Am

Ma

b

a

ARRA

1

StttsARtppbs

0d

J. of Supercritical Fluids 55 (2010) 462–471

Contents lists available at ScienceDirect

The Journal of Supercritical Fluids

journa l homepage: www.e lsev ier .com/ locate /supf lu

comparison between models based on equations of state and density-basedodels for describing the solubility of solutes in CO2

ichael Türka,∗, Marlene Cronea, Thomas Kraskab

Karlsruhe Institute of Technology (KIT), Institut für Technische Thermodynamik und Kältetechnik, GermanyInstitut für Physikalische Chemie, Department für Chemie, Universität zu Köln, Germany

r t i c l e i n f o

rticle history:eceived 7 June 2010eceived in revised form 12 August 2010ccepted 24 August 2010

a b s t r a c t

The poor dissolution behaviour of solid drugs in biological environment leads to a low bioavailability.However, the dissolution rate of such drugs can be enhanced dramatically by reduction of the parti-cle size. At present, supercritical fluid based particle size reduction processes are gaining in importancein pharmaceutical technology. For the design of such particle formation processes and the determina-tion of their best operating conditions the knowledge of phase equilibrium and solute solubility in asupercritical fluid is essential. Today, models based on equations of state, together with different mixingrules, are most widely used to correlate and predict the solubility in supercritical fluids. Therefore theaccurate knowledge of the required solute data, such as critical parameters, acentric factor, solid molarvolume, and sublimation pressure of the solutes is essential. However, the common, non-equation ofstate based group-contribution methods are mostly empirical and often lead to inconsistent and unre-liable results. Thus, due to the lack of information on these data, density-based models are often usedfor the correlation of experimental solubility data. In this investigation, the solubility of Salicylic acid, of

S-Naproxen, of RS-Ibuprofen and of Phytosterol in CO2 is correlated by different methods: two methodsfor the pressure–solubility correlation and two methods for the density–solubility correlation. In addi-tion, the influence of solute data predicted by different group-contribution methods is investigated. Withthe exception of S-Naproxen all systems investigated can be modelled sufficient well with a non-cubicequation of state while a cubic equation of state gives less accurate results. In addition, it is shown thatfor the solutes investigated, the equation of state based method is very sensitive to the values of thesublimation pressure.

. Introduction

The knowledge of phase equilibrium and solute solubility in aCF is essential for the design of particle formation processes andhe determination of their best operating conditions. With regard tohe PGSS process (Particle Generation from Gas Saturated Solution),he ability of the supercritical solvent to melt the solid and to formaturated liquid phase is of major interest. In the GAS process (Gasnti-Solvent) the SCF acts as an anti-solvent while in case of theESS process (Rapid Expansion of Supercritical Solutions) enableshe solvent free formation of submicron particles. In addition, the

roperties of the produced powders such as particle size and mor-hology are often strongly influenced by the underlying phaseehaviour. Until today, much work has been done on producingubmicron poor water soluble substances by RESS and dissolu-

∗ Corresponding author. Tel.: +49 721 608 2330.E-mail address: tuerk@kit.edu (M. Türk).

896-8446/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.supflu.2010.08.011

© 2010 Elsevier B.V. All rights reserved.

tion studies demonstrate that pharmaceuticals show a significantlyimproved dissolution rate [1].

Usually, in the processes named above, mixtures composed ofa supercritical solvent (1) and a solid (2) of low volatility differappreciably in mass, size, interaction strength, polarity, and shape.The phase behaviour of such “asymmetric” mixtures shows someinteresting particularities, which are depicted in Fig. 1. Usually, thetriple point temperature of the solid (TTP,2) is markedly higher thanthe critical temperature of the pure solvent (Tc,1). Beyond this, thesolubility of the supercritical solvent in the liquid phase of thesecond component is limited. These facts lead to a melting pointdepression of the second component and in addition, the criticalmixture curve is interrupted at two distinguished points. Close toTc,1, the lower branch of the critical locus ends at the lower criti-

cal endpoint (LCEP). At higher temperatures, the solid–liquid–gasthree-phase-line (S2LG line) interrupts the critical mixture curveat the upper critical endpoint (UCEP). In the temperature rangebetween the TLCEP and TUCEP only a solid–fluid two-phase equilib-rium (s2 = scf) exists for each pressure. In the region close to the

M. Türk et al. / J. of Supercritical Fluids 55 (2010) 462–471 463

Nomenclature

a attraction parameter of the Peng–Robinson EoS; fitparameter of Eq. (6)

A fit parameter of the sublimation pressure curve ofEq. (5) and Eq. (9)

˛ temperature of the attraction term of thePeng–Robinson EoS

b co-volume parameter of the Peng–Robinson EoS; fitparameter of Eq. (6)

B fit parameter of the sublimation pressure curve ofEq. (5) and Eq. (9)

c fit parameter of Eq. (7)C fit parameter of the sublimation pressure curve of

Eq. (9)d fit parameter of Eq. (7)D fit parameter of the sublimation pressure curve of

Eq. (9)E fit parameter of the sublimation pressure curve of

Eq. (9); enhancement factorkij fit parameter for the binary attractionlij fit parameter for the binary co-volumeω acentric factorp pressurepc critical pressureR gas constant� fluctuation parameter of the LK-EoS�S entropy of fusionT temperatureTm melting temperatureTTP,2 triple temperature of the soluteTc,1 critical temperature of the solventvi molar volume of component ix mole fraction of component i

trsaopia

Ffl

Table 1Physical properties of the substances investigated.

Solid CAS number M (g/mol) Tm (K)a �hfusi

(kJ/mol)a

Salicylic acid 69-72-7 138.12 431.5 27.8RS-Ibuprofen 15687-27-1 206.28 348.6 25.5

iy2 mole fraction of the solute in the supercritical sol-

vent

wo critical endpoints, small changes in pressure and temperatureesult in a considerable increase of the solubility of the solid in theupercritical solvent. Due to the higher solid solubility in the region

round the UCEP in comparison to the LCEP, the former region isf major economic interest. For many processes, such as the RESSrocess, it is desired to take advantage of the increased sensitiv-

ty of the solubility with respect to pressure near the UCEP, but tovoid the formation of a liquid phase.

ig. 1. Typical p–T projection for an asymmetric mixture consisting of a supercriticaluid (1) and a low volatile solid (2).

S-Naproxen 22204-53-1 230.26 427.7 31.4Phytosterol 83-46-5 414.72 411.5 18.9

a Measured with DSC.

Therefore reliable solubility data are essential for an accurateexperimental design and for calculation of the concentration ofsupercritical solutions at different operating conditions. Today,models based on equations of state, together with different mixingrules, are most widely used to correlate and predict the solubility inSCFs. Therefore the accurate knowledge of the required solute data,such as critical parameters, acentric factor, solid molar volume, andsublimation pressure of the solutes is essential. However, the com-mon estimation methods are mostly empirical and often lead toinconsistent and unreliable results. Thus, due to the lack of infor-mation on these data, density-based models are often used for thecorrelation of experimental solubility data.

The four substances, Salicylic acid, RS-Ibuprofen, S-Naproxenand Phytosterol, studied in this work were selected due to theirimportance and as examples for poor water soluble pharmaceuticalsubstances. In Table 1 some important physical properties of theorganic solids investigated here are summarized.

In this paper, solubility data of the above mentioned solidsin CO2 are correlated by four different methods: two methodsfor the pressure–solubility correlation and two methods for thedensity–solubility correlation. In addition, the influence of solutedata predicted by different estimation methods is investigated.Thereby, it turned out that for the solutes investigated, the equa-tion of state based method is very sensitive to the values of thesublimation pressure.

2. Model description

2.1. Equations of state

Cubic equations of state are often used to describe the exper-imental results of the solubility y2 of an organic solid in asupercritical fluid. These equations of state are empirical furtherdevelopments of the van der Waals equation of state [2]. In thepresent investigation we used the original Peng–Robinson Equationof State (PR-EoS) [3] to describe the solubility y2.

p = R · T

(v − b)− a(T)

v2 + 2bv − b2(1)

In Eq. (1) p is the pressure, T the temperature, v the molar vol-ume, and R the gas constant. The PR-EoS was applied to binarysystems using the van der Waals 1-fluid mixing rules:

a =k∑

i=1

k∑j=1

xixjaij aij =√

ai · aj · (1 − kij) (2a)

b =k∑

i=1

k∑j=1

xixjbij bij = bii + bjj

2· (1 − lij) (2b)

The parameters a and b can be calculated from the critical prop-erties of the pure components. The binary interaction parameters

can be obtained by regression of the experimental data with theEoS and the mixing rules (see Eqs. (2a), (2b)):

a = 0.45724R2T2

cpc

˛(T, ω) (2c)

4 ritical

w

˛

a

b

ivsTsifli

y

tfcotmekv

Lu

p

oarhddifldnttdttinfitafi

TV

64 M. Türk et al. / J. of Superc

ith

(T, ω)=(1+0.37464+1.54226ω−0.26992ω2(1−√

T/Tc))2

(2d)

nd

= 0.0778RTc

pc. (2e)

In Eqs. (2c)–(2e) ω is the acentric factor, and Tc and pc the crit-cal data. This procedure requires the accurate knowledge of thearious thermophysical data, such as critical data, acentric factor,olid molar volume, and sublimation pressure of the solutes [4–6].he correlation which was used to calculate the solubility of theolute in the supercritical solvent is shown in Eq. (3). This equations a result of the equifugacity condition between the solid and theuid phase, under the assumption that the solubility of the solvent

s negligible in the solid phase.

2(p, T) = p2,sub(T) · ϕ2,sub(p2,sub, T)p · ϕ2(p, T, y2)

exp

(v2(p − p2,sub)

RT

)(3)

Subscript 2 in Eq. (3) refers to the solid and therefore p2,sub ishe sublimation pressure of the solid at temperature T, ϕ2,sub is theugacity coefficient at the sublimation pressure, ϕ2 is the fugacityoefficient for the solid in the SCF phase, and v2 is the molar volumef the pure solid. Thereby, it is assumed that v2 is independent onhe pressure p. In this work ϕ2 is calculated with the PR-EoS using

ixing rules given in Eqs. (2a) and (2b), while ϕ2,sub can be consid-red as unit. Thus, the calculation of the solubility y2 requires thenowledge of the solid sublimation pressure (p2,sub), solid molarolume (v2) and a reliable equation of state.

Besides the PR-EoS we also applied the accurate non-cubiceonhard–Kraska Equation of State (LK-EoS) to describe the sol-bility of a solid y2:

= pref(a, b) + ppert(a, b, �) with � = �(�, T) (4)

The reference part of this EoS is based on the fundamental resultf van der Waals to describe the different contributions of the inter-ction (repulsion and attraction) by two additive terms. For theepulsion the much later developed hard-sphere term of Carna-an and Starling is used while for the attraction the original vaner Waals term is used. A van der Waals type EoS is not able toescribe the near-critical region properly because they are analyt-

cal equations of state. At the critical point, due to infinite densityuctuations, the fluid exhibits non-analytical behaviour such asivergences expressed, for example, by non-integer critical expo-ents. In order to correct the deviations in the near-critical regionhe LK-EoS contains a perturbation term derived on the basis ofhe reference EoS by introducing fluctuations. These fluctuationso not diverge at the critical point but their contribution improveshe EoS in the near-critical region substantially. More details onhe LK-EoS and the application of the fugacity approach are givenn literature [7]. The critical parameters of the pure solute do not

eed to be estimated by a group-contribution method because wet the attraction and co-volume equation of state parameter forhe solute during the solubility correlation. For the same reasonlso no kij parameter is required. The total number of parameters,tted in this work by a Marquardt–Levenberg algorithm, are four

able 2alues of the pure component parameters for the solids investigated using different grou

Tb (K) Tc (K)

Salicylic acid (14) 571–646 738–913RS-Ibuprofen (13) 542–673 717–891S-Naproxen (14) 584–743 768–990Phytosterol (12) 584–993 707–1219

a Estimated value [16].

Fluids 55 (2010) 462–471

namely two equation of state parameters of the pure solute andtwo parameters for the solid saturation pressure. The experimen-tal determination of the saturation pressure of low volatile organicsubstances is difficult [5,6]. Often the solid saturation pressure isunknown and has to be estimated by empirical methods as shownin Section 3.1. Since the solid saturation pressure is required inthe correlation of the solubility, one can treat it as an adjustableparameter during the fit of the model parameters to solubility data.If solubility data are available for different temperatures one canbuild in a Clausius–Clapeyron-like temperature dependence of thesolid saturation pressure:

ln(p2,sub

p0

)= A −

(B

T

)(5)

In Eq. (5) A and B are adjustable parameters and p0 = 1 MPais the unit pressure. In several investigations it has been shown,that this approach using the LK-EoS gives good correlation forvarious solutes in CO2 and N2O [8–10]. The sublimation pressureobtained from the solubility correlation agrees well with availableexperimental data and behaves systematically as function of themolecular structure [8]. S-Naproxen turns out to be very difficult tomodel with all approaches. Therefore we here compare three differ-ent correlation procedures: 1) the correlation Eq. (5) to the availableexperimental data of the sublimation pressure [11], 2) fitting Eq. (5)to the literature data which are estimated with a group contribu-tion of Coutsikos [12] and 3) treating the sublimation pressure asadjustable property fitting the parameters of Eq. (5) during the sol-ubility correlation. Phytosterol, RS-Ibuprofen and Salicylic acid arecorrelated by implementing Eq. (5) and fitting its parameters tothe solubility isotherms. The value of the molar volume solute isfixed in all correlations to the value given in Table 2 and the com-pressibility of the solute is set to zero. The remaining parameters,which are fitted to the data, are the attraction parameter a and theco-volume parameter b of the solute.

2.2. Density-based models

One of the most commonly used model, which correlates the sol-ubility y2 of a solute in a SCF to the fluids density has been proposedby Stahl et al. [13] and by Kumar and Johnston [14]:

ln(y2) = a + b · ln(�Red) with �Red = �1

�1,c(6)

In Eq. (6) �1 is the density of CO2 at the equilibrium temperatureT and pressure p, �1,c is the critical density of CO2, and a and bare two empirical constants. Mendez-Santiago and Teja [15] haveshown that the following equation:

T · ln(E) = c + d · �1 (7)

can be used to calculate the solubility of numerous solids in CO2. InEq. (7) the enhancement factor E can be regarded as a normalizedsolubility because it removes the effect of the sublimation pressure.

E is defined as the ratio of the mole fraction of the solid over thesolubility in an ideal gas:

E = y2 · p

p2,sub(T)(8)

p-contribution methods (numerary in brackets correspond to number of GCM).

pc (MPa) ω (−) vi (m3/mol)a

4.5–5.7 0.76–0.89 9.59 × 10−5

2.1–2.5 0.74–0.87 1.88 × 10−4

1.9–2.7 0.78–0.94 1.78 × 10−4

0.96–1.2 0.79–1.2 4.11 × 10−4

ritical Fluids 55 (2010) 462–471 465

tptboctc

3

3f

atpdAa

pc Group contribution

methods

Tb / Tc

Tc Edminster-

method

ω

Forman-

Thodos

vc

Miller-

correlation Tb Coutsikos

Fig. 2. Schematic representation of the various “ways” to use different estimation

M. Türk et al. / J. of Superc

Since the constants c and d in Eq. (7) are independent ofemperature, the solubility data for binary systems at different tem-eratures should collapse to a single straight line when plotted inerms of T·ln E vs. the solvents density. The lower limit of this linearehaviour is about half while the upper limit is around the twofoldf the critical density of the solvent [15]. The fact that all isothermsollapse to a single line allows determining the self-consistency ofhe experimental data and allows identifying data sets that are notonsistent with other data.

. Results and discussion

.1. Estimation of critical constants (Tc and pc) and acentricactor (ω)

For the calculation of the solubility in a supercritical fluid usingn EoS it is necessary to have critical properties and acentric fac-

ors of all components. In addition molar volumes and sublimationressures of the solid components are required. If some of theseata are not available, estimation techniques might be employed.s shown in Fig. 2, there are a few methods, which use group ortomic contributions to estimate critical properties [16].

2,4 2,6 2,8 3,0 3,210-4

10-3

10-2

10-1

100

101

102

103

[19]

Eq. (5)

[12]

p 2,s

ub (

Pa)

1000/T (K-1)

(a) Salicylic acid

2,4 2,610-3

10-2

10-1

100

101

p 2,s

ub (

Pa

)

[11]

[12]

Eq. (5)

1000

Fig. 3. Comparison between experimental and calculated sublimation pre

techniques [16] for calculating Tc, pc and ω.

2,8 2,9 3,0 3,1 3,2 3,3 3,4

10-3

10-2

10-1

100

101p 2

,su

b (

Pa

)

[18]

[12]

1000/T (K-1)

(b) RS-Ibuprofen

2,8 3,0

/T (K-1)

(c) S-Naproxen

ssure data for a) Salicylic acid, b) RS-Ibuprofen, and c) S-Naproxen.

466 M. Türk et al. / J. of Supercritical

Table 3Constants of Eq. (5) for the sublimation pressure data (p0 = 1 Pa) and temperaturerange over which the data were determined.

Solute A B (K) T range (K)

Salicylic acid 34.6 −11484 368–408RS-Ibuprofen 42.1 −14554 296–337

btctbblfI(

data for the sublimation pressure. For Phytosterol, the sublimationpressure data obtained from Coutsikos correlation have also been

Fl

S-Naproxen 39.7 −15431 341–397Phytosterol 45.9 −18919 298–343

Several group-contribution methods (GCM) for the normaloiling temperature, which is necessary to estimate the criticalemperature by some methods, the critical temperature, and theritical pressure are used to analyze the reliability of this correla-ion method and to study the influence of each parameter. It shoulde noted that this refers to the estimation methods which are notased on equations of state. The acentric factor has been calcu-

ated by the Edminster-GCM [16]. The estimated properties of the

our solids investigated using various GCM are shown in Table 2.n the case of CO2 the physical properties are taken from NISTTc = 304.21 K, pc = 7.38 MPa and ω = 0.225) [17].

-0,8 -0,4 0,0 0,4 0,810

-6

10-5

10-4

10-3

308 K [20]

313 K [20]

318 K [20]

328 K [20]

323 K [23]

y 2 (

-)

ln(1/

1,C) (-)

(a) CO2 /Salicylic acid

-0,2 0,0 0,2 0,4 0,6 0,810

-5

10-4

313 K

323 K

333 K

343 K

353 K

y 2 (

-)

ln(1/

1,C) (-)

(c) CO2 /Naproxen [6]

ig. 4. Solubility versus reduced solvent density for a) CO2/Salicylic acid [20,23], b) CO2

ines are calculated with Eq. (6).

Fluids 55 (2010) 462–471

3.2. Sublimation pressure data

Experimental sublimation pressure data were available for RS-Ibuprofen [18], Salicylic acid [19] and S-Naproxen [11] in literature.However, since no data has been reported for Phytosterol, pi,subwas calculated for all four substances using the Coutsikos correla-tion [12] for solids. This group-contribution model is based on theconcept of the hypothetical liquid.

ln(pi,sub) = A + B/T + C · ln(T) + D · T + E · T2+(

�Si

T

)·(

1 − Tm

T

)(9)

The constants A to E can be estimated via theAbrams–Massaldi–Prausnitz equation, while for the entropy offusion (�Si) at the melting point (Tm) a simple group-contributionscheme is proposed [12].

In this study, Eq. (5) was used to correlate the experimental

successfully correlated using Eq. (5). The values for the parameterA and B are summarized in Table 3 together with the temperaturerange over which the data were determined.

-0,4 0,0 0,4 0,810

-4

10-3

10-2

308 K

313 K

323 K

y 2 (

-)

ln(1/

1,C) (-)

(b) CO2/RS-Ibuprofen [24]

0,2 0,4 0,610

-5

10-4

323 K

333 K

343 K

y 2 (

-)

ln(1/

1,C) (-)

(d) CO2/Phytosterol [28]

/RS-Ibuprofen [24], c) CO2/S-Naproxen [6], and d) CO2/Phytosterol [28]. The solid

M. Türk et al. / J. of Supercritical Fluids 55 (2010) 462–471 467

Table 4Constants of Eq. (6) for the solubility of solids in sc-CO2.

T (K) Number of datapoints

a b ARD (%)

Salicylic acid [20] 308.15313.15318.15328.15

11151211

−10.520−9.982−9.799−9.186

3.9803.4623.5533.619

5.97.08.16.0

Salicylic acid [21] 313.15333.15

1211

−10.099−8.678

3.9492.630

13.014.8

Salicylic acid [22] 308.15318.15

812

−10.351−9.491

3.9143.206

0.96.9

Salicylic acid [23] 323 7 −10.002 4.531 3.3

RS-Ibuprofen [24] 308.15313.15318.15

1568

−9.125−8.806−8.112

5.9446.3305.523

5.24.521.9

S-Naproxen [25] 313.1323.1333.1

666

−13.266−12.513−11.940

4.4313.9523.653

6.47.66.9

S-Naproxen [26] 308318328338348

88888

−13.614−12.170−11.953−11.004−10.706

4.6573.1233.4192.6343.084

6.97.214.020.831.6

S-Naproxen [27] 313.15 9 −13.979 6.018 6.5S-Naproxen [6] 313

323333343353

34556

−13.230−12.613−12.120−11.570−10.830

4.1654.0793.9423.9123.924

1.92.15.41.44.1

Phytosterol [28] 323.2333.2343.2

878

−12.437−11.632−11.185

5.7415.1435.790

9.03.73.5

A

dIeetmrActl

3

3

s[tderwpSiafdsi

solvent power. Fig. 4 also shows the pronounced temperatureeffect on the solubility in the region outside the retrograderegion. In this region, the effect of the temperature on the solutesublimation pressure overlays the effect of the solvent density,

Table 5Constants of Eq. (7) for the solubility of solids in sc-CO2.

Number ofisotherms

c (K) d (K dm3/mol) ARD (%)

Salicylic acid [20] 4 1180.3 116.9 0.9Salicylic acid [21] 2 1206.5 116.3 2.1Salicylic acid [22] 2 1457.9 102.3 0.7Salicylic acid [23] 1 792.4 138.3 0.3

RS-Ibuprofen [24] 3 1783.0 166.7 0.7

S-Naproxen [25] 3 2304.5 133.2 1.6S-Naproxen [26] 5 2126.6 143.2 2.7S-Naproxen [27] 1 1787.5 167.9 0.4S-Naproxen [6] 5 1871.4 150.4 1.9

RD = 1N

N∑1

∣y2,calc−y2,exp

∣y2,exp

× 100.

In Fig. 3 the comparison between calculated and experimentalata for RS-Ibuprofen, S-Naproxen and Salicylic acid are shown.

n case of RS-Ibuprofen, the Coutsikos correlation represents thexperimental data quite well. The relative deviation betweenxperimental and calculated values increases from 2.3% at 313 Ko 17.5% at 343 K. Larger deviations between experimental and

odelled values are found for S-Naproxen. For this substance, theelative deviation decreases from 87% at 313 K to 62% at 343 K.pplying the Coutsikos correlation for Salicylic acid leads to cal-ulated values which are up to two orders of magnitude lower thanhe experimental data. Thus, it is obviously, that the deviations arearger (≤100%) than for S-Naproxen.

.3. Correlation of experimental solubility data

.3.1. Density-based models

The influence of the system temperature and the solvents den-ity is depicted in Fig. 4 which shows the solubility of Salicylic acid20–23], RS-Ibuprofen [24], S-Naproxen [6,25–27], and of Phytos-erol [28] as a function of the reduced CO2 density. Experimentalata of the solubility of Salicylic acid in CO2 are available in lit-rature for temperatures ranging from (308–333) K and pressuresanging from (8–35) MPa, while solubility data of RS-Ibuprofenere measured at pressures in the range of (8–22) MPa, tem-eratures of (308 and 313) K, and up to 17 MPa for 318 K. For-Naproxen, experimental solubility data for temperatures rang-ng from (308–353) K within the pressure range of (12–35) MPa

re published in literature. Although each individual set of dataollows mostly a common trend, in some cases the publishedata exhibit different trends with respect to temperature or pres-ure [6]. To our knowledge, with the exception of our own datan the range from (323–343) K and pressures between (14 and

31) MPa, no other solubility data has been reported for Phytosterol[28].

For all investigated substances, the experimental results showtrends which are similar to those observed for other solids in thesupercritical region. In agreement with Eq. (6) and as it is illus-trated in Fig. 4, relationship between the logarithmic solubilityand the reduced density shows the expected linear behaviour forall isotherms. At constant temperature, the solubility of a soluteincreases almost linear with the solvents density and therewith

Phytosterol [28] 3 1610.9 206.8 1.7

ARD = 1N

N∑1

∣y2,calc−y2,exp

∣y2,exp

× 100.

468 M. Türk et al. / J. of Supercritical Fluids 55 (2010) 462–471

84 12 16 20 241x10

3

2x103

3x103

4x103

[20]

[21]

[22]

[23]

T ln

(E)

(K)

1 (mol/dm

3)

(a) CO2/Salicylic acid

84 12 16 20 242x103

3x103

4x103

5x103

6x103

308 K

313 K

323 K

T ln

(E)

(K)

1 (mol/dm

3)

(b) CO2/RS-Ibuprofen [24]

84 12 16 20 243x10

3

4x103

5x103

6x103

[6]

[25]

[26]

[27]

T ln

(E)

(K)

1 (mol/dm

3)

(c) CO2/S-Naproxen

128 16 20 243x103

4x103

5x103

6x103

323 K

333 K

343 K

T ln

(E)

(K)

1 (mol/dm

3)

1 (mol/dm

3)

(d) CO2/Phytosterol [28]

4 8 12 16 20 242x10

3

3x103

4x103

5x103

6x103

[11]

[12]

[16]

T ln

( E)

(K)

(e) CO2/Naproxen

p2,sub

calculated according:

Fig. 5. T ln E versus solvent density for a) CO2/Salicylic acid [20–23], b) CO2/RS-Ibuprofen [24], c) CO2/S-Naproxen [6,25–27], d) CO2/Phytosterol [28], and e) CO2/S-Naproxen[11,12,16].

M. Türk et al. / J. of Supercritical Fluids 55 (2010) 462–471 469

F rofenc the ax

rt

ioacrctw((sf

ig. 6. Solubility versus pressure for a) CO2/Salicylic acid [21–23], b) CO2/RS-Ibuporrelations used for S-Naproxen are described in the text. Note that the scaling of

esulting in an increase of the solute solubility with increasingemperature.

To confirm the reliability of the experimental data, we exam-ned the consistency of solubility data using Eq. (6) and the valuesbtained for a and b are summarized in Table 4 along with theverage relative deviation (ARD). The lines depicted in Fig. 4 arealculated with Eq. (5) and demonstrate that there is a good cor-elation between calculated values and the experimental data. Asan be seen from the ARD listed in Table 4, most of the experimen-al data are satisfactorily correlated with this empirical correlation

ith an overall ARD ranging from (0.9–15)% for Salicylic acid, from

4.5–22)% for RS-Ibuprofen, from (1.4–32)% for S-Naproxen and3.5–9.0)% for Phytosterol. Thereby it should be considered that theolubility of RS-Ibuprofen is up to three-hundred times higher thanor the other three solids.

[24], c) CO2/Phytosterol [28], and d)–f) CO2/S-Naproxen [6]. The three differentes is different in the four systems because of large differences in solubility.

The results of fitting Eq. (7) to the experimental solubility dataare depicted in Fig. 5 and summarized in Table 5 for all substancesinvestigated. As can be seen from Fig. 5, most of the Salicylic acidsolubility data published from different authors collapse to a sin-gle line. Thereby, the experimental sublimation pressure data fromDavies and Jones [19] were used to calculate E. For the majorityof the data correlated, an agreement between experimental andcalculated data better than 1.0% was reached. For the CO2 + RS-Ibuprofen system, we were able to correlate all data with anARD-value of 0.7% using the experimental sublimation pressure

data from Ertel et al. [18]. For these data, the pronounced lineartrend was observed for a density range starting around 6 mol/dm3

(about 0.6�c) to about 20 mol/dm3 (about two-fold of �c of CO2),which represent the upper limit of the available experimentaldata.

470 M. Türk et al. / J. of Supercritical Fluids 55 (2010) 462–471

Table 6Resulting values obtained from fitting the four parameters of Eqs. (4) and (5) to the experimental solubility data.

Solute a (K) b (cm3 mol−1) A B (K)

Salicylic acid 987.828 34.029 17.7586 9740.14RS-Ibuprofen 1071.39 52.4292 31.2614 14565.9S-Naproxen (1) 883.735 81.2094 25.9397 15442.4S-Naproxen (2) 892.276 86.9116 35.8954 19194.7S-Naproxen (3) 805.23 53.4022 17.2568 11048.6Phytosterol 660.357 106.492 15.9749 11847.3

Table 7Summary of calculation results for the solute solubility in sc-CO2 using various models. It should be noted that the first two are deviations in the density, the second two inpressure.

Solute Number of: isotherms/data sources Kumar & Johnston ARD (%) Mendez-Santiago & Teja ARD (%) PR-EoS ARD (%) LK-EoS ARD (%)

Salicylic acid 9/4 0.9–15 0.3–2.1 10–44 5RS-Ibuprofen 3/1 4.5–22 0.7 16–33 9S-Naproxen 13/3 1.4–32 0.4–2.7 14–33 10Phytosterol 3/1 3.5–9 1.7 37–77 7

A

wSdvu

totElar

dctaaAv

3

esoaeasfictfFlrdptp

RD = 1N

N∑1

∣y2,calc−y2,exp

∣y2,exp

× 100.

In case of S-Naproxen, the enhancement factor was calculatedith the experimental sublimation pressure of Perlovich et al. [11].

imilar to Salicylic acid most of the solubility data published fromifferent authors collapse to a single line. In most cases, the ARDalue is less than 2%, which compares well with experimentalncertainty.

As mentioned above, for Phytosterol no experimental sublima-ion pressure data has been reported in literature. Thus, pi,sub wasbtained with the Coutsikos correlation [12] for solids to calculatehe enhancement factor E. It is shown in Fig. 5 that, according toq. (7), the three solubility isotherms collapse to a single straightine when plotted in terms of T·ln E vs. the CO2 density. This factnd the very low ARD-value of 1.7% confirmed the consistency andeliability of the experimental solubility data.

For comparison and in order to investigate the influence ofifferent GCM, Eq. (7) was fitted to the enhancement factor data cal-ulated with the sublimation pressure which was estimated withhe Watson correlation [16]. As depicted in Fig. 5, this curve showssignificant deviation up to −35% which is the result of the notice-bly higher values from the estimated sublimation pressure data.pplying the Coutsikos correlation [12] leads to significant higheralues for E from around 10–12%.

.3.2. Equation of stateIn addition to these empirical correlation approaches, we have

mployed two equations of state methods for the correlation of theolubility. While one can only correlate the solubility as functionf the density with the empirical methods discussed above, onelso can correlate the solubility as function of the pressure with anquation of state approach. This is important since the measurednd controlled property in technical processes is rather the pres-ure than the density. Of course it is possible to calculate pressurerom density and vice versa using an accurate equation of staten a second task afterwards, however the direct EoS method givesorrelations in one pour and provides properties not available inhe above mentioned methods. The correlation results obtainedrom the LK-EoS are shown in Fig. 6 and summarized in Table 6.or Phytosterol, RS-RS-Ibuprofen and for Salicylic acid the corre-ation is very good over the complete temperature and pressure

ange. The correlation of the S-Naproxen solubility data is moreifficult. The chosen temperature dependence of the saturationressure is apparently not suitable to correlate all isotherms withhe same accuracy. Even treating the parameters of the saturationressure curve adjustable (p2,sub,C) (Eq. (5)) gives some deviation

for the isotherm at 313 K. Using the saturation pressure estimatedby the method of Coutsikos [12] (p2,sub,A) we get even worse results.It seems that S-Naproxen is an exception because for all othersubstances correlated with this method the agreement is verygood.

The second equation of state approach is based on the PR-EoSfor the binary systems as described above. It is summarized inTable 7 that this approach leads to significant higher deviationsthan the density-based models and the LK-EoS. Depending on theGCM the ARD values range for Salicylic acid from (10–44)%, for RS-Ibuprofen from (16–33)%, for S-Naproxen from (14–33)% and forPhytosterol from (37–77)%. These findings are confirmed by otherresults published in literature. For RS-Ibuprofen, the deviations aresimilar to those reported by Charoenchaitrakool et al. [24] who cor-related the solubility data using the PR-EoS with van der Waalsmixing rules. Depending on the GCM the deviations between mod-elling and experimental data range from (6–44)%. Coimbra et al. [5]investigated the use of traditional cubic EoS in combination with 3mixing rules in order to correlate the solubility of RS-Ibuprofen andS-Naproxen in CO2 at 313 K. Depending on the EoS and the mixingrules, the ARD-value range for S-Naproxen from (3.9–31)% and forRS-Ibuprofen from (4.5–54)%.

4. Conclusions

The solubility of four pharmaceutical substances in supercriticalcarbon dioxide is correlated with empirical correlation models andEquation of State approaches. For the four systems considered inthis investigation, one can conclude that:

a) the cubic EoS approach lead to deviations between experimen-tal and calculated solubility data which are up to one orderof magnitude higher than for the empirical Kumar & Johnstonapproach and up to two orders of magnitude higher than for theMendez-Santiago and Teja approach;

b) the LK-EoS leads to similar deviations than the Kumar & Johnstonapproach.

It should be considered that the empirical approaches can onlycorrelate the solubility as function of the density while the Equationof State approaches allow the practically more important correla-tion as function of the pressure. In order to obtain most accuratecorrelations a non-cubic Equation of State should be used which

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M. Türk et al. / J. of Superc

ccurately reproduces the pvT behaviour of the pure solvent in theear-critical region.

cknowledgments

This work was supported primarily by the Deutsche Forschungs-emeinschaft (DFG, Tu 93/7-1, 7-2, Kr 1598/26-1, 26-2) which theuthors gratefully acknowledge. The authors thank Boris Stehli foris helpful contributions to this investigation.

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