조성변화를 고려한 초임계 CO2내의 Azulene과 Acenaphthylene의

무한희석 부분몰성질.

전영표, Michal Roth↕, 권영중

강원대학교 화학공학과

Infinite-Dilution Partial Molar Properties of Azulene and Acenaphthylene in Supercritical Carbon Dioxide with Composition-change employed

Young Pyo Jeon, Michal Roth↕, and Yong Jung Kwon

Department of Chemical Engineering of Kangwon National University

↕Institute of Analytical Chemistry , ASCR, Czech Republic

Introduction

Supercritical fluid chromatography (SFC) has become a recognized source of thermodynamic information related to the transfer of solute between the mobile and the stationary phase. If the exact mass of the stationary polymer in the column is known, SFC retention data may yield the partition coefficient of the solute between both phases[1,2] or the solute polymer interaction parameter[2]. If the mass of stationary polymer is not known exactly but remains constant during the measurements, variations in the solute capacity factor with pressure, temperature or composition of the mobile-phase fluid may be used to measure partial molar volume[3-6], partial molar enthalpy[4], respectively.

Applications of SFC to determine the partial molar properties of solutes were based on a simplified thermodynamic description of the problem. Namely, the pressure and temperature variations in the equilibrium proportion of the mobile-phase fluid in the stationary phase were usually neglected so that the observed variations in the solute capacity factor were attributed entirely to what happened in the mobile phase. However, the changes in phase ratio and in composition of the stationary phase are translated into the measured capacity factors and, therefore, they affect the resultant partial molar properties. The present work makes use of an earlier theoretical treatment[7,8] to take the composition changes into account when reducing capacity factor data to partial molar properties. The solutes are azulene and acenaphthylene

Experimental

Measurements were performed using a Dionex Series D-600 supercritical fluid chromatography equipped with a pneumatically operated injection valve, a flame ionization detector, and a 10 m long Dionex SB Methyl-100 capillary column with internal diameter of 50 □m, containing a 0.25 □m film of crosslinked poly dimethyl siloxane (PDMS). The solutes were purchased from Aldrich (Seoul, Republic of Korea), and used as received. The injection solutions were prepared by dissolving 1.2 mg of either solute in 10 ml of methylene chloride. The injection valve was fitted with a 500-nL rotor, and the split ratio was 1:15 (column flow rate: split flow rate). The capacity factor of acenaphthylene was measured along 3 isotherms within 48 to 58 □C, and the capacity factor of azulene along 5 isotherms within 33 to 58 □C, separately for each solute. All measurements were carried out in triplicate. The dead retention time, marked by injections of methane, did not drop below 9 minutes. Therefore, the difference between the column inlet pressure and the mean pressure in the column did not exceed 0.5 bar.

Theory

The logarithmic plots of the solute retention factor, [eqn: k_1], versus the molar density of CO2, [eqn: rho_m] , at the mean pressure in the column were smoothed with straight lines by least-squares linear regression. A sample plot is shown in Figure1. The isothermal pressure derivative of [eqn: ln k_1] and the isobaric temperature derivative of [eqn: ln k_1] were obtained from the density-involving derivatives using eqs 1 and 2,

[eqn: left( {partial ln k_1 } over {partial P} right )_T `=` beta_mT ```left( {partial ln k_1} over {partial ln rho_m} right)_T]	(1)

[eqn: left( {partial ln k_1 } over {partial T} right )_P `=` -alpha_mP ```left( {partial ln k_1} over {partial ln rho_m} right)_T - 1 over T^2 left( {partial ln k_1 } over {partial (1/T) } right )_rho_m]	(2)

where P is the pressure, T the absolute temperature, [eqn: alpha_mP] the isobaric expansivity of CO2, and [eqn: beta_mT] the isothermal compressibility of CO2.

The isothermal pressure derivative of [eqn: ln k_1] was converted to the infinite-dilution partial molar volume of the solute using eq 3[7,8],

[eqn: {{barv}_1m}^inf overRT `=` left ( {partial ln k_1} over {partial P} right ) _T &+ {{{barv}_1s}^inf} over RT + beta_mT `+` V_s over V_m beta_sT□## &+ 1 over RT left( partialmu_1s^inf over {partial w_3s} right )_T,P,n_2s left( {partial w_3s} over {partial P} right )_T,sigma]	(3)

where R is the molar gas constant, [eqn: {{barv}_1m} ^ inf] and [eqn: {{barv}_1s} ^ inf] are the infinite dilution partial molar volumes of the solute in CO2 and in the stationary phase, respectively, [eqn: beta_sT□] is the isothermal compressibility of the stationary phase at saturation with the dissolved CO2, [eqn: V_s] and [eqn: V_m] are the geometric volumes of the stationary and the mobile phase in the column, respectively, [eqn: {{barmu}_1s} ^ inf] is the infinite dilution chemical potential of the solute in the stationary phase, and [eqn: w_3s] is the mass fraction of CO2 in the stationary phase. Subscript [eqn: n_2s] refers to insolubility of the stationary polymer in CO2, and subscript □stresses saturation of the stationary phase with the dissolved CO2. The infinite dilution partial molar enthalpy of transfer of the solute from the stationary phase to the mobile phase, [eqn: {{bar h}_1m}^inf `-`{{bar h}_1s}^inf], is related to the isobaric temperature derivative of [eqn: ln k_1] by [7,8],

[eqn: {{bar h}_1m}^inf over RT^2 - {{bar h}_1s}^inf over RT^2 = alpha_mP &- left( {partiallnk_1} over {partial T} right )_P + V_s over V_m alpha_sP□ ## &- 1 over RT left( {partial mu_1s ^inf } over {partial w_3s} right )_T,P,n_2s left( {partial w_3s} over {partialT} right )_P,□]	(4)

where [eqn: {{bar h}_1m}^inf] and [eqn: {{bar h}_1s}^inf] are the infinite-dilution partial molar enthalpies of the solute in CO2 and in the stationary phase, respectively, and [eqn: alpha_sP□]is the isobaric expansivity of the stationary phase at saturation with the dissolved CO2.

In eqs 3 and 4, the quantities was [eqn: beta_sT□] and [eqn: alpha_sP□], the phase ratio [eqn: V_s / V_m], and the slopes ,[eqn: ( partial w_3s / partial P )_T,□] and [eqn: ( partial w_3s / partial T )_P,□] were calculated from the Panayiotou-Vera mean-field lattice model[9] as described before[8,10]. The elastic contribution to the derivative [eqn: ( partial mu_1s ^ inf / partial w_3s ) _T,P,n_2s] was neglected, and the mixing contribution was obtained from a combination of the Flory-Huggins and the regular solution theories[11].

Results and Discussion

The relative importance of the composition correction generally increases with decreasing magnitude of[eqn: {{barv}_1m}^inf] as the temperature moves farther away from the critical temperature of CO2. However, the relatively small effect of the composition correction on the values of[eqn: {{barv}_1m}^inf] for azulene at 33 □C may partly be due to inadequacy of the mean-field theories near the critical point of CO2, in particular, to underestimation of the derivative [eqn: ( partial w_3s / partial P ) _T,□], rather than to actual dominance of the mobile-phase effects in determining the slope [eqn: ( partial ln k_1 / partial P)_T]. The partial molar volumes of azulene at 33 □C are gross approximations because of uncertainties in the CO2 density that result from the near-critical enhancement in compressibility.

Figure 1 shows the infinite-dilution molar enthalpy of transfer of azulene from the stationary phase to the mobile phase, [eqn: {{bar h}_1m}^inf - {{bar h}_1s}^inf]. Part (a) shows the values corrected for the composition changes in the stationary phase while part (b) displays the results of the usual simplified treatment retaining only the first two terms on the rhs of eq 4. Application of the composition correction shifts the transfer enthalpies toward more negative values. Because of the method of calculation, the uncertainty in the resultant enthalpies of transfer exceeds that in the partial molar volumes.

The infinite-dilution partial molar volumes of the solutes may be reduced to several well-behaved quantities characterizing short-range interactions between the solute and the near-critical solvent, such as the Krichevskii parameter[12] [eqn: delta], may be written as

[eqn: delta = {{barv}_1m}^inf rho_m / beta_mT]	(5)

Figure 2 shows the [eqn: delta] values for azulene in CO2, calculated with (a) and without (b) the correction for composition changes in the stationary phase, respectively. Figure 3 presents the [eqn: delta] values for acenaphthylene in CO2. Application of the composition correction makes the [eqn: delta] values more negative.

Conclusions

Nevertheless, as regards the disparity between the chromatographic and solubility data on partial molar volumes, the correction seems to work in the right direction. An important problem of this study is the degree of mutual consistency of the various thermodynamic models involved in the data analysis and in the composition correction. The quantitative performance of the correction has yet to be tested with solutes for which independent data on partial molar volumes in CO2 are available. The work in this direction is in progress.

References

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Fig. a. Enthalpy of Azulene

Fig. 1b. Enthalpy of Azulene

Fig. 2a. The [eqn: delta] of Azulene

Fig. 2b. The [eqn: delta] of Azulene

Fig. 3a. The [eqn: delta] of Acenaphthylene

Fig. 3b. The [eqn: delta] of Acenaphthylene