The Knox Equation During 1972 and 1973 Knox and his co-workers (18), (19), and (20) carried out a considerable amount of work on different packing materials with particular reference to the effect of particle size on the reduced plate height of a column. The concept of reduced plate height (h ) and reduced velocity  (n) was introduced by Giddings (21) and (22) in 1965 in an attempt to form a basis for the comparison of different columns packed with particles of different diameter. The reduced plate height is defined as,                                         &

, as the sample and mobile phase will have the identical composition. Any component that is in excess in the sample will give a positive peak. Conversely, any component that is present in the sample that is below specifications will give a negative peak. The peak area or peak height, for both positive and negative peaks, will give a quantitative estimation of the amount the component deviates from that specified. Temperature Changes During the Passage of a Solute Through a Theoretical Plate in Gas Chromatography Thermal changes resulting from solute interactions with the two phases are definitely second-order effects and, consequently, as such and, as Einstein predicted, their theoretical treatment is more complex. The theoretical treatment of temperature perturbations that result from solute phase interactions, however, provides a good example of the use of the plate concept in a wider sense of chromatography theory.  

Equation (9) is the Van Deemter equation that describes the variance per unit length of a column in terms of the physical properties of the column contents, the distribution system and the linear velocity of the mobile phase. Alternatively the Van Deemter equation can be expressed in the form,   (10)   where (H) is the Height of the Theoretical Plate. The relationship between 0 and (sx) is explained in The Plate Theory and Extensions . Hence the term "HETP equation" for equation (10). This form of the Van Deemter equation is very nearly correct for LC but, due to the compressibility of the gaseous mobile phase in GC, neither the linear velocity nor the pressure is constant along the column. Furthermore, as the diffusivity, (Dm), is a function of pressure, the above form of the equation can only be approximate. However, equation (10) generally gives the correct

The peak height (h) is the distance between the peak maximum and the base line geometrically produced beneath the peak. The peak width (w) is the distance between each side of a peak measure at 0.6065 of the peak height (ca 0.607h). The peak width measured at this height is equivalent to two standard deviations (2s) of the Gaussian curve and thus has significance when dealing with chromatography theory. The peak width at half height (w0.5) is the distance between each side of a peak measured at half the peak height. The peak width measured at half height has no significance with respect to chromatography theory. The peak width at the base (wB) is the distance between the intersections of the tangents drawn to the sides of the peak and the peak base geometrically produced. The peak width at the base is equivalent to four standard deviations (4s) of the Gaussian curve and thus also has significance when

Inflection In order to measure the column efficiency, the position of the points of inflection, where the peak width is to be measured, must be identified. The inflection points are not easily located on a peak, so it is necessary to know the fraction of the peak height at which they occur. The peak represents the concentration profile of the eluting solute, so the fraction of the peak height at which the points of inflexion are located will be the ratio of the solute concentration after () plate volumes of mobile phase has passed through the column to the solute concentration after (n) plate volumes of mobile phase have passed through the column. Therefore, if (f) is the fraction of the height (h) at which the points of inflection occur, then                                        

The resistance to the mass transfer term for the stationary phase must be considered in isolation. The experimentally observed plate height (variance per unit length) resulting from a particular dispersion process [e.g., (hs), the resistance to mass transfer in the stationary phase] will be the sum of the local plate height contributions (h');  i.e.,                                    Consequently, substituting for (h') the expression for the resistance to mass transfer in the stationary phase will be,                     or &