Chromatography Handbook Of Hplc - Katz Eksteen Schocnmakers Miller wiley Sons -114

than the solute size are inaccessible. Size exclusion chromatography (SEC, formerly called gel permeation chromatography; GPC) is based on this principle. This technique is used mainly for macromolecular species [2,371], but the principle acts equally on smaller-sized molecules (see Chap. 7).\n\nIndeed, Aldehai et al. [33] showed that, on a Zorbax C\u2088 reversed-phase column, retention times of both small ions and larger hydrocarbons decreased with the molecular volume or size of the analytes, which is the signature of selectivity based on size exclusion. The total volume of mobile phase present in the column was 2.78 mL, whereas the total interstitial volume was estimated as 1.91 mL. The static intraparticle pore volume thus amounts to 0.87 mL, while the volume of stationary phase present was reported as 0.40 mL. The relative values of volumes are probably representative for silica-based packings, but may differ from one type of packing material to another. Even if we ignore further complications, such as inaccessibility of stationary phase by blocking of small pores in the grafting process of chemically bonded phases for HPLC, and also composition differences of multicomponent mobile phases for RPLC inside and outside the packing particles, the present reasoning indicates that it is not easy to define the fundamental properties (such as the different volumes) of porous packings, thereby obscuring the physical meaning of observed retention and dispersion data. This was the very reason to introduce the capacity factor k\u2091 ≈ k\u2090 based on treating the entire particle as the stationary phase, instead of k, which is based on the \"liquid\" stationary phase within the particle alone.\n\nLet us assume that packings of porous particles into a column volume V\u2091 are to be characterized as being subdivided into the three regions introduced earlier:\n\n1. An interstitial, moving volume fraction ε\u2090 = V\u2096/V\u2091.\n2. A stagnant intraparticle fraction ε\u2091 = V\n\nm/V\u2091 (note that V\nt = V\u2090 + V\n\nm).\n3. A stationary phase volume fraction ε\u2092 = V\u2092/V\u2091, complemented by:\n\n4. The remainder of the column volume to be attributed to the skeleton of the porous particles.\n\nThe latter ranges in practice from ε\u2092 = 0.1 (in GC packings) to 0.6 (for solid nonporous LC packings). Of course, the fraction ε\u2090 = V\u2090/V\u2091 = (V\u2091 - V\u2092)/V\u2091 = (1 - ε\u2091) is the volume fraction occupied by the particles as a whole, and we have the relations: ε\u2090 + ε\u2091 + ε\u2092 = 1, ε\u2091 ranges in practice from 0.01 to 0.10, ε\u2091 is invariably about 0.4, and so ε\u2091 ranges from 0.5 and ε\u2091 from 0.1 to 0.9 depending on the packing. Components are distributed between the mobile and the stationary phase fluids with the equilibrium partition coefficient K* = ε\u2090/ε\u2091*, but also between the moving and the stagnant mobile phases. For small molecules, the latter occurs with a partition coefficient 1; hence, the concentration in the intraparticle stagnant mobile phase equals that in the interstitial space. Long before the proposal by Scott et al. it was custom in technical sciences to define the apparent partition coefficient K\u2091app based on the partitioning of compounds between regions inside the \"whole particle,\" which was treated as the stationary zone [fraction ε\u2091 = (1 - ε\u2090) and the region outside the particle, that was treated as the mobile zone (fraction ε\u2090), and we find:\n\nK\u2091app = (ε\u2092V\u2090 + ε\u2091V\nt)/V\u2091 = [ε\u2091 + K*ε\u2092](1 - ε\u2090)\n\nAlso, the apparent retention factor k\u2090 = K\u2091app/V\u2090 = K\u2091(1 - ε\u2090)/ε\u2091 = (ε\u2091 + K*ε\u2092)/ε\u2090 and now based on partitioning between the moving fraction of the mobile phase (ε\u2090) and the particle as the stationary phase (including the skeleton), can be found in terms of these volume fractions or pieces. The customary chromatographic capacity factor k can also be expressed in terms of porosities as k = K*V\u2090/V\nt) = K*ε\u2092/ε\u2091 = K*ε\u2092/(ε\u2091 + k). Hence, the simple substitution of k\u2090 ≈ 1 + 2k is justified to express our results in terms of k\u2091app = k.\n