Bidirectional Transport of Guest Molecules through the Nanoporous

Dec 22, 2008 - The Raman data, recorded as a function of position along the tunnel ... guest molecules trying to enter both ends of the tunnel structu...
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J. Phys. Chem. C 2009, 113, 736–743

Bidirectional Transport of Guest Molecules through the Nanoporous Tunnel Structure of a Solid Inclusion Compound Javier Martı´-Rujas,† Arnaud Desmedt,‡ Kenneth D. M. Harris,*,† and Franc¸ois Guillaume*,‡ School of Chemistry, Cardiff UniVersity, Park Place, Cardiff CF10 3AT, Wales, and UniVersite´ de Bordeaux, UMR 5255, ISM, Groupe Spectroscopie Mole´culaire, 351 cours de la Libe´ration, 33405 Talence Cedex, France ReceiVed: July 19, 2008; ReVised Manuscript ReceiVed: NoVember 22, 2008

Confocal Raman microspectrometry is used to probe, for the first time, the transport of guest molecules along the one-dimensional tunnels in a crystalline urea inclusion compound under conditions of guest exchange in which new guest molecules are introduced simultaneously at both ends of the urea tunnel structure. We focus on the system comprising 1,8-dibromooctane as the original type of guest and pentadecane as the new type of guest, and results are presented for experiments in which the guest exchange process is probed both ex situ and in situ. The Raman data, recorded as a function of position along the tunnel direction and, in the case of the in situ experiments, as a function of time, demonstrate that pentadecane guest molecules enter the tunnels at both ends of the crystal and that transport of guest molecules occurs in both directions along the crystal. Mechanistic aspects of this bidirectional transport process are discussed, particularly in relation to the corresponding process for unidirectional transport of guest molecules in urea inclusion compounds reported previously. 1. Introduction There is currently much interest in understanding the transport of molecules or ions through channel or tunnel systems. Such systems arise in a wide range of scientific fields, including nanotubes,1 channels in biological systems,2 and nanoporous solid materials.3 Studies of appropriate model systems, such as crystalline tunnels of well-defined and regular structure, can play an important role in understanding fundamental aspects of such transport processes. A specific model system that is applicable in many cases is based on conventional urea inclusion compounds,4 in which guest molecules are located within one-dimensional tunnels in a crystalline urea host structure5 (Figure 1). The tunnel diameter (ca. 5.5 Å) is relatively constant as a function of position along the tunnel, and thus the tunnels are essentially cylindrical. The cross-sectional dimensions of the tunnel are appropriate for inclusion of guest molecules based on n-alkane chains. The guest molecules are densely packed within these tunnels, forming a periodic guest substructure that is usually incommensurate5b,6 with the periodicity of the host substructure along the tunnel. An important feature of urea inclusion compounds is that the urea tunnel structure is stable only when the tunnels are filled with a dense packing of guest molecules. Removal of the guest molecules leads to rapid collapse of the “empty” urea tunnel structure, and formation of the pure crystalline phase of urea. For this reason, guest exchange cannot be carried out via the empty urea tunnel structure. Instead, we demonstrated previously7 that, provided the tunnels in the urea host structure remain filled, the identity of the guest molecules can be changed as a function of time while still maintaining the integrity of the host structure. Previous studies7-11 have demonstrated such guest exchange for the case in which new guest molecules enter the * To whom correspondence should be addressed. E-mail: harriskdm@ cardiff.ac.uk (K.D.M.H.); [email protected] (F.G.). † Cardiff University. ‡ Universite´ de Bordeaux.

tunnel at one end of the crystal (by putting it in contact with the liquid phase of another potential guest). Under these conditions, net transport of guest molecules occurs in one direction along the host tunnels, and the original guest molecules are expelled from the other end of the crystal. We refer to this process as “unidirectional” transport of guest molecules. Confocal Raman microspectrometry has been shown8 to be a powerful in situ probe of such processes, yielding information on the spatial distribution of the original and new guest molecules within the crystal and the variation of this spatial distribution as a function of time. Our previous studies of guest exchange in urea inclusion compounds7-10 have focused mainly on the system with 1,8-dibromooctane as the original type of guest molecule and pentadecane as the new type of guest molecule, although alkane-alkane exchange has also been studied.11 The present paper considers, for the first time, the situation in which both ends of the urea tunnel structure are put in contact with the liquid phase of the new guest molecules. The primary question is whether any exchange of guest molecules occurs at all (under the supposition that the competing effects of new guest molecules trying to enter both ends of the tunnel structure might cancel each other out, leading to no resultant guest exchange), or whether a mechanism exists to allow the new guest molecules to enter the tunnels at both ends of the crystal. 2. Experimental Strategy We monitor the guest exchange process using confocal Raman microspectrometry to quantify the spatial distribution of the original (1,8-dibromooctane) and new (pentadecane) guest molecules in a single crystal of the urea inclusion compound. In the Raman spectrum of the 1,8-dibromooctane/urea inclusion compound,12 the C-Br stretching band for the trans end-group conformation [denoted ν(CBrT)] is at ca. 660 cm-1 and the C-Br stretching band for the gauche end-group conformation [denoted ν(CBrG)] is at ca. 570 cm-1. For pentadecane guest

10.1021/jp806380p CCC: $40.75  2009 American Chemical Society Published on Web 12/22/2008

Bidirectional Transport of Guest Molecules

Figure 1. Structure of a urea inclusion compound at ambient temperature, showing nine complete tunnels (with van der Waals radii) viewed along the tunnel axis. The guest molecules (alkanes) have been inserted into the tunnels illustrating orientational disorder.

molecules (in the all-trans conformation) in the pentadecane/ urea inclusion compound, the methyl rocking band [denoted r(CH3)] is at ca. 900 cm-1.13 The Raman bands for the urea molecules are identical for 1,8-dibromooctane/urea and pentadecane/urea, and the symmetric C-N stretching vibration νs(CN) of urea is an intense band at ca. 1024 cm-1.12,13 From the Raman data, the following intensity ratios8-10 are used to assess the relative amounts of 1,8-dibromooctane and pentadecane guest molecules in different regions of the crystal: (i) To assess the relative amount of 1,8-dibromooctane guest molecules with the trans C-Br end-group conformation, the ratio RT ) I(CBrT)/I(CN) is used, where I(CBrT) and I(CN) are the integrated intensities of the ν(CBrT) and νs(CN) bands, respectively. This ratio is then normalized as RN,T ) RT/RT,0, where RT,0 is the value of RT (averaged over the probed area) for the original 1,8-dibromooctane/urea crystal. Thus, RN,T ) 1 for the original 1,8-dibromooctane/urea crystal and RN,T ) 0 would correspond to a crystal containing no 1,8-dibromooctane guests with trans C-Br end-groups (e.g., pentadecane/urea). (ii) To assess the relative amount of gauche C-Br end-groups for the 1,8-dibromooctane guest molecules, the ratio RG ) I(CBrG)/I(CN) is used, where I(CBrG) is the integrated intensity of the ν(CBrG) band. This ratio is then normalized as RN,G ) RG/RG,0, where RG,0 is the value of RG (averaged over the probed area) for the original 1,8-dibromooctane/urea crystal. Thus, RN,G ) 1 for the original 1,8-dibromooctane/urea crystal, and RN,G ) 0 would correspond to a crystal containing no 1,8dibromooctane guests with gauche C-Br end-groups. (iii) The relative amounts of gauche and trans C-Br endgroups are probed by considering the ratio RN,G/RN,T, which is independent of the absolute amount of 1,8-dibromooctane guest molecules in a given region of the crystal. By definition, RN,G/ RN,T ) 1 for the original 1,8-dibromooctane/urea crystal, and thus changes in RN,G/RN,T indicate changes in the relative amounts of gauche and trans end-groups in comparison with the original 1,8-dibromooctane/urea crystal. From previous studies,12 the gauche/trans ratio in 1,8-dibromooctane/urea is ca. 0.08 at ambient temperature. We emphasize that RN,G/RN,T does not directly indicate the relative amounts of 1,8-dibromooctane guest molecules with gauche and trans end-groups, as the ν(CBrG) and ν(CBrT) modes are polarized differently12 (see Figure 11B in this reference). Nevertheless, studies of the variation of RN,G/RN,T provide a reliable indication of trends in the relative amounts of gauche and trans C-Br end-groups.

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Figure 2. Representative plot showing the sigmoidal distribution for RN,T vs X at a fixed value of time t during a unidirectional guest exchange experiment. The data shown are for the experiments reported in ref 10.

(iv) To assess the relative amount of pentadecane guest molecules, we consider the ratio RM ) I(CH3)/I(CN), where I(CH3) and I(CN) are the integrated intensities of the r(CH3) and νs(CN) bands, respectively. In general, there is significant scatter of the RM data as the r(CH3) band has intrinsically very low intensity. Our previous studies8-10 of unidirectional guest transport showed that, at a given value of time, the variation of RN,T as a function of position X along the tunnel direction is approximately sigmoidal (see Figure 2, which provides an important comparison for the discussion below). In this case, the “limiting regions” of the sigmoidal distribution are the 1,8dibromooctane-rich (RN,T ≈ 1) and pentadecane-rich (RN,T ≈ 0.2) regions of the crystal. As noted previously,8-10 complete guest exchange is not actually observed, and the final value of RN,T in the pentadecane-rich regions does not fall to RN,T ) 0. Between these limiting regions, there is a “boundary region” in which RN,T varies significantly with position X along the tunnel. Within an indiVidual tunnel, there must clearly be a sharp boundary between the original and new guest molecules at a specific point (Xb) along the tunnel, but in general, at a given value of time, different tunnels within the probed region will have different values of Xb corresponding to a well-defined distribution of Xb values. The sigmoidal distribution observed in Figure 2 results from averaging over all tunnels in the probed region. As time progresses, the centroid (denoted Xo) of the sigmoidal distribution translates along the crystal, as the new pentadecane guest molecules advance through the crystal and displace the original 1,8-dibromooctane guest molecules. In the case of unidirectional guest transport studied previously,10 the position of the centroid Xo changes linearly as a function of time and the measured rate of guest transport is in the range ca. 70 - 100 nm s-1 at ambient temperature. 3. Experimental Details In the present work, confocal Raman microspectrometry14 was carried out using a Labram II spectrometer (Jobin-Yvon), an Ar/Kr 2018 Spectra-Physics laser (514.5 nm) and a grating of 1800 lines/mm (spectral resolution ca. 6 cm-1). The laser was focused on the sample through a microscope with 10× Olympus objective of 0.25 numerical aperture and confocal pinhole diameter of 700 µm. The diameter of the probed area was 50 µm (defining the radial resolution of the experiment). Crystals of 1,8-dibromooctane/urea were prepared using standard procedures. An excess of 1,8-dibromooctane (excess

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Figure 3. Schematic representation of the experimental assembly for in situ confocal Raman microspectrometry studies of bidirectional guest exchange in a urea inclusion compound, comprising a single crystal of the urea inclusion compound (green), initially containing 1,8-dibromooctane guest molecules, attached at each end to reservoirs containing liquid pentadecane (blue).

with respect to the expected guest/host molar ratio in the inclusion compound) was added to a saturated solution of urea in methanol at 50 °C. The solution was cooled to 20 °C over several days, producing crystals with long-needle morphology and hexagonal cross-section (typical length ca. 10-30 mm and cross-sectional dimension ca. 1-2 mm). The crystals were collected and washed with 2,2,4-trimethylpentane (to remove any guest molecules adhering to their external surfaces) prior to the Raman experiments. In this work, the guest exchange process was studied by both ex situ and in situ experiments. In each type of experiment, both ends of a long-needle-shaped crystal of 1,8-dibromooctane/ urea were put in contact with liquid pentadecane, thus creating the opportunity for pentadecane molecules to enter at both ends of the tunnel host structure. In the ex situ experiments, a crystal of 1,8-dibromooctane/ urea was fully immersed in liquid pentadecane, recalling that previous studies15 demonstrated the occurrence of guest exchange in urea inclusion compounds under such conditions. After a period of time, the crystal was removed from the liquid pentadecane and studied by confocal Raman microspectrometry. In the in situ experiments, a single crystal of 1,8-dibromooctane/urea was attached at each end to a reservoir containing liquid pentadecane. The experimental setup (Figure 3) for attaching the crystal to the reservoir (using Araldite as a sealing system) was analogous to that described previously8 for unidirectional guest exchange (with only one end of the single crystal attached to a liquid reservoir). In the confocal Raman microspectrometry experiments, the single crystal was mounted on the XY-motorized table of the Raman microscope. The laboratory reference frame (X, Y, Z) is defined in Figure 3. The Z axis was collinear with the direction of the incident laser beam, and the scattered light was collected in the same direction as the incident light (back-scattering geometry). The long axis (tunnel direction) of the needle-shaped crystal was aligned parallel to the X axis of the reference frame. j (in Porto notation16) Polarized spectra were recorded as Z(XX)Z j for the in situ for the ex situ measurements and Z(XX + XY)Z measurements (note that no polarizer was used for the backscattered light). In the ex situ experiment discussed below, a single crystal of 1,8-dibromooctane/urea (dimensions ca. 0.8 × 0.8 × 9 mm3) was immersed in liquid pentadecane for 2 h. The confocal Raman microspectrometry measurement was carried out at a depth Z ) 260 µm beneath the upper surface of the crystal. Raman spectra were recorded in scans along the X axis with a step size of 200 µm and a total scan range of 10 mm. Four separate scans were carried out at Y coordinates separated by 105 µm (the “width” along Y of each scan, determined by the radial resolution, was ca. 50 µm). The time to record each spectrum was 6 s.

Martı´-Rujas et al. In the in situ experiment discussed below, a single crystal of 1,8-dibromooctane/urea (dimensions ca. 1.5 × 1.5 × 35 mm3) was attached at each end to a reservoir containing liquid pentadecane. The Raman measurements were performed at a depth Z ) 300 µm beneath the upper surface of the crystal. Raman spectra were recorded in scans along the X axis with a step size of 300 µm and a total scan range of 37 mm. Six separate scans were carried out at Y values separated by 162 µm (the “width” along Y of each scan, determined by the radial resolution, was ca. 50 µm). The time to record each Raman spectrum was 4 s, and the time to record a complete map was 71 min, which is significantly shorter than the overall time scale of the guest exchange process. The normalized intensity ratios were averaged over the four central scans. Intensities of bands in the Raman spectra were determined by numerical integration of the peak area, with the baseline defined as a straight line between the specified extrema of the spectral window. For a given Raman band, the same extrema of the spectral window were defined for all spectra. All analysis is based on relatiVe intensities of Raman bands, and in particular, the variation in the relatiVe intensities as a function of position (X) along the crystal and (in the case of the in situ measurement) as a function of time. As discussed above, the results were averaged over a set of independent scans at different fixed values of Y. 4. Results and Discussion 4.1. General Observations. First we discuss results from the ex situ experiment, which does not directly probe the timedependence of the guest exchange process but allows a more accurate determination of the intensity ratios.17,18 From the Raman spectra (representative examples of which are shown in Figure 4), the variation of RN,T as a function of position X has been measured. The results, shown in Figure 5a, demonstrate clearly the existence of two boundary regions. Each boundary region displays the same type of sigmoidal distribution of RN,T values as that reported previously for unidirectional guest exchange (see Figure 2), demonstrating clearly that guest exchange occurs at both ends of the crystal. An important feature of the RN,T data (discussed in detail below) is that behind each boundary region the value of RN,T is typically about 0.2. The symmetric shape of the RN,T distribution in Figure 5a suggests that the relative amount of guest exchange is essentially the same at each end of the crystal. For the same set of Raman data, the variation of RM as a function of position X (Figure 5b) also exhibits a sigmoidal distribution at each end of the crystal, but in the opposite sense to RN,T (i.e., RM increases on moving toward the ends of the crystal). The RM data confirm that pentadecane guest molecules enter the tunnels at both ends of the crystal, with transport of guest molecules occurring in both directions through the crystal. As shown in panels c and d of Figure 5, respectively, both RN,G and RN,G/RN,T increase significantly within each boundary region, indicating that the 1,8dibromooctane guest molecules have a significantly increased proportion of gauche end-groups in these regions of the crystal, as also observed for unidirectional guest exchange.9 From the results of the in situ experiment, the variation of RN,T as a function of position X along the tunnel at different values of time after the start of the guest exchange process is shown in Figure 6. These data also demonstrate clearly that boundary regions develop at both ends of the crystal (Figure 6), similar to those observed in the ex situ experiment. Each boundary region advances toward the center of the crystal as time increases. The variation of RM, RN,G, and RN,G/RN,T as a

Bidirectional Transport of Guest Molecules

Figure 4. Representative Raman spectra of the urea inclusion compound after partial exchange of 1,8-dibromooctane guest molecules by pentadecane guest molecules in the bidirectional guest exchange process. The spectra are from the ex situ study (see also Figure 5), and were recorded at X ) 0.5 (green), 1.4 (blue), 1.8 (red), and 3.0 mm (black), thus representing different parts of the boundary region at the left-hand side of Figure 5a. The absolute intensities of all spectra were scaled to give the same intensity of the urea νs(CN) band. The variation in the intensities of bands due to the two types of guest molecule (C-Br stretching bands of the trans and gauche end-group conformations of 1,8-dibromooctane and methyl rocking mode of pentadecane) as a function of position along the tunnel direction should be noted. In contrast, the intensities of the bands due to the urea molecules remain essentially constant as a function of position along the tunnel direction.

function of position X in the in situ experiment are also similar to those discussed above for the ex situ experiment. More detailed analysis of the results from the in situ experiment is discussed in Section 4.3. 4.2. Models of Bidirectional Guest Transport. To rationalize the behavior observed in the bidirectional guest exchange process, we first consider a model in which transport of guest molecules occurs exclusively in one direction (e.g., left-to-right) in some tunnels and exclusively in the opposite direction (rightto-left) in the other tunnels. The left-right symmetry of Figures 5 and 6 implies that, for this model, the numbers of tunnels undergoing guest transport in each direction should be approximately equal. As the cross-sectional dimensions of the guest molecules are comparable to the cross-sectional dimensions of the urea tunnel, there would be insufficient space for guest molecules traveling in opposite directions to pass each other within a given tunnel. Within this model, it is therefore highly improbable for guest transport to occur simultaneously in both directions along a given tunnel. This “idealized model” assumes that guest transport occurs independently in each tunnel, with the transport in a given tunnel extending along the full length of the crystal and with no mechanism for guest molecules to move between adjacent tunnels (Figure 7). Thus, if there are NT tunnels, we may assume that NT/2 tunnels undergo guest transport from left-to-right and

J. Phys. Chem. C, Vol. 113, No. 2, 2009 739 the other NT/2 tunnels undergo guest transport from right-toleft. In the early stages of the guest exchange process, three different regions of the crystal may be identified, denoted L, M, and R in Figure 7. Regions L and R (which in principle are equivalent, given the symmetry of the process) exist between one end of the crystal and the “boundary region” nearest to the same end of the crystal. Within region L (Figure 7), guest exchange has already occurred in the NT/2 tunnels in which the new guest molecules enter at the left-hand end of the crystal and these tunnels (in which guest transport occurs from leftto-right) are occupied by new guest molecules. In the other NT/2 tunnels in region L, guest transport occurs from right-to-left, and at the stage of the transport process shown in Figure 7, these tunnels are still occupied by the original guest molecules. Within region R, guest exchange has already occurred in the NT/2 tunnels in which the new guest molecules enter at the righthand end of the crystal and these tunnels (in which guest transport occurs from right-to-left) are occupied by new guest molecules. In the other NT/2 tunnels in region R, guest transport occurs from left-to-right, and at the stage of the transport process shown in Figure 7, these tunnels are still occupied by the original guest molecules. In region M, NT/2 tunnels undergo guest transport from right-to-left and the other NT/2 tunnels undergo guest transport from left-to-right, but at the stage of the transport process shown in Figure 7, all tunnels in region M are still occupied by the original guest molecules. In the early stages of the guest exchange process (Figure 8a,b), the two boundary regions move toward each other. Thus, regions L and R increase in size and region M decreases in size. When the two boundary regions cross each other (Figure 8c,d), the size of region M is reduced to zero, and during this stage, the identity of the guest molecules at the center of this region changes rapidly from being only original guest molecules to being only new guest molecules. After the two boundary regions have crossed each other, they move away from each other toward opposite ends of the crystal. In this stage of the process (Figure 8e,f), the central region (now denoted M′) represents the intersection of regions L and R. Region M′ contains only new guest molecules and increases in size as the guest exchange progresses. At the end of the guest exchange process, region M′ extends throughout the entire crystal. For this idealized model, and under the assumption that all tunnels undergo guest transport (leading to complete guest exchange at the end of the process), schematic plots of RN,T versus position X along the tunnel at different stages of the guest exchange process are shown in Figure 8. In the early stages (before the boundary regions have crossed), the value of RN,T should be 1 in region M and 0.5 in regions L and R. However, if complete guest exchange does not occur (e.g., if some tunnels do not undergo guest transport) regions L and R should have RN,T > 0.5. It is clear, at least qualitatively, that the behavior of the experimental data (Figures 5a and 6) is similar to that shown for the idealized model in Figure 8, with the crystal divided into three regions, separated by the two boundary regions, which move toward the center of the crystal in the early stages of the process. However, in quantitative terms, the experimental data differ from the idealized model, particularly as the value of RN,T in regions L and R is about 0.2 even from the earliest stages of the process (see Figures 5a and 6) [we note that this value of RN,T is close to that observed in the corresponding region of the crystal in the case of unidirectional guest exchange8-10 (see Figure 2)]. This observation is reproducible in repeated studies (both in situ and ex situ experiments) of bidirectional guest

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Figure 5. Results from the ex situ study of the bidirectional guest exchange process: (a) RN,T vs X, (b) RM vs X, (c) RN,G vs X, and (d) RN,G/RN,T vs X.

Figure 6. Results of RN,T vs X at different values of time from the in situ study of the bidirectional guest exchange process. The data for each value of time are indicated by the following symbols: open circles, t ) 288 min; open squares, 496 min; open diamonds, 842 min; open triangles, 1118 min; filled circles, 1257 min.

exchange for several different single crystals of 1,8-dibromooctane/urea in contact with liquid pentadecane. These observations suggest that aspects of the idealized model are inappropriate for describing the actual process in the experimental system. Thus, it is important to explain the fact that the observed value of RN,T is less than 0.5 in regions L and R. First, we recall that a decrease in the intensity of the ν(CBrT) band in the Raman spectra, leading to a decrease in RN,T, is interpreted as replacement of 1,8-dibromooctane guest molecules by pentadecane guest molecules. To consider this interpretation in more detail, it is necessary to assess other possible reasons that the intensity of the ν(CBrT) band may decay, for example, if the trans end-groups of the 1,8-dibromooctane guest molecules undergo a change of conformation. We recall that, for the

Figure 7. Idealized model for bidirectional transport of guest molecules. Each tunnel undergoes guest transport only in one direction (half the tunnels from left-to-right and the other half from right-toleft). Regions of each tunnel occupied by the original and new guest molecules are shown in green and blue, respectively. The two boundary regions, as well as regions L, M, and R discussed in the text, are indicated.

original 1,8-dibromooctane/urea crystal, the vast majority of 1,8dibromooctane guest molecules have trans end-group conformations, and only a small proportion of 1,8-dibromooctane guest molecules have gauche end-groups (the gauche/trans ratio is ca. 0.0812). During the guest-exchange process, no new bands appear in the relevant region of the Raman spectra,19 indicating that the trans and gauche conformations are the only end-group conformations of the 1,8-dibromooctane guest molecules throughout the process. Thus, the only conformational change that could deplete the amount of trans end-groups would be the formation of gauche end-groups. From Figure 5c, it is clear that the relative amount of gauche end-groups increases in the vicinity of each boundary region (as also observed9 for unidirectional guest

Bidirectional Transport of Guest Molecules

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Figure 8. Schematic graphs of RN,T vs X for the idealized model for bidirectional transport of guest molecules at different stages (a-f) of the process. A schematic representation of the distribution of guest molecules in the crystal is shown above each graph. Regions containing only the original guest molecules are shown in green (RN,T ) 1), regions containing a mixture of the original and new guest molecules are shown in light blue (RN,T ≈ 0.5), and regions containing the final distribution of original and new guest molecules (in principle RN,T ) 0, but in practice RN,T ≈ 0.2) are shown in dark blue.

exchange), corresponding to a maximum RN,G value of ca. 2. Correspondingly, the ratio RN,G/RN,T (Figure 5d) also increases at each boundary region, reaching a maximum value of RN,G/RN,T ≈ 6. However, as now discussed, the increased relative amount of gauche end-groups in the boundary region cannot account for the unexpectedly low value of RN,T observed in regions L and R. In particular, as evident from Figure 5, the increased relative amount of gauche end-groups occurs only in the close vicinity of each boundary region, whereas behind each boundary region (i.e., in regions L and R) the value of RN,G falls toward RN,G ≈ 1, implying that the gauche/trans ratio in regions L and R is similar to that for the original 1,8-dibromooctane/urea crystal. If we use F(X,t) to denote the ratio of the number of 1,8-dibromooctane guest molecules per unit volume at position X and time t during the guest exchange process relative to the number of 1,8-dibromooctane guest molecules per unit volume in the original 1,8-dibromooctane/urea crystal, it can be readily shown that

F(X, t) ) [1 ⁄ (1 + R)]RN,T(X, t) + [R ⁄ (1 + R)]RN,G(X, t) where R is the gauche/trans ratio in the original 1,8-dibromooctane/urea crystal. Using this equation with R ) 0.0812 and values of RN,T and RN,G from our Raman data, the value of F(X,t) behind each boundary region (i.e., in regions L and R) is ca. 0.31 (e.g., in region L at X ≈ 0.5 mm, RN,T ≈ 0.25 and RN,G ≈ 1.1 from panels a and c of Figure 5, respectively). Thus, the proportion of 1,8-dibromooctane guest molecules in regions L and R is significantly less than 0.5, as also implied from the discussion above based on consideration of the measured values of RN,T (Figure 5a). Thus, although there is an increased proportion of gauche end-groups at each boundary region, trans-to-gauche conformational changes cannot account for the fact that the value of RN,T in regions L and R is significantly lower than the value RN,T ) 0.5 expected on the basis of the idealized model for the bidirectional guest exchange process. The idealized model assumes that guest transport occurs only within individual tunnels, with no opportunity for guest

molecules to move between adjacent tunnels. This assumption is consistent with all experimental observations8-10 for unidirectional transport of guest molecules (although more elaborate transport models in which guest molecules can move between adjacent tunnels, as discussed below, may also be consistent with the experimental observations for unidirectional guest transport). In the space-averaged and time-averaged crystal structure of urea inclusion compounds determined from X-ray diffraction data,5 there are no voids or spaces within the tunnel wall that would allow guest molecules to pass from one tunnel to an adjacent tunnel, although clearly the crystal could contain defects that may facilitate such intertunnel transport. Furthermore, given the well-established dynamic properties of the urea molecules in urea inclusion compounds (and in particular for 1,8-dibromooctane/urea20) at ambient temperature, it is possible that the creation of a suitable defect in the tunnel wall to allow intertunnel transport of guest molecules may be associated with the dynamic properties of the urea host structure. If a sufficiently high density of suitable defects exists (either spatially or temporally), a revised transport model based on a three-dimensional network of interconnected tunnels may be applicable (illustrated schematically in two-dimensions in Figure 9), with guest molecules able to pass from a given tunnel into one or more adjacent tunnels at certain sites along the tunnel. In this case, a given guest molecule moving through the crystal could occupy different tunnels at different stages of the process. This more generalized model for guest transport allows the possibility that, for a giVen tunnel, guest transport may occur from left-to-right in some regions of the tunnel and from rightto-left in other regions of the same tunnel (e.g., see the second tunnel from the top of Figure 9). For this “generalized model”, the number of tunnels undergoing guest transport in a given direction along the crystal is not necessarily the same in all regions of the crystal. Thus, it is possible (as shown in Figure 9) that, at an early stage of the guest exchange process, 80% of tunnels undergo guest transport from left-to-right in region L but only 20% of tunnels undergo guest transport from left-toright in region R, and for the same crystal, 80% of tunnels

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Figure 9. Generalized model for bidirectional transport of guest molecules, with guest molecules able to move between adjacent tunnels by means of appropriate defects. The regions of each tunnel occupied by the original and new guest molecules are shown in green and blue, respectively. Directions of transport of guest molecules are indicated by the arrows. In region L, 80% of tunnels undergo guest transport from left-to-right, whereas in region R, 80% of tunnels undergo guest transport from right-to-left.

undergo guest transport from right-to-left in region R but only 20% of tunnels undergo guest transport from right-to-left in region L. In this case, both regions L and R comprise 80% of new guest molecules and 20% of original guest molecules, while region M comprises only original guest molecules. The actual percentages (80% and 20%) discussed above are chosen arbitrarily, but serve to demonstrate that while, as discussed above, the idealized model could not have less than 50% of original guest molecules in both regions L and R in the early stages of the guest exchange process, the generalized model does permit both regions L and R to have less than 50% of original guest molecules. As such, the generalized model is consistent with all the experimental data presented here (Figures 5a and 6) for bidirectional exchange of guest molecules in urea inclusion compounds. An interesting issue for the generalized model is to understand the topological nature of the network of interconnected tunnels and the spatial changes that occur in this network on passing from region L to region M and to region R. Clearly, such spatial changes are required in order to create a situation in which, for example, 80% of the tunnels in region L undergo guest transport from left-to-right but only 20% of the tunnels in region R undergo guest transport from left-to-right, with the implication that there is a continuous variation within region M in the number of tunnels that undergo guest transport in a given direction. Furthermore, given that the boundary regions move through the crystal during the guest exchange process and hence the sizes of regions L, M, and R change as a function of time, it is reasonable to suggest that the network of tunnels that undergo guest transport in a given direction (and the distribution of defects that allow intertunnel transport of guest molecules) must also change as a function of time during the process. 4.3. Kinetics of Bidirectional Guest Transport. To assess kinetic aspects of the bidirectional guest transport process, we consider in more detail the time dependence of the results obtained in the in situ experiment. For each boundary region, we consider the time dependence of [Xo(t) - XoLR(0)], where t ) 0 is the time of the first measurement (rather than the time at which the liquid pentadecane is put in contact with the original 1,8-dibromooctane/urea crystal) and XoLR(0) is the value of Xo at t ) 0 for the boundary region that moves from left-to-right through the crystal. The analysis is analogous to that discussed previously10 for unidirectional transport of guest molecules in

Martı´-Rujas et al.

Figure 10. Plots of [Xo(t) - XoLR(0)] vs t determined independently for both boundary regions from the in situ data, clearly showing the linear dependence discussed in the text. Note that the relatively large error bars on the values of time arise because of averaging the results obtained for Raman spectra recorded at different values of time during each set of scans.

urea inclusion compounds, and plots of [Xo(t) - XoLR(0)] vs t for each boundary region in the in situ experiment are shown in Figure 10. As observed for the case of unidirectional guest transport,10 [Xo(t) - XoLR(0)] varies linearly with time, and from the gradients of the plots in Figure 10, the rate of transport at ambient temperature is determined to be (185 ( 42) nm s-1 for one boundary region [right-to-left transport (negative gradient)] and (262 ( 38) nm s-1 for the other boundary region [left-toright transport (positive gradient)]. Within the estimated errors, the differences between the rates of left-to-right transport and right-to-left transport cannot be considered significant. It is noteworthy that the rate of transport is somewhat higher than that (in the range 70-100 nm s-1) reported previously10 for guest exchange under conditions of unidirectional guest transport (for the same original and new guest molecules and at the same temperature as the bidirectional guest transport process studied here). Although a more comprehensive set of kinetic studies must be completed before detailed conclusions may be reached on the relative rates of unidirectional and bidirectional guest exchange processes, the different rates suggested above may allude to different mechanistic aspects in the two cases. In particular, the existence of pathways for intertunnel transport of guest molecules (and the associated defects that permit intertunnel transport) may play a different role in each case, with the likelihood (as discussed above) that such pathways are relatively more important in the case of bidirectional guest transport. Furthermore, as suggested above, the guest transport process itself may serve a role in creating the defects that allow intertunnel transport, and therefore the nature of the interconnections between tunnels may be fundamentally different for unidirectional and bidirectional guest exchange processes, with clear implications for the relative rates of these processes. 5. Concluding Remarks The results reported in this paper demonstrate that, under conditions of guest exchange in which both ends of the urea tunnel structure are put in contact with the liquid phase of “new” molecules that are thermodynamically more favorable as guests inside the tunnel structure, the new guest molecules enter the tunnels at both ends of the crystal, displacing the “original” guest molecules, and giving rise to transport of guest molecules in both directions along the crystal. Quantitative analysis of the

Bidirectional Transport of Guest Molecules spatial distribution of the original and new guest molecules within the tunnel structure, as well as the time-dependence of this spatial distribution, yield mechanistic insights regarding the bidirectional guest exchange process. Under conditions of bidirectional guest exchange, the mechanism for guest transport is not necessarily the same as the mechanism that operates under conditions of unidirectional guest exchange. Thus, in the bidirectional case, the driving force for guest molecules to enter at both ends of the crystal, as well as the consequent transport of guest molecules in both directions through the host tunnel structure, is necessarily different from the case in which the transport of guest molecules occurs only in one direction, and the guest molecules moving in a given direction may be influenced by the simultaneous movement of other guest molecules in the opposite direction. A related issue is the extent to which guest transport occurs independently in different tunnels. As discussed above, the idealized model for bidirectional guest transport (in which intertunnel transport is forbidden) is not compatible with the experimental results obtained here (in particular, this model cannot explain the observed values of RN,T in regions L and R of the crystal at early stages of the guest exchange process), whereas the generalized model (in which intertunnel transport is allowed) is fully compatible with all the experimental evidence currently available. However, we note that, at this stage, there is no direct experimental evidence to either confirm or refute the occurrence of intertunnel guest transport. According to the generalized model, a three-dimensional transport network exists in which guest molecules are able to move between adjacent tunnels during their transport along the crystal. A possible feature of such networks is that, for a given tunnel, guest transport may occur in a given direction in some parts of the tunnel and in the opposite direction in other parts of the same tunnel (as illustrated in Figure 9). As the pathways for guest molecules to move between adjacent tunnels must rely on appropriate defects (spatial and/or temporal) in the crystalline host tunnel structure, we note that the guest transport process itself may be able to create suitable defects that do not necessarily exist in the original crystal of the inclusion compound before starting the guest exchange process. Although such suggestions are certainly reasonable and are consistent with the evidence currently available, further experimental investigations are required in order to obtain direct evidence that intertunnel transport of guest molecules does indeed occur under conditions of bidirectional guest exchange. Finally, it is interesting to note that the similarity of the RN,G data (and the RN,G/RN,T data) for the ex situ and in situ experiments suggests that the increased proportion of gauche conformations in the boundary region does not “relax” after stopping the guest exchange process (recalling that the guest exchange process must be stopped before making the Raman measurements in the ex situ experiment). Acknowledgment. We are grateful to the European Union (Marie Curie Training Fellowship to J.M.R.), Cardiff University (studentship to J.M.R.), the University of Bordeaux (Visiting Professorship to K.D.M.H.), and Re´gion Aquitaine for financial support. We thank D. Talaga and J. L. Bruneel for technical help and Anabel Morte-Rodenas for experimental assistance. References and Notes (1) (a) Hummer, G.; Rasaiah, J. C.; Noworyta, J. P. Nature 2001, 414, 188. (b) Lee, S. B.; Martin, C. R. J. Am. Chem. Soc. 2002, 124, 11850. (c) Hod, O.; Rabani, E. Proc. Nat. Acad. Sci. 2003, 100, 14661. (d) Kalra, A.; Garde, S.; Hummer, G. Proc. Nat. Acad. Sci. 2003, 100, 10175. (e) Wei,

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