We present model calculations to explore the possibility of colloidal island formation over strained surfaces. Colloids, aggregating due to attractive depletion interactions, are deposited onto a colloidal surface whose lattice constant and geometry can be varied by optical forces. This allows precise control of the strain between the substrate and the colloidal adsorbate. Three different strain fields are considered: fields with either an unidirectional or a hexagonal variation of strain, and fields with a combination of both variations. We find that the unidirectional field induces the formation of infinitely extended ridges, while hexagonal strain fields lead to regular pyramidal island structures which can be distorted in a controlled way by adding the unidirectional strain component. We furthermore study the dependence of island size on strain strength for the hexagonal strain pattern and find that the area occupied by an island is a constant fraction of the strain field's repeat unit. To find out more have a look at J. Phys.: Condens. Matter 21, 245102 (2009).

Fig. 4: Landscape of colloidal islands over a substrate surface, as obtained from the model calculation presented in this work. The white colloidal spheres fixed at the minima of a light-induced potential form a substrate with variable lattice constant and island-forming green spheres are the colloids deposited over the substrate.

Currently I am studying the melting and depinning transition of two-dimensional systems on corrugated surfaces. Such as in J. Phys.: Condens. Matter 20, 245104 (2008) we presented Monte Carlo simulations of two-dimensional colloidal solids interacting with disordered and ordered substrate potentials which in practice are created by interfering laser beams. The filling factor η, the number of colloids per potential minimum of the substrate, is taken to be either 1 or 1/9. For an ordered and commensurate two-dimensional substrate with η = 1, the solid, being pinned to the periodicity of the substrate, always adopts the perfect order of the substrate, irrespective of the strength of the pinning potential. For η = 1/9, a solid phase ('floating-solid') with the same translational order decay characteristic as the free solid can form. We explore the nature of this phase and show phase-diagrams containing all three transitions: liquid to pinned-solid, liquid to floating-solid and floating-solid to pinned-solid. We also consider the case of a disordered substrate with a filling factor η = 1/9 and show that a floating-solid phase can also exist above such a glassy substrate.

Fig. 1: Phase-diagrams spanned by temperature and ordered substrate strength V
Fig. 2: Phase-diagrams spanned by temperature and disordered substrate strength V

The phenomenon that a class of externally driven systems evolves naturally into a state of no single characteristic size or time is known as self-organized criticality (SOC). Examples include Earthquake, Forest fire, Coagulation, River network, Cluster size distribution in anti-percolation, Biological evolution etc. Sandpile Model is used as a prototypical model for studying SOC. In literature there are many different sandpile Models studied. Some of the widely studied modes are Bak, Tang and Wiesenfeld (BTW) Model, Manna Stochastic Model (MSM), Dhar Directed Model, Zhang Model etc. All these models are studied by applying some constraints on the flow of the sands during the evolution of the sandpile. The motivation behined such studies is to find out how the microscopic properties can effect the criticalily of a self organised system. In our work we studied a new sandpile model by imposing a rotational constraint on the flow sand grains. and thus we call our model as Rotational Sandpile Model (RSM). In this new model we found that even though our rules of the movement of the sand grains are deterministic (like BTW), but the critical behaviour of RSM is similar to MSM. To find out more have a look at Phys. Rev. E. 75, 041122 (2007).

Fig. 3: Time auto correlation C(t) is plotted against time t for BTW (solid line), MSM (dashed line) and RSM (dotted line). There is a long range correlation for BTW. The toppling waves are uncorrelated for both MSM and RSM.