Extensive computer simulations are performed for a few model glass-forming liquids in both two and three dimensions to study their dynamics when a randomly chosen fraction of particles are frozen in their equilibrium positions. For all the studied systems, we find that the temperaturedependence of the α relaxation time extracted from an overlap function related to the self part of the density autocorrelation function can be explained within the framework of the Random First Order Transition (RFOT) theory of the glass transition. We propose a scaling description to rationalize the simulation results and show that our data for the α relaxation time for all temperatures and pin concentrations are consistent with this description. We find that the fragility parameter obtained from fits of the temperature dependence of the α relaxation time to the Vogel-Fulcher-Tammann (VFT) form decreases by almost an order of magnitude as the pin concentration is increased from zero. Our scaling description relates the fragility parameter to the static length scale of RFOT and thus provides a physical understanding of fragility within the framework of the RFOT theory. Implications of these findings for the values of the exponents appearing in the RFOT theory are discussed.

Existence and growth of amorphous order in supercooled liquids approaching glass transition is a subject of intense research. Even after decades of work, there is still no clear consensus on the molecular mechanisms that lead to a rapid slowing down of liquid dynamics approaching this putative transition. The existence of a correlation length associated with amorphous order has recently been postulated and also been estimated using multi-point correlation functions which cannot be calculated easily in experiments. Thus the study of growing amorphous order remains mostly restricted to systems like colloidal glasses and simulations of model glass-forming liquids. In this Letter, we propose an experimentally realizable yet simple correlation function to study the growth of amorphous order. We then demonstrate the validity of this approach for a few well-studied model supercooled liquids and obtain results which are consistent with other conventional methods.Glasses are ubiquitous in nature and are of immense practical importance in our day-to-day lives as well as in modern technology. In spite of knowing their presence and usefulness from the early history of mankind, the nature of the glassy state and the glass transition, where the viscosity of a liquid increases by many orders of magnitude within a narrow temperature or density window, still puzzles the scientific community and is believed to be one of the major unsolved problems in condensed matter physics [1][2][3][4][5][6][7][8][9]. The viscosity of a glass forming liquid increases so dramatically that one is often tempted to believe that viscosity probably diverges at a certain critical temperature associated with a thermodynamic phase transition. Thus, not surprisingly, there are two types of theories on glass transition. The first type assumes that the (ideal) glass transition is a thermodynamic phase transition and glassy states are believed to be a thermodynamic state of matter. This approach is taken by the Random First Order Transition (RFOT) theory [10][11][12]. The other approach is to consider the glass transition to be a purely dynamic phenomenon and the slowdown of dynamics is thought to be a result of an ever increasing number of self-generated kinetic constraints with supercooling [13][14][15].In spite of all the differences in opinion about the existence of a true thermodynamic glass transition, there is a consensus about the existence and growth of correlation lengths along with the rapid increase in viscosity or relaxation time [2][3][4][5][7][8][9]. Recently there have been a lot of progress in identifying at least two different length scales -(a) a dynamic length scale akin to the length scale characterizing the heterogeneity present in the dynamics of supercooled liquids [4,5,8] and (b) a static length scale of the so called "amorphous order" [7,[16][17][18][19][20][21]. Simple two-point density correlation functions have been shown to be unsuitable for the identification of the build up of these correlations in the supercooled liquids. A ...

Breakdown of Stokes-Einstein relation in supercooled liquids is believed to be one of the hallmarks of glass transition. The phenomena is studied in depth over many years to understand the microscopic mechanism without much success. Recently it was found that violation of StokesEinstein relation in supercooled liquids can be tuned very systematically by pinning randomly a set of particles in their equilibrium positions. This observation suggested a possible framework where breakdown of Stokes-Einstein relation in the dynamics of supercooled liquids can be studied with precise control. We have done extensive molecular dynamics simulations to understand this phenomena by analyzing the structure of appropriately defined set of dynamically slow and fast particles clusters. We have shown that the Stokes-Einstein breakdown actually become predominant once the cluster formed by the slow particles percolate the entire system size. Finally we proposed a possible close connection between fractal dimensions of these clusters and the exponents associated with the fractional Stokes-Einstein relation.