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Ind. Eng. Chem. Res. 2003, 42, 5924-5930
Thermodynamic Analysis of Micronization Processes from Gas-Saturated Solution Nicola Elvassore,* Marina Flaibani, and Alberto Bertucco Department of Chemical Engineering, University of Padova, via F. Marzolo, 9, I-35131 Padova PD, Italy
Paolo Caliceti Department of Pharmaceutical Sciences, University of Padova, via F. Marzolo, 5, I-35131 Padova PD, Italy
A thermodynamic analysis is developed to interpret the influence of temperature and pressure in the production of solid lipid nano- and microparticles by a high-pressure technique named particle from gas-saturated solution (PGSS). The pressure-temperature charts show three regions above the P-T solid-liquid-fluid coexistence curve, from which sub-cooled solid, solidliquid, or liquid products can be obtained. The relation between the initial and final thermodynamic properties of the PGSS process were calculated by solving simultaneously the energy balance and a proper equation of state. The expansion of high-pressure CO2-lipid saturated solution through the micrometric nozzle was represented by a transformation at constant total enthalpy. To represent the equilibrium and thermodynamic behavior of CO2lipid systems the perturbed-hard-sphere-chain theory (PHSCT) was used. As examples, CO2 absorption isotherms in lipids and residual properties of high-pressure tristearin-CO2 and tristearin-phosphatidylcoline-CO2 systems were calculated. Enthalpy of fusion of pure substances and formation enthalpy of microparticulate PGSS products were measured by differential scanning calorimetry (DSC). Pure lipid EOS parameters were estimated by a group contribution method, whereas the equation of state (EOS) interaction parameters were adjusted on the experimental melting point data under CO2 pressure, measured in a high-pressure windowed cell. Application of operative charts provides useful information in understanding the influence of temperature and pressure on the final properties of lipid particles produced by PGSS. Introduction High-pressure techniques offer an enormous opportunity for particle design and development of highvalue products at micro- and nano-scale. Various methods for the production of micro- and nanoparticulate systems containing lipids and tryglicerides, such as high-pressure homogenization (HPH),1 gas anti-solvent precipitation,2 and DELOS process,3 have been recently proposed. However, among these possibilities, a completely solvent-free process named particle from gassaturated solution (PGSS)4-6 represents a very attractive alternative for micronizing solid lipid systems.7-9 In the PGSS process, a solid is melted in a high-pressure vessel pressurized by a compressed gas. Under these conditions, the gas dissolution into the liquid phase causes the formation of the so-called gas-saturated solution. This solution is expanded through a nozzle where, due to the Joule-Thompson effect and the gas evaporation, it is cooled remarkably, leading to the formation of solid particles or liquid droplets according to the system characteristics. Normally, CO2 is used as compressed gas because it is nontoxic, readily available, environmentally acceptable, nonflammable, and inexpensive. The PGSS process takes advantage of material property changes due to gas dissolution such as softening, swelling, plasticization, changes in surface tension * To whom correspondence should be addressed. Tel: [+39] (049) 8275469. Fax: [+39] (049) 8275461. E-mail:
[email protected].
and viscosity, and depression of the glass transition or melting temperature.10-12 For these reasons it can be used for many purposes, such as polymeric particle coating, bio-polymer processing,13 or drug micronization.7,8 In particular, PGSS shows great advantages when applied to lipid systems. Lipids can easily melt at mild temperature conditions and the rapid depressurization of gas-saturated lipid solution causes the formation of micro- and nanoparticulate products.6-9 Micro and nanoparticles of lipids are of growing importance for production of pharmaceutical and cosmetic formulations. They have many advantages: possibility of controlled drug release and drug targeting, high drug stability, high drug payload, feasibility of incorporation of lipophilic and hydrophilic drugs, no biotoxicity of the carrier, avoidance of organic solvents, no problems with respect to large-scale production, and sterilization.1 At present, solid lipid particles are produced by a high-pressure homogenization technique, at high or low temperature, which subjects both lipid and drug to very high stresses that can deteriorate the bioactive principles.14 Moreover, this technique produces a dispersion of solid lipid nanoparticles (SLN) in water that needs to be lyophilized, with instability problems during the subsequent steps of freezing and resolubilization. On the other hand, the PGSS process has been successfully applied to obtain dry microparticulate lipid systems with suitable pharmaceutical properties.9 For a given experimental setup, lipid drops may solidify
10.1021/ie030278a CCC: $25.00 © 2003 American Chemical Society Published on Web 10/17/2003
Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003 5925
partially or totally depending on the temperature and pressure conditions of the high-pressure saturation vessel. Moreover, lipids show different polymorphism depending on the cooling and condensation rates and the thermal gradients to which they are exposed. In particular, these aspects may give rise to different morphologies of the final product and are particularly important with respect to the stability of pharmaceutical formulations. For example chemico-physical and pharmacological properties, such as the mobility of the drug inside each microparticle, can be strongly related to the operative conditions at which the formulation was prepared. In this work, the thermodynamic properties of particulate lipid products obtained by PGSS techniques will be evaluated. In particular, operating charts allow a rational understanding of the initial temperature and pressure from which solid, saturated solid, saturated liquid, or liquid lipids can be obtained. Two examples are provided for the production of pure tristearin and 50/50 w/w tristearin-phosphatidylcoline formulations. Theoretical Framework The expansion of the lipid-CO2 saturated solution in the PGSS process leads to final products that can be either liquid or solid-liquid with different fractions of solid. The Joule-Thompson effect and the evaporation of CO2 cause cooling of the lipid depending on the initial temperature and CO2 concentration. The energy balance between the conditions before and after the expansion nozzle allows prediction of the properties of the product for given initial conditions. For adiabatic expansion through the nozzle, the energy balance is
Efmix - Eimix ) 0
(1)
where Efmix and Eimix are the total energy of system at the initial and final conditions (after and before the expansion). Under the hypothesis of negligible potential and kinetics energy changes, we obtain f f + (1 - xCO2)Hlipid ] - Himix ) 0 (2) ∆Hf-i ) [xCO2HCO 2 f where ∆Hf-i is the system enthalpy variation, HCO 2 f and Hlipid are, respectively, the enthalpy of pure CO2 and lipid after the expansion, xCO2 is CO2 mole fraction in the starting mixture, and Himix is the saturated liquid enthalpy of this mixture before expansion. To solve the energy balance, expressions of the solubility of CO2 in lipid and of the residual enthalpy of CO2-lipid systems are required. These values can be calculated by a proper equation of state (EOS). A relation between the initial and the final thermodynamic states of the PGSS process can be obtained by solving the system
{
f ∆Hf-i ) [xCO2HCO + (1 - xCO2)Hflipid] - Himix(Ti,xCO2) ) 0 2
Pi ) EOS(Ti,xCO2)
Pi
Ti
(3)
and are pressure and temperature of the where saturated solution before the expansion. Solving eq 3 it is possible to trace the P-T values that satisfy a given final state condition. For example, to know the operative conditions leading to saturated solid products it is
necessary to use in eq 3 the proper values of final enthalpy and, for a given initial pressure Pi, to solve the system 3 with respect to the two unknowns Ti and xCO2. Because in the PGSS process it is important to obtain solid material, we have calculated the initial P-T conditions that lead to a saturated solid product at the final process condition of 0.1 MPa and lipid melting temperature. Same calculations of initial P-T conditions can be repeated for saturated liquid product. The solution of eq 3 requires knowledge of the initial and final enthalpy of the system: the initial enthalpy of the mixture was calculated from
Hmix )
∑ixiHIGi + HRmix
(4)
where HIG i is the ideal-gas enthalpy of component i and Hmix, HRmix are the enthalpy and residual enthalpy of the CO2-lipid mixture, respectively. Liquid tristearin melting point of 329 K at 0.1 MPa was used as reference for zero enthalpy. Ideal-gas enthalpy of component i was calculated from
HIG i )
T CpIG ∫329 i (T) dT
(5)
where CpIG i is the ideal-gas heat capacity of component i. The residual function was calculated with the following equation:
( )
HRmix ) PVRmix + ARmix - T
∂ARmix ∂T
V,xi
(6)
where VRmix is the mixture residual volume obtained from an EOS and ARmix is the mixture residual Helmholtz free-energy calculated as:
∑ixi lnφj i - PVRmix
ARmix ) RT
(7)
where φ j i is the partial molar fugacity coefficient obtained from an EOS. Enthalpy of the final state is calculated assuming that after the expansion of saturated solution to 0.1 MPa, lipid and CO2 are completely separated. At final conditions, CO2 enthalpy was derived assuming that CO2 follows an ideal-gas behavior. On the other hand, the enthalpy of lipid at melting temperature at 0.1 MPa depends on the fraction of solid phase in the final product, ΦS f L,sat ) ΦS∆Hformation + Hlipid Hlipid
(8)
L,sat where Hlipid is the saturated-liquid lipid enthalpy at lipid melting temperature at 0.1 MPa and ∆Hformation is the lipid product formation enthalpy. The enthalpy of the saturated-liquid lipid is calculated by eq 4 at 329 K and 0.1 MPa. The enthalpy of sub-cooled solid products was evaluated by subtracting
) ∆Hsub-cooled system
T (xCO CIG ∫329 P (T)CO f
2
2
+ xlipidCSP(T)lipid) dT (9)
from the enthalpy of the final product. In eq 9 CP(T)i is the heat capacity of ideal gas CO2 and solid tristearin.
5926 Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003
Equation of State. The perturbed-hard-sphere-chain equation of state15 that represents a system of freely jointed tangent spheres consists of a reference term representing the repulsive interactions and a perturbation term for the attractive interactions. The reference term is derived from the modified Chiew equation of state for athermal hard-sphere-chain mixtures16 whereas the perturbation term is given by a simple van der Waals attractive contribution.17 The PHSC has three characteristic segment-based parameters: r is the number of hard spheres per molecule; is the depth at the minimum of the pair potential, and σ is the separation distance between segment centers at this minimum. The cross-mixture parameters are defined by conventional combining rules
σij )
σi + σj (1 - λij) ij ) xij(1 - kij) 2
(10)
where λij and kij are binary interaction parameters. It is convenient to redefine the pure parameters through a characteristic volume, V*, a characteristic surface area, A*, and a characteristic ,cohesive. energy, E*, per mole of molecules as follows:
V* ) (π/6)rσ3NA
(11)
A* ) πrσ2NA
(12)
E* ) rNA
(13)
where NA and Rg are Avogadro’s number and the universal gas constants. Equilibrium Calculations. For equilibrium calculation of a two-component system with three phases (one fluid, F; one liquid, L; and one solid, S), two iso-fugacity conditions between the fluid and liquid phases can be written as follows:
j iL‚P ) yi‚φ j iG‚P i ) 1, 2 xi‚φ
(14)
Assuming that the i components form a pure solid phase, an additional iso-fugacity condition between the fluid phase and the solid phase follows:
j iF‚P fiS ) xi‚φ
(15)
A conventional equation of state cannot be used to directly calculate the fugacity for the solid phase; however, it is possible to relate the solid state with a fictitious liquid state:18
fiS(T,P) )
[ (
fiL(T,P)‚exp
)
]
P‚(VS - VL) ∆Hfus Tfus ‚ 1 + (16) T R‚T R‚Tfus
where fiS and fiL are the fugacities of the solute in the solid and sub-cooled liquid phase, respectively, ∆Hfus is the heat of fusion, Tfus is the melting temperature of the solute, and VSand VL are the molar volumes of solid and liquid phases, respectively. The P-T trace of solid-liquid-vapor equilibrium, i.e., the melting point temperature of lipid as a function of the CO2 pressure, can be described by solving the isofugacity conditions (eqs 14 and 15) for all components
Table 1. Summary of PHSC EOS Characteristic Parameters substance
A* (108 cm2/mol)
V* (cm3/mol)
E* (bar cm3/mol)
carbon dioxide tristearin phosphatidylcoline
41.82 983.18 892.67
16.33 655.01 573.68
42 955 608 412 605 520
and all phases. The CO2 solubility isotherm in the lipid liquid phase can be calculated by solving the iso-fugacity conditions (eq 14) for the fluid-liquid phases. Parameter Determination. The method currently developed was applied to the case of pure tristearin and to a 50/50 w/w tristearin-phosphatidylcoline mixture. Melting point depression was determined experimentally. Tristearin and phosphatidylcoline were obtained from Sigma (St Louis, MO). 99.95% CO2 was purchased from Air Liquide (Padova, Italy). These chemicals were used without further purification. Melting points of tristearin and 50/50 w/w tristearinphosphatidylcoline were measured by visual observation in a 70-mL high-pressure windowed cell (Klinger model 100). The cell, initially loaded with a given amount of lipid or lipid mixture, was pressurized at constant temperature with compressed CO2 by a HPLC pump (Dosapro Milton Roy, model 169-33). After the solid was melted, the system pressure was reduced at a constant rate of 0.1 MPa/min by venting out the CO2 through a fine metering valve (Hoke, model 1316G4y). When solid phase started to nucleate in the liquid phase, the melting point was recorded. The temperature of the cell was controlled by electric resistance. Temperature was measured by Pt 100Ω resistances, and the pressure was measured by a manometer with digital readout. Further details of experimental apparatus and procedure are reported elsewhere.9 EOS parameters used in this work are summarized in Table 1. Parameters for CO2 were obtained by fitting both equilibrium and volumetric properties, whereas parameters for lipids were estimated by a group contribution method recently proposed.19 For the calculation of the tristearin solid fugacity the heat of fusion was estimated by a group contribution method of Dannenfelser and Yalkoesky.20 The melting temperature was taken from the literature.21 For pure tristearin a 184 000 J/mol heat of fusion and a 329 K temperature of fusion were estimated. Pure phosphatidylcoline does not show second-order solid-liquid phase transition in the range of 273-373 K. The difference between the solid and liquid molar volume was estimated using packing fractions (η ) rbF/4) of 0.45 and 0.5 for the solid and the liquid, respectively. The fugacity of the pure solute in the subcooled liquid phase was calculated by the PHSC EOS. For the system CO2-tristearin both interaction parameters λij and kij were fitted on experimental solidliquid-vapor equilibrium data measured in this work. The enthalpy of formation values, ∆Hformation, of pure tristearin and 50/50 w/w tristearin-phosphatidylcoline microparticulate PGSS products were evaluated by DSC analysis (TA Instruments, Milano, Italy). The lipid microparticles used for this analysis were obtained by expanding a CO2-lipid saturated solution through a 180-µm convergent sapphire nozzle starting from different temperatures and pressures to atmospheric conditions. Further details about the equipment and the production procedure are reported elsewhere.9 The values of formation enthalpy obtained by averaging a
Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003 5927
Figure 1. Melting point temperature of pure tristearin under CO2 pressure. The squares (9) are experimental data, and the line is obtained by the model indicated in this work.
number of samples were found to be similar for all PGSS products obtained from experiments in the ranges of 13-15 MPa and 313-333 K. Values of 113 000 and 62 300 J/mol, respectively were evaluated for pure tristearin and 50/50 w/w tristearin-phosphatidylcoline formulations. Interestingly, for the same substance, the formation enthalpy was found to be lower than the enthalpy of fusion. This result could be explained by supposing that the high supersaturation conditions of the PGSS process affect the solid lipid structure. The ideal-gas Cp for CO2 was calculated by interpolating experimental data from Encyclopedie Des Gaz.22 Tristearin and phosphatidylcoline ideal-gas Cp values were estimated using the group contribution method of Joback.23 Cp values of solid phase were estimated by the method of Ru`zicka e Domalski.23 Results and Discussion Thermodynamic. First we checked that the proposed model is able to describe both enthalpy and solubility of CO2-lipid systems. Among different data that can be used for adjusting the equation of state binary interaction parameters, we used a P-T trace of solid-liquid-vapor curve because this measurement can be easily performed by visual observation in highpressure optical cells. Figure 1 shows experimental points for the system CO2-tristearin of the solid-liquid-fluid coexistence curve measured in this work where the melting point depression is visible. The line, which represents the PHSC correlation of the three-phase system, was obtained using the values of the interaction parameters λij ) 0.16 and kij ) -0.06. Figure 1 shows that by using two PHSC interaction parameters a fair phenomenological representation of the P-T trace can be given. It is worth noting that a maximum temperature depression of 17 K at about 9 MPa was observed. This result is very interesting for processing pharmaceutical or thermally instable materials by PGSS techniques at mild temperatures. The equation of state allows evaluation of the composition of both solid-liquid-vapor and liquid-vapor equilibrium at different pressure and temperature conditions. Figure 2 shows a P-x diagram for the system CO2-tristearin, where x is the CO2 mole fraction in the liquid phase. The CO2 mole fraction in the vapor phase, y, is always close to unity and is not graphically
Figure 2. Mole fraction of CO2 in the liquid and vapor phases for the system CO2-tristearin. Triangles (2) are experimental data, and lines are obtained by the model developed in this work. Continuous line indicates CO2 concentration in case of three phase (S-L-F) coexistence. Broken lines are CO2 absorption isotherms at 315, 325, 335, 345, and 355 K.
Figure 3. Pressure vs residual enthalpy for CO2-tristearin liquid phase. Reference temperature (Tref) was 329 K. Continuous line indicates residual enthalpy in case of three phase (S-L-F) coexistence. Broken lines are enthalpy isotherms at 315, 325, 335, 345, and 355 K.
evidenced. Continuous lines are the three-phase coexistence curve, whereas the broken curves are the CO2 absorption isotherms. Using the intersection between the absorption isotherm and P-x solid-liquid-vapor equilibrium curve, experimental points can be evidenced in Figure 2. Calculations were performed up to the pressure of 20 MPa at which y ) 0.9998 and x ) 0.91. Further increase in the pressure does not change significantly the composition of either the liquid or vapor phase. The isotherms exist only above the solid-liquid-fluid coexistence curve, where the liquid phase is stable. All isotherms end on the three-phase curve, and, for example, Figure 2 shows that the isotherm at lowest temperature 315 K exists only between 7.34 MPa and 13.6 MPa. As described above, the residual enthalpy is needed to calculate the mixing enthalpy change. Figure 3 shows an example of residual enthalpy of the saturated liquid phase for the system CO2-tristearin as a function of the CO2 molar fraction. The continuous line indicates the residual enthalpies of the solid-liquid-vapor system, whereas the broken curves are the residual enthalpy of the saturated liquid phase at constant temperature. It is worth noting that the residual enthalpy increases when the pressure is raised at constant
5928 Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003
Figure 4. Operating chart for pure tristearin. Continuous line is the solid-liquid-fluid coexistence curve, the dashed line between region I and II is the saturated solid product curve, and the dot-dash line between region II and III is the saturated liquid product curve. The thin dotted curves in region II represent the condition from which partially melted product with 70, 45, and 15% fraction of solid phase is obtained. The four symbols ([, 2, 9, and b) represent the start and end points of the “operative line” (broken line).
Figure 5. Operating chart for 50/50 w/w tristearin-phosphatidylcoline mixture. Continuous line is the solid-liquid-fluid coexistence curve, the dashed line between region I and II is the saturated solid product curve, and the dot-dash line between region II and III is the saturated liquid product curve. The triangles (2) represent the start and end points of the “operative line” (broken line) for three different initial pressures, 7.34, 8.12, and 9.98 MPa, at initial temperature of 315 K. The squares (9) represent the start and end points of the “operative line” (broken line) for three different initial pressures (6.37, 7.66, and 9.03 MPa) at initial temperature of 320 K.
temperature, whereas it decreases by increasing the temperature at constant pressure. The results obtained in Figures 2 and 3 were used to solve the energy balance. Operating Charts. Figures 4 and 5 show two examples of P-T operating charts for PGSS process. They refer to a CO2-tristearin mixture and to a CO2-tristearinphosphatidylcoline (50/50 w/w tristearin-phosphatidylcoline) system, respectively. The solid-liquid-vapor coexistence curve separates the solid-vapor equilibrium zone from the liquid-vapor equilibrium one. The starting condition for the PGSS process is of course a melted saturated lipid solution. The P-T chart above the solidliquid-fluid coexistence curve can be divided into three regions according to the characteristic of the final products. In fact, depending on the initial pressure and temperature, cooling of the system can lead to either solid or liquid lipid particles. Region I includes the initial operative conditions from which a complete solid lipid product can be obtained. On the other hand,
starting from regions II and III, partially solid or totally liquid products are obtained. The two lines separating region I from II and region II from III represent the condition at which saturated-solid and saturated-liquid lipid products are obtained. In region II the dotted lines indicate the initial P-T conditions from which a product with a given fraction of solid phase can be produced. Figures 4 and 5 give details. For pure tristearin (Figure 4) region I is quite narrow, and only 10 K above the melting temperature at 20 MPa allows obtention of complete solid products. However, it is interesting to note that region I disappears completely in the range 0-20 MPa if the enthalpy of formation of the solid lipid products equals the heat of fusion of pure tristearin. The DSC measurement highlights that the enthalpy of fusion of unprocessed product is about 1.5 times greater than the heat of formation of processed lipid. This difference may be related to the high supersaturation conditions of the PGSS process that affect the solid structure of lipid products and consequently their enthalpy value. “Operative lines” reported in Figures 4 and 5 are hypothetical connections between the initial and final state properties. The influence of the different operative conditions on the characteristic of the final product can be easily highlighted by proper operative lines. It is important to underline that they do not represent a real thermodynamic pathway between the initial and the final state. In particular, looking at Figure 4, it is possible to see the effect of temperature changes at constant pressure. For example, starting from region I at 13.6 MPa and 315 K, the final temperature of the solid product is 5 K higher than the initial temperature. When the initial point is in region II the product is always at 329 K, independently from Ti and Pi values. However, initial conditions influence the fraction of solid phase present in the product, which can be predicted using the dotted lines indicate in Figure 4. Increasing Ti from 327 to 334 K at 13.6 MPa, the solid-phase percentage decreases from 80 to 50%. Figure 5 is related to the case of CO2-tristearinphosphatidylcoline. For thermodynamic of solid-liquidfluid and liquid-fluid equilibrium calculations, lipids in the liquid and fluid phases were treated as a single pseudo-component with 50/50 w/w tristearin-phosphatidylcoline averaged EOS pure parameters. Parameters for both components are reported in Table 1. The solid phase is constituted by pure tristearin, because pure phosphatidylcoline does not show second-order solid-liquid phase transition in the range of 273-373 K as observed by DSC analysis. The melting point depression of 50/50 w/w tristearin-phosphatidylcoline mixtures measured in this work is similar to that presented in Figure 1. A fair reproduction of the experimental behavior is obtained using the same interaction parameters as used for the system CO2tristearin. We note that the main difference between the two cases is the value of product formation enthalpy, which is lower for the lipid mixture with respect to pure tristearin. Figure 5 shows a wider region I, and therefore, it is easier to obtain solid product when a lipid mixture is processed. In fact, the saturated solid product curve is shifted to the right allowing operation at lower pressure in order to obtain solid products. On the other hand, the saturated liquid product curves reported in Figures 4 and 5 display similar behavior.
Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003 5929
Finally, in Figure 5 some examples of “operative lines” are showed. This highlights the effect of a pressure change at constant temperature on the final product properties. By increasing the initial pressure, the CO2 concentration in the molten lipid increases and a consequently its cooling effect is stronger, so that solid product can be obtained. It is interesting to note that solid particles can be produced from operating conditions as low as 6 MPa and 318 K. Conclusions A thermodynamic analysis of the micronization process from gas-saturated solutions, applied to CO2-lipid systems, was carried out from both an experimental and a theoretical point of view. A thermodynamic model was developed to calculate the enthalpy variation upon the expansion of saturated-liquid solution. P-T operative charts were proposed. These diagrams allow us to understand if solid particles or lipid droplets are formed starting from given P and T conditions. Starting from experimental data of melting temperature depression obtained with a high-pressure windowed cell and from DSC measurement of microparticles enthalpy of formation, an operative chart could be easily drawn. The effects of nonequilibrium phenomena of the given experimental setup are taken into account by microparticles enthalpy of formation. Two examples were discussed referring to the micronization of tristearin and 50/50 w/w tristearin-phosphatidylcoline. Optimization of process conditions can be simply performed on the basis of these operative charts. Acknowledgment Partial support granted to this work by the University of Padova is gratefully acknowledged. We thank Dr. M. Modesti and Dr. A. Lorenzetti for DSC measurements. Nomenclature A ) Helmholtz energy [J/mol] Cp ) heat capacity [J/mol K] E ) total energy [J/mol] f ) fugacity [MPa] H ) enthalpy [J/mol] kij ) EOS binary interaction parameter NA ) Avogadro’s number [1/mol] P ) pressure [MPa] r ) number of segments per molecule R ) universal gas constant [J/mol K] T ) absolute temperature [K] V* ) characteristic volume [cm3/mol] A* ) characteristic surface [108 cm2/mol] E* ) characteristic cohesive energy [10-1 MPa cm3/mol] V ) molar volume [cm3/mol] x ) mole fraction Greek Symbols φ j ) fugacity coefficient ) depth at the minimum of the pair potential [J] λij ) EOS binary interaction parameter σ ) separation distance between segment centers at this minimum [cm] ∆H ) enthalpy variation [J/mol] ∆Hfus and ∆Hformation ) enthalpy of fusion and enthalpy of particle formation [J/mol]
Superscripts f ) final F ) fluid fus ) fusion i ) initial IG ) ideal gas L ) liquid R ) residual property S ) solid sat ) saturated Subscripts i and j ) component property m ) melting property mix ) mixture property
Literature Cited (1) Mehnert, W.; Ma¨der, K. Solid lipid nanoparticles production, characterization and applications. Adv. Drug Delivery Rev. 2001, 47, 165. (2) Cocero, M. J.; Ferrero, S.; Miguel, F. Phospholipid precipitation from soybean lecithin by continuous gas process. Presented at 8th Meeting on Supercritical Fluids, Bordeaux, France, April 14-17, 2002. (3) Ventosa, N.; Sala, S.; Veciana, J. The DELOS process: a new ecoefficient tool for particle engineering. Presented at 8th Meeting on Supercritical Fluids, Bordeaux, France, April 14-17, 2002. (4) Weidner, E.; Knez, Zˇ ;; Novak, Z. Process for preparing particles of powders. European Patent 7,449,22, 1995. (5) Weidner, E.; Knez, Zˇ ;; Novak, Z. Process for the production of particles or powders. U.S. Patent 6,056,791, 2000. (6) Weidner, E.; Knez, Zˇ ;; Novak, Z. PGSS (Particles from Gas Saturated Solutions)-A new process for powder generation. Presented at the 3rd International Symposium on Supercritical Fluids; ISASF: Strasbourg, France, 1994. (7) Knez, Zˇ ; Novak, Z. Material processing with dense gases. Presented at the 5th Meeting on Supercritical Fluids; Nice, France, March 23-25, 1998. (8) Knez, Zˇ ; Weidner, E. Precipitation of solids with dense gases. In Supercritical-Fluids Technology: Foundamentals and Applications; Bertucco, A., Vetter, G., Eds.; Elsevier: Amsterdam, 2001. (9) Elvassore, N.; Flaibani, M.; Vezzu`, K.; Bertucco, A.; Caliceti, P. Lipid system micronization for pharmaceutical applications by PGSS techniques. Presented at the 6th International Symposium on Supercritical Fluids; Versailles, France, April 28-30, 2003. (10) Weidner, E.; Wiesmet, V.; Knez, Zˇ ;; Sˇ kerget, M. Phase equilibrium (solid-liquid-gas) in poly(ethylene glycol)-carbon dioxide systems. J. Supercrit. Fluids 1997, 10, 139. (11) Fukne´-Kokot, K.; Ko¨nig, A.; Knez, Zˇ .; Sˇ kerget, M. Comparison of different methods for determination of the S-L-G equilibrium curve of a solid component in the presence of a compressed gas. Fluid Phase Equilib. 2000, 173, 297. (12) Fukne´-Kokot, K.; Sˇ kerget, M.; Ko¨nig, A.; Knez, Zˇ ; Modified freezing method for measuring the gas solubility along the solidliquid-gas equilibrium line. Fluid Phase Equilib. 2003, 205, 233. (13) Mandel, F. S.; Don Wang, J. Manufacture of specialty meterials in supercritical fluid carbon dioxide. Inorg. Chim. Acta 1999, 294, 214. (14) Mu¨ller, R. H.; Ma¨der, K.; Gohla, S. Solid lipid nanoparticles (SLN) for controlled drug deliverysa review of the state of the art. E. J. Pharm. Biopharm. 2000, 50, 161. (15) Song, Y.; Lambert, S. M.; Prausnitz, J. M. A PerturbedHard-Sphere-Chain Equation of State for Normal Fluids and Polymers. Ind. Eng. Chem. Res. 1994, 33, 1047. (16) Chiew, Y. C. Percus-Yevick Integral Equation Theory for Athermal Hard-Sphere Chains. Mol. Phys. 1990, 70, 129. (17) Song, Y.; Hino, T.; Lambert, S. M.; Prausnitz, J. M. Liquid-Liquid Equilibria for Polymer Solutions and Blends, Including Copolymers. Fluid Phase Equil. 1996, 117, 69.
5930 Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003 (18) Prausnitz, J. M.; Lichtenthaler, R. N.; Gomes de Azevedo, E. Molecular Thermodynamics of Fluid-phase Equilibria; Prentice Hall: Upper Saddle River, NJ, 1999. (19) Elvassore, N.; Bertucco, A.; Fermeglia, M. Group Contribution Perturbed-Hard-Sphere-Chain Equation of State for Phase Equilibria Calculation of Normal Fluids and High Molecular Weight Compound. AIChE J. 2002, 48 (2), 359. (20) Dannenfelser, R. M.; Yalkowsky, S. H. Estimation of Entropy of Melting from Molecular Structure: A Non-Group Contribution Methodology Ind. Eng. Chem. Res. 1996, 35, 1483. (21) Lide, D. R., Ed. Handbook of Chemistry and Physics, 81st ed.; CRC Press LLC: Boca Raton, FL, 2000.
(22) Encyclopedie Des Gaz (Gas Encyclopaedia); Elsevier: Amsterdam, 1976. (23) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 2001.
Received for review April 1, 2003 Revised manuscript received August 20, 2003 Accepted August 22, 2003 IE030278A
