Dwaipayan Chakrabarti

Self-assembly of anisotropic particles

We discuss the main features of the potential energy landscape that are associated with efficient ‘structure-seeking’ systems for particles interacting via anisotropic, pairwise additive forces. The interparticle potentials employed here are intended for a coarse-grained description of mesoscopic building blocks, such as colloids or functionalised metal clusters. We show that the anisotropy of the building blocks and the orientation-dependent interaction strengths are the most important factors that govern self-assembly into particular target morphologies. By varying the model parameters, the self-assembling behaviour can be systematically tuned. Design principles are outlined for various structures, and we postulate a sufficient condition for building-blocks to self-assemble into helical strands.

Emergent Complexity from Simple Anisotropic Building Blocks: Shells, Tubes, and Spirals

We describe a remarkably simple, generic, coarse-grained model involving anisotropic interactions, and characterize the global minima for clusters as a function of various parameters. Appropriate choices for the anisotropic interactions can reproduce a wide variety of complex morphologies as global minima, including spheroidal shells, tubular, helical and even head-tail morphologies, elucidating the physical principles that drive the assembly of these mesoscopic structures. Our model captures several experimental observations, such as the existence of competing morphologies, capsid polymorphism, and the effect of scaffolding proteins on capsid assembly.

Rational design of helical architectures

Nature has mastered the art of creating complex structures through self-assembly of simpler building blocks. Adapting such a bottom-up view provides a potential route to the fabrication of novel materials. However, this approach suffers from the lack of a sufficiently detailed understanding of the noncovalent forces that hold the self-assembled structures together. Here we demonstrate that nature can indeed guide us, as we explore routes to helicity with achiral building blocks driven by the interplay between two competing length scales for the interactions, as in DNA. By characterizing global minima for clusters, we illustrate several realizations of helical architecture, the simplest one involving ellipsoids of revolution as building blocks. In particular, we show that axially symmetric soft discoids can self-assemble into helical columnar arrangements. Understanding the molecular origin of such spatial organisation has important implications for the rational design of materials with useful optoelectronic applications.

Designing a bernal spiral from patchy colloids

A model potential for colloidal building blocks is defined with two different types of attractive surface sites, described as complementary patches and antipatches. A Bernal spiral is identified as the global minimum for clusters with appropriate arrangements of three patch-antipatch pairs. We further derive a minimalist design rule with only one patch and antipatch, which also produces a Bernal spiral. Monte Carlo simulations of these patchy colloidal building blocks in the bulk are generally found to corroborate the global optimization results.

Decoupling Phenomena in Supercooled Liquids: Signatures in the Energy Landscape

A significant deviation from the Debye model of rotational diffusion in the dynamics of orientational degrees of freedom in an equimolar mixture of ellipsoids of revolution and spheres is found to begin at a temperature at which the average inherent structure energy of the system starts falling with drop in temperature. We argue that this onset temperature corresponds to the emergence of the process as a distinct mode of orientational relaxation. Further, we find that the coupling between rotational and translational diffusion breaks down at a still lower temperature where a change occurs in the temperature dependence of the average inherent structure energy.

Design principles for Bernal spirals and helices with tunable pitch.

Using the framework of potential energy landscape theory, we describe two in silico designs for self-assembling helical colloidal superstructures based upon dipolar dumbbells and Janus-type building blocks, respectively. Helical superstructures with controllable pitch length are obtained using external magnetic field driven assembly of asymmetric dumbbells involving screened electrostatic as well as magnetic dipolar interactions. The pitch of the helix is tuned by modulating the Debye screening length over an experimentally accessible range. The second design is based on building blocks composed of rigidly linked spheres with short-range anisotropic interactions, which are predicted to self-assemble into Bernal spirals. These spirals are quite flexible, and longer helices undergo rearrangements via cooperative, hinge-like moves, in agreement with experiment.

Universal Power Law in the Orientational Relaxation in Thermotropic Liquid Crystals

We observe a surprisingly general power law decay at short to intermediate times in orientational relaxation in a variety of model systems (both calamitic and discotic, and also lattice) for thermotropic liquid crystals. As all these systems transit across the isotropic-nematic phase boundary, two power law relaxation regimes, separated by a plateau, emerge, giving rise to a steplike feature (well known in glassy liquids) in the single-particle second-rank orientational time correlation function. In contrast to its probable dynamical origin in supercooled liquids, we show that the power law here can originate from the thermodynamic fluctuations of the orientational order parameter, driven by the rapid growth in the second-rank orientational correlation length.

Exploring Energy Landscapes: Metrics, Pathways, and Normal-Mode Analysis for Rigid-Body Molecules

We present new methodology for exploring the energy landscapes of molecular systems, using angle-axis variables for the rigid-body rotational coordinates. The key ingredient is a distance measure or metric tensor, which is invariant to global translation and rotation. The metric is used to formulate a generalized nudged elastic band method for calculating pathways, and a full prescription for normal-mode analysis is described. The methodology is tested by mapping the potential energy and free energy landscape of the water octamer, described by the TIP4P potential.

Complete breakdown of the Debye model of rotational relaxation near the isotropic-nematic phase boundary: Effects of intermolecular correlations in orientational dynamics

The Debye-Stokes-Einstein (DSE) model of rotational diffusion predicts that the orientational correlation times tau l vary as [l(l+1)]-1, where l is the rank of the orientational time correlation function (given in terms of the Legendre polynomial of rank l). One often finds significant deviation from this prediction, in either direction. In supercooled molecular liquids where the ratio tau 1/tau 2 falls considerably below 3 (the Debye limit), one usually invokes a jump diffusion model to explain the approach of the ratio tau 1/tau 2 to unity. Here we show in a computer simulation study of a standard model system for thermotropic liquid crystals that this ratio becomes much less than unity as the isotropic-nematic phase boundary is approached from the isotropic side. Simultaneously, the ratio tau 2/eta, eta, being the shear viscosity of the liquid, becomes much larger than the hydrodynamic value near the I-N transition. We also analyze the breakdown of the Debye model of rotational diffusion in ratios of higher order orientational correlation times. We show that the breakdown of the DSE model is due to the growth of orientational pair correlation and provide a mode coupling theory analysis to explain the results.

Coupled linear and rotary motion in supramolecular helix handedness inversion

We report on a remarkable pathway for the inversion of handedness in a model supramolecular helix that exhibits repeated extension and contraction coupled with correlated rotation. The pathway involves a boundary between two segments of opposite handedness, which propagates along the helix through a hopping mechanism, causing periodic opening and closing of a gap between the two segments, while they rotate cooperatively in opposite directions. While the hopping mechanism is likely to have wider implications for reversal of helix handedness in general, the existence of such a pathway suggests the possibility of designing a novel class of nanoscale machines exploiting helix handedness inversion.