Phase Behaviour & Dynamics Of An Agitated Monolayer Of Granular Rods

Abstract

In this thesis we have explored the no equilibrium phase behavior and dynamics of an agitated monolayer of macroscopic rod-like particles. The main objective of this thesis was to highlight the ways in which even the simplest nonequilibrium 2Dliquid-crystallinen system differs qualitatively from its thermal equilibrium counter part. One major finding of ours is the extreme sensitivity to shape in these nonequilibrium systems. In chapter 3 we saw that tapering the ends of the particles induced a change from 2–fold ordering to 4–fold ordering. As far as we know, this is the first experimental observation of ‘tetratic’ correlations in equilibrium or nonequilibrium settings. This shape dependence is also pronounced in the single particle dynamics where, in chapter 5, we saw that similar-shaped objects behave differently even if they have dissimilar aspect ratios. Another important finding of ours is that the density fluctuations in the nonequilibrium nematic are not merely larger than, but qualitatively different from, those seen in their equilibrium counterparts: the fluctuations of the population, in a region containing on average N particles, grow much faster than √N . Then on equilibrium nature of the systems we study is clearly visible even at the single-particle level where we observe violations of equipartition in all the particles we study. The anomalous fluctuations we observe can be under stood in the light of theories of flocking. We have motivated why our system can be thought of as a granular flock and in chapter 4 presented various quantitative observations that justify this claim: we see giant fluctuations that decay only logarithmically in time as predicted by a theory of active nematics. This supports the idea that granular systems can provide a faithful imitation of the collective dynamics of living flocks, thus offering an attractive and easily control able system on which to test the predictions of flocking theories. A part from being a table-top experiment, , our system has the two substantial advantages over living systems that there are no products of metabolism which need removing and that the population remains constant. Our work highlights the fact that the fascinating phenomena of flocking ,coherent motion and large-scale in homogeneity seen in living matter can be obtained in a system in which particles do not communicate except by contact, have no sensing mechanisms and are not influenced by the spatially-varying pressures and incentives of a biological environment. Directions to go from here are aplenty. There is a lot that needs to be done towards understanding the origins of the anomalous fluctuations: do they arise due to the coupling of mass currents to gradients in the nematic director field or is there some other mechanism at play? Though the observed motion of disclinations suggests the former, a thorough hand systematic study of defect behavior is lacking. How defects interact and whether there is any analogy to thermal-equilibrium defect-behavior is completely unexplored, theoretically and experimentally. Indeed, this would be of interest purely as a problem in nonequilibrium statistical mechanics independent of whether or not the system is described by theories of active nematics. A part from settling the important, fundamental issues regarding the giant fluctuations, one can explore the entire spectrum of rod-like particles and study its dynamics and phase behaviour. What happens to collections of javelins that are agitated in 2D geometries? Do they form steadily-moving flocks? What about the short cylinders? We have seen that in the dilute limit they behave in a polar fashion but at high area fractions they form a polar, 4–fold correlated states. At Intermediate densities will they form a polar phase? Why is it that the long cylinders do not show any polar dynamics? What factors govern whether a particle is polar or not? Can one engineer particles to efficiently translate random impulses in to directed motion? Thus, even the single particle dynamics offers many avenues for experimental exploration. However, there is also scope for theoretical work in this direction. A sound theoretical understanding of the individual particle’s behaviour will then pave the way for a microscopic theory for the collective granular-rod state.. This can then be compared to the active and flocking literature which his, largely, of a phenomenological nature as of now. In conclusion, we would like to say that our experiments have revealed many important and fascinating nonequilibrium phenomena. Our experiments demonstrate situations where ‘effective equilibrium’ approaches are in adequate. Such descriptions can accommodate neither the slow, giant, collective fluctuations we observe nor the non-equipartition at the single-particle level. Finally, as is often the case, our studies have thrown open many more questions than they have answered. We hope our experiments stimulate further studies and we believe that we are witnessing the birth of a new subfield at the crossroads of granular physics and the physics of flocks.