## GC Simulator

### Quick Start

A few basic factors control the shape of GC peaks and the potential for high-resolution separations. Of course, real GC includes temperature ramps, but here we concentrate on the basics.

### GC Simulator

L Length m
d Internal Diam mm
h Thickness μm
D Diff.Coef. cm²/min
V Flow Rate ml/min
tmax
DCa
DCb
CFa
CFb
PWa
PWb
Phase Ratio
v Velocity cm/min
t0
ta
tb
R Resolution
H Plate Height cm
N Theoretical Plates
α Selectivity

The simulation here closely follows an excellent Excel spreadsheet from Prof Tom O'Haver at University of Maryland with some minor simplifications

There are a basic set of inputs, the length of the column, L, the internal diameter, d, the thickness, h, of the stationary phase coated onto the walls, the diffusion coefficient, D, in the gas phase, the flow rate, V, and the Distribution Coefficients, DCa and DCb of two analytes, a and b. You can also set the tmax of the plot.

Many parameters are then calculated from these inputs, with x representing a or b and when b is mentioned this is the peak with the longest retention time.

1. Phase Ratio, β = d/(4h)
2. Capacity Factors CFx = DCx/β
3. Selectivity, α = CFb/CFa
4. Flow Velocity, v =V/(π(d/2-h)²)
5. t0 = L/v
6. tx = t0(1+CFx)
7. Plate Height, H = 2D/v+v((d/2)²*((1+6*CFb+11.CFb²)/(24*(1+CFb)*(1+CFb)))/D)
8. No. Theoretical Plates, N = L/H
9. Peak Width, PW = t/√(N/16)
10. Resolution, R = 0.25√N(α-1)/α.CFb/(1=CFb)

The retention times of the peaks are controlled by DCa and DCb. If they are close together then the ability to resolve them depends on the number of theoretical plates which come from the column length and the plate height. This depends on the diffusion coefficient and flow velocity. As you are unlikely to change D (which depends on the choice of gas in the column), then it all comes down to the trade-off of analysis time (high v is preferred) and resolution (low v is preferred). The velocity, v, depends on gas flow rate for a given column, but on diameter and stationary phase thickness if you can choose the column.

So the simulation lets you see the broad effects of column choice and and flow rates. How you can influence the Distribution Functions via choice of the stationary phase is a different topic!