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New X-ray method for investigation of mass transport in disperse porous systems
Colloids and Surfaces A: Physicochemical and Engineering Aspects 160 (1999) 123 – 127 www.elsevier.nl/locate/colsurfa
New X-ray method for investigation of mass transport in disperse porous systems G.M. Plavnik *, T.P. Purjaeva, G.N. Chrustaleva Institute of Physical Chemistry, Russian Academy of Sciences, Leninsky Prospect 31, 117095, Moskow, Russia
Abstract The new X-ray method, based on small-angle X-ray scattering (SAXS) data, was proposed for studying mass transport in porous systems. It is based on the dependence of SAXS intensity on the difference in electron densities for pores and matrix. During the filling of pore space (by vapour, liquids) the electron density differences and, accordingly, the SAXS intensities decrease. The reverse effect takes place during the refilling of pores. Using this dependence, we succeeded in calculating the scattering for filled pores and determining the size distributions in pore volumes. It enabled us to connect different stages of the adsorption – desorption process to the sizes of filled pores. The SAXS method was used to investigate systematically adsorption – desorption of a number of fluids (water, benzene, glycerol, trixylylphosphate) in carbon adsorbents. It was shown that different characters of these processes depend on the liquid structure and sizes of its molecules, and on the peculiarity of micro- and mesoporous structures of adsorbents. An analytical expression was obtained, which permitted us to describe the kinetics of desorption using SAXS data. The sizes of micropores, which were inaccessible for large molecules of adsorbed fluids were estimated. It was shown that there are micropores, into which whole molecules could not penetrate, but only their fragments. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Small-angle X-ray scattering (SAXS) method; Adsorption; Carbon adsorbents; Microporous systems
1. Introduction Most studies of porous systems by the SAXS method are limited to the investigation of a porous structure without considering mass transfer processes in it. Only a few studies are known, carried out on carbon adsorbents, in which the SAXS method to some extent applied to study * Corresponding author. Fax: +7-95-9525308. E-mail address: [email protected] Plavnik)
(G.M.
these processes [1–6]. In these cases, the interpretation of observed phenomenon proved to be ambiguous. The use of the SAXS method to investigate the mass transfer in porous materials structures is based on decreasing intensity in filling the pores due to a decrease in the difference between the electron densities of the matrix and pores. The first experiments on activated carbons (AC) held in an atmosphere of saturated water vapor showed the unusual character of the changes in the intensity [1,2]. Instead of a uniform decrease
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in the whole angular range, this was observed only in the region of comparatively big values of h, whereas in the region of small values of h the intensity somewhat increased (h = 4p sin u/l is the angular vector, where 2u = 8 is the scattering angle, l is the wavelength of the radiation used). This effect was explained by a partial filling of the porous space: the micropores were filled, whose scattering was predominant in the region of large h, and, hence, their intensity decreased. The mesopores were not filled, and their scattering was concentrated at the initial segment of curve, while their intensity changed slightly. The effective sizes of micropores were L 5 2 nm, and of mesopores L= 2–50 nm. Later, similar effects were observed on a number of other AC of various origins and with different porous structures [6], as well as on carbonized fibres too [3,4]. In the latter case, the authors [3,4] explained the different shapes of SAXS curves by the swelling of micropores, resulting in an increase in their sizes by 1.3–1.6 times. In this paper, we tried to unambiguously interpret the changes in the SAXS intensity during adsorption (desorption), and to apply the SAXS method to studying these processes on the basis of this interpretation.
2. Experimental The SAXS investigation was carried out on a KRM-1 camera using the filtered Cu – Ka radiation. The intensities were measured in a range of 0.0036–0.71 A − 1 (0.05 – 10°). As samples to be tested carbon adsorbents of the types were used: FAS-1 (the volume of micropores v =0.3 cm3 g − 1, the width of the slitlike micropores L= 0.6 nm) and FAS-2 (v = 0.6 cm3 g − 1, and L= 1.2 nm [7]). A batch of AC powder mixed with a definite amount of liquid drops (the weight of a drop of about 10 − 2 g) was put in a flat cell with windows of polymeric film. In the case of glycerol and trixylylphosphate (TXP), the amount of liquid drops were gradually increased and the SAXS intensity was measured at every stage of investigation. In the case of evaporating liquids (benzene,
water) the measurements were made first on a completely filled sample and then after the cell was unsealed by puncturing holes in it. The intensity of scattering by filled pores DI was determined in terms of a difference between the scattering intensities of the samples: for the initial (dry) sample and for the same sample mixed with a corresponding amount of liquid. The linear sizes of pores are characterized by the radius of inertia Ri-parameter that is applicable for pores of any shape. The calculation of the pore size distribution: f(R) was made on the basis of a method suggested in Ref. [8], which takes into account collimational distortions.
3. Results and discussion To elucidate how the shape of scattering curves depends on the filling of either micro- or mesopores the experiments on the TXP adsorption were carried out, the sizes of TXP molecule ( 1.0 nm) exceeding the width of micropores L in FAS-1, but they being smaller than L values in FAS-2. The scattering curves of adsorbents in the initial (dry) state and after the filling of TXP are shown in logariphmic coordinates in Fig. 1. In the case of FAS-1 AC, the scattering intensity changes in opposite way to [1–5]: it falls sharply in the range of the smallest angles and remains practically unchanged in the range of large angles (curves 2 and 3). It means that the mesopores are filled whose scattering is predominant in the range of small h (h50.005 nm − 1). Micropores are not filled, with the exception of the biggest ones and individual pores, into which penetrate the fragments of molecules [9]. On the contrary, in the case of FAS-2 AC, the changes in the scattering intensity are similar to those observed in Refs. [1–5] at first, the micropores and then mesopores are filled. This interpretation is illustrated in Fig. 2 by the curves of distribution of the sizes of filled pores, calculated from the data of Fig. 1. Thus, the experiments with TXP convincingly show that the changes in the shape of scattering curves, which are similar to those observed in Refs. [1–5], take place on a partial filling of the pore space: filled are either micro- or mesopores.
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Dependence of the shape of a scattering curve on the filling of different portions of pores is also observed on the mixing of FAS-1 AC powder with glycerol. The time of the pore filling with glycerol is long enough because of its high viscosity to allow the observation of the kinetics of this process. At the initial stage, during half an hour after mixing, the scattering intensity in the range of small angles decreases: this is indicative of the mesopores filling (Fig. 3). At the large h interval, the scattering intensity changes little: the most part of micropores remains empty. Then the gradual overflow of glycerol from meso- into micropores occurs; and due to this, the intensity falls off in the range of large h and increases in the range of small h (curve 3). Further additions of glycerol result in the filling of mesopores. As a result, the scattering intensity decreases at small angles. This Fig. 2. Size distribution of filled pores for AC samples mixed with TXP: FAS-1 (1) initial AC; (2) AC + 3 drops; (3) AC +7 drops; FAS-2 (4) initial AC; (5) AC + 1 drop; (6) 5 drops; and (7) 10 drops.
Fig. 3. Scattering curves log I−log h for the FAS-1 AC samples with glycerol: (1) initial AC; (2) AC + 1 drop after 0.5 h; (3) AC +1 drop after 9 days; (4) AC + 2 drops; (5) complete filling. Fig. 1. Scattering curves log I− log h for the AC samples with trixylylphosphate (TXP): FAS-1: (1) initial AC; (2) AC +3 drops; (3) AC+ 7 drops; FAS-2: (4) initial AC; (5) AC+10 drops; (6) AC+ 15 drops. The values of log I for FAS-1 are shifted.
process is more obviously represented by the curves of distribution of the filled pores sizes with f(R) (Fig. 4).
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The obtained results confirm our interpretation: if both pore fractions (micro and meso) are filled, the decrease in the scattering intensity occurs over the whole run of the scattering curve; if only one
Fig. 6. Size distribution of filled pores for FAS-1 AC samples mixed with water: (1) completely filled; (2) after 2 days; (3) after 11 days; and (4) after 27 days.
Fig. 4. Size distribution of filled pores for AC samples mixed with glycerol: (1) AC + 1 drop after 0.5 h; (2) AC +1 drop after 1.5 h; (3) AC + 1 drop after 24 h; (4) AC +1 drop after 9 days; (5) complete filling.
Fig. 5. Size distribution of filled pores for AC samples mixed with benzene: FAS-1: (1) initial AC; (2) after 15 days; (3) after 365 days; FAS-2 (4) initial AC; (5) after 30 days.
fraction is filled, the shape of the scattering curve is distorted. These results also provide evidence of a substantial contribution of the mesopore scattering to the total intensity, especially considerable in the region of small h. The authors of other interpretations did not take this component into account, presumably on the assumption that the volume of mesopores in the tested AC samples is very small. Meanwhile, it is necessary to consider that the SAXS intensity I R 6, and the mesopore sizes exceed the micropore sizes by one and even more orders of magnitude. Therefore, even a small amount of mesopores causes an intense scattering, especially in the region of small h. The kinetics of benzene desorption in FAS-1 AC obtained from the SAXS data is shown in Fig. 5. The desorption rate is very slow: only after 15 days most mesopores are empty, whereas a considerable part of micropores remain filled after even a year exposure. The water desorption in FAS-I AC is more intensive, and is completed after 30 days (Fig. 6). The kinetics of water desorption can be described analytically as the dependence of the filled micropore volume Vt on time t: Vt = V0 exp(− kt), where V0 is the micropore volume in a sample (in relative units), k is the constant characterizing the desorption rate. Vt
G.M. Pla6nik et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 160 (1999) 123–127
and V0 were obtained from the area just under the corresponding curves f(R) (Fig. 6) [9]. In the case of FAS-2 AC samples, the desorption processes go to completion quicker than in those of FAS-1 AC. The desorption of benzene is mainly completed after several days; but the smallest micropores remain filled even after a month (Fig. 5). The desorption of water is completed after 5 – 6 days. The intensive rate of desorption in FAS-2 is evidently due to a more developed and accessible structure of micro- and mesopores, and a larger sizes of micropores [6,9].
4. Conclusions The new X-ray method has been developed enabling one to study the mass transfer processes in porous systems in terms of changes in the intensity of small-angle scattering. This method was applied to investigate the kinetics of adsorption and desorption processes of a series of fluids (water, glycerol, benzene and trixylylphosphate) in carbon adsorbents. An analytical expression was derived characterizing the
.
127
dependence of the volume of micropores filled with water on the desorption time. The change of the shapes of SAXS curve in the adsorption and desorption processes is explained by the fact that only one of the pore fractions is filled: either micro- or mesopores. Other interpretations are incorrect, because they ignore scattering on mesopores. References [1] M.M. Dubinin, G.M. Plavnik, E.D. Zaverina, Carbon 2 (1964) 261. [2] G.M. Plavnik, M.M. Dubinin, Izv. Akad. Nauk SSSR Ser. Khim. 4 (1964) 628. [3] K. Kaneko, Y. Fujiwara, K. Nishikawa, J. Colloid Interf. Sci. 127 (1989) 298. [4] Y. Fujiwara, K. Nishikawa, T. Iijima, K. Kaneko, J. Chem. Soc. Faraday Trans. 87 (1991) 2763. [5] G.M. Plavnik, T.P. Purjaeva, M.M. Dubinin, Izv. Akad. Nauk SSSR Ser. Khim. 1 (1993) 1220. [6] G.M. Plavnik, T.P. Purjaeva, Zh. Fiz. Khim. 71 (1997) 1460. [7] R. Sh. Vartapetyan, A.M. Voloshchuk, V.V. Gur’yanov, et al., Izv. Akad. Nauk SSSR Ser. Khim. 1 (1993) 56. [8] G.M. Plavnik, Kristallograflya 39 (1994) 600. [9] G.M. Plavnik, T.P. Purjaeva, Zh. Fiz. Khim. 71 (1997) 2036.
New X-ray method for investigation of mass transport in disperse porous systems G.M. Plavnik *, T.P. Purjaeva, G.N. Chrustaleva Institute of Physical Chemistry, Russian Academy of Sciences, Leninsky Prospect 31, 117095, Moskow, Russia
Abstract The new X-ray method, based on small-angle X-ray scattering (SAXS) data, was proposed for studying mass transport in porous systems. It is based on the dependence of SAXS intensity on the difference in electron densities for pores and matrix. During the filling of pore space (by vapour, liquids) the electron density differences and, accordingly, the SAXS intensities decrease. The reverse effect takes place during the refilling of pores. Using this dependence, we succeeded in calculating the scattering for filled pores and determining the size distributions in pore volumes. It enabled us to connect different stages of the adsorption – desorption process to the sizes of filled pores. The SAXS method was used to investigate systematically adsorption – desorption of a number of fluids (water, benzene, glycerol, trixylylphosphate) in carbon adsorbents. It was shown that different characters of these processes depend on the liquid structure and sizes of its molecules, and on the peculiarity of micro- and mesoporous structures of adsorbents. An analytical expression was obtained, which permitted us to describe the kinetics of desorption using SAXS data. The sizes of micropores, which were inaccessible for large molecules of adsorbed fluids were estimated. It was shown that there are micropores, into which whole molecules could not penetrate, but only their fragments. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Small-angle X-ray scattering (SAXS) method; Adsorption; Carbon adsorbents; Microporous systems
1. Introduction Most studies of porous systems by the SAXS method are limited to the investigation of a porous structure without considering mass transfer processes in it. Only a few studies are known, carried out on carbon adsorbents, in which the SAXS method to some extent applied to study * Corresponding author. Fax: +7-95-9525308. E-mail address: [email protected] Plavnik)
(G.M.
these processes [1–6]. In these cases, the interpretation of observed phenomenon proved to be ambiguous. The use of the SAXS method to investigate the mass transfer in porous materials structures is based on decreasing intensity in filling the pores due to a decrease in the difference between the electron densities of the matrix and pores. The first experiments on activated carbons (AC) held in an atmosphere of saturated water vapor showed the unusual character of the changes in the intensity [1,2]. Instead of a uniform decrease
0927-7757/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 9 9 ) 0 0 3 5 2 - 0
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in the whole angular range, this was observed only in the region of comparatively big values of h, whereas in the region of small values of h the intensity somewhat increased (h = 4p sin u/l is the angular vector, where 2u = 8 is the scattering angle, l is the wavelength of the radiation used). This effect was explained by a partial filling of the porous space: the micropores were filled, whose scattering was predominant in the region of large h, and, hence, their intensity decreased. The mesopores were not filled, and their scattering was concentrated at the initial segment of curve, while their intensity changed slightly. The effective sizes of micropores were L 5 2 nm, and of mesopores L= 2–50 nm. Later, similar effects were observed on a number of other AC of various origins and with different porous structures [6], as well as on carbonized fibres too [3,4]. In the latter case, the authors [3,4] explained the different shapes of SAXS curves by the swelling of micropores, resulting in an increase in their sizes by 1.3–1.6 times. In this paper, we tried to unambiguously interpret the changes in the SAXS intensity during adsorption (desorption), and to apply the SAXS method to studying these processes on the basis of this interpretation.
2. Experimental The SAXS investigation was carried out on a KRM-1 camera using the filtered Cu – Ka radiation. The intensities were measured in a range of 0.0036–0.71 A − 1 (0.05 – 10°). As samples to be tested carbon adsorbents of the types were used: FAS-1 (the volume of micropores v =0.3 cm3 g − 1, the width of the slitlike micropores L= 0.6 nm) and FAS-2 (v = 0.6 cm3 g − 1, and L= 1.2 nm [7]). A batch of AC powder mixed with a definite amount of liquid drops (the weight of a drop of about 10 − 2 g) was put in a flat cell with windows of polymeric film. In the case of glycerol and trixylylphosphate (TXP), the amount of liquid drops were gradually increased and the SAXS intensity was measured at every stage of investigation. In the case of evaporating liquids (benzene,
water) the measurements were made first on a completely filled sample and then after the cell was unsealed by puncturing holes in it. The intensity of scattering by filled pores DI was determined in terms of a difference between the scattering intensities of the samples: for the initial (dry) sample and for the same sample mixed with a corresponding amount of liquid. The linear sizes of pores are characterized by the radius of inertia Ri-parameter that is applicable for pores of any shape. The calculation of the pore size distribution: f(R) was made on the basis of a method suggested in Ref. [8], which takes into account collimational distortions.
3. Results and discussion To elucidate how the shape of scattering curves depends on the filling of either micro- or mesopores the experiments on the TXP adsorption were carried out, the sizes of TXP molecule ( 1.0 nm) exceeding the width of micropores L in FAS-1, but they being smaller than L values in FAS-2. The scattering curves of adsorbents in the initial (dry) state and after the filling of TXP are shown in logariphmic coordinates in Fig. 1. In the case of FAS-1 AC, the scattering intensity changes in opposite way to [1–5]: it falls sharply in the range of the smallest angles and remains practically unchanged in the range of large angles (curves 2 and 3). It means that the mesopores are filled whose scattering is predominant in the range of small h (h50.005 nm − 1). Micropores are not filled, with the exception of the biggest ones and individual pores, into which penetrate the fragments of molecules [9]. On the contrary, in the case of FAS-2 AC, the changes in the scattering intensity are similar to those observed in Refs. [1–5] at first, the micropores and then mesopores are filled. This interpretation is illustrated in Fig. 2 by the curves of distribution of the sizes of filled pores, calculated from the data of Fig. 1. Thus, the experiments with TXP convincingly show that the changes in the shape of scattering curves, which are similar to those observed in Refs. [1–5], take place on a partial filling of the pore space: filled are either micro- or mesopores.
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Dependence of the shape of a scattering curve on the filling of different portions of pores is also observed on the mixing of FAS-1 AC powder with glycerol. The time of the pore filling with glycerol is long enough because of its high viscosity to allow the observation of the kinetics of this process. At the initial stage, during half an hour after mixing, the scattering intensity in the range of small angles decreases: this is indicative of the mesopores filling (Fig. 3). At the large h interval, the scattering intensity changes little: the most part of micropores remains empty. Then the gradual overflow of glycerol from meso- into micropores occurs; and due to this, the intensity falls off in the range of large h and increases in the range of small h (curve 3). Further additions of glycerol result in the filling of mesopores. As a result, the scattering intensity decreases at small angles. This Fig. 2. Size distribution of filled pores for AC samples mixed with TXP: FAS-1 (1) initial AC; (2) AC + 3 drops; (3) AC +7 drops; FAS-2 (4) initial AC; (5) AC + 1 drop; (6) 5 drops; and (7) 10 drops.
Fig. 3. Scattering curves log I−log h for the FAS-1 AC samples with glycerol: (1) initial AC; (2) AC + 1 drop after 0.5 h; (3) AC +1 drop after 9 days; (4) AC + 2 drops; (5) complete filling. Fig. 1. Scattering curves log I− log h for the AC samples with trixylylphosphate (TXP): FAS-1: (1) initial AC; (2) AC +3 drops; (3) AC+ 7 drops; FAS-2: (4) initial AC; (5) AC+10 drops; (6) AC+ 15 drops. The values of log I for FAS-1 are shifted.
process is more obviously represented by the curves of distribution of the filled pores sizes with f(R) (Fig. 4).
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The obtained results confirm our interpretation: if both pore fractions (micro and meso) are filled, the decrease in the scattering intensity occurs over the whole run of the scattering curve; if only one
Fig. 6. Size distribution of filled pores for FAS-1 AC samples mixed with water: (1) completely filled; (2) after 2 days; (3) after 11 days; and (4) after 27 days.
Fig. 4. Size distribution of filled pores for AC samples mixed with glycerol: (1) AC + 1 drop after 0.5 h; (2) AC +1 drop after 1.5 h; (3) AC + 1 drop after 24 h; (4) AC +1 drop after 9 days; (5) complete filling.
Fig. 5. Size distribution of filled pores for AC samples mixed with benzene: FAS-1: (1) initial AC; (2) after 15 days; (3) after 365 days; FAS-2 (4) initial AC; (5) after 30 days.
fraction is filled, the shape of the scattering curve is distorted. These results also provide evidence of a substantial contribution of the mesopore scattering to the total intensity, especially considerable in the region of small h. The authors of other interpretations did not take this component into account, presumably on the assumption that the volume of mesopores in the tested AC samples is very small. Meanwhile, it is necessary to consider that the SAXS intensity I R 6, and the mesopore sizes exceed the micropore sizes by one and even more orders of magnitude. Therefore, even a small amount of mesopores causes an intense scattering, especially in the region of small h. The kinetics of benzene desorption in FAS-1 AC obtained from the SAXS data is shown in Fig. 5. The desorption rate is very slow: only after 15 days most mesopores are empty, whereas a considerable part of micropores remain filled after even a year exposure. The water desorption in FAS-I AC is more intensive, and is completed after 30 days (Fig. 6). The kinetics of water desorption can be described analytically as the dependence of the filled micropore volume Vt on time t: Vt = V0 exp(− kt), where V0 is the micropore volume in a sample (in relative units), k is the constant characterizing the desorption rate. Vt
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and V0 were obtained from the area just under the corresponding curves f(R) (Fig. 6) [9]. In the case of FAS-2 AC samples, the desorption processes go to completion quicker than in those of FAS-1 AC. The desorption of benzene is mainly completed after several days; but the smallest micropores remain filled even after a month (Fig. 5). The desorption of water is completed after 5 – 6 days. The intensive rate of desorption in FAS-2 is evidently due to a more developed and accessible structure of micro- and mesopores, and a larger sizes of micropores [6,9].
4. Conclusions The new X-ray method has been developed enabling one to study the mass transfer processes in porous systems in terms of changes in the intensity of small-angle scattering. This method was applied to investigate the kinetics of adsorption and desorption processes of a series of fluids (water, glycerol, benzene and trixylylphosphate) in carbon adsorbents. An analytical expression was derived characterizing the
.
127
dependence of the volume of micropores filled with water on the desorption time. The change of the shapes of SAXS curve in the adsorption and desorption processes is explained by the fact that only one of the pore fractions is filled: either micro- or mesopores. Other interpretations are incorrect, because they ignore scattering on mesopores. References [1] M.M. Dubinin, G.M. Plavnik, E.D. Zaverina, Carbon 2 (1964) 261. [2] G.M. Plavnik, M.M. Dubinin, Izv. Akad. Nauk SSSR Ser. Khim. 4 (1964) 628. [3] K. Kaneko, Y. Fujiwara, K. Nishikawa, J. Colloid Interf. Sci. 127 (1989) 298. [4] Y. Fujiwara, K. Nishikawa, T. Iijima, K. Kaneko, J. Chem. Soc. Faraday Trans. 87 (1991) 2763. [5] G.M. Plavnik, T.P. Purjaeva, M.M. Dubinin, Izv. Akad. Nauk SSSR Ser. Khim. 1 (1993) 1220. [6] G.M. Plavnik, T.P. Purjaeva, Zh. Fiz. Khim. 71 (1997) 1460. [7] R. Sh. Vartapetyan, A.M. Voloshchuk, V.V. Gur’yanov, et al., Izv. Akad. Nauk SSSR Ser. Khim. 1 (1993) 56. [8] G.M. Plavnik, Kristallograflya 39 (1994) 600. [9] G.M. Plavnik, T.P. Purjaeva, Zh. Fiz. Khim. 71 (1997) 2036.