Temperature Effects on LC Dynamics
This post is link to the previous post Temperature Effects on Liquid Chromatography Dynamics
Linearized non-isothermal Model
In this post-linear, non-isothermal EDM model is consider for a single solute component
(Nc = 1). Analytical solution is derive using Laplace transformation for linear isotherms (Eq. (2.17)) with different inlet and outlet boundary conditions given by Eqs. (2.15a)-(2.16b). In this part, pulse injections of concentration and energy (or temperature) is assume as Dirichlet BCs at the column inlet.
8
< c1;inj ; if 0 · ¿ · ¿inj @c1 c1(0; ¿) = ; (1; ¿) = 0 ; (3.25a) : @x 0 ; ¿ > ¿inj
8
< c2;inj ; if 0 · ¿ · ¿inj @c2 c2(0; ¿) = ; (1; ¿) = 0 ; (3.25b) : @x 0 ; ¿ > ¿inj
where
L
c2;inj = ½
c
L
p
(Tinj ¡ Tref ):
(3.26)
Here 
denotes the time of injection, c1;inj and Tinj are the mass and temperature of the injected sample.
Moment Analysis
Moment analysis of chromatographic peak is an effective technique for deducing fundamental information about the chromatographic processes in the column. In this post first four moments
are mention in order to characterize the chromatographic peak completely. Inverse Laplace transformation of the model equations provides an analytical solution, but this solution is not enough to study the dynamics of the chromatographic band in the column.
Moment analysis relates the retention equilibrium constant and parameters for mass transfer kinetics. A method of statistical moments use for describing chromatographic peaks in this chapter. The central moments till order four are calculat for non-isothermal EDM utilizing the Dirichlet BCs. The zeroth moment gives information about the total mass of the solute or peak area whereas the first and second moments tell about the retention time and variance of the concentration profiles, respectively. The third moment corresponds to skewness and the fourth moment is related to kurtosis.
Now, moments of energy profile calculated from the final solution given by Eq. (3.52) are presented below.
Zeroth energy moment: Using the above relation, the zeroth energy moment is expressed
as