Journal of Supercritical Fluids 24 (2002) 219–229

Measurement of diffusion coefficients for 2-nitroanisole,1,2-dichlorobenzene and tert-butylbenzene in carbon dioxide

containing modifiers

Luis M. Gonzalez, Julio L. Bueno, Ignacio Medina *Departamento de Ingenierıa Quımica y T.M.A., Uni�ersidad de O�iedo, 33071 O�iedo, Spain

Received 10 September 2001; received in revised form 5 February 2002; accepted 9 February 2002

Abstract

The molecular diffusion coefficients of 2-nitroanisole, 1,2-dichlorobenzene and tert-butylbenzene in supercriticalcarbon dioxide and carbon dioxide containing modifiers were determined by using the Taylor–Aris dispersiontechnique. Experimental values are reported for temperatures ranging from 313 to 333 K and pressures between 15.0and 35.0 MPa. The influence of pressure, temperature, density and viscosity on the binary diffusion coefficients wasexamined. The addition of low proportions of methanol and n-hexane as modifiers had an important effect on thediffusion coefficient of the three solutes.© 2002 Elsevier Science B.V. All rights reserved.

Keywords: Supercritical fluid; Mass transfer; Diffusion; Carbon dioxide; Chromatography; Modifier

Nomenclature

dcoil diameter of the tubing coilinternal diameter of the tubedtube

molecular diffusion coefficientD12

Dean numberDeheight equivalent to a theoretical plateHdiffusion tube lengthL

P pressureinternal radius of the diffusion tuber0

Schmidt numberScT absolute temperatureU0 average linear velocity of the carrier fluid

www.elsevier.com/locate/supflu

* Corresponding author. Tel.: +34-985-103-510; fax: +34-985-103-434E-mail address: medina@sauron.quimica.uniovi.es (I. Medina).

0896-8446/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved.

PII: S0896 -8446 (02 )00036 -0

L.M. Gonzalez et al. / J. of Supercritical Fluids 24 (2002) 219–229220

W0.607 peak width at 0.607 times the peak height

Greek letterssolvent viscosity�

solvent density�

�2 total peak variance

1. Introduction

Many of the stated advantages of supercriticalfluid extraction are directly related to the wide-spread use of carbon dioxide as the extractingfluid. The most common fluid to date has beensupercritical carbon dioxide because of its fa-vourable properties. It has characteristics that al-low it to solvate numerous compounds ranging inpolarity from nonpolar to moderately polar.However, there is some interest in exploring theuse of organic solvent-modified CO2 particularlyfor the extraction of increasingly polar com-pounds. Modified fluids have been used to intro-duce selectivity to the separation as well as toincrease extraction efficiencies. The most commonmodifier employed has been methanol because ofits high solvent polarity parameter.

The key factor in the design and optimizationof a process involving supercritical fluids is theavailability of accurate and reliable solubility andmass transfer coefficient data. Numerous researchgroups have measured the solubility of manycomponents in different supercritical fluids. How-ever, diffusivity measurements of organic materi-als in supercritical fluids are limited. The majorityof experimental studies have dealt with binarysystems consisting of a single solute. Data derivedfrom multicomponent systems, in contrast, arerelatively scarce. The addition of a liquid organiccosolvent has been shown to modify diffusivitiesin supercritical fluids. The diffusion coefficient ofbinary mixtures of supercritical carbon dioxideand the solute characterises the nature of solute–solvent interactions whereas the diffusion coeffi-cient of ternary mixtures includes the influence ofsolute–solute interactions as well.

Despite the great potential of using cosolvents,the literature contains only a few examples ofexperimental diffusivity data for cosolvent-super-critical fluid systems. Previously, Sassiat et al. [1]measured the diffusivity of benzene in CO2/methanol mixtures. Smith et al. [2] reported someexperimental diffusivities of acridine, phenan-threne, and benzoic acid in a mixture of CO2 with5.5 mol% methanol as cosolvent. Funazukuri etal. [3] measured the diffusivity of vitamin K3 inmixtures of CO2 and n-hexane. Olesik et al. [4]have determined diffusion coefficients for benzeneand m-cresol in two supercritical fluids (carbondioxide and propane) containing polar modifiers(acetonitrile, propylene carbonate, and water).

Diffusion coefficients can be determined fromsupercritical fluid chromatography experimentsaccording to the peak broadening method using along void column (Taylor dispersion technique).A chromatographic technique is attractive be-cause data can be obtained rapidly and very littlesolute is necessary. In this work, data are reportedfor the diffusion coefficients of 2-nitroanisole, 1,2-dichlorobenzene and tert-butylbenzene in super-critical carbon dioxide at 313, 323, and 333 K andin supercritical carbon dioxide containing n-hex-ane (10 mol%) and methanol (5, and 10 mol%) ascosolvents. Diffusion coefficients have been mea-sured over the pressure range from 15.0 to 35.0MPa. There is not much information about solu-tion processes from the point of view of solutediffusion in the mixtures of carbon dioxide andmodifiers. The objective is to understand funda-mentally and to predict cosolvent-induced diffu-sivity enhancement as a function of the physicalproperties of the pure components. The solutesand cosolvents were chosen in an attempt to giveinsight into different types of molecular-scale in-

L.M. Gonzalez et al. / J. of Supercritical Fluids 24 (2002) 219–229 221

teractions in solution. The dependence of temper-ature, pressure, density and viscosity on the diffu-sion coefficient is discussed. The effect ofmolecular geometry was also investigated by ob-serving the diffusion coefficients of solutes.

2. Theoretical background

The chromatographic broadening technique isbased on the theory of diffusion in empty tubesadvanced by Taylor [5]. Taylor analyzed the dis-persion of a pulse of solute dissolved in a solventinto a tube in which the solvent is moving inlaminar flow. The pulse is dispersed due to thecombined action of convection in the axial direc-tion and diffusion in the radial direction.

The temporal variance of the Gaussian curve,which represents, at the time of elution, the con-centration distribution of the initial narrow pulseof the solute that passes throughout the detector,may be interpreted as follows:

�2=2D12L

U0

+r0

2U0L24D12

(1)

where D12 is the infinite dilution diffusivity ofsolute 1 in solvent 2, L is the dispersion tubelength, U0 is the average velocity of the mobilephase, r0 is the dispersion tube inner radius, and�2 is the variance of the curve in units of length.

According to the height of the theoretical plate,H, or relative peak broadening concept, being

H=�2

L(2)

Eq. (1) may be written as:

D12=U0

4�

H��

H2−�r0

2

3�n1

2�(3)

which provides values of D12 as a function ofdesign parameters (r0 and L) and experimentaldata (U0 and �2).

The theoretical plate height is experimentallydetermined by first measuring the width of thepeak at 0.607 times the peak height and then byapplying the equation

H=U0

2W0.6072

4L(4)

The mathematical model may be applied tocoiled columns with only a few restrictions in thehydrodynamics and mass transfer throughout thecolumn, which may be summarized in the adimen-sional condition

(De)(Sc)1/2�10 (5)

in accordance with the Giddings, Koudski,Moulijn, Tijsen, Nunge and Janssen criteria [6].

De and Sc are the Dean and Schmidt numbers,respectively, and are defined as

De=�U0dtube

�

�dtube

dcoil

(6)

and

Sc=�

�D12

(7)

where � is the solvent density, � the solventviscosity, dtube the internal diameter of the tube,and dcoil the diameter of the tubing coil.

Ternary diffusion is a more complex processthan binary diffusion. However, if the concentra-tion of the solute is low, often the binary mixtureis treated as though it is a pseudopure fluid. Then,effective binary diffusion coefficients are deter-mined by the same method. This approximationfor supercritical fluid mixtures has been used inthis study.

Detailed reviews of the criteria for design andoperation of the Taylor dispersion technique aregiven by Bueno et al. [6], Roth [7], Liong et al. [8],and Levelt-Sengers et al. [9]. All the sources oferrors mentioned and discussed in these workshave been considered.

3. Experimental section

The experimental diffusion coefficients of 2-ni-troanisole, 1,2-dichlorobenzene and tert-butylben-zene were measured using a commerciallyavailable Hewlett-Packard G1205A supercriticalfluid chromatograph (HP SFC). The HP SFCsystem consists of a pumping module, a mass flowsensor, a column oven, an injection valve, a

L.M. Gonzalez et al. / J. of Supercritical Fluids 24 (2002) 219–229222

choice of detectors and the SFC ChemStationsoftware. A schematic of the experimental appara-tus is shown in Fig. 1.

The HP SFC introduces the sample to thecolumn through a heated manual injection valve.A Rheodyne model 7520 injector of ultralow dis-persion with a 0.2 �l loop was used. Samples areinjected as liquids at room temperature, andlooped directly into the supercritical stream. Inthe present work, this unit uses a multiple wave-length UV detector (MWD). The HP SFC uses anelectrothermally cooled reciprocating pump tosupply supercritical fluids to the system. Whenthis reciprocating pump was used in our experi-ments, the dispersion curve for all experimentswas Gaussian with a linear correlation coefficientof 0.9996–0.9998 between ln�c� and �2 (�c�being the cross-sectional average concentrationand � the distance from the peak apex). Thesecondary moment calculation was particularlysensitive to noise, therefore, the calculated valueswere checked by overlaying the experimental peakwith the Gaussian peak of known variance andvisually confirming the calculated peak variance.Peaks that have an asymmetric factor greater than1.05 have been rejected for analysis. A secondpump is for the addition of the modifier to thesupercritical fluid to create modified mobilephases. The HP SFC provides programmable on-

line mixing of mobile phase from 0 to 100%. Byeliminating the need for multiple modifier tanks,the modifier pump reduces method developmenttime and cost, and yields more reproducible mo-bile phase composition. The variable restrictor isa programmable, backpressure control device lo-cated inside the pump module. The mass flowsensor is a device located inside the pumpingmodule. The mass flow sensor gives immediatefeedback for flow diagnostics such as if the pumpis working correctly, or if the fixed restrictor isplugged.

The solutes used during this study, 2-nitroan-isole, 1,2-dichlorobenzene and tert-butylbenzene,were obtained from Merck (synthesis grade). The2-nitroanisole and the 1,2-dichlorobenzene had aminimum purity of 98% and the tert-butylbenzenea minimum purity of 99%. Also, the cosolventsused, n-hexane and methanol, were obtained fromMerck (LiChrosolv grade). The n-hexane and themethanol had a minimum purity of 98 and 99.9%,respectively. The chemicals were used without fur-ther purification. The carbon dioxide supplied byAir Liquide had a minimum purity of 99.998%.

Compression of the carbon dioxide is accom-plished by pumping it as a liquid from a standardcylinder with a syphon. After pressurization, theCO2 is heated to the desired temperature in theoven, passed through the column and detector

Fig. 1. Schematic diagram of the experimental apparatus.

L.M. Gonzalez et al. / J. of Supercritical Fluids 24 (2002) 219–229 223

Table 1Experimental diffusion coefficients D12 (in m2 s−1) for 2-nitroanisole

T (K) D12×109 (m2 s−1)P (MPa)

Pure CO2 5% methanol 10% methanol 10% n-hexane

9.30 8.08313 7.6615 9.30313 20 8.32 7.80 7.22 8.42

7.45 7.13313 6.8925 8.577.19 6.8530 6.24313 8.306.87 6.28313 5.9835 7.62

10.92 9.1415 8.11323 9.8220323 9.53 8.36 7.56 8.87

8.87 7.7825 7.28323 8.0130323 8.11 7.52 6.73 7.73

7.67 7.00323 6.5835 7.5213.05 10.7015 7.71333 12.8310.90 9.76333 7.8820 10.859.96 9.2425 8.19333 10.288.99333 9.0130 8.12 9.838.63 8.45 7.77 9.2935333

under laminar flow conditions, and exits throughthe variable restrictor as a gas to the atmosphere.

The diffusion column consisted of a coiled (coildiameter 0.26 m) stainless steel tubing of 0.762mm i.d.×30.48 m long. The diffusion columnwas coiled to allow it to fit into the oven. In orderto reduce the dead volume of the system, lowdead volume connections and a low dead volumeUV detection cell were utilized. In any measure-ment made in the present study, the measuredpressure and temperature fluctuations were lessthan 0.1 MPa and 1 K. The pressures, at theentrance and exit points of the diffusion column,were measured by pressure sensors. The pressuredifference between these two points was within 0.1MPa. When the pressure, temperature, and flowrate reached the desired levels, 0.2 �l of organicsolute was injected as a pulse into the flowingfluid at the column inlet. Five to ten pulses wereinjected into the column per run and were spacedat 12–15 min intervals. This time lapse was suffi-cient to prevent the peaks from overlapping dur-ing elution from the diffusion column. Linearvelocities between 0.4 and 0.5 cm s−1 were em-ployed in the majority of experimental runs, re-sulting in residence times of approximately100–120 min for the runs. Reynolds numbers

were about 100 or lower. The solute concentrationprofile leaving the capillary column was moni-tored by the UV detector. The wavelengths em-ployed to monitor the solutes were determinedfrom a UV spectrum obtained for each solutefrom a commercially available UV scanningdevice (Philips PU 8720 UV/VIS). The wave-lengths were 221, 250 and 307 nm for 2-nitroan-isole, 264, 271 and 279 nm for 1,2-dichloro-benzene, and 253, 259 and 306 nm for tert-butyl-benzene. Fortunately, no tailing was observed,and the peaks were symmetrical in all the runs.The diffusion coefficient was then determinedfrom the shape of the peak recorded.

4. Results and discussion

The reliability of the experimental equipmentwas investigated in a previous work by comparingthe binary diffusion coefficients of benzene insupercritical carbon dioxide with data obtainedfrom the literature [8,9].

Tables 1–3 present the data obtained for thediffusion coefficients of 2-nitroanisole, 1,2-di-chlorobenzene and tert-butylbenzene in supercriti-cal carbon dioxide and in supercritical carbon

L.M. Gonzalez et al. / J. of Supercritical Fluids 24 (2002) 219–229224

dioxide containing n-hexane (10 mol%) andmethanol (5, and 10 mol%) as cosolvents togetherwith the temperatures and pressures at which theresults were obtained. Both temperature and pres-sure can affect the diffusivity of a solute in asupercritical fluid. Thus, in supercritical fluid dif-fusivity studies, the diffusivity should be deter-mined as a function not only of pressure, but alsoof temperature. The experiments for the threesolutes were carried out at three temperatures,313, 323, and 333 K, and pressures of 15.0, 20.0,25.0, 30.0, and 35.0 MPa. The experimental diffu-sivities ranged from 5.98×10−9 to 15.76×10−9

m2 s−1. The reproducibility of the measured dif-fusivies was normally 2% (absolute average devia-tion) or better for a total of 5–10 injections.

4.1. Binary systems

Even though the three solutes have differentstructures, it is possible to order the diffusivitiesof the three solutes in supercritical carbon dioxideat the same conditions as follows: D12 (1,2-dichlorobenzene)�D12 (tert-butylbenzene)�D12

(2-nitroanisole). The diffusion coefficient of 1,2-dichlorobenzene is about 1.06 times larger thanthat of tert-butylbenzene, and about 1.16 times

larger than that of 2-nitroanisole at the sameconditions. The size and shape of solute moleculesinfluence the rate of diffusion in the supercriticalcarbon dioxide [1,6,8,10]. The tert-butylbenzenemolecule is the smallest of the three solutes, fol-lowed by 1,2-dichlorobenzene and 2-nitroanisole.The 1,2-dichlorobenzene molecule has the advan-tage of a more compact shape. This effect be-comes evident and the diffusion coefficient valuesare higher than those found for the other benzenederivatives.

The diffusion coefficients of the three soluteswere determined as a function of pressure andtemperature. The relationship between diffusioncoefficient and pressure at constant temperaturefor the investigated systems is shown in Fig. 2 forthe 2-nitroanisole–carbon dioxide system. Similarbehaviour was found for the three solutes. Thegeneral trend is that the diffusion coefficient de-creases with increasing pressure. The influence ofpressure on the diffusion coefficient also varieswith temperature, with decreasing temperaturediffusion becomes less pressure dependent; andwith increasing temperature the pressure depen-dence of the diffusion coefficient becomes morepronounced. Fig. 2 makes it clear that the sharpchange in diffusivities at low pressures indicates

Table 2Experimental diffusion coefficients D12 (in m2 s−1) for 1,2-dichlorobenzene

T (K) D12×109 (m2 s−1)P (MPa)

Pure CO2 5% methanol 10% methanol 10% n-hexane

15 10.41313 10.42 9.98 9.909.828.479.369.5320313

25 8.86313 8.64 8.10 9.01313 30 8.59 7.98 7.69 9.03313 35 8.12 7.71 7.19 8.07

11.539.7412.62323 12.56158.97 9.7710.81323 9.8620

323 9.578.589.2510.24258.229.08 8.939.2630323

8.5835 9.18 8.56 8.1332315 15.76333 15.02 9.24 13.14

333 20 12.58 13.46 9.70 11.4711.219.7711.9911.39333 25

30 10.44333 10.67 10.00 11.0935333 10.02 10.03 9.60 10.96

L.M. Gonzalez et al. / J. of Supercritical Fluids 24 (2002) 219–229 225

Table 3Experimental diffusion coefficients D12 (in m2 s−1) for tert-butylbenzene

T (K) D12×109 (m2 s−1)P (MPa)

Pure CO2 5% methanol 10% methanol 10% n-hexane

10.73 9.22313 8.2815 10.07313 20 9.15 8.33 7.57 8.90

8.12 7.78313 6.8625 8.467.36 7.2630 6.74313 7.176.86 7.22313 6.5335 6.89

12.47 10.8215 9.92323 11.7820323 10.56 10.06 8.88 10.77

9.80 9.2225 8.43323 9.7030323 8.36 8.67 8.10 8.91

323 35 8.08 8.33 6.99 8.6015.58 13.3215 8.47333 14.03

20333 12.35 11.12 8.67 11.1811.19 10.59 8.57333 10.092510.19 9.2530 8.64333 9.39

333 9.5135 9.11 8.30 9.37

that the solvent density is an important factor, asthis property changes more rapidly at lower pres-sures. In the supercritical region the pressure de-pendence of the diffusion coefficient approachesthat of normal gases predominantly at low pres-sures and high temperatures. In general, the diffu-sion coefficient is approximately proportional tothe inverse of the pressure. The binary diffusioncoefficients of the systems investigated decrease byabout 25–35% for pressure rising from 15.0 to35.0 MPa.

As expected, a very high temperature depen-dence of the diffusion coefficient at constant pres-sure was observed. The relationship between thediffusion coefficient of 1,2-dichlorobenzene andtemperature at isobaric conditions is illustrated inFig. 3. A similar trend was found for tert-butyl-benzene and 2-nitroanisole. The binary diffusioncoefficient values increase by about 35% whentemperature increases from 313 to 333 K. Theresults also show that as the pressure is increased,the dependence of diffusion on temperature falls.The higher temperature dependence at lower pres-sures may be linked to the increasing temperaturedependence of the fluid density in the supercriticalregion which becomes increasingly higher at pres-sures closer to the critical pressure.

As was expected, it was found that the diffusioncoefficients were a strong function of density inthe temperature and pressure ranges investigated.Therefore, the role of density in the diffusionalprocess is important. The diffusion coefficientshave been determined over a considerable rangeof density from 609 to 936 kg m−3. Fig. 4 pre-sents the diffusion coefficient of tert-butylbenzeneas a function of supercritical carbon dioxide den-sity. As the density of the carbon dioxide becomes

Fig. 2. Binary diffusion coefficients of 2-nitroanisole in super-critical carbon dioxide as a function of pressure.

L.M. Gonzalez et al. / J. of Supercritical Fluids 24 (2002) 219–229226

Fig. 3. Binary diffusion coefficients of 1,2-dichlorobenzene insupercritical carbon dioxide as a function of temperature.

Fig. 5. Influence of the viscosity of supercritical carbon dioxideon the diffusion coefficient of 2-nitroanisole.

greater the diffusion coefficient decreases. Also, itwas observed that the decrease in diffusivity withrespect to rising fluid density was linear. Raisingthe density from 609 to 936 kg m−3 gives a solutediffusion coefficient decrease of 47–56%. The re-duction in diffusivity with increasing carbon diox-ide density can be explained by the increasedcollision frequency and the reduced mean freepath of the solutes.

Based on the Stokes–Einstein relationship, thediffusion coefficient is inversely proportional to

the viscosity of the solvent. In this work, theviscosity of carbon dioxide varied between 47.6and 102.3 �N s m−1. The trend observed is thatthe diffusion coefficient decreases with rising sol-vent viscosity. Fig. 5 shows the influence of theviscosity of the supercritical carbon dioxide on thediffusivity of 2-nitroanisole. Within the limits ofexperimental error, the data yielded a straight linewith a small positive intercept. Similar behaviourwas observed for 2-nitroanisole and 1,2-dichlorobenzene. The results obtained are consis-tent with the trends found by previous researchers[11,12].

4.2. Ternary systems

Solutes and modifiers used were chosen basedon their varying physical and chemical character-istics so that they might interact differently. Apolar modifier such as methanol and a nonpolarmodifier such as n-hexane have been added tocarbon dioxide to know how diffusion coefficientsvary against the modifier content in carbon diox-ide. It is well established that small amounts of acosolvent may have a significant effect on thediffusion coefficient of a solute in carbon dioxide.A small amount of a liquid cosolvent may beadded to carbon dioxide to produce a more polarsolvent. The most common modifier employed

Fig. 4. Influence of the density of supercritical carbon dioxideon the diffusion coefficient of tert-butylbenzene.

L.M. Gonzalez et al. / J. of Supercritical Fluids 24 (2002) 219–229 227

Fig. 6. Diffusion coefficients of 2-nitroanisole measured in themixture of CO2 and methanol. Fig. 8. Diffusion coefficients of tert-butylbenzene measured in

the mixture of CO2 and methanol.

was methanol, chosen because of its high solventpolarity parameter. Potential interactions includeinduced dipole interactions, hydrogen-bonding in-teractions, dipole moment, and Brønsted acidity.Tables 1–3 and Figs. 6–11 show the diffusioncoefficients for the three solutes, 2-nitroanisole,1,2-dichlorobenzene and tert-butylbenzene, fordifferent concentrations of methanol as a modifierin carbon dioxide, and for n-hexane as a modifierin carbon dioxide. The general shapes of thecurves in these figures are very similar to thoseobtained using supercritical carbon dioxide with-

out a modifier. These data indicate that the diffu-sion coefficients of the three solutes could bemarkedly affected by the presence of methanol orn-hexane as modifiers. In general, solutes diffusedmore slowly in the solutions than in pure super-critical carbon dioxide at the same conditions ofpressure and temperature. The diffusion coeffi-cients for the three solutes decreased as themethanol content rose and the effect of methanolcontent fell with increasing solvent density. Twomethanol concentrations were used to determinethe effect of the modifier concentration on the

Fig. 7. Diffusion coefficients of 1,2-dichlorobenzene measuredin the mixture of CO2 and methanol.

Fig. 9. Diffusion coefficients of 2-nitroanisole measured in themixture of CO2 and n-hexane.

L.M. Gonzalez et al. / J. of Supercritical Fluids 24 (2002) 219–229228

Fig. 10. Diffusion coefficients of 1,2-dichlorobenzene mea-sured in the mixture of CO2 and n-hexane.

The diffusion coefficients of tert-butylbenzeneand 2-nitroanisole are clearly reduced by the pres-ence of methanol. The diffusion coefficients of1,2-dichlorobenzene indicate the slight effect ofmethanol. Cussler [14] observed in supercriticalfluids that solvent molecules condense around thesolute, resulting in clusters of varying size. Thediffusion coefficient diminishes with increasingcluster size. Chemical association should occur fortert-butylbenzene and methanol, and for 2-nitroan-isole and methanol. The diffusion coefficient de-creases due to the increasing size and mass of theresultant cluster. 1,2-dichlorobenzene does not as-sociate with methanol or the size of the cluster isnot as pronounced as other solutes and the diffu-sion coefficient is slightly affected. Compared withthe n-hexane–carbon dioxide system, the interac-tions in the methanol–carbon dioxide system aremuch stronger.

The addition of n-hexane as a modifier oftencaused a decrease in the diffusion coefficient ratherthan an increase. The cluster formation betweensolutes and n-hexane is less important than for thesolutes–methanol systems. The dielectric constantand the dipole moment of n-hexane are clearlylower and then the solvation is less pronounced.Figs. 9–11 also show that the addition of n-hexaneat high pressures raises the diffusion coefficient oftert-butylbenzene at 323 K; the diffusion coefficientof 1,2-dichlorobenzene at 313 and 333 K; and thediffusion coefficient of 2-nitroanisole at 333 K. Asthe pressure is increased, the repulsive forces dis-rupt the weaker solvation.

The pressure dependence of the diffusion coeffi-cients is negative and the isothermic line is concavenear the critical pressure of the carbon dioxide. Inthe high pressure range the diffusion coefficientsconverge to a constant value. In general, thetemperature dependence of the diffusion coefficientis positive but this dependence is inverse at lowpressures in the carbon dioxide containingmethanol (10 mol%). At 333 K and with 10 mol%of methanol there is no change in the diffusioncoefficient of the three solutes with pressure. At-tracting forces at the highly compressible (lowdensity) region cause considerable clusteringaround solutes.

diffusion coefficient. The 5 mol% methanol concen-tration was chosen because it does not significantlychange the diffusivity. In contrast, the 10 mol% hasshown dramatic differences and complexity inmodifier effects. Surprisingly pressure had no effecton the diffusivities compared to pure carbon diox-ide at 333 K. The modifier effect is nonlinear inmodifier concentration, which is typical of thebehaviour of systems containing strong specificinteractions [13]. At some conditions, generallyhigh pressures, the effect of n-hexane affected byincreasing the diffusion coefficients.

Fig. 11. Diffusion coefficients of tert-butylbenzene measuredin the mixture of CO2 and n-hexane.

L.M. Gonzalez et al. / J. of Supercritical Fluids 24 (2002) 219–229 229

It could be argued that the difference in thediffusion coefficient between pure carbon dioxideand 10 mol% methanol at 333 K is due to the typeof interactions between carbon dioxide andmethanol because the three solutes present thesame behaviour. This indicates that the interac-tions between carbon dioxide and methanol arestronger than the interactions between solutes andsolvents. This behaviour is characteristic of asaturate interaction and is evident at all pressures.A better understanding of the interactions be-tween the CO2 and the methanol would help toexplain this unusual pressure dependence for dataat 333 K. Spectroscopic analysis must be used toprovide evidence of the formation of clustering. Itis possible to conclude that the diffusivities incarbon dioxide containing modifiers are influ-enced by chemical and physical forces.

The data that were measured in this studyprovide a useful insight into the molecular charac-teristics of interactions between carbon dioxideand modifiers. It will probably be necessary toobtain new data at different concentrations ofmethanol and at different temperatures to evalu-ate the pressure dependence.

Acknowledgements

Financial support from the PPQ2001-3619 pro-ject is gratefully acknowledged.

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