Ind. Eng. Chem. Res. 2005, 44, 6477-6484
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Diffusion of Linear Paraffins in Nanoporous Silica S. Z. Qiao and S. K. Bhatia* Division of Chemical Engineering, The University of Queensland, Brisbane QLD 4072, Australia
The diffusion of hexane, heptane, octane, and decane in nanoporous MCM-41 silica at various temperatures is investigated by the zero-length-column method. The diffusion coefficients are derived by a complete-time-range analysis of desorption curves at different purge flow rates and temperatures. The results show that the calculated low-coverage diffusivity values decrease monotonically, and the derived Henry’s law constants increase, as the carbon number of paraffins increases. The study reveals that transport is strongly influenced by intracrystalline diffusion and dominated by the sorbate-sorbent interaction. The diffusion activation energy and adsorption isosteric heat at zero loading increase monotonically with the carbon number of linear paraffins, but their ratio is essentially constant for each adsorbate compound. Introduction The adsorption equilibrium of common gases (such as nitrogen, argon, oxygen, and carbon dioxide) as well as hydrocarbons on ordered mesoporous materials has received considerable attention in recent years.1-8 However, only a very limited number of studies on the adsorption kinetics and diffusion in mesoporous materials have been reported.9-12 To study adsorption theory and phenomena as well as to facilitate the potential use of mesoporous materials in adsorption and heterogeneous catalysis, it is essential to investigate widely the adsorption of various chemicals, especially their diffusion, on the ordered pore materials. A variety of microscopic methods (pulsed field gradient NMR, NMR relaxation, and quasielastic neutron scattering) and macroscopic methods (uptake rate measurement, frequency response, infrared spectroscopy, and chromatographic methods) are often used for the measurement of diffusivities in porous materials.13,14 Since the late 1980s, a zero-length-column (ZLC) chromatographic technique15 has been developed to measure transport diffusivities in porous adsorbent particles. This technique involves the investigation of the experimental desorption dynamics curve for a small sample under a high flow rate of gas and the subsequent matching of this curve to the theoretical solution of the diffusion equation. This method can eliminate the intrusion of axial dispersion, heat-transfer, and bed diffusion resistances by the use of large crystals, a low adsorbate concentration, and a very small adsorbent sample amount as well as a high carrier flow rate during desorption. In the theoretical analysis, the short-time (ST) approximate or long-time (LT) asymptote of the desorption curve15,16 is used to extract the relevant parameters. However, it is found that these methods often yield diffusivity values differing by as much as an order of magnitude.17,18 The reason is that both methods are simplified, different time regions are chosen in the fitting of the desorption curve, and the nature of the errors is different in these regions. LT analysis uses only the data from the tail of the desorption curve, which is the region of greatest experimental uncertainty. On the * To whom correspondence should be addressed. Tel.: +617-33654263. Fax: +61-7-33654199. E-mail: sureshb@ cheque.uq.edu.au.
other hand, in ST analysis, the effect of any experimental error on the initial time and dead-volume contribution is very significant. To overcome these disadvantages, some effort has been made to develop a full-time19 or a moment analysis method,20 in which diffusion parameters can be extracted by fitting the entire desorption curve, but they are not widely used because of their greater complexity. Recently, Han et al.18 used a simple technique to fit over the complete time range of the desorption curve while maintaining the accuracy of the ZLC method. Our recent study has investigated the effect of the pore size, temperature, and purge flow rate on the diffusion of decane in ordered mesoporous MCM-41 materials using the ZLC technique12 along with the fulltime-range analysis method. It has demonstrated that the diffusivity values are strongly dependent on the temperature but essentially independent of the flow rate and the effect of the pore size on diffusion is weak. Mechanistically, the results suggested that decane diffuses by sliding on the surface in a wormlike manner, with the individual CH2 or CH3 end sites locally vibrating and losing momentum upon collision with the surface. This surface diffusion picture was supported by the good agreement between the theoretical potential energy of a flat-lying decane molecule based on a united atom (UA) model21 calculation and the experimental isosteric heat. The results also showed that the ZLC method is an effective tool to investigate the diffusion kinetics of hydrocarbons in mesoporous MCM-41 materials. A complete-time-range analysis of desorption curves is a simple and effective method to derive the diffusion coefficient of rapidly diffusing and strongly adsorbed species (low vapor pressure), for which it is difficult, in practice, to achieve experimental conditions corresponding to diffusion control. However, these conclusions need to be further confirmed using different adsorptive molecules. It is also important to study the diffusion and interaction mechanisms using different size adsorbates. To the best of our knowledge, detailed investigations of the effect of the adsorbate property on diffusion in ordered mesoporous materials have not yet been reported. In this study, the diffusion of linear paraffins with different carbon numbers in ordered mesoporous MCM41 material is investigated by the ZLC method, with a
10.1021/ie048931x CCC: $30.25 © 2005 American Chemical Society Published on Web 03/05/2005
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Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005
full-time-range procedure analysis of desorption curves to derive the diffusion coefficients. The accuracy of the method is validated by an alternate data analysis approach developed previously by Brandani and Ruthven.22 The diffusion mechanism and the effect of interaction on diffusivity, the equilibrium constant, and activation energy are also discussed. Theory The detailed models and the mathematical formulation of the ZLC method have been described elsewhere.15,17 In the technique, a small sample of adsorbent, sandwiched between sintered disks, is first equilibrated with an adsorptive at low pressure. Subsequently, desorption is conducted under a high flow rate of carrier gas. Modeling of the desorption involves solution of the diffusion equation for the Henry’s law region with constant intraparticle diffusivity. For uniform spherical particles with radius R, the relationship between relative effluent concentration c/c0 and time t is given by
c c0
∞
) 2L
∑
exp(-βn2Dt/R2)
n)1 β
2
+ L(L - 1)
n
(1)
where D is the intraparticle diffusivity, L is a dimensionless parameter, and the eigenvalues βn are given by the roots of
βn cot βn + L - 1 ) 0
(2)
with
L)
1 F R2 3 KVs D
(3)
in which F is the gas volumetric flow rate, K is the Henry’s law constant, and Vs is the volume of the solid phase, which can be obtained by
Vs )
ms ms ) Fs F(1 - p)
(4)
where ms is the sample mass, F is the pore wall density, Fs is the particle density, and p is the particle porosity. The experimental desorption curve, c/c0 vs t, was fitted to the above equations over the full data range using a nonlinear least-squares method to obtain the best-fitting parameters D/R2 and L. In the summation in eq 1, a total of eight terms is chosen in this study, which was found to be adequate for convergence. The temperature dependence of the diffusivity is correlated by the Arrhenius form
D ) D0 exp(-E/RgT)
(5)
The activation energy for surface diffusion, E, can be obtained by
(∂ ln∂TD)
E ) RgT 2
(6)
where T is the temperature and Rg is the ideal gas constant. Further, the isosteric heat of adsorption at zero loading, qst, is obtained from the Henry’s law constant, K, following8,23
qst ) -RgT 2
(∂ ln∂TK)
(7)
Experimental Section The MCM-41 sample used in this study was prepared using a cetyltrimethylammonium bromide surfactant as the structure-directing agent and a sodium silicate solution as the silicon source, according to procedures described in detail elsewhere.7 Briefly, the sodium silicate solution was added drop by drop to the surfactant solution with vigorous stirring at room temperature. After being continuously stirred for 1 h, the gel mixtures were transferred to an autoclave reactor and heated at 384 K for 3 days. Subsequently, the mixture was cooled to room temperature, filtered, and washed with copious amounts of deionized water. The sample was dried at 378 K and calcined in air at 823 K for 4 h, with a temperature increase rate of 1 K/min. The obtained MCM-41 sample was characterized by X-ray diffraction (XRD) and nitrogen adsorption techniques. The Brunauer-Emmett-Teller surface area of the sample was calculated from the nitrogen adsorption data in the relative pressure range of 0.05-0.2. The pore size and primary mesopore volume were determined by the high-resolution Rs-plot comparative analysis of the nitrogen adsorption isotherm combined with XRD results.7 The particle porosity can be determined by
p )
V pF 1 + Vp F
(8)
in which Vp is the primary mesopore volume and the pore wall density, F, is assumed to be 2.2 cm3/g for silica with amorphous pore walls. The average particle size of samples was measured using a particle size analyzer (Mastersizer 2000, Malvern Instruments Ltd., Worcestershire, U.K.) and determined as the median of the mass distribution. The structural properties of the adsorbent are listed in Table 1. The corresponding solidphase volume of the sample is calculated by eq 4, based on the porosity p, and is also listed in Table 1. The diffusion data of hydrocarbons in MCM-41 were collected using the ZLC chromatographic method in Figure 1. A very low adsorbate vapor concentration (the Henry’s law region) is used in the diffusion measurement. The vapor gas is produced by passing a small flow of pure helium gas through liquid adsorbate contained in a bubble vapor producer immersed in a silica oil bath (Polyscience, Niles, IL) controlled at low temperature. The adsorbate vapor concentration can be accurately controlled by mixing of an adsorbate vapor stream (stream 3) and a pure gas stream (stream 2). Stream 1 is the pure helium gas line used in desorption or the sample degas process, which uses a separate line in order to avoid an adsorbate parasite and inaccurate definition of zero time. The flow rate of each stream is independently controlled by a separate MKS mass flow controller (R-1, R-2, or R-3). Porter regulators (P-1, P-2, and P-3) are installed before the mass flow controllers to maintain a constant pressure of 138 kPa. The ZLC is a very thin layer of MCM-41 particles placed between two sintered porous filter disks in a 1/8in. stainless steel Swagelok union inside a gas chromatographic oven (Varian CP-3800). The temperature of the oven is controlled to within (0.5 °C. To ensure a constant temperature of gases in the ZLC, 2-m-length tubes are coiled and connected to a six-way valve in the
Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005 6479 Table 1. Structural Properties, Weight, and Solid-Phase Volume of the MCM-41 Sample mesopore volume Vp (cm3/g)
pore diameter d (nm)
surface area S (m2/g)
particle diameter 2R (µm)
particle porosity p
sample weight ms × 103 (g)
sample volume Vs × 103 (cm3)
0.85
3.79
1132.6
23.56
0.65
1.6
2.08
Figure 1. Schematic drawing of an experimental ZLC apparatus for measuring desorption kinetics.
oven to provide a sufficient heat-transfer area. The concentration of the ZLC effluent stream is monitored online by a flame ionization detector (FID). To eliminate the effect of the dead volume, the tube length between the six-way valve and the FID should be as small as possible. In this study, high-purity hexane (>99.0%; LabScan Analytical Sciences, Dublin, Ireland), heptane (99.5%; Ajax Fine Chemicals, Sydney, Australia), octane (>99.0%; Unilab, Ajax Fine Chemicals, Sydney, Australia), ndecane (>99.0%; ICN Biomedicals Inc., Ohio), and highpurity helium (99.99%) provided by BOC Gases Australia, Ltd. (Chatswood, Australia), were used as adsorptives or carrier gases. To eliminate the intrusion of heat-transfer and bed diffusion resistance, a very low adsorbate concentration (partial pressure 0.006-0.05 mmHg, to ensure that adsorption is in the Henry’s law region), a small adsorbent sample amount (0.0016 g), and a high carrier flow rate (100 or 140 mL/min) during desorption were used in the diffusion experiments. Before measurement was started, the sample needed to be degassed at 250 °C overnight in a pure helium carrier stream. After the sample was cooled to the measurement temperature, the carrier gas (helium), containing a very low concentration of hydrocarbon, was passed through the sample column at a high flow rate until it was saturated, as confirmed by monitoring of the effluent stream by the FID. Then a six-way valve was switched (at time zero), a pure carrier gas at the same rate was fed to the ZLC, and the adsorbent was purged. The time-dependent effluent concentration of hydrocarbon was measured by the FID and recorded automatically by the gas chromatograph and was used to evaluate the diffusion coefficient. The reproducibility of the desorption curves was found to be within 5% in repeat experiments for several cases for which this was tested. Results and Discussion Adsorption diffusion experiments of different linear paraffins on MCM-41 were carried out in the temperature range of -10 to +90 °C and at the purge gas flow
rate of 100 and 140 mL/min. The experimental desorption curve was fitted to eqs 1-3 using a nonlinear leastsquares method to obtain the best-fitting parameters D/R2 and L. For the fitting procedure, the initial L value was first guessed, and the eigenvalues, β1, β2, ..., β8, were calculated by eq 2. Subsequently, the value of D/R2 was evaluated by fitting eq 1 to the experimental desorption curve. The above processes were repeated until the error was less than a given accuracy. Because the experiments were carried out at very low concentration within the Henry’s law region, the diffusion parameters obtained are considered as the diffusivities at zero surface loading. Effect of the Purge Flow Rate on Diffusion Coefficients. The desorption curves of various alkanes (hexane, heptane, octane, and decane) for diffusion on MCM-41 at different temperatures are given in Figures 2 and 3 for purge flow rates of 100 and 140 mL/min, respectively. The symbols represent experimental data, and the solid lines are theoretical fitting results. Good agreement is observed between the experiment and theory. The diffusion parameters obtained are summarized in Table 2. It may be seen that the diffusion time constant, D/R2, is essentially independent of the purge flow rate, supporting the data analysis method. The consistency of diffusivity for different purge flow rates indicates that the transport process is strongly affected by intraparticle diffusion and not controlled by some other extraparticle rate process. Table 2 shows that the fitted L value, at a given temperature, is proportional to the flow rate, which is consistent with eq 3. It can be seen that the KVs values, calculated by eq 3, are also essentially independent of the purge flow rate at the same temperature. Because the solid-phase volume Vs is constant for the same sample, it can be concluded that the equilibrium constant K obtained is independent of the purge flow rate, as it should be. Validation of the Method. The value of the parameter L is important for determining whether the transport process is controlled by equilibrium effects or pore diffusion.17,20 If the L value is very low (
