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Also, investigations of the chromatographic behavior of a variety of aromatic and cyclic stationary phases produced by both monomeric- and polymeric-bonding schemes have been reported. Examples of these stationary phases include the following: phenylmethyl-, nitro-phenylethyl-, diphenyl-, triphenyl-, naphthylethyl-, and pyrenylethyl-bonded silica [70-74] as well as norpinyl-, decadiynyl-, phenylbutyl- and /3-naphthyl- , and adamantyl-bonded [75,76] silica-based stationary phases.
The bonding in polymeric syntheses typically varies from one synthesis to the next owing to the presence of multiple, easily hydrolyzable leaving groups attached to the organosilane. Thus, with increasing polymerization, the polymeric network extends farther away from the silica surface (see Fig. 2B) and, simultaneously, the bonded mass, or carbon content, also increases. The surface coverage of these stationary phases is difficult to define. The concept of bonded chain density employed for monomeric stationary phases is incalculable for polymeric stationary phases because the bonding density is defined as the number of chains per unit surface area. Comparison of monomeric and polymeric stationary phases is, therefore, typically based on the carbon contents of the phases to approximately represent the differences in stationary phase loadings. For ease of comparison only, bonding densities of polymeric stationary phases are reported in this chapter to allow a convenient means of comparing monomeric and polymeric stationary phases. Polymeric phases tend to give higher retention values because of the increased mass of the stationary phases. Additionally, the thick poly-meric layers partially shield residual silanols and result in stationary phases that are more hydrolytically stable than monomeric stationary phases.
Sander and Wise  have demonstrated that, under carefully controlled reaction conditions, such as water content, reproducible polymeric stationary phases can be produced. They prepared a polymeric C18 phase with a relative standard deviation of only 0.96% in surface coverage over four trials. Wirth and Fatunmbi  horizontally polymerized a mixture of C18- and C3-trichlorosilanes such that significant Si-O-Si bridging of the silanes occurred parallel to the silica surface. The chromatographic behavior of the resulting stationary phase was more similar to that of conventional monomeric stationary phases than polymeric sta-tionary phases. Simpson and co-workers  synthesized oligomeric and polymeric stationary phases using the fluidizcd bed technique. They were able to control the polymerization by performing stepwise silanization reactions alternating with the hydrolysis of unreacted chlorine atoms to produce oligomeric layers of the derivatizing agent. In addition, Den and Lee  synthesized a series of oligomeric and polymeric stationary phases using 1,8-disilyloctanes.
Reversed-Phase Stationary Phases
C. Selectivities of Monomeric and Polymeric Stationary Phases
Chromatographic selectivity a is an expression of the relative retention of two solutes in a chromatographic separation, and it is a useful experimental parameter for examining the solute
retention process. Selectivity reflects the difference in the Gibbs free energy of transfer from
the mobile phase to the stationary phase of two solutes a and b:
Ê . . -A(AG)
a k' and hi a - - ~ (1)
where k'a and ê’ü are the solute capacity factors, AG is the Gibbs free energy, R is the gas constant, and T is the absolute temperature. Identification and optimization of the relevant interactions that affect selectivity has been an ongoing topic of interest in the chromatographic literature because small improvements in selectivity can result in substantial improvements in both resolution and time of analysis.
The improvement in resolution Rs with enhanced selectivity can be illustrated through the use of the fundamental resolution equation:
P --- Vat a --- 1 -,
“s 4 a Li + K\ \z)
where Rs is a measure of the degree of separation between two peaks; N is the column efficiency or number of theoretical plates, and k’h is the capacity factor for the later of the two eluting solutes. This expression can be derived by assuming gaussian peak shapes and that the two peaks are closely spaced and thus have equal peak widths. Should the peaks be cut and collected at the valley between them, an /?s value of 1.0 corresponds to solute purities of about 97.73% in each of the two gaussian peaks, whereas baseline resolution is achieved at Rs = 1.5 and the peaks are now about 99.87% pure. As indicated in Eq. (2), resolution depends on the square root of efficiency, which implies that, to double the resolution, the efficiency must be quadrupled. This fourfold increase in efficiency would require fourfold increases in column length, time of analysis, pressure drop, and solvent consumption, as well as further dilution of the solutes. Additionally, it may be very difficult to obtain such an increase in efficiency; therefore, increasing the efficiency is not typically a convenient means of adjusting the resolution.