## Effect of Mobile Phase Density

SFC retention is related to the solubility in the mobile phase and hence to its density, which is varied by changing the pressure. SFC chromatographs usually have software to calculate the pressure necessary to achieve a given density at a given temperature from polynomials fitted to the pressure/density isotherm. Programmed elution is achieved by changing the pressure during the run - the analogue of temperature programming in gas chromatography (GC) and gradient elution in high performance liquid chromatography (HPLC).

The rate of density programming of a homologous series is determined from the relation:

where AHT is the enthalpy of transfer of solute between phases. It follows that ln k is a linear function of 1/T and that increasing the analysis temperature at constant density always results in a decrease in k.

where A0, B0 and m are constants, p is the density and n is the carbon number of the member of the series. From eqn [3], it can be shown that:

l mn

Figure 2 Contributions to (ln k # ln (p/c") - ln ipm) for fluorene as a function of reciprocal temperature. Squares, ln k; continuous line, ln (p/c"); dashed line, ln <pm; circles, (ln k# ln (p/c") - ln 0m). (Redrawn from Bartle KD, Clifford AA, Kithinji JP and Shilstone GF (1988) Journal of the Chemical Society, Faraday Transactions 84: 4487, reprinted with permission.)

Figure 2 Contributions to (ln k # ln (p/c") - ln ipm) for fluorene as a function of reciprocal temperature. Squares, ln k; continuous line, ln (p/c"); dashed line, ln <pm; circles, (ln k# ln (p/c") - ln 0m). (Redrawn from Bartle KD, Clifford AA, Kithinji JP and Shilstone GF (1988) Journal of the Chemical Society, Faraday Transactions 84: 4487, reprinted with permission.)

where B0/m = pA is the density at which all members of the series co-elute. Thus, as p approaches pA, resolution decreases as linear density programming elutes successive members of the series. To elute members of the series at regular time intervals:

where j is a constant and t is the reference elution time. Hence:

where K is another constant. It follows that, if pA is known, homologues can be eluted regularly by asymptotic density programming. pA may be determined from a graph of elution density versus 1/n in a linear density run by extrapolation to 1/n = 0.

It is noteworthy that, as p increases, the diffusion coefficient of the solute decreases with concomitant increase of the plate height and loss of resolution. To offset this, the column temperature may be increased during density programming. However, since increasing temperature increases solute vapour pressure and hence solubility (see above), the above approach does not hold when density and temperature programming are combined. In fact, the combined influence of column pressure, P, and temperature, T, on retention and resolution may be demonstrated by three-dimensional diagrams in which k or mean resolution is plotted versus P or T (Figure 1). Once the general shape of such diagrams is known for a given class of substrate, only a few chromatograms are required to determine how P and T must be changed to improve resolution.

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