Amitabha Chakrabarti

Morphology of thin block copolymer films on chemically patterned substrates

We present results from a numerical study of a coarse-grained model of di-block copolymer (BCP) thin films confined between two hard walls. One of these walls is neutral to the components of the BCP melt and the other one contains chemical inhomogeneities with a repeat spacing length scale comparable to the linear size of the BCP molecules. We find that the morphology of the BCP thin film is strongly influenced by the commensurability between the bulk unconstrained lamellar size λ*, and the linear size of the surface inhomogeneities w. When w≈λ*/2, the ordered morphology of the diblock copolymers has a strong overlap with the pre-assigned substrate chemical pattern throughout the film. However, for w≈λ*, the overlap strongly depends on the distance from the substrate surface. Close to the substrate surface, the overlap of the morphology with the pre-assigned chemical pattern is large but the pattern becomes out-of-phase at a distance of approximately λ*/2 from the substrate. For w≈3λ*/4, the morphology of...

Self-assembly of ligated gold nanoparticles: phenomenological modeling and computer simulations.

We study the assembly of ligated gold nanoparticles by both phenomenological modeling and computer simulations for various ligand chain lengths. First, we develop an effective nanoparticle-nanoparticle pair potential by treating the ligands as flexible polymer chains. Besides van der Waals interactions, we incorporate both the free energy of mixing and elastic contributions from compression of the ligands in our effective pair potentials. The separation of the nanoparticles at the potential minimum compares well with experimental results of gold nanoparticle superlattice constants for various ligand lengths. Next, we use the calculated pair potentials as input to Brownian dynamics simulations for studying the formation of nanoparticle assembly in three dimensions. For dodecanethiol ligated nanoparticles in toluene, our model gives a relatively shallower well depth and the clusters formed after a temperature quench are compact in morphology. Simulation results for the kinetics of cluster growth in this case are compared with phase separations in binary mixtures. For decanethiol ligated nanoparticles, the model well depth is found to be deeper, and simulations show hybrid, fractal-like morphology for the clusters. Cluster morphology in this case shows a compact structure at short length scales and a fractal structure at large length scales. Growth kinetics for this deeper potential depth is compared with the diffusion-limited cluster-cluster aggregation (DLCA) model.

Ordering of block copolymer melts in confined geometry

Microphase separation of symmetric diblock copolymers between two rigid walls is simulated by a coarse‐grained model to study the geometry of the microdomains without presupposing their basic shape. The geometry is found to be dependent on the wall separation and the domains can be either aligned horizontally or vertically. The horizontal geometry is induced by wetting at the walls and lamellas parallel to them develop quickly after a quench from the one‐phase region. The vertical geometry involves domains oriented perpendicular to the walls and develops much more slowly. For identical walls, some segregation of the wetting phase to the walls is observed for the vertical geometry. This segregation does not significantly change the structure. If the vertical phase develops between walls that attract opposite phases, however, a linear concentration profile develops. In some cases the structure of this vertical phase is found to be quite different from simple, perpendicularly oriented lamellas.

Dynamics of phase separation in a binary polymer blend of critical composition

We report results of a detailed numerical study of the phase separation process in a three dimensional model of polymer blends. The model system considered by us is described by Flory–Huggins–de Gennes free‐energy functional. For a critical quench, we numerically integrate the corresponding time evolution equation for the conserved order parameter based on the above free‐energy functional. We study the time dependence of the characteristic domain size as well as the pair correlation function and the structure factor for several quench temperatures. The results indicate that the growth law for the characteristic domain size is given by a modified Lifshitz–Slyozov law and the growth law exponent is independent of the quench temperature. We also find that both the pair correlation function and the structure factors show dynamical scaling at late times.

Surface‐induced ordering in block copolymer melts

Surface‐induced ordering in block copolymer melts is studied numerically. For symmetric copolymers, the thickness of the surface‐enrichment layer is found to scale as Req∼Nθ with θ≊0.6, suggesting the system is undergoing a surface‐induced strong segregation. The density profile perpendicular to the interacting surface is described quite well by the form predicted by Fredrickson in a mean‐field analysis. In asymmetric copolymers, the surface is found to have a profound effect on domain formation. For some off‐critical compositions, domains were found to form near the surface with a geometry different from that in the bulk; while for stronger asymmetry in composition, minority domains were nucleated near the wall only, long before any formed in the bulk. These interesting pattern formation processes should be observable in experiments using a depth profiling technique.

Phase separation dynamics in off-critical polymer blends

A numeric integration of the spinodal decomposition process in an off‐critical mixture of binary polymer blends is carried out to late times. The thermal fluctuation term in the evolution equation is found to be essential to avoid ‘‘freezing’’ of domain growth for such systems, an effect not present in small molecule systems. For deep quenches, late time domain growth follows the Lifshitz–Slyozov law and the scaling hypothesis is found to hold, although the scale invariant function differs in shape from the one obtained for a critical quench to the same temperature. For shallow quenches, although no freezing is observed, domain growth is found to be progressively slower as the spinodal curve is approached. For the model considered here, we do not find any evidence of the sharp transition in behavior that would be associated with a ‘‘transnodal’’.

Does Shape Anisotropy Control the Fractal Dimension in Diffusion-Limited Cluster-Cluster Aggregation?

Motivated by recent experiments of soot formation in premixed flames where a minority population of the “stringy” aggregates is found to have a fractal dimension as low as 1.2 instead of the classic diffusion-limited cluster-cluster aggregation (DLCA) value of 1.8, we address this same question in our simulation study: is there a distribution of fractal dimensions in a given ensemble of aggregates and does shape anisotropy of clusters control the fractal dimension? Our results, however, clearly show classic DLCA yields aggregates of a broad range of shapes all with Df≈1.8 independent of their shape, but with a shape dependent pre-factor k0 , in the relation between radius of gyration Rg , mass N, monomer radius a, and fractal dimension . Thus the pre-factor k0 gains in status as a descriptor of aggregate morphology so that aggregates should be described by the pair of parameters Df and k 0 , i.e., (Df, k0).

Extinction and the optical theorem. Part I. Single particles

We study the extinction caused by a single particle and present a conceptual phase-based explanation for the related optical theorem. Simulations of the energy flow caused by a particles presence in a collimated beam of light demonstrate how the extinction process occurs. It is shown that extinction does not necessarily cause a reduction of the energy flow along the exact forward direction. Implications regarding the measurement of the single-particle extinction cross section are discussed. This work is extended to noninteracting and interacting multiparticle groups in Part II [J. Opt. Soc. Am. A25, pp. 1514 (2008)].

A three parameter description of the structure of diffusion limited cluster fractal aggregates

A three parameter description of fractal aggregates is derived from the pair correlation function of the monomeric units that compose the aggregate. The parameters describe the mass fractal scaling with linear size (the fractal dimension), the packing fraction density of the spherical monomers, and the overall shape of the aggregates. Values for these three parameters are determined for diffusion limited cluster aggregates (DLCAs) in three dimensions. The effects of these parameters are found in terms of measureable quantities in both real and reciprocal space.

The sol to gel transition in irreversible particulate systems

A review of the process by which irreversible aggregation of solid particles creates fractal aggregates which eventually fill the entire system volume to form a gel, the sol to gel transition, is presented. Both simulation and experiment present a coherent description of the kinetics and resulting morphologies of this process. Enhanced kinetics occurs when the system is cluster dense. Surprisingly, the enhanced kinetics is governed by the mean-field Smoluchowski equation deep into the aggregation process, displays universality with cluster volume fraction (or, equivalently the ratio of cluster separation to size, or time normalized by the gel time), and is described by one parameter, the aggregation kernel homogeneity. Aggregates show canonical cluster–cluster morphology until the point where the cluster volume fraction is unity; then hybrid superaggregates with fractal dimensions of ca. 1.8 over small length scales and 2.6 over large length scales form.