Table 1.

Definition of the Various Sample Mixtures^a

Case	Mixture Sampleb	Mixture Type	1tR, first	1tR, last	1 φ 0c	1 φ find
1.e	A and B	Ideally retained	=1to	=1to+1tg	=0	3≤1φmaxi
2.f	C	Weakly retained	>~1to	=1to+1tg	=0	≤ 1 φ max i
3.g	D	Well retained	>1to	=1to+1tg	=0	≤ 1 φ max i
4.h		Too strongly retained	≥ 1to	>1to+1tg	=0	≤ 1 φ max i

^aThese are the conditions for optimizing the first dimension.

^bThese are the mixture designators used in the text and calculation. Both mixtures A and B have a solute which elutes at ¹t_o even when ¹φ_o=0. The second solute in mixture A elutes at a time slightly larger than ¹t_o whereas the second solute in mixture B elutes substantially later than ¹t_o. Mixture C is the same as A but the un-retained component is missing and D is the same as B but again the un-retained component is missing.

^cIt is assumed that the initial eluent composition is pure water. This is just a convenience for this work; any value could be substituted.

^dIt is assumed that there will be an upper limit of ¹φ_fin so as to avoid problems related to focusing the solutes in the second dimension. Any value would do.

^eIn case 1 it is assumed that the solute set has a species which elutes at ¹t_o even when ¹φ_o=0 as well as a species that elutes at ¹t_o+¹t_g even if ¹φ_fin<0.8.

^fIn case 2 we assume the presence of a very weakly retained solute which elutes close to or slightly later than ¹t_o.

^gIn case 3 we assume that the least retained solute elutes at a time greater than ¹t_o given ¹φ_o=0.0.

^hIn case 4 we assume that the solute set contains a solute which is so strongly retained that it elutes later than ¹t_o+¹t_g at ¹φ_fin above the allowed limit.

ⁱ¹φ_max, the maximum first dimension eluent composition, is 0.8 in this study.