## Theory

To demonstrate the importance of mass transfer coefficients in liquid chromatography, the van Deemter equation (eqn [2]) is used to model the variation of the chromatographic band dispersion, H, in packed column as a function of linear velocity, u. A is a constant that measures the contribution to band dispersion caused by multiflow paths, B describes the band dispersion caused by longitudinal diffusion and C describes the band dispersion caused by nonequilibrium in both the stationary and mobile phases:

where A and p are constants that are characteristic of the solute and T is the absolute temperature. There-

By taking the derivative of the van Deemter equation with respect to u, equating the derivative to zero, and substituting in appropriate definitions for A, B and C,

the optimum velocity, uopt, is described by eqn [3]: Cstag (eqn [4]):

Cstag d

The use of enhanced-fluidity mobile phases is expected to increase the diffusion coefficients of the solute and therefore shift uopt to larger values.

For most HPLC separations that involve packed columns containing porous particles and function at linear velocities greater than uopt, the predominant contribution to band dispersion is the diffusion in the stagnant mobile phase inside the porous packing, k is the retention factor and Dm is the diffusion coefficient of the solute in the mobile phase. Therefore, since solutes in enhanced-fluidity liquid mixtures have significantly higher diffusion coefficients than in the organic solvent, chromatographic band dispersion decreases (as will be illustrated later). In addition to higher diffusion rates in enhanced-fluidity solvents, the addition of the liquefied gas often lowers

Figure 2 Variation in the diffusion coefficient of benzene for: squares, 0.70:30 mol fraction methanol-H2O; triangles, 0.56 : 0.24: 0.20 mol fraction methanol-H2O-CO2 circles, 0.49 : 0.21 : 0.30 mol fraction methanol-H2O-CO2; diamonds, 0.42 : 0.18 : 0.40 mol fraction methanol-H2O-CO2 as a function of temperature. (Reproduced with permission from Lee and Olesik (1994).)

Figure 2 Variation in the diffusion coefficient of benzene for: squares, 0.70:30 mol fraction methanol-H2O; triangles, 0.56 : 0.24: 0.20 mol fraction methanol-H2O-CO2 circles, 0.49 : 0.21 : 0.30 mol fraction methanol-H2O-CO2; diamonds, 0.42 : 0.18 : 0.40 mol fraction methanol-H2O-CO2 as a function of temperature. (Reproduced with permission from Lee and Olesik (1994).)

the capacity factor of solutes in some liquid chromatographies. Significant improvements in efficiency can result from the combination of the two effects.

The separation time for a chromatographic analysis is proportional to the slope of a plot of H versus u. Therefore the separation time is also shortened when using enhanced-fluidity solvents. Finally, Darcy's law (eqn [5]) shows that the pressure drop across a packed chromatographic column is linearly related to the product of the linear velocity, u, and the mobile-phase viscosity,

uyeL

Figure 4 Variation of Kamlet-Taft n* as a function of mixture composition for methanol-CO2 mixtures at 25°C and 170 atm. (Reproduced with permission from Cui and Olesik (1991).)

where B0 is the specific permeability, AP is the pressure drop across the column, e is the interparticle porosity, y is the viscosity and L is the length of the column.

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