Dr. Davis' group research addresses physical aspects of analytical separations. Two principal areas are currently under study. The first is the use of probability theory to model the extent of peak overlap in separations. The second is the study of dispersion in electrokinetic separations.
Dr. Davis' research has focused for many years on developing statistical theories to describe this peak overlap, characterizing these theories by computer simulation, testing them by experiment, and applying them to real-world samples. Of particular interest is the use of theory to estimate the number m of detectable mixture components from the number p of observable maxima. This estimation facilitates comparison of p and m: when p ~ m, then the separation is good, but when p << m, then the separation is poor.
He and his group have studied extensively one-dimensional (1-D) separations, in which separation occurs along a single axis (e.g., chromatography). Early work verified the predictions of theory with controlled mixtures of known composition and confirmed that specifics of the separation (e.g., stationary phase in gas chromatography) were irrelevant. Several developments within the last three years have made the theory for 1-D separations more applicable to real-world samples. Specifically, the density of components (i.e., the number per unit interval of separation space) along the separation axis now can change, such that one can forego time-consuming searches for experimental conditions compatible with simpler theory. In addition, new developments have made it possible to model overlap in poorly resolved separations, which was impossible before.
Figure 1 shows an example of the improvement in modeling overlap in poorly resolved separations. In Figure 1a , early theory (as represented by the line) is followed only in the most efficient of separations developed by Guiochon and co-workers (Anal. Chem., 1984, 56, 995). Figure 1b shows the same data, but as interpreted by new theory (as represented by the curve). Clearly, the new interpretation is better than the former and describes overlap in not only relatively good separations but poor ones as well.
His statistical interests also include two-dimensional and n-dimensional separations, in which separation occurs along two or more axes. In such separations, one has more physical space in which to place components and thus reduces the overlap problem.
Also of recent interest are the statistical consequences of heartcutting, in which small eluant volumes are transferred from one column to another to augment separation. We have developed a preliminary theory that describes the probability that m components are transferred in a heartcut, given the number of observed peaks on both columns, the temporal width and peak capacity of the heartcut, and the peak capacity of the second column. The theory, as tested by computer simulation, appears very promising.
The group carries out a variety of experiments to study peak overlap. The methods used include gas chromatography, liquid chromatography, overpressure layer chromatography (OPLC), and TLC. In addition, the separations of other groups sometimes are interpreted.
A recent review describes the work of Davis and others in this field (Davis, J.M. In Advances in Chromatography, V. 34, P.R. Brown and E. Grushka, Ed., Marcel Dekker, New York, 1994, p. 109).
The group's current studies address dispersion, or band broadening, in MEKC. In general, dispersion is undesirable, because broad bands overlap more easily than narrow bands. Usually, dispersion of pure analytes in MEKC is dominated by longitudinal diffusion. As shown first by Sepaniak and Cole (Anal. Chem. 1987, 59, 472), however, hydrophobic derivatives of primary amines undergo an unusual dispersion at large electric field strengths E in SDS-based surfactants. Specifically, the efficiency, as measured by theoretical plate number N, decreases rapidly for E's exceeding 10-20 kV/m.
The group has reproduced this dispersion for the 4-chloro-7-nitrobenzofuran (NBD) derivative of cyclohexylamine and also has found that other highly retained compounds (e.g., pyrene, 1-nitropyrene, and perylene) exhibit a similar behavior in SDS-based systems. However, weakly retained compounds are not subject to this dispersion at these E's.
The curves represent a theory for N, when longitudinal diffusion and the width of the injected analyte plug control dispersion. By comparing theory and experiment, one sees the NBD-cyclohexylamine clearly is subject to efficiency losses at high E's, whereas the weakly retained nucleotide, 2'-deoxyadenosine (dA), does not exhibit this behavior.
The group has examined quantitatively several possible origins of this dispersion. The most probably origin is the radial dispersion of micellar electrophoretic mobility, which is brought about by Joule heating. In general, previously calculations of this dispersion by us and others suggested that it was unimportant. However, measurements by Morris and co-workers (Anal. Chem. 1994, 66, 3744) have shown the radial temperature variation responsible for this dispersion is underestimated by theory. We have taken their measured temperature profiles and calculated using Taylor-dispersion theory the extent of dispersion expected under their experimental conditions (e.g., 3.0 W/m power density, 30 kV/m in a 75-micron-diameter capillary). The expected dispersion under these conditions agrees closely with that determined as the residual variance calculated from the simple theory and experiment shown in Figure 2. This finding is the first report of near-quantitative agreement between predicted and observed dispersion brought about by Joule heating.
The reason that weakly retained compounds (e.g., dA) do not show this behavior is because they occupy the electrophoretically dispersed micelles for smaller fractions of time than strongly retained compounds.
A second project addresses the origin of the near linear increase in plate number N that is observed with increasing concentration of various organized media (e.g., SDS micelles, mixed micelles, sugar-borate complexes, and cyclodextrins) in electrokinetic chromatography. This behavior has been explained by the enhancement of mass-transfer rates, reduction of distances between micelles (or other media), a decrease in polydispersity, a reduction of analyte diffusion coefficient, and micellar overload. While these explanations may be valid, they have not been proven.
Our experiments cast some doubts on these interpretations. Specifically, we have investigated the dispersion of hydrophilic, intermediate-polarity, and hydrophobic analytes in MEKC for 15, 50, and 100 mM SDS in 50-micron-diameter capillaries for E's < 31 kV/m. In contrast to the reported increase of N with media concentration, the N's of hydrophilic and intermediate-polarity analytes were found to be independent of [SDS] over the investigated SDS range, and the N's of the hydrophobic species were found to be independent of [SDS] until (what appears to be) Joule heating became significant. The latter conclusion is based on the near-quantitative agreement between theory for Joule heat and experiment, as discussed above.
Figure 3a shows the near-independence of N on surfactant concentration for the weakly retained analyte, dA (the capacity factor is less than 0.4). Here, the fraction of time that analyte occupies the micellar phase is too small for Joule heating to affect dispersion, and band broadening is governed by longitudinal diffusion and plug size. This behavior results, because both analyte mobility and diffusion coefficient decrease at equal rates with increasing surfactant concentration; since N is proportional to their ratio at low E's, it is independent of surfactant concentration. This dispersion can be modeled quantitatively, as shown previously above. In contrast, Figure 3b shows the strong dependence of N on surfactant concentration at high field strengths E for the "infinitely" retained micellar marker, 1-nitropyrene. Dispersion increases significantly with surfactant concentration and the amount of Joule heat liberated. The low-E behavior, however, is identical to that in Figure 3a.
Similar studies currently are underway to clarify the dependence of N on organic-modifier concentration.
