Measurements of Binary Diffusion Coefficients for Ferrocenes in Supercritical Carbon Dioxide

The binary diffusion coefficients of ferrocene and 1,1’-dimethylferrocene at infinite dilution in supercritical carbon dioxide, D12, were measured by the chromatographic impulse response (CIR) method at temperatures from 308.2 to 323.2 K and pressures from 9 to 40 MPa. The D12 data for ferrocene were also measured by the Taylor dispersion method. The diffusion data of ferrocene measured by the Taylor disperion method were consistent with those measured by the CIR method. In addition, it was found that all the measured D12 data were well represented by the correlation of (D12/T)M as a function of carbon dioxide viscosity. INTRODUCTION The organometallic compounds such as ferrocene and its derivatives have been investigated for a variety of applications in organic synthesis and biological systems, etc, due to the unique properties such as electrochemical and photoinduced electron transfer properties [1]. Recently, the behavior of organometallic compounds in supercritical carbon dioxide has become focus of attention due to the compounds not only having relatively high solubility in supercritical fluids but also having the potential to control solvation and reaction behavior via changes in the physical conditions of the system [2]. Then, the estimation of mass transfer properties of the organometallic compounds in supercritical carbon dioxide are essential for process design. So far, considerable experimental data have been reported regarding the diffusion coefficients of organic compounds in supercritical carbon dioxide [3,4]. Unfortunately, the diffusion data for organometallic compounds in supercritical carbon dioxide have not been reported except for copper(II) trifluoroacetylacetonate [5], at the limited conditions, which were measured by the Taylor dispersion method [6]. On the other hand, the authors [7] have demonstrated that the diffusion coefficients measured by the CIR method are more reliable than those by the Taylor dispersion method, especially in the near critical region. The application of supercritical fluids is usually carried out at higher pressures in order to achieve higher solvent power. Thus, the objectives of this study are (1) to measure the diffusion coefficients of ferrocene and its dirrevative in supercritical carbon dioxide at pressures up to 40 MPa, and (2) to examine the effectiveness of the Taylor dispersion method for measuring the diffusion coefficients in the system of carbon dioxide and ferrocenes. THEORY The detail theories for the Taylor dispersion and the CIR methods have been described by Alizadeh et al. [6] and in our previous study [8], respectively. When a tracer is pulse-injected into a fully developed laminar flow in a cylindrical diffusion column, the continuity equation in terms of the tracer concentration c(r, x, t) together with the initial and boundary conditions are given as Eqs (1), (2a), (2b), (3a) and (3b) in Table 1. Approximate solutions Ca(t) for the cross-sectional average concentration of the tracer at diffudion column exit are given by Eqs (4a) and (4b). The validity of both measurements can be evaluated in terms of root-mean-square (r-m-s) error ε between measured curve Ca,meas(t) and calculated curve Ca(t) using Eq. (5). The curve fitting is considered good when ε < 1%, and acceptable when ε < 2 ~ 3% [8]. Table 1. Fundamental equations of the Taylor dispersion and the CIR methods Taylor dispersion method CIR method c(r, x, t) ±∞ = = ∂ ∂ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ∂ ∂ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ ∂ ∂ = ∂ ∂ x c x c R r u x c r c r r r D t c