1904
Ind. Eng. Chem. Res. 1999, 38, 1904-1910
Solubility, in Supercritical Carbon Dioxide, of Paraffin Waxes Used as Binders for Low-Pressure Injection Molding Thierry Chartier,† Eric Delhomme,† and Jean F. Baumard† Science des Proce´ de´ s Ce´ ramiques et des Traitements de Surface, UMR CNRS 6638, ENSCI, 87065 Limoges Cedex, France
Philippe Marteau, Pascale Subra, and Roland Tufeu* Laboratoire d’Inge´ nierie des Mate´ riaux et des Hautes Pressions, CNRS, Institut Galile´ e, 93430 Villetaneuse, France
Paraffin waxes, commonly used as binders in ceramic-forming processes, can be removed from ceramic bodies with supercritical carbon dioxide. Therefore, the solubility of three industrial paraffin waxes (melting at 42, 52, and 62 °C, respectively) in supercritical CO2 was investigated. The concentrations of these paraffin waxes in the solvent-rich phase in equilibrium with the paraffin-rich phase were measured at 343 K in the pressure range 12-30 MPa by using infrared absorption spectroscopy. Some n-alcane-CO2 binaries were also investigated. A model was developed by analogy with polydisperse polymers in solvents. It relates the concentration of the paraffin waxes to the concentration of the pure n-alcanes for n-alcane-CO2 binary systems. This model gives accurate overall concentration values for paraffin-CO2 mixtures and reproduces the n-alcane distribution in the solvent-rich phase. Introduction Most of the fabrication processes involved in the technical ceramics field, such as extrusion, injection, or tape-casting, require the use of organic additives such as binders, plasticizers, and lubricants to give the ceramic composition suitable rheological properties and cohesion during the forming step. These organic compounds must be removed prior to the last sintering step. This removal operation, called debinding, is currently performed by thermal treatment using slow heating rates and long isothermal steps. It is thus time-consuming.1-4 Furthermore, thermal debinding, based on the pyrolitic degradation of organic compounds, may lead to defects which affect the properties of the sintered pieces.5 The extraction of binders by supercritical fluids, based on the unique dissolving characteristics and transport properties of these fluids, appears to be an interesting alternative to reduce debinding time and to avoid the creation of defects. The removal of paraffin waxes from injection-molded ceramic bodies with supercritical CO2 has been investigated.6,7 As shown by these previous studies, two phenomena control supercritical debinding: solubilization of paraffin molecules and diffusion of dissolved paraffin species. In this paper, we report solubility measurements in supercritical carbon dioxide of industrial paraffin waxes and n-alcanes which compose these waxes. These measurements were performed in the same pressure range at 343 K. Experimental Section Materials. Phase equilibria of CO2 with three paraffin waxes and with seven n-alcanes present in these * To whom correspondence should be addressed. Tel: +33 (0)1 49 40 34 47. Fax: +33 (0)1 49 40 34 14. † Tel: +33 (0)5 55 45 22 25. Fax: +33 (0)5 55 79 09 98.
waxes were investigated. We chose paraffin waxes commonly used in the low-pressure injection-molding process: one melts at 42 °C (paraffin 42, Aldrich Chimie), one melts at 52 °C (paraffin 52, industrial paraffin (Citgo, USA)), and one melts at 62 °C (paraffin 62, industrial paraffin (Citgo, USA)). The compositions of the paraffin waxes were determined by gas chromatography (gas chromatograph GC 6000 from Carlo Erba Instruments) using a capillary column (capillary column Hewlett-Packard 25 m × 0.2 mm, 0.5 µm film thickness) and a flame ionization detector. The column and the detector were maintained at 320 °C. The chromatogram peaks of the three paraffin waxes correspond to nalcanes and isomers. The isomers represent 7.25, 11.7, and 7 wt % of the paraffin waxes 42, 52, and 62, respectively. In the following study, we will assume that the paraffin waxes are entirely composed of n-alcanes by combining n-alcanes and isomers of the same molar mass. The mass fraction Wpn of the alcane with n carbon atoms (molar mass Mn) in every paraffin wax is given in Table 1. The average molar masses Mw of the paraffin waxes given by
Mw )
∑WpnMn
(1)
are 326.2, 371.1, and 422 g/mol for the paraffins 42, 52, and 62, respectively. They correspond to the molar masses of theoretical alcanes having n j carbon atoms, with n j equal to 23.16, 26.36, and 30 for the paraffins 42, 52, and 62, respectively. According to the compositions of the paraffin waxes, we have chosen to study the solubility of seven nalcanes: heptadecane (C17H36), nonadecane (C19H40), heneicosane (C21H44), tetracosane (C24H50), hexacosane (C26H54), and dotriacontane (C32H66). The solubility of octacosane (C28H58) was also investigated for comparison with the results obtained by Swaid et al.8 The n-alcanes
10.1021/ie980552e CCC: $18.00 © 1999 American Chemical Society Published on Web 03/17/1999
Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 1905 Table 1. Weight Fractions Wpn (wt %) of Alcanes in the Paraffin Waxes (n is the Number of Carbon Atoms of the Alcane Molecule) Wpn (wt %) n
paraffin 42
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
0.20 1.28 3.87 7.81 12.17 15.75 16.76 15.18 11.76 7.16 3.51 1.98 1.15 0.68 0.46 0.30
paraffin 52
0.41 2.12 5.35 8.58 11.73 12.09 13.34 11.93 10.73 9.21 6.77 4.27 1.92 1.01 0.54
paraffin 62
0.14 0.30 0.89 2.48 3.58 5.30 7.18 9.57 11.69 12.58 13.10 13.67 8.13 5.50 3.45 1.45 0.63 0.30
Table 2. Melting Temperature and Purity of the n-Alcanes (Data Supplied by Aldrich Chimie, France) C17H36 C19H40 C21H44 C24H50 C26H54 C28H58 C32H66
heptadecane nonadecane heneicosane tetracosane hexacosane octacosane dotriacontane
melting temp (K)
purity (%)
295-297 305-307 313-315 322-325 330-331 334-336 341-343
99 99 99 99 99 99 97
were supplied by Aldrich Chimie. Their purities and melting points reported in Table 2 are the values given by the supplier. Concentration Measurement Device. CO2-paraffin mixtures and CO2-alcane mixtures are compressed and heated in an optical high-pressure cell as described in a previous work.9 The pressure is adjusted by varying the internal volume of the cell. The cell is set in a furnace, and the temperature is controlled within (0.2 °C. The pressure is measured with an accuracy of 0.05 MPa by using a calibrated strain gauge pressure transducer fitted on the top of the cell. The distance between the sapphire windows can be adjusted to any desired value from a few tenths of a millimeter up to 16 mm so that the absorption of light by the fluid can always be made measurable for the chosen spectral bands. For the present measurements, the distance between the windows was set to 16.0 ( 0.05 mm. The cell and the furnace can be rotated around the optical axis, to observe either the gas phase or the liquid phase and also to mix the solute-solvent system to reach thermodynamic equilibrium. The infrared spectra were recorded with a spectrometer (Bohmem MB155) fitted with an InAs detector. The concentrations of each species in the CO2-rich phase are deduced from these spectra in a very simple way as the absorption bands of the alcanes are well separated from those of CO2 (Figure 1). It was also verified that no significant absorption due to CO2 occurs in the absorption frequency range of alcanes and reciprocally. It must also be noticed that n-alcanes and waxes considered in this work have the same spectral
Figure 1. Paraffin-CO2 mixture absorption spectrum.
behavior, qualitatively and quantitatively. Under these conditions, the concentrations are derived from the absorption intensities, without any further mathematical treatment, through the Beer-Lambert law:
c)
I0(ν) 1 ln R(ν) la I(ν)
(2)
where la is the absorption path length, R(ν) is the absorption coefficient at the frequency ν, and I0(ν) and I(ν) are the transmitted intensities through the empty cell and through the sample, respectively. The concentrations of CO2 in the gas phase were determined according to eq 2, by summing the absorption peak intensities of the 4ν2 + ν3 and 2ν1 + ν3 absorption bands located at 4860.5 and 5109 cm-1, respectively. As a matter of fact, although neither of these two bands linearly varies with concentration, their sum keeps a linear behavior, at least at 343 K in the 10-40 MPa pressure range. The concentrations of solute were determined in three different ways, either by measuring, as made by Swaid et al.,8 the integrated intensities of the overtone and combination bands centered at about 5800 and 4200 cm-1, respectively, or by measuring the absorption intensity at a fixed frequency, namely, 4180 cm-1. A calibration of these absorptions was initially made with pure CO2 and with CO2-alcanes mixtures of known compositions in the one-phase state. It is noteworthy that the absorption intensities of alcanes and waxes diluted in CO2 are weaker, by a 1.5 factor approximately, than they are in the liquid state. This explains the discrepancy observed between the present results and those previously published,10 for which the calibration had been preliminarily based upon the liquid state. Experimental Values of Solubility. The concentrations Cn and CCO2 of n-alcane and of carbon dioxide (kg/m3) in the CO2-rich phase and the mass of solute per kilogram of solvent in the CO2-rich phase (mass concentration), noted Wsn ) Cn/CCO2, are reported in Table 3. C17H36 and supercritical carbon dioxide are completely miscible under pressures higher than 20 MPa. The solubility of the n-alcanes decreases strongly as their number of carbon atoms n increases, as shown in Figure 2. For example, the mass concentration of C32H66 is about 18 times lower than the mass concentration of C19H40 under 20 MPa. A number of investigations on the phase behavior of heavy n-paraffin-CO2 systems are reported in the
1906 Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 Table 3. Experimental Mass Concentrations Wsn of the n-Alcanes in the CO2-Rich Phase as a Function of Pressure (T ) 343 K) n-alcane
P (MPa)
Cn (kg‚m-3)
CCO2 (kg‚m-3)
100Wsn (kg‚kg-1)
C17H36
12.88 13.94 14.92 15.98 17.86 19.68 14.45 15.70 16.90 18.90 19.45 20.85 21.45 22.10 23.20 24.00 24.90 13.95 15.70 17.90 19.91 21.11 23.16 25.54
2.8 6.4 12.3 22.3 49.9 93.9 4.6 10.1 16.5 27.7 38.0 53.2 61.1 71.4 88.0 102.8 122.7 1.9 6.3 14.4 24.5 31.6 45.8 63.8
349 419 478 536 616 675 437 510 557 609 641 670 686 701 722 730 737 407 508 590 642 671 705 740
0.8 1.53 2.57 4.16 8.10 13.9 1.05 1.98 2.96 4.55 5.93 7.94 8.91 10.18 12.09 14.08 16.65 0.47 1.24 2.44 3.82 4.71 6.50 8.62
C19H40
C21H44
n-alcane
P (MPa)
Cn (kg‚m-3)
CCO2 (kg‚m-3)
100Wsn (kg‚kg-1)
C24H50
18.47 20.52 22.39 24.48 26.38
8.82 14.88 21.50 28.64 36.06
586 636 672 703 721
1.50 2.34 3.20 4.07 5.00
C26H54
15.83 17.72 19.49 21.69 23.71 26.01
1.91 4.19 7.42 11.44 15.99 22.28
495 569 621 658 690 721
0.38 0.74 1.19 1.73 2.32 3.09
C28H58
16.20 18.10 20.00 24.00 18.46 22.00 25.00 28.00 31.00
1.29 2.62 4.91 9.82 1.36 3.53 5.79 8.30 10.35
523 582 628 689 607 658 699 742 748
0.25 0.45 0.78 1.42 0.23 0.53 0.83 1.12 1.38
C32H66
Table 4. Experimental Mass Concentrations Wsp of the Paraffin Waxes in the CO2-Rich Phase as a Function of Pressure (T ) 343 K) paraffin 42
Figure 2. Mass concentration of the alcanes in the CO2-rich phase as a function of the number of carbon atoms n at constant temperature (343 K) and constant pressure (20 MPa).
literature. They concern the solubilities of solid nalcanes in carbon dioxide11,12 or fluid-fluid phase equilibria.8,13-16 We have compared our results to the values obtained at the same temperature by Swaid et al. 8 on the system octacosane-CO2 by using the spectroscopic method and by Kordikowski and Schneider16 on the system nonadecane-CO2 by using an analytical method. A good agreement is observed for the C28-CO2 system. For the binary C19-CO2, one value can be compared with our result at 25 MPa and 343 K: our value is 20% lower than the value obtained by Kordikowski.16 The mass concentrations Wsp of the paraffin waxes 42, 52, and 62 in the solvent-rich phase are reported in Table 4. As for the n-alcanes, the solubility of the paraffin waxes decreases as their n-alcane distributions are shifted to the higher numbers of carbon atoms. These results have been obtained for phase equilibria realized with a mixture of approximately 0.8 g of paraffin and of 4 g of CO2. Modeling of the Solubility. Definition of the Mass-Based Partition Coefficient. For modeling the extraction of the paraffin waxes from molded ceramic
P (MPa)
100Wsp (kg‚kg-1)
14.1 15.9 17.8 19.8 21.8 23.8 25.8 27.9
0.41 0.89 1.71 2.72 3.84 4.91 6.05 7.40
paraffin 52 P (MPa)
100Wsp (kg‚kg-1)
13.9 16.3 18.2 20.2 22.2 24.1 26.7 28.2 30.0
0.15 0.57 0.95 1.48 2.06 2.68 3.50 3.81 4.28
paraffin 62 P (MPa)
100Wsp (kg‚kg-1)
18 20.2 22.2 24.2
0.54 0.99 1.12 1.51
samples, the knowledge of their solubility in the supercritical fluid is not enough. One must also know the evolution of the paraffin composition, both in the paraffin-rich phase and in the CO2-rich phase during the extraction. So, we will determine a partition coefficient K′n for each n-alcane between the paraffin-rich phase and the CO2-rich phase. This mass-based partition coefficient related to the alcane containing n carbon atoms is defined by
K′n ) Wsn/W′p n
(3)
where Wsn is the mass concentration of the n-alcane in the solvent-rich phase and W′p n is the mass fraction of the same n-alcane in the paraffin-rich phase on a solvent-free basis. Consequently, according to the definition of K′n, for a binary alcane-CO2 system, K′n is equal to the mass concentration Wsn of the n-alcane in the CO2-rich phase because W′p n ) 1. n-Alcane Partition Coefficient in CO2. At constant pressure, a domain can be found where ln(K′n) (equal to ln(Wsn)) varies linearly with n (Figure 3). This behavior is the same as the one observed when studying the solubility of oligomers in a supercritical solvent17,18 and is predicted by the theories of Flory19 and of Kumar et al.20 For low values of n, i.e., when the alcanes can no
Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 1907
Figure 3. ln(K′n) as a function of the number of carbon atoms n of the alcanes for three pressures (T ) 343 K). Figure 5. Comparison between experimental and calculated mass concentrations in the CO2-rich phase of the three paraffin waxes considered as n-alcanes with the same average molar mass (T ) 343 K).
Figure 4. Experimental and calculated mass concentration of n-alcanes in the CO2-rich phase as a function of pressure (T ) 343 K).
longer be considered as oligomers (n < 20), deviation from linearity is observed and complete miscibility can be reached as noted previously. At constant temperature, the partition coefficient can be expressed by
ln(K′n) ) -σn + β
(4)
where σ and β are pressure dependent. The best fit of our experimental data was found with the following expressions for σ and β:
b σ)a+ P - P0
(5)
d β)c+ P - P0
(6)
where a ) 0.178 938 1, b ) 0.664 863 MPa, c ) 3.351 614, d ) -26.969 38 MPa, and P0 ) 5.5 MPa. Using relations (4)-(6), one can calculate the mass concentrations of the pure n-alcanes in the CO2-rich phase. Calculated and experimental values are compared in Figure 4. Calculated values are in good agreement with experimental results on the whole investigated pressure range for n larger than 21. For C21H44 and C19H40, calculated values deviate from the experimental ones as the region of complete miscibility between the solute and the solvent is approached. The case of C17H36 is not represented as the monophasic region is reached under a pressure of 20 MPa.
As the polydispersities of the paraffin waxes are low (∼1.01), one can, as a first try, calculate their mass concentration in the CO2-rich phase by using eq 4 with n j corresponding to the average molar weight of each paraffin wax. In this calculation, we assume, of course, that the paraffin waxes in the paraffin-rich phase and in the solvent-rich phase have the same composition as the initial paraffin. The calculated values are systematically smaller than the experimental mass concentrations (Figure 5). It is seen that this calculation can only give a good order of magnitude of the mass concentration of solute in the supercritical carbon dioxide. Partition Coefficient of Paraffin Waxes in CO2. As paraffin waxes are composed of n-alcanes with a carbon number larger than 20, a model has been developed by analogy with the case of mixures of oligomers. Following Kumar et al.,17 we will assume the independence of K′n with W′p n , which means that the equilibrium solubility of an alcane is not affected by the presence of other alcanes in the solution. This hypothesis is based on some experimental observations.17,18 The mass concentration Wsp of the paraffin wax in the CO2-rich phase is related to the mass fractions of the n-alcanes in the paraffin-rich phase (solvent-free basis):
Wsp )
∑Wsn ) ∑n K′nW′pn
(7)
To take account of the evolution of the paraffin wax composition W′p n in the paraffin-rich phase which differs from the paraffin composition in the CO2-rich phase, an iterative computing program has been used to determine Wsp. The initial mass m of paraffin wax introduced in the cell and the volume occupied by the CO2-rich phase must be known. The mass M of CO2 in the CO2-rich phase is easily calculated because the concentration of CO2 is measured. The mass m(n) of an n-alcane with n carbon atoms in the CO2-rich phase is calculated by iterating over the following equation:
i
m (n) ) MK′n
i-1 mW′p,0 (n) n - m
m-
∑n m
i-1
(n)
(8)
1908 Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 Table 5. Calculated Mass Concentrations of the Paraffin Waxes in the CO2-Rich Phase as a Function of Pressure (T ) 343 K) paraffin 42
paraffin 52
paraffin 62
P (MPa)
100Wsp (kg‚kg-1)
∆w (%)
P (MPa)
100Wsp (kg‚kg-1)
∆w (%)
P (MPa)
100Wsp (kg‚kg-1)
∆w (%)
14.1 15.9 17.8 19.8 21.8 23.8 25.8 27.9
0.38 0.90 1.65 2.62 3.72 4.87 6.04 7.27
+7 -1 +4 +4 +3 +1 0 -2
13.9 16.3 18.2 20.2 22.2 24.1 26.7 28.2 30.0
0.16 0.51 0.92 1.46 2.06 2.68 3.53 4.03 4.61
-7 +10 +3 +1 0 0 -1 -6 -8
18.0 20.2 22.2 24.2
0.39 0.67 0.96 1.28
+28 +21 +14 +15
Figure 6. Experimental and calculated mass concentrations of paraffin waxes in the CO2-rich phase as a function of pressure (T ) 343 K).
with i ) 1, 2, ..., m0(n) ) 0 and W′p,0 the initial mass n fraction of the alcane containing n carbon atoms in the paraffin wax. MK′n represents the solvent power of CO2 related to the alcane n, and the fraction corresponds to the mass fraction of the alcane n still available in the i-1(n) is the mass of the paraffin-rich phase. mW′p,0 n -m alcane n remaining in the paraffin-rich phase before iteration i, and m - ∑nmi-1(n) is the mass of paraffin wax remaining in the paraffin-rich phase before iteration i. Calculated values of Wsp and deviation ∆w from experimental points are reported in Table 5 and compared to the experimental results in Figure 6. In the case of the paraffin waxes 42 and 52, the differences ∆w between the calculated and measured values are lower than 10%. In the case of the paraffin 62, the differences are higher. For the paraffin 62, the discrepancies can be explained by (1) the higher inaccuracy in the measurements of the low concentration of this paraffin in the solvent, (2) the less precise determination of the composition of the paraffin composed of high molar mass n-alcanes, and (3) the location of the average molar mass of the paraffin at the end of the experimental range used for the fit ln(K′) ) f(n) (eq 4). The agreement between the model and the experience can thus be considered as excellent considering the simplicity of the model. For the paraffin 42, the results of the model should strictly not be acceptable under pressures higher than 20 MPa as, in this region, one component at least is completely miscible in the supercritical carbon dioxide for a binary alcane-CO2. This is why ln(K′n) deviates from a linear behavior for n smaller than 19. We have,
Figure 7. Experimental and calculated n-alcane distribution in the CO2-rich phase for the system CO2-paraffin 42. T ) 343 K and P ) 26.1 MPa.
however, used in eq 7 the values of K′n given by eq 4 considering that the error introduced on Wsp should be negligible, according to the low mass fraction of these light components in the paraffin wax 42. Paraffin Wax Compositions in the Two Phases in Equilibrium. The model allows the determination of the evolution of the n-alcane distributions in the CO2rich phase as a function of pressure and the calculation of the remaining mass fractions of n-alcanes in the paraffin-rich phase. To control the validity of our model, samples of the CO2-rich phase obtained from a mixture of paraffin 42 and CO2 (P ) 26.1 MPa, T ) 343 K) and from a mixture of paraffin 52 and CO2 (P ) 25.2 MPa, T ) 343 K) were collected from the optical cell and analyzed by gas-phase chromatography to determine their n-alcane distributions. These distributions were compared to the distributions obtained using eqs 4-6 and 8. Taking into account the imprecision on the chromatographic analysis, experimental and calculated distributions are in good agreement as shown in Figures 7 and 8 and in Table 6. Discussion of the Validity of the Model. In the case of the calculation of the n-alcane distribution in the CO2-rich phase for the paraffin 52-CO2 equilibrium at 25.2 MPa and 343 K, none of the n-alcanes which compose the paraffin 52 is completely miscible in CO2 and a straightforward application of the model can be made. This is not the case for paraffin 42, for which the lighter components are completely miscible in CO2 at 26.1 MPa and 343 K when binary mixtures are considered. In other words, for these components at these
Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 1909
Figure 8. Experimental and calculated n-alcane distribution in the CO2-rich phase for the system CO2-paraffin 52. T ) 343 K and P ) 25.2 MPa. Table 6. Average Molar Weights of the Initial Paraffin Waxes and of the Paraffin Waxes in the CO2-Rich Phase (Experimental and Calculated) average molar mass in the CO2-rich phase (g/mol) initial experimental calculated
paraffin wax 42 52 326.2 316.3 313.8
371.1 352.5 352.2
temperature and pressure conditions, K′n is not defined. Conversely, for multicomponent mixtures such as paraffin wax-CO2 systems and as far as two phases are present, all of the n-alcanes are partitioned between the two phases and K′n exists for all n. Let us consider, for example, the case of octadecane. Octadecane and CO2 are completely miscible under 26.1 MPa at 343 K. However, for the multicomponent CO2-paraffin 42 system, we verify experimentally (Appendix A) that octadecane is partitioned between the paraffin-rich phase and the CO2-rich phase. Considering now heneicosane, one can see (Appendix B) that K′21 determined from the binary mixture equilibrium and that determined from the multicomponent mixture equilibrium have the same value within experimental error. Consequently, K′n, which must be determined for all n to model CO2-paraffin wax equilibria, can be obtained at each temperature from binaries alcane-CO2 equilibria in the pressure range where two phases are present (and not too close from the critical pressure corresponding to each temperature). Outside this pressure range, as shown by the agreement between calculated and experimental n-alcane distributions in the CO2-rich phase on the one hand and between calculated and experimental overall solubility of the paraffin waxes on the other hand, it appears that one can take partition coefficients given by eq 4. Conclusion As presented in a previous paper,21 supercritical carbon dioxide is an efficient solvent to remove organic additives, such as paraffin waxes, from ceramic green parts for pressures larger than 25 MPa. This step, known as debinding, is the most critical step of ceramic processing. Compared to classical debinding methods, supercritical CO2 allows one to remove the organic additives faster and creates less defects in the micro-
structure of the ceramic parts. The solubility of the binders in the supercritical fluid is one of the mechanisms that governs supercritical debinding. A semiempirical model was thus developed that allows the determination of the solubility of the paraffin waxes, once their n-alcane distribution has been determined and the solubility of these n-alcanes has been measured in the same temperature and pressure ranges. Calculated values are in very good agreement with experimental results according to the simplicity of the model used. Furthermore, this model allows the calculation of the evolution of the composition of the paraffin wax rich phase during the extraction with supercritical carbon dioxide. As expected, its composition is shifted toward heavier n-alcanes, which means that the solubility of a given paraffin wax will decrease with time during debinding under constant pressure and temperature. This result that will help us to optimize the supercritical debinding method. Appendix A: Calculation of the Initial and Solubilized Masses of Octadecane From the initial mass of paraffin wax 42 introduced in the high-pressure optical cell (0.8 g) and its n-alcane composition, we can calculate the initial mass of octadecane mC18 which is given by mC18 ) 0.8 × 0.0128 ) 10 mg. From the mass of carbon dioxide in the CO2-rich phase (∼3 g) and the mass concentration of the paraffin in the CO2 under 26.1 MPa (0.06 g/g), we determine the solubilized mass of paraffin wax which is equal to 180 mg. A total of 2.6% of these 180 mg corresponds to octadecane as determined by the gas-phase chromatography of the paraffin in the CO2-rich phase sample. Thus, only 4.7 mg of octadecane is solubilized in the carbon dioxide, which is roughly half the available mass of octadecane mC18. Appendix B: Calculation of the Partition Coefficient of Heneicosane The partition coefficient K′21 of heneicosane in the multicomponent mixture is deduced from eq 8 with i ) 1 as a first approximation:
K′21 ) m(C21)/(MW′p n ) ) m(C21)/(3 × 0.1217) The mass of heneicosane in the CO2-rich phase (m(C21)) is obtained as follows. From the mass of carbon dioxide in the CO2-rich phase (∼3 g) and the mass concentration of the paraffin in the CO2-rich phase under 26.1 MPa (0.06 g/g), we determine the solubilized mass of paraffin wax which is equal to ∼180 mg. A total of 16% of this 180 mg corresponds to heneicosane as determined by the gas-phase chromatography of the paraffin in the CO2-rich phase sample. Thus, m(C21) is equal to 0.029 g, and K′21 is equal to 0.08. This value is in good agreement with K′n in the case of a binary mixture, which is roughly equal to 0.09 for the heneicosane under 26 MPa, at 343 K (see Table 3). Literature Cited (1) Zangh, J. G.; Edirisinghe, M. J.; Evans, J. R. G. A catalogue of ceramic injection moulding defects and their causes. Ind. Ceram. 1989, 9, 72. (2) Lange, F. F.; Davis, B. I.; Wright, E. J. Processing related fracture origins: IV, elimination of voids produced by organic inclusions. J. Am. Ceram. Soc. 1989, 69, 66.
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Received for review August 21, 1998 Revised manuscript received December 15, 1998 Accepted January 23, 1999 IE980552E
