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Measurement of Intracrystalline Diffusion by Zero Length Column Tracer Exchange
J. Weitkamp, H.G. Karge, H. Pfeifer and W. HBlderich (Eds.) Zeolires and Related Microporous Marerials: &are of rhe A n 1994 Studies in Surface Science and Catalysis, Vol. 84 0 1994 Elsevier Science B.V. All rights reserved.
1323
Measurement of Intracrystalline Diffusion by Zero Length Column Tracer Exchange Jeffrey R. Hufton*, Stefan0 Brandani and Douglas M. Ruthven Department of Chemical Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada The zero length column (ZLC) technique has been adapted to the measurement of tracer self-diffusivities in zeolite crystals. In this new variant the method is applicable over the entire range of sorbate loadings and the resulting diffusivity values should be directly comparable with PFG NMR self-diffusivities. The application of the technique is illustrated by a detailed study of the C3H,-5A system. 1.
INTRODUCTION
The zero length column (ZLC) technique, introduced by Eic and Ruthven in 1988('), has found widespread application as a simple way of measuring limiting diffusivities for hydrocarbons and other simple molecules in zeolite adsorbentd2). The method involves following the transient desorption curved obtained when a previously equilibrated sample of zeolite is purged, at a relatively high flow rate, with an inert carrier such as He or Ar. The diffusional time constant (and hence the diffusivity) is found by matching the desorption curve to the appropriate transient solution of the Fickian diffusion equation. This method offers several advantages, including the use of very small quantities of zeolite (typically 2-5 mg) and the applicability to faster processes then can be studied by most other macroscopic methods. However, it suffers from the important disadvantage that it is applicable only to the measurement of limiting diffusivities (at very low sorbate concentration). We report here the development of a new variant of this technique, "tracer ZLC, which allows the measurement of tracer selfdiffusivities over the entire concentration range. Since the new technique measures the self-diffusivity, rather than the transport diffusivity, the data should be directly comparable with the values obtained by the PFG NMR method. The practical application of this approach is illustrated by an experimental study of the diffusion of propane in SA zeolite. *Present Address: Air Products and Chemicals Inc., Allentown, PA
1324
2.
EXPERIMENTAL
The apparatus, shown in figure 1, is essentially the same as for the traditional ZLC experiment except that the detector (FID or TCD) is replaced by a mass spectrometer. Details of the gas sampling device are shown in the insert of figure 1. The zeolite sample, held between sinter discs, is dehydrated at 300°C overnight in a helium purge. It is then cooled to the measurement temperature and equilibrated with a gas stream containing a known mole fraction of the sorbate (GH,) of which a certain proportion is in the fully deuterated form (C,D,). At time zero the flow is switched to a purge stream containing the same total mole fraction of light propane (C,H,) at the same flow rate. The desorption of the deuterated species is followed by monitoring the decrease in the intensity of the GDs peak (mass 34) on a quadrupole mass spectrometer. This is the largest peak among the decomposition products of C3D,.(3) The sampling interval was typically 0.1 sec. The experiment may also be performed with the light species (breakdown product GH,, mass 29) as the tracer using a purge containing only the deuterated form, but that is more expensive since a greater quantity of GD, is needed. Traditional ZLC desorption curves, measured with C,H,-He and GD,-He at low concentrations were essentially identical, confirming that there is no significant difference in either kinetics or equilibrium between the two isotopic forms and that C,D, can therefore be considered as a true tracer. To obtain reliable results it is essential, as with the traditional ZLC experiment, to minimize all dead volume and to keep the lines between the switch valve, ZLC and detector as short as possible. Because the zeolite sample is small the system is very sensitive to any traces of water. All leaks must be carefully eliminated and 3A molecular sieve columns are included in both carrier and purge lines. In addition it is essential that the pressures in the two propane cylinders be exactly the same to ensure that there is an equimolar exchange with no net adsorption or desorption. Apart from the applicability in a tracer exchange system, an important advantage of the mass spectrometer detector is that any traces of water in the system can be detected immediately. The analysis of the ZLC exchange curves is essentially the same as for the traditional ZLC experiment. The system is accurately linear and the long-time asymptote of the desorption curve is given by:
where p1 is the first root of the equation
p cot p
+
L
-
1=0
(4
In contrast to the traditional ZLC experiment in which K represents the limiting
1325
Figure 1
0.0
Figure 2
Schematic of the Experimental System (Insert shows the gas sampling system).
I
I
Experimental
I
I
I
GD, desorption curves for 30 pm
I
6
crystals at. 85°C.
1326
1E-09
0
Figure 3
I
0.5
I
1
I
1.5
I
I
2 2.5 Q (moleC~e/cage)
I
3
35
Variation of tracer self diffusivity with sorbate loading showing comparison with PFG NMR self-diffusivities at 85°C.
1327
and L = FR2/3VsKD
(3)
slope of the equilibrium isotherm, expressed in dimensionlessform, in a tracer ZLC experiment, K represents the ratio q/c (adsorbed phase concentration/gas phase concentration at equilibrium). Of course, within the Henry’s Law region, these two quantities are identical. According to Eq. 1 a semi-logarithmic plot of (c/c,) vs t should approach a straight line of slope 8:D/R2 and intercept 2L/[p? + L (Ll)]from , which the values of D/R2 and KV, may be easily found. Representative experimental desorption curves are shown in figure 2 at two different hydrocarbon partial pressures. 3.
RESULTS AND DISCUSSION
3.1 Consistency of K Values Table 1 shows the experimental values of KV,, obtained at 85°C with the same zeolite sample, at four different propane pressures, together with values of K = q/c calculated from the experimental gravimetric equilibrium i~0then-d~).It is evident that the values of V,, calculated from the experimental values of KV,, are approximately constant and consistent with the value estimated from the sample weight. 3.2 Diffusivity Data
Table 2 summarizes the experimented diffusivity data which are also plotted against sorbate concentration in figure 4. At 85°C measurements were carried out with two different zeolite crystal sizes (30 pm and 50 pm). The good agreement between the diffusivityvalues for the two crystal sizes confirms that the exchange rate was indeed controlled by intracrystalline diffusion, rather than by some other extracrystalline rate process. The activation energy, estimated from the data at 45°C and 85°C is approximately 3 kcal/mol.
It is evident from figure 3 that there is a significant increase of self-diffusivity with sorbate concentration. Extrapolation to zero concentration yields a limiting value which is consistent with the measured ZLC transport diffusivity at low concentration. The tracer diffusivity values are smaller than the PFG selfdiffusivities(’) by a factor of about three but the trends with sorbate loading are very similar.
1328
3.3 External Film Resistance
The analysis of the sorption exchange curves according to Eq. 1 assumes that external fluid film resistance is negligible in comparison with intracrystalline diffusional resistence. This assumption can be justified by a simple order of magnitude calculation. Assuming a Shenvood Number of two (the limiting value) gives kf D,/R and the corresponding time constant for external mass transfer T,,, = KR2/3 D,. For the experimental conditions (at low partial pressure at 85OC) this gives T,,, sec. which may be compared with the time constant for intracxystalline diffusion 7diff = R2/15 D which, even using the NMR value for D, gives rdifffi? 5 sec. Clearly 7diff > > r,,, so the effect of external film resistance should be insignificant. The validity of this conclusion has been confirmed experimentally by replicate measurements with He and Ar as carrier which show no significant difference in desorption rates.
-
-
4. CONCLUSIONS
The new technique appears to provide a useful extension of the traditional ZLC method to the measurement of tracer exchange diffusivities at any desired sorbate loading. It is evident that the diffusivity data obtained from the tracer experiments are self-consistent and in reasonably close agreement with the PFG NMR selfdiffusivities, measured under similar conditions.
1329
Table 1 Consistency of Equilibrium Data from Tracer ZLC and Gravimetric Isotherm at 85°C P(Torr)' 24 48 405 760
KVs(cm3)
q/c*
v s
3.74
1080 744 149 84.4
3.46~ 10"
0.51 0.28
(cm3)
3.42 3.3
+Propanepartial pressure *From gravimetric isotherm (dimensionless)
Table 2 Tracer Exchange Diffusivity Data for C3H,-5A
T("C) 85
85 45
P(Torr) O*
24 48 405 760 400 405 760
q
Crystal Diam(pm)
(Molecule/ Cage)
D/R2(s")
30 30 30 30 30 50 30 30
-0 1.3 1.9 3.2 3.4 3.2 3.5 3.6
0.003 0.006 0.009 0.022 0.023 0.009 0.0013 0.00134
+
'From equilibrium isotherm of Ruthven and L,~ughlin(~) *TraditionalZLC experiment C3H,-He and GD8 -He
D(m2.s-')
1330
NOTATION
tracer concentration in gas phase initial steady state tracer concentration intracrystabe diffusivity molecular diffusivity (gas phase) purge gas flow rate (at experimental conditions) dimensionless equilibrium constant or ratio (q/c) external mass transfer coefficient defined by Eq. 3 sorbate partial pressure sorbate concentration in adsorbed phase crystal radius time volume of solid defined by Eq. 3 REFERENCES 1.
M. Eic and D.M. Ruthven, Zeolites, 8, 1988,40.
2.
J. Urger and D.M. Ruthven, Diffusion in Zeolites and other Microporous Solids, Ch 10, Wiley, N.Y., 1992.
3.
A. Cornu and R. Massot, Compilation of Mass Spectral Data, Heyden, London, 1966.
4.
D.M. Ruthven and K.F. Loughlin, J. Chem. SOC.Faraday Trans. I 68,1972,696.
5.
J. n g e r and D.M. Ruthven, J. Chem. SOC.Faraday Trans I, 77, 1981, 1485.
1323
Measurement of Intracrystalline Diffusion by Zero Length Column Tracer Exchange Jeffrey R. Hufton*, Stefan0 Brandani and Douglas M. Ruthven Department of Chemical Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada The zero length column (ZLC) technique has been adapted to the measurement of tracer self-diffusivities in zeolite crystals. In this new variant the method is applicable over the entire range of sorbate loadings and the resulting diffusivity values should be directly comparable with PFG NMR self-diffusivities. The application of the technique is illustrated by a detailed study of the C3H,-5A system. 1.
INTRODUCTION
The zero length column (ZLC) technique, introduced by Eic and Ruthven in 1988('), has found widespread application as a simple way of measuring limiting diffusivities for hydrocarbons and other simple molecules in zeolite adsorbentd2). The method involves following the transient desorption curved obtained when a previously equilibrated sample of zeolite is purged, at a relatively high flow rate, with an inert carrier such as He or Ar. The diffusional time constant (and hence the diffusivity) is found by matching the desorption curve to the appropriate transient solution of the Fickian diffusion equation. This method offers several advantages, including the use of very small quantities of zeolite (typically 2-5 mg) and the applicability to faster processes then can be studied by most other macroscopic methods. However, it suffers from the important disadvantage that it is applicable only to the measurement of limiting diffusivities (at very low sorbate concentration). We report here the development of a new variant of this technique, "tracer ZLC, which allows the measurement of tracer selfdiffusivities over the entire concentration range. Since the new technique measures the self-diffusivity, rather than the transport diffusivity, the data should be directly comparable with the values obtained by the PFG NMR method. The practical application of this approach is illustrated by an experimental study of the diffusion of propane in SA zeolite. *Present Address: Air Products and Chemicals Inc., Allentown, PA
1324
2.
EXPERIMENTAL
The apparatus, shown in figure 1, is essentially the same as for the traditional ZLC experiment except that the detector (FID or TCD) is replaced by a mass spectrometer. Details of the gas sampling device are shown in the insert of figure 1. The zeolite sample, held between sinter discs, is dehydrated at 300°C overnight in a helium purge. It is then cooled to the measurement temperature and equilibrated with a gas stream containing a known mole fraction of the sorbate (GH,) of which a certain proportion is in the fully deuterated form (C,D,). At time zero the flow is switched to a purge stream containing the same total mole fraction of light propane (C,H,) at the same flow rate. The desorption of the deuterated species is followed by monitoring the decrease in the intensity of the GDs peak (mass 34) on a quadrupole mass spectrometer. This is the largest peak among the decomposition products of C3D,.(3) The sampling interval was typically 0.1 sec. The experiment may also be performed with the light species (breakdown product GH,, mass 29) as the tracer using a purge containing only the deuterated form, but that is more expensive since a greater quantity of GD, is needed. Traditional ZLC desorption curves, measured with C,H,-He and GD,-He at low concentrations were essentially identical, confirming that there is no significant difference in either kinetics or equilibrium between the two isotopic forms and that C,D, can therefore be considered as a true tracer. To obtain reliable results it is essential, as with the traditional ZLC experiment, to minimize all dead volume and to keep the lines between the switch valve, ZLC and detector as short as possible. Because the zeolite sample is small the system is very sensitive to any traces of water. All leaks must be carefully eliminated and 3A molecular sieve columns are included in both carrier and purge lines. In addition it is essential that the pressures in the two propane cylinders be exactly the same to ensure that there is an equimolar exchange with no net adsorption or desorption. Apart from the applicability in a tracer exchange system, an important advantage of the mass spectrometer detector is that any traces of water in the system can be detected immediately. The analysis of the ZLC exchange curves is essentially the same as for the traditional ZLC experiment. The system is accurately linear and the long-time asymptote of the desorption curve is given by:
where p1 is the first root of the equation
p cot p
+
L
-
1=0
(4
In contrast to the traditional ZLC experiment in which K represents the limiting
1325
Figure 1
0.0
Figure 2
Schematic of the Experimental System (Insert shows the gas sampling system).
I
I
Experimental
I
I
I
GD, desorption curves for 30 pm
I
6
crystals at. 85°C.
1326
1E-09
0
Figure 3
I
0.5
I
1
I
1.5
I
I
2 2.5 Q (moleC~e/cage)
I
3
35
Variation of tracer self diffusivity with sorbate loading showing comparison with PFG NMR self-diffusivities at 85°C.
1327
and L = FR2/3VsKD
(3)
slope of the equilibrium isotherm, expressed in dimensionlessform, in a tracer ZLC experiment, K represents the ratio q/c (adsorbed phase concentration/gas phase concentration at equilibrium). Of course, within the Henry’s Law region, these two quantities are identical. According to Eq. 1 a semi-logarithmic plot of (c/c,) vs t should approach a straight line of slope 8:D/R2 and intercept 2L/[p? + L (Ll)]from , which the values of D/R2 and KV, may be easily found. Representative experimental desorption curves are shown in figure 2 at two different hydrocarbon partial pressures. 3.
RESULTS AND DISCUSSION
3.1 Consistency of K Values Table 1 shows the experimental values of KV,, obtained at 85°C with the same zeolite sample, at four different propane pressures, together with values of K = q/c calculated from the experimental gravimetric equilibrium i~0then-d~).It is evident that the values of V,, calculated from the experimental values of KV,, are approximately constant and consistent with the value estimated from the sample weight. 3.2 Diffusivity Data
Table 2 summarizes the experimented diffusivity data which are also plotted against sorbate concentration in figure 4. At 85°C measurements were carried out with two different zeolite crystal sizes (30 pm and 50 pm). The good agreement between the diffusivityvalues for the two crystal sizes confirms that the exchange rate was indeed controlled by intracrystalline diffusion, rather than by some other extracrystalline rate process. The activation energy, estimated from the data at 45°C and 85°C is approximately 3 kcal/mol.
It is evident from figure 3 that there is a significant increase of self-diffusivity with sorbate concentration. Extrapolation to zero concentration yields a limiting value which is consistent with the measured ZLC transport diffusivity at low concentration. The tracer diffusivity values are smaller than the PFG selfdiffusivities(’) by a factor of about three but the trends with sorbate loading are very similar.
1328
3.3 External Film Resistance
The analysis of the sorption exchange curves according to Eq. 1 assumes that external fluid film resistance is negligible in comparison with intracrystalline diffusional resistence. This assumption can be justified by a simple order of magnitude calculation. Assuming a Shenvood Number of two (the limiting value) gives kf D,/R and the corresponding time constant for external mass transfer T,,, = KR2/3 D,. For the experimental conditions (at low partial pressure at 85OC) this gives T,,, sec. which may be compared with the time constant for intracxystalline diffusion 7diff = R2/15 D which, even using the NMR value for D, gives rdifffi? 5 sec. Clearly 7diff > > r,,, so the effect of external film resistance should be insignificant. The validity of this conclusion has been confirmed experimentally by replicate measurements with He and Ar as carrier which show no significant difference in desorption rates.
-
-
4. CONCLUSIONS
The new technique appears to provide a useful extension of the traditional ZLC method to the measurement of tracer exchange diffusivities at any desired sorbate loading. It is evident that the diffusivity data obtained from the tracer experiments are self-consistent and in reasonably close agreement with the PFG NMR selfdiffusivities, measured under similar conditions.
1329
Table 1 Consistency of Equilibrium Data from Tracer ZLC and Gravimetric Isotherm at 85°C P(Torr)' 24 48 405 760
KVs(cm3)
q/c*
v s
3.74
1080 744 149 84.4
3.46~ 10"
0.51 0.28
(cm3)
3.42 3.3
+Propanepartial pressure *From gravimetric isotherm (dimensionless)
Table 2 Tracer Exchange Diffusivity Data for C3H,-5A
T("C) 85
85 45
P(Torr) O*
24 48 405 760 400 405 760
q
Crystal Diam(pm)
(Molecule/ Cage)
D/R2(s")
30 30 30 30 30 50 30 30
-0 1.3 1.9 3.2 3.4 3.2 3.5 3.6
0.003 0.006 0.009 0.022 0.023 0.009 0.0013 0.00134
+
'From equilibrium isotherm of Ruthven and L,~ughlin(~) *TraditionalZLC experiment C3H,-He and GD8 -He
D(m2.s-')
1330
NOTATION
tracer concentration in gas phase initial steady state tracer concentration intracrystabe diffusivity molecular diffusivity (gas phase) purge gas flow rate (at experimental conditions) dimensionless equilibrium constant or ratio (q/c) external mass transfer coefficient defined by Eq. 3 sorbate partial pressure sorbate concentration in adsorbed phase crystal radius time volume of solid defined by Eq. 3 REFERENCES 1.
M. Eic and D.M. Ruthven, Zeolites, 8, 1988,40.
2.
J. Urger and D.M. Ruthven, Diffusion in Zeolites and other Microporous Solids, Ch 10, Wiley, N.Y., 1992.
3.
A. Cornu and R. Massot, Compilation of Mass Spectral Data, Heyden, London, 1966.
4.
D.M. Ruthven and K.F. Loughlin, J. Chem. SOC.Faraday Trans. I 68,1972,696.
5.
J. n g e r and D.M. Ruthven, J. Chem. SOC.Faraday Trans I, 77, 1981, 1485.