MD-Simulation of Viscous Toluene
Ulf R. Pedersen & Thomas Schrøder
Department of Mathematics and Physics (IMFUFA),DNRF centre ”Glass and Time”,
Roskilde University, Postbox 260,DK-4000 Roskilde, Denmark
Outline
Toluene like model Molecular Dynamics are found
using Newtonian mechanics. Here, forces are given by Lennard-
Jones potentials. Chemical structureof toluene
A simple 1-component system
that does not crystallize:
Type A: OPLS-UA CH3 group
Type B: Benzene from theLewis-Wahnström OTP model
500 ns/day using512 molecules on 4 processors
OPLS-UA: J. A. Chem Soc. 1984, vol. 106, p. 6638-6646
LW: Phys. Rev. E, 1994, vol, 50, num. 5, p. 3865-3877
The Lennard-Jones potential
jiij
jiij
ijijijij rrrV
)(
4)(
21
61121
Structure g(r), radial distribution function
ij
ijrrN
Vrg )()(
2
~0.73 nm
~0.55 nm ~0.40 nm
A: methyl
B: benzene
A B
m [au] 15.035 77.106
[kJ/mol] 0.66944 5.72600
[nm] 0.3910 0.4963
The density during a cooling ramp
Cooling rate: 37.5 K/ns
Transition from liquid to solid on the simulated timescale
Tm: Melting temperature
Tc: Critical temperature where hopping accurse in dynamics
Tg: Glass transition temperature (= 100 s)
Mean Square Displacement
)0()()(
)()()()()( 2222
xtxtx
tztytxtrtMSD
22)( vttr
140K
Dttr 6)( 2
t
trD
6
)(t
2
Diffusion constant
Van Hove correlation function at high temperature
i
iis rtrrN
trG )0()(1
),(
Hopping of benzene/CM ?
4r2 G
s(r,
t)
4r2 G
s(r,
t)
Hopping of methyl
Van Hove correlation function at low temperature
i
iis rtrrN
trG )0()(1
),(
Hopping of benzene/CM ?
4r2 G
s(r,
t)
4r2 G
s(r,
t)
Hopping of methyl
Two aspects of the dynamics, diffusion and rotation
))]0()((cos[),( xtxqtqISF )()0( tnn
Dipole-dipole correlationIntermediate scattering function
17.15 Åq
Fit to stretch exponentals are shown, f(t)=A exp(-(t/)). is a characteristic time, and is the stretch
Non-exponential relaxation!
Characteristic time and stretching exponents
140K (hopping)
Relaxation becomes more stretchwith decreasing temperature
Characteristic times do not followan Arrhenius law, (T) = 0exp(Ea/kbT)
Non-Arrhenius relaxation!
Relaxation in time and frequency domain
dtetEEkT
c tidtd
0
02)()0(
1)(
2
)()(
E
tEtECEE
Prigogine-Defay ratio and the one-parameter hypothesis
EtEtE )()(
130 K
Conclution
Future work
One-parameter hypothesis (Prigogine-Defay ratio)
Compare dynamics between idealized model and more realistic model
Finite size effects?
not the end …
Mish
The -process
Movie
Quench dynamics at 120 K, 1 sek ~ 0.7 ns
Center of mass Methyl
MSD and diffusion
Mean Square Displacement
)0()()(
)()()()()( 2222
xtxtx
tztytxtrtMSD
140K
0,60,65
0,70,75
0,80,85
0,90,95
1
10 100 1000 10000 100000
time [ps]
str
etc
h
ISF(ISF) 1atm
Rot(Rot) 1atm
Rot(Rot) 2 GPa
ISF(ISF) 2GPa
Rot(ISF) 2GPa
Rot(ISF) 1 atm
UA-OPLS
25 ns/day
