Solvent e†ect on monomer–dimer equilibrium in supercritical Ñuid :Spectroscopic and thermodynamic studies

Jie Lu, Buxing Han* and Haike Yan

Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100080, China.E-mail : hanbx=pplas.icas.ac.cn

Received 26th October 1998, Accepted 2nd December 1998

The monomerÈdimer equilibrium of lauric acid in supercritical was studied at di†erent temperatures andCO2pressures using FTIR spectroscopy. The equilibrium constant and thermodynamic properties of thedimerization were obtained based on the spectroscopic determinations. It has been found that Ñuid densityplays an important role on the dimerization. Thermodynamic studies on the equilibrium suggested that theremay be di†erential solvent e†ects on the monomer and dimer. At lower density, the solvent aggregates aboutthe solute and, therefore, the di†erential solvent e†ect is signiÐcant. With increase in density the solventÈsoluteclustering and di†erential solvent e†ect decrease, and the supercritical solution becomes more homogeneous.

IntroductionSupercritical Ñuids (SCFs) have a strong ability to dissolvelow volatile substances and can change their physicochemicalproperties with small changes in pressure and temperature,especially in the near-critical region. In the past, intermolecu-lar interactions in systems containing SCFs have been investi-gated extensively using various techniques.1h12 Someresearchers have studied intermolecular interactions in super-critical Ñuids using the IR technique,13h16 which has provento be a powerful tool for gaining insight into the microstruc-ture of supercritical solutions. For instance, Gupta et al. inves-tigated the solvent e†ect on hydrogen bonding of methanoland triethylamine throughout the gas, supercritical, and liquidstates in the relatively inert solvent SF6 .13

is nontoxic, nonÑammable, cheap and with convenientCO2critical temperature and pressure, which makes it a popularsolvent in practical applications. Therefore, the solvent e†ectin supercritical is of great interest in practice. InCO2 (scCO2)this work, we selected a long-chain fatty acid, lauric acid, as amodel low volatile solute in to study the solvent e†ectscCO2on the monomerÈdimer equilibrium using FTIR spectroscopy.

Experimental

1 Materials

([99.995% purity) was provided by Beijing AnalysisCO2Instrument Factory. Lauric acid (analytical grade, BeijingChemical Plant) was recrystallized repetitively from ethanolprior to use and the melting range of the puriÐed product was43.4È44.1 ¡C. Ethanol and diethyl ether (analytical grade,[99.0%, Beijing Chemical Plant) were used as received.

2 Apparatus and procedures

All the IR spectra were recorded by a PerkinÈElmer 2000FTIR spectrometer (number of times scanned : 32, resolution :4 cm~1). A Digital PC was connected to perform all the dataanalysis. A stainless steel cell with 0.95 cm path length and0.87 cm3 constant internal volume was used in the experi-ments. The cell has two ZnS windows, which are transparent

over the full range of 4000È800 cm~1. The outside of the cellbody was coiled with electrical heating wire and heat insula-tion material. The contents of the cell were stirred by a smallsteel bead. The FTIR apparatus is shown in Fig. 1. Pressuredetermination was carried out with a pressure sensor (ICSensors Co., Model 93) and a digital indicator with a preci-sion of ^0.2 bar in the range of 0È200 bar. The cell tem-perature was monitored and controlled with a platinum 100resistance thermometer and a temperature controller (XMT,Beijing Chaoyang Automatic Instrument Factory). The tem-perature measurement uncertainty was within ^0.2 ¡C andthe temperature Ñuctuation of the cell was less than ^0.1 ¡C.

The desired amount of lauric acid in diethyl ether wasadded to the clean optical cell. The solvent was then removedunder vacuum. The cell was connected to the apparatus asshown in Fig. 1. Ñowed slowly through the cell to replaceCO2air in the pipe line and the cell. The cell was then Ðlled with

to the desired pressure after the cell temperature wasCO2stable. The spectrum was recorded after the dimerization reac-tion reached equilibrium. In the constant density measure-ment, the cell temperature was controlled originally at thelowest value (308.15 K) and a certain amount of wasCO2loaded into the cell. The FTIR spectrum was recorded and

Fig. 1 Schematic diagram of the apparatus for FTIR spectroscopicmeasurement of supercritical solutions. (1) Gas cylinder ; (3) high pres-sure pump; (5) pressure gauge ; (9) FTIR spectrometer ; (10) high-pressure IR cell ; (11) thermometer ; (13) temperature controller ; (14)vacuum pump; (2), (4), (6), (7), (8), (12) values.

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then the cell temperature was increased to the next valuewithout further addition of The concentration of lauricCO2 .acid in the study was Ðxed at 2.0 ] 10~3 mol L~1. Because ofthe low concentration of solute in all experiments, the densityof the mixed Ñuid was assumed to be the same as that of thepure which can be obtained from the empirical equationCO2 ,of Huang.17

Results and discussion1 FTIR spectrum

Two organic acid molecules can form a hydrogen bondedcyclic dimer by hydrogen bonding in the following way :14

It is known experimentally that has a transparentCO2spectrum over the range from 2000È1600 cm~1, which corre-sponds to the characteristic vibration of the carbonyl group.Fig. 2 shows the typical determined and deconvoluted FTIRspectra of the lauric acid in supercritical from 1850 cm~1CO2to 1650 cm~1. In two absorption bands of lauric acidCO2can be observed in the spectral region of interest. Similarly,Tsugane et al.14 studied the dimerization of benzoic acid inpure supercritical The frequencies of the CxO stretch-CO2 .ing vibration of the monomer and the dimer are 1745 and1705 cm~1, respectively. Based on the study by Tsugane etal.14 and other work18h20 for the dimerization of organic acid,the two deconvoluted absorption bands are assigned to theCxO fundamental stretching vibration of monomer anddimer of lauric acid, respectively. The fundamental stretchingvibration band for the free CxO group appears at 1764cm~1, while that for the hydrogen bonded CxO groupappears at 1716 cm~1.

2 Molar integrated absorption coefficient

The quantitative investigation of the monomerÈdimer equi-librium of lauric acid is based on the known absorption coeffi-cient (e) and absorption intensity of each of the bands fromthe LambertÈBeer law. In the work, e is deÐned as its inte-

Fig. 2 Determined and deconvoluted spectra of acidscCO2Èlauricat 308.15 K (concentration of lauric acid 2] 10~3 mol L~1).

grated form

e \P

a(l) dl (1)

in which l is wavenumber and a(l) is the absorption coefficientat wavenumber l.

In some supercritical Ñuid systems, the molar absorptioncoefficients have been found to be dependent on the Ñuiddensity in SCFs, but the temperature e†ect on e can be negligi-ble.21,22 For the equilibric system studied in the work, it isdifficult to obtain the value of e of each species (monomer anddimer) according to the traditional method (working curvemethod) because the equilibric concentration of any speciescannot be known. A normalization method has been used todeal with the polymer solutions containing two equilibricspecies with Ðxed total concentration by Lichkus andPainter.23 In this work, the method was used to obtain themolar integrated absorption coefficients of monomer anddimer at di†erent densities of (o) and then the densityCO2dependence of e was investigated. IR spectra of lauric acid atdi†erent densities were determined at temperatures rangingfrom 308.15 to 324.15 K and the representative spectra at a

density of 15.1 mol L~1 are shown in Fig. 3. The bandsCO2of monomer and dimer were deconvoluted and the corre-sponding integrated absorbance areas were thus obtained.According to the material balance equation it is known that

Amem b

]Aded b

\ C0 (2)

where A refers to the integrated absorption area of the IRband ; b is the path length of cell ; subscripts m and d stand forthe monomer and dimer, respectively ; is the total concen-C0tration of lauric acid loaded into the cell. Eqn. (2) is rear-ranged to

Ad \ ed bC0 [edem

Am (3)

At a given density, we obtain a series of and and plotAd Am ,the curve of against The intercepts and slopes of theAd Am .plots are and respectively. Thus, the value of(ed bC0) [(ed/em),

and at di†erent densities can be obtained. Fig. 4 showsed emthe relationship between e of monomer and dimer and thedensity of Correlating and with density yieldsCO2 . ed em

em\ 17 910[ 454o (4a)

ed\ 2466 ] 878o (4b)

in which the unit of o is mol L~1.The values of and of lauric acid in liquid wereem ed CCl4also determined according to the method described above.

The and values were calculated to be 28 300 and 8660 Lem edmol~1 cm~1, respectively.

Fig. 3 FTIR spectra of acid at density of 15.1scCO2Èlauric CO2mol L~1 and at di†erent temperatures.

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Fig. 4 Plots of against of lauric acid in at di†erentAd Am scCO2density.

3 Monomer–dimer equilibrium constant

The monomerÈdimer equilibrium of lauric acid can be moni-tored using FTIR spectroscopy and the equilibrium constant

can be calculated by the LambertÈBeer law(Kc)

Kc \[dimer]

[mono]2\

(Ad/2ed b)

(Am/em b)2(5)

where [dimer] and [mono] denote the equilibric concentra-tions of dimer and monomer, respectively.

We determined for the dimerization of lauric acid at dif-Kcferent pressures and temperatures in and investigatedscCO2the solvent e†ects on the equilibrium in supercritical solutions.

3.1 Pressure e†ect on the equilibrium constant

Fig. 5 illustrates some FTIR spectra of lauric acid in atscCO2308.15 K and at di†erent pressures. It is obvious that the for-mation of dimer is disfavored by increasing pressures.CO2The equilibrium constants for dimerization of lauric acid in

calculated from eqn. (5) are given in Fig. 6. lnscCO2 Kcdecreases sharply with pressure at pressures lower than 90bar. It should be noted that the density of also undergoesCO2a similar sharp increase over the same pressure range. The

densities at corresponding pressures are also plotted inCO2

Fig. 5 FTIR spectra of lauric acid in at 308.15 K.scCO2

Fig. 6 Pressure dependence of ln and density at 308.15 K.Kc CO2

Fig. 6. Fig. 7 shows the linear relationship between ln andKcthe density of It can be concluded that the supercriticalCO2 .Ñuid density plays a very important role in the equilibrium.The increasing density shifts the equilibrium towards themonomer form. The results may be explained by the solventÈsolute clustering in the supercritical solutions. At low den-sities, the solventÈsolute clustering is more remarkable thanthat at higher densities, which results in the decreases in activ-ity coefficients of monomer and dimer, and the decreased Kc .The dimerization will become more difficult when more CO2molecules are involved in the solvation shell and surround thesolute molecule.

3.2 Temperature dependence of equilibrium constant andthermodynamics of the dimerization

In order to investigate the dimerization in more detail, westudied the temperature dependence of and the thermody-Kcnamic properties of the process based on the above spectro-scopic experiments. Typical spectra investigating thetemperature dependence have been given in Fig. 3.

Under the isochoric condition, the standard internal energychange (*U0), standard free energy change (*F0) and standardentropy change (*S0) can be obtained from the equilibriumconstants determined experimentally.

The value of *F0 for the equilibrium can be calculatedaccording to

(*F0)T, V \ [RT ln Kc (6)

where R denotes the gas constant, and T stands for absolutetemperature.

The calculation of *U0 is based on the temperature depen-dence of at constant density according to the followingKc

Fig. 7 Relationship between ln and the density of atKc CO2308.15 K.

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Fig. 8 Plots of ln against 1/T in di†erent solvents.Kc

thermodynamic relationship

(ln Kc)V \ [*U0RT

] c (7)

Fig. 8 shows plots of against 1/T in at di†erentln Kc scCO2densities. The equilibrium constants of the dimerization inliquid at di†erent temperatures were also determinedCCl4and the results are given in Fig. 8. In liquid the experi-CCl4 ,ments were carried out at the isobaric condition. Thus in*U0eqn. (7) should be replaced by *H0. The di†erence in *U0 and*H0 is very small in the incompressible liquids and, therefore,

Table 1 *U0 and *S0 of the dimerization of lauric acid in varioussolvents

oCO2/ *U0/ *S0 (308.15 K)/

Solvent mol L~1 kJ mol~1 J mol~1 K~1

scCO2 7.9 [31.5 [1629.0 [36.3 [175

10.5 [31.0 [15412.8 [33.2 [15615.1 [31.6 [146

Liquid CCl4 È [57.2 [274

Fig. 9 *S0 of dimerization of lauric acid in di†erent solvents.

*U0 in liquid can also be calculated from eqn. (7) with aCCl4reasonable approximation. It is shown clearly from Fig. 8 thatis the linear function of 1/T in all the solvents studied inln Kcthis work. Thus, *U0 is independent of temperature over the

range investigated and the slopes of the curves are [*U0/R,which can be used to calculate *U0. *U0 values obtainedfrom Fig. 8 and eqn. (7) are given in Table 1.

It is apparent that the dimerization of lauric acid in an exo-thermic process and the *U0 values in all the solvents studiedin this work are negative (as shown in Table 1). The *U0value in liquid is more negative than those in atCCl4 scCO2all densities. One reasonable explanation for this may be that

hydrogen bonds with monomer, stabilizes the monomer,CO2and thus decreases the internal energy di†erence of monomerand dimer. On the other hand, the values of *U0 in doscCO2not vary remarkably over the wide density range. It demon-strates that the hydrogen bond energy in the dimer of lauricacid changes little with the solvent density. The result is con-sistent with that proposed by Gupta et al.24 based on thestudy on the hydrogen bonding of methanol and triethylaminein scSF6 .

The *S0 value can be calculated from and *U0 at corre-Kcsponding conditions according to the thermodynamicrelationship

*S0 \ [R ln Kc ] *U0/T (8)

Fig. 9 shows the values of *S0 at di†erent temperatures inand Table 1 also gives *S0 at 308.15 K. TherescCO2 CCl4 .

are three important phenomena associated with the resultsgiven in Fig. 9 and Table 1. Firstly, *S0 in is at leastscCO2100 J mol~1 K~1 less negative than that in liquid ItCCl4 .may also result from the hydrogen bonding interactionbetween and monomer, which greatly decreases theCO2entropy of monomer and, therefore, *S0 of the dimerization.Secondly, *S0 in displays a small tendency towardsscCO2less negative values with an increase in density. The resultsmay be attributable to the di†erential solvent e†ect in com-pressible supercritical Ñuids. Di†erential solvation has beenobserved for the azo-hydrazone tautomeric equilibrium of 4-(phenylazo)-1-naphthol in liquid and supercritical andCO2compared with the case for supercritical TheCHF3 C2H6 .25large di†erences of solutes in polarity and acidityÈbasicity areconsidered to be the reasons for the equilibrium shifts. Simi-larly, a concept of preferential solvation has been presented byother researchers.24 For this case, the di†erential solvent e†ectcan also be thought of as preferential clustering of solventabout the di†erent solutes. Two separate monomer moleculesmay be solvated by more e†ectively than one dimer mol-CO2ecule due to the larger molecular surface of the former. Atlower Ñuid density, has strong tendency to aggregateCO2about the solutes and the solution is highly inhomogeneous.Therefore, the di†erential solvent is more remarkable underthis condition. With the increase in density, the clustering isless important and the solution becomes more and morehomogeneous. Apparently, the di†erential solvent e†ectdecreases and, therefore, the di†erence in the solvent structureabout the monomer and dimer also decreases. Finally, theabsolute values of *S0 decreases with enhanced temperaturein all the solutions studied. At higher temperatures, the abso-lute entropy of monomer and dimer will increase. Because ofthe larger molecule size of the dimer, one can expect that theincrease in entropy for dimer will be less than the sum of theincreases for two separate monomers.

3 ConclusionA linear relationship has been found between and theln Kcdensity of over density ranging from 7.9 to 17.7 mol L~1CO2at 308.15 K. Solvent aggregation around the solute in super-

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critical solutions has been demonstrated. At low densities, thesolventÈsolute clustering is more remarkable than that athigher densities, which results in the decrease in activity coeffi-cients of monomer and dimer and the is thus decreased.KcThe thermodynamic studies suggested that mayCO2hydrogen bond with monomer at low densities studied and,moreover, the hydrogen bond strength between monomer and

changes little with the change in Ñuid density. hasCO2 scCO2a di†erential solvent e†ect on the monomerÈdimer equi-librium. Two separate monomer molecules may be solvatedby and become more oriented than one dimer moleculeCO2due to the larger molecular surface of the former. At lowerÑuid density, has strong tendency to aggregate about theCO2solutes and the di†erential solvent is more remarkable. Withan increase in density, clustering is less important and the dif-ferential solvent e†ect decreases.

AcknowledgementThe authors are grateful to NNSFC for Ðnancial support (No.29725308, 29633020).

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