Exploring the effect of ethanol-water structuring on the transport properties of ethanol in porous silicas

Abstract

The transport properties of liquid mixtures confined within porous media can change significantly from those observed for bulk mixtures due to changes in the liquid structuring within the pore space. Here, pulsed field gradient NMR was used to measure the diffusion coefficient of ethanol in ethanol-water liquid mixtures confined within silicas with pore diameters of 6 nm and 3 nm as a function of composition. For liquids imbibed within the 6 nm pores, the composition dependence of the ethanol diffusion coefficient closely followed that of the bulk liquid mixture and the absolute diffusion coefficients were reduced by a tortuosity factor of 3, with a minor contribution due to liquid-surface interactions. For liquids imbibed within the 3 nm pores, the diffusion coefficient of ethanol decreased as the composition of ethanol within the pore space increased, and for single-component ethanol imbibition the effective tortuosity was 63. Fast field cycling NMR experiments showed that the diffusion behaviour was not controlled by an increase in ethanol adsorption strength. A geometric analysis of the pore space was consistent with a highly confined system in which most molecules interacted with the pore walls. Under such confinement, the liquid structuring within the bulk pore space did not reflect that of the bulk liquid mixtures, and the observed decrease in diffusion coefficient as ethanol composition increased was consistent with an increase in confinement due to the larger size of the ethanol molecule.

Graphical abstract

1. Introduction

The study of liquid transport within porous materials is of fundamental and practical significance for many chemical and physical processes, such as catalysis [1,2], separations [3], and energy storage [4]. Understanding how molecular interactions and pore structures influence the diffusion behaviour of imbibed fluids is central to understanding and optimising the performance of these processes.

Bulk liquid mixtures of ethanol and water are known to exhibit non-ideal mixing despite being miscible at all mixture compositions. This is manifested by strong interactions between ethanol and water, typically associated with hydrogen-bonding networks present in the mixtures [5]. Diffusion studies of water and ethanol mixtures show how the structuring effect can influence the transport behaviour of ethanol within the mixture, with the minimum diffusion coefficient observed at the same composition as the greatest degree of structuring [6]. The dynamic behaviour of ethanol-water mixtures is further complicated when confined within porous silicas due to interactions at the solid-liquid interface. Preferential water adsorption has been observed in molecular dynamics studies of water droplets being added to a β-cristobalite silica surface covered in ethanol [7]. A mixed ethanol-water surface layer was formed, which changed composition as the ratio of water and ethanol within the system was varied. Positron annihilation spectroscopy techniques have also shown preferential water adsorption at the silica surfaces in porous silicas with pore sizes in the range of 4–10 nm when the ethanol mole fraction of the imbibed fluid was lower than 0.2 [8]. When the ethanol mole fraction was greater than 0.3, the silica samples showed preferential ethanol adsorption for pore sizes up to 6 nm. At larger pore sizes (10 nm) no phase separation was observed due to the reduced surface-to-volume ratio of the pores. The balance between bulk liquid properties and interfacial effects will have important consequences for the transport behaviour of the confined fluids and direct measurements of diffusion are essential to understanding mass transport within these systems.

Mass transport of liquids imbibed within porous media has been extensively studied using pulsed field gradient nuclear magnetic resonance (PFG NMR), with the structure of the porous materials shown to have a profound effect on the transport properties of the liquids confined within them[[9], [10], [11], [12], [13], [14]]. In particular, structural heterogeneity, hierarchical pore systems, micropore confinement, and many other complex structural phenomena have been shown to influence molecular transport using PFG NMR. In the simple case of non-interacting liquids in a homogeneous porous medium, the diffusion coefficient of the imbibed liquid is slowed by the structural tortuosity, $\tau$, of the medium such that [15]:

$$\tau =D_{\mathrm{b}}/D_{\mathrm{p}}\text{,}$$ (1)

where $D_{\mathrm{b}}$ is the diffusion coefficient of the bulk liquid and $D_{\mathrm{p}}$ is the diffusion coefficient of liquid confined within the pores. In this definition of $D_{\mathrm{p}}$, it is a requirement that most of the diffusing molecules will have traversed several pore diameters. Such an approach has been used to describe the structural properties of heterogeneous catalytic materials [15,16] and the effect of the synthesis process on the resultant transport properties [17]. When there exist strong interactions between confined molecules and the surface, thereby forming a ‘surface-affected’ region, the measured diffusion coefficient, $D_{\mathrm{p}}$, is no longer only a function of the structural tortuosity of the pore space. Under these conditions, Eq. (1) no longer holds as the measured diffusion coefficient is moderated by the molecules interacting more strongly with the surface diffusing more slowly. In this case, and assuming fast exchange between the surface and bulk pore fluid, the observed diffusion coefficient is given by:

$$D_{\mathrm{p}}=p_{\mathrm{S}}{D}_{\mathrm{S}}+p_{\mathrm{B}}{D}_{\mathrm{B}}\text{,}$$ (2)

where $p_{\mathrm{S}}$ and $p_{\mathrm{B}}$ are the population fraction of ¹H spins affected by the surface and in the bulk pore space respectively. $D_{\mathrm{S}}$ and $D_{\mathrm{B}}$ are the corresponding diffusion coefficients, again with the requirement that most of the diffusing molecules will have traversed several pore diameters during the timescale of the measurement. D'Agostino et al. showed the effect of adsorption on the diffusion coefficient for a range of liquids confined within the pores of alumina, silica, and titania [18]. In that work, alkanes represented molecules that did not have specific functional groups and therefore had minimal interaction with the pore surface. It follows that the tortuosity factor obtained from the diffusion of alkanes most closely represented the true structural tortuosity of the materials under study. For all three supports, the value of the tortuosity measured for monoalcohols and carboxylic acids was larger than the values measured with alkanes and it was argued that the observed diffusion coefficient was associated with an effective tortuosity, ${\tau }_{\text{eff}}$, deviating from the structural tortuosity due to strong liquid-surface interactions. For polyols, a significant decrease in the tortuosity was observed, with measured values that were consistently smaller than the alkane tortuosity. It was suggested that the low tortuosity values resulted from a disruption of the hydrogen bond network of the polyols when confined within the pore space leading to enhanced polyol diffusion [18]. Recent fast field cycling (FFC) NMR and PFG NMR studies have shown strong competitive adsorption of molecules when present in binary liquid mixtures imbibed within porous silicas [19]. FFC data demonstrated a partial phase separation of the two fluids at the pore surface, which resulted in significant reduction in the diffusion coefficient of both the strong and weakly interacting species, with observed tortuosity values of up to 12. These observations highlight that the adsorption and liquid structuring within the pore space must be considered alongside the physical properties of a porous medium when understanding mass transport.

In the present work, the diffusion behaviour of ethanol in ethanol-water binary liquid mixtures is measured as a function of composition when imbibed within porous silicas with nominal pore sizes of 6 nm (Q6) and 3 nm (Q3). FFC NMR experiments are used to understand the adsorption behaviour, and the effect of the differing degrees of confinement on the liquid structuring and mass transport properties of ethanol are discussed.

2. Materials and methods

Silica supports were obtained from Fuji Silyasia Chemical LTD as spheres of 1.7–4 mm diameter. Physical properties of the silicas used within this work are listed in Table 1. Q6 was used as received and a large batch of Q3 pellets was crushed and sieved to a size class of 1–1.7 mm for PFG NMR measurements to reduce sample-to-sample variation. All silicas were dried at 200°C overnight prior to imbibition in ethanol-water liquid mixtures with ethanol molar compositions between 0 and 1. Excess liquid was removed immediately prior to measurements and samples were dried on filter paper to remove extra-particle liquid. Ethanol, cyclohexane, ethanol-OD, and deuterium oxide were obtained from Merck Life Sciences at a purity of >99% and used without further purification. Deionised water was prepared in-house using an Elga Purelab DV25 system.

Table 1.

Physical properties of the silicas used in this work and the key NMR parameters used for PFG NMR experiments. The pore size, d_p, surface area, S_p, and pore volume, V_p, provided by the manufacturer are listed.

Silica	dp/nma	Sp/(m2 g−1)a	Vp/(cm3 g−1)a	$\Delta$/ms	$\delta$/ms	$g_{\max }$/(G cm−1)
Q6	6	450	0.6	100	1	278
Q3	3	550	0.3	250	2	278

^aValues provided by manufacturer.

PFG NMR experiments were performed on a Bruker Avance 300 MHz spectrometer, equipped with a microimaging probe and a 5 mm ¹H coil. A 13-interval bipolar gradient stimulated echo sequence [20] was used with variable gradient strength, $g$, to achieve signal decay, as implemented in our earlier work [13]. The sample temperature was held at 25 ± 0.2°C and samples were thermally equilibrated for >15 min prior to the start of experiments. 24 gradient steps and 8–16 scans were used for each measurement. For samples using Q6 and Q3, the parameters of the diffusion measurement were optimised and the observation time, $\Delta$, gradient pulse duration, $\delta$, and maximum gradient strength, $g_{\max }$, are given in Table 1. For systems that can be defined by a single diffusion coefficient, the signal decay, $S\left(g\right)/S_0$ of the resultant Stejskal Tanner plot is described by [21]:

$$\frac{S\left(g\right)}{S_0}=\exp \left(-{\gamma }^2{\delta }^2{g}^2\left(\Delta -\frac{\delta }{12}-\frac{{\tau }_{\text{SE}}}{2}\right)D\right)\text{,}$$ (3)

where $\gamma$ is the ¹H gyromagnetic ratio, ${\tau }_{\text{SE}}$ is the duration between π/2 and π pulses, and $D$ is the measured diffusion coefficient. In the presence of multiple diffusion coefficients, as was observed for crushed samples of Q3, each component decays as shown in Eq. (3), and the observed signal is the population weighted sum of the signal decay from all components:

$$\frac{S\left(g\right)}{S_0}={\int }_0^{\infty }P\left(D\right)\exp \left(-bD\right)\mathrm{d}D\text{,}$$ (4)

where $P\left(D\right)$ is the probability density function of diffusion coefficients and ${b=\gamma }^2{\delta }^2{g}^2\left(\Delta -\delta /12-{\tau }_{\text{SE}}/2\right)$. $P\left(D\right)$ was obtained using an in-house inverse Laplace transformation script with Tikhonov regularization [22]. The diffusion coefficient was calculated as the logarithmic average of the diffusion distribution to account for changes in the diffusion coefficient due to particle-to-particle variation without bias towards the faster diffusion coefficients present. The application of the inverse Laplace transform also allows particular diffusion coefficients to be removed prior to calculating the logarithmic average. For liquids imbibed within Q6, the logarithmic average was taken across the full distribution resulting from the inverse Laplace transform. For Q3, diffusion values above 2 $\times$ 10⁻¹⁰ m² s⁻¹ were excluded from the averaging process to ensure that the measured diffusion coefficient was representative of only the liquid confined within the pore space.

FFC NMR experiments were performed on a series of ethanol-OD-D₂O binary liquid mixtures using a Stelar Spinmaster Duo relaxometer equipped with a 10 mm ¹H coil. The sample temperature was held at 25 ± 0.5°C using a temperature-controlled compressed air gas stream. For each sample, a prepolarized sequence [23] was used with a polarization field of 25 MHz and a detection field of 16.3 MHz. 32 relaxation delays were used, which were logarithmically spaced between 1 ms and 6 × T₁. The longitudinal relaxation rate, $R_1$, was measured at 20 ¹H Larmor frequencies logarithmically spaced between 10 kHz and 10 MHz to generate a nuclear magnetic relaxation dispersion (NMRD) profile. For liquids imbibed within Q6 and Q3, data were well-described by a monoexponential relaxation process, such that the signal, $S\left(\tau \right)\text{,}$ could be expressed as [23]:

$$S\left(\tau \right)=S_{\infty }+\Delta S_{\text{eff}}\exp \left(-\tau R_1\right)\text{,}$$ (5)

where $\tau$ is the relaxation delay, $S_{\infty }$ and $\Delta S_{\text{eff}}$ are fitting parameters which approximate respectively the long-time signal in the relaxation field, and the difference between the signal immediately after polarization and at long-times. The relaxation rate, $R_1$, was extracted by fitting Eq. (5) to the signal decay data at each frequency using a NNLS regression algorithm in Matlab.

3. Results and discussion

Fig. 1 shows the ¹H spectra of ethanol imbibed within pellets of Q6 and Q3 silica. When imbibed within the pellets, a significant line broadening effect was observed, with peaks showing a full width at half maximum of 0.2 ppm and 0.6 ppm respectively. Such broadening is typical of liquids imbibed within porous media and the increase in linewidth with decreasing pore size was consistent with previous studies of water in silicas [24]. Despite the line broadening, the CH₃, CH₂ and OH ¹H chemical environments of ethanol were well-resolved in both silicas. For liquid mixtures of water and ethanol, the water signal overlapped with the hydroxyl environment of ethanol and the integration region was restricted to the CH₃ functionality to unambiguously identify the ethanol dynamics for all pellet samples. Large pellet-to-pellet variation was observed for the measured average diffusion coefficient of liquids imbibed within Q3, with variations in the logarithmic average diffusion coefficient of up to 72% observed for samples of ethanol in individual Q3 pellets. Therefore, a large number of pellets were crushed and sieved to a size class of 1–1.7 mm to obtain a representative distribution of pore structures characterising the batch property. For the crushed Q3 samples, the maximum observed variation in the diffusion coefficient of ethanol was reduced to 17% for these experiments. Crushing the pellets did not affect the magnitude of the diffusion coefficient for liquids imbibed within Q3 or Q6 and there was no evidence of damage to the pore structure as a result of this process. The crushed pellets caused significantly greater line broadening, and it was not possible to clearly resolve each ¹H functionality; however, by restricting the integration region to –5–2.5 ppm it was possible to isolate the signal associated with the ethanol molecule. There was significant overlap of the CH₃ and CH₂ functionalities within this region, but limited overlap of the ethanol or water hydroxyl functionalities. Furthermore, the T₂ of water in Q3 silica was measured as 2.1 ms, which is comparable to the gradient pulse duration (δ = 2 ms), meaning that the influence of the water signal on the integration region was further reduced due to relaxation weighting. It was therefore possible to obtain chemically specific diffusion data for ethanol at all mixture compositions in both Q3 and Q6 silica.

Fig. 1.

The ¹H spectra of ethanol imbibed within pellets of Q6, Q3, and crushed Q3 silica. Peaks at approximately δ = 1.2, 3.6, and 5.3 ppm correspond to the CH₃, CH₂ and OH functionalities of ethanol respectively.

Fig. 2a shows the PFG NMR data for bulk ethanol and for ethanol imbibed within each silica. The signal decay is compared to a single component fit of Eq. (3). For bulk ethanol and ethanol within Q6, the signal decay was well-described by single component decay behaviour for over 3 orders of magnitude, consistent with quasi-homogeneous diffusion of ethanol within these samples. In contrast, ethanol contained within Q3 showed a much slower diffusion decay and significant curvature below S/S₀∼0.1. The non-linear nature of the signal decay was accounted for by fitting Eq. (4) to the PFG NMR data to produce a distribution of diffusion coefficients characterising the sample. It is noted that the diffusion coefficient showed no dependence on $\Delta$ in the range 50 ms $<\Delta <$ 500 ms.

Fig. 2.

(a) PFG NMR data for bulk ethanol and ethanol imbibed within samples of Q6 and Q3. For each sample, the fits from Eq. (3) are shown as solid lines and for Q3 the fit from Eq. (4) is shown as a dotted line. (b) Corresponding diffusion distributions obtained for ethanol in Q6 and Q3 from an inverse Laplace transform of the decay data.

The diffusion distributions for ethanol in Q6 and Q3 obtained from fits to Eq. (4) are shown in Fig. 2b. Ethanol in Q6 showed a symmetrical distribution with diffusion coefficients between 10⁻⁹ and 10⁻¹⁰ m² s⁻¹. Such behaviour is expected for a single-component signal decay (as seen in Fig. 2a) but is broadened due to the regularization process. When imbibed in Q3, the distribution of diffusion coefficients was broader and asymmetric. A minor environment was observed around 10⁻⁹ m² s⁻¹, which was removed preferentially by drying the sample at 75°C for 15 min. This minor environment was assigned as liquid on external surfaces, inter-pellet liquid bridges, or liquid in large structural features i.e. cracks, and was excluded from the logarithmic average when calculating the diffusion coefficient. The values measured for liquids imbibed within Q3 in this study were consistent with literature values from PFG NMR studies of liquids imbibed within the same material [25].

Fig. 3 shows the diffusion coefficient of ethanol in Q6 and Q3 as a function of the composition of ethanol in the binary-liquid mixture. Preferential uptake of either of the two components may result in the composition within the pore space changing relative to the compositions of the imbibing fluid and distorting the observed trends. Integration of the ¹H NMR spectra of ethanol-water mixtures in Q6 and Q3 pellets showed that the composition of the liquid within the pores was within 6% of the imbibing fluid at all compositions, consistent with previous studies of binary liquid adsorption within porous aluminas [26] and silicas [27]. For crushed samples of Q3, the compositions could not be directly measured due to the increased line broadening and, to allow a direct comparison between Q6 and Q3, the ethanol compositions, ${\chi }_{\mathrm{E}}$, given in Fig. 3 are the ethanol composition of the imbibing fluid for all silicas.

Fig. 3.

The diffusion coefficient of ethanol in ethanol-water liquid mixtures imbibed within (a) Q6 and (b) Q3 as a function of ethanol composition. The inset in Fig. 3(a) shows the diffusion coefficient of ethanol in the bulk ethanol-water mixture as a function of composition for comparison.

As ${\chi }_{\mathrm{E}}$ was increased for mixtures imbibed within Q6, the diffusion coefficient of ethanol initially decreased, reaching a minimum of 1.7 $\times$ 10⁻¹⁰ m² s⁻¹ at ${\chi }_{\mathrm{E}}$ = 0.2, before increasing to a value of 3.1 $\times$ 10⁻¹⁰ m² s⁻¹ for single-component ethanol (${\chi }_{\mathrm{E}}$ = 1). The shape of this graph closely followed the composition dependent behaviour of the bulk liquid mixtures, which are well-known to exhibit non-ideal mixing and diffusion behaviour [6,28]. Diffusion coefficients of ethanol within Q6 were approximately a factor of 3 smaller than the bulk diffusion coefficients across the entire composition range. For liquid mixtures imbibed within Q3, the ethanol diffusion coefficient decreased as ${\chi }_{\mathrm{E}}$ increased, with the diffusion coefficient measured for single-component ethanol being 2.2 times smaller than ethanol in a mixture of ${\chi }_{\mathrm{E}}$ = 0.1. The decrease in the magnitude of $D_{\mathrm{p}}$ was largest at small values of ${\chi }_{\mathrm{E}}$, before reducing more slowly as ${\chi }_{\mathrm{E}}\to$ 1.

Fig. 4 shows the effective tortuosity, ${\tau }_{\text{eff}}$, values of ethanol as a function of composition in the silicas. In each case, the ${\tau }_{\text{eff}}$ measured for cyclohexane is shown for comparison. When imbibed within Q6, ${\tau }_{\text{eff}}$ of cyclohexane was 3.1, in good agreement with previous studies of alkane adsorption in Q6 [25]. The value of ${\tau }_{\text{eff}}$ for ethanol was within 0.6 of the cyclohexane value across the entire composition range. A small decrease in the effective tortuosity was observed as ${\chi }_{\mathrm{E}}$ increased from 0.2 to 0.6; however, the effective tortuosity remained similar to the value measured for cyclohexane at all compositions and this decrease was small in comparison to the effects of the structural tortuosity factor (approximated by the tortuosity of cyclohexane). For ethanol-water mixtures imbibed within Q3, the ethanol tortuosity showed a large and consistent increase as ${\chi }_{\mathrm{E}}$ increased, rising by a factor of 3.3 across the measured composition range. For single-component ethanol imbibition the tortuosity factor was 63, an order of magnitude larger than typically quoted structural tortuosities and indicative of a significant reduction in mass transport. The value of ${\tau }_{\text{eff}}$ measured for cyclohexane was larger than the value measured for ethanol when ${\chi }_{\mathrm{E}}$ <0.3. Several studies have shown that when imbibed in small pore silicas, alkanes cannot be considered as non-interacting and therefore cannot be used as a probe of the structural tortuosity [25,29,30].

Fig. 4.

The effective tortuosity, ${\tau }_{\text{eff}}$, of ethanol in ethanol-water liquid mixtures imbibed within (a) Q6 and (b) Q3 as a function of ethanol composition. The value of ${\tau }_{\text{eff}}$ for cyclohexane imbibed within each material is shown as the solid line.

The adsorption behaviour of ethanol within the binary liquid mixtures was further explored using FFC NMR. Fig. 5 shows the NMRD profiles of the ethanol component of ethanol-OD-D₂O mixtures as a function of the ethanol composition. For Q6, as ${\chi }_{\mathrm{E}}$ increased from 0.1 to 0.4, the NMRD profiles became shallower and converged below the value for single-component imbibition for ${\chi }_{\mathrm{E}}$ = 0.4–0.8. Such behaviour is consistent with competitive adsorption occurring at the silica surface, with water outcompeting ethanol for surface binding sites. Similar behaviour has been previously observed for mixtures of methanol and THF imbibed within γ-alumina, where the methanol partially displaced THF at the pore surface, resulting in a reduction of the magnitude of the NMRD profile of THF [26]. This decrease in the slope of the NMRD profiles was consistent with a weakening of the ethanol-silica interaction strength and the small decrease in the tortuosity experienced by ethanol, which occurred over the same composition range.

Fig. 5.

The NMRD profiles of ethanol in EtOD-D₂O liquid mixtures imbibed within (a) Q6 and (b) Q3 as a function of ethanol composition.

For ethanol imbibed within Q3, the NMRD profiles showed a small decrease in slope as the composition of ethanol in the mixture was increased. This was consistent with a weakening of the ethanol-silica interaction strength until the NMRD profiles overlapped for ${\chi }_{\mathrm{E}}$ = 0.4–1. If the adsorption properties of ethanol dominated the diffusion behaviour of ethanol imbibed within Q3, the decreasing interaction strength as ${\chi }_{\mathrm{E}}$ increased would result in an increase in the diffusion coefficient. This is opposite to the observed data and suggests that the diffusion of ethanol in ethanol-water mixtures within Q3 is not controlled by the ethanol-silica interaction strength.

Despite varying by only a few nm in pore size, very different diffusion behaviour was observed for ethanol imbibed within the two silicas, both in terms of the magnitude of the diffusion coefficient and the behaviour of ethanol as a function of the mixture composition. Within Q6, the diffusion coefficient of ethanol closely followed the composition dependent behaviour shown by ethanol in the bulk mixtures (see inset of Fig. 3a). For bulk liquid mixtures, the initial decrease in ethanol diffusion at low values of ${\chi }_{\mathrm{E}}$ has been ascribed to the formation of water solvation shells around ethanol molecules [31], which increased in number and connectivity until a maximum structuring was obtained at ${\chi }_{\mathrm{E}}\sim$ 0.2, corresponding to the minimum in diffusion coefficient [6]. Above this value the alcohol molecules aggregated further until ethanol became the continuous phase with water molecules preferentially forming clusters [6]. Adsorption within Q6 did not change the composition dependent behaviour or the position of the minimum diffusion coefficient, suggesting a weak effect of Q6 on the liquid structuring throughout the pore space and that the liquid in the centre of the pores behaved as a bulk fluid. Such behaviour is consistent with MD simulations of water-ethanol mixtures confined between silanol slabs, which showed pronounced changes in density adjacent to the pore surface, but the density tended towards bulk values for distances >1 nm from the pore walls as the influence of the interface was reduced [32].

The reduction of the ethanol diffusion coefficient observed for liquids within Q6 can be attributed to the effective tortuosity of the silica. For mesoporous materials this property is often measured using non-interacting probe molecules (commonly alkanes) [17]. The value of 3.1 obtained for cyclohexane was consistent with the values previously reported for cyclohexane, n-pentane, n-heptane, and acetone imbibed within Q6 [25]. Care must be taken when applying this method to small pore materials as it has been shown that the assumption of a non-interacting alkanes begins to break down for silica pores smaller than 6 nm in diameter [25], however, the coincidence of the effective tortuosity for such a wide array of different probe molecules suggest that value of ∼3 is a good approximation of the true structural tortuosity of this material. The decrease in effective tortuosity from 3.4 ± 0.2 at ${\chi }_{\mathrm{E}}$ = 0.1 to 2.8 ± 0.1 at ${\chi }_{\mathrm{E}}$ = 0.6 was consistent with the weakening of the ethanol-surface interaction observed in the NMRD profiles over the same composition range, but it is noted that this adsorption effect is small and that the measured diffusion coefficients are primarily reduced by the structural tortuosity.

For liquid mixtures imbibed within Q3, the diffusion coefficient of ethanol was independent of the behaviour of the bulk liquid mixtures and decreased significantly as the composition of ethanol in the liquid mixture increased. Large decreases in the diffusion coefficient of confined liquids have recently been observed for a range of binary liquid mixtures imbibed within a Vycor glass with 4 nm pores [19]. In that study, it was suggested that the largest decreases in diffusion coefficient occurred for mixtures due to a phase separation of the two fluids at the pore surface. In the present work, the smallest diffusion coefficient was measured for single-component ethanol imbibition, suggesting a different physical origin of the transport limitations. FFC data shown in Fig. 5b were consistent with a slight weakening of the ethanol-surface interaction strength as ${\chi }_{\mathrm{E}}$ increased and therefore the decrease in the observed diffusion coefficient cannot be explained by the change in ethanol adsorption strength. Instead, it is important to consider the nature of the liquid structuring occurring within the pore space. Assuming cylindrical pores, a single monolayer coverage, and using the kinetic diameters of water (0.27 nm) and ethanol (0.46 nm), the surface affected spin population ($p_{\mathrm{S}}$ in Eq. (2)) can be estimated as 0.33 and 0.52 for the two extremes of single-component water and ethanol imbibition respectively. These values suggest that a significant proportion of the pore fluid is directly affected by the silica surface. For materials with small pores, estimates of the surface affected spin fraction strongly depend on the pore diameter and thickness of the adsorbed layer. Recent Barrett-Joyner-Halenda (BJH) analysis of the N₂ adsorption isotherms obtained for Q3 silica showed a broad pore size distribution with an average pore diameter of 2 nm derived from both the adsorption and desorption isotherms [33]. Furthermore, multilayer adsorption of water is well-known [34] and molecular dynamics simulations show that ethanol preferentially adsorbs as a monolayer on silica surfaces, with the hydrophobic alkyl group pointing towards the bulk pore space [35,36]. The hydrophobic alkyl groups create a region of near zero density before subsequent ethanol layers form, increasing the effective thickness of the ethanol monolayer when imbibed within silica materials. These observations are consistent with the majority of molecules within the pore space interacting with the walls, meaning that the bulk pore space is a highly confined region, unable to support the same liquid structuring observed for the bulk liquids. As ethanol molecules are larger than water molecules, increasing ${\chi }_{\mathrm{E}}$ increases the fraction of spins affected by the surface and the degree of confinement of the bulk pore fluid, consistent with the observed trends in diffusion and tortuosity shown in Fig. 3, Fig. 4. For completeness we note that we have not considered any potential influences of different surface moieties, in particular hydroxyl concentration and type, in the two silicas studied.

4. Conclusion

PFG NMR was used to study the diffusion coefficient of ethanol in ethanol-water liquid mixtures as a function of composition when imbibed within silicas of pore diameters of 6 nm and 3 nm. Despite varying by only a few nm in pore size, significant differences were observed in the mass transport behaviour of liquid mixtures confined within each silica. Diffusion coefficients for ethanol imbibed within Q3 were an order of magnitude smaller than those observed for ethanol imbibed within Q6 and showed differing trends as the composition of ethanol in the mixture was varied. For liquids imbibed within Q6, the diffusion coefficient of ethanol was consistent with the bulk-pore liquid structuring being unaffected by the silica surface and dominating the composition dependence of the measured diffusion coefficient. The observed diffusion coefficients were slowed by a tortuosity factor of ∼3, which agreed well with the structural tortuosity of 3.1 measured with cyclohexane. A small contribution to the effective tortuosity due to changes in the ethanol-surface interaction was observed, but this effect was minor in comparison to the structural tortuosity. For Q3, the data reported are consistent with most molecules interacting significantly with the pore walls, leading to a strong reduction in the observed diffusion coefficient and a highly confined bulk-pore liquid. As the composition of ethanol within the pore space increased, the measured diffusion coefficient of ethanol decreased, consistent with an increase in liquid confinement due to the larger molecular size of ethanol. Significant changes in mass transport behaviour were observed due to variations in liquid structuring within pores even though the nominal pore sizes were much larger than the molecular diameters of the probe molecules of interest. This methodology can be applied to understand the mass transport behaviour of a wide range of liquid mixtures imbibed within micro or mesoporous materials. It is noted, however, that significant line broadening or small chemical shift differences may prevent the spectral resolution of components within the mixture. Under such conditions, additional signal discrimination methods, such as relaxation weighting or partial deuteration, would be required to accurately characterise the dynamics of the components of interest. This study highlights the importance of understanding the effects of liquid structuring, as well as the physical structure of the porous material, on the transport properties of liquids when designing and optimising nanoporous materials for liquid phase applications.

CRediT authorship contribution statement

Jordan Ward-Williams Writing – original draft, Conceptualization, Formal analysis, Investigation. Andrew Sederman Writing – review & editing, Conceptualization, Supervision. Michael Mantle Conceptualization, Supervision. Matthias Appel Supervision, Funding acquisition. Lynn Gladden Funding acquisition, Supervision, Writing – review & editing, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Biographies

Jordan Ward-Williams obtained his MSci in Chemistry and PhD in Chemical Engineering from the University of Cambridge. He is currently an Assistant Research Professor in the Department of Chemical Engineering & Biotechnology at the University of Cambridge, where his research focuses on the development of magnetic resonance relaxation and diffusion methods to study transport phenomena in porous media.

Lynn Gladden graduated in chemical physics at the University of Bristol before training as a physics teacher at the University of Oxford. She then studied for a PhD in the Structural Studies of Inorganic Glasses at the University of Cambridge. She is currently Shell Professor of Chemical Engineering in the Department of Chemical Engineering & Biotechnology at the University of Cambridge; her research interests focus on the development of operando magnetic resonance imaging techniques to study transport and reaction processes in porous media.