J. Phys. Chem. 1996, 100, 6889-6897
6889
Probing the Scale of Local Density Augmentation in Supercritical Fluids: A Picosecond Rotational Reorientation Study Mark P. Heitz and Frank V. Bright* Department of Chemistry, Natural Sciences and Mathematics Complex, State UniVersity of New York at Buffalo, Buffalo, New York 14260-3000 ReceiVed: December 5, 1995; In Final Form: January 31, 1996X
We report on the rotational reorientation kinetics of N,N′-bis-(2,5-tert-butylphenyl)-3,4,9,10-perylenecarboxodiimide (BTBP) in several liquids and in three supercritical fluids (fluoroform, carbon dioxide, and ethane). In liquids, BTBP follows near perfect Debye-Stokes-Einstein (DSE) behavior under sticky boundary conditions. However, in supercritical fluids the rotational dynamics of BTBP are distinctly different. In close proximity to the critical density (Fr ≈ 1), the recovered rotational reorientation times are up to 12-fold greater than predicted by simple DSE theory with sticky boundary conditions. Upon increasing the fluid density, the recovered rotational reorientation times steadily decrease until they fall within hydrodynamic predictions (i.e., DSE theory). This extraordinary behavior is explained in terms of local solute-fluid density augmentation which is a feature particular only to supercritical fluids. The local density augmentation surrounding the solute is quantified in several ways. By using a model recently developed by Anderton and Kauffman (J. Phys. Chem. 1995, 99, 13759), the local fluid density is found to exceed the bulk by up to 300%. Upon increasing the pressure and moving away from the high compressibility region we see that the extent of local density augmentation decreases to a value approaching the bulk density. In an alternative interpretation, we explain the observed rotational reorientation dynamics in terms of the size of the solutefluid cluster. At low fluid density (near the critical density) the radius of the “solute-fluid cluster” is a factor of 2 greater than the solute alone. Again, as pressure is increased, there is a decrease in the cluster size and the radius of the reorienting species (BTBP + clustered fluid molecules) approaches the predicted value based on DSE theory using friction/boundary terms determined for BTBP in normal liquid solvents.
Introduction Supercritical fluids are gaining popularity as a result of their unique properties.1-18 Recently, supercritical fluids have become more widely recognized as alternative solvents for a variety of chemical processes. As examples, they have been used extensively in chromatography,19,20 extractions,21,22 and chemical reactions.23-25 In conventional liquid solvents, one requires a variety of different solvents in order to vary the physicochemical properties (e.g., solvent strength, density, dielectric constant, chemical potential). Supercritical fluids, in contrast, are substantially more flexible and provide one with the means to actually tune the physicochemical properties simply by adjusting the fluid temperature and/or pressure.1-18 Thus, a supercritical fluid is generally considered a continuously tunable solvent. Additional features have attracted interest in supercritical fluids as alternatives to traditional liquid solvents. For example, conventional liquid solvents may be difficult to remove from reaction products. Some liquid solvents are expensive; they may be difficult to dispose of; and/or they can adversely impact the environment. Slow mass transfer in liquids can also limit efficient reactions and separations. As a result, there is substantial motivation to replace traditional liquid solvents with effective yet environmentally friendly alternatives. Supercritical fluids represent a viable, alternative solvent system. In 1983, Eckert and co-workers reported large, negative partial molar volumes for naphthalene in supercritical ethylene which suggested that the ethylene had collapsed (clustered) around the solute.26 Following from this exciting discovery, many re* Author to whom all correspondence should be directed. X Abstract published in AdVance ACS Abstracts, April 1, 1996.
0022-3654/96/20100-6889$12.00/0
searchers have used a myriad of approaches and techniques in an effort to understand these special intermolecular interactions and the scale of these solute-fluid clusters.1-18,27-38 Spectroscopy has proven an excellent tool to probe the solute-fluid clustering and to provide a more clear molecular-level view of solvation in supercritical fluids.1-6,10,11,13,14,27-33,35,36 Static optical methods (e.g., absorbance, fluorescence) and solvatochromic solutes have been used to characterize the local solute environment.7,29 For example, Sun and Bunker, using pyrene, recently observed abnormally large pyrene excimer emission in supercritical CO2.30 This anomalous behavior was attributed to an enhanced local pyrene (monomer) concentration in the vicinity of an excited pyrene molecule. Betts and Bright used steady-state and time-resolved fluorescence to investigate the effects of solute-fluid clustering in supercritical CF3H and N2O.32 From this work the authors were able to show that (1) there are an ensemble of solute-fluid clusters; (2) there is a substantial local density augmentation surrounding the solute and that the local density can exceed the bulk density by up to 250%; and (3) there are relatively strong, persistent intermolecular interactions occurring within these solute-fluid clusters. Various scattering techniques have also been used to estimate the correlation length and provide a measure of clustering within neat supercritical fluid systems.35 Most recently, Anderton and Kauffman have reported on the rotational reorientation dynamics of 1,4-diphenylbutadiene and 4-(hydroxymethyl)stilbene in supercritical CO2 and developed a model for interpreting the observed dynamics within a local density augmentation framework.28a Solute-fluid interactions have also been modeled using integral equations and fluctuation analysis.36-38 For example, Randolph and co-workers have compared molecular dynamics © 1996 American Chemical Society
6890 J. Phys. Chem., Vol. 100, No. 17, 1996 and Monte Carlo simulations with electron paramagnetic resonance measurements to demonstrate that long-lived, geometrically defined clusters persist in the vicinity of a solute molecule.36 Molecular correlation function integrals have also been used to determine that the local density change surrounding a solute arises from short-range phenomena.37 Additionally, Petsche and Debenedetti have shown that solute-fluid clusters are dynamic entities and there is a constant exchange of fluid molecules between the cluster and the bulk fluid.38 On the basis of all of the aforementioned research, the emerging picture is that the local fluid density surrounding a typical solute molecule becomes either augmented (attractive solute-fluid interactions) or rarefied (repulsive solute-fluid interactions) in neat supercritical fluids and that the extent of augmentation is most significant at or below the critical region. However, we still lack complete molecular-level insight into these intermolecular solute-fluid interactions. For example, we still lack experimental information on the actual scale/ dimension of these so-called solute-fluid clusters and the dynamics that occur within such a microheterogeneous system. One of the best methods to determine the extent of solutesolvent interaction involves measuring the rotational reorientation dynamics of the solute. In the simplest formalism, the experimental measurable, the rotational correlation time (φ), is described in terms of hydrodynamic theories (e.g., the DebyeStokes-Einstein expression) (Vide infra) which predicts that φ should be proportional to η/T, where η is macroscopic solvent viscosity and T is the Kelvin temperature; the proportionality constant can be estimated from the molecular dimensions of the solute. Unfortunately, these simple theories generally fail to describe the observed dynamics and one is forced to invoke more realistic models that incorporate molecular aspects of the solute and the solvent (Vide infra). However, φ data can provide a convenient link between the solute and the local solvent/fluid microstructure and hence, in principle, solute-fluid clustering. In this paper we report on the time-resolved rotational reorientation kinetics of N,N′-bis-(2,5-tert-butylphenyl)-3,4,9,10perylenecarboxodiimide (BTBP) in liquid and supercritical fluoroform (CF3H), carbon dioxide (CO2), and ethane (C2H6). Ben-Amotz and Drake39a have reported previously on the rotational dynamics of BTBP in a series of liquid n-alkanes and n-alcohols and showed that BTBP “nearly perfectly”39a follows the Debye-Stokes-Einstein (DSE) hydrodynamic model. BTBP is also attractive for several additional reasons. First, it has a quantum yield of 0.99.40 Second, the relatively large molecular volume (733 Å3)39a should slow the rotational reorientation to the point that the dynamics become more readily measured in the low viscosity supercritical fluids. Third, the excited-state intensity decay kinetics are best described by a single exponential decay law in liquids.39a Finally, BTBP is soluble in a wide variety of solvents such as alkanes, alcohols, and both apolar and polar aprotic solvents (Vide infra). Thus, BTBP appears to be an ideal solute to quantify the dynamics associated with solute-fluid clustering. From our time-resolved anisotropy decay data, two independent interpretations are considered to explain the observed BTBP rotational reorientation kinetics. In the first approach, the solute is assumed to move independent of the solute-fluid cluster and the new model developed by Anderton and Kauffman28a is used to quantify the actual local fluid density augmentation surrounding BTBP in CF3H, CO2, and C2H6. In an alternative interpretation, the solute and fluid cluster are assumed to reorient as a single entity. In this interpretation, the scale/size of the solute-fluid cluster is determined.
Heitz and Bright Theory Section The rotational reorientation time of a fluorescent molecule provides a means to conveniently probe the local microstructure and coupling between a solute and solvent.28a,32b,39,41-49 To effectively model this process, one requires a relationship between solvent-solute forces, solute shape, and solute motion. Many theories have been developed to describe molecular reorientation based on Brownian diffusion.41-49 In the simplest formalism, the Debye-Stokes-Einstein (DSE) expression, the rotational reorientation of a molecule is written:41
φ)
ηV RT
(1)
where φ is rotational reorientation time, η is the bulk solvent viscosity, R is the gas constant, and T is the absolute temperature. Implicit in the use of this model is the hydrodynamic stick boundary condition where the frictional portion of probesolvent interactions are strong enough that the solute and solvent experience a significant interaction. This model has been used successfully to describe rotational diffusion of macroscopic particles but it generally fails when applied to microscopic solutes.44,45 As a result of this nonhydrodynamic behavior, several modifications to the DSE theory have been made.46-49 The Gierer-Wirtz scheme46 models the solvent-solute interactions by separating the solvent into a series of concentric shells, the thickness of which is equal to the diameter of a solvent molecule. Each solvent layer has an independent angular velocity which results in a frictional gradient that diminishes as the distance from the solute increases. Other more sophisticated models47,48 are based on the Enskog hard-sphere fluid treatments of the solvent-solute interactions. However, knowledge of the solvent radial distribution function is required to apply these models to the anisotropy decay data. A compromise between these models is the Dote-Kivelson-Schwartz (DKS) approach49 which simultaneously accounts for the solvent size and interstitial spaces between solvent molecules. In the original rotational reorientation experiments carried out by Ben-Amotz and Drake, using a wide range of solutes (BTBP among them), the DKS model was shown to quantitatively describe the turnover from macroscopic to microscopic behavior with decreasing solute size in contrast to generalized hydrodynamic models (e.g., simple DSE, eq 1).39a Most recently, hydrodynamic models have been extended further to account for enhanced solvent-solute interactions in associated systems such as supercritical fluids. Anderton and Kauffman developed a convenient model based on a radial distribution function formalism.28a The density dependence of these functions are connected via an integral equation over the solute-fluid spacial coordinates according to28a
FL(r) ) F[1 + F(g(r12))]
(2)
where FL (r) is the local fluid density, F is the bulk fluid density, and F(g(r12)) is an integral over a function of the solvent-solute pair correlation function. The resulting expression describing the observed rotational correlation time, φ, takes the form:28a
φ)
η(FL)Vprobe fstickC(FL) + φ0 kT
(3)
In this expression, η(FL) is the local viscosity associated with the locally dense region surrounding the solute and is calculated using the Jossi method,28a,50 Vprobe is the van der Waals volume of the solute, fstick accounts for the shape of the solute43 and is calculated from the solute axial ratio (A) (Vide infra),39a C(FL)
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is the density-dependent boundary condition factor, k is the Boltzmann constant, T is the absolute temperature, and φ0 is the inertial rotor time of the solute. fstick for BTBP is calculated using eq 4:28b
2(A + 1)(A - 1) 2
fstick )
2
1.5
3A[(2A - 1) ln[A + (A2 - 1)0.5] - A(A2 - 1)0.5] (4) 2
2π I 0.5 9 kT
( )
solvent
viscositya (cP)
λa (nm)
λf (nm)
τb (ns)
φc (ns)
acetone acetonitrile THF chloroform DMF p-dioxane
0.316 0.345 0.46 0.542 1.2 2.0
484 486 486 491 489 487
532 533 533 537 540 535
3.68 3.66 3.62 3.56 3.78 3.69
0.185 0.219 0.268 0.329 0.443 0.865
a From the 70th ed. CRC Handbook of Chemistry and Physics. b The uncertainties in the lifetimes (τ) are less than 6%. c The uncertainties in the rotational reorientation times (φ) are less than 13%.
The inertial rotor time (φ0) is calculated as follows:39b
φ0 )
TABLE 1: Steady-State and Time-Resolved Parameters for BTBP in Liquid Solvents
(5)
In the current work, we have used the Anderton-Kauffman model to describe the rotational reorientation times of BTBP in supercritical fluids. The relevant parameters calculated for BTBP are Vprobe ) 441 cm3/mol,39a fstick ) 2.87, and φ0 ) 8.7 ps. Experimental Section Materials. BTBP was purchased from Aldrich and used as received. CF3H was from Matheson (99%) and SFC grade CO2 and CP grade (99.0%) C2H6 were obtained from Scott Specialty Gases. All gases were purified further by passage through an oxygen trap (Matheson) before entering the high-pressure pump. Stock solutions (1.0 mM) of BTBP were prepared in absolute ethanol. Sample Preparation. Fresh samples of BTBP were prepared prior to each set of experiments and the following procedure adopted to prepare a sample for study. For the liquid studies, we introduce an aliquot of stock ethanol solution into a standard 1-cm fluorescence cuvette and evaporate the ethanol. Following this, the liquid of choice is added such that the final fluorophore concentration is 1-2 µM. For the supercritical fluid studies, the procedure is as follows. The high-pressure cell is charged with a small aliquot of the BTBP stock solution. The actual analytical concentration of the fluorophore was kept between 0.5 and 1 µM. The ethanol is then removed by flowing a gentle stream of nitrogen into the cell. A magnetic stirring bar is placed into the high-pressure cell and we evacuate the entire high-pressure apparatus to remove any residual ethanol and O2. Finally, the high-pressure optical cell is heated and maintained at the desired temperature ((0.1 °C) and the fluid, from a syringe pump (Isco 260-D), is pumped into the cell to the starting pressure. Pressure is monitored using an analog Heise gauge ((1 psi). Samples are stirred constantly throughout an experiment and are allowed to equilibrate for 10-20 min between pressure changes. The general details of the high-pressure apparatus and high-pressure optical cells have been described elsewhere.51 Instrumentation and Methodology. Absorbance measurements were performed on a Milton Roy Spectronic 1201 UVvis spectrophotometer with 1-nm resolution. All steady-state and time-resolved fluorescence measurements were carried out using a multiharmonic frequency-domain fluorometer (SLM Aminco Model 48000 MHF).51 For steady-state measurements, a Xe arc lamp provided excitation at either 458 or 488 nm and all bandpasses were fixed at 8 nm. An argon ion laser (Coherent; Innova Model 400-10) operating at 488.0 or 514.5 nm served as the excitation source for all time-resolved experiments. An interference filter was placed in the excitation beam path to eliminate extraneous contributions to the fluorescence from the laser plasma discharge. Fluorescence was monitored through 520 (λex ) 488.0)
or 550 nm (λex ) 514.5) interference filters. Magic angle polarization was used to eliminate polarization biases.52 R6G in water was used as the reference lifetime standard; its lifetime was assigned a value of 3.85 ns.53 The Pockels cell modulator was operated at 5 MHz and data are acquired from 5 to 180 MHz (36 total frequencies). The theory of frequency-domain fluorescence spectroscopy has been described in detail elsewhere.54-57 Multifrequency phase and modulation data were fit to several test models using a commercially available software package (Globals Unlimited).58 The following experimental conditions were used unless otherwise noted. All reduced quantities are defined as the ratio of the parameter of interest to that critical parameter (e.g., Tr ) T/Tc). The reduced temperature (Tr) was always 1.01. BTBP solubility inevitably dictated the lowest pressure studied in each fluid; the upper pressure limit was approximately 3000 psia which corresponds to a reduced density (Fr) of about two for all fluids used here. Tests of statistical significance (t-test) were performed on all data. All ensuing references to such are asserted at the 95% confidence level unless otherwise specified. Checking for Cell/Pressure-Induced Artifacts. Early in this work significant effort was expended to address the issue of pressure-induced window birefringence in the high-pressure optical cells. Experimental details demonstrating that such is not an issue is available as supporting information. Results and Discussion Liquid Solvents. Prior to any investigations in supercritical fluids, we examined BTBP in a series of conventional liquid solvents (Table 1). Specifically, we measured the absorbance and fluorescence spectra and the current results are in good agreement with previous reports.40 Ben-Amotz and Drake have reported the excited-state intensity and anisotropy decay of BTBP in a series of n-alkanes and n-alcohols at several temperatures.39a They reported that the excited-state decay kinetics are described by a single lifetime of 3.7 ( 0.1 ns.39a Our fluorescence lifetimes in aprotic solvents (Table 1) are in good agreement with this value. Results from new timeresolved anisotropy decay data are also summarized in Table 1. Again, we observe very good correlation with previous results (not shown).39a In summary, both steady-state and timeresolved fluorescence measurements on BTBP in liquids shows that the particular solvent used has little influence on the BTBP emission or intensity decay and the rotational reorientation dynamics scale with solvent viscosity and are well approximated by DSE hydrodynamic theory. Supercritical Fluids. As mentioned at the outset, in the lowdensity region near the critical point, a supercritical fluid demonstrates a proclivity to cluster about a solute molecule leading to an augmentation in the local density surrounding the solute.1-18,27-38 Fluorescence decay of anisotropy measure-
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Heitz and Bright
TABLE 2: Solvent Properties in Supercritical Fluids and Range of Experimental Conditions fluid
VVDWa (Å3)
pressure (psia)
F (g/mL)b
η (µP)c
CF3H CO2 C2H6
23.9 19.7 27.3
800-3000 1280-3000 2200-3000
0.49-1.01 0.65-0.90 0.39-0.42
390-950 480-875 110-135
a van der Waals volume, calculated from ref 59. b Bulk fluid density range for these experiments. The densities are from a commercial software program: SF Solver, Isco Inc. c Bulk fluid viscosity calculated from ref 50, p 424.
Figure 2. Multifrequency phase and modulation traces for BTBP in supercritical CF3H at Tr ) 1.01, and several reduced densities [Fr ) 1.04 (b), 1.40 (3), 1.76 (0), 2.01 (9)]. Symbols represent the experimental data and the traces are the best fit to a single exponential decay model. Data for BTBP in supercritical CO2 and C2H6 display similar behavior.
Figure 1. Typical steady-state fluorescence spectra of BTBP in supercritical CF3H at Tr ) 1.01, and several reduced densities (Fr). The emission spectra of BTBP in supercritical CO2 and C2H6 display similar behavior.
ments provide a direct means to probe this clustering process because the rotational reorientation time is directly proportional to the solute size and shape and the intermolecular interactions occurring within the immediate microenvironment surrounding the solute41-49 (i.e., these solute-fluid clusters). However, on the basis of a simple DSE argument (eq 1), the rotational reorientation time of a solute in our particular supercritical fluids is expected to be at least 1 order of magnitude faster than in liquid solvents due to the low fluid viscosity (Table 2). As a result, the rotational reorientation time of a typical solute in a supercritical fluid is expected to be on the order of several picoseconds (Vide infra).27,32b Because the rotational reorientation time scales directly with the solute volume one can potentially alleviate the obvious problems associated with measuring fast rotational motions by using a solute with a relatively large volume. The reorientational behavior of BTBP in liquids (Table 1) suggests that we can successfully recover the rotational reorientation dynamics of BTBP in supercritical fluids. For completeness, Table 2 collects the key parameters for each fluid and provides the range over which the measurements are made. Static Fluorescence. Figure 1 shows typical BTBP emission spectra in supercritical CF3H as a function of reduced density, Fr. As one proceeds from the lower to the upper panel in Figure 1, a 300-fold increase in the fluorescence intensity is observed as reduced density is increased from 0.97 to 2.00. The emission spectra in supercritical CO2 show similar behavior. As was seen
Figure 3. Recovered excited-state fluorescence lifetimes for BTBP in supercritical CF3H at Tr ) 1.01 as a function of reduced density (Fr). The error bars depict the standard deviations based on several replicate determinations. The solid lines are a guide to the eye.
in conventional liquids,40 the distinctive vibronic bands are clearly present, most pronounced at high reduced density (Figure 1, upper panel). In CF3H at low reduced densities, we observed an additional shoulder at ∼535 nm (Figure 1, lower panel). This shoulder corresponds to a shift of ∼3000 cm-1 from the excitation wavelength (458 nm) and we conclude that it is due to Raman scatter from the ν1 symmetric stretching mode of CF3H.60 The steady-state behavior in supercritical fluids can be summed up as follows. Fluid density has little influence on the emission characteristics of BTBP in either supercritical CF3H or CO2. Consistent with the emission spectra in liquids (Table 1), the wavelength of the individual fluorescence maxima change slightly with each fluid. At low fluid densities, weak fluorescence is observed due to the low solubility of BTBP in the fluids. As density increases, there is a concomitant increase in BTBP fluorescence intensity, which arises from an increase in BTBP loading. Time-ResolVed Fluorescence. Figure 2 depicts four representative sets of multifrequency phase and modulation traces for BTBP in supercritical CF3H at reduced densities of 1.04 (b), 1.40 (3), 1.76 (0), and 2.01 (9). Similar traces are observed in supercritical CO2 and C2H6. The solid line through the symbols represents the fit to a single exponential decay law. One can see that these data are all described well by a single excited-state fluorescence lifetime (τ). In addition, the excitedstate decay traces are clearly density dependent. Figure 3 summarizes the effects of fluid density on the fluorescence lifetime of BTBP in supercritical CF3H (b), CO2 (O), and C2H6 (2). Clearly, as fluid density increases there is a concomitant decrease in the BTBP lifetime.
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Figure 5. Recovered kinetic terms for the time-resolved decay of anisotropy for BTBP in supercritical CF3H (b), CO2 (9), and C2H6 ([) at Tr ) 1.01 as a function of fluid density. The error bars depict the standard deviations based on several replicate determinations. “Stick B.C.” denotes predictions based on the sticky boundary condition (eq 1).
Figure 4. Typical multifrequency differential phase angle (upper panel) and polarized modulation traces (lower panel) for BTBP in supercritical CF3H at Tr ) 1.01, and several reduced densities.
The classic Strickler and Berg theory provides a relationship between the radiative decay rate and the solvent refractive index.61 In its most elementary form, the Strickler-Berg relationship predicts that a change in solvent refractive index will, in and of itself, produce a predictable change in the radiative decay rate. In supercritical fluids, the physicochemical properties of the fluid are a strong function of pressure and temperature, thus an increase in fluid pressure (or density) produces a concomitant increase in the fluid refractive index.1-18 If a single exponential decay law governs the radiative decay (see Figures 2 and 3) and the BTBP quantum yield is unity,40 a simple plot of 1/τ vs n2 can confirm Strickler-Berg behavior. Analysis of the Figure 3 data (results not shown) yields a straight line (r2 ) 0.98) and confirms that the majority of the decrease in τ is simply due to the change in fluid refractive index. Rotational Reorientation. Figure 4 presents typical densitydependent multifrequency differential phase (upper panel) and polarized modulation traces (lower panel) for BTBP in supercritical CF3H. The solid points represent the actual experimental data and the lines are drawn as a visual aid. The best fit to these data resulted from an isotropic rotor model. An anisotropic rotor model (two reorientation times) was also tested, but offered no statistical improvement (χ2) in the fit. In all cases the recovered time zero anisotropy [r(0)] was 0.33 ( 0.03, suggesting (ro ) 0.32-0.36) that there was no change in the angular orientation between the BTBP absorbance and emission transition moments in the supercritical fluids. Figure 5 summarizes the effects of fluid density on the rotational reorientation times for BTBP in supercritical CF3H (b), CO2 (2), and C2H6 ([). The error bars are based on at least triplicate measurements on replicate samples and represent one standard deviation. The dotted curve represents the predicted rotational reorientation time of BTBP in CF3H using eq 1 based on the bulk fluid viscosity,50 BTBP’s volume (733 Å3),39a and a temperature of 303 K. (The predictions for the other fluids look similar to CF3H calculations but are slightly below the curve shown.) Several interesting trends are readily apparent when one compares the experimental data to the simple DSE predictions. First, at the highest densities, in the liquid-
like region, the rotational reorientation times show very good agreement with DSE theory and are consistent with values one would expect based the behavior of BTBP in normal liquid solvents.39a Second, the BTBP rotational reorientation time in the low density region [Fr ≈ 0.9-1.3, for CF3H (b), CO2 (2)], exhibits a substantially larger value compared to DSE predictions. Third, as the fluid density is increased, the BTBP rotational reorientation time decreases, counter to the DSE-based predictions (dashed trace). Finally, in the low-density region, invoking a simple DSE argument to explain the observed rotational reorientation dynamics fails to describe the experimental data. These seemingly anomalous data can be understood from the perspective of solute-fluid clustering and local density augmentation. However, two different, unrelated interpretations of these results are tenable depending on the extent of intermolecular interaction between BTBP and the fluid cluster. For example, if the motion of the BTBP molecule is independent of the solute-fluid cluster, then the BTBP rotational motion will depend on the local fluid density (viscosity) within the cluster. Thus, the rotational reorientation data can provide information about the degree of local fluid density augmentation within the cybotatic region surrounding the solute. Local density augmentation surrounding a solute in a supercritical fluid is well documented1-18,23-38 and density augmentations of up to 2.5 times that of the bulk density are not uncommon.1-18,23-38 Moreover, the local density augmentation is strongly dependent on the fluid pressure and temperature1-18,23-38 and even the state of the solute.62 An alternative explanation for the anomalous rotational reorientation times is based on the concerted motion of the solute and fluid cluster moving as a single entity. In this scenario, maximal interaction occurs between the solute and the fluid cluster. Because the probe moves with (not necessarily within) the fluid cluster, the solute rotational reorientation is dictated by the bulk fluid viscosity and the dimensions of the solute-fluid cluster. In this interpretation, the scale of solute-fluid clustering (e.g., the dimensions of the solute-fluid cluster) can be determined. The implications of both scenarios are discussed below. 1. Dynamics Within the Solute-Fluid Cluster. In the independent solute motion case, one must recognize that the local density augmentation will modify the fluid properties (e.g., viscosity) in the immediate vicinity of the solute. Thus, the rotational reorientation time of the solute will be proportional to local fluid viscosity which is written as a function of the local density surrounding BTBP (eq 3). In addition, the boundary conditions must be modified to compensate for the
6894 J. Phys. Chem., Vol. 100, No. 17, 1996
Figure 6. Augmentation of the local fluid density surrounding BTBP in supercritical CF3H at Tr ) 1.01 determined from the Anderton and Kauffman model.28a The symbols are the experimentally measured rotational reorientation times (from Figure 5). The curves represent increasing values of F(g(r12)), defined in eq 2. For F(g(r12)) ) 0, the local fluid density surrounding the probe is equal to the bulk fluid density. See text and ref 28a for complete computational details.
changing local fluid density surrounding BTBP. We apply the Anderton-Kauffman model28a (see Theory Section) to quantify the density-dependent local density augmentation surrounding BTBP in supercritical CF3H, CO2, and C2H6. Figure 6 illustrates typical results and predictions for BTBP in CF3H. The solid symbols represent the actual rotational reorientation times (the solid lines between points are a visual aid) and the curves are the input parameter, F(g(r12)), used to calculate the local density augmentation (eq 2 and ref 28a). In the Anderton-Kauffman formalism, when F(g(r12)) ) 0 the local density surrounding the solute equals the bulk density and the rotational reorientation times are identical to the values predicted by the simple DSE theory (eq 1). If F(g(r12)) ) 1, the local density is twice that of the bulk. Inspection of Figure 6 shows that we observe a local fluid density augmentation in excess of 250% at Fr ≈ 1. However, as the bulk fluid density increases, the BTBP rotational reorientation time decreases, with a concomitant decrease in the corresponding local density augmentation. For example, at Fr ≈ 1.6-1.8, the BTBP rotational reorientation time is approximately equal to the value predicted by the DSE hydrodynamic theory under stick boundary conditions (i.e., F(g(r12)) ≈ 0). This fact clearly demonstrates that increasing the fluid density to relatively high levels (1.6-1.8 times the critical density) eliminates local density augmentation between BTBP and CF3H. Table 3 collects the local density augmentation factor, F(g(r12)), for BTBP as a function of fluid density in supercritical CF3H, CO2, and C2H6. Inspection of these results shows that BTBP in CF3H exhibits the greatest extent of local fluid density enhancement as is indicated by the F(g(r12)) value, 1.85 at the lowest density investigated. As one increases the density, the value of F(g(r12)) decreases. At a CF3H density of 0.8 g/mL only minimal density augmentation is observed, and above this value augmentation ceases (Table 3). Interestingly, F(g(r12)) actually becomes “negative” at the higher fluid densities indicating that the local fluid density surrounding BTBP diminishes to a level which is consistent with the deviations from hydrodynamic predictions observed for BTBP in normal liquid solvents (Vide infra).39a BTBP in CO2 displays similar trends and behaviors, although we were unable to obtain reliable data below a density of 0.65 g/mL due to poor BTBP solubility. A more clear illustration of the extent of local density augmentation surrounding excited-state BTBP is obtained by determining the relative effects of density on the local density. Toward this end, we determined the local density by using the experimental rotational reorientation times and eqs 2 and 3 to
Heitz and Bright provide a measure of Flocal through F(g(r1,2)). Figure 7 shows the effects of fluid density on Flocal/Fbulk for BTBP in supercritical CF3H (b), CO2 (9), and C2H6 (2). The dotted line indicates the situation if there were no solute-fluid clustering and the local and bulk densities equal one another. These data show that the greatest extent of density augmentation, nearly 300%, is observed in CF3H, at a reduced density near unity. As pressure is increased, the degree of local density augmentation decreases significantly. Interestingly, when the entire data set is considered we see that BTBP apparently behaves similarly in each supercritical fluid. This particular behavior is consistent with BTBP not undergoing any type of solvent-dependent intermolecular interactions in liquids (cf. Table 1 and refs 39a and 39c). On the basis of the theoretical modeling of Chialvo and Cummings,37 one would expect to observe a maximum in Flocal/ Fbulk at a reduced density of about 0.5. However, attempts to measure the BTBP reorientation dynamics in the very low fluid density region were hampered by the inability of these fluids to sufficiently solubilize BTBP. 2. Size of the Solute-Fluid Cluster. As previously discussed, if the solute-fluid cluster reorients as a single entity, the scale (dimensions) of the solute-fluid cluster can be determined from the rotational reorientation data. This alternative interpretation of the rotational reorientation dynamics can provide an estimate of the size of the rotating unit. In the preceding discussion, the volume term used in eq 3 to determine the local density augmentation surrounding BTBP was that of BTBP only, calculated on the basis of the molecular dimensions of BTBP alone. Estimation of the solute-fluid cluster dimensions is possible if one considers that all deviation from DSE predictions (Figure 5) are a result of rotational reorientation of the entire solute-fluid cluster. The dimensions are calculated by assuming that the volume in eq 3 is that of the solute-fluid cluster and the viscosity is the bulk fluid viscosity. Blanchard and coworkers have used a somewhat related type of “solvent attachment” model in describing the solvent microstructure surrounding methylene blue.63 The hydrodynamic volume of the solute-fluid cluster is estimated using our experimental reorientation times in eq 3 with η(FL) equal to the bulk fluid viscosity, and assuming sticky boundary conditions (i.e., C(FL) ) 1). We then obtain the contribution due to the fluid by decoupling the solute (VBTBP) and fluid cluster (Vcluster) volumes from the total volume (Vtotal):
Vtotal ) VBTBP + Vcluster
(6)
By using the average radius previously reported for BTBP, 5.6 Å,39a Vcluster is calculated. The results of these calculations are collected in Table 4 and they show that, in the low density region, the observed radius of the rotating unit is significantly greater than predicted for BTBP alone on the basis of the DSE hydrodynamic theory. Further, as the density is increased the value of the cluster radius also decreases. The density dependence of the solute-fluid cluster to BTBP radius ratio (rcluster/rBTBP) provides a more convenient means to compare the individual fluids. On the basis of our calculated radii (Table 4) and the Ben-Amotz and Drake data,39a we have estimated the relative size increase of the solute-fluid cluster by calculating rcluster/rBTBP. The results of these calculations are presented in Figure 8 for BTBP in supercritical CF3H (b), CO2 (9), and C2H6 (2). The dotted line represents a clusterto-BTBP radius ratio of unity. These results show clearly that near the critical density in CF3H (Fr ) 1), the radius of the solute-fluid cluster is 2-fold greater than that of BTBP alone. By using the van der Waals volume for the fluid (Table 2) and
Scale of Local Density Augmentation
J. Phys. Chem., Vol. 100, No. 17, 1996 6895
TABLE 3: Effects of Density and Fluid on the Local Density Augmentation Factor [F(g(r12))]a for BTBP in Supercritical CF3H, CO2, and C2H6 CF3H
CO2
C2H6
density (g/mL)
reduced density
F(g(r12))
density (g/mL)
reduced density
F(g(r12))
density (g/mL)
reduced density
F(g(r12))
0.49 0.53 0.61 0.69 0.71 0.73 0.81 0.89 1.02
0.96 1.04 1.21 1.36 1.39 1.45 1.60 1.76 2.00
1.85 1.80 1.22 0.93 0.62 0.43 0.02 -0.05 -0.15
0.65 0.69 0.72 0.75 0.78 0.84 0.90
1.38 1.45 1.53 1.58 1.65 1.79 1.91
0.77 0.59 0.36 0.27 0.15 -0.06 -0.17
0.39 0.41 0.42
1.91 2.00 2.07
0.07 0.04 0.02
a
The uncertainties in the F(g(r12)) terms are typically less than 15%.
Figure 7. Excited-state density enhancement (Flocal/Fbulk) as a function of density for BTBP in supercritical CF3H (b), CO2 (9), and C2H6 (2) at Tr ) 1.01. The dotted line indicates a ratio of 1. The error bars depict the uncertainties based on the average of several replicate determinations.
Vcluster we can estimate the number of solvent layers involved in the BTBP-fluid cluster. We estimate that up to three layers of fluid molecules are intimately associated with BTBP at the lowest densities investigated. Similar behavior is displayed by BTBP in supercritical CO2. Interestingly, our data show that the radius ratio decreases to a value slightly less than unity at the highest densities. This may appear somewhat anomalous; however, one must realize that BTBP displays nearly ideal DSE behavior. Specifically, Ben-Amotz and Drake have reported that the recovered BTBP rotational dynamics are only 85% of the values predicted based on sticky boundary hydrodynamics.39a The arrow outside Figure 8 indicates the predicted BTBP radius, assuming a 15% reduction relative to the idealized DSE hydrodynamic behavior. Our high-density, liquid-like data for CF3H and CO2 are in excellent agreement with this aspect of BTBP. Thus, the radius ratio indicates that the pronounced size enhancement, near the critical point, diminishes to the predicted hydrodynamic limit at sufficiently high fluid densities. Figure 8 also shows that the rcluster/rBTBP values for BTBP in supercritical C2H6 (2) stay well above unity even at the highest densities investigated (Fr ≈ 2.0). Recently, Heitz et al.64 reported on the pressure-dependent T1 relaxation dynamics of perylene in supercritical C2H6. In this report, we showed that the short-range (
