Nonlinear Hydrodynamics of a Hard Sphere Fluid Near the Glas(9)

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

arisesfromnonlinearitiesofdensity uctuationsintheliquidorfromtransitionsamongdi erentglassyminimaofthefreeenergy.Itisnotpossibletodistinguishbetweenthee ectsofthesetwokindsofprocessesinconventionalMDsimulations.

Wehavestudiedthetime-decayofS(q,t),thesphericallyaveragedspatialFouriertransformofthetime-dependentdensitycorrelationfunctionofthehard-sphereliquid,fordi erentvaluesofwavevectorqandforanumberofvaluesofthereduceddensityn (n ≡ρ0σ3,whereρ0istheaveragenumberdensityandσisthehardspherediameter)intherange0.75 0.93.ItwasfoundinRef.(36)thatahardspheresystemdescribedbyadiscretizedversionoftheRYfreeenergyexhibitsacrystallizationtransitionnearn =0.83.SincethepresentcalculationusesthesamediscretizedfreeenergyasthatofRef.(36),thesystemmaybeconsideredtobeinthe‘supercooled’regimeforalargepartofthedensityrangeconsideredbyus.Thenumericale ciencyoftheLangevindynamicsarisingfromtheuseofcoarsegrainedvariablesenablesustoverifythatthestaticsofthesystemremainstationarythroughoutthelongtimeintervalsthatweconsider.Theob-serveddynamicbehaviordescribedlaterindetailexhibitsanumberofcharacteristicglassyfeatures.Theseincludestretchedexponentialdecayofcorrelations,two-stagerelaxation,andVogel-Fulchergrowthofrelaxationtimes.OurresultsareinagreementwithexistingMDdata28onthedynamicsofthehard-sphereliquidandinqualitativeagreementwithotherMDresultsobtainedforsimilarbutdi erentsystems.ThisobservationestablishesthecorrectnessoftheNFHdescriptionusedinthisworkandalsodemonstratesthattheRYfreeenergycontainstheessentialphysicsofthedynamicsofthissystem.Ourcalcu-lationsalsoreproducequalitativelyanumberofpredictionsofMCtheories,however,we ndsigni cantdeviationsfromsomeofthequantitativeMCpredictions40fortheglassykineticsofthehard-spheresystem.Ourstudyindicatesthattheonsetofglassyfeaturesin