy in structural systems are related to the critical manifold problem in statistical physics. We develop a theory of critical manifolds in GBE materials, which has three distinct regimes: (i) low concentrations, where random manifold theory applies, (ii) critical concentrations where percolative scaling theory applies, and (iii) high concentrations, c> c(SAP) , where the theory of periodic elastic media applies. Regime (iii) is perhaps most important practically and is characterized by a critical length L(c) , which is the size of cleavage regions on the critical manifold. In the limit of high contrast epsilon-->0 , we find that in two dimensions L(c) proportional, gc/ (1-c) , while in three dimensions L(c) proportional, g exp [ b(0) c/ (1-c) ] / [c (1-c) ](1/2) , where g is the average grain size, epsilon is the ratio of the bonding energy of the weak boundaries to that of the strong boundaries, and b(0) is a constant which is of order 1. Many of the properties of GBE materials can be related to L(c) , which diverges algebraically on approach to c=1 in two dimensions, but diverges exponentially in that limit in three dimensions. We emphasize that GBE percolation processes and critical manifold behavior are very different in two dimensions as compared to three dimensions. For this reason, the use of two dimensional models to understand the behavior of bulk GBE materials can be misleading.

Scaling laws for critical manifolds in polycrystalline materials.

We study the surfaces of lowest energy through model polycrystalline materials in two and three dimensions. When the grain boundaries are sufficiently weak, these critical manifolds (CM's) lie entirely on grain boundaries, while when the grain boundaries are strong, cleavage occurs. A scaling theory for the intergranular to transgranular transition of CM's is developed. The key parameters are the average grain size g, the ratio of grain boundary to the grain interior energy, epsilon, and the sample size L. The key result is that a critical length scale exists, L(c)(g,epsilon), so that on short length scales lL(c), the critical manifold is rough. We develop a scaling theory for L(c) and find that in two dimensions L(c) approximately gx(y(2)), while in three dimensions L(c) approximately g exp(bx(y(3))), where x=epsilon/(1-epsilon) and b is a constant. Data from realistic polycrystalline grain structures are used to test the scaling theory. The exact lowest energy surface through model grain structures is found using a mapping to the minimum-cut/maximum-flow problem in computer science. As a function of grain-boundary energy, we observe the crossover from grain-boundary rupture to mixed mode failure (a mixture of transgramular and intergranular modes) and finally cleavage and that the two-dimensional data are consistent with y(2) approximately 3.0+/-0.3, while the three-dimensional data are more difficult to analyze, but are consistent with y(3) approximately 3.5+/-1.0.