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Johnson Matthey Technol. Rev., 2020, 64, (2), 152

doi:10.1595/205651320x15747624015789

Observing Solvent Dynamics in Porous Carbons by Nuclear Magnetic Resonance

Elucidating molecular-level dynamics of in-pore and ex-pore species

    • Luca Cervini
    • Department of Chemistry, Lancaster University, Lancaster, LA1 4YB, UK
    • Nathan Barrow
    • Johnson Matthey, Blounts Court Road, Sonning Common, Reading, RG4 9NH, UK
    • John Griffin*
    • Department of Chemistry, Lancaster University, Lancaster, LA1 4YB, UK; Materials Science Institute, Lancaster University, Lancaster, LA1 4YB, UK
    • Email: *j.griffin@lancaster.ac.uk
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Article Synopsis

The adsorption and diffusion of species in activated carbons is fundamental to many processes in catalysis and energy storage. Nuclear magnetic resonance (NMR) gives an insight into the molecular-level mechanisms of these phenomena thanks to the unique magnetic shielding properties of the porous carbon structure, which allows adsorbed (in-pore) species to be distinguished from those in the bulk (ex-pore). In this work we investigate exchange dynamics between ex-pore and in-pore solvent species in microporous carbons using a combination of one-dimensional (1D) and two-dimensional (2D) NMR experiments. We systematically compare the effects of four variables: particle size, porosity, solvent polarity and solvent viscosity to build up a picture of how these factors influence the exchange kinetics. We show that exchange rates are greater in smaller and more highly activated carbon particles, which is expected due to the shorter in-pore–ex-pore path length and faster diffusion in large pores. Our results also show that in-pore–ex-pore exchange of apolar solvents is slower than water, suggesting that the hydrophobic chemistry of the carbon surface plays a role in the diffusion kinetics, and that increased viscosity also reduces the exchange kinetics. Our results also suggest the importance of other parameters, such as molecular diameter and solvent packing in micropores.

Introduction

Understanding the performance of activated carbons in their applications as energy storage materials or catalyst supports requires a description of the behaviour of adsorbates, including solvents, gases, organic molecules or ions. NMR allows adsorption of species in porous carbons to be studied due to the nucleus-independent chemical shift (NICS) arising from the aromaticity of the pore walls (1, 2). The NICS allows adsorbed species to be distinguished from ex-pore species in the bulk solution external to the carbon particles and has been shown to depend on, among other parameters, the distance between the adsorbate and the pore walls. In recent years, several studies have exploited this to use NMR as a probe of the pore structure of a range of porous carbons. Borchardt et al. showed that the NICS of adsorbed organic electrolyte species varied in accordance with the pore size of titanium carbide-derived carbons (CDCs) which have very well-defined porosity (3). This was supported in work by Forse et al. who also showed that ion adsorption in CDCs is significantly reduced when the average pore size is smaller than the solvated ion size (4). In a subsequent study, density functional theory (DFT) was used to show that for model carbon slit pores, the NICS depends upon both the pore width and the size and curvature of carbon fragments making up the pore walls (5). Xing et al. used DFT calculations to derive a relationship between the magnitude of the NICS and the pore size assuming a slit pore geometry, which was found to agree well with experimental measurements of NICS for aqueous species adsorbed on poly-ether-ether-ketone (PEEK) derived carbons (PDCs) (6).

Another important phenomenon that can be studied by NMR is the dynamics of the often highly mobile adsorbate and solvent species. Diffusion coefficients of adsorbed species can be determined experimentally via NMR using pulsed field gradient (PFG) techniques (7). A number of PFG NMR studies have shown that diffusion of species confined in carbon micropores is reduced significantly compared to bulk solution. Furtado et al. observed a broad distribution of local diffusivities for a carbon with a bimodal pore size distribution which was interpreted in terms of restricted internal diffusion between pores of different sizes (8). PFG NMR measurements on ethylene carbonate and dimethyl carbonate mixtures by Alam and Osborn Popp showed that diffusion coefficients for species adsorbed in carbon micropores were reduced by up to a factor of five compared to bulk solution (9). Forse et al. used PFG NMR to study microporous carbon supercapacitor electrodes and observed significant reductions in the diffusion coefficients of adsorbed species, although acetonitrile solvent species were found to diffuse faster than the larger electrolyte ions (10).

While PFG NMR provides significant insight into the dynamics of species confined within the porous carbon network, further information regarding the dynamic exchange of species between pore environments and also between the in-pore and ex-pore environments can be obtained from exchange spectroscopy (EXSY) measurements (11). In this experiment, for which the pulse sequence is shown in Figure 1, the first pulse and subsequent delay allows the single-quantum magnetisation to precess at a characteristic frequency. The second pulse converts this coherence into a population state, which is maintained for a duration called the mixing time, tmix. For zero mixing time it is expected that there will be no diffusion and for long mixing times it is expected that the solvent molecules will reach an equilibrium between the different pore locations. After the mixing time a third pulse is applied and the spins once again precess at their characteristic frequencies and a signal is detected. After a Fourier transformation of both time dimensions is performed, a 2D spectrum is obtained. Magnetisation that has not been exchanged will have precessed at the same characteristic frequency during both times, giving rise to a peak on the diagonal of the spectrum. Magnetisation that has been exchanged between in-pore and ex-pore locations will have precessed at one frequency initially and another during detection. A peak will appear off-diagonal in the spectrum and at the direct-dimension chemical shift of the spin where the molecule finally resided. These two cases give rise to diagonal peaks and cross-peaks, respectively. Further information can be extracted by performing the experiment with varying mixing times. Integrating the cross-peak area and plotting as a function of mixing time yields a build-up curve, from which exchange rate constants can be extracted (12, 13).

Fig. 1.

Pulse sequence of the EXSY experiment. For each tmix chosen, the sequence is repeated with increasing t1 values

Pulse sequence of the EXSY experiment. For each tmix chosen, the sequence is repeated with increasing t1 values

The EXSY approach was applied by Alam and Osborn Popp who showed that the in-pore environment is inhomogeneously broadened due to species occupying a range of pore environments, between which exchange takes place on the millisecond timescale (9). Griffin et al. showed for a commercial porous carbon saturated with an organic electrolyte that in-pore–ex-pore exchange of the anionic species also takes place on the millisecond timescale, although did not fit well to a single exchange process (14). Fulik et al. subsequently showed that build up curves in EXSY data for commercial activated carbon saturated with organic electrolyte can be interpreted in terms of two processes with different rates, i.e. a slow process attributed to diffusion from the centre of the particle to the surface, and a much faster process attributed to effective exchange between ex-pore and in-pore (15). In addition, it was shown that exchange dynamics can also affect the observed NICS and lineshape in 1D spectra, whereby the onset of in-pore–ex-pore exchange upon saturation of the micrometre-sized particles leads to a reduction of the observed NICS (4). In these typical cases, the diffusion path between the ex-pore and in-pore environment is much shorter, allowing faster exchange of species between ex-pore and in-pore which leads to partial or complete exchange averaging of the in-pore and ex-pore resonances.

However in our previous work (16) we showed that the NICS did not change upon saturation for 100 μm PDC particles soaked with water. An example of this observation is shown in Figure 2(a). This was attributed to the relatively large particle size used in the experiments, meaning that in-pore–ex-pore exchange does not take place on the timescale of the NMR experiment. Furthermore, nitrogen gas sorption analyses of PDCs revealed the presence of at least three different pore widths of 0.8 nm, 1.2 nm and 2.2 nm, (Figure 2(b)) whereas only a single in-pore resonance was observed. This was rationalised in terms of fast exchange between micro- and mesopores within the pore network, leading to motional averaging of the in-pore resonance. However, the single in-pore resonance was found to be subject to inhomogeneous broadening, as evidenced by a purely diagonal in-pore diagonal peak in 2D EXSY spectra at short mixing time. This means that within a particle, there are regions of different averaged NICS, which can be due to a variation of aromaticity as well as local average pore size. The latter depends mostly on the inhomogeneity of activation throughout the carbon particles. This was experimentally minimised by activating smaller particles. The symmetric in-pore components coming from the regions of fast averaged NICS can, as shown by Merlet et al., be broadened by slow intra-particle exchange (17). The size of these regions of averaged NICS can be estimated to be around 1 μm in diameter, assuming that the in-pore diffusion coefficient is the same as ex-pore, and that a 1 kHz frequency is enough for the fast regime. From ex-pore to in-pore however, the diffusion path was much longer in our particles. It arises that there must be regions with fast in-pore–ex-pore exchange and more isolated regions.

Fig. 2.

(a) 1H NMR spectra of a typical PDC wetted with increasing amounts of water shown in terms of multiples of the total pore volume (PV); (b) corresponding N2 gas sorption pattern

(a) 1H NMR spectra of a typical PDC wetted with increasing amounts of water shown in terms of multiples of the total pore volume (PV); (b) corresponding N2 gas sorption pattern

In this work, we systematically investigate the effects of carbon particle size, porosity and solvent properties on in-pore–ex-pore and in-pore–in-pore exchange dynamics as viewed by NMR spectroscopy. We chose PDCs as our model system due to the ease of synthesis and tunability of the porosity whereby the pore volume (PV) and average pore size vary approximately linearly with burn-off (BO) and activation time (18), in addition to these materials giving rise to generally strong NICS, facilitating structural characterisation and analyses of adsorbate behaviour (1921). We first provide a review of the effects of two-site exchange on 1D NMR spectra with specific reference to a model for a carbon particle saturated with solvent species. We then discuss the experimental results in three sections: first, we compare PDC particles of ~80 μm diameter with ~15–20 μm particles obtained from the same sample, to confirm that our samples show minimal exchange broadening due to a longer path between the two environments. Second, we compare PDC samples that were steam-activated with 20% BO and 54% BO to see the extent at which diffusion coefficients in pores of different sizes influence the exchange rate constants. Finally, we compare PDC samples saturated with different solvents, namely water, hexane and cyclohexane. These solvents were chosen because of their comparable or different polarity and viscosity, two parameters which are expected to influence the diffusion of the solvent molecules in the pores. The pore filling is assessed in unsaturated samples to determine the accessibility of the pore network. Ex-pore–in-pore exchange rate constants were determined using exchange experiments and were then used to better understand how various exchange regimes perturb 1D NMR spectra.

Exchange Averaging in One-Dimensional Nuclear Magnetic Resonance Spectra

Averaging of NMR signals is a common phenomenon observed when individual nuclei explore several magnetic environments. In the case of a solvent adsorbed in porous carbons, the diffusion of solvent molecules between regions giving rise to different NICS affects the NMR spectrum. The perturbation depends on the average time each molecule remains in each environment. Considering a nucleus able to explore two environments, several cases can be distinguished: the slow exchange regime where both peaks may be broadened but without being shifted, the intermediate regime where both peaks have merged into a single very broad peak and the fast exchange regime where the single peak narrows. To understand these observations, we can turn to the underlying principles of the Fourier transform.

In the fast exchange regime, the resulting peak is located at the average of the chemical shifts weighted by the residence time in each environment. To illustrate this, various NMR signals were simulated using cosine waves and subsequently Fourier transformed by fitting cosine functions of variable frequencies, whereby the NMR spectrum is obtained as the integral of the product between the original and the fitted functions (full details of the simulation are given in Supplementary Information (SI)). This simulation is a simplified case of fast exchange where motional broadening is not accounted for. Its purpose is to show how the averaged chemical shift depends on the relative dwell times. Figure 3(a) shows the simulated NMR signals; the blue component oscillates at a frequency of 30 Hz and the red components oscillate at 50 Hz. The ratio of the time spent oscillating at either frequency is given: an average of approximately 32 Hz is obtained when adopting 30 Hz for 0.1 ms and 50 Hz for 0.01 ms, and an average of 40 Hz is obtained when oscillating at both frequencies for the same time. For better visibility, the angle in radians travelled as a function of time is plotted in Figure 3(b). The spectra obtained after Fourier transformation, Figure 3(c), show how the apparent frequency of the exchange-averaged peak depends on the residence time in each environment. When the residence times of the nucleus in both environments are identical, we call it a symmetric exchange. This is found for example in an acid-base mixture when pH = pKa, where by definition both acid and conjugated base are equimolar. However, asymmetric exchange is more relevant to the present study due to the large population difference between the in-pore and ex-pore environments, and also between the volume of the different connected pores.

Fig. 3.

(a) Portion of simulated cosine waves oscillating at 30 Hz (blue) or 50 Hz (red) for various periods of time; (b) angle evolution as a function of time; and (c) corresponding Fourier transformed spectra

(a) Portion of simulated cosine waves oscillating at 30 Hz (blue) or 50 Hz (red) for various periods of time; (b) angle evolution as a function of time; and (c) corresponding Fourier transformed spectra

Different chemical shifts can be attributed to different regions inside and around a porous carbon particle. Figure 4 illustrates a carbon particle (black continuous line) saturated with a solvent. Molecules in the green region adopt the ex-pore chemical shift, and molecules in the blue region an in-pore chemical shift. The deeper the colour, the more likely the molecule is to change environment within a certain time. The dashed lines represent the boundaries between molecules undergoing fast and slow exchange: within the dashed lines, the in-pore–ex-pore exchange (orange arrows) is frequent enough for the chemical shift to be averaged. Note that the ex-pore dashed line is at a constant distance from the particle surface because the ex-pore diffusion coefficient is constant. The in-pore dashed line however is distorted due to inhomogeneities of in-pore diffusion coefficients and wraps around big mesopores penetrating deep into the particles. In summary we expect two non-exchanging peaks corresponding to ex-pore solvent far from the particle and in-pore solvent in the core of the particle, and a broadened peak, corresponding to solvent molecules undergoing fast exchange.

Fig. 4.

Scheme of an activated carbon particle (black continuous line, delimiting the ex-pore/in-pore boundary) saturated with solvent, blue for adsorbed and green for bulk. The orange arrows represent fast exchange of molecules between the two environments. The colour gradient represents the probability of a solvent molecule exchange during data acquisition. Molecules between the two dashed lines may exchange fast enough to appear at the exchange-averaged chemical shift, with Vinexch and Vexexch standing for the volume of such exchanging solvent initially in-pore or ex-pore respectively

Scheme of an activated carbon particle (black continuous line, delimiting the ex-pore/in-pore boundary) saturated with solvent, blue for adsorbed and green for bulk. The orange arrows represent fast exchange of molecules between the two environments. The colour gradient represents the probability of a solvent molecule exchange during data acquisition. Molecules between the two dashed lines may exchange fast enough to appear at the exchange-averaged chemical shift, with Vinexch and Vexexch standing for the volume of such exchanging solvent initially in-pore or ex-pore respectively

The position of the exchange-averaged peak depends on the time the molecules spend in each environment. However in practice, when adsorption and desorption are at equilibrium, the solvent molecules exchange by pairs because the volumes of exchanging adsorbed solvent Vinexch and exchanging free solvent Vexexch are constant. The diffusion coefficient in the pores is smaller than in the bulk, so for the in-pore molecules to exchange in the fast regime they must reside closer to the interface. Therefore, Vinexch is smaller than Vexexch. The residence time of the exchanging solvent molecules can now be correlated to Vexexch and Vinexch and the in-pore/ex-pore ratio of diffusion coefficients. Experimentally it is possible to calculate Vexexch and Vinexch from the position and volume of the broad ex-pore peak.

Results

Particle Size Effects

To directly observe the impact of particle size on 1D NMR spectra, two activated PDC samples were reduced from approximately 100 μm particle size to approximately 15–20 μm by sieving (see Methods in SI). The samples were named xBO_y, where x is the percentage of BO and y the median particle size D50, measured by dynamic light scattering. The samples were in the first instance wetted using a microsyringe with a defined volume of deionised water less than the PV, then with a volume greater than PV, to observe the 1H NMR spectrum before and after saturation. We have previously shown that this method allows us to compare the NICS averaged over the whole pore network without, and then including, perturbations related to in-pore–ex-pore exchange. This is because the in-pore peak before sample saturation corresponds to water located in completely filled particles that are not yet surrounded by water. Figures 5(a) and 5(b) show the spectra of sample 54BO_80 and 54BO_21, respectively. The in-pore peak shifts by approximately 0.2 ppm upon saturation, regardless of the particle size. This means that in this range of particle size, diffusion of water out of the pores has a negligible impact on the NICS for most of the adsorbed water and the width of the in-pore peak is solely due to the distribution of average NICS. However, exchange averaging has a measurable impact on the ex-pore peaks. In both samples they were fitted with a narrow and a broad component, the intensity and full width at half maximum (FWHM) of which vary. The broad component is assigned to ex-pore water having experienced the pores for a period of time and is therefore also partially homogeneously broadened by exchange-averaging; the longer the residence time in the pores, the broader and the more shifted the broad component is, i.e. the bigger the ratio Vinexch/Vexexch as per Figure 4. In big particles, the broad component amounts to 30% of the ex-pore peak with a FWHM = 0.30 ppm and is located within 0.10 ppm of bulk water chemical shift. On the other hand, with small particles the broad component represents 82% of the total ex-pore water with a much bigger FWHM = 0.70 ppm and is shifted by 0.20 ppm relative to bulk water. This indicates a slight increase of Vinexch/Vexexch when the particles are reduced; in other words, a bigger proportion of ex-pore water is able to experience the in-pore environment for a longer time.

Fig. 5.

1H NMR spectra of: (a) 54BO_80 injected with 0.2*PV (red) and 2.3*PV (blue) of water; and (b) 54BO_21 injected with 0.3*PV (red) and 2.3*PV (blue) of water. The dashed lines show the maxima of the in-pore peaks

1H NMR spectra of: (a) 54BO_80 injected with 0.2*PV (red) and 2.3*PV (blue) of water; and (b) 54BO_21 injected with 0.3*PV (red) and 2.3*PV (blue) of water. The dashed lines show the maxima of the in-pore peaks

To explain the broadening of the ex-pore peak, we must adopt the point of view of water molecules that spend the majority of their time in the ex-pore environment, where we believe the packing of the particles plays an important role. A simple model consisting of spherical particles (Figure S3 in the SI) allows exchange rates to be calculated in function of the particle diameter (Figure S4). With 80 μm particles (similar to 54BO_80) we find exchange rates of 2.5 Hz, and of 36.7 Hz with 54BO_21 particles (see SI for more details on the calculations). The NICS being around 3000 Hz, the exchange regime would be slow in both cases, which is consistent with our observations, and increases by a factor of 15 when reducing the particle size from 80 μm to 21 μm.

Examples of 2D EXSY NMR spectra are shown in Figures 6(a) and 6(b) corresponding to sample 54BO_80 and 54BO_21 saturated with water. The mixing time (tmix) was 20 ms for both spectra, and it can be seen that the cross-peaks are more pronounced with small particles, giving a first indication that the exchange is faster. Figures 6(c) and 6(d) show the build-up curves of the intensity ratio of cross-peaks over diagonal peaks. Visually, we can see that the curve for big particles reaches the maximum after long tmix intervals, whereas for small particles the build-up is complete within 0.1 s.

Fig. 6.

2D exchange spectra for: (a) 54BO_80; and (b) 54BO_21 recorded with tmix = 20 m, with (c) and (d) corresponding build-up curves of the ratio of cross- and diagonal peak intensities (Icross/Idiag) as a function of mixing time

2D exchange spectra for: (a) 54BO_80; and (b) 54BO_21 recorded with tmix = 20 m, with (c) and (d) corresponding build-up curves of the ratio of cross- and diagonal peak intensities (Icross/Idiag) as a function of mixing time

In principle, the build-up of the ratio of cross- and diagonal peak intensity (Icross/Idiag) in EXSY spectra can be described by a single dependence on tanh(ktmix), where k is the exchange rate constant. However, Fulik et al., have shown that better agreement is observed if two processes with different rates are assumed, i.e. a slow process attributed to diffusion from the centre of the particle to the surface and a much faster process attributed to effective exchange between ex-pore and in-pore (15). However, over the course of our experiments, it was observed that the ex-pore resonance reduced in intensity due to evaporation from the NMR rotor leading to a global reduction in Icross/Idiag for EXSY spectra recorded at the end of the series with long mixing times. Although the exact kinetics of the solvent evaporation are complex and were not studied in detail, we found that this could be accounted for with sufficient accuracy through the incorporation of an exponential term with a characteristic decay constant Tevap (see SI). Rate constants were therefore extracted from the EXSY data using Equation (i):

 

(i)

 

where I0 is an additional constant introduced to account for t1 noise giving rise to spurious off-diagonal low-intensity signal at zero mixing time. The fits were optimised by minimising the root mean squared deviation (RMSD) between calculated and experimental points, to converged values around 10–2. The errors on the data points were calculated from the signal-to-noise ratio of each peak for a selection of 2D spectra and propagated to Icross/Idiag, and were found to be smaller than 0.02%. The best fit for 54BO_80 was obtained with k1 = 57 Hz and k2 = 4 Hz, and for 54BO_21 with k1 = 597 Hz and k2 = 50 Hz. The carbon particles with D50 = 21 μm showed around 10 times faster in-pore–ex-pore diffusion versus the D50 = 80 μm particles. This is close to the factor of 15 which we obtained from our simple calculations based on spherical particles (see Figure S4) and shows the impact of the particle size on the rate of the exchange processes, with larger particles significantly reducing the exchange kinetics between the in-pore and ex-pore environments. Therefore, particle size is an important factor to take into account when comparing in-pore–ex-pore exchange phenomena in porous carbon samples.

Regarding the in-pore resonances, the shape and position in the NMR spectrum is largely unaffected by in-pore–ex-pore exchange despite the difference in particle size. We can therefore assume that the diffusion path out of the particle from any point of the pore network, apart from the very surface, is simply too long and exchange-averaging of the in-pore environment is in the slow regime. This would mean that if the particle size is decreased further, at some point the in-pore peak should also become affected by faster diffusion of in-pore water into the ex-pore environment. To test this hypothesis, 6 μm-sized YP50 particles were wetted with deionised water. YP50 is a commercial activated carbon, and similar to our PDCs with respect to composition, pore size distribution and average pore size (see Figure S13). The 1H NMR spectra before and after saturation are shown in Figure 7. As expected due to the small particle size, an ex-pore peak with sharp and broad components is observed. Relative to 54BO_21, the broad component is shifted five times more, consistent with smaller inter-particle voids that facilitate adsorption of ex-pore water in close proximity. The in-pore peak shifts from a NICS of 7.3 ppm to 7.0 ppm upon saturation, which is similar to 54BO_21, however the intensity decreases significantly, and we notice that the peak exhibits a tail towards the ex-pore peak. This means that after saturation, a significant proportion of adsorbed water is able to quickly diffuse into the ex-pore environment and therefore does not appear at the purely in-pore chemical shift, but rather intermediate between the ex-pore and the in-pore chemical shifts. The exchange rate constants were estimated to be k1 = 1117 Hz and k2= 165 Hz. Assuming that k1 relates to the ex-pore–in-pore exchange process that we calculate as a function of the particle size (Figure S4), we find that 4 μm particles give a similar exchange rate. This is good agreement considering that 20% of YP50 particles are smaller than 2.5 μm (Figure S14), especially because for particles smaller than 10 μm the exchange rate increases sharply. This explains why YP50 presents a relatively flat valley between the two broad peaks: even a narrow particle size distribution in the few-micrometre range gives a very broad distribution of exchange rates, therefore generating exchange-averaged peaks at a continuum of shifts.

Fig. 7.

1H NMR spectra of YP50 wetted with 0.5*PV (red) and 5.3*PV (blue) of water. The dashed lines show the maxima of the in-pore peaks

1H NMR spectra of YP50 wetted with 0.5*PV (red) and 5.3*PV (blue) of water. The dashed lines show the maxima of the in-pore peaks

One point worth addressing is whether the inhomogeneous broadening of the in-pore peak is responsible for broadening the exchange-averaged ex-pore peak, which can give an idea of the reliability of the exchange rate constants obtained. The spectrum of Figure 7 was successfully reproduced in Express software (22) in the case of a homogeneous as well as a inhomogeneous broadening of the broad ex-pore peak, so the simulation does not allow it to be determined whether the exchange-averaged peak is homogeneously or inhomogeneously broadened. Refer to SI for further detail. However in 2D EXSY spectra, for any tmix, the ex-pore peak shows symmetrical off-diagonal broadening meaning the broadening is homogeneous. This suggests that one component of the in-pore peak is much more exposed to the ex-pore environment than the other components. In consequence the values of exchange rate constants may be more reliable than if the broadening were inhomogeneous. This result is consistent with a radial distribution of NICS in the particle, in agreement with our previous observations where the centre of particles of diameter greater than 100 μm is poorly affected by steam activation. The particles employed here were smaller than 100 μm but it seems that a small gradient of activation still remains. It is possible that the valley between ex-pore and in-pore is the result of in-pore–ex-pore exchange broadening, in the fast or slow regime, of the other components of the in-pore peak, which are located further and further away from the surface, and therefore have access to smaller and smaller volumes Vexexch.

In summary, from these observations it could be deduced that particles smaller than 10 μm offer a diffusion path short enough for water to diffuse out of the pores at a rate that affects the in-pore peak as well. However, given that the diffusion coefficient of adsorbed water depends on the pore size, we cannot compare 54BO_21 and YP50 because they have different average pore sizes. Using the equation provided previously (6), these can be estimated using the NICS before saturation. We obtain for 54BO_21 and YP50, 1.17 nm and 1.10 nm respectively. Therefore, it is necessary to investigate the effect of average pore size, which can be tuned by controlling the BO, on the diffusion of water and the appearance of the spectra.

The Effect of Burn-off

The effect of BO, and thus average pore size, on the dynamics of water in PDCs can be described by comparing 54BO samples (high BO) with 20BO samples (low BO). Figure 8(a) shows samples 20BO_83 and Figure 8(b) shows 20BO_15 injected with water. The NICS of samples 20BO are 8.4–9.0 ppm, giving an average pore size less than 1.0 nm based on the previous equation (6), which is smaller than sample 54BO, in agreement with the linear dependence of the average pore size on the BO (18, 19, 23). The in-pore peaks appear to contain two components as is sometimes observed for samples with low BO. Possibly, the degree of activation was not homogeneous from the surface to the centre of the particles. In sample 20BO_83, the in-pore peak is constant regardless of the injected volume (shift < 0.10 ppm). Half the ex-pore peak was fitted with a sharp component of FWHM <0.1 ppm, and half with a broad component of FWHM = 0.16 ppm with a difference in chemical shift < 0.10 ppm. This suggests in the first instance that the in-pore–ex-pore exchange process is in a slower regime than in 54BO_80, where the broad component was broader and the in-pore peaks were shifted slightly, in agreement with the study mentioned earlier (24). With small particles 20BO_15, 90% of the ex-pore peak is broad, FWHM = 0.35 ppm but within 0.10 ppm of the bulk water, suggesting again limited exchange with negligible Vinexch.

Fig. 8.

1H NMR spectra of: (a) 20BO_83 injected with 0.7*PV (red) and 3.6*PV (blue) of water; and (b) 20BO_15 injected with 0.2*PV (red) and 3.6*PV (blue) of water. The dashed lines show the maxima of one component of the in-pore peaks

1H NMR spectra of: (a) 20BO_83 injected with 0.7*PV (red) and 3.6*PV (blue) of water; and (b) 20BO_15 injected with 0.2*PV (red) and 3.6*PV (blue) of water. The dashed lines show the maxima of one component of the in-pore peaks

The exchange rate constants provide a more quantitative description of the impact of average pore size. For the big particles 20BO_83, k1= 54 Hz and k2 = 4 Hz, which are comparable to the values for 54BO_80 (57 Hz and 4 Hz). This was perhaps not expected from the 1D spectra, where 20BO_83 appeared much less affected by diffusion. However, one must keep in mind that the exchange regime depends not only on the actual rates, but also on the chemical shift difference of the two environments involved. The NICS of samples 20BO is higher than in samples 54BO, so even identical exchange rates still situate 20BO in a slower regime than 54BO.

For the small particles 20BO_15, k1 = 162 Hz and k2 = 6 Hz, which are three times as fast when compared to 20BO_83. However, the calculated factor was 31, which is a clear discrepancy. Given that sample 20BO_15 contains particles smaller than sample 54BO_21, we can attribute the discrepancy to a BO effect and not to a particle size effect. Besides the average pore sizes, other structural parameters that could perhaps vary with BO are oxygen content and tortuosity due to the smaller amount of mesopores. These observations also raise the question of homogeneity of the diffusion coefficients within the particle: it is likely that at low BOs a bigger gradient of activation within the particle is present.

Overall, these results show that a smaller average pore size hinders exchange as opposed to a smaller particle size, which promotes it. Since YP50 has a smaller average pore size than 54BO_21 but higher exchange rate constants, we can safely deduce that in YP50, the particles are truly small enough to allow for in-pore–ex-pore exchange to affect the in-pore peak. These conclusions are in agreement with simulations (25), and also an experimental study focusing on diffusion measurements in hydrophobic slit pores by neutron-scattering (23). The material contained approximately 95% carbon with 5% oxygen atoms on the surface of the pores and average pore sizes of 1.2 nm and 1.8 nm, which is similar to our PDCs. It was found that the diffusion coefficients of water in the 1.2 nm and 1.8 nm pores are 40% and 30% smaller than that of bulk water, respectively. Furthermore, on the very surface of pore, water diffuses at 0.035 × 10–5 cm2 s–1 and 0.014 × 10–5 cm2 s–1 respectively, which is two orders of magnitude slower than in the bulk. Counterintuitively, the value on the surface of the bigger pores was found to be nearly half that in the smaller pores, which was attributed to the promotion of slightly faster concerted motion in extreme confinement, although the centre of the pore followed an overall slower regime.

The Effect of Solvent Properties

Many applications of porous carbons (such as electric double-layer capacitors) commonly employ electrolytes in organic solvents as an alternative to aqueous electrolytes. To extend the knowledge presented here to such systems, it is desirable to be able to predict how the NICS may be affected. The viscosity and the polarity are the two parameters that will be considered here as tools to predict the diffusion regime adopted by any solvent.

The effect of polarity can be estimated by comparing water and cyclohexane which have the same viscosity, but different dipole moments. YP50 is chosen for this comparison because the exchange rates are high enough to significantly impact the NMR spectra. The exchange rate constants were measured to be 1117 Hz and 165 Hz for water, and 257 Hz and 23 Hz for cyclohexane, which means that cyclohexane diffuses roughly four times slower. On one hand, this could be related to increased van der Waals interactions with the hydrophobic surface of the pores, as was also found to be the case in a xerogel using the same solvents (24). On the other hand, the bulk self-diffusion coefficient of cyclohexane is smaller than for water (1.42 × 10–5 cm2 s–1 vs. 2.3 × 10–5 cm2 s–1) (26), which could also contribute. At this stage it is unclear whether other parameters such as the different molecular sizes of water and cyclohexane play a role. Figure 9 shows the 1H NMR spectrum of YP50 wetted with cyclohexane. As expected with such high exchange rate constants, we see a narrow and a broad ex-pore peak, and an in-pore peak that decreases and shifts upon saturation, much like in Figure 7 with water in YP50. With water and cyclohexane, the in-pore peaks are similar; they shift by 0.30 ppm and are broadened by a factor two upon saturation. Interestingly, we note that the NICS of cyclohexane (and hexane) is smaller than water by 0.2–0.3 ppm, which means that the apolar solvents are on average located in slightly bigger pores than water. The diffusion being faster in big pores, this is in contrast with the slower exchange kinetics measured, showing that solvent parameters are prevalent over pore size effects. The broad ex-pore peak is narrower and less shifted in cyclohexane (FWHM = 0.64 ppm and shift = 0.27 ppm) than in water (FWHM = 1.69 ppm and shift = 0.98 ppm), consistent with smaller exchange rate constants.

Fig. 9.

1H NMR spectra of YP50 injected with 0.3*PV (red) and 2.9*PV (blue) of cyclohexane. The dashed lines show the maxima of the in-pore peaks

1H NMR spectra of YP50 injected with 0.3*PV (red) and 2.9*PV (blue) of cyclohexane. The dashed lines show the maxima of the in-pore peaks

The effect of viscosity can be observed by comparing cyclohexane (0.89 cP) and hexane (0.30 cP) which have the same very low polarity. Figure 10 shows the 1H NMR spectrum of YP50 wetted with hexane. Unlike water and cyclohexane, hexane shows two ex-pore peaks, which are simply due to the two visible proton environments on the molecule; 1.28 ppm are the methylene (CH2) and 0.88 ppm are the terminal methyl (CH3) protons. The in-pore peak before saturation can be fitted with two broad peaks 0.30 ppm apart, which is similar to the difference between the CH2 and CH3 chemical shifts (refer to SI for details on the fits). This suggests that all protons of adsorbed hexane molecules roughly experience the same NICS, therefore the molecule is either tumbling isotropically or aligned with the pore wall. The exchange rate constants are k1 = 784 Hz and k2 = 104 Hz for hexane in YP50, which is approximately three times the rates seen for cyclohexane. Therefore in this case, the exchange rate was roughly proportional to the viscosity, as hexane is three times less viscous than cyclohexane.

Fig. 10.

1H NMR spectra of YP50 injected with 0.3*PV (red) and 3.0*PV (blue) of hexane. The dashed lines show the maxima of the in-pore peaks

1H NMR spectra of YP50 injected with 0.3*PV (red) and 3.0*PV (blue) of hexane. The dashed lines show the maxima of the in-pore peaks

More interestingly, the broad ex-pore peak is shifted by 0.61 ppm relative to the average between the two narrow peaks, and the FWHM = 1.30 ppm. These values are between the values for cyclohexane and water. This is consistent with the shift and width being proportional to the exchange rate constants as they are even higher for water in YP50. Overall, pronounced solvent exchange affects the ex-pore and in-pore peaks and the valley between the two peaks, but the ex-pore peak seems to be the most reliable indicator to estimate at a glance perturbations due to exchange effects.

Further discussion is required about parameters that could not be assessed with this set of experiments, for example the kinetic diameter of the solvent molecules. This factor was not considered separately because it was first assumed to be reflected in the viscosity parameter, although in pores of similar size, viscosity and diameter may have independent contributions to the exchange kinetics. In addition, to identify the impact of this factor alone, two solvents with similar viscosity and polarity but different molecular sizes should be compared. The kinetic diameter of water and cyclohexane perhaps contributes to the exchange rate difference.

The behaviour of cyclohexane was peculiar in the case of sample 20BO_83 and 20BO_15. In the big particles, exchange was too slow to be observed, and by decreasing the particle size, the exchange became visible but the rate was higher than that of hexane and also of cyclohexane in the other PDC samples, which goes against the trends. Another interesting observation was that there were two in-pore peaks in 20BO before saturation and both peaks shifted to the right upon saturation, meaning exchange-averaging takes place within different pores but not with ex-pore, while in 54BO there was only one in-pore peak (see Figures S5 and S6). We believe these observations are all related and hint towards the ability of cyclohexane to form organised structures in slit-like micropores, which affects its diffusion coefficient. The diffusion coefficient of confined cyclohexane was shown by Fomin et al. to drop to zero in slit pores smaller than 2.1 nm, and its density to increase two-fold from 2.6 nm to 1.2 nm pores (27). Another study showed that cyclohexane forms a monolayer in 0.8 nm pores and a bilayer in 1.0 nm pores with a denser hexagonal packing structure resembling the solid phase (28). Similar behaviour has also been observed for propylene carbonate which was observed to form an ordered structure upon nanoconfinement (29). In a disordered structure the packing is expected to be less efficient, nonetheless the diffusion coefficient may still be significantly lower. The exchange rate constants determined take into account the diffusion of species in all types of pores located in Vinexch. When cyclohexane forms an immobile structure in the smallest pores, only the diffusion coefficient in the biggest pores where it is still liquid contributes to the exchange rate constant, explaining why in 20BO_15 the exchange rates are much higher than in the other PDC samples. The amount of mesopore is smaller than in 54BO and YP50, so the long-range diffusion within the particles is probably significantly slower. In that regard, the gradient of NICS will be less well averaged, and even more so with slow diffusing solvents like cyclohexane. The 3.3 ppm NICS of the small peak gives a pore size of 2.2 nm and the 7.7 ppm NICS of the main peak 1.0 nm. The small in-pore peak is therefore likely to come from few isolated mesopores while the other from micropores and mesopores in contact.

Conclusions

The series of exchange experiments in this work provide a quantitative description of the in-pore–ex-pore exchange rate constants of water, hexane and cyclohexane adsorbed in PDC samples. This allowed us to distinguish the contributions of particle size, porosity and solvent properties. We showed that exchange rate constants are higher in small particles and increase with BO. We also showed that the exchange rate constants are solvent dependent and increased in the order cyclohexane < hexane < water, which was attributed to differences in viscosity and stronger van der Waals interactions between apolar solvents and the pore walls. However some discrepancies were noted in low activated samples saturated with cyclohexane and assigned to its unusual packing in micropores. More work is necessary to understand the contribution of other solvent properties such as the kinetic diameter. Based on these findings, we were able to rationalise the width and shift of the ex-pore and in-pore peaks in 1H NMR spectra. The appearance of the ex-pore peak in particular provides a quick and reliable estimate of the extent of exchange-averaging. For studying adsorption phenomena in porous carbons by NMR spectroscopy, we recommend the use of 50–100 μm activated carbon particles as well as small, viscous and apolar solvents to minimise exchange and to observe the ‘true’ NICS.

Experimental methods and further details are given in SI. The research data supporting this publication can be accessed at Lancaster University Research Depository (30).

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Acknowledgements

We acknowledge Engineering and Physical Sciences Research Council (EPSRC) and Johnson Matthey Plc for the provision of an iCASE studentship. We also thank Lancaster University and the European Regional Development Fund (ERDF) for the provision of characterisation facilities under the Collaborative Technology Access Program (cTAP).

The Authors


Luca Cervini graduated with a BSc from the Department of Chemistry at the University of Geneva, Switzerland, in 2012. In 2014 he obtained a MSc jointly with the École Polytechnique Fédérale de Lausanne (EPFL), Switzerland, after a thesis on organic photochromic solar cells. In 2016 he started an industrial Cooperative Awards in Science & Technology (CASE) PhD in chemistry at Lancaster University, UK, supervised by John Griffin and Nathan Barrow where he has been studying dynamics in porous materials, specifically aqueous electrolytes in activated carbons using mostly NMR spectroscopy and gas sorption analysis.


Nathan Barrow is currently a Principal Scientist in the Advanced Characterisation department at Johnson Matthey, Sonning Common, UK. He graduated with an MPhys in 2006 from the University of Warwick, UK, where he remained to gain a PhD in solid-state NMR. In 2010 Barrow was a Knowledge Transfer Partnership associate between the University of Warwick and Johnson Matthey, helping to install and run a solid-state NMR service. His current research focuses on applying advanced characterisation to materials such as porous carbons, zeolites, alumina, glasses and battery materials.


John Griffin is a lecturer in Materials Chemistry at Lancaster University. He obtained his PhD from the University of Warwick in 2008 before moving to the University of St Andrews, UK, to carry out postdoctoral research in the group of Professor Sharon Ashbrook. In 2012 he moved to the University of Cambridge, UK, to join the group of Professor Clare Grey FRS. In 2015 he took up his current position where his current research interests concern the development and application of solid-state NMR methodologies for the study of energy conversion and storage materials.

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