Chromatographic theory

The following treatment of chromatographic theory deals only with the bare essentials needed for the separations described later. It is highly recommended that the reader becomes acquainted with more comprehensive treatments (e.g., Yost et al. 1980). 

For practical purposes, several terms need to be defined. These are capacity factor (k ), theoretical plate number (N), height equivalent to one theoretical plate (F1ETP), selectivity (a) and peak asymmetry (b/a). As will be discussed later in specific examples (Sects. 9.2.4 and 9.2.5), these parameters are of crucial importance in monitoring and maintaining HPLC column efficiency. 

Regardless of the stationary phase, most applied solutes are eluted at larger retention volumes (VR) than that required for solvent passage through the 

From this equation, an important parameter termed the capacity factor, k, can be calculated. This factor is a comparison of the adjusted retention volume of a particular constituent on the FIPLC column relative to the interstitial volume, V0, and is given by  

For practical purposes, values ranging from k 1 to 10 are used higher values tend to be accompanied by severe line-broadening of the peaks of eluted components. 

The practices of isocratic and gradient sorptive chromatography are very different. Isocratic chromatography tends to be very sensitive to the details of mobile phase preparation, temperature, pump speed, and sample composition. Gradient chromatography is usually more tolerant of small variations in these factors but may be extremely sensitive to column history, equilibration time, and gradient preparation. 

The theoretical parameters of isocratic chromatography are often described using the plate model. One can imagine the analyte to be distributed 

K Wn Capacity factor Peak width at half height t /to  

N Theoretical plates 5.54( t /wj Other formulae are also used 

Neff Effective plates NK/fl+k JP Useful for comparing columns 

One of the equations developed merely expressed mathematically that the least adsorbed solute would be eluted first and that if data on the resin and the column dimensions were known, the solvent volume required to elute the peak solute concentration could be calculated. Simpson and Wheaton expressed this equation as  

Theoretical Plate Height. A second important equation for chromatography processes is that used for the calculation of the number of theoretical plates, i.e., the length of column required for equilibration between the solute 

Here W is measured in the same units as This form of the equation is probably the easiest to calculate from experimental data. Once the number of theoretical plates has been calculated, the height equivalent to one theoretical plate (H.E.T.P.) can be obtained by dividing the resin bed height by the value of P. 

The column height required for a specific separation of two solutes can be approximated by.[ J 

Zone Spreading. The net forward progress of each solute is an average value with a normal dispersion about the mean value. The increased band or zone width which results from a series of molecular difrusion and non-equilibrium factors is known as zone spreading. 

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According to chromatographic theory, the reduced plate height is related to the reduced velocity by equation (4.2)... 

J. A. Jonsson, Chromatographic theory and basic principles. Marcel Dekker Inc., New York 1987. 

It was known from gas chromatographic theory that efficiency could be improved if the particle size of the stationary phase materials used in lc could be reduced. High performance liquid chromatography developed steadily during the late 1960s as these high efficiency materials were produced, and as improvements in instrumentation allowed the full potential of these materials to be realised. As hplc has developed, the particle size of the stationary phase used has... 

Valocchi, A. J, R. L. Street and P. V. Roberts, 1981, Transport of ion-exchanging solutes in groundwater, chromatographic theory and field simulation. Water Resources Research 17, 1517-1527. 

J0NSSON, J. A., in Chromatographic Theory and Basic Principles (Jonsson, J. A. ed.), Chapter 3, Dispersion and Peak Shapes in Chromatography (Marcel Dekker, 1987). 

Enhanced-Fluidity Liquid s Properties and Chromatographic Theory. .. 435... 

The review is organized in the following sections. The chromatographic theory relevant to EFLC and HT-HPLC is first described. Next a detailed description of the physicochemical properties of EEL mixtures is included. This is followed by a survey of the scope of liquid chromatography (LC) techniques that are presently using the attributes of EELs. Finally, a discussion of future applications of EF-HPLC is included. 

ENHANCED-FLUIDITY LIQUID S PROPERTIES AND CHROMATOGRAPHIC THEORY... 

Basic chromatographic theory relates the retention factor of a solute to the equilibrium constant for adsorption, K, according to... 

It can be seen that the numerical value of (k ), the capacity ratio of the first eluted peak of the critical pair, can make a significant difference to the value of Hfnm. To simplify expressions in chromatographic theory it is often assumed that, to the first approximation, (Hmtn) can be taken as 2dp, it is clearly seen that, in column design, such assumptions could lead to significant errors particularly at extreme values of (k ). 

In the previous sections it has been stipulated that there are several response variables which can be modeled. The success of the optimization procedure depends on the selection of the response variable(s). There are several criteria which can be used to select a response variable [12,17]. The response variable should have a homoscedastical error structure and have to change continuously and smoothly. Both experimental data and chromatographic theory can be used to check these properties. 

From chromatographic theory [2] it is clear that the R value should result in simple models. For this reason it is preferred over, the k or the Rj. These latter response values can be calculated from predicted R values. It is more difficult to determine the error structure of the R . It is believed however that logarithmic transformation of the k values should result in homoscedastical error structures [3]. 

The chromatographic behaviour of solutes, as described in equations (5) and (6), only predicts the effects of temperature and relative humidity. According to the formula the R should decrease with an increase of the relative humidity (F decreases because the active sites are covered with water). When the quantitative effects are examined it appears that this effect exists, but with one exception. When methanol is used as solvent an increase in the relative humidity causes an increase in the R values for all solutes but strychnine. A second effect predicted fi-om the chromatographic theory is that temperature increase will decrease the activity. The experimental results show that an increase of temperature can, depending on the composition of the solvent, both increase and decrease the activity. 

Optimization of the separation of these samples is much more challenging than samples of homologues or oligomers. Basic chromatographic theory (equations 1-4 and related text) provides little direction for these separations, due to peak reversals that occur almost universally when conditions are changed, particularly temperature or composition. Historically, researchers have generally focused on only one or, at most, two experimental variables at a time, and have chiefly used trial-and-error as their optimization "strategy". 

Chromatographic Theory and Basic Principles, edited by Jan Ake Jdnsson... 

There is a fundamental relationship described in chromatographic theory between the retention volume of a elution peak and the mid-point of a breakthrough curve achieved by operating the column under frontal analysis conditions (41 ). In the Henry s Law region of the adsorption isotherm, the net retention volume and its measurement can be used to describe the variation of sorbate breakthrough volume as illustrated in Figure 8. Utilizing the experimental apparatus described in the last section, retention volumes were measured as a function of pressure at 40°C (T =... 

It is not my purpose to expound chromatographic theory, or to discuss the fine points of column preparation, solvent selection, or new advances in detectors. The papers that follow deal with recent developments in these areas, and what they report is as applicable to pesticide metabolism analyses as to residue analyses. Instead, I shall describe a working radiochromatograph for the pesticide research laboratory and discuss some of the problems associated with this type of instrument. 

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