Nonlinear Hydrodynamics of a Hard Sphere Fluid Near the Glas(3)

We conduct a numerical study of the dynamic behavior of a dense hard sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free energy functional of the Ramakrishnan-Yussouff form. We find that th

I.INTRODUCTION

Despiteextensiveexperimental,numericalandtheoreticalinvestigations1,2overseveraldecades,thepresentunderstandingoftheslownon-exponentialdynamicsofdenseliquidsneartheglasstransitionremainsincomplete.Whenaliquidiscooledrapidlyenoughtotemperaturesbelowtheequilibriumfreezingtemperature,crystallizationisbypassedandthesystemundergoesatransitionintoanamorphoussolidstatecalledaglass.Thecharacteristicrelaxationtimet ,asre ectedinalargenumberofexperimentallymeasuredquantitiessuchasviscosityanddielectricrelaxation,growsrapidlyinthesupercooledstateasthetemperatureisdecreasedorthedensityincreased.Theglasstransitiontemperature(oralternatively,density)Tg(ρg)isconventionallyde nedasthetemperature(density)wheretheviscosityreachesavalueof1013poise.

Inrecentyears,considerableprogressinthedevelopmentofatheoreticalandex-perimentalunderstandingofthephenomenaassociatedwithglassformationandtheglasstransitionhasbeenachieved.Inparticular,theso-calledmodecoupling(MC)theoriesoftheglasstransition3 10haveledtoaframeworkforunderstandingandinterpretingmanyexperimentalresults.InMCtheories,theslowingdownofthedynamicsneartheglasstransitionisattributedtoanonlinearfeedbackmechanismarisingfromcorrelationsofdensity uctuationsintheliquid.TheMCequationsforthedynamicsneartheglasstransitionwereoriginallyderived4,5fromthekinetictheoryofdense uidsandwerelater

6,7generalizedandextendedbyG¨otzeandco-workers

theories4,5.IntheoriginalversionofMC,thecharacteristictimescalesoftheliquidarepredictedtoexhibitapowerlawdivergenceatan‘idealglasstransition’orcrossovertemperatureTc,higherthanTg.However,thisdivergenceisnotfoundexperimentally:thepowerlawformbreaksdown,andrelaxationtimesatTcaretypicallyoforder10 8s.Morerecentcalculations

9,10have