9Be NMR Relaxation Measurements of Bis(acetylacetonato)beryllium

Supercritical Fluid Research Center, National Institute of Advanced Industrial Science and Technology (AIST), Nigatake 4-2-1, Miyagino-ku, Sendai 983-...
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11114

J. Phys. Chem. B 2002, 106, 11114-11119

9Be

NMR Relaxation Measurements of Bis(acetylacetonato)beryllium(II) in Liquid and Supercritical Carbon Dioxide: A Clear Evidence of Near-Critical Solvation Effect on Rotational Correlation Time Tatsuya Umecky,*,†,‡ Mitsuhiro Kanakubo,*,† and Yutaka Ikushima† Supercritical Fluid Research Center, National Institute of AdVanced Industrial Science and Technology (AIST), Nigatake 4-2-1, Miyagino-ku, Sendai 983-8551, Japan, CREST, Japan Science and Technology Corporation (JST), Honcho 4-1-8, Kawaguchi, Saitama 332-0012, Japan, Department of Chemistry, Graduate School of Science, Tohoku UniVersity, Aramaki, Aoba-ku, Sendai 980-8578, Japan ReceiVed: December 31, 2001; In Final Form: July 24, 2002

9

Be NMR longitudinal relaxation times (T1) of bis(acetylacetonato)beryllium(II) in liquid and supercritical carbon dioxide were precisely measured at four different temperatures of 293.4, 313.2, 332.9, and 351.4 K over a wide pressure range from 8.0 to 25.0 MPa. Because the quadrupolar 9Be relaxes only through intramolecular interaction with the electric field gradient, the rotational correlation time (τr) of the complex was purely determined from T1 with a known value of the quadrupole coupling constant. It was observed that τr increased with increasing density of CO2 at each temperature. The plot of τr vs η/T, where η is the viscosity of CO2 and T is the thermodynamic temperature, gave a straight line at each temperature except for in the near-critical regime. This fact indicates that the viscosity of solution is the predominant factor in the change in τr of the complex in CO2. At near-critical temperatures of 313.2 and 332.9 K, moreover, it was clearly found that τr deviates upward beyond the experimental errors at intermediate η/T. The upward deviation was discussed in terms of solute-solvent interactions.

1. Introduction Supercritical carbon dioxide (SC-CO2), of which the critical temperature (Tc ) 304.2 K) and pressure (pc ) 7.38 MPa)1 are relatively moderate, is of growing importance as one of the “green”2 solvents. A variety of attempts to use SC-CO2 as a reaction, separation, and extraction media have been made.3,4 It is worth, in particular, noting that unusual reaction products, rates, and selectivities in chemical reactions were frequently observed.5 To characterize such unusual behaviors in SC-CO2, it will be necessary and important to understand the solvent’s roles in terms of intermolecular solute-solvent interactions. Over the past decade, many researchers have studied the timeaveraged solvation structures around probe molecules in SCCO2 by observing various spectral energy shifts as a function of pressure (i.e., solvent density).11-18 It has become apparent that, under such conditions, the densities of solvent molecules surrounding solutes are typically in excess of the values that would be expected on the basis of the bulk properties. The maximum solvent density enhancement is frequently observed at bulk density much less than the critical density. As yet, however, there have been only a few reports19-22 discussing quantitatively the dynamic motions of solute molecules in SCCO2 and the relation of these motions to the solvation phenomena. The rotational motion of a molecule in solution is very sensitive to its surroundings. Consequently, the determination of the rotational correlation time (τr) can provide meaningful * To whom correspondence should be addressed at the Supercritical Fluid Research Center. E-mail: [email protected]; [email protected]. Fax: +81-22-237-5224. † Supercritical Fluid Research Center and CREST. ‡ Tohoku University.

information about the solute-solvent interactions. Bright et al.19,23 determined the rotational correlation times of two fluorescence probes in CO2, N2O, and CF3H. The observed rotational correlation time increased remarkably at relatively low density and remained unchanged at higher density. Heitz and Maroncelli,24 on the other hand, observed a different behavior for the rotational correlation times of three fluorescence probes in CO2. In their report, it was shown that τr increased with increasing density and did so nearly linearly with the macroscopic viscosity of the solvent. A similar behavior for τr was observed for another two fluorescence probes by Anderton and Kauffman.20 More recently, Randolph et al.21 using EPR spectroscopy determined the rotational correlation time of a copper β-diketonate complex with fluorinated substituents in CO2. These authors observed an anomalous increase of τr with decreasing density, consistent with the findings of Bright and co-workers.19,23 The strange behavior of τr, as mentioned by Randolph et al.,21 still remains “physically unreasonable”. The inconsistency in the above studies has strongly prompted us to examine profoundly how effectively the rotational correlation time in SC-CO2 changes with density and temperature. NMR longitudinal relaxation times (T1) have frequently been used to determine rotational correlation times (τr) of molecules in liquid25 and SC-CO226-31 solutions. Two or three practical approaches have been proposed for obtaining τr from T1 appropriately. One such approach involves the measurement of T1 for a magnetic dipolar nucleus, such as 13C, together with a nuclear Overhauser enhancement (NOE) factor between the observed and coupled spins.28-30 The NOE factor can determine the contribution to T1 which purely arises from the magnetic dipole-dipole interaction.32,33 If the necessary coupled spins are unavailable, the isotope enrichment technique may some-

10.1021/jp0147271 CCC: $22.00 © 2002 American Chemical Society Published on Web 10/04/2002

9Be

NMR Relaxation Measurements

J. Phys. Chem. B, Vol. 106, No. 43, 2002 11115

Figure 1. Molecular structure of bis(acetylacetonato)beryllium(II), [Be(acac)2].

times be used effectively.34-36 One of the other methods involves the measurement of T1 for a quadrupolar nucleus, which relaxes only through intramolecular interaction with the electric field gradient at the nucleus of interest. If the proportionality constants of the quadrupole coupling constant and asymmetry parameter are known, then τr can also be determined from the quadrupolar relaxation time.26, 37-40 This latter approach forms the basis of the present study, in which we focus on the 9Be quadrupolar relaxation times of bis(acetylacetonato)beryllium(II), [Be(acac)2], in CO2. With this approach, the value of the 9Be quadrupole coupling constant, which we have previously obtained from a combination of the first two approaches mentioned above, i.e., the dual-spin-probe technique,39 allows τr of the complex molecule to be precisely determined. We then examine τr as a function of density at four different temperatures, 293.4, 313.2, 332.9, and 351.4 K. The present metal complex (Figure 1) is symmetric, almost spherical, and much larger than the solvent molecule as well as being sufficiently soluble in CO2. Moreover, it has been found that τr in liquid solutions was almost expressed by the conventional hydrodynamic model.39 Hence, we expect that the present complex should be one of the most desirable model solutes for examining rotational dynamics in SC-CO2. 2. Experimental Section 9Be

NMR relaxation times (T1) of [Be(acac)2] in CO2 were determined at four temperatures of 293.4, 313.2, 332.9, and 351.4 K over a pressure range from 8.0 to 25.0 MPa. The highpressure NMR system employed in this work has previously been described in detail.41,42 Here, we denote only the modifications and improvements. A batchwise high-pressure NMR cell was shown in Figure 2. The high-pressure cell was made of a strong, easy-machinable, and ideally nonmagnetic poly(etherether ketone), which was first introduced by Wallen et al.43 The high-pressure cell had a very simple structure, consisting of the main three parts, viz., an outer tube, inner tube, and head cap. The outer tube had a 10 mm outer diameter (o.d.) and 5.2 mm inner diameter (i.d.). The inner tube had a 5.0 mm o.d. and 1.0 mm i.d., and worked as a spacer, which can effectively prevent harmful convection arising from the temperature gradient along the z axis in the high-pressure cell, and thus, it maintained a very homogeneous sample temperature. The temperature fluctuations preliminarily measured with a calibrated thermistor thermometer (TAKARA, D641) were found within (0.1 K in the range of 293.4-332.9 K and within (0.2 K at 351.4 K. The inner volume of the high-pressure cell was ∼1.02 cm3, though only a part of the sample solution was observed. The high-pressure cell withstood temperatures and pressures, at least, up to 373 K and 35 MPa, respectively. The sample solutions were prepared in the high-pressure cell by the following procedure. A 10-5 mol (2.1 mg) of [Be(acac)2] was exactly put into the cell, and then air containing paramagnetic oxygen inside the cell was carefully replaced by ca. 3 MPa

Figure 2. Side cut-away view of the high-pressure NMR cell.

of CO2 gas several times. After replacing the air, CO2 was pressurized into the cell to a desired pressure with a syringe pump (ISCO 260D). Then, the high-pressure valve between the cell and syringe pump was closed. The sample thus prepared was allowed to stand for several hours at pressures less than 10 MPa and, at least, 1 h at higher pressures. It was confirmed that the sample solutions attained equilibria by comparing the signal integrals before and after each relaxation measurement. The sample concentrations were kept 10 mmol dm-3 or less in all of the measurements. Because in this concentration range no apparent concentration dependence of T1 was observed at any pressures, the measured T1 was regarded as the infinitely diluted value. An absolute pressure of sample solution was measured with a precise digital indicator (Druck, DPI 145) that had been traceably calibrated. The pressure fluctuation during each measurement was within (0.1 MPa. 9Be NMR spectra were obtained on a Varian Inova 500 spectrometer with a standard 10 mm probe, where the resonance frequency was 70.2 MHz. The number of accumulation time ranged from 64 to 256, dependent on the signal-to-noise ratio. The relaxation time was determined with the conventional inversion recovery sequence (PD-π-t-π/2-detect), where PD was the fixed pulse delay longer than 5T1 and t was the variable delay. T1 was calculated by the following single-exponential function:

At ) A∞(1 - 2 exp(-t/T1))

(1)

where At and A∞ were the signal heights at t and at t > 5T1, respectively. In each measurement, a set of more than 20 different values were used for t, and in particular, the shorter values of t rather than T1 were favorably chosen because the signal decay was remarkable in such a time range. The fitting errors in T1 were estimated to be (2% at most, and T1 values were reproduced within less than (4% on different runs even at near-critical temperatures and pressures.

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Figure 3. Density dependence of 1/T1 (left-hand axis) and τr (righthand axis) of [Be(acac)2] in CO2 at 293.4, 313.2, 332.9, and 351.4 K.

A sample of [Be(acac)2] obtained from Tokyo Kasei Kogyo was recrystallized from benzene before use. Pure grade CO2 (99.9%) from Sumitomo Seika Chemicals was used as received. 3. Results and Discussion The 9Be longitudinal relaxation time (T1) of [Be(acac)2] in CO2 is reciprocally plotted against the density1 (F) of CO2 in Figure 3. For several data points, we denote the estimated 95% confidence limits of 1/T1 and the maximum errors in CO2 density calculated from the temperature and pressure fluctuations by the vertical and horizontal error bars, respectively. The density and temperature dependence of 1/T1 is clearly found to be significant. In the present complex, as shown in Figure 1, the four ligating oxygen atoms positioned at apexes of a slightly distorted tetrahedron bring about the electric field gradient, of which the principal axis should coincide with the C2(z) axis.39 Furthermore, the nuclear quadrupole moment (eQ) of 9Be with the spin quantum number (I) being 3/2 is large enough for the nucleus to relax through the quadrupolar interaction only.44 Hence, the observed relaxation time can be directly related to the rotational correlation time (τr) of C2(z) of the complex molecule under the extreme narrowing condition:45

(

)(

2

ηq 1 3π2 (2I + 3) ) 1+ T1 10 I2 (2I - 1) 3

eQq 2 τr h

)

(2)

where ηq is the asymmetry parameter and eQq/h is the quadrupole coupling constant. We have previously determined the eQq/h of [Be(acac)2] in acetonitrile at different temperatures in the range of 240-309 K by the dual-spin-probe technique on the assumption that ηq , 1 in view of the molecular symmetry.39 The eQq/h in acetonitrile provided a virtually constant value of 348 kHz independent of temperature. The value was in a fairly good agreement with the reported 350 kHz in chloroform.46 This fact indicates that the eQq/h of this complex is predominantly determined by the intramolecular structure and is not strongly affected by temperature and solvent. Moreover, it has been confirmed that the molecular structure of this complex remains almost the same under extreme conditions of gaseous (at 413 K47) and solid (at room temperature48 and at 119 K49) states. In the present study, therefore, we calculate τr of [Be(acac)2] in CO2 with the known value of eQq/h (348 kHz), which can be reasonably assumed to be independent of temperature and pressure. The rotational correlation time (τr), thus determined, of [Be(acac)2] in CO2 is also plotted against F in Figure 3 (please see the right-hand axis). It has become apparent that τr increases with a raise of F at each temperature in the present system. This could not be in agreement with the previous behavior

Figure 4. Relation between τr and η/T in [Be(acac)2]-CO2 at 293.4, 313.2, 332.9, and 351.4 K. The solid line was obtained by fitting the data to eqs 4-7 at each temperature, whereas the dotted line was given by the linear regression of the data.

observed by Bright19,23 and Randolph21 but by Maroncelli24 and Kauffman.20 Figure 3 shows, more interestingly, that the increase in τr with F is not monotonic and a upward deviation beyond the experimental errors can be detected at near-critical temperatures of 313.2 and 332.9 K. In harmony with the unique behavior for τr observed in the present system, the recent calculation results of rotational dynamics of toluene in CO2 suggested some anomalous behavior near the critical point.22 It has frequently been observed that the rotational correlation time (τr) of a molecule in liquids is proportional to a macroscopic viscosity (η) of solution and inversely proportional to temperature (T), where the general expression is given by the following form:

η τr ) A + B T

(3)

Substituting A ) V/kB and B ) 0, where V is the volume of a sphere and kB is the Boltzmann constant, one can obtain the well-known Stokes-Einstein-Debye (SED) equation on the basis that a molecular reorientation is expressed as a small step angular random walk (i.e., Debye diffusion model) and is related to η by means of the hydrodynamic model.50 For the present complex molecule in acetonitrile, we have found that τr is simply proportional to η/T over the wide temperature range, where it has been obtained that A ) 0.956 × 10-5 Pa K and B ) 0 ps.39 We attempt to plot τr of this molecule in CO2 against η/T in Figure 4. It is shown that τr in liquid CO2 at 293.4 K linearly increases with η/T, where the values of A ) 0.84 × 10-5 Pa K and B ) 1.95 ps reproduce τr in liquid CO2. Although the plot in liquid CO2 gives a larger intercept of B and a smaller slop of A than in acetonitrile, the linear η/T dependence strongly indicates the validity of eq 3; hence, the Debye diffusion model is almost applicable to the molecular rotation of this complex in liquid CO2. As is also seen from Figure 4, the data points at higher η/T at 313.2 K almost lie on the same straight line at 293.4 K. However, τr remains virtually invariable at intermediate η/T and again starts decreasing at lower η/T. A similar nonlinear behavior of τr is observed at 332.9 K. Unfortunately, a conclusion of linear or nonlinear behavior at 351.4 K could not be reached because only four data points were obtained in the limited range. These observations lead to the following two conclusions. (i) The viscosity of solution remains the predominant factor in the change in τr of this complex in nonviscous CO2, but we cannot immediately explain why τr deviates downward at higher temperatures of 332.9 and 351.4 K even at a constant η/T. (ii) The unique nonlinear behavior for τr of the complex in CO2 at near-critical temperatures reminds us of

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TABLE 1: Values of a, b, c, d, e, and γmax in eqs 4-7 for τr vs η/T in [Be(acac)2]-CO2 Solutionsa solvent CO2

CH3CNc

T/K

η0b/10-5 Pa s

a/10-5 Pa-1 K

b/ps

293.4 313.2 332.9 351.4 240-309

1.47 1.57 1.67 1.75

0.84 (0.02) 0.75 (0.02) 0.83 (0.02) 0.39 (0.05) 0.956 (0.008)

1.95 (0.05) 2.22 (0.05) 1.83 (0.04) 2.48 (0.06) 0

c

d/10-7 Pa s K-1

e/10-5 Pa-1 K

γmax/10-7 Pa s K-1

2.1 (0.1) 3.0 (0.7)

0.51 (0.02) 0.71 (0.02)

1.07 (0.08) 1.10 (0.06)

0.37 0.62

a The uncertainties are given by the 95% confidence limit. b The extrapolated viscosity at zero density, η , was calculated at each temperature 0 according to the literature procedure.52 c The values of a and b in CH3CN were previously determined by the temperature-variable experiments in ref 39.

the fact that the similar density dependence of solvent-induced spectral shifts have frequently been observed by various kinds of spectroscopy, which sensitively reflect time-averaged solvation structures in the vicinity of solute molecules.11-18 To reproduce the viscosity dependence of τr at near-critical temperatures in the present system, let us introduce the following empirical equation, in which τr is expressed by a combination of f and g as a function of η/T, in accordance with the previous analyses of the density dependence of solvent-induced spectral shifts:17, 18, 51

τr ) f(η/T) + g(η /T) + b

(4) Figure 5. Plots of ξex (solid line) and ξex/(η/T) (broken line) against η/T in [Be(acac)2]-CO2 at 313.2 and 332.9 K.

where

f(η/T) ) aη/T

(5)

and

( ) { ( )} [{

g(η/T) ) e c - 1 1/c c

(η - η0)/T - γmax + d c-1 c (η - η0)/T - γmax c - 1 1/c + exp + d c c-1 (6) c c-1 c

-c-1/c

(

)

} ]

with

γmax ) d

(c -c 1)

1/c

(7)

Here, a, b, c, d, and e are the coefficients, η0 is the extrapolated viscosity at zero density, and g(η/T) is called the Weibull line shape function with a maximum value being at η/T ) η0/T +γmax. Let g(η/T) be zero, and one will find that eq 4 is equal to eq 3 with the relations of a ) A and b ) B. As shown by the solid lines in Figure 4, these functions can reproduce the viscosity dependence of τr very well at 313.2 and 332.9 K, where the coefficients a-e and γmax are obtained at each temperature by the least-squares fitting in Table 1. Similarly, according to the previous studies,17,18,51 we consider that the former term f(η/T) represents the contribution arising from the change in the macroscopic viscosity of solution, whereas the latter term g(η/T) provides the additional contribution, which cannot be explained by considering the change in the viscosity alone and, therefore, should arise from specific solute-solvent interactions in the near-critical regime. Assuming that f(η/T) can provide a reference value of τr, the excess solvent parameter (ξex) can be defined in terms of τr: def

ξex )

g(η/T) a

The present analysis of the viscosity dependence of τr is not rigorous but can be rationalized as follows. Dote, Kivelson, and Schwartz (DKS)53 have widely discussed the validity of eq 3 for molecular rotation in liquids and presented an expression for the slope A by the quasi-hydrodynamic model:

τr )

fV η C + τr0 kB T

Here, f is the shape factor of rotating molecule often expressed by the Perrin’s equation,54 C is a measure of the coupling between the rotating molecule and its surroundings, and τr0 is an experimentally determined parameter. Recently, Anderton and Kauffman20 have introduced a parameter of local solvent density (Fl12) into the DKS equation on the basis of the radial distribution function formalism. If one considers the radius (R) of the solvation sphere and the distance (r) between solvent 1 and solute 2 molecules, then Fl12(R) can be given by the following integral equation in the radial distribution function (g12(r)):

F112(R) ) F {1 + F(g12(r))}

Values of ξex calculated with a and g(η/T) at 313.2 and 332.9 K are plotted against η/T in Figure 5.

(10)

They represented both C and η as a function of Fl12 using two kinds of models. More recently, Heitz and Maroncelli24 discussed a variation of C as a function of solvent conditions, η/T, where C was obtained by dividing the observed rotational correlation time by the calculated one under the stick boundary condition. In the present analytical procedure, we take the Cη/T term as a single variable parameter55 and assume that the effective Cη/T on τr is expressed as an addition of the bulk and excess terms in a similar style as of eq 10:

{

(Cη/T)eff ) (Cη/T) 1 + (8)

(9)

}

(Cη/T)ex (Cη/T)

(11)

If the condition of lim(Cη/T)exf0, which corresponds to limF(g12(r))f0 in eq 10, is satisfied, (Cη/T)eff is identical with the bulk term of Cη/T. At a fixed temperature, hence, it is reasonably expected

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that (Cη/T)eff approaches to (Cη/T)bulk at higher densities (i.e., at higher viscosities). As observed in this study, the relationship between τr and η/T is almost linear at higher viscosities, so that C remains constant. In such a case, (Cη/T)bulk can be rewritten as a product of Cbulk and η/T. Thus, substituting the right-hand side of eq 11 into Cη/T in eq 9 and connecting eq 9 with eqs 4-7, one can obtain the following relations:

fV bulk C )a kB (Cη /T)ex C

bulk

)

g(η/T) a

(12)

(13) Figure 6. Density dependence of estimated excess local solvent density (Fex) around [Be(acac)2] in CO2 at 313.2 and 332.9 K.

and

τ0r ) b

(14)

Equation 13 can give a clear explanation for our defined excess solvent parameter, ξex. Before discussing ξex in detail, it is meaningful to survey the linear coefficient a and the intercept b in the plot of τr vs η/T for [Be(acac)2] in CO2 and acetonitrile. It seems that the coefficient a in CO2 is not strongly dependent on temperature except for at 351.4 K and is smaller than in acetonitrile. Despite b in acetonitrile being almost zero, on the other hand, b in CO2 has a positive value and will decrease with increasing T. The intercept b was sometimes interpreted as the free-rotor correlation time, τ0 ) (2π/9)(I/kBT)0.5, where I is the moment of inertia.21,23,29,31 This model could give a negative temperature dependence of b in agreement with our results.56 It should be noted, however, that the values of a and b depend significantly on the method; that is, the values in CO2 were obtained from the density-variable experiments at a fixed temperature, whereas in acetonitrile, they are obtained from the temperature-variable experiments at a fixed pressure (nearly at a fixed density). In fact, the plot of τr vs η/T at a fixed pressure of ∼25 MPa in CO2 gives a relatively larger a of 0.94 × 10-5 Pa-1 K and smaller b of 1.61 ps. If the hydrodynamic continuum model was completely applicable to the present system such that no strong solute-solvent interactions existed, the relationship between τr and η/T could be simply drawn by a single straight line without discrepancy in a and b. In the real system, however, the solute-solvent interactions do exist which brings about an enhancement in τr apart from that observed in the near-critical regime. Considering the contribution of solute-solvent interactions, it may be reasonable to notice the enhancement in τr is less effective at higher temperatures, where molecules have higher kinetic energies. In our experiment, τr in CO2 decreases with increasing temperature even at a fixed η/T (Figure 4) because it would be attributable to the change in surroundings around the solute complex rather than to a failure in the Debye diffusion model.57 As shown in Figure 5, ξex at 313.2 K has the maximum value of 0.50 × 10-7 Pa s K-1 at η/T ) 0.87 × 10-7 Pa s K-1, whereas at 332.9 K, the maximum value of ξex is 0.35 × 10-7 Pa s K-1 at η/T ) 1.12 × 10-7 Pa s K-1. On increasing the temperature from 313.2 to 332.9 K, ξex decreases appreciably and the position of the maximum ξex shifts to higher η/T, i.e., higher density. Figure 5 also shows the η/T dependence of ξex/ (η/T) that can be equal to the relative excess value of Cη/T to the bulk one, (Cη/T)ex/(Cη/T)bulk. In analogy with the relationship between the excess local density and the relative excess local density, the relative excess parameter ξex/(η/T) reaches

the maximum at slightly lower η/T than does ξex. From these data, if direct information about the local solvent density around the solute complex can be extracted out, it would be of great interest. Although we cannot rigorously distinguish two contributions to ξex arising from changes in C and η/T, we attempt to estimate roughly the excess local solvent density (Fex) from ξex by using the F-η relation on the assumption that C remains unchanged at a given temperature. Figure 6 illustrates the bulk solvent density dependence of the excess local solvent density around the solute complex. Fex at 313.2 K approaches the maximum of 0.21 g cm-3 at F ≈ 0.37 g cm-3 less than the critical density (Fc ) 0.47 g cm-3) of CO2, whereas Fex at 332.9 K has the maximum of 0.13 g cm-3 at F ≈ 0.50 g cm-3 more than Fc. It is reasonable that Fex decreases at much higher temperature of 332.9 K than critical temperature. It is certain that the location of the maximum local solvent density will depend on a number of factors. However, Tucker14 mentioned two important factors, the spatial range responsible for a measured property and the relative strength of the solutesolvent and the solvent-solvent interaction potentials. The position of the maximum local solvent density shifts toward lower bulk densities as the spatial range is smaller and/or as the solute molecule is more attractive. Although it may be expected that the solute complex in this work is not attractive to CO2 very much, the present results further imply that the rotational correlation time would be influenced by relatively long-range spatial correlations. 4. Conclusion We studied the rotational dynamics of [Be(acac)2] in liquid and supercritical CO2. The complex molecule chosen proved to be a good candidate for investigating the solute-solvent interactions. The rotational correlation times of [Be(acac)2] in CO2 were precisely determined from the 9Be NMR longitudinal relaxation times at four different temperatures of 293.4, 313.2, 332.9, and 351.4 K over a wide pressure range from 8.0 to 25.0 MPa. It was clearly found that τr of the complex in CO2 linearly increased with η/T at each temperature except for in the nearcritical regime, where τr appreciably deviated upward beyond the experimental errors. A simple analytical procedure using an empirical function has been introduced to express the unique behavior of τr in the near-critical regime. The present analytical procedure can be rationalized in accordance with a quasihydrodynamic relation. The excess solvent parameter thus determined can be discussed in terms of solute-solvent interactions in relation to the time-averaged local solvent density augmentation. A systematic investigation on the basis of time-averaged as well as dynamic properties will promote understanding of

9Be

NMR Relaxation Measurements

the solvent’s roles of SC-CO2, as a result, will expand use of SC-CO2 in a variety of fields. Acknowledgment. T. U. and M. K. gratefully acknowledge Dr. Z. Shervani for his helpful advice and Ms. J. Yoshimura and Mr. H. Yamazaki of Nikkiso Co., Ltd., for their kind assistance to construct the high-pressure NMR cell. References and Notes (1) Angus, S.; Armstrong, B.; de Reuck, K. M. International Thermodynamic Table of the Fluid State-3 Carbon Dioxide; IUPAC.; Blackwell Science: Oxford, 1976. (2) Anastas, P. T.; Warner, J. C. Green Chemistry: Theory and Practice; Oxford University: Oxford, 1998. (3) InnoVations in Supercritical Fluids; Hutchenson, K. W., Foster, N. R., Eds.; ACS Symposium Series, Volume 608; American Chemical Society: Washington, DC, 1995. (4) Chemical Synthesis Using Supercritical Fluids; Jessop, P. G., Leitner, W., Eds.; Wiley-VCH: New York, 1999. (5) See, for example, refs 4 and 6-10. (6) Savage, P. E.; Gopalan, S.; Mizan, T. I.; Martino, C. J.; Brock, E. E. AIChE J. 1995, 41, 1723. (7) Brennecke, J. F.; Chateauneuf, J. E. Chem. ReV. 1999, 99, 433. (8) Jessop, P. G.; Ikariya, T.; Noyori, R. Chem. ReV. 1999, 99, 475. (9) Darr, J. A.; Poliakoff, M. Chem. ReV. 1999, 99, 495. (10) Kawanami, H.; Ikushima, Y. Chem. Commun. 2000, 2089. (11) Refs 12-14 especially provide recent reviews of a number of researches on solvation phenomena in supercritical carbon dioxide. (12) Tucker, S. C.; Maddox, M. W. J. Phys. Chem. B 1998, 102, 2437. (13) Kajimoto, O. Chem. ReV. 1999, 99, 355. (14) Tucker, S. C. Chem. ReV. 1999, 99, 391. (15) Fulton, J. L.; Yee, G. G.; Smith, R. D. J. Am. Chem. Soc. 1991, 113, 8327. (16) Meredith, J. C.; Johnston, K. P.; Seminario, J. M.; Kazarian, S. G.; Eckert, C. A. J. Phys. Chem. 1996, 100, 10837. (17) Song, W.; Biswas, R.; Maroncelli, M. J. Phys. Chem. A 2000, 104, 6924. (18) Kanakubo, M.; Umecky, T.; Kawanami, H.; Aizawa, T.; Ikushima, Y.; Masuda, Y. Chem. Phys. Lett. 2001, 338, 95. (19) Betts, T. A.; Zagrobelny, J.; Bright, F. V. J. Am. Chem. Soc. 1992, 114, 8163. (20) Anderton, R. M.; Kauffman, J. F. J. Phys. Chem. 1995, 99, 13759. (21) DeGrazia, J. L.; Randolph, T. W.; O’Brien, J. A. J. Phys. Chem. A 1998, 102, 1674. (22) Siavosh-Haghighi, A.; Adams, J. E. J. Phys. Chem. A 2001, 105, 2680. (23) Heitz, M. P.; Bright, F. V. J. Phys. Chem. 1996, 100, 6889. (24) Heitz, M. P.; Maroncelli, M. J. Phys. Chem. A 1997, 101, 5852. (25) See, for example: Hertz, H. G. In Water, A ComprehensiVe Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 3, Chapter 7. Grant, D. M.; Mayne, C. L.; Liu, F.; Xiang, T. Chem. ReV. 1991, 91, 1591. Kanakubo, M.; Ikeuchi, H.; Satoˆ, G. P. J. Magn. Reson. 1995, A112, 13. Yonker, C. R.; Wallen, S. L.; Palmer, B. J.; Garrett, B. C. J. Phys. Chem. A 1997, 101, 9564. Wakai, C.; Saito, H.; Matubayasi, N.; Nakahara, M. J. Chem. Phys. 2000, 112, 1462. (26) Lamb, D. M.; Adamy, S. T.; Woo, K. W.; Jonas, J. J. Phys. Chem. 1989, 93, 5002. (27) Chen, S.; Miranda, D. T.; Evilia, R. F. J. Supercrit. Fluids 1995, 8, 255.

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