J. Phys. Chem. C 2007, 111, 3059-3065
3059
Mesostructured Silica SBA-16 with Tailored Intrawall Porosity Part 2: Diffusion Oliver C. Gobin,† Qinglin Huang,§ Hoang Vinh-Thang,† Freddy Kleitz,‡ Mladen Eic´ ,§ and Serge Kaliaguine*,† Department of Chemical Engineering, LaVal UniVersity, Ste-Foy, Que´ bec, Canada G1K 7P4, Department of Chemistry, LaVal UniVersity, Ste-Foy, Que´ bec, Canada G1K 7P4, and Department of Chemical Engineering, UniVersity of New Brunswick, P.O. Box 4400, Fredericton, N.B., Canada, E3B 5A3 ReceiVed: June 8, 2006; In Final Form: September 13, 2006
In this Part 2 of the present work, the diffusivities of n-heptane, cumene, and mesitylene in the SBA-16 silica samples described in Part 1 have been measured by the zero length column (ZLC) method. A comparison is made between the diffusivities and diffusion apparent activation energies in these materials and in a series of SBA-15 samples of similar pore size and pore volume. The latter series was discussed in a previous work. Clear differences are indeed observed and rationalized in terms of differences in the pore structure of the two series of solids. βn cot βn + L - 1 ) 0
Introduction In recent studies,1,2 the diffusional properties of several hydrocarbons in well-characterized SBA-15 materials with tailored micro- and mesopores have been investigated by the chromatographic zero length column (ZLC) technique. Differences between the diffusion in the intrawall micropores and in the cylindrical mesopores could be quantified and led us to underline the interesting properties of SBA-15 materials. For instance, the overall diffusion process was controlled by a combination of micro- and mesopore diffusion resistances. In Part I of this paper a series of SBA-16 materials, also with tailored micro- and mesoporosity, were synthesized and properly characterized.3 In this second part of the study the diffusion of n-heptane, cumene, and mesitylene in selected samples of the SBA-16 series was investigated using the ZLC technique. These three probe molecules represent one linear alkane and two monoaromatic compounds with similar values of the molecular mean free path. The results were compared with those obtained previously with the same probe molecules in SBA-15 materials. Theory. Zero length column (ZLC) chromatography has been developed by Eic´ and Ruthven4 to measure intracrystalline diffusivities in microporous materials. In the past decade, the application of the ZLC method has been extended to many different systems, including materials with both micro- and mesoporosity.5-9 In the case of uniform spherical particles being in linear adsorption equilibrium at very low sorbate partial pressures, neglecting the hold-up in the ZLC bed and assuming perfect mixing throughout the ZLC cell, the normalized effluent sorbate concentration c/c0 is described by the following set of equations4
c c0
∞
)
∑
n)1
2L β2n + L(L - 1)
exp
(
-β2n
Deff R2
t
)
(1)
* Corresponding author. Tel: 418-656-2708. Fax: 418-656-3810. E-mail:
[email protected]. † Department of Chemical Engineering, Laval University. ‡ Department of Chemistry, Laval University. § Department of Chemical Engineering, University of New Brunswick.
L)
1 F R2 3 Vs KHDeff
(2) (3)
where R is the particle radius, KH is Henry’s constant based on the particle, and Deff is the effective diffusivity. βn are the positive roots of eq 2, L is given by eq 3, and Vs is the volume of the solid bed. By fitting this set of equations against the experimental data in the complete time range, it is possible to determine the effective diffusion time constant, Deff/R2. However to minimize particle size distribution effects, which only appear at short times,10 the so-called long-time solution is considered more accurate. It is obtained by neglecting all of the higher order terms of the sum in eq 1 that yields a straight line on a semilogarithmic plot of the normalized effluent sorbate concentration versus time.4 From the slope
m ) -β21
Deff R2
(4)
and the intercept
i)
β21
2L + L(L - 1)
(5)
of the plot and under consideration of eq 2 the effective diffusion time constant is obtained. Experimental Section Materials. The synthesis and characterization of the SBA16 materials are described in the first part of this paper.3 These well-ordered SBA-16 samples are prepared according the method proposed by Kleitz et al.11,12 The diffusion measurements were only carried out on six selected SBA-16 materials. The samples are denoted as S-T-t with the time t between 1 and 5 days and the temperature T in the range from 45 to 100 °C. Important structural properties of the materials have been evaluated in our first paper and are summarized in Table 1.
10.1021/jp063583t CCC: $37.00 © 2007 American Chemical Society Published on Web 01/31/2007
3060 J. Phys. Chem. C, Vol. 111, No. 7, 2007
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TABLE 1: Structural Properties of SBA-16 Materialsa samples
SBET (m2‚g-1)
Vt (cm3‚g-1)
V1 (cm3‚g-1)
V2 (cm3‚g-1)
(V1 + V2)/Vt
dme (nm)
hw (nm)
r1 (nm)
me (-)
S-45-1 S-60-1 S-80-1 S-80-5 S-100-1 S-100-2
370 414 621 843 821 886
0.23 0.28 0.42 0.68 0.66 0.77
0.072 0.071 0.101 0.045 0.047 0.018
0.001 0.005 0.021 0.110 0.100 0.132
0.32 0.27 0.29 0.23 0.22 0.19
7.72 8.35 9.15 11.35 11.33 12.17
8.64 7.24 5.90 4.39 4.43 3.95
0.60 0.60 0.65 0.70 0.70 0.70
0.23 0.28 0.34 0.46 0.46 0.51
a The notation in Table 1 is as follows: SBET, BET specific surface area; Vt, total pore volume; V1, intrawall micropore volume; V2, intrawall second micropore population volume; dme, primary mesopore diameter; hw, pore wall thickness; r1, intrawall micropore radius; and me, mesoporosity.
Figure 1. Ft plots for S-100-2.
Measurements. The ZLC setup was described in detail by Jiang and Eic´.13 The ZLC column and switching valve were placed in a gas chromatographic oven (Hewlett-Packard Series II 5890). The flow rates were controlled using mass flow controllers. A small amount of the SBA-16 sample powder (1-2 mg) was loaded into the ZLC column and activated at 270 °C for at least 6 h to eliminate possible impurities and residual moisture in particular. Helium of 99.95% purity was used as the inert carrier gas. A sorbate, for example, n-heptane, cumene, or mesitylene (99% grade, Aldrich) was kept in the bubbler, and its vapor was carried by a small flow of helium before being diluted in the main helium stream. The sorbate concentrations were adjusted and maintained at a low level corresponding to the linear region of the adsorption isotherm (Henry’s Law region). In the adsorption step, the samples were equilibrated with sorbate diluted in a helium flow, usually for about 1 h. Then desorption was performed under helium at a flow rate high enough to minimize external mass and heat resistances on the surface of the sample. Flow rates of 100-200 cm3/min were chosen to verify that the desorption process was kinetically controlled. A flow rate of 100 cm3/min was chosen as standard flow rate for all samples. The relative concentrations (c/c0) of the effluent sorbates from the ZLC column were determined using a flame ionization detector. The desorption step was then performed until the baseline was essentially reached. The effective diffusivity was calculated from the kinetically (diffusion) controlled long-time region of the ZLC curve. The
Figure 2. ZLC curves for cumene in selected SBA-16 samples.
apparent activation energies were calculated from Arrhenius plots of the corresponding effective diffusivities measured at different temperatures. The particle dimensions of the powder samples were determined from SEM images. Results The effect of different purge flow rates on the ZLC response is displayed in Figure 1, where the normalized sorbate effluent
Part 2: Diffusion
J. Phys. Chem. C, Vol. 111, No. 7, 2007 3061
TABLE 2: Diffusivity Data of n-Heptane, Cumene, and Mesitylene for SBA-16 Samples T (°C)
L
Deff/R2 × 104 (s-1)
n-heptane
10 30 50
40 43 69
S-45-1 (20 µm) 1.59 0.634 2.11 0.845 2.68 1.070
cumene
30 50 70
59 67 112
mesitylene
30 50 70
246 361 641
n-heptane
10 30 50
25 41 80
cumene
50 70 90
16 20 43
1.75 3.95 8.86
mesitylene
50 70 90
12 15 30
1.71 3.67 6.98
sorbate
1.36 1.59 1.79
EA (kJ/mol)
T (°C)
L
Deff/R2 × 104 (s-1)
10.0
10 30 50
40 53 87
S-60-1 (15 µm) 3.41 0.767 4.62 1.040 5.62 1.370
6.4
50 70 90
18 29 50
7.4
50 70 90
27 41 81
20.0
10 30 50
25 52 96
0.926 2.090 4.280
37.3
50 70 90
15 20 59
1.53 2.82 8.05
0.907 1.940 3.690
34.2
50 70 90
17 26 34
1.36 3.12 6.26
Deff × 1013 (m2s-1)
0.544 0.636 0.730
1.51 0.604 1.84 0.737 2.21 0.883 S-80-5 (23 µm) 3.12 1.650 4.82 2.550 8.92 4.720
concentrations are plotted versus the total purge volume, Ft. At the short time asymptotes (Ft < 200 mL) the ZLC desorption curves are independent of the total purge volume, indicating that the transport is approaching the equilibrium control limit. The curves start to diverge at Ft ) 200 mL, and the diversion becomes apparent as time increases, thus confirming that all of them are in the kinetically controlled diffusion regime regardless of the purge flow rate.14 The same results indicating diffusion controlled regime were obtained for the other two sorbates investigated in this study, that is, n-heptane and mesitylene. The values of the effective diffusional time constant (Deff/R2) derived from the model fitting with experimental ZLC curves at different purge flow rates are also presented in Figure 1. They were in a small error range for all flow rates, further confirming the ZLC measurements being conducted in the kinetically controlled regime. Representative experimental ZLC cumene desorption curves from three SBA-16 samples are presented in Figure 2. The
1.57 2.38 5.03
EA (kJ/mol)
T (°C)
L
Deff/R2 × 104 (s-1)
11.0
10 30 50
20 27 55
S-80-1 (20 µm) 3.25 1.300 4.80 1.920 6.55 2.620
19.1
50 70 90
12 13 48
17.8
50 70 90
12 13 21
22.3
10 30 50
14 23 53
0.812 1.490 4.260
40.4
50 70 90
20 28 36
1.93 4.61 13.80
1.110 2.850 6.960
44.7
0.722 1.650 3.311
37.1
50 70 90
20 24 36
1.57 3.66 8.75
0.907 2.110 4.650
39.8
Deff × 1013 (m2s-1)
0.353 0.535 0.773
1.22 0.274 1.78 0.400 2.85 0.570 S-100-1 (23 µm) 2.40 1.270 4.52 2.390 7.75 4.100
1.25 2.24 4.34
Deff × 1013 (m2s-1)
0.498 0.896 1.490
1.19 0.477 2.10 0.841 3.45 1.380 S-100-2 (24 µm) 4.51 2.600 7.46 5.090 16.70 9.620
EA (kJ/mol)
13.3
26.7
25.9
24.8
S-45-1 sample, having the lowest intrawall pore volume, exhibits a very sharp initial concentration drop not observed with the other samples. The same effects were also observed with the other two sorbates. In the adsorption step of these ZLC experiments, the sorbate partial pressure was below 0.01 Torr. Experimental adsorption capacity measurements (not shown here) indicated that this partial pressure is well within the linear region of the adsorption isotherm as required by the ZLC theory. The Deff values extracted from the linear part of the ZLC curves are reported in Table 2. Because these values were obtained at various temperatures, an Arrhenius plot allows us to determine an activation energy (EA) for the diffusion of each of the three sorbates in every sample. These EA values are also given in Table 2. Figure 3A shows the series of Arrhenius plots for diffusivities of cumene in the various SBA-16 samples, whereas Figure 3B shows similar data obtained for cumene in a series of SBA-15
Figure 3. Arrhenius plot for Deff of cumene in SBA-16 (A) and SBA-15 (B) (SBA-15 data are from refs 1 and 2).
3062 J. Phys. Chem. C, Vol. 111, No. 7, 2007
Gobin et al.
KH )
q0 F ht de ) c0 Vs
(6)
where htde is the average desorption time defined as
ht de )
(
∫0∞ cc0 -
)
cblank dt c0
(7)
In eq 7, cblank is the time-dependent concentration determined during a blank experiment run in the absence of adsorbent. Values of KH calculated using eq 6 are reported in Table 3. Some limited microbalance measurements (not shown here) allowed us to confirm that the KH values estimated from eq 6 are in reasonable agreement with these more direct experimental determinations. Discussion Figure 4. Diffusion activation energies in SBA-15 and SBA-16 samples (SBA-15 data are from refs 1 and 2).
materials and reported in ref 2. This comparison shows that systematically higher effective diffusivities are found in SBA16, which is very likely associated with the 3D pore lattice compared to the 1D pore diffusion in SBA-15 materials. Completely similar results were obtained with the other two sorbates. Figure 4 shows plots of the activation energies for diffusion as functions of (V1 + V2)/Vt for both the SBA-16 samples from the present work and SBA-15 materials presented in refs 1 and 2. Contrary to the Deff values, the activation energies are globally higher in SBA-16 than SBA-15. Moreover, the trends of variations of activation energies as functions of (V1 + V2)/Vt are also opposite for the two series of materials. A smaller (V1 + V2)/Vt corresponds to a higher synthesis temperature owing to the very large increase in the specific mesopore volume, Vmeso.
Effective diffusivities of hydrocarbons in such solids as SBA15 and SBA-16 are resulting from a complex transfer process involving diffusion in the primary mesopore lattice with simultaneous adsorption/diffusion on the mesopore surface and in the intrawall micropores. Do has indicated that in the case of pore diffusion of a molecule simultaneously adsorbed on the internal surface of the pore the effective diffusivity can be represented as15
Deff )
meDme + (1 - me)KDw
(8)
τ[me + (1 - me)K]
where Dme is the diffusivity within the mesopores, Dw is the surface diffusivity in the adsorbed phase, τ is the tortuosity factor, and K is Henry’s constant based on particle volume, with
KH ) [me + (1 - me)K]
(9)
Neglecting vapor phase accumulation, eqs 8 and 9 yield
As discussed below, further treatment of these data requires some estimates of Henry’s constant (KH) in the conditions of the ZLC measurements
Deff )
me Dw Dme + τKH τ
(10)
TABLE 3: Henry’s Constants and Adsorption Isosteric Heats at Low Surface Coverage for Various Hydrocarbons in SBA-16 Samples sorbate
T (°C)
n-heptane
10 30 50
cumene
30 50 70
mesitylene
30 50 70
n-heptane
10 30 50
cumene
50 70 90
mesitylene
50 70 90
htde (s)
KH × 10-5
S-45-1 (20 µm) 62 1.37 48 1.07 25 0.56 34 28 17
T (°C) 10 30 50
0.77 0.63 0.37
50 70 90
0.38 0.23 0.14
50 70 90
2.14 1.09 0.37
10 30 50
202 86 36
4.49 1.91 0.81
50 70 90
232 108 48
5.17 2.41 1.07
50 70 90
17 10 6 S-80-5 (23 µm) 96 49 17
htde (s)
KH × 10-5
S-60-1 (15 µm) 48 1.07 33 0.73 24 0.53 151 79 35
T (°C) 10 30 50
htde (s)
KH × 10-5
S-80-1 (20 µm) 70 1.56 49 1.09 26 0.59
3.36 1.76 0.77
50 70 90
2.80 1.57 0.75
50 70 90
1.80 0.91 0.45
10 30 50
198 92 36
4.80 2.04 0.81
50 70 90
138 64 22
3.08 1.42 0.48
223 97 41
4.95 2.15 0.91
50 70 90
160 68 27
3.56 1.50 0.61
126 71 34 S-100-1 (23 µm) 81 41 20
311 149 68 319 174 78 S-100-2 (24 µm) 74 41 19
6.91 3.31 1.51 7.09 3.86 1.73 1.64 0.91 0.42
Part 2: Diffusion
J. Phys. Chem. C, Vol. 111, No. 7, 2007 3063
TABLE 4 Dw/τ2 × 1013 (m2‚s-1)
(Dw/τ2)/Deff (%)
0.289 0.293 0.312
45.5 34.7 29.1
0.587 0.641 0.680
0.344 0.363 0.380
44.8 34.9 27.7
0.94
0.995 1.058 1.117
0.559 0.613 0.741
43.0 31.9 28.3
10.7 10.6 10.2
0.82
0.869 0.905 0.970
0.738 0.773 1.076
44.7 30.3 22.8
10 30 50
14.8 14.3 14.1
0.93
0.625 0.669 0.700
0.535 0.866 0.943
42.1 36.2 23.0
0.51
10 30 50
8.5 8.3 8.2
0.73
1.168 1.237 1.293
1.057 1.604 1.727
40.6 31.5 17.9
S-45-1
0.23
30 50 70
S-60-1
0.28
50 70 90
6.6 6.3 6.1
1.92
1.007 1.087 1.155
0.122 0.147 0.167
34.5 27.4 21.6
S-80-1
0.34
50 70 90
4.0 3.9 3.8
1.08
1.820 1.923 2.031
0.192 0.221 0.255
38.6 24.7 17.1
S-80-5
0.46
50 70 90
6.3 6.1 6.0
0.80
1.433 1.526 1.596
0.242 0.285 0.397
26.2 13.6 9.3
S-100-1
0.46
50 70 90
6.4 6.3 6.2
0.77
1.409 1.475 1.541
0.177 0.260 0.372
21.8 17.5 8.7
S-100-2
0.51
50 70 90
8.8 8.5 8.4
0.57
1.100 1.174 1.222
0.194 0.384 0.435
17.5 13.5 6.3
S-45-1
0.23
30 50 70
S-60-1
0.28
50 70 90
13.5 13.0 12.8
1.31
0.492 0.527 0.550
0.138 0.141 0.166
50.5 35.3 29.1
S-80-1
0.34
50 70 90
5.3 5.2 5.1
0.94
1.373 1.443 1.513
0.252 0.357 0.364
52.8 42.4 26.4
S-80-5
0.46
50 70 90
6.3 6.2 6.1
0.86
1.429 1.501 1.569
0.315 0.486 0.549
34.7 25.0 14.9
S-100-1
0.46
50 70 90
8.1 7.9 7.8
0.92
1.113 1.176 1.225
0.246 0.435 0.459
34.0 26.3 13.9
S-100-2
0.51
50 70 90
10.9 10.8 10.5
0.81
0.888 0.924 0.974
0.267 0.531 0.558
29.5 25.2 12.0
me (-)
T (°C)
S-45-1
0.23
10 30 50
S-60-1
0.28
10 30 50
11.6 11.0 10.7
1.54
S-80-1
0.34
10 30 50
7.5 7.3 7.1
S-80-5
0.46
10 30 50
S-100-1
0.46
S-100-2
sample
R
A (kJ/mol)
DK × 107 (m2‚s-1)
A. effective diffusivity parameters for n-heptane 7.0 0.899 6.2 2.54 1.059 6.1 1.095
B. effective diffusivity parameters for cumene
C. effective diffusivity parameters for mesitylene
In the case of a microporous wall, eq 10 can be modified by considering the intrawall pores like a surface rugosity that imposes a different value for the tortuosity of the adsorbed diffusion pathway. Moreover, because for all data reported here the sorbates mean free path is smaller than the pore diameter, Dme should be replaced by DK where DK is the Knu¨dsen diffusivity. Finally, the measured effective diffusivities may be
represented as
Deff )
me Dw DK + τ1KH τ2
where DK should be written as
(11)
3064 J. Phys. Chem. C, Vol. 111, No. 7, 2007
Gobin et al.
Figure 5. Evolution of the contribution of surface diffusion to effective diffusivity at 50 °C.
4 DK ) K0 3
x
8RT πM
1/ A g 0 (12)
K0 is a parameter designated as the Knu¨dsen flow parameter, which depends on the geometry of the pore lattice, the surface rugosity, and the gas-surface scattering law.16 In the case of a single long straight circular tube of radius r with diffuse scattering, K0 ) rme/2 where r is expressed in centimeters. Combining eqs 11 and 12 yields a useful expression of Deff with essentially two adjustable parameters, namely, K0/τ1 and Dw/τ2. To model the evolution of Deff with synthesis temperature, we found that it was necessary to introduce an adimensional parameter R such as
rme 2R
K0 )
with R ) R0 eA/RT
(13) (14)
moreover following ref 17 τ1 was represented as
1 me
(15)
8RT e-A/RT Dw + πM R0 τ2
(16)
τ1 ) Thus, combining eqs 11-15
Deff )
2merme 2 KH 3
x
Figure 6. Contribution of cage-to-cage hopping to apparent activation energy for Knu¨dsen diffusion.
Table 4 lists the values of parameters R, A, and Dw/τ2 used in fitting the experimental values of Deff for each of the three sorbates. These values are not uniquely determined because in spite of the large amount of data, each of these three parameters depends on the sample morphology, state of silica condensation, pore size and shape, as well as nature of the sorbates. Moreover, both R and Dw/τ2 are temperature-dependent. The values in Table 4 are therefore reported here as an indication that a realistic and physically meaningful set of these data can be found to represent the experimental Deff values given in Table 2 properly. In selecting the R parameter values reported in Table 4, the following criteria have been applied:
2/ Dw/τ2 g 0 3/ Dw/τ2 must be an increasing function of temperature. From the results in Table 4, it may be appreciated that the values adopted for the surface diffusivity term Dw/τ2 are a significant fraction of Deff ranging from 6% to over 50%. In Figure 5, this term is plotted as a function of (V1 + V2)/Vt because the intrawall adsorption/diffusion was indeed lumped into this parameter. As expected, at constant temperature (50 °C) Dw/τ2 was found to increase steadily with the intrawall pore volume for each of the three sorbates under study. The comparison of apparent activation energies for effective diffusivities between SBA-15 and SBA-16 reported in Figure 4 is discussed below. For both series of solids, decreasing the ratio of intrawall pore volume to total pore volume (V1 + V2)/Vt corresponds to an increased synthesis temperature or time. This change follows essentially from the increased total pore volume, Vt. In SBA15, the corresponding decrease in activation energy follows from the decreased heat of adsorption affecting the KH term in eq 16. For example, the low coverage isosteric heat of adsorption for n-heptane decreases from 107 to 72 kJ/mol for the four samples reported here. Such a decrease will appear as an apparent decrease in activation energy for the first term of the right-hand member of eq 16. Thus, in SBA-15 the R parameter is likely not activated. This suggests that the corresponding increase in apparent activation energy for SBA-16 is associated with the difference in pore lattice geometry between SBA-16 and SBA-15. We suggest that the much higher activation energy observed in SBA-16, especially at higher synthesis temperature, is associated with the cage structure of its pores. The molecules transferred by the Knu¨dsen diffusion process are scattered in each cage in such a way that those with higher kinetic energy have a higher probability of jumping to the next cage through the smaller aperture. We therefore propose that the energy, A, in eq 14 represents the energy barrier for this jump. The values of A from Table 4 are plotted as functions of Dme in Figure 6. The three curves corresponding to the individual sorbates are almost identical, suggesting that the cage size and shape is more determinant of A than the nature of the diffusing molecule.
Part 2: Diffusion Conclusions For a series of well-characterized SBA-16 mesostructured silicas described in Part I of this contribution, systematic measurements of effective diffusivities have been made for n-heptane, cumene, and mesitylene using the ZLC technique. The comparison with similar data obtained in SBA-15 materials of comparable mesopore diameters and intrawall porosities indicates that the pore structure has a direct influence on the effective diffusivities. The tridimensional cage structure of SBA16 allows a much more rapid diffusion than the straight cylindrical pore shape of SBA-15. Surprisingly, the diffusivity apparent energy of activation is significantly higher in SBA-16 than in SBA-15. This effect is suggested to be related to the cage structure of SBA-16. The hopping process from one cage to the next is proposed to be activated with a corresponding increase in activation energy for the Knu¨dsen diffusivity term. This increase is found to depend on cage diameter. A model is proposed as eq 16 in which the overall apparent diffusivity is represented by the addition of two terms respectively associated with Knu¨dsen diffusion and surface diffusion in the adsorbed phase. Even though the data do not allow a unique set of fitting parameters to be established, it was shown that a realistic combination of these parameters can be found to represent the whole series of Deff values. According to this model, adsorption in the intrawall porosity affects both terms first through the effect of an increased capacity of adsorption (increased KH), which decreases the Knu¨dsen diffusivity term drastically, and second by affecting surface diffusivity mostly by increasing the surface tortuosity factor, τ2. Such conclusions are made possible by the exceptional control over the pore lattice morphology and size afforded by the synthesis of mesostructured materials such as SBA-15 and SBA-16.
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