Nonlinear rheology of a highly supercooled liquid

Abstract

We numerically examine nonlinear rheology of a highly supercooled two-dimen- sional fluid in shear flow via molecular-dynamics simulation. The viscosity exhibits marked shear-thinning behavior when the shear rate _ exceeds the inverse of the relaxation time . Bond breakage events among particle pairs are found to occur collectively in clusters. The characteristic size of such clusters grows strongly with lowering the temperature and decreases rapidly with increasing _ as b (_ ) 1= 4 .H ere 1=b (_ ) is the bond breakage rate tending to 1= for _ 1a nd growing as _for _ 1. The viscosity is of order b (_ ) in glassy states. In highly supercooled fluids below the melting temperature the structural relaxations are very slow (1), (2). The zero-shear viscosity (0) is expected to be proportional to a long rheological time . An experiment on polymers suggested that is on the order of the so-called relaxation time (3). Then we are interested in a nonlinear response regime in shear flow when the shear rate _ exceeds the inverse of (4). Though experiments on glass-forming fluids in this direction have not been abundant (5)-(7), Simmons et al. found that the viscosity (_ )= xy= _ exhibits marked shear-thinning behavior (_ ) =(0)=(1 + _) in soda-lime-silica glasses in steady states under shear. After application of shear, they also observed overshoots of the shear stress before approach to steady states. However, because recent theoretical eorts have been focused on slow relaxation of time correlation functions, such nonlinear, nonequilibrium regimes have not attracted enough attention. The aim of this letter is to numerically examine nonlinear rheology in a two-dimensional model fluid mixture in supercooled amorphous states. Our system is composed of two dierent atomic species, 1 and 2, with the numbers N1 = N2 = 5000, interacting via the soft-core potentialv(r )= (=r)12 with =( + ) =2, wherer is the distance between two particles and; = 1 ;2 (8). The interaction is truncated at r =4 : 5 1. The leapfrog algorithm is adopted to solve the dierential equations with a time step of 0:0050. The space and time are measured in units of1 and0 =( m 1 2 1=)1=2. The average density is xed atn =0 : 8=2 1. We take the size and mass ratios at2=1 =1 : 4a ndm 2=m1 =2 . In our two-component system the dierence of the particle sizes prevents crystallization at low temperatures, which will occur in one-component systems. We specify the thermodynamic