Molecular Simulations of Retention in Chromatographic Systems: Use of Biased Monte Carlo Techniques to Access Multiple Time and Length Scales - Multiscale Molecular Methods in Applied Chemistry - page 185

nonbonded interactions (longer cutoff, reciprocal-space part of the Ewald sum)
[ 3 , 9 ]. In another application, the CBMC technique (with preselection of moves
based on an empirical potential) has also been used to enable the simulation of
phase equilibria using a first principles description of the interaction system [ 10 ].
The main advantage of the GEMC/CBMC approach in the study of chromatog-
raphy is the multiple time and length scales that can be accessed. In chromatogra-
phy, observing the distribution of analyte molecules between the mobile and
stationary phases is of utmost importance. The time scale of this event, which
depends on the diffusion of molecules over large distances, is simply inaccessible in
a traditional molecular dynamics simulation that is limited to a few nanoseconds.
Furthermore, events such as the re-equilibration of the RPLC stationary phase after
switching solvents, which has been shown to take tens of minutes in the laboratory
[ 11 - 13 ], can be observed in a GEMC/CBMC simulation.

3 Gas Chromatography

In gas chromatography, the mobile phase is a low-density gas. It is further divided
into gas-solid chromatography (GSC) and gas-liquid chromatography (GLC)
according to the nature of the stationary phase. The former is sometimes referred
to as gas adsorption chromatography and the latter as gas-liquid partition chroma-
tography, indicating the thermodynamic processes that are the main driving forces
for the retention processes. The liquid phase in GLC is only one part of the
stationary phase which is coated (bonded) to a solid support material such as
fused silica. Thus adsorption at the gas-liquid and liquid-solid interfaces (and, if
the phase loading is low or if the liquid does not wet the support, also at the gas/
solid interface) can contribute to retention [ 14 ].
The Kovats retention index [ 15 ] has proved to be one of the most useful concepts
in GLC, allows for direct comparison of experimental and simulated retention data,
and can be expressed either in terms of specific retention volumes or partition
coefficients:

" #

log V 0 x = V 0 n

ð K x = K n Þ

log

I x ¼ 100 n þ 100 ¼ 100 n þ 100 ; (2)

log V 0 nþ 1 = V 0 n

log ð K nþ 1 = K n Þ

where the subscripts x , n , and n + 1 represent the analyte of interest, the highest
normal alkane (having n carbon atoms) that elutes before and the lowest normal
alkane that elutes after the analyte, respectively. Use of the Kovats retention index
has many advantages: (1) if interfacial adsorption can be neglected than I should be
independent of phase loading; (2) I is far less temperature dependent than V 0 x or K x ;
(3) in any homologous series (at least for higher homologs) I should increase by
100 per methylene group added; and (4) experimentally measured I values are
extremely reproducible.