Transcript MD-simulations of viscous toluene

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 LennardJones potentials.
Chemical structure
of toluene
A simple 1-component system
The Lennard-Jones potential

Vij (r )  4 ij  ij r
   r  
1 12
that does not crystallize:
1 6
ij
 ij  12 ( i   j )
 ij   i j
Type A: OPLS-UA CH3 group
Type B: Benzene from the
Lewis-Wahnström OTP model
500 ns/day using
512 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
Structure
g(r), radial distribution function
g (r ) 
A: methyl
B: benzene
A
B
m [au]
15.035
77.106
 [kJ/mol]
0.66944
5.72600
 [nm]
0.3910
0.4963
~0.55 nm
~0.73 nm
~0.40 nm
V
 (r  rij )
2 
N j i
The density during a cooling ramp
Transition from liquid to solid on the simulated timescale
Tm: Melting temperature
Tc: Critical temperature
where hopping accurse in
dynamics
Tg: Glass transition
temperature (t = 100 s)
Cooling rate: 37.5 K/ns
Mean Square Displacement
Diffusion constant
r (t ) 2  6 Dt
140K
r (t ) 2  vt 
2
MSD(t )  r (t ) 2  x(t ) 2  y (t ) 2  z (t ) 2
x(t )  x(t )  x(0)
D
r (t ) 2
6t
t 
Van Hove correlation function at high
temperature
Hopping of benzene/CM ?
4pr2Gs(r,t)
4pr2Gs(r,t)
Hopping of methyl
1
Gs (r , t ) 
N
  r  r (t )  r (0)
i
i
i
Van Hove correlation function at low
temperature
Hopping of benzene/CM ?
4pr2Gs(r,t)
4pr2Gs(r,t)
Hopping of methyl
Gs (r , t ) 
1
N
  r  r (t )  r (0)
i
i
i
Two aspects of the dynamics, diffusion
Non-exponential relaxation!
and rotation
q  15.7 Å 1
Intermediate scattering function
ISF(q, t )  cos[q( x(t )  x(0))]
Dipole-dipole correlation


n(0)  n(t )
Fit to stretch exponentals are shown, f(t)=A exp(-(t/t)g).
t is a characteristic time, and g is the stretch
Characteristic time and stretching exponents
Non-Arrhenius relaxation!
140K (hopping)
Characteristic times do not follow
an Arrhenius law, t(T) = t0exp(Ea/kbT)
Relaxation becomes more stretch
with decreasing temperature
Relaxation in time and frequency domain
Prigogine-Defay ratio
and the one-parameter hypothesis
130 K
CEE 
E (t )E (t  t )
E
2
t
E(t )  E(t )  E
1
c( )  2
kT


0
d
dt
E (0) E (t ) 0e it dt
Conclution
Future work
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

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
Center of mass
Methyl
Quench dynamics at 120 K, 1 sek ~ 0.7 ns
MSD and diffusion
Mean Square Displacement
140K
MSD(t )  r (t ) 2  x(t ) 2  y (t ) 2  z (t ) 2
x(t )  x(t )  x(0)
stretch
ISF(ISF) 1atm
Rot(Rot) 1atm
Rot(Rot) 2 GPa
ISF(ISF) 2GPa
Rot(ISF) 2GPa
Rot(ISF) 1 atm
1
0,95
0,9
0,85
0,8
0,75
0,7
0,65
0,6
10
100
1000
time [ps]
10000
100000
UA-OPLS
25 ns/day