<%= SiteHeaderTitle %> 

 

The Non-equilibrium Behavior of Fluctuation Induced Forces:  While techniques to compute thermal fluctuation induced, or pseudo-Casimir, forces in equilibrium systems are well established, the same is not true for non-equilibrium cases. We present a general formalism that allows us to unambiguously compute non-equilibrium fluctuation induced forces by specifying the energy of interaction of the fluctuating fields with the boundaries. For a general class of classical fields with dissipative dynamics, we derive a very general relation between the Laplace transform of the time-dependent force and the static partition function for a related problem with a different Hamiltonian. In particular, we demonstrate the power of our approach by computing, for the first time, the explicit time dependence of the non-equilibrium pseudo-Casimir force induced between two parallel plates, upon a sudden change in the temperature of the system. We also show how our results can be used to determine the steady-state behavior of the non-equilibrium force in systems where the fluctuations are driven by colored noise.

David S. Dean and Ajay Gopinathan, "The Non-equilibrium Behavior of Pseudo-Casimir Forces", J. Stat. Mech. L08001 (2009)

David S. Dean and Ajay Gopinathan, “The Non-equilibrium Thermal Casimir Effect”, Submitted to Phys. Rev. E

 

Non-trivial geometries in shrinking plastic sheets: Biaxially oriented polystyrene thermoplastic sheets (shrinky dinks) have been recently used by one of us (Khine, Lab on a Chip, 2008) as a template for rapid and non-photolithographic microfluidic pattern generation. This method utilizes the shrinkage properties of the shrinky dinks upon heating to generate microscale structures. During the heating process the sheets show a variety of non-trivial three dimensional intermediate structures before returning to a shrunken flat state upon completion of the process. We show that these structures arise due to the imposition of a non-uniform spatial metric on the sheet which in turn is governed by the dynamic temperature gradients generated in the sheet. Our results allow us to quantitatively describe the dynamic sequence of structures generated and suggest routes to the design and fabrication of different structures in a controllable fashion.

Anthony Grimes, Michelle Khine, Arnold Kim and Ajay Gopinathan (in preparation)

 

Controllable biaxial and uniaxial nanowrinkles (see figure) can also be fabricated by a simple two-step approach  using the shrinking plastic substrate -  metal deposition and subsequent heating. The wavelengths of the wrinkles can be tuned by controlling the thickness of deposited metal. Ready integration of the nanowrinkles into microchannels and their effectiveness in surface enhanced sensing indicates a host of potential applications.

Chi-Cheng Fu, Anthony Grimes, Maureen Long, Christopher G. L. Ferri, Brent D. Rich, Somnath Ghosh, Sayantani Ghosh, Luke P. Lee, Ajay Gopinathan, Michelle Khine, "Tunable Nanowrinkles on Shape Memory Polymer Sheets", Advanced Materials (Early view : DOI 10.1002 / adma.200902294)

 

 Charge Transport in Fractal Networks:  We examine how the fractal nature of the interpenetrating networks in bulk heterojunction materials affects the transport of charges in such systems. Such systems can be potentially used in next generation solar cells and understanding in such systems is of critical importance and point to directions for the improvement of such materials.

Wanli Ma, Ajay Gopinathan and Alan. J. Heeger, “Nanostructure of the Interpenetrating Networks in Poly(3-hexylthiophene)/fullerene Bulk Heterojunction Materials: Implications for Charge Transport”, Advanced Materials, 19(21), 3656 (2007)

 

 

Statistically locked-in transport : Measurements of colloidal transport through arrays of micrometer-scale potential wells created with holographic optical tweezers were performed at the Grier Lab . Varying the orientation of the trap array relative to the external driving force resulted in a hierarchy of lock-in transitions analogous to symmetry-selecting processes in a wide variety of systems with implications for immediate applications for continuously fractionating particles, biological cells, and macromolecules. Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a Devil's staircase hierarchy of commensurate trajectories depending on the orientation of the driving force.The experiments did indeed reveal such a hierarchy, but not with the predicted structure. The microscopic trajectories, moreover, appeared to be random, with commensurability emerging only in a statistical sense. We introduced an idealized model for periodically modulated transport in the presence of randomness that captures both the structure and statistics of such statistically locked-in trajectories.

Ajay Gopinathan, D.G. Grier, "Statistically Locked-in Transport through Periodic Potential Arrays", Phys. Rev. Lett., 92, 130602 (2004)

 

 

Self Assembly of Nanowires : Experiments at the Jaeger lab have shown that when metals are evaporated and deposited on a templated substrate, like a phase separated diblock copolymer surface, certain metals show a marked preference for one phase over the other and in certain cases form continuous wires of nanometer scale. What surprised us was the stability of these wires which by surface energy considerations should exhibit the pearling instability (a liquid cylinder breaking up into drops ). We proposed an explanation based on the rate limiting step of nanocluster coalescence being nucleation of new terraces. We show that the different morphologies obtained can be understood in terms of the relative importance of the energetics and kinetics. We also show the existence of ``non-trivial'' correlations  between adjacent wires that can be understood based on a purely kinetic mechanism. We also compare these correlations quantitatively to those obtained from simulations done with the relevant experimental parameters and find them in good agreement.

Ajay Gopinathan, "Kinetic Self-Assembly of Metals on Co-Polymer Templates", Phys. Rev. E, 71(4) 041601 (2005)

 

 

 Non-equilibrium kinetics :  Deliberately miscutting a crystal surface can  produce a regular array of monoatomic steps. Under suitable conditions (temperature, oxygen dosage) these steps can be made to merge to form double height double width steps. Experiments performed at the Sibener lab have been instrumental in elucidating the mechanism of this process. It is found that step doubling proceeds via a nucleation step where two adjacent step edges come together at a "point" and then the two steps "zipper" together irreversibly. Theoretical effort has gone into describing the mechanism for a pair of steps. However when there is a large array of steps, as in reality, the dynamical process of nucleation and zippering gives rise to a non-equilibrium evolution of the surface morphology. One also expects defect structures of various types.  We study the time evolution of the surface morphology by making an approximate mapping to the parking lot problem. This allows us to predict the number and nature of the defects as well as the time evolution. We also suggest protocols that can help generate surfaces with fewer defects in less time.

Defect Formation and Kinetics of Atomic Terrace Merging, Ajay Gopinathan and T.A. Witten, Phys. Rev. E 70, 041603 (2004)

Crumpling - Dynamics : A crumpled sheet has certain characteristic features that we are all familiar with. There are the sharply curved places - ridges and the almost flat places- the facets. Extensive work characterizing the static properties of the ridges and facets has been done by Witten and coworkers. But we knew of no characterization of the dynamics. We were interested in the question : what happens if we tap a certain point on a crumpled sheet and listen at another? What changes in elastic wave propagation arise due to the unique structures in a crumpled sheet ? To answer this we first derived the wave equation governing transverse elastic waves on an arbitratily curved and strained surface using a Lagrangian formalism. Our analysis led us to the conclusion that the ridges act as barriers leading to the trapping of certain modes within the facets!!

Trapping of Vibrational Energy in Crumpled Sheets :  Ajay Gopinathan, T.A. Witten and S.C. Venkataramani. Phys. Rev. E., 65, 036613 (2002)

 

Charged Colloidal Systems : There is now a growing body of evidence that like charge colloidal spheres dispersed in water need not simply repel each other. Under certain conditions they actually attract. Experiments like those performed at the Grier Lab are helping us gain insights into this phenomenon.In this work we investigated the influence of geometric confinement on the free energy of an idealized model for charge-stabilized colloidal suspensions. The mean-field Poisson-Boltzmann formulation for this system predicts pure repulsion among macroionic colloidal spheres. However fluctuations in the simple ions distribution provide a mechanism for the macroions to attract each other at large separations.Although this Casimir interaction long-ranged,we found it was too weak to influence colloidal crystals dynamics.

Weak Long-Ranged Casimir Attraction in Colloidal Crystals : Ajay Gopinathan, Tong Zhou, S.N. Coppersmith, L.P.  Kadanoff and D.G. Grier. Europhys. Lett., 57 (3), 451 (2002)

 

 

Phase Ordering Kinetics :  Consider a collection of spins at a high temperature that is suddenly quenched to zero temperature. What follows is domain coarsening where domains of up and down spins grow and grow. An interesting question is : given a spin what is the probability that after time t it still retains its original state without ever having flipped? An exponent characterizing how this probability scales with the typical length scale in the system is called the persistence exponent  beta. We found an exact expression for this quantity for 1D q-state Potts' system (spin with q states) with a suitably chosen model of coarsening.

Scaling Exponent Beta for Coarsening in a 1D q-state Potts' System : Ajay Gopinathan. J.Phys. A, 31 (1998) 5499