Theory of chromatography

Height h and number n of theoretical plates are related to the length l of the column by a simple equation, Eq. (8.80). 

Empirically, the plate height h has been found to depend on the linear liquid velocity u through the column in the manner described by Eq. (8.81), as found by van Deemter (1961). 

and C are constants. Importantly, the van Deemter equation, Eq. (8.81), states that there is a point of minimum plate height hmin, at u = (A/B)0 5, whereas h increases at both higher and lower velocity through the column. 

The key performance parameter in a chromatography column is its resolution Rn, a measure of the overlap of different peaks. It is defined by Eq. (8.82), where Ve2 and Vel are elution volumes for peaks 2 and 1, as manifested by their distances on the chromatogram, and wt and w2 are their corresponding peak widths at the baseline. 

The last term, (V,2 - Vgfi/V ], can be expressed [Eq. (8.85)] in terms of the capacity factor k, where k= [(Ve- V0)/V0],andin turn V0 is the void volume and thus also the minimum volume possible in the chromatogram, and of the relative retention or selectivity 8, where 8 = k2/kt. 

The theory of chromatography is basically concerned with zone spreading. The dispersion of sample zones, which results in chromatographic peaks, causes a distribution of the sample concentration. For a good separation, zones should not overlap. Often a separation is not totally effective because the zones spread into one another. 

If the eluted chromatographic peak follows a Gaussian distribution, the zone spreading is related to the height of the chromatographic curve H, which is equivalent to a theoretical plate (or plate height), in the form 

Here is the variance in statistics. The quantity H can also be calculated from 

In general, H measures the specific column frequency and N measures the system efficiency. 

According to the current chromatography theory, the flow of solute through a column in the presence of a stationary phase and a mobile phase undergoes three processes, which correspond to the three components of H or c. Following are the three physical processes that determine zone spreading (the volume of c ) or H  

A number of modes of separation are used in liquid chromatography. The commonly used modes in forensic science are reversed phase (RP), normal phase (NP), and ion exchange (lEC). Each of these will be discussed in greater detail in Chapter 4. 

Separation of compounds takes place in the HPLC stationary phase packed within the column (usually stainless steel, but other housing materials 

The separation is dependent on the distribution of the compounds between the stationary and the mobile phases and can be represented by the distribution coefficient, K, 

A compound that has a higher affinity for the stationary phase will take longer to travel through the column than one that has a higher affinity for the mobile phase. In order for separation to occur, the distribution coefficient for each of the compounds must be different for a given mobile and stationary phase. Some of the chemical properties of solutes that affect K will be discussed later in this chapter. 

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D. E. Martire, Unified Approach to the Theory of Chromatography Incompressible Binary Mobile Phase (Liquid Chromatography) in Theoretical Advancement in Chromatography and Related Separation Techniques (Ed. F. Dondi, G. Guiochon, IGuwer, Academic Publishers, Dordrecht, The Netherlands,(l993)261. 

Cs Horvath and W. R. Melander, Theory of chromatography , in Chromatography Fundamentals and Applications of Chromatographic and Electrophoresis Methods. Part A Fundamentals and Techniques, Helftmann E. (Ed.), Journal of Cliromatography Library, Vol. 22, Ch. 3, A28-A135 (1983). 

Glueckauf E. (1955) Theory of Chromatography Part 10 - Formula for Diffusion into Spheres and Their Application to Chromatography, Trans. Faraday Soc. 51 1540-1551... 

Martin AJP, Synge RLM. A new form of chromatogram employing two liquid phases A theory of chromatography. 2. Application to the micro-determination of the higher monoamino-acids in proteins. Biochem. J. 1941 35 1358-1368. 

The various theoretical and practical aspects of the use of HPLC methods have been recently discussed in exquisite books, such as the application of HPLC-MS in drug analysis [59], the theory of chromatography [60], the fundamentals of chromatography [61, 62], the practice and theory of ion-chromatography [63], problem solving in HPLC [64], the... 

The theory of chromatography of linear and cyclic polymers with functional groups has also been developed. A linear in-pore partition function Q 1) was created for polymeras with one specific functional group a. Q 1) can be expressed by... 

GLUECKAUF, E. Trans. Faraday Soc. 51 (1955) 34. Theory of chromatography, Part 9 the theoretical plate concept in column separation. 

Yan, C. and Martire, D.E., Molecular theory of chromatography for blocklike solutes in isotropic stationary phases and its application to supercritical fluid chromatographic retention of PAHs, J. Phys. Chem., 96, 7510, 1992. 

This is the most direct and simple theory of chromatography. The transport of the solute down the column will depend upon the distribution constant (partition coefficient), K, and the ratio of the amounts of the two phases in the column. Band (zone) shape does not change during this movement through the column. The system could be visualized as illustrated in Figures 1.10, 1.11. 

This text represents a blending of the basic theories of chromatography with the experiences of each author. It is the product of a Gas Chromatography Short Course which has been presented annually in Philadelphia by the Chromatography Forum of Delaware Valley. The course has been offered each year with the highest level of participation. It has been structured for not only beginners but for existing workers in the field and specialists of other fields who wish and need to know more about this powerful... 

M. J. E. Golay, Theory of chromatography in open and coated tubular columns with round and rectangular cross-section, in Gas Chromatography Amsterdam 1958 (Amsterdam Symposium), Desty D. H. (Ed.), Butterworths Scientific Publications, London, pp. 36-55 (1958). 

D. E. Martire and R. E. Boehm, Unified molecular theory of chromatography and its application to supercritical fluid mobile phases. 1. Fluid-liquid (absorption) chromatography , J. Phys. Chem. 91 2433-2446 (1987). 

Fortunately, controlling separations is not nearly as complicated as much of the literature may make it seem. My aim is to cut through much of the detail and theory to make this a usable technique for you. The separation models I present are those that have proven useful to me in predicting separations. I make no claim for their accuracy, except that they work. There are many excellent texts on the market, in the technical literature, and on the Internet, continuously updated and revised, that present the history and the current theory of chromatography separations. 

A Molecular-Dynamic Theory of Chromatography, J. C. Giddings and H. Eyring, J. Phys. Chem., 59, 416 (1955). 

Nonequilibrium and Diffusion A Common Basis for Theories of Chromatography, J. C. Giddings, J. Chromatogr., 2, 44 (1959). 

Dynamics of Mass Transfer and the Generalized Nonequilibrium Theory of Chromatography, J. C. Giddings, Ber. Bunsenges. Phys. Chem., 69, 773 (1965). Theory A Practical Tool in Gas Chromatography, J. C. Giddings, Methodes Phys. Anal. (GAMS), 1, 13 (1966). 

The theory of chromatography has been treated in earlier chapters, but the planar methods have some special characteristics that need further discussion. 

What is H anyway The original interpretation, taken from distillation theory, was height equivalent to a theoretical plate, or HETP. We have seen that this concept was inadequate, and the preceding discussion of the van Deemter equation has presented it as a measure of the extent of spreading of an analyte zone as it passes through a column. Thus, a more appropriate term might be column dispersivity. In fact, another, independent approach to the theory of chromatography defines H as... 

Golay, M. J. E., Theory of Chromatography in Open and Coated Tubular Columns with Round and Rectangular Cross-sections, in Gas Chromatography (D. H. Desty Ed.), pp. 36-49. Butterworth, London (1958). 

The theory of chromatography depends on the assumption of a linear system with diffusivity independent of concentration over the relevant range. The validity of this assumption may be conveniently tested by varying the pulse (or step) size. 

Horvath Cs, Melander WR. In Heftmann E, ed. Theory of Chromatography. Amsterdam Elsevier, 1983 A27. 

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