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Adsorption of Pure Vapor Species on Microporous Silica Membranes and Silica Pellets Ben Bettens,† Adrian Verhoef,†,‡ Henk M. van Veen,§ Carlo Vandecasteele,† Jan Degre`ve,‡ and Bart Van der Bruggen*,† Laboratory of Applied Physical Chemistry and EnVironmental Technology, Department of Chemical Engineering, K.U.LeuVen, W. de Croylaan 46, B-3001 LeuVen, Belgium, Laboratory of Chemical and Biochemical Process Technology and Control, Department of Chemical Engineering, K.U.LeuVen, W. de Croylaan 46, B-3001 LeuVen, Belgium, and Department of Energy Efficiency in Industry, Energy Research Centre of The Netherlands, ECN, Westerduinweg 3, 1755 ZG Petten, The Netherlands ReceiVed: February 23, 2010; ReVised Manuscript ReceiVed: April 15, 2010
The adsorption and diffusion of pure water, methanol, ethanol, isopropanol, and butanol in microporous silica membranes and (methylated) silica top layer pellets are studied by performing vapor adsorption experiments at 40 °C using a gas chromatograph equipped with a headspace system and using a conventional gravimetrical microbalance, respectively. For silica pellets, the pure vapor adsorption equilibrium is adequately described by a Langmuir isotherm. Adsorption kinetics is described by the internal diffusion model, where surface diffusivities are estimated to be on the order of 10-13 m2/s. The surface diffusivity of water (DS ) (5.5-6.2) × 10-13 m2/s) is a factor of 2 higher than the alcohol diffusivities (DS ≈ 3 × 10-13 m2/s). The methylated silica pellets display a higher alcohol adsorption and lower water adsorption. For the microporous silica membranes, methanol adsorption is reduced by a factor of 1000. This may reflect the different structure of the membrane compared to the pellets or the incomplete methanol vapor penetration into the membrane. 1. Introduction In pervaporation, transport through microporous silica membranes is governed by adsorption and diffusion processes.1-4 Hence, knowledge of both processes allows predicting membrane performance in terms of flux and selectivity. In the absence of experimental data, adsorption and diffusion properties can be calculated by molecular dynamics simulations that describe the trajectories of molecules through membranes.5,6 A popular method for the experimental determination of adsorption and diffusion properties in membranes is transient permeation (time lag). In this method a series of step changes in feed activity are applied and the corresponding transient response on the permeate side is measured by a mass spectrometer or Fourier transform infrared spectroscopy (FT-IR). For a given step change in feed activity, the cumulative transient flux is plotted against time. The linear part of the plot is extended back to the x axis. The x intercept thus obtained is the time lag. Procedures to determine adsorption and diffusion properties from this time lag are described by Gardner et al.,7 Shah et al.,8,9 Ash,10 Ye et al.,11 and Ruthven.12 Alternatively, adsorption and diffusion properties of membranes can also be determined by bringing the membrane to equilibrium with a liquid or a vapor. In the first method, the membrane sample is immersed directly into the liquid (volumetric experiments). At regular time intervals, the immersed sample is rapidly removed from the liquid. Liquid drops adhering to the surface are blotted off with filter paper, and the sample is weighed and immediately placed back into the liquid. This procedure is repeated until equilibrium * Corresponding author: tel, +32 16 322340; fax, +32 16 322991; e-mail,
[email protected]. † Laboratory of Applied Physical Chemistry and Environmental Technology, Department of Chemical Engineering, K.U.Leuven. ‡ Laboratory of Chemical and Biochemical Process Technology and Control, Department of Chemical Engineering, K.U.Leuven. § Department of Energy Efficiency in Industry, Energy Research Centre of The Netherlands.
is reached. In the second method, the membrane sample is contacted with the vapor phase. Vapor uptake can be measured by means of one of the following techniques: weighing using a conventional gravimetrical microbalance or a magnetic suspension balance;13 monitoring changes in the oscillating frequency of a continuous oscillating tapered element holding the sample using a tapered element oscillating microbalance (TEOM);14 measuring the heat of adsorption using differential scanning calorimetry;15 monitoring changes in the electron density perpendicular to the sample surface using X-ray reflectometry;16,17 monitoring changes in the refractive index of the sample surface using ellipsometry.17 The vapor uptake methods have several advantages: better control of the activity of the adsorbing species and no residues of the solution (other than the adsorbate) left on the membrane surface.18 This paper studies adsorption and diffusion processes of pure vapors (water, methanol, ethanol, isopropanol, and butanol) in microporous silica membranes and in (methylated) pellets made from the same material as the membrane top layer. A gas chromatograph equipped with a headspace system and a conventional gravimetrical microbalance is used, respectively. The experimentally determined adsorption isotherms (vapor uptake as a function of the partial vapor pressure) are fitted against the Langmuir isotherm model. On the other hand, the kinetics of adsorption (vapor uptake as a function of time) is described by the internal diffusion model, from which a rough estimate of the diffusion coefficients is made. Finally, the adsorption behavior of membranes and pellets are compared and discussed. 2. Theory 2.1. Adsorption Equilibrium. Brunauer et al.19 divided pure vapor adsorption isotherms into six different types, which are shown in Figure 1. Isotherms of type I are associated with
10.1021/jp101600t 2010 American Chemical Society Published on Web 05/05/2010
Adsorption on Silica Membranes and Pellets
J. Phys. Chem. C, Vol. 114, No. 20, 2010 9417 is not exclusively related to the kinetics of the adsorption process (i.e., the rate of actual physical adsorption) but rather to internal diffusion processes.20,22,24-29 Internal diffusion comprises two different diffusion mechanisms: the pore diffusion mechanism and the surface diffusion (or solid diffusion) mechanism.24-29 When both mechanisms occur in parallel within a silica particle, the isothermal diffusion inside the particle is described by26,28,29
Figure 1. Classification of the six types of adsorption isotherms.
εp
(
)
∂cp ∂q ∂cp 1 ∂ ∂q 1 ∂ 2 r εpDp + 2 r2DS + ) 2 ∂t ∂t ∂r ∂r ∂r ∂r r r
(
) (4)
systems where adsorption does not proceed beyond the monomolecular layer. Isotherms for microporous adsorbents are generally of this type.20 The other types of isotherms involve multilayer formation. For vapor species, the amount adsorbed is usually expressed as the number of moles of the species, adsorbed per mass or per volume of adsorbent. The relative pressure is the ratio of the partial pressure pi of the vapor species to its saturated vapor pressure Pivap at the sorption temperature TS.21 Although only six shapes of isotherms have been observed, many theories and models have been developed for interpretation. The Langmuir theory assumes that an adsorption system is in dynamic equilibrium, in which the rate of evaporation (desorption) equals the rate of condensation (adsorption). The Langmuir isotherm is described as21,22
θ)
bLp qeq ) qsat 1 + bLp
(1)
where θ is the fractional coverage of the surface, the ratio of the number of occupied adsorption sites (or the adsorbed phase concentration at equilibrium qeq) to the total number of possible adsorption sites (or the adsorbed phase concentration at saturation qsat), bL is the Langmuir adsorption constant, and p is the partial pressure of the vapor species. In the derivation of eq 1, it was assumed that the adsorbed species is held at localized sites and that each site can accommodate only one species. Depending on the expression for the adsorption constant bL, no interactions between neighboring adsorbates are assumed or lateral adsorbate-adsorbate interactions due to van der Waals forces are allowed.22 The Langmuir adsorption isotherm is useful to fit type I and the initial part of type II isotherms. For small p values, the Langmuir isotherm reduces to the Henry isotherm
θ ) bLp
(2)
In order to take the possibility of occurrence of two different types of adsorption sites into account, adsorption can be described by a dual-site Langmuir isotherm15,23
bAp bBp qeq ) qsat,A + qsat,B 1 + bAp 1 + bBp
(3)
with the subscripts A and B indicating the two adsorption sites. 2.2. Adsorption Kinetics and Diffusion. In modeling the adsorption process, one is interested not only in the adsorption equilibrium but also in the rate of adsorption. Since adsorption must be preceded by migration to an adsorption site, this rate
where cp is the vapor concentration in the particle pores, q is the adsorbed phase concentration, r is the radial coordinate, εp is the particle porosity, Dp is the pore diffusivity, and Ds is the surface diffusivity. The initial (IC) and boundary conditions (BC) are26,28,29 IC:
cp(r, 0) ) 0
and
q(r, 0) ) 0
∂cp )0 ∂r
r)0
cRp ) c
r)R
t)0
(5)
BC1:
BC2:
where cRp is the vapor concentration at the pellet surface and c is the interpellet vapor concentration (i.e., the vapor concentration in the fixed bed of silica pellets that is assumed constant). Moreover, when equilibrium is assumed for adsorption at an interior adsorption site, c(r,t) and q(r,t) are related by the instantaneous equilibrium isotherm (Henry, Langmuir, ...). Assuming furthermore that (1) diffusion in the pores can be neglected compared to that along the pore surface, (2) surface diffusivity is concentration independent and (3) adsorbate accumulation in the vapor phase can be neglected, eq 4 takes the form20,22,26,28,29
(
∂q ∂2q 2 ∂q ) DS + ∂t ∂r r ∂r
)
(6)
The solution to eq 6 and its initial and boundary conditions 5 is given by Crank24
(
( )∑
qt 6 )1- 2 qeq π
∞
DSn2π2t 1 exp 2 R2 n)1 n
)
(7)
For values of qt/qeq > 0.5, eq 7 is approximated by the first two terms, resulting in
( )
(
qt DSπ2t 6 ) 1 - 2 exp - 2 qeq π R
)
(8)
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Alternatively, in the short time region (qt/qeq < 0.5), eq 7 is approximated by24
qt 6 ) qeq R
DSt π
(9)
For internal diffusion in microporous silica membranes, Crank’s equation for diffusion in a plane sheet, which is deduced in a way similar to eq 6, can be applied(The radius of the tubular membrane (5 mm) is much larger than the size of a diffusing molecule (
