J. Phys. Chem. B 1997, 101, 2923-2928
CO2 Clustering of 1-Decanol and Methanol in Supercritical Fluids by Spin-Lattice Relaxation
2923 13C
Nuclear
Shi Bai,† Craig M. V. Taylor,† Fang Liu,† Charles L. Mayne,† Ronald J. Pugmire,‡ and David M. Grant*,† Departments of Chemistry and Chemical and Fuels Engineering, UniVersity of Utah, Salt Lake City, Utah 84112 ReceiVed: May 8, 1996; In Final Form: December 9, 1996X
A sapphire high-pressure NMR cell, capable of independently controlling sample pressure, temperature, and concentration, is used to measure 13C spin-lattice relaxation times for carbons 1, 5, and 9 of 1-decanol in dense carbon dioxide at pressure between 80 and 200 atm. These NMR experiments, carried out along four isotherms between 288 and 348 K, provide relaxation data for 1-decanol in liquid and supercritical fluid CO2. The nuclear spin-lattice relaxation mechanisms for carbons 1, 5, and 9 of 1-decanol as well as for the carbon nucleus in carbon dioxide of this mixture are discussed. The relaxation data are analyzed using a modified Stokes-Einstein-Debye equation, together with an AK model, that postulates the formation of CO2 clusters with the 1-decanol molecule in CO2-decanol mixture at supercritical and near-critical liquid densities. Such CO2 cluster formation with methanol molecules was also detected in earlier relaxation measurements in CO2-methanol mixtures at the comparable densities. Possible solvent clustering gradients along the aliphatic chain in 1-decanol in dense CO2 are also suggested.
Introduction An understanding of molecular interactions between solute and solvent molecules in supercritical fluids (SCF) is essential to an explanation of clustering phenomena, considered responsible for the unique SCF solvating characteristics compared to gases.1-3 Although both theoretical4-6 and experimental efforts7-12 have been made to increase the understanding of these phenomena, a complete picture of clustering in SCF CO2 is still evolving. The accumulation of experimental NMR relaxation data is expected to improve our physical picture of solvent clustering in SCF. Because the nuclear spin-lattice relaxation rates depend on the fluctuating molecular reorientation and molecular collision frequency, their measurement proves to be an effective method for studying such molecular interactions and dynamics in fluids.13 One of the advantages of utilizing NMR relaxation data is that they provide not only information, similar to optical methods, on overall molecular motions but also site-specific information on intramolecular motions. Nuclear spin-lattice relaxation rates have been measured under SCF conditions by Jonas et al.14 and Kobayashi et al.15-17 for various SCF mixtures. NMR chemical shift measurements18 were also used to relate 129Xe chemical shift data to the local solvent structures of SCF Xe. Attempts19 have recently been made in our laboratory to explore SCF fluid structures in a CO2-CH4 mixture. Information on the nature and average rate of molecular motions may be obtained by determining the nuclear spinlattice relaxation rates of nuclei in the molecules under investigation. The nuclear spin relaxation rate, 1/T1, depends on fluctuations in molecular reorientations as a consequence of molecular collisions, where T1 is the time constant defining the exponential return of a perturbed nuclear spin to its equilibrium state. Many nuclear spin interaction mechanisms affect T1 values. Among them, spin-rotation and dipolar interactions are the most important ones at sub- and supercritical densities †
Department of Chemistry. Department of Chemical and Fuels Engineering. X Abstract published in AdVance ACS Abstracts, February 1, 1997. ‡
S1089-5647(96)04048-5 CCC: $14.00
of CO2. Detailed descriptions of spin-rotation and dipolar interactions may be found in the review articles by Grant et al.13 and Jameson.20 Briefly, determination of NMR nuclear relaxation rates provides the angular momentum20 and rotational reorientation correlation times13 from spin-rotation and dipoledipole interactions, respectively. Spin-rotation interactions are directly related to molecular collision frequencies and depend on macroscopic properties such as fluid density and temperature. Dipolar interactions, however, are often related to fluid viscosity and temperature. Since the fluid viscosity may be treated as a function of local density in the compressible regions of CO2, both correlation times may be considered as functions of local densities. Therefore, clustering phenomena in SCF resulting in fluctuations of local density may in principle be observed by NMR relaxation measurements. In this paper, spin-lattice relaxation times (T1) are reported for carbons 1, 5, and 9 of 1-decanol in CO2 at liquid and SCF densities. There are several reasons to collect T1 data on this mixture. Complete detailed coupled spin-lattice relaxation studies21 have already been carried out on 1-decanol in conventional solvents in our laboratory. Previous studies provide a basis for analyzing 1-decanol molecular dynamics in SCF solvents using the T1 relaxation times measured under SCF CO2 conditions. Together with relaxation measurements22 of methanol in SCF CO2, these data increase our knowledge of molecular dynamics of alcohols in SCF CO2. The function of the hydroxyl group in solute-induced solvent clustering in SCF CO2 appears to be especially important. Experimental Section A sapphire high-pressure NMR cell, consisting of a movable piston inside the cell body to control the sample pressure, has been described previously23 and is used to measure 13C spinlattice relaxation times along with the associated NOE data. Two Isco pumps with better pressure control, calibration, and settings are used to replace the two Varian high-pressure pumps in our previous high-pressure apparatus. Natural abundance CO2 was obtained in high purity from Air Products. The 13C-labeled © 1997 American Chemical Society
2924 J. Phys. Chem. B, Vol. 101, No. 15, 1997
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1-decanols at positions 1, 5, and 9 described elsewhere21 were used once again in this study. The CO2-decanol mixture was prepared by introducing three 13C-labeled decanol samples (15 µL each) into the sapphire tube prior to assembly of the cell. CO2 was then introduced into the high-pressure cell at 288 K and 80 atm. The 13C spectra with gated proton decoupling indicated the total mole fraction of 1-decanols was 0.01 in CO2. A standard inversion recovery pulse sequence24 (10T1-πτ-π/2) is used to measure spin-lattice relaxation times, and the reproducibility of 13C T1 measurements is about 5%. The systematic errors, arising from local heating of the sample during acquisition, were minimized using gated decoupling instead of continuous broad-band decoupling. The magnitude of the nuclear Overhauser effect (NOE) effect is given by24
NOE(A{X}) ) I*A/I0A
(1)
where I* A is the integrated intensity of a decoupled spectrum with saturation of the nucleus X, and I0A is the equilibrium intensity of A in the coupled spectrum. The maximum possible NOE of 13C{1H} occurs when 13C and 1H relax only by the dipolar mechanism given by24
NOE(max) ) 1 + (γH/2γC) ) 2.988
(2)
Figure 1. Spin-lattice relaxation time (T1) isotherms as a function of sample pressure for a CO2-decanol mixture. The top, middle, and bottom parts of the plot show T1 for carbons 1, 5, and 9 of 1-decanol, respectively.
where γH and γC are the magnetogyric ratios for 1H and 13C, respectively. The NOE effect may be determined as a ratio of spectral intensities with proton decoupling to that of gated proton decoupling. Since the 13C in CO2 does not exhibit an NOE, its signal intensity may be used as a fiducial reference for the carbons of 1-decanol. The relative accuracies of NOE values are estimated to be within (5%. All nuclear spin-lattice relaxation and NOE measurements were carried out on a Varian UnityPlus 500 NMR spectrometer with a Nalorac 10 mm broadband probe. The variable temperature control unit in the spectrometer was calibrated with the standard temperature calibration samples of methanol and ethylene glycol. Densities of CO2 at a given temperature and pressure may be calculated using the software25 NIST-14 and SF-Solver for analyzing SCF’s; both programs gave comparable results. Densities of CO2-decanol mixtures are calculated using a procedure described by Pitzer et al.26 This approach is reasonably reliable when the mole fraction of one component is relatively small (0.01). Results and Discussion Spin-Lattice Relaxation Times. Four 13C spin-lattice relaxation time isotherms (288.2, 308.2, 328.2, and 348.2 K) have been measured for carbons 1, 5, and 9 of 1-decanol at pressures ranging from 80 to 200 atm. Spin-lattice relaxation times (T1) for CO2 were simultaneously determined. Minor differences have been noted between CO2 T1 in CO2-decanol mixtures and in neat CO2 at the same temperature and pressure as expected. The 13C spin-lattice relaxation processes in CO2 are dominated by spin-rotation interactions15,19,27 and will not be discussed here. T1 values for carbons 1, 5, and 9 of 1-decanol in CO2 are presented in Figures 1 and 2 as a function of fluid pressure and temperature. From Figure 1, it is noted that the T1 for all carbons decreases slowly with increasing pressure. As pressure increases at constant temperature, the viscosity of the mixture increases and, therefore, rotational reorientation correlation times of molecules increase. Spin-lattice relaxation times, T1, decrease as the reorientation correlation times of
Figure 2. Spin-lattice relaxation time (T1) of carbons 1, 3, and 5 in 1-decanol as a function of sample temperature.
molecules increase. These observations indicate the intramolecular dipole-dipole interactions dominate the nuclear relaxation processes in 1-decanol. NOE values were also measured along the isotherms and found to be independent of pressure within experimental errors. The average NOE values are 2.36 ( 0.12, 2.51 ( 0.24, and 2.41 ( 0.13 for carbon positions 1, 5, and 9, respectively. Thus, the predominant role of the intramolecular dipole-dipole interactions in decanol is again verified by the NOE measurements. All measured values are close to the maximum possible NOE value of 2.98 for 13C{1H} (cf. eq 2). From Figure 2, we note that T1 values vary more with temperature than with pressure. This is reasonable because
1-Decanol and Methanol in Supercritical Fluids
J. Phys. Chem. B, Vol. 101, No. 15, 1997 2925
the viscosity of CO2 changes more rapidly with temperature than with pressure for the temperature and pressure ranges in this study. A spin-lattice relaxation time order of [T1(C9) > T1(C1) > T1(C5)] for 1-decanol from previous study21 demonstrates that the central carbon (C5) has less trans-gauche isomerizational motion than do the outer carbons (carbons 1 and 9) in conventional viscous solvents. Anisotropic molecular motion in conventional solvents increases as one moves along the molecular chain from the OH group. It can be observed from Figure 2 that T1 values for carbon positions 1, 5, and 9 in SCF CO2 exhibit the following time relationships:
coefficient by assuming that each CH2 bead is roughly spherical and rotates randomly:30
T1(C9) > T1(C1) ≈ T1(C5)
τc ) 1/6D
The relationship between T1(C9) and T1(C1) exhibits the decrease expected from the anchoring effect of the OH group in the C1 position. The overall reduction in viscosity and the apparent variations of differentiating differences in motions between T1(C1) and T1(C5) leave these two relaxation times comparable in magnitudes in SCF mixtures. Significant Mechanism in Spin-Lattice Relaxation: Overall Rotational Motion. Both overall tumbling and internal rotations contribute to spin-lattice relaxation processes for each carbon-13 nuclear label. In general, the overall rotational motions of solute molecules depend on the intermolecular frictional forces between the solute and solvent molecules and, therefore, are dependent upon the solvent viscosity. The solvent viscoelastic response, in turn, is also dependent on various relaxation mechanisms of solvent molecules. Internal rotational motions including various local isomerization movements are driven by torsional forces.21 For the C-C-C-C linkages, the torsional forces are given by the Ryckaert-Bellemans (R-B) potentials.28 The trans-gauche barrier is 2.95 kcal/mol, much larger than the thermal energy kT. A Jorgensen 1-propanol torsional potential29 or a modified Jorgensen potential for 1-decanol21 is adequate to describe internal torsional potentials for the C-C-C-OH linkage. Here, the trans-gauche barrier is found to be 3.07 kcal/mol. Our previous study21 of 1-decanol in conventional solvents concluded that the overall rotation of the molecule is a sufficient explanation for spin-lattice relaxation in the chain center, but that the outer CH2 structural moieties for carbons 1 and 9 have more isomerizational motion than the center CH2 moiety at carbon 5. The rotational reorientation correlation time, τC, may be extracted from NMR spin-lattice relaxation time measurements, within the extreme narrowing limit, using the following expression:24
From the temperature dependence of rotational diffusion coefficients at fixed viscosity, one can determine effective rotational activation energies. Table 1 lists these energies for 1-decanol in CO2 at fluid viscosity of 0.09 cP, along with some of the previous activation energies. The new results are comparable with the previous energies for carbons 1 and 5, but reduced for carbon 9. This implies that the isomerization transition motion of 1-decanol in CO2 is relatively less significant than in diglyme. The apparent activation energies for carbons 5 and 9 are also much smaller than the trans-gauche barrier for C-C-C-C linkages (2.95 kcal/mol), and the apparent activation energy for carbon 1 is also much smaller than the isomerization transition barrier for the C-C-C-OH linkages (3.07 kcal/mol). As these lower activation energies would be closely related to internal rotational barriers if internal rotation dominates the relaxation, these data seem to indicate the average molecular structure of the 1-decanol molecules in CO2 at both liquid and supercritical densities remains relatively fixed. Therefore, the overall molecular tumbling motion appears to be the significant mechanism in spin relaxation processes of 1-decanol in CO2 near the critical density. CO2 Clustering with 1-Decanol and Methanol Molecules. The rotational reorientation correlation time, τc, can be expressed by a modified Stokes-Einstein-Debye (SED) equation:31
-1 13 ( C) ) VγC2γH2p2τC/r6 T1,DD
(3)
where r is the bond distance between 1H and 13C (measured as 1.085 Å), and V is the number of protons directly attached to the 13C nucleus, which is two for carbons 1, 5, and 9 in -1 13 1-decanol. The dipole-dipole relaxation rate, T1,DD ( C), may be obtained from the standard relationship between the overall T1 and NOE measurements:24
NOE ) 1 +
-1 13 ( C) γH T1,DD -1 2γC T (13C)
(4)
1,Tot
The reorientation correlation time obtained in this manner is an average assuming isotropic reorientation of the C-H vector. This correlation time may be related to a rotational diffusion
TABLE 1: Apparent Activation Energies (kcal/mol) for 1-Decanol in CO2 and Diglyme C position 1 5 9
xxa c
2.0(0.2) 1.3(0.2) 2.3(0.2)
yya
zza
this workb
1.6(0.3) 1.2(0.2) 2.1(0.2)
1.7(0.4) 1.2(0.2) 2.0(0.2)
1.7(0.2) 1.2(0.1) 1.1(0.1)
a The previous results for Cartesian modes and at fixed viscosity of 2.39 cP in diglyme. b The results obtained in CO2 at a viscosity of 0.09 cP. c The number in parentheses is a standard deviation.
τc )
ηVp f C + τ0 kT stick
(5)
(6)
where η is the fluid viscosity, Vp is the volume of solute molecule, fstick is a well-defined shape parameter dependent only on the structure of solute molecules,32 C is a boundary parameter dependent on the nature of the solute and solvent and upon their concentration, and finally τ0 is the free-rotor correlation time. The success of this model strongly depends on the selection of parameters C and fstick. Recently, Roy et al.32 noted that the Dote, Kivelson, and Schwartz (DKS) model31 is the best model for predicting reorientational correlation times for solutes with radii up to about 4.5 Å. Anderson and Kauffman33 further modified the calculation of the smallest Volume of free space per solVent molecule, ∆V, in the DKS model, and more recently, these two workers34 related fluid viscosity and the parameter C in the SED model to the local density by introducing a radial distribution function into the hydrodynamic model. These modifications33,34 by Anderson and Kauffman are referred to as the AK model. In the AK model, the viscosity for CO2 is expressed as a function of local density Fl12 by eq 7 described by Jossi et al.,35
[(η - η0)ξT + 1]1/4 ) 1.023 + 0.23364Fr + 0.58533Fr2 - 0.40758Fr3 + 0.093324Fr4 (7)
2926 J. Phys. Chem. B, Vol. 101, No. 15, 1997
Bai et al.
where Fr ) Fl12/Fc and ξT ) (TC/M3PC4)1/6. Fc, Tc, and Pc represent the critical density, temperature, and pressure for CO2, respectively. M is the molecular weight in the unit of g/mol. The local density of CO2 is related to the bulk density F by a radial distribution formalism:
Fl12 ) F[1 + F(g12(r))]
(8)
where F(g12(r)) is an integral equation in the pair distribution function, g12(r), over the spatial coordinates and r is the distance between solvent and solute molecules. F(g12(r)) is a measure of the excess solvent density near the solute molecule and is treated as an adjustable parameter in the AK model. When F(g12(r)) ) 0, the local density equals the bulk density, and when F(g12(r)) ) 1.0, the local density is twice the bulk density. In the AK model, the parameter C(Fl12), equivalent to C in the SED model, is also treated as a function of local density of CO2. According to the DKS model
C(Fl12) )
fslipVp fslipVp + γVp
Figure 3. Effects from temperature on the AK model is compared with that from the local density enhanced factor: F(g12(r)). It is apparent that the temperature effects on curve shapes are much smaller than that of F(g12(r)).
(9)
where fslip is a factor for the slip boundary condition whose value estimated from fstick by the method reported by Hu and Zwanzig36 and γ is defined as
γ)
( )[ ( ) ] Vp ∆V 4 Vp Vs
2/3
+1
(10)
In eq 10, Vs is the solute molecular volume and ∆V is the free space volume for a solvent molecule. For supercritical fluids in their compressible regions, a large variation in the free space is expected, and ∆V is given by eq 11 relating molecular weight (MW) and local density:
∆V )
MW - Vs Fl12
(11)
Therefore, the parameter C(Fl12) is expressed as a function of local density Fl12 though the free space volume ∆V. Combining eqs 6-11, the AK version of the SED equation may be expressed as34
η(Fl12)VP fstickC(Fl12) + τ0 τc ) kT
(6′)
Equation 6′ relates the reorientation correlation time, τc, to the CO2 local density at a given temperature. Since the nuclear spin relaxation measurements of 1-decanols in CO2 were carried out at four isotherms, the AK model was used numerically to examine the dependence of the reorientation correlation time on temperature and the factor F(g12(r)). The calculations show that the factor F(g12(r)) plays a significant role in the response of the τC vs bulk density (F) curve. However, the temperature dependence is relatively small in the AK model between 288 and 348 K. An example of these calculations is given in Figure 3. These small temperature effects allow one to use the temperature midpoint for the four isotherm temperatures in calculating the reorientation correlation time τc by eq 6′. Assuming on average that 1-decanol molecules remain in their most stable conformation, the parameter fstick and fslip are found to be 2.20 and 0.95, respectively. The van der Waals volumes are 189.0 Å3 for 1-decanol33 and 19.7 Å3 for CO2.37 The τ0 was chosen to be 0.35 ps based on fitting results from our lowviscosity data, with uncertainty of 0.07 ps. For various carbon
Figure 4. Experimental rotational reorientation correlation times for carbons 1, 5, and 9 in 1-decanol are compared with the predictions from the AK model at 318 K (the midpoint of the experimental temperature range). The solvent local densities for carbon positions 1 and 5 in 1-decanol are about 15% more dense than the bulk density. It appears that carbon 9 in 1-decanol experiences the bulk density.
positions in a CO2-decanol mixture, the τC against bulk density, F, plot is presented in Figure 4. The solid lines were calculated using eq 6′ with a set of input parameters of F(g12(r)) at the midpoint in the range of experimental temperatures. It is interesting to note that the local density of CO2 with carbons 1 and 5 would seem to be about 15% more dense than the bulk density. The uncertainty of this local density increase is estimated to be (5%. The CO2 local density in the region of carbon 9 is approximately the same as the bulk density. Since carbon 1 is closer to the hydroxyl group than carbon 9, it is reasonable to propose that the solute-induced CO2 clustering phenomenon arises from the specific interactions between OH groups and CO2. Examining Figure 4 carefully, one notes for bulk densities greater than 0.9 g/cm3 that the carbon dioxide clustering around carbon 5 appears to be slightly less dense than that around carbon 1, indicating a CO2 clustering gradient along the molecule. The data scattering at low-density region in Figure 4 may result from experimental errors in measuring the spin-lattice relaxation time at the low densities. By performing a comparison experiment on trans,trans-1,4-diphenylbutadiene (DPB) solute in CO2, Anderson and Kauffman34 also observed that CO2 solvent clustering only occurs in the vicinity of trans-4(hydroxymethyl)stilbene (HMS) molecules. Because the extended π-electron systems existing in DPB and HMS are similar,
1-Decanol and Methanol in Supercritical Fluids
J. Phys. Chem. B, Vol. 101, No. 15, 1997 2927
Figure 5. Experimental rotation reorientation correlation times for methanol in a CO2-methanol mixture (mole percent of methanol is 4%) are plotted with the predictions by the AK model at 302 K (the midpoint of the experimental temperature range). The enhanced local solvent density is clearly noted for methanol in this mixture.
Anderson and Kauffman concluded that the OH group in HMS is responsible for the association between the solute and solvent molecules. The one-to-one association between solute and solvent molecules may initiate further CO2 clustering whenever strong many-body interactions affect the solvent structure in supercritical fluids in the compressible density region. The CO2 clustering gradients observed along the aliphatic chain of 1-decanol molecules in this study appear to support the observations by Anderson and Kauffman. To verify further the importance of alcohol enhanced clustering, the same procedure was applied to a CO2-methanol mixture, where a specific association between CO2 and CH3OH has been observed also by the IR studies.8 Such solvent-solute interactions may initiate CO2 solvent clustering.34 The spin-lattice relaxation time measurements were performed for this mixture in our laboratory, and the results are reported elsewhere.22 Calculations of fstick and fslip for methanol are found to be 0.69 and 0.10, respectively, and the van der Waals volume is 41.8 Å3.37 The τc data for methanol, obtained from spinlattice relaxation and NOE measurements, is given as a function of bulk density in Figure 5. The free-rotor correlation time is determined to be 0.17 ( 0.08 ps by fitting the low-density data. The low-pressure limit free-rotor correlation time can be calculated using the following expression:38
τ0 )
()
2π I⊥ 9 kT
1/2
are the free molecules would be enough to stimulate such solvent cluster formation.34 The data, presented here for methanol, provide direct evidence for differential CO2 clustering near solute molecules and for the importance of hydrogen bonding with the OH group in alcohols. More Evidence for the Formation of CO2 Clusters in the Vicinity of Methanol. As stated above, NOE measurements allow the separation of the dipole-dipole contributions to spinlattice relaxation rates from other mechanistic contributions. For methanol, the remaining relaxation contributions result essentially from the spin-rotation mechanisms described previously.22 These spin-rotation relaxation rates allow one to calculate an angular momentum exchange correlation time, τJ, which is strongly dependent on the fluid density. Methanol is a quasisymmetric top molecule, but the relation between τJ and spinrotation relaxation rates for symmetric top molecules may be 39 is used as a good approximation for TSR 1 . The expression
1/TSR 1 )
(13)
where R ) p2/(2kTI⊥) and I⊥ is the perpendicular part of the moment of inertia for methanol. The effective spin-rotation, Ceff, may be expressed as
Ceff2 ) k1Ca2 + k2CaCd + k3Cd2
(14)
In eq 14, the structure parameters, ki, only depend on molecular structure. Ca and Cd are the isotropic and anisotropic components of the spin-rotation tensor. According to earlier estimates,22 based on the experimental chemical shift tensor measurements for methanol, Ca and Cd were found to be 6.2 and -9.5 kHz, respectively. Therefore, in principle, an experimental angular momentum correlation time, τJ, may be estimated using eq 13. Since τJ is linearly related to the time between molecular collisions, τBC, one may calculate τJ using a gas kinetic theory. The slope of this linear relationship, called an effective collision number and referred to as Z,40 provides the average number of collisions needed for an effective molecular angular momentum exchange. This number is found to be between 1.4 and 3.4 for many collision pairs (cf. Table 3 in ref 40). In the use of a hard-sphere model (HSM) for calculating cross sections, choosing the effective collision number of 2 appeared to be a good approximation in the work of Maryott, Malmberg, and Gillen,40 and therefore, this value is used in the following discussion. The expression for computing τJ is given by15
(12)
where I⊥ is the perpendicular component of the moment of inertia for methanol molecules. The calculated τ0 from eq 12 is 0.20 ps, which agrees well with the 0.17 ps from fitting the low-density data. A 35 ( 10% increase in the CO2 local densities in the vicinity of a methanol molecule is noted in Figure 5. It is not surprising that CO2 clustering is more dense in methanol than in 1-decanol. A possible explanation for the enhancement of CO2 density near a methanol molecule is that CO2 clustering may completely surround a methanol molecule. However, the solvent clustering around C1 of 1-decanol is restricted in the domain of the aliphatic chain of 1-decanol. It is interesting to note that the hydrogen bond aggregations are formed among the methanol molecules in a CO2-methanol mixture.8,22 It is estimated that only 2% of methanol molecules are the free molecules for a 4% CO2-methanol mixture.8 Since the methanol molecules only initiate the CO2 solvent clusters, even 2% methanol that
2π2 C 2τ R eff J
τJ ) Z/FνjσK
(15)
where F is fluid density, νj is the average velocity of molecules, and σK is the kinetic collisional cross section between solute and solvent molecules. Both νj and σK may be estimated from molecular properties of methanol and CO2. If the density term, F, in eq 15 is replaced by a local density (cf. eq 8), the estimated τJ becomes a function of the excess solvent density parameter, F(g12(r)). In this case, eq 15 becomes
τJ )
Z F(1 + F(g12(r)))νjσK
(16)
A plot is given in Figure 6 comparing the experimental τJ at different temperatures for methanol in CO2 along with the estimated τJ using eq 16 vs the bulk density. All estimated τJ values (represented by solid lines) are calculated at 302 K, which is the midpoint for the temperature range. The symbols represent the experimental data obtained at the various temper-
2928 J. Phys. Chem. B, Vol. 101, No. 15, 1997
Bai et al. DE FG02-94ER14452. This work is also supported at Los Alamos National Laboratory by EPA Environmental Technologies Initiative through Grant EPA/IAG DW89936500-01. References and Notes
Figure 6. Experimental angular momentum correlation times for methanol in CO2-methanol mixture are compared with the calculated correlation times using eq 15. A 30% local solvent density enhancement is noted once again for methanol in CO2.
atures. Figure 6 demonstrates that there is good agreement between theoretical and experimental data when a 30% increase in local density is employed in the predictions of τJ. This observation coupled with the 35% increase, obtained from the reorientation correlation method described above, provides additional evidence for the formation of CO2 solvent clustering in the vicinity of solute molecules. Specific interactions between methanol and CO2 at SCF conditions have been noted by Smith et al.8 using IR results. Similar interactions between ethanol and CO2 were reported by Gupta et al.41 using cross virial coefficient measurements. The results represented here further demonstrate the existence of specific interactions between alcohol molecules and CO2 at SCF or near-critical liquid conditions. Supposedly, these interactions are induced by the hydroxyl functional group present in alcohol molecules. Conclusion The nuclear spin-lattice relaxation and NOE values for carbon positions 1, 5, and 9 of 1-decanol in CO2 at liquid and supercritical fluid densities have been approximated for the first time. The results of these measurements indicate that dipoledipole interactions dominate the spin-lattice relaxation processes in 1-decanol. The dominant spin relaxation mechanism in CO2 at the densities studied is the spin-rotation interaction. From the temperature dependence of the diffusion coefficients, we conclude that the overall molecular motion is the significant mechanism for dipole-dipole relaxation in a CO2-decanol mixture at liquid and supercritical fluid densities. The AK model successfully describes the solute-induced clustering formation in the compressible regions of supercritical CO2. Rotational reorientation correlation times derived from the relaxation time measurements suggest the formation of CO2 solvent clustering near the decanol molecules, but an effective density gradient appears to be observed for differential clustering along the 1-decanol aliphatic chain. In 1-decanol, the intensity of the solvent clustering is higher at the hydroxyl end than the methyl end, confirming that the OH group is likely responsible for the specific interactions between CO2 and alcohol molecules. Clustering is also observed for methanol molecules in CO2methanol mixtures at comparable density ranges based on both angular momentum and reorientation correlation time data. The density enhancement factors obtained from these two methods agree well one with another. Acknowledgment. This work was supported at the University of Utah by the Basic Energy Sciences at DOE through Grant
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