My research interests lie within the broad area of statistical mechanics and soft matter. I have working experience on the following topics

Cellular uptake of hard and deformable nanoparticles: 

Transport of engineered particles across lipid-bilayer membranes is important for cells to exchange information and material with the environment.  Large particles often get wrapped by membranes, a process that has been intensively investigated in the case of hard particles. However, many particles in vivo and in vitro are deformable, e.g., vesicles, filamentous viruses, macromolecular condensates, polymer-grafted nanoparticles, and microgels. We use vesicles as a generic model system for deformable particles. Here, we study the interaction of spherical and non-spherical vesicles of various sizes, shapes, and elastic properties with planar lipid-bilayer membranes. Using the Helfrich Hamiltonian, triangulated membranes, and energy minimization, we predict the interplay of vesicle shapes and wrapping states. The calculation of deformation energy in the wrapping process helps us to extract phase diagrams that show different wrapping transitions from non-wrapped to partial-wrapped to complete-wrapped states. 

Membrane-mediated interaction of elastic nanoparticles:

The wrapping of particles leads to local membrane deformation. Such deformation induces membrane-mediated interaction between partial-wrapped particles. We calculate the membrane-mediated pair interaction between partial-wrapped vesicles.  We predict purely repulsive interaction between the vesicles in deep-wrapped states. For shallow-wrapped states, the interaction potential depends on the orientation of the vesicles, with attraction for tip-to-tip orientation, and repulsion for side-by-side orientation. Our predictions may guide the design and fabrication of deformable particles for efficient use in diagnostics and therapeutics.

Evaporation-induced self-assembly:

Self-assembly of the colloidal particles via evaporation of colloidal drop suspensions is crucial for various applications, e.g., painting, coating, washing, or agriculture. The complete evaporation of the solvent from a suspension leaves a  deposited solid,  called supraparticle. Depending on material properties and evaporation rate, the structure of the supraparticles can be porous, amorphous, or crystalline. For a binary (particles with different sizes) colloidal suspension we have shown that the morphology of the supraparticles is controlled by the evaporation rate and the colloid size ratios. At fast evaporation rate a supraparticle with core-shell morphology can be achieved where the outer region is predominantly occupied by small colloids with crystalline structures, and the interior region is amorphously packed with a mixture of small and large colloids. 

Phase behavior and wetting phenomena of flexible and semiflexible polymers:

Phase behavior of flexible and semiflexible polymers is investigated by systematically varying the polymer length, stiffness, and solvent quality. The stiff polymers exhibit a single transition from an isotropic fluid to a nematic fluid. For less stiff polymers, however, also unmixing between isotropic fluids of different concentrations (ends at a critical point) occurs for temperatures above a triple point. We have shown that the critical behavior of these systems is compatible with the Ising universality class. Further, we study the wetting phenomena of flexible and semiflexible polymer solutions by systematically varying the polymer length, stiffness, and solvent quality. The wetting transitions of flexible and semiflexible polymers were quantified using Young’s equation for contact angle. Furthermore, we have studied the phase behavior of binary semiflexible polymer mixtures. The phase diagrams are predicted either with a triple point (isotropic phase coexists with two nematic phases) or with a nematic-nematic critical point.

Structural and mechanical properties of polymer-grafted nanoparticle melts:

Polymer-grafted nanoparticles (GNPs) have gained significant attention due to their wide range of applications in drug delivery, desalination, and photonic and phononic materials. Typically, GNPs exhibit core-shell morphology (a hard core and a soft corona). The softness of the corona can be tuned by changing the degree of polymerization of the grafted chains (on the surface of the nanoparticles) and grafting density. We have studied the structural and mechanical properties of GNP melts systematically varying the grafting density and degree of polymerization at fixed core size. At high grafting density, chain-sections close to the NP are extended and form a dry-layer. Further away from the NP, there is an interpenetration-layer with overlapping polymers from neighboring GNPs and the chain-sections have almost unperturbed conformations. Such partitioning is understood by developing a two-layer model, where the grafted polymers around an NP is represented by a spherical dry-layer and an interpenetration-layer. Our model quantitatively predicts the thicknesses of the two layers that depend on one universal parameter called the “overcrowding parameter” which represents the degree of overcrowding of grafted chains relative to chains in the melt. We have shown that the relative chain extension free energy non-monotonically increases with chain lengths at a fixed grafting density, and exhibits a well-defined maximum in the intermediate chain length which indicates the crossover from the dry layer-dominated to interpenetration layer-dominated regime. Such non-monotonic behavior of the relative chain extension energy is connected to the anomalous transport property of GNP melts. 

The mechanical property of these systems is also understood by looking at the elastic moduli which can be tuned by varying the NP loading through the grafting density and/or the length of the grafted polymers [8]. We have shown that even at a fixed NP loading, the mechanical properties of GNPs depend on their microscopic details. Further, we have investigated the transport of free molecules/macromolecules through GNP melts.

Kinetics of phase transition and critical phenomena:

We are interested in equilibrium and nonequilibrium statistical mechanics of materials in connection with phase transitions of different types, viz., paramagnetic to ferromagnetic, solid-solid, vapor-liquid, and vapor-solid transitions. To study these systems we have employed different toy models of statistical physics via Monte Carlo, molecular dynamics, and continuum model simulations. We addressed some of the important questions and queries related to dynamic critical phenomena, domain coarsening phenomena, and aging dynamics.

When phase transition occurs the thermodynamically unstable systems go towards an ordered equilibrium state via the formation and growth of domains of like-particles or spins. Depending on the composition or overall density of the systems, various types of patterns can emerge during the evolution process. The growth of these patterns typically follows power-law behavior. Via state-of-the-art methods the growth exponent is quantified for different phase-separating systems and we have shown that the value depends on the dimensionality and composition or overall density of the systems. Further, we have investigated aging dynamics which is related to the relaxation of an out-of-equilibrium system via the two-time order-parameter correlation function which follows power-law decay. Here we provide a full form of the autocorrelation function and then accurately estimated the aging exponent for different phase-separating systems via the application of finite-size scaling analysis. In the context of dynamic critical phenomena, the critical singularities of different transport, quantities are quantified via the application of finite-size scaling theory.