height of the elution concentration profile of each different sample. Curve width is the width of the concentration profile curve of the different samples in the chromatogram in units of time. A simplified method of calculating chromatogram resolution is to use the plate model. The plate model assumes that the column can be divided into a certain number of sections, or plates and the mass balance can be calculated for each individual plate. This approach approximates a typical chromatogram curve as a Gaussian distribution curve. By doing this, the curve width is estimated as 4 times the standard deviation of the curve, 4σ. The retention time is the time from the start of signal detection to the time of the peak height of the Gaussian curve. From the variables in the figure above, the resolution, plate number, and plate height of the column plate model can be calculated using the equations: Resolution (Rs) Rs = 2(tRB – tRA)/(wB + wA) Where: tRB = retention time of solute B tRA = retention time of solute A wB = Gaussian curve width of solute B wA = Gaussian curve width of solute A Plate Number (N): N = (tR)2/(w/4)2 Plate Height (H): H = L/N Where L is the length of the column. Column adsorption equilibrium For an adsorption column, the column resin (the stationary phase) is composed of microbeads. Even smaller particles such as proteins, carbohydrates, metal ions, or other chemical compounds are conjugated onto the microbeads. Each binding particle that is attached to the microbead can be assumed to bind in a 1:1 ratio with the solute sample sent through the column that needs to be purified or separated. Binding between the target molecule to be separated and the binding molecule on the column beads can be modeled using a simple equilibrium reaction Keq = [CS]/([C][S]) where Keq is the equilibrium constant, [C] and [S] are the concentrations of the target molecule and the binding molecule on the column resin, respectively. [CS] is the concentration of the complex of the target molecule bound to the column resin. Using this as a basis, three different isotherms can be used to describe the binding dynamics of a column chromatography: linear, Langmuir, and Freundlich. The linear isotherm occurs when the solute concentration needed to be purified is very small relative to the binding molecule. Thus, the equilibrium can be defined as: [CS] =