J. of Supercritical Fluids 55 (2010) 462471

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The Journal of Supercritical Fluids

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A comp tiomodels in

Michaela Karlsruhe Ins rmanb Institut fr Ph

a r t i c l

Article history:Received 7 JunReceived in reAccepted 24 A

lid drh drubase

in 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 uid 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 uids. 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-

1. Introdu

The knoSCF is essenthedetermithePGSSprthe ability osaturated liAnti-SolvenRESS procethe solventproperties ophology arbehaviour.submicron

CorresponE-mail add

0896-8446/$ doi:10.1016/j.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, ofS-Naproxen, of RS-Ibuprofen and of Phytosterol in CO2 is correlated by different methods: two methodsfor the pressuresolubility correlation and two methods for the densitysolubility correlation. In addi-tion, the inuence of solute data predicted by different group-contribution methods is investigated. Withthe exception of S-Naproxen all systems investigated can be modelled sufcient 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.

2010 Elsevier B.V. All rights reserved.

ction

wledge of phase equilibrium and solute solubility in atial for the design of particle formation processes andnationof their best operating conditions.With regard toocess (ParticleGeneration fromGas Saturated Solution),f the supercritical solvent to melt the solid and to formquid phase is of major interest. In the GAS process (Gast) the SCF acts as an anti-solvent while in case of thess (Rapid Expansion of Supercritical Solutions) enablesfree formation of submicron particles. In addition, thef the produced powders such as particle size and mor-

e often strongly inuenced by the underlying phaseUntil today, much work has been done on producingpoor water soluble substances by RESS and dissolu-

ding author. Tel.: +49 721 608 2330.ress: tuerk@kit.edu (M. Trk).

tion studies demonstrate that pharmaceuticals showa signicantlyimproved 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 solidliquidgasthree-phase-line (S2LG line) interrupts the critical mixture curveat the upper critical endpoint (UCEP). In the temperature rangebetween the TLCEP and TUCEP only a soliduid two-phase equilib-rium (s2 = scf) exists for each pressure. In the region close to the

see front matter 2010 Elsevier B.V. All rights reserved.supu.2010.08.011arison between models based on equafor describing the solubility of solutes

Trka,, Marlene Cronea, Thomas Kraskab

titute of Technology (KIT), Institut fr Technische Thermodynamik und Kltetechnik, Geysikalische Chemie, Department fr Chemie, Universitt zu Kln, Germany

e i n f o

e 2010vised form 12 August 2010ugust 2010

a b s t r a c t

The poor dissolution behaviour of soHowever, the dissolution rate of succle size. At present, supercritical uidm/locate /supf lu

ns of state and density-basedCO2

y

ugs in biological environment leads to a low bioavailability.gs can be enhanced dramatically by reduction of the parti-d particle size reduction processes are gaining in importance

M. Trk et al. / J. of Supercritical Fluids 55 (2010) 462471 463

Nomenclature

a attraction parameter of the PengRobinson EoS; tparameter of Eq. (6)

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

temperature of the attraction term of thePengRobinson EoS

b co-volume parameter of the PengRobinson EoS; tparameter of Eq. (6)

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

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

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

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

Eq. (9); enhancement factorkij t parameter for the binary attractionlij t parameter for the binary co-volumeppcRSTTmTTP,2Tc,1vixiy2

two criticalresult in a csupercriticaaround theof major ecprocess, it iity of the soavoid the fo

Fig. 1. Typicaluid (1) and a

Table 1Physical properties of the substances investigated.

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

Salicylic acidRS-IbuprofeS-NaproxenPhytosterol

a Measured

Thereforexperimentsupercriticamodels basrules, aremSCFs. Theresuch as critisublimationmon estimainconsistenmation on tcorrelation

The fourytosancences.c solihis parepresolacentric factorpressurecritical pressuregas constantuctuation parameter of the LK-EoSentropy of fusiontemperaturemelting temperature

and Phimportsubstaorgani

In tin CO2for thedensitytriple temperature of the solutecritical temperature of the solventmolar volume of component imole fraction of component imole fraction of the solute in the supercritical sol-vent

endpoints, small changes in pressure and temperatureonsiderable increase of the solubility of the solid in thel solvent. Due to the higher solid solubility in the regionUCEP in comparison to the LCEP, the former region isonomic interest. For many processes, such as the RESSs desired to take advantage of the increased sensitiv-lubility with respect to pressure near the UCEP, but tormation of a liquid phase.

pTprojection for an asymmetricmixture consisting of a supercriticallow volatile solid (2).

data predicThereby, ittion of statsublimation

2. Model d

2.1. Equatio

Cubic eqimental resupercriticadevelopmepresent invof State (PR

p = R T(v b)

In Eq. (1ume, and Rsystems usi

a =k

i=1

kj=1

b =k

i=1

kj=1

The paraerties of thcan be obtaEoS and the

a = 0.4572469-72-7 138.12 431.5 27.8n 15687-27-1 206.28 348.6 25.5

22204-53-1 230.26 427.7 31.483-46-5 414.72 411.5 18.9

with DSC.

e reliable solubility data are essential for an accurateal design and for calculation of the concentration ofl solutions at different operating conditions. Today,ed on equations of state, together with different mixingostwidely used to correlate and predict the solubility infore the accurate knowledge of the required solute data,cal parameters, acentric factor, solidmolar volume, andpressure of the solutes is essential. However, the com-tion methods are mostly empirical and often lead tot and unreliable results. Thus, due to the lack of infor-hese data, density-based models are often used for theof experimental solubility data.substances, Salicylic acid, RS-Ibuprofen, S-Naproxen

terol, studied in this work were selected due to theirand as examples for poorwater soluble pharmaceuticalIn Table 1 some important physical properties of theds investigated here are summarized.aper, solubility data of the above mentioned solidscorrelated by four different methods: two methods

ssuresolubility correlation and two methods for theubility correlation. In addition, the inuence of soluteted by different estimation methods is investigated.turned out that for the solutes investigated, the equa-e based method is very sensitive to the values of thepressure.

escription

ns of state

uations of state are often used to describe the exper-sults of the solubility y2 of an organic solid in al uid. These equations of state are empirical furthernts of the van der Waals equation of state [2]. In theestigationweused theoriginal PengRobinsonEquation-EoS) [3] to describe the solubility y2.

a(T)v2 + 2bv b2 (1)

) p is the pressure, T the temperature, v the molar vol-the gas constant. The PR-EoS was applied to binary

ng the van der Waals 1-uid mixing rules:

xixjaij aij =

ai aj (1 kij) (2a)

xixjbij bij =bii + bjj

2 (1 lij) (2b)

meters a and b can be calculated from the critical prop-

e pure components. The binary interaction parametersined by regression of the experimental data with themixing rules (see Eqs. (2a), (2b)):

R2T2cpc

(T,) (2c)

464 M. Trk et al. / J. of Supercritical Fluids 55 (2010) 462471

with

(T,)=(1+0.37464+1.542260.269922(1

T/Tc))2

(2d)

and

b = 0.0778RTcpc

. (2e)

In Eqs. (2c)(2e) is the acentric factor, and Tc and pc the crit-ical data. This procedure requires the accurate knowledge of thevarious thermophysical data, such as critical data, acentric factor,solid molar volume, and sublimation pressure of the solutes [46].The correlation which was used to calculate the solubility of thesolute in the supercritical solvent is shown in Eq. (3). This equationis a result ouid phase,is negligible

y2(p, T) =p

Subscripthe sublimafugacity coecoefcient fof the purethe pressurmixing ruleered as uniknowledgevolume (v2)

BesidesLeonhardKubility of a

p = pref(a, bThe refe

of vanderWaction (reprepulsion than and Stader Waalsdescribe thical equatiouctuationsdivergencesnents. In orthe LK-EoSthe referendo not divethe EoS inthe LK-EoSin literatureneed to be et the attrathe solute dalso no kij ptted in thi

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 difcult [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 t of the model parameters to solubility data.If solubility data are available for different temperatures one canbuild in a ClausiusClapeyron-like temperature dependence of thesolid saturation pressure:

ln(p2,sub

p0

)= A

(B

T

)(5)

q. (unitis a

s soled frmentlar swithrelatmentliteraCouble pcorrtedlubilin allilityare ume

ensity

of thy2 ofl et

= a +

q. (6presso emthat

) = cusedtheity bnedity in

2 p,sub(T

Table 2Values of the p ibutio

pc (MP

Salicylic acid 4.5RS-Ibuprofe 2.1S-Naproxen 1.9Phytosterol 0.96

a Estimatedf the equifugacity condition between the solid and theunder the assumption that the solubility of the solventin the solid phase.

2,sub(T) 2,sub(p2,sub, T)p 2(p, T, y2)

exp

(v2(p p2,sub)

RT

)(3)

t 2 in Eq. (3) refers to the solid and therefore p2,sub istion pressure of the solid at temperature T, 2,sub is thefcient at the sublimation pressure, 2 is the fugacityor the solid in the SCF phase, and v2 is themolar volumesolid. Thereby, it is assumed that v2 is independent one p. In this work 2 is calculated with the PR-EoS usings given in Eqs. (2a) and (2b), while 2,sub can be consid-t. Thus, the calculation of the solubility y2 requires theof the solid sublimation pressure (p2,sub), solid molarand a reliable equation of state.the PR-EoS we also applied the accurate non-cubicraska Equation of State (LK-EoS) to describe the sol-

solid y2:

) + ppert(a, b, ) with = (, T) (4)rence part of this EoS is based on the fundamental resultaals to describe the different contributions of the inter-

ulsion and attraction) by two additive terms. For thehe much later developed hard-sphere term of Carna-rling is used while for the attraction the original van

term is used. A van der Waals type EoS is not able toe near-critical region properly because they are analyt-ns of state. At the critical point, due to innite density, the uid exhibits non-analytical behaviour such asexpressed, for example, by non-integer critical expo-

der to correct the deviations in the near-critical regioncontains a perturbation term derived on the basis ofce EoS by introducing uctuations. These uctuationsrge at the critical point but their contribution improvesthe near-critical region substantially. More details onand the application of the fugacity approach are given[7]. The critical parameters of the pure solute do notstimated by a group-contribution method because wection and co-volume equation of state parameter foruring the solubility correlation. For the same reasonarameter is required. The total number of parameters,s work by a MarquardtLevenberg algorithm, are four

In Eis thethat thvariouobtainexperimolecumodelent corexperito thetion ofadjustaubilitycorrelathe soxed ipressibwhichco-vol

2.2. D

Oneubilityby Stah

ln(y2)

In ET andare twshown

T ln(Ecan beEq. (7)solubilE is desolubil

E = yp2

ure component parameters for the solids investigated using different group-contr

Tb (K) Tc (K)

(14) 571646 738913n (13) 542673 717891(14) 584743 768990(12) 584993 7071219

value [16].5) A and B are adjustable parameters and p0 =1MPapressure. In several investigations it has been shown,pproach using the LK-EoS gives good correlation forutes in CO2 and N2O [810]. The sublimation pressureom the solubility correlation agrees well with availableal data and behaves systematically as function of thetructure [8]. S-Naproxen turns out to be very difcult toall approaches. Thereforewehere compare threediffer-ionprocedures: 1) the correlationEq. (5) to theavailableal data of the sublimation pressure [11], 2) tting Eq. (5)ture data which are estimated with a group contribu-tsikos [12] and 3) treating the sublimation pressure asroperty tting the parameters of Eq. (5) during the sol-

elation. Phytosterol, RS-Ibuprofen and Salicylic acid areby implementing Eq. (5) and tting its parameters toty isotherms. The value of the molar volume solute iscorrelations to the value given in Table 2 and the com-of the solute is set to zero. The remaining parameters,tted to the data, are the attraction parameter a and theparameter b of the solute.

-based models

emost commonlyusedmodel,whichcorrelates the sol-a solute in a SCF to the uids density has been proposedal. [13] and by Kumar and Johnston [14]:

b ln(Red) with Red =11,c

(6)

) 1 is the density of CO2 at the equilibrium temperatureure p, 1,c is the critical density of CO2, and a and bpirical constants. Mendez-Santiago and Teja [15] havethe following equation:

+ d 1 (7)to calculate the solubility of numerous solids in CO2. In

enhancement factor E can be regarded as a normalizedecause it removes the effect of the sublimation pressure.as the ratio of the mole fraction of the solid over thean ideal gas:

)(8)

n methods (numerary in brackets correspond to number of GCM).

a) () vi (m3/mol)a

5.7 0.760.89 9.591052.5 0.740.87 1.881042.7 0.780.94 1.781041.2 0.791.2 4.11104

M. Trk et al. / J. of Supercritical Fluids 55 (2010) 462471 465

Since the constants c and d in Eq. (7) are independent oftemperature, the solubilitydata for binary systemsatdifferent tem-peratures should collapse to a single straight line when plotted interms of TlnE vs. the solvents density. The lower limit of this linearbehaviour is about half while the upper limit is around the twofoldof the critical density of the solvent [15]. The fact that all isothermscollapse to a single line allows determining the self-consistency ofthe experimental data and allows identifying data sets that are notconsistent with other data.

3. Results and discussion

3.1. Estimation of critical constants (Tc and pc) and acentricfactor ()

For the calculation of the solubility in a supercritical uid usingan EoS it is necessary to have critical properties and acentric fac-tors of all components. In addition molar volumes and sublimationpressures of the solid components are required. If some of thesedata are not available, estimation techniques might be employed.As shown in Fig. 2, there are a few methods, which use group oratomic contributions to estimate critical properties [16].

pc Group contribution

methods

Tb / Tc

Tc Edminster-

method

Forman-

Thodos

vc

Miller-

correlation Tb Coutsikos

Fig. 2. Schematic representation of the various ways to use different estimationtechniques [16] for calculating Tc, pc and .

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

2,8 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

3,0

101

(c) S-Naproxen

ata for a) Salicylic acid, b) RS-Ibuprofen, and c) S-Naproxen.2,4 2,6 2,810-3

10-2

10-1

100

p 2,s

ub (

Pa

)

[11]

[12]

Eq. (5)

1000/T (K-1)

Fig. 3. Comparison between experimental and calculated sublimation pressure d

466 M. Trk et al. / J. of Supercritical Fluids 55 (2010) 462471

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

Solute A B (K) T range (K)

Salicylic acid 34.6 11484 368408RS-Ibuprofen 42.1 14554 296337S-Naproxen 39.7 15431 341397Phytosterol 45.9 18919 298343

Several group-contribution methods (GCM) for the normalboiling temperature, which is necessary to estimate the criticaltemperature by some methods, the critical temperature, and thecritical pressure are used to analyze the reliability of this correla-tionmethod and to study the inuence of each parameter. It shouldbe noted that this refers to the estimation methods which are notbased on equations of state. The acentric factor has been calcu-lated by the Edminster-GCM [16]. The estimated properties of thefour solids investigated using various GCM are shown in Table 2.In the case of CO2 the physical properties are taken from NIST(Tc = 304.21K, pc = 7.38MPa and =0.225) [17].

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+(

SiT

)(

1 TmT

)(9)

The constants A to E can be estimated via theAbramsMassaldiPrausnitz 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 experimentaldata for the sublimation pressure. For Phytosterol, the sublimationpressure data obtained from Coutsikos correlation have also beensuccessfully 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.

-0,8 -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

-0,4 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]

(c) CO2 /Naproxen [6] 323 K

333 K

343 K

Fig. 4. Solubillines are calcu10-4

313 K

323 K

333 K

343 K

353 K

y 2 (

-)

10-4

y 2 (

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

-5

ln(1/

1,C) (-)

10-5

(d) C

ity versus reduced solvent density for a) CO2/Salicylic acid [20,23], b) CO2/RS-Ibuprofenlated with Eq. (6).0,2 0,4 0,6

ln(1/

1,C) (-)

O2/Phytosterol [28]

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

M. Trk et al. / J. of Supercritical Fluids 55 (2010) 462471 467

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

T (K) Number of datapoints

a b ARD (%)

Salicylic acid 20296

3.9803.4623.5533.619

5.97.08.16.0

Salicylic acid 998

3.9492.630

13.014.8

Salicylic acid 511

3.9143.206

0.96.9

Salicylic acid 02 4.531 3.3

RS-Ibuprofe 562

5.9446.3305.523

5.24.521.9

S-Naproxen 661340

4.4313.9523.653

6.47.66.9

S-Naproxen 1470530406

4.6573.1233.4192.6343.084

6.97.214.020.831.6

S-Naproxen 79 6.018 6.5S-Naproxen 30

13207030

Phytosterol 373285

ARD = 1NN1

In Fig. 3data for RSIn case of Rexperimentexperimentto 17.5% atmodelled vrelative devApplying thculated valuthe experimlarger (10

3.3. Correla

3.3.1. Dens

The inusity is depic[2023], RSterol [28] adata of theerature forranging frowere measperatures oS-Naproxening from (3are publishfollows modata exhibisure [6]. Toin the rang

a, no[20] 308.15313.15318.15328.15

11151211

10.59.989.799.18

[21] 313.15333.15

1211

10.08.67

[22] 308.15318.15

812

10.39.49

[23] 323 7 10.0n [24] 308.15

313.15318.15

1568

9.128.808.11

[25] 313.1323.1333.1

666

13.212.511.9

[26] 308318328338348

88888

13.612.111.911.010.7

[27] 313.15 9 13.9[6] 313

323333343353

34556

13.212.612.111.510.8

[28] 323.2333.2343.2

878

12.411.611.1

y2,calcy2,exp

y2,exp

100.

the comparison between calculated and experimental-Ibuprofen, S-Naproxen and Salicylic acid are shown.

31)MP[28].S-Ibuprofen, the Coutsikos correlation represents theal data quite well. The relative deviation betweenal and calculated values increases from 2.3% at 313K343K. Larger deviations between experimental and

alues are found for S-Naproxen. For this substance, theiation decreases from 87% at 313K to 62% at 343K.e Coutsikos correlation for Salicylic acid leads to cal-es which are up to two orders of magnitude lower thanental data. Thus, it is obviously, that the deviations are0%) than for S-Naproxen.

tion of experimental solubility data

ity-based models

ence of the system temperature and the solvents den-ted in Fig. 4 which shows the solubility of Salicylic acid-Ibuprofen [24], S-Naproxen [6,2527], and of Phytos-s a function of the reduced CO2 density. Experimentalsolubility of Salicylic acid in CO2 are available in lit-temperatures ranging from (308333)K and pressuresm (835)MPa, while solubility data of RS-Ibuprofenured at pressures in the range of (822)MPa, tem-f (308 and 313)K, and up to 17MPa for 318K. For, experimental solubility data for temperatures rang-08353)K within the pressure range of (1235)MPaed in literature. Although each individual set of datastly a common trend, in some cases the publishedt different trends with respect to temperature or pres-our knowledge, with the exception of our own datae from (323343)K and pressures between (14 and

For all intrends whicsupercriticatrated in Fand the redall isothermincreases asolvent poweffect on tregion. In tsublimation

Table 5Constants of E

Salicylic acidSalicylic acidSalicylic acidSalicylic acid

RS-Ibuprofe

S-NaproxenS-NaproxenS-NaproxenS-Naproxen

Phytosterol

ARD = 1NN14.1654.0793.9423.9123.924

1.92.15.41.44.1

5.7415.1435.790

9.03.73.5

other solubility data has been reported for Phytosterolvestigated substances, the experimental results showh are similar to those observed for other solids in thel region. In agreement with Eq. (6) and as it is illus-ig. 4, relationship between the logarithmic solubilityuced density shows the expected linear behaviour fors. At constant temperature, the solubility of a solute

lmost linear with the solvents density and therewither. Fig. 4 also shows the pronounced temperature

he solubility in the region outside the retrogradehis region, the effect of the temperature on the solute

pressure overlays the effect of the solvent density,

q. (7) for the solubility of solids in sc-CO2.

Number ofisotherms

c (K) d (Kdm3/mol) ARD (%)

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

n [24] 3 1783.0 166.7 0.7

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

[28] 3 1610.9 206.8 1.7

y2,calcy2,exp

y2,exp

100.

468 M. Trk et al. / J. of Supercritical Fluids 55 (2010) 462471

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 lnE versus solvent density for a) CO2/Salicylic acid [2023], b) CO2/RS-Ibuprofen [24], c) CO2/S-Naproxen [6,2527], d) CO2/Phytosterol [28], and e) CO2/S-Naproxen[11,12,16].

M. Trk et al. / J. of Supercritical Fluids 55 (2010) 462471 469

Fig. 6. Solubilcorrelations us

resulting intemperatur

To conined the coobtained foaverage relcalculated wrelation betcan be seental data arewith an ove(4.522)% f(3.59.0)% fsolubility offor the otheity versus pressure for a) CO2/Salicylic acid [2123], b) CO2/RS-Ibuprofen [24], c) CO2/ed for S-Naproxen are described in the text. Note that the scaling of the axes is different

an increase of the solute solubility with increasinge.rm the reliability of the experimental data, we exam-nsistency of solubility data using Eq. (6) and the valuesr a and b are summarized in Table 4 along with theative deviation (ARD). The lines depicted in Fig. 4 areith Eq. (5) and demonstrate that there is a good cor-

ween calculated values and the experimental data. Asfrom the ARD listed in Table 4, most of the experimen-satisfactorily correlated with this empirical correlationrall ARD ranging from (0.915)% for Salicylic acid, fromor RS-Ibuprofen, from (1.432)% for S-Naproxen andor Phytosterol. Thereby it should be considered that theRS-Ibuprofen is up to three-hundred times higher thanr three solids.

The resuare depicteinvestigatesolubility dgle line. TheDavies andof the datacalculatedIbuprofenARD-valuedata from Etrend was o(about 0.6which reprdata.Phytosterol [28], and d)f) CO2/S-Naproxen [6]. The three differentin the four systems because of large differences in solubility.

lts of tting Eq. (7) to the experimental solubility datad in Fig. 5 and summarized in Table 5 for all substancesd. As can be seen from Fig. 5, most of the Salicylic acidata published from different authors collapse to a sin-reby, the experimental sublimation pressure data fromJones [19] were used to calculate E. For the majoritycorrelated, an agreement between experimental and

data better than 1.0% was reached. For the CO2 +RS-system, we were able to correlate all data with anof 0.7% using the experimental sublimation pressurertel et al. [18]. For these data, the pronounced linearbserved for a density range starting around 6mol/dm3

c) to about 20mol/dm3 (about two-fold of c of CO2),esent the upper limit of the available experimental

470 M. Trk et al. / J. of Supercritical Fluids 55 (2010) 462471

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

Solute a (K) b (cm3 mol1) A B (K)

Salicylic acid 987.828 34.029 17.7586 9740.14RS-IbuprofeS-NaproxenS-NaproxenS-NaproxenPhytosterol

Table 7Summary of ca be nopressure.

Solute endez

Salicylic acid 32.1RS-Ibuprofe 7S-Naproxen 42.7Phytosterol 7

ARD = 1NN1

In case owith the exSimilar to Sdifferent auvalue is lesuncertainty

As menttion pressuobtained wthe enhancEq. (7), theline when pand the verreliability o

For comdifferentGCculated witthe Watsona signicanably higherApplying thvalues for E

3.3.2. EquaIn additi

employed tsolubility. Wof the densalso can corequation ofand controlsure than thfrom densiin a secondcorrelationsthe above mfrom the LKFor Phytostlation is verange. Thedifcult. Thpressure isthe same acpressure cu

isotmeths th

nces

secobin

7 thae de

he ARfen fterolpubto ththerulend egateruleoxenhe Aprofe

clusn 1071.39 52.4292(1) 883.735 81.2094(2) 892.276 86.9116(3) 805.23 53.4022

660.357 106.492

lculation results for the solute solubility in sc-CO2 using various models. It should

Number of: isotherms/data sources Kumar & Johnston ARD (%) M

9/4 0.915 0.n 3/1 4.522 0.

13/3 1.432 0.3/1 3.59 1.

y2,calcy2,exp

y2,exp

100.

f S-Naproxen, the enhancement factor was calculatedperimental sublimation pressure of Perlovich et al. [11].alicylic acid most of the solubility data published fromthors collapse to a single line. In most cases, the ARDs than 2%, which compares well with experimental.ioned above, for Phytosterol no experimental sublima-re data has been reported in literature. Thus, pi,sub wasith the Coutsikos correlation [12] for solids to calculateement factor E. It is shown in Fig. 5 that, according tothree solubility isotherms collapse to a single straightlotted in terms of TlnE vs. the CO2 density. This fact

y low ARD-value of 1.7% conrmed the consistency andf the experimental solubility data.parison and in order to investigate the inuence ofM, Eq. (7)wastted to theenhancement factordata cal-h the sublimation pressure which was estimated withcorrelation [16]. As depicted in Fig. 5, this curve showst deviation up to 35% which is the result of the notice-values from the estimated sublimation pressure data.e Coutsikos correlation [12] leads to signicant higherfrom around 1012%.

tion of stateon to these empirical correlation approaches, we havewo equations of state methods for the correlation of the

for theby theIt seemsubstagood.

Thefor theTablethan thGCM tIbuproPhytosresultssimilarrelatedmixingelling ainvestimixingS-Naprrules, tRS-Ibu

4. Conhile one can only correlate the solubility as functionity with the empirical methods discussed above, onerelate the solubility as function of the pressure with anstate approach. This is important since the measuredled property in technical processes is rather the pres-e density. Of course it is possible to calculate pressure

ty and vice versa using an accurate equation of statetask afterwards, however the direct EoS method givesin one pour and provides properties not available inentioned methods. The correlation results obtained

-EoS are shown in Fig. 6 and summarized in Table 6.erol, RS-RS-Ibuprofen and for Salicylic acid the corre-ry good over the complete temperature and pressurecorrelation of the S-Naproxen solubility data is moree chosen temperature dependence of the saturationapparently not suitable to correlate all isotherms withcuracy. Even treating the parameters of the saturationrve adjustable (p2,sub,C) (Eq. (5)) gives some deviation

The solucarbon dioxEquation ofthis investi

a) the cubital andof magnapproacMendez

b) theLK-Eapproac

It shouldcorrelate thof State apption as funccorrelation31.2614 14565.925.9397 15442.435.8954 19194.717.2568 11048.615.9749 11847.3

ted that the rst two are deviations in the density, the second two in

-Santiago & Teja ARD (%) PR-EoS ARD (%) LK-EoS ARD (%)

1044 51633 91433 103777 7

herm at 313K. Using the saturation pressure estimatedodof Coutsikos [12] (p2,sub,A)we get evenworse results.at S-Naproxen is an exception because for all othercorrelated with this method the agreement is very

nd equation of state approach is based on the PR-EoSary systems as described above. It is summarized int this approach leads to signicant higher deviationsnsity-based models and the LK-EoS. Depending on theD values range for Salicylic acid from (1044)%, for RS-rom (1633)%, for S-Naproxen from (1433)% and forfrom (3777)%. These ndings are conrmed by other

lished in literature. For RS-Ibuprofen, the deviations areose reported by Charoenchaitrakool et al. [24]who cor-solubility data using the PR-EoS with van der Waalss. Depending on the GCM the deviations between mod-xperimental data range from (644)%. Coimbra et al. [5]d the use of traditional cubic EoS in combination with 3s in order to correlate the solubility of RS-Ibuprofen andin CO2 at 313K. Depending on the EoS and the mixing

RD-value range for S-Naproxen from (3.931)% and forn from (4.554)%.

ionsbility of four pharmaceutical substances in supercriticalide is correlated with empirical correlation models andState approaches. For the four systems considered in

gation, one can conclude that:

c EoS approach lead to deviations between experimen-calculated solubility data which are up to one orderitude higher than for the empirical Kumar & Johnstonh and up to two orders of magnitude higher than for the-Santiago and Teja approach;oS leads to similardeviations than theKumar& Johnstonh.

be considered that the empirical approaches can onlye solubility as functionof thedensitywhile theEquationroaches allow the practically more important correla-tion of the pressure. In order to obtain most accurate

s a non-cubic Equation of State should be used which

M. Trk et al. / J. of Supercritical Fluids 55 (2010) 462471 471

accurately reproduces the pvT behaviour of the pure solvent in thenear-critical region.

Acknowledgments

Thisworkwas supportedprimarilyby theDeutscheForschungs-gemeinschaft (DFG, Tu 93/7-1, 7-2, Kr 1598/26-1, 26-2) which theauthors gratefully acknowledge. The authors thank Boris Stehli forhis helpful contributions to this investigation.

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A comparison between models based on equations of state and density-based models for describing the solubility of solutes in CO2IntroductionModel descriptionEquations of stateDensity-based models

Results and discussionEstimation of critical constants (Tc and pc) and acentric factor ()Sublimation pressure dataCorrelation of experimental solubility dataDensity-based modelsEquation of state

ConclusionsAcknowledgmentsReferences