Partition Chromatography
Partition chromatography is defined as a differential migration separation technique that employs the distribution of a migrating component between two or more different states whose relative velocities are not all equal to zero.
Example No. 1: Gas-Liquid Partition Chromatography As an example, consider gas-liquid partition chromatography, where a pulse containing a mixture of voltatile components is injected at the inlet of a long, hollow, stainless-steel or glass capillary column coated on the inside with a thin film of a non-volatile liquid. The column is long, perhaps 10 meters or more.
A continuous, steady flow of helium gas passes through the column. After injection, the components later appear, in sequence, as a series of separated, broadened, Gaussian pulses at the exit of the column (Figure 1).
Why is the injected mixture separated into its components by this apparatus? Because each component has a unique value of its solubility in the non-volatile liquid. A component that is completely insoluble in the liquid phase passes quickly through the capillary column with a residence time equal to the residence time of the flowing helium gas.
A component that is highly soluble in the liquid phase takes considerably longer to elute from the column. Components with solubilities that are intermediate between "insoluble" and "highly soluble" elute at intermediate times. What is the Gimmick Associated with Ideal Partition Chromatography?
The basic "gimmick" behind ideal partition chromatography is the existence of two phases -- one stationary and one mobile -- between which the components of a mixture rapidly equilibrate. In the ideal case, the equilibration of each component is ideal, in the sense that there exist no mass-transfer limitations to equilibration and the quantity of each component is sufficiently small such that linear partition coefficients apply.
Ideal partition chromatography can be considered to be, in effect, an example of two-dimensional thermodynamics. The three vector directions in Example No. 1 include a single, axial coordinate direction (the length of the capillary tubing; see Figure 1) and two lateral coordinate directions (one being the radial direction) over which thermodynamic equilibrium exists at every point z and at all times t within the chromatographic column.
Typical Chromatographic Apparatus: A Tubular Flow System Figure 1. Non-steady-state diffusion and convection in a tubular flow system. A mixture of components is injected rapidly into the column at z=0 and t =0 and elutes later in time as a series of separated Gaussian peaks at the exit, z = L .
What is the Theoretical Basis for Partition Chromatography? The teaching of the basic principle behind partition chromatography has not been a part of chemical engineering curriculum for decades, with the significant exception of Howard Saltzman when he was a faculty member at the University of Rochester. For example, the author needed to understand a basic derivation for partition chromatography while at the Monsanto Corporation several years after he received his Ph.D. degree in 1965. He found it difficult to find a satisfactory answer in textbooks (most of which focused on either the discrete Craig countercurrent apparatus or on HETP), most of which were oriented towards chemists.
At the time, the author discovered the key gimmick to chromatography in an unusual place, namely, the classic textbook, "The Mathematics of Diffusion", by J. Crank [1]. Crank's Chapter VIII treats simultaneous diffusion and chemical reaction. Section 8.2 in Crank's book [1] describes instantaneous reeaction, in which "In the simplest case, the concentration, S , of immobilized substance is directly proportional to the concentration C of a substance free to diffuse," i.e,
(1) The result is given by Crank as: (2) S RC = 2 2 1 C D C t R x ? ? = ? + ? Page 3 3 Crank stated [1]: "Clearly the effect of the instantaneous reaction is to slow down the diffusion process. Thus, if R + 1 = 100, the overall process of diffusion with reaction is slower than the simple diffusion process by a hundredfold. In fact, if the linear relationship (1) holds, solutions of the diffusion-with- reaction problem for given initial and boundary conditions are the same as for the corresponding problem in simple diffusion, except that the modified diffusion coefficient D/(R + 1) is to be used. This is true irrespectively of whether the diffusion-with-reaction occurs in a plane sheet, cylinder, or sphere, or any other geometric shape, and whether diffusion occurs in one dimension or more." [1] In the author's opinion, Equation (1) describes the partitioning of a component between immobilized (S) and freely diffusing (C) states. This so-called "instantaneous reaction" appears to be a reversible equilibrium rather than an irreversible reaction of C to S. Equations (1) and (2) provided the key clue to the author as to why a partition chromatographic separation yields an individual elution peak for each component.
Partition Chromatography as a Linear Multistate System The author has rederived Equation (2) based upon the following linear partition coefficient between states 1 and 2 for an eluting component i ,
(3) which has units of concentration/concentration. The resulting conservation-of-species equation -- involving diffusion, convection, and irreversible first-order reaction along the axial coordinate direction z -- is,
(4) In the absence of axial convection and first-order reaction, Equation (4) simplifies to,
(5) which is identical to Equation (2). What is a State? Partition chromatography basically is the superposition of two-dimensional thermodynamics -- a mobile phase and a stationary phase -- upon non-steady-state diffusion, reactopm. and convection in a third dimension. For simplicity, the two-dimensional equilibrium and third-dimension dynamics can be characterized by a pair of states for each eluting component in a chromatographic column (see Figure 2). 2 2 1 i i i c c ? = 2 2 0 is is is is ieff ieff ieff c c c c t z z D v k ? ? ? ? + + = ? ? ? 2 2 0 is is ieff c c t z D ? ? ? = ? ? Page 4 4 Figure 2. Box representation of the two states (for each eluting component i ) in gas-liquid partition chromatography (in a tubular column system). In Figure 2, the subscript i represents an eluting component; the subscript numbers 1 and 2 represent the mobile and stationary phases, respectively; D is the diffusion coefficient in a phase; and v is the convective velocity of phase 1
. At the bottom of each state box, the value 0 indicates that no irreversible first-order reaction is occurring in each phase.
Archer John Porter Martin was born on March 1st, 1910, in London where his father was a general medical practitioner. He attended Bedford School from 1921 to 1929 when he entered Cambridge University to graduate in 1932. After a year in the Physical Chemistry Laboratory he obtained a post at the Dunn Nutritional Laboratory, where he worked under L.J. Harris and Sir Charles Martin, and in 1938 he moved to the Wool Industries Research Association at Leeds. From 1946 to 1948 he was Head of the Biochemistry Division of the Research Department of Boots Pure Drug Company at Nottingham and in 1948 he joined the staff of the Medical Research Council, first at the Lister Institute and later at the National Institute for Medical Research. He was appointed Head of the Division of Physical Chemistry at the Institute in 1952 and he was Chemical Consultant from 1956 to 1959. Since 1959 he has been a Director of Abbotsbury Laboratories Ltd. Martin entered Cambridge University with the intention of becoming a chemical engineer but, due to the influence of Professor J.B.S. Haldane, then Reader of Biochemistry at Cambridge, he eventually specialized in biochemistry. His first researches, as an undergraduate, resulted in a method of detecting pyro-electricity by observing the attraction of a metal plate for crystals that had been immersed in liquid air. At Cambridge he worked on ultraviolet adsorption spectra and at the Nutritional Laboratory he was concerned with the attempted isolation of Vitamin E and in the pathological effects of prolonged Vitamin E deficiencies. In these latter studies he used solvent extraction and chromatographic methods which were to lay the foundation for his later work on chromatography. He also worked, along with others, on the B2 group of vitamin deficiencies in pigs. At the Wool Industries Research Association he worked on the felting of wool, first with R.L.M. Synge and later with Consden and Gordon, and on amino-acid analysis. It was here that he developed his method of partition chromatography; more recently, with A.T. James, he has developed the method of gas-liquid chromatography. Dr. Martin, a Fellow of the Royal Society (1950), was made Companion of the British Empire in 1960. He received the Berzelius Medal of the Swedish Medical Society (1951), the John Scott Award (1958), the John Price Wetherill Medal (1959), the Franklin Institute Medal (1959), and the Leverhulme Medal (1963). In 1963, he was appointed to deliver special lectures (as "buitengewoon hoogleraar") at the Technological University of Eindhoven, The Netherlands. In 1943 he married Judith Bagenal; they have one son and three daughters
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