1 Evaluation of separation processes

1.1 Ideal and real separations

The aim of a separation operation is to separate a mixture of – in the simplest case – two substances A and B as completely as possible. If the separation is complete, the mixture is divided into two parts, one of which contains exclusively substance A, the other exclusively B.

However, such a complete partitioning is not achievable in practice; there will always still be some B as impurity in the part with substance A, and correspondingly some A in the part with B (cf. Fig 1.1).

◯ = Separation operation.

Fig. 1.1: Separation of a two-substance mixture.

1.2 Separation factor – enrichment factor – depletion factor

The result of a separation operation can be expressed by specifying the impurities in A and in B or by specifying the yields of A and B; thus, to unambiguously characterize the efficiency, two numbers are required for the separation of two substances (correspondingly more for systems with more than two components). To arrive at a simpler description, one uses the separation factor β (probably first given by Chlopin), which is defined as follows:

The separation factor is a measure of the effectiveness of the separation of two substances. If, after separation, the concentration ratio in both parts is the same, i.e. [A]/[B] in part 1 = [A]/[B] in part 2, then β = 1; no separation has taken place.

For an (ideal) complete separation, either the numerator or the denominator of the double fraction would have to become zero, so that β would take the values 0 or ∞. β and 1β thus denote the same separation effect, since the choice of numerator and denominator is arbitrary. However, it is common to write the fraction so that β ≥ 1, so that the separation factor increases with an improvement in separation.

Instead of the separation factor, the term enrichment factor is sometimes used. For example, the enrichment factor f for substance A (cf. Fig 1.1) is defined as the concentration ratio in Part 1 after separation divided by the concentration ratio in the starting material before separation:

Accordingly, one obtains the depletion factor f′ for A:

The depletion factor becomes smaller as the separation improves (decreasing concentration of A in part 2); more illustrative is the reciprocal value d of this factor, which increases as the efficiency of the separation increases. Referring again to the depletion of A (Fig. 1.1):

The quantity d is used above all in radiochemistry when the effectiveness of the removal of interfering radioactive substances is to be described; d is then referred to as the decontamination factor.

1.3 Separation factors required for analytical separations

In analytical chemistry, the term quantitative separation is generally used. This is usually understood to mean the 100 percent separation of the substance sought. According to what has been said so far, complete separations cannot be achieved in practice, and one must therefore define the term quantitative arbitrarily.

If a separation is to be sufficient for analytical purposes, it will normally be required that at least 99.9% of substance A is in part 1 and at least 99.9% of substance B is in part 2 after the separation operation (cf. Fig 1.1). The separation factor β is then

Such a high separation factor is a requirement that can be modified depending on the needs present in the specific case, but on the whole it should be justifiable.

1.4 Limits of applicability of the separation factor – selectivity and specificity of separations

A value of about 106 for the separation factor is a necessary but not sufficient condition for analytical applications. If one component of the mixture to be separated is present to an extreme extent in one part after separation, a very large separation factor can be achieved without the other component having to be sufficiently separated.

If, for example, the iron is precipitated with ammonia from a solution containing 100 mg Fe3+ and 100 mg Zn2+ ions, 10 mg Zn2+ ions may be entrained by the iron precipitate and, on the other hand, 0.0003 mg Fe3+ ions may be dissolved in the filtrate. The separation factor would then be 3 ⋅ 106, thus clearly exceeding the minimum value of 106 given above, although only 90% of the zinc was separated from the iron and the separation would therefore be insufficient for analytical purposes.

The separation factor is therefore of limited applicability, and one must specify the yields of both components of the mixture or their impurities for definite statements.

If the analytical sample contains more than two substances (which is usually the case), several separation factors must be specified according to the number of components, which can make the labeling of the separation effect quite complicated.

Therefore, when evaluating a separation process, the selectivity must also be taken into account, i.e. the number of substances from which the component sought is separated at the same time. The greater this number, the more efficient the process obviously is. Ideally, even all the impurities in question are sufficiently removed in a single separation operation; then there is a specific separation. Some examples of separations that have historically been considered specific are given in Tab. 1.1 (some of these separations require additional masking reactions).

Nowadays, the term specific appears to be of little value in the light of the high detection sensitivity of modern analytical methods. Even supposedly highly pure reagents or solvents still contain detectable trace substances.

It is much used in immunology; there it tries to describe the (almost) exclusive interaction of antigens with antibodies. But even there, the concept of so-called cross-reactivity is better used to describe the achievable selectivity or specificity.

General literature

R.E. Langman, The specificity of immunological reactions, Molecular Immunology 37, 555–561 (2000). 

B.-A. Persson & J. Vessman, The use of selectivity in analytical chemistry – some considerations, TrAC Trends in Analytical Chemistry 20, 526–553 (2001). 

D. Thevenot, K. Tóth, R. Durst & G. Wilson, Electrochemical biosensors: recommended definitions and classification, Pure and Applied Chemistry 71, 2333–2348 (1999).