J. Phys. Chem. B 2000, 104, 5421-5429
5421
FEATURE ARTICLE Ultrafast Spectroscopic Studies of the Dynamics of Liquids Confined in Nanoporous Glasses Brian J. Loughnane, Richard A. Farrer, Alessandra Scodinu, Thomas Reilly, and John T. Fourkas* Eugene F. Merkert Chemistry Center, Boston College, Chestnut Hill, Massachusetts 02467 ReceiVed: January 27, 2000; In Final Form: March 28, 2000
The reorientational dynamics of liquids confined in nanoporous sol-gel glasses have been investigated in detail using femtosecond optical Kerr effect spectroscopy. We review the results of experiments performed on both weakly wetting and strongly wetting liquids in nanoconfinement. In all cases the liquid partitions into bulk-like and surface populations, each of which has unique dynamics. We demonstrate how optical Kerr effect spectroscopy can be used to probe the dynamics and structure of these populations in quantitative, molecular-level detail.
I. Introduction Nanoscopic confinement (i.e., confinement on distance scales up to a few times larger than the dimensions of a single molecule) can have a profound influence on the structure and dynamics of liquids.1-7 Nanoconfined liquids are found throughout nature, from water trapped in proteins to oil trapped in porous rocks. Confined liquids also play an important role in numerous technological applications, including separations, heterogeneous catalysis, lubrication, and microfluidics. As a result, the study of confined liquids has attracted increasing attention over the past two decades. The effects of confinement on liquids arise from an interplay of several factors. First, liquids are characterized by structural correlations that persist for several molecular diameters. When the distance scale of confinement of a liquid approaches its structural correlation length, the structure of the liquid (and thereby its dynamics) is disrupted. Second, nanoscopic confinement can only be achieved in a medium with a high surfaceto-volume ratio. If the liquid/surface interactions are comparable to or stronger than the interactions between liquid molecules, then the surfaces of the confining medium will play a major role in determining the properties of the confined liquid. Indeed, even in the absence of strong interactions with the liquid, the rigidity of the confining surfaces can influence the behavior of a liquid significantly. Nanoporous sol-gel glasses8 have proven to be excellent media with which to study the effects of nanoconfinement on liquids. These glasses can be synthesized readily in the form of powders, thin films, or monoliths. By varying the synthetic conditions, one can attain average pore diameters that range from 15 to 100 Å with a relatively narrow distribution of pore sizes about the average.8 The highly interconnected network of pores in these materials absorbs liquids readily. The pores are considerably smaller than the wavelength of visible light, such that excellent optical quality can be achieved for thin films and monoliths. In addition, the surface chemistry of these materials is well understood, so that surface modification techniques can
be used to tune the interactions between the pore surfaces and the liquids confined within them. The earliest studies of the dynamics of liquids confined in sol-gel glasses were performed by Warnock, Awschalom, and Shafer,9 who used a picosecond time-dependent birefringence method to study how molecular reorientation is affected by nanoconfinement. Since that time, numerous techniques have been used to study the dynamics of liquids confined in these materials, including Raman spectroscopy,10-13 NMR,14-27 dielectric spectroscopy,28-39 Rayleigh-wing scattering,40 and timedependent phosphorescence spectroscopy.41,42 The picture that arose from the earliest experiments was that the dynamics of weakly wetting simple liquids are essentially unaffected by confinement, whereas strongly wetting liquids develop a surface layer that has significantly inhibited dynamics.9 Subsequent NMR experiments supported this two-state model for strongly wetting liquids in confinement.14 NMR measurements also proved to be sensitive enough to reveal a modest degree of inhibition in the surface dynamics of weakly wetting liquids, which was further verified by Raman spectroscopy.12 In this paper we will review the results of detailed studies of the orientational dynamics of liquids confined in nanoporous sol-gel glasses that we have performed over the past few years using optical Kerr effect43-46 (OKE) spectroscopy.47-53 OKE spectroscopy allows us to measure the collective orientational correlation function of confined liquids on time scales ranging from femtoseconds to hundreds of picoseconds, thus providing a powerful means of obtaining quantitative microscopic information on the dynamics and dynamic populations of nanoconfined liquids. Because OKE spectroscopy measures collective dynamics, it is an ideal complement to techniques such as NMR and Raman spectroscopy, which measure single-molecule dynamics.54 Combining single-molecule and collective dynamic information on the same system enables us to develop an even more detailed picture of the microscopic structure of confined liquids. The outline of the remainder of this article is as follows. We begin, in the following section, by describing the experimental
10.1021/jp000323h CCC: $19.00 © 2000 American Chemical Society Published on Web 05/17/2000
5422 J. Phys. Chem. B, Vol. 104, No. 23, 2000 techniques employed. In sections III and IV we discuss the orientational dynamics of weakly wetting and strongly wetting confined liquids, respectively. In section V we consider the intermolecular vibrational dynamics of confined liquids, followed by concluding remarks in section VI. II. Experimental Methods A. Preparation and Characterization of Sol-Gel Glasses. To perform OKE experiments we require monolithic sol-gel samples of high optical clarity and low birefringence. Such samples can be synthesized via the two-step acid/base-catalyzed hydrolysis of tetraethyl orthosilicate (TEOS).8 Deionized water, ethanol, and a 98% TEOS solution are mixed together rapidly in a 12:2:1 molar ratio. The solution is acidified with a small amount of HCl, and acid-based hydrolysis proceeds in a heat bath at 40 °C until the solution becomes clear (about 40 min). The solution is then transferred to an ice bath, where it is diluted by another 12 parts of deionized water and made basic with NH4OH, the amount of which depends on the desired average pore size. The solution is then poured into 1.5-cm-diameter polystyrene vials that are subsequently capped tightly. The samples generally gel within about 30 min. The final average pore size is controlled by the aging of the gelled samples. To achieve a small average pore size, the samples are aged for one week at room temperature. Samples with larger pores can be made by aging for longer periods at an elevated temperature. Still larger pore sizes can be attained by treatment with 0.1 M NH4OH for 24 h after high-temperature aging. After aging, the samples are dried over a period of about 1 month by uncapping the sample vials and resealing them with Parafilm in which a pinhole has been made to allow the liquid to evaporate slowly. The gels harden and shrink considerably during the drying process. The dried monoliths are placed in ceramic crucibles and are heated in a muffle furnace to 800 °C at a rate of 0.5 °C per minute. Generally, 90% of the monoliths survive firing without cracking. For our experimental studies we employ disk-shaped samples that are approximately 2 mm thick. The cylindrical monoliths that we synthesize can either be cut with a diamond saw or ground down to the appropriate thickness using wet/dry sandpaper. The disks are then polished to optical quality using a TEXMET 100 polishing cloth with 24-, 6-, and 1-µm diamond paste, sequentially. To remove any water and organic impurities that may have permeated the samples during polishing, they are heated again to 450 °C. The samples are characterized by nitrogen adsorption and desorption isotherms obtained at liquid nitrogen temperature using a Brunauer, Emmett, and Teller55 (BET) sorptmeter. Pierce adsorption isotherms56 reveal an interconnected pore network with a narrow distribution of pore sizes. Specific surface areas range from about 350 m2/g to 650 m2/g, depending on the average pore size. Desorption isotherms exhibit hysteresis, which is typical for mesoporous materials.55 The sol-gel samples are hydrophilic; depending on the thermal history of a sample, pore surfaces have between two and six hydroxyl groups per nm2.8 Interactions between the pore walls and confined liquids can be tuned by functionalizing these hydroxyl groups. In particular, to make the surfaces hydrophobic, dried samples are refluxed in a 50% solution of chlorotrimethylsilane57 in dry toluene at 110 °C for several days. The samples are then washed sequentially with toluene, benzene, and methanol. Holding the samples at 100 °C in a vacuum oven for 24 h removes any remaining volatile impurities. The success
Loughnane et al. of the surface treatment can be verified using IR spectroscopy as well as by a significant decrease in the BET constant of the samples. To prepare samples for optical experiments, polished monoliths of different pore sizes are sealed in 2 mm path length quartz cells along with the liquid to be studied. The liquids used are distilled and filtered multiple times through 0.1 µm Millipore filters before introduction into the sample cell. The samples are allowed to soak in liquid for at least 24 h before any experiments are performed. To control the temperature of the samples, the cell is mounted on the coldfinger of a continuous-flow, liquidnitrogen-cooled vacuum cryostat. A silicon-diode probe is mounted directly on the face of the sample cell to measure temperature. B. Viscosity Measurements. The viscosity of each liquid studied was measured at every temperature at which OKE data were obtained. The measurements were made using an Ubbelohde viscometer, which allows the time that it takes for a liquid to pass through a calibrated capillary to be converted to a kinematic viscosity. The kinematic viscosity is converted to the shear viscosity through multiplication by the liquid density. To make the measurements, 15 mL of filtered liquid is placed in the viscometer reservoir. The viscometer is mounted securely in a clear Dewar flask, after which it is immersed in ethanol that is stirred vigorously. The temperature of the ethanol, which is measured with an accuracy of 0.1 °C by a temperature probe mounted in the Dewar, is controlled by adding dry ice. Once the sample has stabilized at the desired temperature, the liquid is drawn from the reservoir by a pipet bulb, and the time required for it to pass through the capillary and back into the reservoir is measured. To verify the reproducibility of the procedure, multiple measurements are made at each temperature. The viscosity measurements are estimated to be accurate to within 0.3%. C. Optical Kerr Effect Measurements. In OKE spectroscopy,45,46 a liquid composed of molecules with anisotropic polarizabilities is exposed to a short, nonresonant “pump” pulse of laser light. The pump pulse preferentially induces a dipole moment along the axis of maximum polarizability of the molecules. The induced dipole moment interacts with the instantaneous electric field of the laser pulse, providing an impulsive torque that drives the axis of maximum polarizability of the molecules toward alignment with the polarization of the pump pulse. Subjecting the molecules of a liquid to an impulsive torque has two immediate effects. First, because liquids are dense media, molecules cannot rotate far without colliding with other molecules. Thus, the pump pulse sets the molecules of the liquid into coherent, frustrated oscillatory motions (librations). Since the molecules of a liquid exist in a broad range of ever-changing local potentials, the initially coherent librations dephase on a time scale between hundreds of femtoseconds and several picoseconds. Second, the impulsive torque provided by the pump pulse creates a small but significant net alignment of the liquid molecules. This alignment persists until such time as it is washed out by orientational diffusion, which has a characteristic time scale that can range from several to tens or even hundreds of picoseconds, depending on the size of the liquid molecules and the viscosity of the liquid. Since the coherent librations are initiated and the alignment of the liquid is induced via the axis of maximum polarizability, and since it is the polarizability of the molecules in a liquid that determine its index of refraction, the pump pulse generates a temporary, time-dependent birefringence. This birefringence
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Figure 1. Heterodyne-detected OKE setup. DX ) doubling crystal, GLP ) Glan laser polarizer, GTP ) Glan-Thompson polarizer, HWP ) half-wave plate, PD ) photodiode, PDC ) prism dispersion compensator, QWP ) quarter-wave plate, SF ) spatial filter. [Reproduced from ref 47.]
can be monitored by a second, “probe” laser pulse. This pulse is polarized at a 45° angle to the polarization of the pump pulse. After the sample it is incident on a polarizer that is set to pass light that is polarized at a -45° angle to the polarization of the pump pulse. In the absence of birefringence in the sample, no probe light can pass through this analyzer polarizer. The amount of light that does leak through is proportional to the birefringence in the sample, which is in turn proportional to the degree of molecular alignment. Thus, by monitoring the amount of leakage as a function of the delay time between the pump and probe pulses, the response of the liquid to the pump pulse can be monitored, including the coherent librations at early time and the orientational diffusion at longer times. Our experimental OKE setup (shown in Figure 1) is based upon the optical-heterodyne-detected OKE method developed by McMorrow and Lotshaw.58 A modified commercial, modelocked Ti:sapphire laser produces pulses with a center frequency near 800 nm at a repetition rate of 76 MHz. A pair of external LaFN28 prisms is used to compress the pulses and to compensate for dispersion caused by the optics in the experimental setup. The pulses that reach the sample are nearly transform limited, and generally have a duration of approximately 45 fs. After the prism dispersion compensator, the laser output is spatially filtered, and then is split into a strong pump beam and a weaker probe beam. The two beams are chopped at frequencies with a 7:5 ratio by the two rings of slots in the wheel of a mechanical chopper. The pump beam then passes through a halfwave plate and a Glan laser polarizer set to pass light polarized at 45° to the vertical, after which it is focused into the sample. The probe beam traverses an optical delay line with 0.1-µm resolution. It then passes through a Glan laser polarizer that is set to pass vertically polarized light, followed by a quarterwave plate with its fast axis set to be along the vertical. The probe beam is then focused into the same spot in the sample as the pump beam (care is taken to ensure that the beams cross only within the sol-gel sample, so that no signal arises from the surrounding bulk liquid). After the sample, the probe beam is recollimated by another lens and then it is incident on a GlanThompson polarizer that is set to pass horizontally polarized light. The leakage through the analyzer polarizer is spatially filtered and then is detected by a low-noise, amplified photodiode. To implement optical heterodyne detection,58 the first polarizer in the path of the probe beam is rotated off of the vertical by a small amount (generally between and 1° and 2°). This
J. Phys. Chem. B, Vol. 104, No. 23, 2000 5423 allows a small horizontally polarized component of the probe beam to pass along the slow axis of the quarter-wave plate, where its phase is retarded by 90°. This horizontal component passes through the analyzer polarizer, and thus can serve as a local oscillator that will amplify and linearize the OKE signal (which is also 90° out of phase with the probe beam). By collecting data at equivalent positive and negative heterodyne angles and subtracting one set from the other, the homodyne contribution to the signal can be removed, leaving the pure heterodyne component. We have made several adaptations to the experimental setup to improve the signal-to-noise ratio. First, the pump beam is picked off after the sample and is frequency-doubled in a KDP crystal. The doubled light is detected with a photodiode and lock-in amplifier. Because second-harmonic generation has the same nonlinearity as the heterodyne-detected OKE signal, the doubled light can be used to normalize for any long-term intensity variations in the laser. Second, a small portion of the probe beam is picked off after the chopper and detected by a photodiode that is matched to the signal photodiode. The outputs of the signal and reference photodiodes are connected to the differential inputs of a low-noise preamplifier. With the pump beam blocked, the intensity of the reference beam is adjusted to zero the output of the preamplifier, thus removing the contribution of the local oscillator to the detected intensity. The pump beam is then unblocked, and the output of the preamplifier is sent to a lock-in amplifier that is referenced to the sum of the two chopping frequencies. The data acquisition is completely computer controlled using programs written in LabView. The computer moves the delay line, reads and averages the values in the data buffers of each lock-in amplifier, and then saves the normalized signal for that data point. No data are acquired unless the temperature of the sample is within 0.5 °C of the desired value. Between consecutive scans, the computer reverses the angle of the first polarizer in the probe path to switch the heterodyne angle. Data are generally acquired with short-step scans out to delays of several picoseconds, and then with long-step scans for longer delays. Generally, 4 short-step scans and 50 long-step scans are taken at each heterodyne angle at each temperature. To construct the Bose-Einstein-corrected Rayleigh-wing spectrum of a liquid, we follow a procedure derived from that of McMorrow and Lotshaw.58 The long-step scans are fit with an appropriate function, and the fit is used to strip a tail with an identical point spacing onto the short-step scans. The concatenated data set is used in conjunction with a secondharmonic-generation autocorrelation trace obtained at the same point spacing to perform a Fourier-transform deconvolution, which removes the effects of the finite pulse length from the OKE data.58 The reorientational tail is removed from the data (generally assuming a rise time of approximately 150 fs), and then a Fourier transform yields the Rayleigh-wing spectrum with the effects of reorientation removed. III. Weakly Wetting Liquids in Confinement A. Historical Background. The earliest studies of weakly wetting liquids confined in nanoporous sol-gel glasses were performed by Warnock, Awschalom, and Shafer,9 who used a picosecond OKE technique to probe the orientational dynamics of nanoconfined CS2. Their measurements were unable to detect any change in the orientational diffusion of this liquid upon confinement. Subsequent NMR experiments by Jonas and coworkers demonstrated that the constraints presented by pore surfaces have a notable effect on the spectral density of
5424 J. Phys. Chem. B, Vol. 104, No. 23, 2000
Figure 2. Representative data obtained at 290 K in methyl iodide in the bulk and confined in pores 83, 42, and 24 Å in diameter. Hindered surface reorientational diffusion is evident in the data for the confined liquid, which show significant signal well after the bulk liquid has relaxed. [Reproduced from ref 47.]
nonwetting liquids in confinement.18,20,21 More recent NMR27 and Raman12 experiments by this group have suggested that there is indeed a significant retardation of the dynamics of weakly wetting liquids near pore surfaces. Korb et al. proposed that this retardation can be explained by assuming that molecular reorientations parallel to the pore walls are unaffected by confinement whereas rotations perpendicular to the walls are inhibited, with the degree of inhibition depending on the distance of a given molecule from a pore surface.27 We discuss a related but distinct mechanism for the inhibition of surface reorientation of weakly wetting liquids below. CS2 was also the subject of our earliest experiments on a weakly wetting liquid in nanoconfinement.47 Because of the improved temporal resolution and stability of our Ti:sapphire laser as compared to the dye laser employed by Warnock, Awschalom, and Shafer,9 we were able to detect inhibited orientational dynamics that presumably arise from interactions with the pore surfaces. Since that time, we have studied the dynamics of other weakly wetting liquids in confinement as well, including methyl iodide49 and chloroform.53 In this section we review our results for CS247,52 and methyl iodide49 to demonstrate how OKE spectroscopy can be used to develop a detailed microscopic picture of the dynamics and structure of nanoconfined liquids. B. Two-State Dynamics. The reorientational portion of the OKE decay of a liquid composed of highly symmetric molecules is expected to be described by a single exponential.59 The OKE data in Figure 2 show that this is indeed the case for bulk methyl iodide at 290 K at delay times greater than 4 ps (the decay at earlier time is influenced by librations and by the “intermediate” relaxation60). However, this figure also demonstrates that upon confinement another, slower relaxation component appears in the OKE decays, and that this feature becomes increasingly prominent in moving from pores that are 83 Å in diameter down to pores that are 24 Å in diameter. [As a point of reference, a 10 Å long cylindrical pore that is 24 Å in diameter can hold 44 molecules of methyl iodide and 45 molecules of CS2 at the room-temperature densities of these liquids. In both cases roughly half of the molecules will be touching the pore surfaces.] The reorientational portion of the decays in the confined liquid can be fit well by the sum of two exponentials, one of which has the same time constant as the decay in the bulk liquid and the other of which has a significantly larger time constant. Furthermore, the time constant of the slower decay component increases with decreasing pore size. We have observed the same type of behavior over the entire liquid range of both methyl
Loughnane et al.
Figure 3. Arrhenius plot of the viscosity of bulk methyl iodide (circles) and the calculated viscosity of the surface layer for 24-Å (triangles), 42-Å (squares), and 83-Å (diamonds) pore-diameter samples. The solid lines are linear least-squares fits. [Adapted from ref 47.]
iodide49 and CS252 (although in the latter case the slower portion of the relaxation is nonexponential and contains components that relax more than an order of magnitude more slowly than the bulk liquid). The data for methyl iodide and CS2 suggest that even though there are no strong attractive interactions between weakly wetting liquids and the pore surfaces, a two-state model nevertheless provides a reasonable description of the dynamics of these liquids in confinement. Presumably the faster, bulklike component of the relaxation of the confined liquids corresponds to molecules that are in the centers of the pores, whereas the slower component of the relaxation arises from molecules that have inhibited dynamics due to the proximity to the pore surfaces. A first obvious question to ask is whether the inhibition of reorientation at the pore surfaces is energetic in origin. To do so we can consider the temperature dependence of the reorientational data. The Debye-Stokes-Einstein (DSE) equation predicts that the orientational correlation time of a liquid is given by61
τ)
ηVHf kBT
(1)
where η is the viscosity, VH is the hydrodynamic volume for reorientation, f is a factor that takes into account the boundary conditions for reorientation, kB is Boltzmann’s constant, and T is the temperature. Although the DSE equation refers to the single-molecule orientational correlation time and OKE spectroscopy measures the collective orientational correlation time, it is still generally the case that a plot of the OKE relaxation time versus η/T yields a straight line.60 There are three factors in eq 1 that might be different at the pore surfaces than in the bulk, thus leading to inhibition of reorientation: the viscosity, the hydrodynamic volume, and the boundary conditions for reorientation. Of these factors, the only one that is likely to have a significant temperature dependence is the viscosity, which in simple liquids generally exhibits Arrhenius temperature behavior. If a change in the viscosity at the pore surfaces were solely responsible for the observed inhibition of surface reorientation, then according to eq 1 we should be able to compute the surface viscosity from
ηsurf )
τsurf η τbulk bulk
(2)
Figure 3 shows Arrhenius plots of the bulk viscosity and the surface viscosities of methyl iodide in different pore sizes as computed from eq 2. The activation energies for reorientation
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J. Phys. Chem. B, Vol. 104, No. 23, 2000 5425
in the bulk and at the surfaces are quite similar, implying that the inhibition of reorientation at the surfaces is not energetic in nature. We have observed analogous behavior in confined CS2. To further test this point, we have also studied the reorientation of both methyl iodide49 and CS252 in pores that have been surface modified as described above. Trimethylsilyl groups should be large enough to make any surface trapping sites unavailable to the confined liquid, thereby removing any significant attractive interactions between the liquid and the pore surfaces. However, the surface reorientation in surface-modified glasses is slower than in unmodified glasses, presumably because the surface modification decreases the effective pore diameter. We can therefore rule out any significant role for attractive interactions between the pore surfaces and the confined liquid in the inhibition of surface orientational dynamics. The inhibition of surface relaxation must therefore arise from some combination of boundary conditions that differ from those in the bulk and an increased hydrodynamic volume for reorientation. We will return to the source of the retardation of surface relaxation below. C. Surface Populations. The amplitudes of the exponentials in the OKE decays of confined liquids carry just as much information as do the time constants. The OKE signal is the negative time derivative of the collective orientational correlation function of the liquid.62 Since all of the molecules in the pores are identical, the amplitudes of the contributions of the bulklike and surface molecules to the collective orientational correlation function are proportional to the populations of these molecules. If each population has exponential reorientational dynamics, then the reorientational portion of the OKE signal will be given by
S(t) ∝
pbulk -t/τbulk psurf -t/τsurf e + e τbulk τsurf
(3)
where p denotes a population and τ denotes a relaxation time. Thus, once the time constants in the OKE decays have been measured, the amplitudes of the exponential components can be used to compute the relative bulk-like and surface populations of molecules. Since the pores of the sol-gel glasses are known to be roughly cylindrical, we can use the relative populations in conjunction with the average pore radius to estimate the thickness of the surface layer that has inhibited reorientational dynamics. Note that whatever the true morphology of the pore surfaces might be, the surface-to-volume ratio must be at least as large as that of a cylinder, so estimates of the surface-layer thickness derived in this way should be viewed as the maximum possible values. The estimated surface-layer thickness averaged over the different pore sizes studied is shown as a function of temperature for methyl iodide and CS2 in Figure 4. There are two notable features to the data in Figure 4. First, the surface-layer thickness for both liquids shows an unmistakable increase as the temperature is lowered. Second, since the shortest dimension of both methyl iodide and CS2 is roughly 4 Å, it is clear that the surface-layer thickness is significantly less than one monolayer over most of the normal liquid range for both substances. The same holds true in surface-modified samples. We are therefore forced to conclude that despite the fact that we can rule out the existence of surface traps, only a fraction of the molecules at the pore surfaces exhibit inhibited reorientational dynamics. D. Hydrodynamic Volume, Geometrical Constraints, and the Inhibition of Surface Dynamics. The logical conclusion
Figure 4. Estimated surface-layer thicknesses for CS2 (triangles) and methyl iodide (circles). [Adapted from refs 47 and 50.]
Figure 5. Schematic depiction of the reorientation of CS2 molecules at a surface that is wetted only weakly by this liquid. (a) The reorientation of a surface molecule that is perpendicular to the surface is bulk-like because the hydrodynamic volume for this reorientation is equivalent to that in the bulk. (b) For a molecule that lies flat on a pore surface to rotate off of the surface it must tumble end over end rather than about its center of mass, so the hydrodynamic volume for this reorientation is significantly greater than in the bulk. (c) A molecule at a flat surface is free to rotate in the plane of the surface, whereas at a curved surface (d) this motion is inhibited by geometric constraints.
that we can draw from our observations on the surface-layer thickness is that whether the dynamics of a surface molecule will be inhibited depends on the orientation of that molecule relative to the surface. To see why this might be the case, imagine a cylindrical molecule that sits on a pore surface with its cylindrical axis along the surface normal (Figure 5a). So long as the attraction between the molecule and the surface is no greater than its attraction to the surrounding liquid, this molecule can rotate as if it were in the bulk, so its orientational dynamics are unaffected by proximity to the pore surface. Now consider a cylindrical molecule that lies with its cylindrical axis along the surface of a curved pore (Figure 5b). Although in the bulk liquid this molecule could rotate about its center of mass, for it to rotate off of the surface of the pore (i.e., about an axis parallel to the pore surface) its center of mass must translate away from the pore surface. Thus, the hydrodynamic volume required for the molecule to rotate off of a pore surface is greater than that required for rotation in the bulk. According to eq 1, this effect leads to an increased orientational correlation time. The larger the aspect ratio of the molecule, the more important this hydrodynamic-volume effect becomes. The same cylindrical molecule lying flat on a pore surface will also experience inhibited orientational dynamics parallel to the pore surface due to the surface curvature. As was the case for the hydrodynamic volume effect, this geometric confinement effect becomes more important as the aspect ratio of the molecule increases (Figure 5c,d). However, whereas the hydrodynamic volume effect does not depend on the pore size,
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Loughnane et al. methyl iodide shows that the hydrodynamic volume factor in this liquid is about 1.5. These results suggest that for both liquids, the geometric confinement effect plays a larger role in the inhibition of surface dynamics than does the hydrodynamic volume effect, particularly in smaller pores. IV. Strongly Wetting Liquids in Confinement
Figure 6. Surface reorientation rate of CS2 versus pore curvature at, from bottom to top, 165, 174, 194, 271, 254, 272, 290, 293, and 310 K. [Reproduced from ref 50.]
Figure 7. Ratio of the orientational correlation time at a flat surface to that in the bulk as a function of temperature for CS2. Within the estimated experimental uncertainty (error bars), the ratio is equal to the average value of 2.0 for all temperatures, which indicates that the hydrodynamic volume for CS2 reorientation is twice as large at a flat surface as in the bulk liquid. [Reproduced from ref 50.]
geometric confinement becomes more important in smaller pores (which explains the greater inhibition of surface dynamics in smaller pores observed for both methyl iodide and CS2). Taken in conjunction with this model, the observation that the surface-layer thickness increases with decreasing temperature suggests that there is a tendency for the liquid molecules to lie flat on the pore surfaces as the available thermal energy diminishes. This idea is supported by experimental63,64 and simulation65,66 studies that demonstrate that liquids tend to form layers near flat surfaces, and that these layers become more pronounced at lower temperatures.67 Since the geometric confinement effect is only operative at curved surfaces, we can determine the importance of the hydrodynamic volume effect by using the pore-size dependence of the surface reorientation rate to gauge the degree of inhibition of reorientation at a flat surface. Figure 6 shows plots of the surface reorientation rate of CS2 versus pore curvature as a function of temperature. By extrapolating these plots back to an infinite radius of curvature, we can estimate the reorientational rate at a flat surface as a function of temperature. Figure 7 illustrates that, within the uncertainty of this procedure, the ratio of the reorientational time of CS2 at a flat surface to that in the bulk is independent of temperature. The average value of these ratios is 2.0, implying that the increased hydrodynamic volume for reorientation off of the pore surfaces doubles the correlation time for such motions. Since the aspect ratio of methyl iodide is smaller than that of CS2, we would expect hydrodynamic volume to play less of a role in the inhibition of surface dynamics. Indeed, a similar analysis50 of the confined
A. Historical Background. Warnock, Awschalom, and Shafer9 were also the first to study the orientational dynamics of a wetting liquid confined in nanoporous glasses. They found that confined nitrobenzene exhibited a biphasic OKE decay, with one component matching the decay of the bulk liquid and the second component decaying approximately 3 times more slowly. They also observed that the slower component disappears upon surface modification of the glass. Since that time, Jonas and co-workers have performed detailed NMR studies of the orientational dynamics of wetting liquids in porous sol-gel glasses.18,22,25 These studies take advantage of the fact that the spin-lattice relaxation time (T1) of deuterium is inversely proportional to the orientational correlation time of the molecule containing this atom. Since T1 is generally on the order of seconds for deuterium, each confined molecule samples all possible environments in a pore statistically long before spin-lattice relaxation is complete. Assuming that the confined liquid is characterized by a bulk-like component and a surface component, the so-called two-state, fast-exchange18 model predicts that the measured orientational correlation time is given by
τobs ) τbulk +
2 (τ - τbulk) R surf
(4)
where is the thickness of the surface layer and R is the pore radius. According to this equation, a plot of τobs versus 1/R at constant temperature should yield a straight line, which has indeed been found to be the case for numerous wetting liquids. The slope of the line contains information about the thickness of the surface layer and the surface relaxation time. However, the contributions of these factors to the slope cannot be determined uniquely without further information. In this section we will review the results of our OKE studies of acetonitrile confined in sol-gel glasses.48,51 Due to its ability to accept hydrogen bonds, this liquid is strongly wetting on silica. In addition to the expected considerable inhibition of surface dynamics of acetonitrile, we have found that the behavior of this wetting liquid in confinement differs significantly from that of weakly wetting liquids. The combination of OKE and NMR data has further allowed us to develop a detailed microscopic model of the structure of this liquid at the pore surfaces. B. Two States or Three? As in the cases of methyl iodide and CS2, the reorientational portion of the bulk acetonitrile OKE decay is exponential. As might be expected, the decays of confined acetonitrile show that the dynamics of a large fraction of the confined molecules are highly retarded compared to those in the bulk.48,51 The decays can be described well by the sum of three exponentials, the fastest of which matches the decay of the bulk liquid and the slowest of which decays roughly 20 times more slowly. Furthermore, at any given temperature only the amplitudes of the slower two decays change with pore size, whereas the time constants remain the same, suggesting that each of the fit exponentials has physical meaning. The simplest explanation for the triexponential decays is that there are three distinct liquid populations: molecules in the centers of the pores with bulk-like dynamics, molecules at the
Feature Article
Figure 8. Arrhenius plots of the bulk viscosity (circles) and the estimated viscosity derived from the intermediate exponential (triangles) and slow exponential (squares) for the OKE decays of confined acetonitrile. [Adapted from ref 49.]
surfaces with severely inhibited dynamics, and an intermediate layer with moderately inhibited dynamics. To explore this possibility, we can use eq 2 to estimate the viscosities that correspond to the exponential components. These viscosities are plotted in Arrhenius form in Figure 8. The slowest exponential has an activation energy (8.5 kJ/mol) that is similar to that for the bulk liquid (7.2 kJ/mol). However, the slope of the plot for the intermediate exponential (4.7 kJ/mol) is significantly less than that of the bulk liquid. It is difficult to explain how the activation energy for reorientation of an intermediate layer of molecules could be smaller than that for the bulk, so we are forced to conclude that the three-state model does not provide a reasonable explanation of the observed behavior. If the time scales for reorientation in the bulk and at the pore surfaces are disparate enough, it is possible for exchange between the two populations to take place on a time scale that is intermediate between the two. If the exchange is slow compared to the bulk relaxation rate, then all of the bulk-like molecules will relax before they exchange. If the exchange is fast compared to the surface relaxation rate, then a new relaxation channel is opened for those surface molecules at the interface between the two populations: by exchanging into the bulk, they can reorient at the bulk relaxation rate. A simple kinetic model of this process shows that it indeed leads to decays that are triexponential, and that the amplitudes and time constants of the exponentials can be used to determine all of the relevant rates and populations.48,51 C. The Nature of the Surface Layer. Figure 9 illustrates the thickness of the surface layer as derived from the kinetic model, as well as its breakdown into exchangeable and nonexchangeable components. Again, the thickness of the surface layer increases as the temperature decreases. As would be expected for a wetting liquid, the surface layer is at least one monolayer thick at all temperatures. The populations of exchangeable and nonexchangeable surface molecules are roughly equal at all temperatures. To test the validity of the exchange model for confined acetonitrile, our results can be compared to the NMR data of Zhang and Jonas22 for acetonitrile-d3. As mentioned above, OKE spectroscopy measures the collective reorientation time whereas NMR measures the single-molecule reorientation time. These quantities are related by the static orientational correlation parameter, g2.54 This parameter generally depends only weakly on temperature, and the larger its value, the greater the degree of orientational order in the liquid. Arrhenius plots of the OKE and NMR orientational correlation times for bulk acetonitrile-d3 reveal that g2 takes on a value
J. Phys. Chem. B, Vol. 104, No. 23, 2000 5427
Figure 9. Temperature dependence of the estimated thickness of the total surface layer of molecules (squares) and its breakdown into exchangeable (circles) and nonexchangeable (triangles) components for confined acetonitrile. The estimates were made based on data from both acetonitrile and acetonitrile-d3 and were averaged over all of the pore sizes studied. [Reproduced from ref 49.]
of approximately 1.6 over the entire liquid range of this substance, implying a modest degree of orientational ordering. To compare the OKE and NMR data for the surface layer of the confined liquid, we must use eq 4 to derive the surface orientational correlation time from the NMR data based on the bulk NMR orientational correlation time and the surface-layer thickness derived from OKE measurements. An Arrhenius plot of the NMR surface orientational correlation times derived from this procedure is again parallel to an Arrhenius plot of the OKE data,51 giving independent support to the analysis of the OKE data using the kinetic exchange model. The value of g2 derived from these plots is 2.1, implying that there is a significant increase in the degree of orientational order at the pore surfaces, as might be expected from the polarity and the hydrogen-bondaccepting nature of this liquid. One might imagine that the extreme inhibition of surface reorientation of acetonitrile arises because hydrogen bonds must be broken in order for the molecules to reorient. To explore this possibility, we performed experiments in glasses in which the hydrogen atoms in the surface hydroxyl groups had been exchanged with deuterium. Since an O-D bond has a lower zero-point energy than does an O-H bond, deuterated hydroxyl groups form weaker hydrogen bonds than do undeuterated hydroxyl groups. However, we observed no change in the dynamics of acetonitrile confined in deuterated pores, suggesting that the surface relaxation arises from the rocking of acetonitrile molecules about hydrogen bonds rather than from the breaking of hydrogen bonds. On the basis of these experiments, we can develop a plausible picture of the surface structure and dynamics of the confined liquid. The data from the deuterium-exchanged pores suggest that the hydrogen bonds between the pore surfaces and the liquid are long-lived, and the comparison of the NMR and OKE data implies an increased degree of molecular ordering at the pore surfaces. These data are consistent with the existence of a population of anchored surface molecules that point roughly outward from the surface. However, acetonitrile has a substantial dipole moment of 3.92 D,68 so it is not favorable for all of the surface molecules to point in the same direction. It therefore seems likely that acetonitrile molecules with antiparallel orientations would be found interdigitated among those bound to the pore surfaces. These interdigitated molecules should reorient at the same rate as the molecules that they are trapped amidst. However, because the interdigitated population is not hydrogen bonded to the surface, these molecules are prone to exchange. This picture is supported by the fact that the surface population
5428 J. Phys. Chem. B, Vol. 104, No. 23, 2000 is composed of roughly equal numbers of exchangeable and nonexchangeable molecules at all temperatures. The differences between this model and the one we have proposed for the inhibition of reorientation in weakly wetting liquids also provide an explanation for why an intermediate exponential arising from molecular exchange is not observed in the OKE data for weakly wetting liquids. In wetting liquids the mechanism for exchange is translation of molecules away from the pore surfaces. These translations only need be over short enough distances that the process probably should not be described as diffusive. On the other hand, in weakly wetting liquids it is the molecular orientation at the pore surfaces that determines the reorientational rate, and it is reorientation itself that causes molecules to exchange between the two populations. As a result, no additional exponential appears in the OKE decays of such liquids. D. Dynamics in Surface-Modified Pores. To further test our model for the dynamics of acetonitrile confined in porous glasses, we have performed experiments using surface-modified sol-gel samples.51 The behavior of acetonitrile in these samples is completely consistent with that of weakly wetting confined liquids.49,52 The OKE decays in the modified pores are biexponential; the time constant of the faster component matches that of the bulk liquid and the time constant of the slower component depends on the pore size. The activation energy for reorientation is only slightly greater at the pore surfaces than in the bulk, and the estimated surface-layer thickness is less than one monolayer over the entire liquid range of acetonitrile. V. Intermolecular Dynamics in Confinement As discussed above, the early-time component of the OKE decay arises from coherently excited intermolecular vibrations. As such, this portion of the OKE decay is sensitive to changes in the local potential energy landscape of a liquid. Since nanoconfinement imposes structural changes upon liquids, and since the potential between a hard wall and a molecule is likely to differ significantly from that between a molecule and the liquid that surrounds it, one might expect to see notable changes in the early-time OKE dynamics of a liquid upon confinement. To investigate this issue, we have used the Fourier-transform deconvolution58 to compute the Bose-Einstein-corrected Rayleigh-wing spectrum of several liquids in the bulk and in confinement. For every liquid that we have investigated, once the reorientational portion of the OKE signal has been removed the spectrum in confinement has proven to be identical to that in the bulk at the same temperature, regardless of the pore size. To illustrate this point, representative data for CS2 in the bulk and confined in 25-Å pores are shown in Figure 10.52 The reasons for this unexpected lack of change of the intermolecular spectrum upon confinement remain to be elucidated. Hubbard69 demonstrated that if the molecules in a liquid reorient diffusively, then the product of the angular momentum correlation time and the orientational correlation time should be constant. Given the inhibition of reorientation at the pore surfaces that we have observed for every liquid that we have studied, the Hubbard relation69 would suggest that the intermolecular density of states for the surface population of liquid should extend to higher frequencies than that of the bulk liquid. Of course, reorientational diffusion is biased at a surface, so the Hubbard relation should not be exact, but it is still surprising to see no significant difference in the intermolecular spectra of liquids upon confinement. To investigate this issue further, we are studying intermolecular spectra under conditions of even
Loughnane et al.
Figure 10. Bose-Einstein-corrected Rayleigh-wing spectra for CS2 in the bulk (solid line) and confined in 25-Å pores (dashed line). The reorientational component has been removed from both spectra. The resulting intermolecular spectra are identical to within the experimental accuracy. [Reproduced from ref 50.]
more extreme confinement by employing liquids composed of significantly larger molecules. VI. Concluding Remarks In this article we have reviewed some of the highlights of our recent OKE studies of the dynamics of liquids confined in nanoporous glasses. OKE spectroscopy is a powerful tool that has allowed us to develop a detailed and quantitative picture of the microscopic structure and dynamics of the systems that we have studied. Here we outline briefly some of the interesting facets of nanoconfined liquids that remain relatively unexplored. The partitioning of a confined liquid into two components must break down upon tight enough confinement. Surprisingly, we have seen no sign of such an effect, even for CS2 confined in pores 21 Å in diameter. If this liquid were to layer completely in confinement, cylindrical pores of this size could hold only three layers of molecules. To search for a breakdown of twostate behavior, it will clearly be necessary to study liquids composed of larger molecules. Presumably molecular shape will play an important role in determining the pore size at which such a breakdown will occur, so it will be interesting to study the differences among the dynamics of rod-like, disk-like, and spherical molecules in confinement. By the same token, the relative strength of liquid/liquid and liquid/surface interactions should have a strong influence on the dynamics of confined liquids. In a fascinating set of experiments, Kremer and co-workers have shown that for a highly hydrogen-bonded liquid, confinement in a zeolite channel that is only two molecules wide produces liquid-like dielectric behavior.70,71 They have also found that highly networked supercooled liquids relax more quickly in hydrophobic pores than in the bulk.32,34 These experiments underscore the importance of the interplay between liquid/liquid and liquid/surface interactions in controlling the behavior of confined liquids, and it will be of great interest to explore this interplay further. We hope that the information gained in studies such as those reported here will eventually prove useful in controlling chemical events in confined systems. For instance, being able to tailor the dynamic properties of a solvent at a surface may have important implications for the design of new systems for heterogeneous catalysis. Indeed, the experiments described here have just begun to scratch the surface of a field that promises to hold many more surprises. Acknowledgment. This work was supported by the National Science Foundation, Grant CHE-9501598. J.T.F. is a Research
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