General HETP Equation for the Study of Mass-Transfer Mechanisms in RPLC

Abstract

Classical HETP equations including the Van Deemter and the Knox equations, are semiempirical, approximate equations that provide apparent mass-transfer coefficients with little sound physical justifications. The conventional A and B coefficients are revisited, the former through the use of the fundamental theory of eddy diffusion due to Giddings, the latter by taking into account the intraparticle diffusion (pore and surface diffusion). Our work confirms that eddy diffusion originated from three different sources in RPLC: trans-channel, short-range interchannel, and long-range interchannel velocity biases. Accordingly, the eddy diffusion term is given by the ratio of two third-degree polynomials. Finally, the C term is the sum of two terms corresponding to the resistance to mass transfer due to diffusion through the external stationary film of liquid phase surrounding the silica particles and to the classical resistances to mass transfer due to diffusion through the silica particles. It is easily related to the physical characteristics of the phenomena involved. Experimental HETP data were derived from moment analysis for phenol on a C(18)-Sunfire column, with a mixture of acetonitrile and water as the mobile phase (15/85, v/v). The linear interstitial velocity ranged between 0.027 cm/s and 4.7 mL/min, and six temperature (21, 36, 45, 55, 67, and 77 degrees C) were applied successively. The HETP equation obtained was tested to study the mass-transfer mechanism. An excellent agreement was found between the experimental and theoretical HETP. The model allows the precise calculation of the activation energy for surface diffusion (E(S) = 31.3 kJ/mol) and the coefficient beta that relates the restriction energy for molecular diffusion on the C(18)-bonded surface to the isosteric heat of adsorption Q(st) (beta = 0.80).