Handbook of Solvents - George Wypych - ChemTech - Ventech!

8.8 Practical applications of modeling 491
∞
000
∫(
00 ( ) )
2
ρkTκ = 1+ 4πρ g R −1
R dR
T
0
12 12
12
[8.137]
and exploiting SSOZ can be calculated from any site-site distribution function g αβ as:
∫(
() )
∞
ρkTκT = 1+ 4πρ gαβ r −1
r dr
2
0
[8.138]
For acetone and chloroform, the obtained results are too large.
Relaxation times and diffusion coefficients
Let us now consider an example of how to calculate dynamic properties of pure liquids by
computational methodologies. As already said in Section 8.7.2, molecular dynamics simulations
are able to take into account the time-dependence in the calculation of liquid properties.
Paying attention to pure acetone, Brodka and Zerda 116 have calculated rotational relaxation
times and translational diffusion coefficients by molecular dynamics simulations. In
particular, the calculated rotational times of the dipole moment can be compared with a molecular
relaxation time τM obtained from the experimentally determined τD by using the following
expression, which considers a local field factor:
τ
M
2εs
ε
=
3ε
+ ∞
s
τ
D
[8.139]
where ε s and ε ∞ are the static and optical dielectric constants, respectively. The calculated
data are in good agreement with experimental values.
Diffusion coefficients can be calculated directly from the velocity correlation functions
or from mean square displacements, as:
∞
vcf 1
D = ∫ v() t v( 0)
dt
3
D
msd
0
=
i→∞
lim
t
1
6
() ( )
rt r
0 2
[8.140]
[8.141]
The values obtained by using the [8.140] or the [8.141] are almost the same, and properly
describe the experimental temperature and density dependencies of the diffusion coefficients,
even if about 30% smaller than obtained using NMR spin-echo techniques.
Among the pure solvents we have treated so far, other available data regard the calculation
of the self diffusion coefficient (D) for liquid ethanol at different temperatures. 115d
The D parameter was obtained from the long-time slope of the mean-square displacements
of the center of mass: experimental changes of D over the 285-320K range of temperatures
were acceptably reproduced by molecular dynamics simulations.