The phase ratio

The phase ratio V/ Vm occurs in eqn.(l. 10) as one of the factors that determine retention (k) in chromatography. We can influence the phase ratio by varying one or more of several parameters  

In particular, we can choose between open (capillary) columns and packed columns. A wall coated open tubular (WCOT) column has a much smaller phase ratio than a packed column, due to the small surface area of the wall. 

If open columns are used, then the phase ratio will vary with the column diameter (provided that the film thickness is kept constant). The cross-sectional area of the column (and hence the mobile phase volume) is proportional to the square of the column diameter, while the wall area is proportional to the diameter itself. Hence, the phase ratio is inversely proportional to the column diameter. 

The area available for the stationary phase will directly affect the phase ratio. If a solid material is used as the stationary phase in a packed column, if a liquid phase is deposited on a solid adsorbent with a constant film thickness, or if chemically bonded phases are employed, the phase ratio (through VJ will be directly proportional to the available surface area. The surface area of an adsorbent is usually given per unit weight (i.e. the specific surface area in m2/g). However, it should be noted that the relevant quantity is the surface area per unit volume (m2/ml) in the packed column. 

This is the fraction of the column volume that remains available for the mobile phase after packing. There are two contributions to the total column porosity. One part of the volume available to the mobile phase is in between the particles (interparticle space). For uniform, spherical particles this is about 40% of the column volume. The second contribution is due to the very porous structure of materials with large specific surface areas. This makes a significant part of the intraparticle volume available to the mobile phase (usually 20 to 30% of the column volume). 

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An eluted solute was originally identified from its corrected retention volume which was calculated from its corrected retention time. It follows that the accuracy of the measurement depended on the measurement and constancy of the mobile phase flow rate. To eliminate the errors involved in flow rate measurement, particularly for mobile phases that were compressible, the capacity ratio of a solute (k ) was introduced. The capacity ratio of a solute is defined as the ratio of its distribution coefficient to the phase ratio (a) of the column, where... 

It is clear that the separation ratio is simply the ratio of the distribution coefficients of the two solutes, which only depend on the operating temperature and the nature of the two phases. More importantly, they are independent of the mobile phase flow rate and the phase ratio of the column. This means, for example, that the same separation ratios will be obtained for two solutes chromatographed on either a packed column or a capillary column, providing the temperature is the same and the same phase system is employed. This does, however, assume that there are no exclusion effects from the support or stationary phase. If the support or stationary phase is porous, as, for example, silica gel or silica gel based materials, and a pair of solutes differ in size, then the stationary phase available to one solute may not be available to the other. In which case, unless both stationary phases have exactly the same pore distribution, if separated on another column, the separation ratios may not be the same, even if the same phase system and temperature are employed. This will become more evident when the measurement of dead volume is discussed and the importance of pore distribution is considered. 

It is seen that the separation ratio is independent of the phase ratios of the two columns and the flow rates employed. It follows that the separation ratio of a solute can be used more reliably as a means of solute identification. Again, if the data is being processed by a computer, the corrected retention times will be used to calculate the separation ratios. In practice, a standard substance is often added to a mixture and the separation ratio of the substance of interest to the standard is used for identification. 

In partition chromatographic systems, the selectivity and degree of retention are mainly determined by the compositions of the liquid stationary and mobile phases and by the phase ratio of these two liquids. 

In fact, the solute retention depends on the solubihty parameters of the solute, 8 , of the mobile phase, 8 , of the stationary phase, 8, and of the phase ratio given by Equation 4.7 [24] ... 

The determination of log Poa is far from being trivial whether potentiometric, shake-flask, chromatographic or other techniques are used and, often, this value is derived from the back-calculation discussed above, using logDj and pKj, which of course has to be known. This is often done in shake-flask determinations so that there is appreciable aqueous solubility (and thus partition) in the aqueous phase for highly Hpophilic drugs and it may also be accompanied by a variahon of the phase ratio, in favor of the phase where the compound is expected to be less soluble, to avoid saturation phenomena. 

However, as stated above, the partition coefficients measured by the shake-flask method or by potenhometric titration can be influenced by the potenhal difference between the two phases, and are therefore apparent values which depend on the experimental condihons (phase volume ratio, nature and concentrahons of all ions in the solutions). In particular, it has been shown that the difference between the apparent and the standard log Pi depends on the phase volume raho and that this relationship itself depends on the lipophilicity of the ion [80]. In theory, the most relevant case for in vivo extrapolation is when V /V 1 as it corresponds to the phase ratio encountered by a drug as it distributes within the body. The measurement of apparent log Pi values does not allow to differentiate between ion-pairing effect and partihoning of the ions due to the Galvani potential difference, and it has been shown that the apparent lipophilicity of a number of quaternary ion drugs is not due to ion-pair partitioning as inihally thought [80]. 

In gas chromatography the value of the partition coefficient d ends only on the type of stationary phase and the column temperature. It is independent of column type and instrumental parameters. The proportionality factor in equation (l.ll) is called the phase ratio and is equal to the ratio of the volume of the gas (Vg) and liquid (V ) phases in the column. For gas-solid (adsorption) chromatography the phase ratio is given by the volume of the gas phase divided by the surface area of the stationary phase. 

Some guidelines for predicting the results from distributing a sample between two immiscible solvents are summarized in Table 8.3 [67,68]. The efficiency of an extracting solvent, E, depends primarily on the affinity of the solute for the extracting solvent, Kd) the phase ratio, V, and the number of extractions, n. For simple batchwlse extractions K, should be l u ge, as there is a practical limit to the volume of the extracting solvent and the... 

The method EBC patented essentially for achieving oil-water separation was based on hydrocyclones [267], In this design, the fact that an oil-loving biocatalyst such as Rhodococcus tends to partition at the oil-water interface was made use of. The separation was achieved by controlling the phase ratio and operating in sequential steps using multiple hydrocyclones. 

Ettre, L.S., Welter, C., Kolb, B. (1993) Determination of gas-liquid partition coefficients by automatic equilibrium headspace-gas chromatography utilizing the phase ratio variation method. Chromatographia 35, 73-84. 

As this represents a ratio of masses, if combined with a volume ratio, a ratio of concentrations, which is an equilibrium constant, can be obtained. The volume ratio is called the phase ratio and is the ratio of the volume of the mobile phase to the volume of the stationary phase. 

The retention factor is related to the thermodynamic equilibrium constant K for solute binding by k = (IK, where f is the phase ratio of the column. The free-energy change for the chromatographic process is expressed by... 

An open-tubular column is a capillary bonded with a wall-supported stationary phase that can be a coated polymer, bonded molecular monolayer, or a synthesized porous layer network. The inner diameters of open-tubular CEC columns should be less than 25 pm that is less than the inner diameters of packed columns. The surface area of fused silica tubing is much less than that of porous packing materials. As a result, the phase ratio and, hence, the sample capacity for open-tubular columns are much less than those for packed columns. The small sample capacity makes it difficult to detect trace analytes. 

One way to increase the phase ratio of open-tubular columns is to use a polymeric stationary phase instead of a bonded molecular monolayer (Figure 6). 

Another way to increase sample capacity is to increase the surface area for conventional chemically bonded phases. Two methods have been reported for increasing surface area (a) laying down a thin layer of porous material on the surface and (b) etching the surface. The precursors and catalyst dictate the characteristics of the final sol-gel. Manipulation of the components and procedures in the sol-gel process can control the phase ratio and the retention properties of the sol-gel-derived phase. 

Distribution data can be obtained in two ways. The first employs variation of the phase ratio of the aqueous and organic phases the second involves recontacting the organic phase with fresh aqueous phase until the saturation loading of the solvent is reached. 

A distribution isotherm is then constructed by plotting the metal concentration in the organic phase against the concentration in the aqueous phase, as a function of the phase ratio. An example of such an isotherm is shown in Fig. 7.1, for the extraction of nickel by DEHPA(Na) at pH 6, showing three different concentrations of extractant [1]. 

For most exploratory work, analysis of the organic phase is not necessary. If no volume change of the phases occurs and no third phase or crud is formed, the analysis of the aqueous raffinates is sufficient, since the metal concentration in the solvent can be readily calculated from the initial metal concentration of the feed solution and the phase ratio used. 

This not only shows how the extent of extraction varies with phase ratio at a constant distribution ratio, but also how varying the phase ratio affects the relative purity of the product. Increasing the phase ratio by a factor of 100 nearly doubles the recovery, but drops the relative purity by a factor of over 25. Note that, in a single stage, it is not possible to achieve both high recovery and a high degree of separation simultaneously. Also,... 

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