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Pore size analysis by nitrogen adsorption and thermal desorption
Colloids and Surfaces A: Physicochem. Eng. Aspects 214 (2003) 231 /237 www.elsevier.com/locate/colsurfa
Pore size analysis by nitrogen adsorption and thermal desorption Wojciech Stefaniak a, Jacek Goworek a,*, Bogdan Bilin´ski b a
Department of Adsorption, Faculty of Chemistry, Maria Curie-Sklodowska University, M. Curie-Sklodowska Sq. 3, 20-031 Lublin, Poland b Department of Interfacial Phenomena, Faculty of Chemistry, Maria Curie-Sklodowska University, 20-031 Lublin, Poland Received 8 May 2002; accepted 21 August 2002
Abstract Thermogravimetric analysis was applied to the characterization of the porosity of silica gel. Thermal desorption of liquids from silicas for column chromatography was measured. Benzene, n -hexane and carbon tetrachloride were used as liquid adsorbates. Pore size distributions for silica gels of differentiated porosity were determined on the basis of thermogravimetric curves using the Kelvin equation. Pore dimensions were corrected in respect to the surface film thickness estimated from adsorption isotherms of the same adsorbates measured above their boiling point. The resulting pore size distributions and total pore volumes were compared with those obtained from the nitrogen method. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Porosity; Surface film thickness; Thermogravimetric analysis
1. Introduction In the last time there has been increasing interest in the study of fluids confined in pores of various dimensions. Most of these investigations concern assessment of micro- and meso-porosity of solids. The oldest technique, which is used to quantifying porosity, is a gas/vapor adsorption. Textural characterization of solids may be derived from adsorption /desorption isotherms of various ad-
* Corresponding author. Tel.: /48-81-537-5716; fax: /4881-533-3348. E-mail address: [email protected] (J. Goworek).
sorbates at the boiling point of liquid adsorbate. Alternatively, another approach is based on a thermodynamic relationship in which the melting and freezing temperatures of liquid present in pores are lower then those of the bulk liquid as in thermoporometry [1]. Both above-mentioned methods consists on the curvature of liquid meniscus inside the pore against pressure and temperature, respectively. The newer techniques for pore structure investigations include nuclear magnetic resonance (NMR) [2], small angle scattering of X-rays (SAXS) and neutrons (SANS) [3,4] or thermoporometry [1]. Another empirical approach for assessment of mesoporosity is thermo-gravimetric method [5 /7]. The method consists of thermal
0927-7757/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 0 2 ) 0 0 4 1 3 - 2
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W. Stefaniak et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 214 (2003) 231 /237
desorption of liquid adsorbates filling the pores of solid. Recently, similar approach was presented in [8] In the temperature programmed desorption (TPD) after evacuation of the core of pore, there remains on the pore walls a liquid film, which does not take part in desorption at a given temperature. The thickness of this film is a function of the temperature and it diminishes when temperature increases. This is impossible to establish unambiguously from TG data appropriate standard values of corrections to core radius calculated from the Kelvin equation. The differences of the pore dimensions estimated from TG data and nitrogen isotherms depend on liquid adsorbate used in thermodesorption. Generally, one can say that for hydrocarbons the shape of PSD and location of maximum are similar in comparison to nitrogen curve. Some discrepancies appears for polar adsorbates and may be explained by the formation of multilayer surface phase with hydrogen bonded molecules of adsorbate. Evacuation of strongly held liquid film requires higher temperature. It is usually to assume that desorption of the liquid being in contact directly with the polar surface is non-isothermic process. Desorption temperature is not constant and changes against the structural transformations within adsorbed layer as well as energetical topography of silica gel. Similar effect occurs in the case of polar adsorbates like alcohols, ketones or amines [9]. In our previous papers, the pore structure of silica gels was analyzed on the basis of both nitrogen isotherms and TPD isobars. Pore size distribution (PSD), dV /dR /f(R ), in this last case may be calculated taking into account the following relationship: dV dV dT dR dT dr
(1)
First derivative is accessible from the experiment after transformation of mass desorbed into the volume. The derivative dT /dR may be calculated using the Kelvin equation. The Kelvin equation for the cylindrical pores is given by:
2gVL 1 rK ln(p=p0 ) RT
(2)
where g is the surface tension of the liquid, VL the molar volume of liquid, rK the average radius of the meniscus, and p/p0 is relative pressure, where p0 is the saturation pressure of the gas. The above-presented form of the Kelvin equation traditionally is used in calculations based on isothermal data, i.e. adsorption/desorption isotherm. The pore radius rp is obtained using following expression rp /rK cos U/t , where t is the surface film thickness remaining on the walls of pores after core evacuation. For liquid wetting the solid perfectly cos U /1. Hence, rp /rk/t. In the case of nitrogen adsorption data the problem of the surface film thickness is solved by using adsorption data for nonporous sorbent and calculation on this base the thickness of the surface layer [10]. Usually equations which relate thickness, pore radius and relative pressure are used for these purposes [10]. The aim of the present paper is to estimate the surface film thickness from adsorption isotherms measured above normal boiling point of liquid and calculation of the pore radii from TG data. Pore structure of several silica gels is analyzed on the basis of both the thermal desorption data and the nitrogen isotherms.
2. Experimental Compmercial silica gels Si-100 and Si-60 for column chromatography (Merck, Germany), dp / 0.1 /0.2 mm. were used for experiments. Estimation of structural parameters for investigated silicas was made using adsorption data of nitrogen at /195 8C. The adsorption/desorption isotherms of nitrogen at /195 8C were measured with an automated apparatus ASAP 2010 (Micromeritics, USA). The specific surface areas SBET were calculated from the linear form of the BET equation taking the cross-sectional area of the nitrogen molecule to be 16.2 /10 20 m2 (linearity region between 0 and 0.35 p/p0). Total pore volume was estimated from single point on adsorption isotherm at p/p0 /0.975. Pore size dis-
W. Stefaniak et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 214 (2003) 231 /237
tributions were calculated in the standard manner by using BJH method [11]. The adsorption isotherms of benzene n -hexane and carbon tetrachloride above their boiling point were measured using gas chromatography. Prior to the measurements the silica samples were dried for 2 h at 200 8C, and they were stored in a desiccator. Silica gels were packed into a glass column of 40-cm length and 3 mm i.d. Each column packing was conditioned for 2 h at 200 8C under the flow of carrier gas (hydrogen ˚ molecular sieve) in order to remove dried with 4 A the traces of water, which might adsorb during the column preparation. Adsorption isotherms of nhexane, benzene and carbon tetrachloride were determined at their boiling point, and then at the temperatures higher by 10 and 20 8C. The measurements were performed using the standard gas chromatograph (GCHF 18.3, Chromatron, Germany) with a thermal conductivity detector, and the detector signal was registered directly on a computer by an analog /digital transmitter with appropriate software (Medson, Poland). At the temperature equal to, as well as above the boiling point, it was impossible to apply the measurement procedure for low temperatures, which consisted in calibrating of the detector by placing into the oven a saturator containing liquid adsorbate and registering the signal corresponding to saturated vapor pressure [12,13]. Therefore, the detector constant was determined in each measurement, based on the slope of linear dependence between the peak area and the injected volume of adsorbate [14 /16]. Then, the equilibrium vapor pressure was computed from the peak height and the detector constant [14 /16]. The adsorbed amount (a ) was calculated from the experimentally determined so-called retention curve, i.e. the dependence between the retention volume and the equilibrium vapor pressure, according to the equation [14,15]: 1 a RT
p
gV
R
dp
(3)
0
where VR is the retention volume (related to the unit of sample area) and p is the equilibrium pressure. Prior to the final calculation of adsorp-
233
Fig. 1. Nitrogen adsorption/desorption isotherms at /195 8C for silica gels: (1) Si-60; (2) Si-100. Open points, adsorption; filled points, desorption.
tion isotherms, the retention curves were smoothed by a local parabolic equation, as well as corrected for the measurement temperature and for the sorption effect [15,17]. In TG experiments the Hungarian Derivatograph, equipped with the so-called quasi-isothermal (QI) program, was used [18]. Prior to experiment the silica gels were outgassed to facilitate the penetration of liquid adsorbate into pores. The experiment starts with the sample of porous solid mixed with excess of wetting liquid. The QI program regulates automatically the heating rate according to transformations of the sample. During intensive evaporation resulting in high weight loss values, exceeding fixed weight loss level, the isothermal conditions are established. Thus, TPD consists of periods of linear increasing temperature and periods when temperature of the sample remains constant. The switch of heating mode depends on fixed weight loss level. When the differential mass loss with time descends below a fixed value, a linear increase of temperature takes over. Such especially programmed thermodesorption provide to estimate the total pore volume and dimensions of mesopores. This technique is correct
30.8 69.9 28.3 66.9 0.69 1.02
3. Results and discussion
0.66 0.95 30.5 60.8 Rp , pore radius corrected in respect to the surface film thickness.
27.4 57.5 0.65 0.97 34 66 0.72 1.1 450 328
Vp (cm3 g 1) Vp (cm3 g 1)
Benzene SBET (m2 g 1)
when saturated vapor pressure of liquid filling the pores is attained. Desorption was measured in platinum crucibles with two tightly closed parts where liquid vapor is in contact with the external atmosphere through a small row between these parts [18]. Thus, one can assume that, above the sample, the self-generated atmosphere of the saturated vapor is present.
27.1 57.2
29.4 59.8
˚) Rp (A Vp (cm3 g 1) ˚) R p (A
Si-60 Si-100
Adsorbent
Nitrogen method
Vp (cm3 g 1)
˚) Rp (A
TG method
˚) Rp (A
˚) R p (A
n -Hexane
˚) Rp (A
Carbon tetrachloride
˚) R p (A
W. Stefaniak et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 214 (2003) 231 /237
Table 1 Parameters characterizing the porous structure of the adsorbents investigated
234
Adsorption/desorption isotherms of nitrogen at /195 8C for silica gels Si-60 and Si-100 are shown in Fig. 1. As is seen, the shape of these isotherms is characteristic for mesoporous material with wellvisualized hysteresis. Parameters characterizing the porosity of these silicas i.e. specific surface areas SBET, total pore volumes (Vp) and average pore radii (Rp) are given in Table 1. Thermodesorption curves of benzene, n-hexane and carbon tetrachloride for silica gels Si-60 and Si-100 are shown in Fig. 2. Perpendicular segments of these curves correspond to the boiling point of liquids and represent the evaporation of the excess of liquid out of pores. Next, starts desorption from pores. At lower temperatures below boiling point only slow evaporation occurs. During the thermal desorption when temperature increases evacuation of the pore cores with a smaller and smaller diameter takes place. Simultaneously, the increasing temperature causes the thickness of the surface film in empty cores to decrease. Thus, at each stage of the process, the desorbed amount of adsorbate is made up of the core volume plus the volume released by thinning of the surface film in pores already evacuated. This effect changes the shape of TG desorption curve in comparison to that which would be obtained at the absence of the surface film. The hight of TG curve above boiling point of liquid is a measure of the total pore volume. Taking into account the changes of the surface film thickness for a given group of pores i.e. given temperature interval it is possible to calculate real pore volumes DVi ,pore from the relation:
W. Stefaniak et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 214 (2003) 231 /237
235
Fig. 3. Adsorption isotherms of benzene on silica gel Si-100 at various temperatures.
Fig. 2. Thermodesorption curves of CCl4 (1); benzene (2); and n -hexane (3) onto silica gels: Si-100 (A), Si-60 (B).
DVi;pore DVi;core
r¯k t¯ r¯k
(4)
where r¯k is the main core radius, and t¯/is a mean surface film thickness for the ith group of cores. The share of the surface film thinning in desorbed volume for succeeding group of pores may be expressed as Dtt ai 1 j;core where S j;core j 1 S i 1 aj 1 2DVj;core =Rj;core is the surface of evacuated cores. The surface film thickness for used adsorbates at three temperatures was estimated from adsorption data. Initial segments of adsorption isotherms of benzene measured using GC technique above boiling point of adsorbate are shown for illustrative purposes in Fig. 3. Taking into account the area occupied by adsorbate molecule on the silica surface equal to ˚ for benzene, n-hexane and 43.6, 56.2 and 39.2 A carbon tetrachloride [19], respectively, one can
calculate the surface coverage of silica surface at a given temperature. From adsorption data we obtain that for all used adsorbates above boiling point at the silica surface is held relatively small amount of adsorbate molecules, lower then monolayer coverage. For example, molecular coverage of silica Si-100 surface for various adsorbates at temperature 10 8C higher then their boiling point and p /302 Torr are equal to U /0.75, 0.33 and 0.23 for benzene, n -hexane and carbon tetrachloride, respectively. It means that at all temperatures the adsorbed amount does not exceed a monolayer. Thus, in further calculations the statistical thickness of the surface layer was taken into account. Small surface coverages were observed also by Naono and Hakuman [20] for adsorption of water on hydrophobic surfaces. Similar effect appears in the case when non-polar adsorbate molecules are adsorbed on strongly polar silica surface. Thickness of adsorbate monolayer on silica surface was estimated from van der Waals model ˚ for benzene, n and is equal to 3.4, 4.3 and 7 A hexane and carbon tetrachloride, respectively. Calculated coverages of silica gels under study at various temperatures and for various adsorbates are given in Table 2. The adsorbed amounts for calculations of the surface film thicknesses were taken for p /302 Torr. For example, for temperature corresponding to boiling point of a benzene the end of adsorption
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Table 2 Surface coverages of various adsorbates at different temperatures and p /302 Torr for systems investigated Silica gel
Si-100
Si-60
Benzene
n -Hexane
Carbon tetrachloride
T (8C)
T
T (8C)
U
T (8C)
U
80 90 100 80 90 100
0.95 0.75 0.57 0.91 0.70 0.55
70 80 90 70 80 90
0.43 0.33 0.26 0.41 0.32 0.25
80 90 100 80 90 100
0.29 0.23 0.18 0.29 0.23 0.18
isotherm corresponds to p /p0 :/0.4 and is located near the beginning of capillary condensation. Usually, the surface film thickness present on a given adsorbent surface is estimated from the adsorption data for nonporous solid of the same type. In the case of TG experiment similar estimation is impossible due to very small weight changes of sample characterized by very low specific surface. However, for illustrative purposes, in Fig. 4 are shown segments of thermodesorption curves of benzene for Si-100 silica and macroporous Si-500 ˚ , SBET /69 m2 g 1 and Vp / silica gel (Rp /135 A 3 1 0.68 cm g , data from Ref. [21]). Since the above 100 8C both curves are identical, one can assume that these parts of curves represent desorption of the surface film only. Very steep segments of TG curves at lower temperatures correspond to capillary condensed liquid. The filled points in Fig. 4 indicate recalculated amounts of benzene taken from adsorption isotherms presented in Fig. 3, i.e. the amount of benzene remaining on the silica surface at a given temperature. For our measuring range of temperature the surface film thickness variation against temperature is practically linear. Pore/core size distributions calculated from TG data and nitrogen method for silica gel Si-100 are compared in Fig. 5. In order to estimate the radii of cores for pores evacuated at different temperatures in thermogravimetric experiments, the Kelvin equation calculation should be slightly modified. In TG experiment p is maintained constant and equal to external pressure, whereas p0, VL and g vary with temperature. Temperature relations of these variables can be found in literature [22]. Taking into account the dependence
Fig. 4. Termodesorption curves of benzene from silica gels Si100 and Si-500 and magnitudes of adsorbed benzene at different temperatures for p /302 Torr (points).
of p0, VL and g against temperature appropriate core size distribution was calculated. Dashed line in Fig. 5 represents PSD derived directly from thermal desorption curves using Kelvin equation in the manner described previously [5 /7]. In fact this curve represents distribution of core of pores. Core radii were next corrected in respect to the surface film thickness estimated from adsorption data presented in Fig. 3 (solid line in Fig. 5). Shaded area represents PSD calculated on the basis of nitrogen adsorption data. The thickening of the surface film within temperature range corresponding to TG measurements was taken into account in calculations. Numerical values of the parameters characterizing the porosity of investigated silica gels are collected in Table 2.
W. Stefaniak et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 214 (2003) 231 /237
237
References
Fig. 5. PSDs for silica gel Si-100. Dashed line, PSD derived from thermal desorption of benzene; solid line, PSD corrected in respect to the surface film thickness; shaded area, nitrogen method.
Comparing the results presented in Fig. 5 and Table 2, one can say, that for investigated systems the effect of the surface film is small and changes only slightly the shape of PSD. The best correlation between PSDs from nitrogen adsorption and thermogravimetry is observed in the case of nhexane and carbon tetrachloride. For benzene, which is adsorbed specifically on silica surface forming strongly held surface layer this correlation is less satisfactory. Introduction of corrections in respect to the surface film thickness improves slightly the characteristics of porosity for mesoporous silicas. Mean pore radii derived from liquid nitrogen data and thermal desorption data of CCl4 are close together.
[1] M. Brun, A. Lallemand, J.F. Quinson, C. Eyraud, Thermochim. Acta 21 (1997) 59. [2] D.P. Gallegos, K. Munn, D.M. Smith, D.L. Stermer, J. Colloid Interf. Sci. 199 (1987) 127. [3] M.A. Gardner, A.N. North, J.C. Dore, C. SalinasMartinez de Lecea, D. Cazorla-Amoros, in: J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing, K.K. Unger (Eds.), Characterization of Porous Solids III, Elsevier, Amsterdam, 1994, p. 273. [4] J.D.F. Ramsay, S. Kallus, E. Hoinkis, in: K.K. Unger, G. Kreysa, J.F. Baselt (Eds.), Characterization of Porous Solids V, Elsevier, Amsterdam, 2000, p. 439. [5] J. Goworek, W. Stefaniak, Colloids Surf. 69 (1992) 23. [6] J. Goworek, W. Stefaniak, Mater. Chem. Phys. 32 (1992) 244. [7] J. Goworek, W. Stefaniak, Colloids Surf. 80 (1993) 251. [8] V. Chevrot, P.L. Llewellyn, F. Rouquerol, J. Godlewski, J. Rouquerol, Thermochim. Acta 360 (2000) 77. [9] M. Hunger, U. Schenk, M. Breuninger, R. Gla¨ser, J. Weitkamp, Microporous Mesoporous Mater. 27 (1999) 261. [10] S.J. Gregg, K.S.W. Sing, Adsorption, Surface Area and Porosity, Academic Press, London, 1982. [11] E.P. Barrett, L.G. Joyner, P.H. Halenda, J. Am. Chem. Soc. 73 (1951) 373. [12] E. Chibowski, B. Bilinski, A. Waksmundzki, W. Wo´jcik, J. Colloid Interf. Sci. 86 (1982) 559. [13] B. Bilinski, E. Chibowski, Powder Technol. 35 (1983) 39. [14] B. Bilinski, J. Colloid Interf. Sci. 225 (2000) 105. [15] G.M. Dorris, D.G. Gray, J. Colloid Interf. Sci. 71 (1979) 93. [16] M. Domingo-Garcia, F.J. Lopez-Garzon, R. Lopez-Garzon, C. Moreno-Castilla, J. Chromatogr. 324 (1985) 19. [17] G.M. Dorris, D.G. Gray, J. Colloid Interf. Sci. 77 (1980) 353. [18] F. Paulik, J. Paulik, J. Thermal Anal. 5 (1973) 253. [19] A.L. McClellan, H.F. Harnsberger, J. Colloid Interf. Sci. 23 (1967) 577. [20] H. Naono, M. Hakuman, J. Colloid Interf. Sci. 145 (1991) 405. [21] J. Goworek, W. Stefaniak, in: J. Rouquerol, F. RodriguezReinoso, K.S.W. Sing, K.K. Unger (Eds.), Characterization of Porous Solids III, Elsevier, Amsterdam, 1994, p. 401. [22] R.C. Weast (Ed.), CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, 1988.
Pore size analysis by nitrogen adsorption and thermal desorption Wojciech Stefaniak a, Jacek Goworek a,*, Bogdan Bilin´ski b a
Department of Adsorption, Faculty of Chemistry, Maria Curie-Sklodowska University, M. Curie-Sklodowska Sq. 3, 20-031 Lublin, Poland b Department of Interfacial Phenomena, Faculty of Chemistry, Maria Curie-Sklodowska University, 20-031 Lublin, Poland Received 8 May 2002; accepted 21 August 2002
Abstract Thermogravimetric analysis was applied to the characterization of the porosity of silica gel. Thermal desorption of liquids from silicas for column chromatography was measured. Benzene, n -hexane and carbon tetrachloride were used as liquid adsorbates. Pore size distributions for silica gels of differentiated porosity were determined on the basis of thermogravimetric curves using the Kelvin equation. Pore dimensions were corrected in respect to the surface film thickness estimated from adsorption isotherms of the same adsorbates measured above their boiling point. The resulting pore size distributions and total pore volumes were compared with those obtained from the nitrogen method. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Porosity; Surface film thickness; Thermogravimetric analysis
1. Introduction In the last time there has been increasing interest in the study of fluids confined in pores of various dimensions. Most of these investigations concern assessment of micro- and meso-porosity of solids. The oldest technique, which is used to quantifying porosity, is a gas/vapor adsorption. Textural characterization of solids may be derived from adsorption /desorption isotherms of various ad-
* Corresponding author. Tel.: /48-81-537-5716; fax: /4881-533-3348. E-mail address: [email protected] (J. Goworek).
sorbates at the boiling point of liquid adsorbate. Alternatively, another approach is based on a thermodynamic relationship in which the melting and freezing temperatures of liquid present in pores are lower then those of the bulk liquid as in thermoporometry [1]. Both above-mentioned methods consists on the curvature of liquid meniscus inside the pore against pressure and temperature, respectively. The newer techniques for pore structure investigations include nuclear magnetic resonance (NMR) [2], small angle scattering of X-rays (SAXS) and neutrons (SANS) [3,4] or thermoporometry [1]. Another empirical approach for assessment of mesoporosity is thermo-gravimetric method [5 /7]. The method consists of thermal
0927-7757/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 0 2 ) 0 0 4 1 3 - 2
232
W. Stefaniak et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 214 (2003) 231 /237
desorption of liquid adsorbates filling the pores of solid. Recently, similar approach was presented in [8] In the temperature programmed desorption (TPD) after evacuation of the core of pore, there remains on the pore walls a liquid film, which does not take part in desorption at a given temperature. The thickness of this film is a function of the temperature and it diminishes when temperature increases. This is impossible to establish unambiguously from TG data appropriate standard values of corrections to core radius calculated from the Kelvin equation. The differences of the pore dimensions estimated from TG data and nitrogen isotherms depend on liquid adsorbate used in thermodesorption. Generally, one can say that for hydrocarbons the shape of PSD and location of maximum are similar in comparison to nitrogen curve. Some discrepancies appears for polar adsorbates and may be explained by the formation of multilayer surface phase with hydrogen bonded molecules of adsorbate. Evacuation of strongly held liquid film requires higher temperature. It is usually to assume that desorption of the liquid being in contact directly with the polar surface is non-isothermic process. Desorption temperature is not constant and changes against the structural transformations within adsorbed layer as well as energetical topography of silica gel. Similar effect occurs in the case of polar adsorbates like alcohols, ketones or amines [9]. In our previous papers, the pore structure of silica gels was analyzed on the basis of both nitrogen isotherms and TPD isobars. Pore size distribution (PSD), dV /dR /f(R ), in this last case may be calculated taking into account the following relationship: dV dV dT dR dT dr
(1)
First derivative is accessible from the experiment after transformation of mass desorbed into the volume. The derivative dT /dR may be calculated using the Kelvin equation. The Kelvin equation for the cylindrical pores is given by:
2gVL 1 rK ln(p=p0 ) RT
(2)
where g is the surface tension of the liquid, VL the molar volume of liquid, rK the average radius of the meniscus, and p/p0 is relative pressure, where p0 is the saturation pressure of the gas. The above-presented form of the Kelvin equation traditionally is used in calculations based on isothermal data, i.e. adsorption/desorption isotherm. The pore radius rp is obtained using following expression rp /rK cos U/t , where t is the surface film thickness remaining on the walls of pores after core evacuation. For liquid wetting the solid perfectly cos U /1. Hence, rp /rk/t. In the case of nitrogen adsorption data the problem of the surface film thickness is solved by using adsorption data for nonporous sorbent and calculation on this base the thickness of the surface layer [10]. Usually equations which relate thickness, pore radius and relative pressure are used for these purposes [10]. The aim of the present paper is to estimate the surface film thickness from adsorption isotherms measured above normal boiling point of liquid and calculation of the pore radii from TG data. Pore structure of several silica gels is analyzed on the basis of both the thermal desorption data and the nitrogen isotherms.
2. Experimental Compmercial silica gels Si-100 and Si-60 for column chromatography (Merck, Germany), dp / 0.1 /0.2 mm. were used for experiments. Estimation of structural parameters for investigated silicas was made using adsorption data of nitrogen at /195 8C. The adsorption/desorption isotherms of nitrogen at /195 8C were measured with an automated apparatus ASAP 2010 (Micromeritics, USA). The specific surface areas SBET were calculated from the linear form of the BET equation taking the cross-sectional area of the nitrogen molecule to be 16.2 /10 20 m2 (linearity region between 0 and 0.35 p/p0). Total pore volume was estimated from single point on adsorption isotherm at p/p0 /0.975. Pore size dis-
W. Stefaniak et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 214 (2003) 231 /237
tributions were calculated in the standard manner by using BJH method [11]. The adsorption isotherms of benzene n -hexane and carbon tetrachloride above their boiling point were measured using gas chromatography. Prior to the measurements the silica samples were dried for 2 h at 200 8C, and they were stored in a desiccator. Silica gels were packed into a glass column of 40-cm length and 3 mm i.d. Each column packing was conditioned for 2 h at 200 8C under the flow of carrier gas (hydrogen ˚ molecular sieve) in order to remove dried with 4 A the traces of water, which might adsorb during the column preparation. Adsorption isotherms of nhexane, benzene and carbon tetrachloride were determined at their boiling point, and then at the temperatures higher by 10 and 20 8C. The measurements were performed using the standard gas chromatograph (GCHF 18.3, Chromatron, Germany) with a thermal conductivity detector, and the detector signal was registered directly on a computer by an analog /digital transmitter with appropriate software (Medson, Poland). At the temperature equal to, as well as above the boiling point, it was impossible to apply the measurement procedure for low temperatures, which consisted in calibrating of the detector by placing into the oven a saturator containing liquid adsorbate and registering the signal corresponding to saturated vapor pressure [12,13]. Therefore, the detector constant was determined in each measurement, based on the slope of linear dependence between the peak area and the injected volume of adsorbate [14 /16]. Then, the equilibrium vapor pressure was computed from the peak height and the detector constant [14 /16]. The adsorbed amount (a ) was calculated from the experimentally determined so-called retention curve, i.e. the dependence between the retention volume and the equilibrium vapor pressure, according to the equation [14,15]: 1 a RT
p
gV
R
dp
(3)
0
where VR is the retention volume (related to the unit of sample area) and p is the equilibrium pressure. Prior to the final calculation of adsorp-
233
Fig. 1. Nitrogen adsorption/desorption isotherms at /195 8C for silica gels: (1) Si-60; (2) Si-100. Open points, adsorption; filled points, desorption.
tion isotherms, the retention curves were smoothed by a local parabolic equation, as well as corrected for the measurement temperature and for the sorption effect [15,17]. In TG experiments the Hungarian Derivatograph, equipped with the so-called quasi-isothermal (QI) program, was used [18]. Prior to experiment the silica gels were outgassed to facilitate the penetration of liquid adsorbate into pores. The experiment starts with the sample of porous solid mixed with excess of wetting liquid. The QI program regulates automatically the heating rate according to transformations of the sample. During intensive evaporation resulting in high weight loss values, exceeding fixed weight loss level, the isothermal conditions are established. Thus, TPD consists of periods of linear increasing temperature and periods when temperature of the sample remains constant. The switch of heating mode depends on fixed weight loss level. When the differential mass loss with time descends below a fixed value, a linear increase of temperature takes over. Such especially programmed thermodesorption provide to estimate the total pore volume and dimensions of mesopores. This technique is correct
30.8 69.9 28.3 66.9 0.69 1.02
3. Results and discussion
0.66 0.95 30.5 60.8 Rp , pore radius corrected in respect to the surface film thickness.
27.4 57.5 0.65 0.97 34 66 0.72 1.1 450 328
Vp (cm3 g 1) Vp (cm3 g 1)
Benzene SBET (m2 g 1)
when saturated vapor pressure of liquid filling the pores is attained. Desorption was measured in platinum crucibles with two tightly closed parts where liquid vapor is in contact with the external atmosphere through a small row between these parts [18]. Thus, one can assume that, above the sample, the self-generated atmosphere of the saturated vapor is present.
27.1 57.2
29.4 59.8
˚) Rp (A Vp (cm3 g 1) ˚) R p (A
Si-60 Si-100
Adsorbent
Nitrogen method
Vp (cm3 g 1)
˚) Rp (A
TG method
˚) Rp (A
˚) R p (A
n -Hexane
˚) Rp (A
Carbon tetrachloride
˚) R p (A
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Table 1 Parameters characterizing the porous structure of the adsorbents investigated
234
Adsorption/desorption isotherms of nitrogen at /195 8C for silica gels Si-60 and Si-100 are shown in Fig. 1. As is seen, the shape of these isotherms is characteristic for mesoporous material with wellvisualized hysteresis. Parameters characterizing the porosity of these silicas i.e. specific surface areas SBET, total pore volumes (Vp) and average pore radii (Rp) are given in Table 1. Thermodesorption curves of benzene, n-hexane and carbon tetrachloride for silica gels Si-60 and Si-100 are shown in Fig. 2. Perpendicular segments of these curves correspond to the boiling point of liquids and represent the evaporation of the excess of liquid out of pores. Next, starts desorption from pores. At lower temperatures below boiling point only slow evaporation occurs. During the thermal desorption when temperature increases evacuation of the pore cores with a smaller and smaller diameter takes place. Simultaneously, the increasing temperature causes the thickness of the surface film in empty cores to decrease. Thus, at each stage of the process, the desorbed amount of adsorbate is made up of the core volume plus the volume released by thinning of the surface film in pores already evacuated. This effect changes the shape of TG desorption curve in comparison to that which would be obtained at the absence of the surface film. The hight of TG curve above boiling point of liquid is a measure of the total pore volume. Taking into account the changes of the surface film thickness for a given group of pores i.e. given temperature interval it is possible to calculate real pore volumes DVi ,pore from the relation:
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235
Fig. 3. Adsorption isotherms of benzene on silica gel Si-100 at various temperatures.
Fig. 2. Thermodesorption curves of CCl4 (1); benzene (2); and n -hexane (3) onto silica gels: Si-100 (A), Si-60 (B).
DVi;pore DVi;core
r¯k t¯ r¯k
(4)
where r¯k is the main core radius, and t¯/is a mean surface film thickness for the ith group of cores. The share of the surface film thinning in desorbed volume for succeeding group of pores may be expressed as Dtt ai 1 j;core where S j;core j 1 S i 1 aj 1 2DVj;core =Rj;core is the surface of evacuated cores. The surface film thickness for used adsorbates at three temperatures was estimated from adsorption data. Initial segments of adsorption isotherms of benzene measured using GC technique above boiling point of adsorbate are shown for illustrative purposes in Fig. 3. Taking into account the area occupied by adsorbate molecule on the silica surface equal to ˚ for benzene, n-hexane and 43.6, 56.2 and 39.2 A carbon tetrachloride [19], respectively, one can
calculate the surface coverage of silica surface at a given temperature. From adsorption data we obtain that for all used adsorbates above boiling point at the silica surface is held relatively small amount of adsorbate molecules, lower then monolayer coverage. For example, molecular coverage of silica Si-100 surface for various adsorbates at temperature 10 8C higher then their boiling point and p /302 Torr are equal to U /0.75, 0.33 and 0.23 for benzene, n -hexane and carbon tetrachloride, respectively. It means that at all temperatures the adsorbed amount does not exceed a monolayer. Thus, in further calculations the statistical thickness of the surface layer was taken into account. Small surface coverages were observed also by Naono and Hakuman [20] for adsorption of water on hydrophobic surfaces. Similar effect appears in the case when non-polar adsorbate molecules are adsorbed on strongly polar silica surface. Thickness of adsorbate monolayer on silica surface was estimated from van der Waals model ˚ for benzene, n and is equal to 3.4, 4.3 and 7 A hexane and carbon tetrachloride, respectively. Calculated coverages of silica gels under study at various temperatures and for various adsorbates are given in Table 2. The adsorbed amounts for calculations of the surface film thicknesses were taken for p /302 Torr. For example, for temperature corresponding to boiling point of a benzene the end of adsorption
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Table 2 Surface coverages of various adsorbates at different temperatures and p /302 Torr for systems investigated Silica gel
Si-100
Si-60
Benzene
n -Hexane
Carbon tetrachloride
T (8C)
T
T (8C)
U
T (8C)
U
80 90 100 80 90 100
0.95 0.75 0.57 0.91 0.70 0.55
70 80 90 70 80 90
0.43 0.33 0.26 0.41 0.32 0.25
80 90 100 80 90 100
0.29 0.23 0.18 0.29 0.23 0.18
isotherm corresponds to p /p0 :/0.4 and is located near the beginning of capillary condensation. Usually, the surface film thickness present on a given adsorbent surface is estimated from the adsorption data for nonporous solid of the same type. In the case of TG experiment similar estimation is impossible due to very small weight changes of sample characterized by very low specific surface. However, for illustrative purposes, in Fig. 4 are shown segments of thermodesorption curves of benzene for Si-100 silica and macroporous Si-500 ˚ , SBET /69 m2 g 1 and Vp / silica gel (Rp /135 A 3 1 0.68 cm g , data from Ref. [21]). Since the above 100 8C both curves are identical, one can assume that these parts of curves represent desorption of the surface film only. Very steep segments of TG curves at lower temperatures correspond to capillary condensed liquid. The filled points in Fig. 4 indicate recalculated amounts of benzene taken from adsorption isotherms presented in Fig. 3, i.e. the amount of benzene remaining on the silica surface at a given temperature. For our measuring range of temperature the surface film thickness variation against temperature is practically linear. Pore/core size distributions calculated from TG data and nitrogen method for silica gel Si-100 are compared in Fig. 5. In order to estimate the radii of cores for pores evacuated at different temperatures in thermogravimetric experiments, the Kelvin equation calculation should be slightly modified. In TG experiment p is maintained constant and equal to external pressure, whereas p0, VL and g vary with temperature. Temperature relations of these variables can be found in literature [22]. Taking into account the dependence
Fig. 4. Termodesorption curves of benzene from silica gels Si100 and Si-500 and magnitudes of adsorbed benzene at different temperatures for p /302 Torr (points).
of p0, VL and g against temperature appropriate core size distribution was calculated. Dashed line in Fig. 5 represents PSD derived directly from thermal desorption curves using Kelvin equation in the manner described previously [5 /7]. In fact this curve represents distribution of core of pores. Core radii were next corrected in respect to the surface film thickness estimated from adsorption data presented in Fig. 3 (solid line in Fig. 5). Shaded area represents PSD calculated on the basis of nitrogen adsorption data. The thickening of the surface film within temperature range corresponding to TG measurements was taken into account in calculations. Numerical values of the parameters characterizing the porosity of investigated silica gels are collected in Table 2.
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References
Fig. 5. PSDs for silica gel Si-100. Dashed line, PSD derived from thermal desorption of benzene; solid line, PSD corrected in respect to the surface film thickness; shaded area, nitrogen method.
Comparing the results presented in Fig. 5 and Table 2, one can say, that for investigated systems the effect of the surface film is small and changes only slightly the shape of PSD. The best correlation between PSDs from nitrogen adsorption and thermogravimetry is observed in the case of nhexane and carbon tetrachloride. For benzene, which is adsorbed specifically on silica surface forming strongly held surface layer this correlation is less satisfactory. Introduction of corrections in respect to the surface film thickness improves slightly the characteristics of porosity for mesoporous silicas. Mean pore radii derived from liquid nitrogen data and thermal desorption data of CCl4 are close together.
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