Handbook of Solvents - George Wypych - ChemTech - Ventech!

492 Jacopo Tomasi, Benedetta Mennucci, Chiara Cappelli
Shear viscosity
To end this section, we would like to report an example of calculation of the shear viscosity
again taking as an example pure acetone.
The viscosity can be computed by using molecular dynamics simulations from the
virial form of the molecular pressure tensor P, which can be represented as a sum of four
contributions:
N pp i i
PV = + PV S + PRV+ PV C
m
∑ 1
i=
i
[8.142]
where V is the volume of the cell, N the number of molecules, pi and mi the momentum and
mass of molecule i.
The first term in eq. [8.142] is the kinetic contribution, while PS is the short-range potential
interaction contribution, PR the reciprocal-space portion of the pressure tensor, and
PC a correction tensor term.
From the xy elements of the time-averaged molecular pressure tensor [8.142] and the
applied shear (or strain) rate γ = ∂vx / ∂y,
the viscosityηcan be computed using the constitutive
relation:
η =−
Pxy −Pyx
2γ
[8.143]
the calculated values for acetone (extrapolated data) are in reasonable agreement with experimental
data, as well as results for acetone/methanol and acetone/water mixtures. 117
8.9 LIQUID SURFACES
Until now our task has been relatively easy, as we have only considered the general methodological
aspects of the computational description of liquids.
To proceed further, we have to be more specific, entering into details of specific problems,
all requiring the introduction and the characterization of different properties, and of
the opportune methodological (computational) tools to treat them. We also note that, as additional
complication, it can happen that things change considerably when the full range of
macroscopic variables (temperature, pressure, volume) is considered, and when other components
are added to the liquid system.
Not much effort is needed to convince readers of the overwhelming complexity of the
task we are here considering. Let us take a simple pure liquid: to span the range of the
thermodynamical variables means to consider systems in which the liquid is in presence of
the solid, of the vapor, including supercritical as well as super-cooled states, and all the related
phenomena, as ebullition, vaporization, condensation and freezing.
All states and all dynamical processes connecting states are of interest for chemistry,
chemical engineering, and physical chemistry. Some properties can be defined for all the
states (such as the thermodynamic basic quantities); others are specific for some situations,
such as the surface tension. But also for properties of general definition, the techniques to
use have often to be very different. It is not possible, for example, to use the same technique