Gas Chromatography

To analyze of the separation of two peaks is achieved, the following equation is used: Rs = d / Wb Where Rs is the resolution, d Is the distance between the maxima of two adjacent peaks and Wb is the peak width. Peak width, Wb, increases as the square root of the column length, L, and d increases directly with L. In other words Rs is proportional to L / L^(1/2) = L^(1/2) Resolution is proportional to the square root of the column length. If we plot d or Wb versus L, d will surpass Wb at a sufficient large value of L and the separation is achieved. The conclusion is that the chromatographic process in effective even if it produces peak broadening. Of course, in practice there are many methods to achieve a separation and the analyst rarely relies only in the column length.

A comparison of the effect of the carrier gas on the rate equation for a capillary column (H) is made. The following analysis holds for isothermal operation. The process can be optimized for column efficiency (plate number) or the analysis time. For a given column, the solute diffusivity is minimized (term B) using a higher-molecular-weight gas and more plates are generated. Nitrogen shows the minimum H, at the expense of slower analysis. To optimize for speed, however, it is better to choose a lighter carrier gas, like hydrogen or helium. The minima in the figure of H versus average linear velocity for nitrogen, helium and hydrogen are around 12 cm/s, 20 cm/s and 40 cm/s, respectively. On the other hand, hydrogen has the smallest slope beyond the minimum. Thus, an increase in hydrogen flow rate produces only a small loss in efficiency, while considerably speeding up the analysis. Regarding film thickness, high efficiencies are good to separate high-boiling compounds. However, the sa...

Plots depicting the Height plate (H, usually in mm) versus the linear velocity (u, typically in cm/s) are called Van Deemter plots. In such a picture, the three terms of the Golay equation are plotted. In the equation for H, one of the terms is multiplied by u and another is multiplied by it. This leads to the presence of a minimum in the curve for H, an optimal point of velocity which provides the highest efficiency and smallest plate height. Chromatographers manipulate the Van Deemter equation to get the best performance while minimizing the analysis time. The CM term is the most important contribution as the velocity increases. Plots are used to calculate H, and the van Deemter equation is rarely used to achieve this.

Mass transfer in the mobile phase can be related to the solute profile due to the nonturbulent flow through a tube. The molecules in the center of the tube move faster than those near the wall. Therefore, inadequate mixing (slow kinetics) result in band broadening. Columns with small diameter minimizes broadening because the mass transfer distances are reduced. The CM term for the Golay equation is: CM = (1+6k+11k^2)*rc^2 / (24*(1+k)^2*DG) Where rc is the radius of the column, k is the retention factor and DG is the diffusion coefficient. The relative importance of the two terms CM or Cs is dependent on the column radius and film thickness. In columns of small inner diameter, the term CM is less dominant than Cs. On the other hand, for thin films (<0.2 µm) the mass transfer in the mobile phase (CM) controls the C term; in thick films (2-5.0 µm), the C term is controlled by the stationary phase mass transfer (Cs); for intermediate films (0.2-2.0 µm) both factors are important. ...

A figure is used to describe the mass transfer in the stationary phase. We have a mid-horizontal line representing the interface. Above, we have the mobile phase and below, the stationary phase. At a given moment, an equilibrium is stablished, and two peaks with the base in the mid-horizontal line, but pointing to the top and to the bottom are depicted. An instant later the mobile gas moves the upper curve downstream, which gives rise to a situation of base size increase and the broadening of the overall zone of molecules. The solute molecules that moved ahead now participate in another partition between both phases, and vice versa for those that are in the stationary phase. The band broadening is inversely proportional to the speed of this process. The Cs term in the Golay equation is: Cs = (2*k*df) / (3*(1+k)^2*Ds) Where df is the average film thickness of the liquid stationary phase, Ds is the diffusion coefficient of the solute in the stationary phase and k is the retention f...

 Capillary columns are open tubes; hence their rate equation does not have the A term from Van Deemter equation. Golay introduced a new term to account for the diffusion process in the gas phase for the open tubular columns. His equation additionally has two C terms: one for mass transfer in stationary phase, Cs and another for mass transfer in the mobile phase, CM. The simple Golay equation is: H = B/ µ + (Cs + CM) µ The term B accounts for molecular diffusion. The equation for molecular diffusion is: B = 2DG Where DG is the diffusion coefficient for the solute in the carrier gas. A small value for the diffusion coefficient is desired to decrease the value of B and for H. The usage of gases of high molecular masses like nitrogen or argon as carrier gases aids in this sense. Additionally, a high linear velocity also decreases the time a solute spends in the column and the time available for molecular diffusion drops. On the other hand, the C terms are related to mass trans...

Van Deemter identified three effects that contribute to peak broadening in packed columns: Eddy diffusion (term A), longitudinal molecular diffusion (the term B) and mass transfer in the stationary phase (the term C). The Van deemter Equation is: H = A + B/ µ + C µ Where H is the plate height, and µ the linear gas velocity. A small value indicates a narrow peak (the desired condition). Minimize each term is the way to maximize column efficiency.

Column resolution Rs is another measure of efficiency and represents the degree to which two adjacent peaks are separated. Rs is defined by dividing the distance between the peak maxima for two solutes A and B by the sum of the baseline lengths of both peaks. This equation is strictly valid when both peaks have the same height. The larger the resolution, the better the separation. To produce a complete baseline separation, a resolution of at least 1.5 is required.

The plate height, H, is defined as: H = L / N Where L is the column length and N is the plate number. H has units of length and is better suited for comparing efficiencies of columns of different lengths. It is also called height equivalent to one theoretical plate (HETP). A good column will have a large N and a small H

A broadening of peaks with retention time is a natural phenomenon of the chromatographic process. Due to this fact, the most common measure of efficiency is the plate number, N, defined as: N = (tR/S)^2 = 16(tR/Wb)^2 = 5.54(tR/W_(1/2))^2 Where W_(1/2) is the width of the peak measured at half its height N is unitless. A high value of N indicates an efficient column, a very desirable quality. If the chromatogram has several peaks, the value of N for each compound will vary. However, it is common practice to assign a value to a column, based only on one measurement.

Theoretical discussion assumes an ideal Gaussian peak. Some of its characteristics are the following: The inflection points occur at 0.607 of the peak height. The tangents to those points produce a triangle with a base width Wb, equal to four standard deviations, 4σ, and a width at half height, Wh of 2.354σ. The width of the peak at the inflection point is 2σ.

The ideal peak shape, or the distribution of the molecules of a compound, can be approximated as being normal or Gaussian. The presence of asymmetry in peaks are an indication of the presence of undesirable interactions during the chromatographic process. In packed columns, broad peaks are common and usually indicate that mass transfer kinetics are slow. Asymmetric peaks can be classified as tailing or fronting depending on whether the peak seems to be compacted on the right side (fronting) or on the left side (tailing). The tailing factor (TF) is used to evaluate the extent of the asymmetry. It is defined as TF = b / a Where a and b are the peak width at the left and at the right of the maximum intensity of the peak. a and b are usually measured at 10% of the peak height. US Pharmacopeia recommends 5% of the peak height and the following formula: TF = (a+b) / 2a Care must be taken when using tailing factor for column comparisons, because there are several common definition...

The selectivity (α) of a separation is calculated as the ratio of the adjusted retention times of two adjacent peaks: Alpha = t’R(2) / t’R(1) The numbers 1 and 2 are for the earlier (1) and later (2) eluting peaks. Selectivity can also be written as the equality between the ratio of the retention factors (k1 and k2) and equal to the two partition coefficients (K1 and K2). The selectivity is a consequence of the differences on intermolecular interactions between the compounds and the stationary phases. Selectivity increases as the differences in those interactions increase. In GC capillary columns, the selectivity required to perform a separation can be as low as 1.02 or less.

  The retention factor, k, is the ratio of the mass of solute (not its concentration) in the stationary phase to the mass in the mobile phase: The retention factor is measured experimentally as the ratio of the adjusted retention time, t′R, to the gas hold‐up time tM The larger the value of k, the longer the solute will be retained in the column. The relevance of this factor is that can be obtained easily from the chromatogram. The retention factor and the distribution constant are related through the phase ratio (beta). Kc can be broken down into two terms: Kc equals the product of the retention factor and the phase ratio In formula: Kc = k x beta Beta is defined as the ratio between the volume of the mobile phase (VM) and the stationary phase (Vs). In formula Beta = Vm / Vs For capillary columns, with a known value of film thickness (df), beta is given by: Beta equals the square difference between the radius of the capillary column (rc) and the film thickness (d...

  The distribution constant, Kc, is a parameter that defines how fast a solute moves down the column. For a solute A that moves between the mobile phase and the stationary phase, in an equilibrium reaction, we can write the equilibrium constant Kc as the ratio between the concentration of A in the stationary phase and its concentration in the mobile phase. Larger values of this coefficient mean the solute is retained for longer periods because its sorbs more readily in the stationary phase. Even though an equilibrium constant is used, that does not imply the process is in equilibrium, because the mobile gas phase is continuously moving solute molecules down the column. However, the partition coefficient is adequate as a descriptor when the kinetics of mass transfer are fast, because the system will operate near to equilibrium conditions. Another assumption in the development of the theory is that the solutes do not interact with one another. Thus, the formation of azeotropes an...