Specific Surface Area of Stoeber Silica Determined by Various

The N2 adsorption isotherms at 77 K were analyzed using the BET equation, the modified BET equations of Tóth, and equations of the uniform interpreta...
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Langmuir 2002, 18, 2678-2685

Specific Surface Area of Stoeber Silica Determined by Various Experimental Methods Ma´rta Szekeres,*,† Jo´zsef To´th,‡ and Imre De´ka´ny† Department of Colloid Chemistry and Nanostructured Materials Research Group of the Hungarian Academy of Sciences, University of Szeged, Szeged, Aradi vt. 1, Hungary H-6720, and Institute of Applied Chemistry, University of Miskolc, Miskolc-Egyetemva´ ros, Pf. 2, Hungary H-3515 Received August 29, 2001. In Final Form: December 14, 2001 The specific surface area of amorphous Aerosil 200 and silica particles with 270 nm diameter prepared by the Stoeber method was investigated by a variety of experimental methods: nitrogen adsorption at 77 and 253 K; adsorption from ethanol/cyclohexane mixture; heats of wetting measurements; small-angle X-ray scattering (SAXS) experiments. The N2 adsorption isotherms at 77 K were analyzed using the BET equation, the modified BET equations of To´th, and equations of the uniform interpretation method of To´th. For Aerosil 200, the values of the specific surface varied slightly depending on the applied method. For Stoeber silica, the results from nitrogen adsorption at 77 K ranged between 18 and 24 m2/g; these values were 20-30 times smaller than those derived from N2 adsorption at 253 K, binary liquid mixture adsorption, and heats of wetting or SAXS experiments (439-670 m2/g). The specific surface area of Stoeber silica estimated from nitrogen adsorption measurement at 77 K could not be applied to adsorption data from liquid medium; the other methods, however, provided reliable surface area and charge density values. According to the pore size distribution curves from thermogravimetry, two mean pore diameter values are distinguished (2 and 16 nm), but larger pores also exist in the structure of the Stoeber silica particles. According to the SAXS results Stoeber silica has a mass fractal structure (Dm ) 1.73) on the length scale of 5-25 nm.

Introduction In adsorption experiments it is of crucial importance to obtain the proper estimate of the surface area of the adsorbent that can be reached by the adsorbate molecules in the given adsorption equilibrium. The specific surface area data applied in the calculations of the surface density of the adsorbate, surface charge density, thickness of the adsorption layer, or of thermodynamic properties of the adsorbed layer must reflect the physically real surface area. Generally, specific surface area is determined at solid/gas interfaces mainly from N2 adsorption at 77 K by using the BET equation. Applying the BET surface area in solid/liquid adsorption systems can lead to unrealistic results for surface density of the adsorbate. A widely known example is that the BET surface area of montmorillonite is around 20-50 m2/g determined by N2 adsorption at 77 K but as large as 300-350 or 800 m2/g can be determined in a binary liquid mixture or in organic cation exchange reactions, respectively.1-3 Stoeber silica particles serve as a model adsorbent because of the regular spherical shape of the particles of uniform size. It has been established by several authors (ref 4 and references therein) that Stoeber silica has a microporous structure. Measurement of surface charge density and investigation of cationic surfactant adsorption also reveal that this adsorbent must have microporous and mesoporous compartments in its structure.4 Applying * Corresponding author. E-mail: [email protected]. † University of Szeged. ‡ University of Miskolc. (1) De´ka´ny, I.; Sza´nto´, F.; Weiss, A.; Lagaly, G. Ber. Bunsen-Ges. Phys. Chem. 1986, 90, 422. (2) De´ka´ny, I.; Sza´nto´, F.; Weiss, A.; Lagaly, G. Ber. Bunsen-Ges. Phys. Chem. 1986, 90, 427. (3) De´ka´ny, I.; Sza´nto´, F.; Nagy, L. G. J. Colloid Polym. Sci. 1988, 266, 82. (4) Szekeres, M.; De´ka´ny, I.; de Keizer, A. Colloids Surf. 1998, 141, 327.

BET surface area data to potentiometric acid-base titration results leads to unrealistically high surface charge density. Specific surface area data based on N2 and Kr adsorption isotherms also do not correlate well with the total surface silanol (Si-OH) group concentration determined by 29Si MAS NMR.5 The reasons for the discrepancy between the specific surface area determined in a solid/gas system and the surface area accessible for the adsorptives in solutions can be the following: (i) There is swelling and disaggregation. (ii) Porous and microporous adsorbents and adsorbents with fractal surface exhibit different surface areas for different molecular size adsorptives; the phenomenon is known as the molecular sieve effect.6 (iii) Adsorbate molecules only slightly smaller than the pore diameter of porous adsorbents have insufficient kinetic energy to enter the pores, and the system only reaches quasi equilibrium (activated diffusion).6 (iv) Strong interaction of some adsorptives with the high-energy surface sites, especially at the entrance of pores, can prevent adsorption inside the pores (activated entry).7,8 (v) For adsorbents which are subject to reversible changes in pore size distribution due to temperature changes, the specific surface area at low temperature (77 K) is not necessarily the same as that at high temperature (298 K, ambient temperature). (vi) The classical theoretical adsorption isotherm equations usually underestimate the specific surface area as a result of the inconsistency between these models and thermodynamics of adsorption.9 (5) Labrosse, A.; Burneau, A. J. Non-Cryst. Solids 1997, 221, 107. (6) Dabrowski, A. In Adsorption-its development and applications for practical purposes; Dabrowski, A., Ed.; Elsevier: Amsterdam, 1999; Vol. 1, pp 3-69. (7) Gregg, S. J.; Sing K. S. W. Adsorption, Surface area, Porosity; Academic Press: London, 1967; Chapter 4. (8) Isobe, H.; Kaneko, K. J. Colloid Interface Sci. 1999, 212, 234. (9) To´th, J. Adv. Colloid Interface Sci. 1995, 55, 1.

10.1021/la011370j CCC: $22.00 © 2002 American Chemical Society Published on Web 03/03/2002

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We investigated Aerosil 200 and another silica sample prepared by the method of Stoeber10,11 with a variety of specific surface area assessments methods. By comparing the results of the different experimental and calculation methods, it was possible to find a good estimate of the specific surface area of the Stoeber silica sample accessible for small ions such as protons in an aqueous medium. We used five different experimental methods (gas/vapor adsorption, adsorption from liquid mixture, immersional wetting heat measurements, small-angle X-ray scattering, and thermal desorption of liquids) and a number of theoretical adsorption isotherm analysis methods for specific surface area determination and for the investigation of the adsorbent structure. Experimental Methods Stoeber silica was prepared by the method of Stoeber modified by Matijevic.11 A mixture of 0.79 M NH3, 14.4 M H2O, and 46.5 vol % ethanol was stirred and held at 40 °C to get the hydrolysis product of silica by the programmed addition of 0.2 M TEOS (tetraethyl orthosilicate). The addition of TEOS was controlled in a way that the temperature of the mixture did not rise above 45 °C. Stirring was continued during 30 min. TEOS was obtained from BDH and used without further purification. Analytical grade ethanol (Fluka) dried over molecular sieve and 25 wt % analytical grade ammonia solution from Reanal (Budapest, Hungary) was used. The suspension of the silica particles was purified and concentrated by distillation at 77-80 °C. After distillation, the slurry was washed with deionized water (Millipore, MilliQ RG water purification system), filtered through a Millipore filter of pore size of 0.22 µm several times, and then dried in an oven at 120 °C overnight. The particle size distribution was measured by dynamic light scattering (DLS) using a Zetasizer 4 (Malvern, Worcestershire, U.K.) instrument. The mean particle diameter was 270 nm. According to TEM pictures (OPTON 920 electron microscope, Carl Zeiss, Jena, Germany) the average diameter of the spherical silica particles was 250 ( 40 nm. We have used a commercial silica sample, Aerosil 200 (Degussa AG), as a nonporous, flat surface reference sample. The average particle diameter is 12 nm, and the specific surface area is 200 ( 25 m2/g as given by the manufacturer. TEM pictures reveal the existence of loose aggregates of the primary particles of the size of about 100 nm. Dynamic light scattering measurements also indicated the presence of particle units, with an average hydrodynamic diameter of about 100 nm. The adsorption isotherms of N2 at 77 and 253 K were measured in a Gemini 2375 surface area analyzer (Micromeritics Instruments Corp., Norcross, GA). Prior to measurements the samples were heated at 140 °C for 24 h under a vacuum of about 10-3 mbar. The span of the adsorption isotherm measurement was 1.5 h. Adsorption excess isotherm of ethanol/cyclohexane mixture was determined at 25 °C on dried Stoeber silica, and the adsorption capacity (Schay-Nagy extrapolation method12) was used for calculation of the equivalent specific surface area. For drying, the sample was put into a vacuum oven at 140 °C for 24 h. The change in the composition of the liquid mixture (∆x1) due to adsorption was determined by differential interferometry at 25 ( 0.1 °C. The adsorption excess was calculated by the equation n1σ ) no(∆x1/m), where no is the total molar amount of the liquids and m is the mass of the adsorbent. We estimated the specific surface area from heats of immersion in water and methanol determined in a bath sorption cell of an LKB 2107 sorption microcalorimeter (LKB Instrument GmbH, Bromma, Sweden) at 25 ( 0.01 °C. Aerosil 200 was used as a reference sample of known surface area. The samples were dried (10) Stoeber, W.; Fink, A.; Bohn, E. J. Colloid Interface Sci. 1968, 26, 62. (11) Hsu, W. P.; Yu, R.; Matijevic, E. J. Colloid Interface Sci. 1993, 156, 56. (12) Shay, G. Surface area determination; Proceedings of the International Symposium on Surface Area Determination, Bristol, U.K., 1969; Everett, D. H., Ottewill R. H., Eds.; Butterworth: London, 1970; p 273.

Figure 1. (a) Adsorption isotherms of N2 at 77 K on Aerosil 200 (open symbols, adsorption; filled symbols, desorption branch) and Stoeber silica (open symbols, adsorption branch). (b) Adsorption isotherm of N2 at 77 K on Stoeber silica (enlarged from (a)) (open symbols, adsorption branch; filled symbols, desorption branch). before the measurements in the same way as in the gas adsorption and liquid mixture adsorption experiments. The results are average values of 5-10 experiments. The specific surface area and fractal dimensions were determined by small-angle X-ray scattering experiments using a Kratky slit-collimation compact camera type KCEC/3 (AntonPaar KG, Graz, Austria), attached to a Philips PW1830 X-ray generator, λ(CuKR) ) 0.1542 nm, under He atmosphere. The scattered intensities were measured step-by-step with a position sensitive detector, controlled automatically by a PW 1710 microprocessor and SDC (scattering data controlling) program. The raw scattering functions were normalized and corrected by the normalized scattering function of background. No desmearing correction was applied. We investigated the porosity of Stoeber silica by thermal desorption of water and dried (Merck molecular sieves of 0.4 nm with moisture indicator) cyclohexane from the pores. Thermal gravimetric curves were measured in a Derivatograph Q-1500 D (MOM, Budapest, Hungary), using the quasi isotherm-quasi isobar method, maintaining equilibrium conditions (controlled transformation rate thermogravimetry, CRTG).13 A platinum labyrinth type crucible was used. Stoeber silica was dried before the experiment at 140 °C for 24 h in a vacuum oven. After heat treatment the samples were immersed immediately in the liquids and kept there for 24 h. The weight loss was measured at a heating rate of 5 °C/min. The heating stopped when the weight loss rate exceeded 0.2 mg/min.

Experimental Results The results of the surface area determination and structure analysis of the adsorbents are collected in Tables 1-3. The N2 vapor adsorption isotherms on Aerosil 200 and Stoeber silica adsorbents measured at 77 K (Figure 1a,b) (13) Paulik, F.; Paulik, J. J. Therm. Anal. 1973, 5, 253.

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Szekeres et al. Table 1. Specific Surface Area (m2/G) Values of the Aerosil 200 and Stoeber Silica Resulting from Various Methods of Determinationa method

conditions

A200

Stoeber silica

BET t-plot de Boer BET modified DR cloud F (UI), pr < 0.15 T (UI), pr < 0.1 Bond-Spencer ads from liquid mixture ∆Himm SAXS (Porod plot)

N2/77 K N2/77 K N2/77 K N2/77 K N2/77 K N2/77 K N2/253 K EtOH/cyclohexane

197 194 253 N/A 218 N/A 200 (ref) not measd

18 10 20 21 N/A 24 670 570

MeOH, H2O

200 (ref) 175

452 439

a The specific surface area value for Aerosil 200 of 200 m2/g was used as reference value when indicated as (ref).

Table 2. Structural Characterization of Aerosil 200 and Stoeber Silica: Average Particle Diameter from Dynamic Light Scattering, Micropore Volume from the t-plot Method, Average Pore Diameter from Thermal Gravimetry, and Fractal Dimensions from Gas Adsorption and SAXS Experiments param primary particle diameter (nm)

method

Figure 2. (a) deBoer t-plot of the N2 (77 K)/Aerosil 200 adsorption isotherm. (b) deBoer t-plot of the N2 (77 K)/Stoeber silica adsorption isotherm.

agglomerate diameter (nm) vmp,t-plot (cm3/g) N2/77 K Dm SAXS

are both type II isotherms, expressing multilayer adsorption, without hysteresis loops between the adsorption and desorption branches. The BET linear representation14 in the range of prel between 0.05 and 0.35 has a regression of 0.9996 for the Aerosil 200 and 0.995 for the Stoeber silica. The calculated specific surface area is 197 m2/g for Aerosil 200 corresponding well to the manufacturer data and 18 m2/g for the Stoeber silica. The poor fit between the measured isotherm and the BET equation for Stoeber silica implies the ambiguity of the BET specific surface area result. The analysis of the N2 adsorption isotherm by the t-plot method15 (Figure 2a) shows that Aerosil 200 has a nonporous structure. There are no signs of the presence of micro- or mesopores. Stoeber silica, on the other hand, shows a micropore volume of 0.003 cm3/g, and the volume of N2 adsorbed in the micropores is 2.03 cm3/g STP (Table 2; Figure 2b). The specific surface area from the t-plot method (Table 1) for the Aerosil 200 is equal to the BET surface area, but for the Stoeber silica it is about half of the BET area, indicating the presence of micropores. The results of the analysis of N2 adsorption isotherms at 77 K by the modified BET methods derived by To´th9 are shown in Figures 3a,b and 4a,b. The experimental Ψ(pr) functions

Ds Ds,FHH av dpore (nm)

Ψ(pr) )

f(pr) 1 f ′(pr) p

(1)

have a decreasing part for both adsorbents, characteristic of multilayer adsorption. The best fit of the Ψ(pr) functions (14) Brunnauer, S.; Emmett, P. H.; Teller, E. J. Am. Chem. Soc. 1938, 60, 309.

Aerosil 200

Stoeber silica

manufacturer 12 N/A data DLS no primary 270 particles DLS 100 no agglomerates 0 not mass fractal 2.03 2.60 N/A

SAXS N2/77 K TG

0.003 1.73 2.008 2.65 2, 16, >16a

a There are pores of average diameter of 2 nm and of 16 nm and a series of pores with continuously increasing diameter from 16 nm up to a flat surface.

calculated from the measured f(pr) curves and those calculated by using modified BET equations was searched by finding the minimum value of the relative deviation (δ) between the two series of ns data:

δ)

1 N

[∑( ) ] N

ncs - ns

1

ns

2 1/2

(2)

Here N is the number of measured points, ncs is the adsorbed amount from model calculation, and ns is the measured excess adsorbed amount. The experimental Ψ(pr) function of Aerosil 200 (Figure 3a) is nearly constant (Ψ ≈ 4.5) in the low-pressure range, approximately below pr ) 0.15, indicating that the adsorption isotherm in this range can be described by a Freundlich equation with an exponent of 1/4.5.9 This can be the case if the surface heterogeneity is considerable. The decreasing part of the Ψ(pr) function at pressures above pr ) 0.15 indicates that this part can be described by a multilayer isotherm equation. For a heterogeneous surface, the adsorption in the low-pressure range is mainly monomolecular. For this reason we applied the modification of the original BET equation that supposes that the multilayer adsorption starts only at a given pressure, pr,e ) 0.15, and that the adsorption in multilayers is not a condensation process but has an affinity constant kt different from 1: (15) Lippens, B. C.; de Boer, J. H. J. Catal. 1965, 4, 319.

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Figure 3. (a) Plot of Ψ(pr) functions for the N2 adsorption isotherms at 77 K on Aerosil 200: (b) calculated from the experimental ns-pr functions; (---) calculated from the theoretical BET equation (kt ) 1 and pr,e ) 0); (s) calculated from theoretical modified (To´th) BET equation (kt ) 0.77 and pr,e ) 0.15) in the range of relative pressures between 0.15 and 0.7. (b) Fit of theoretical BET equation and of modified (To´th) BET equation to the measured adsorption isotherm of N2 at 77 K on Aerosil 200.

Θ)

cpr [1 + ktpr,e + (c - kt)pr][1 - kt∆pr]

(3)

pr > pr,e Here kt * 1 and ∆pr ) pr - pr,e. This modification describes well the adsorption in the pressure range 0.15 < pr < 0.7. Above pr ) 0.7, condensation can occur, so that the modified BET equation cannot be applied in this range. In the figure, the Ψ(pr) function calculated from the original BET equation using the best-fit BET constants is also given. The δ values are 0.222 for the BET model and 0.00075 for the modified BET model in the fitted pr ) 0.15-0.7 range. The modified BET model seems to describe more accurately the measured adsorption isotherm (Figure 3b), and the calculated specific surface area is 28% larger than the original BET surface area (Table 1). As can be seen in Figure 4 a, the shape of the theoretical Ψ(pr) functions for Stoeber silica is very sensitive to the choice of the adsorption model. We applied the modified BET eq 3 with the supposition that the adsorption in the second and subsequent layers is a process different from condensation and that the isotherm has a separate monolayer part. We used also the cloud model of To´th9

n1s(pr) ns(pr) ) 1 - kpr

(4)

with the DR (Dubinin-Radushkevic) equation of the

Figure 4. (a) Plot of Ψ(pr) functions for the N2 adsorption isotherms at 77K on Stoeber silica: (b) calculated from the experimental ns-pr functions; (---) calculated from the theoretical BET equation with kt ) 1 and pr,e ) 0; (s) calculated from theoretical modified (To´th) BET equation with kt ) 0.7 and pr,e ) 0.05; (--‚‚) calculated from the theoretical Cloud model with the DR equation. (b) Fit of theoretical BET, modified (To´th) BET, and DR cloud (To´th) equation with the measured adsorption isotherm of N2 at 77 K on Stoeber silica.

adsorption in micropores inserted for the first layer adsorption (n1s(pr)). The best fit between calculated and experimental Ψ(pr) functions was achieved by the use of the DR- cloud model assuming that micropore filling takes place at the lowest relative pressures. The minimum relative deviations of the measured and calculated adsorption isotherms in the entire pressure range (Figure 4b) are δ ) 0.09999, 0.0378, and 0.019 for the BET, BETmodified, and DR-cloud models, respectively. The value of the specific surface area increased by 11% due to the modifications in the BET model and by 17% by applying the DR-cloud model compared with the BET surface area. We applied monolayer UI-isotherm equations, derived by To´th16,17 by the UI (uniform interpretation) method from classical analytical adsorption isotherms, for the monolayer parts of the N2/77 K adsorption isotherms on Aerosil 200 and Stoeber silica. Since the experimental Ψ(pr) function of the N2 adsorption isotherm at 77 K on Aerosil 200 at low pressures is constant, the UI method for the Freundlich isotherm equation can be applied to this part of the isotherm:

Θ)

( ) 1 pm

1/n

p1/n

(5)

The specific surface area according to this analysis method is larger by 11% than the BET surface area (Table 1). The minimum relative deviation between the measured and (16) To´th, J. J. Colloid Interface Sci. 1993, 163, 299. (17) To´th, J. Colloids Surf. 1993, 71, 233.

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Figure 5. Fit of the theoretical T (UI) equation with the measured adsorption isotherm of N2 at 77 K on Stoeber silica in the low-pr range.

Figure 6. Adsorption of N2 at 253 K on Aerosil 200 and Stoeber silica. The slopes are 1.97 × 10-4 for Stoeber silica and 5.88 × 10-5 for Aerosil 200. The intercept of the lines is set to 0.

calculated ns values is δ ) 0.0022 in the corresponding pressure range (pr < 0.15). The separate analyses of the monolayer and multilayer parts of the isotherm led to somewhat different specific surface area values, but both were significantly larger than the BET surface area. In contrast to Aerosil 200, the N2 adsorption isotherm at 77 K on Stoeber silica had an increasing Ψ(pr) function at low pressures. In Figure 5, the fit between the monolayer part of the adsorption isotherm and the T(UI) equation (uniform interpretation method applied to the To´th isotherm equation)

Θ)

(1 + 1/KT)1/mpr (1/KT + prm)1/m

(6)

can be seen at relative pressures pr < 0.1. KT and m are the constants of the To´th equation. The minimum relative deviation obtained by this analysis method is δ ) 0.011, giving the best agreement between theory and experiment among the applied methods. The specific surface area from this analysis is larger by 33% than the standard BET area. The Henry-law-range adsorption isotherms (N2 adsorption measured at 253 K) on Aerosil 200 and on Stoeber silica are shown in Figure 6. The adsorption isotherms deviate from linear at 100 Torr for the Aerosil 200 and at 200 Torr for the Stoeber silica. We analyzed the p < 100 Torr part of the isotherms. The first measured points deviate from the linear trend possibly because the pressure drop due to adsorption is in the range of the accuracy limit of the determination. On the basis of the analysis method of Bond and Spencer,18 the surface area of Stoeber silica is 670 m2/g (Table 1), in reference to the known

Figure 7. Adsorption excess isotherm of ethanol (1)-cyclohexane (2) mixture on Stoeber silica. The Schay-Nagy linear extrapolation method yields ns1,m ) 2.38 mmol/g and ns2,m ) 0.86 mmol/g.

surface area of Aerosil 200. At 253 K, the adsorption is higher on Stoeber silica than on Aerosil 200, opposite to the adsorption order at 77 K (Figure 1a). The excess adsorption isotherm of ethanol/cyclohexane mixtures on Stoeber silica at 25 ( 0.5 °C, together with the Schay-Nagy extrapolation12,19-23 of the linear part of the isotherm, can be seen in Figure 7. The resulting specific surface area, the so-called equivalent specific surface area from this method, is 570 m2/g (Table 1). The heats of wetting data at 25 ( 0.01 °C lead to 452 m2/g for the surface area of the Stoeber silica, in reference to the known specific surface area of Aerosil 200 (Table 1). The measured heats of immersional wetting in methanol and water are nearly the same in the case of both adsorbents: 31 ( 3 J/g (in methanol) and 32 ( 3 J/g (in water) for Aerosil 200 and 70 ( 5 J/g (both in methanol and water) for Stoeber silica. Small-angle X-ray scattering24,25 gives a specific surface area as large as 439 m2/g for the Stoeber silica, but for Aerosil 200 it corresponds well with the BET specific surface area, 175 m2/g (Table 1). The scattering functions for the two adsorbents are shown in Figure 8, and the Porod plots of these functions in Figure 9. The results of the fractal analysis from SAXS experiments26 are reported in Table 2. Aerosil 200 has a smooth surface (Ds ) 2.03) in the range of 1-10 nm. Stoeber silica can be characterized by mass fractal dimension, Dm ) 1.73, in the 5-25 nm range and with smooth surface (Ds ) 2.008) in the 0.5-4 nm range. The Porod constant Kp, the first moment M1 of the scattering curves,27-31 and the correlation lengths of the solid phase (l1) and of the gas phase (l2), together with the average correlation length values (lc)27,28,31 for (18) Bond, R. L.; Spencer, T. H. Proceedings of the Third Biennial Conference on Carbohydrates; Pergamon: Oxford, U.K., 1959; p 357. (19) De´ka´ny, I.; Sza´nto´, F.; Nagy, L. G.; Fo´ti, G. J. Colloid Interface Sci. 1975, 50, 265. (20) Schay, G.; Nagy, L. G. Period. Polytech. 1960, 4, 45. (21) Schay, G. Surface and Colloid Science; Matijevic, E., Ed.; Wiley: London, 1969; Vol. 2, p 155. (22) De´ka´ny, I.; Nagy, L. G.; Schay, G. J. Colloid Interface Sci. 1978, 66, 197. (23) De´ka´ny, I.; Sza´nto´, F.; Nagy, L. G. Colloid Polym. Sci. 1978, 65, 125. (24) Guinier, A.; Fournet, G. Small Angle Scattering of X-rays; Wiley: New York, 1955. (25) De´ka´ny, I.; Turi, L. Colloids Surf. 1997, 126, 59. (26) Kriechbaum, M.; Degovics, D.; Tritthardt, J. Prog. Colloid Polym. Sci. 1989, 79, 101. (27) Glatter, O.; Kratky, O. Small-Angle X-ray Scattering; Academic Press: New York, 1982. (28) Porod, G. Kolloid Z. 1951, 124, 83. (29) Porod, G. Kolloid Z. 1952, 125, 1. (30) Kratky, O. Angew. Chem. 1960, 72, 467. (31) Janosi, A. Monatsh. Chem. 1993, 124, 815.

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Figure 8. Small-angle X-ray scattering curves of Aerosil 200 and Stoeber silica.

Figure 9. Porod plot of the small-angle X-ray scattering curves of Aerosil 200 and Stoeber silica.

Figure 10. FHH analysis of N2 (77 K) adsorption isotherms on Aerosil 200 and Stoeber silica. The Ds fractal dimensions (data shown in Table 1) are calculated in the capillary condensation range starting from the second adsorbed layer in the 0.7-9.4 nm range for Aerosil 200 and 0.73-7.43 nm range for Stoeber silica. Table 3. Calculated Small-Angle X-ray Scattering Parameters for Aerosil 200 and Stoeber Silica

a

param

Aerosil 200

Stoeber silica

KP (Cps/nm-3)a M1 (Cps/nm-2) lc (nm) l1 (nm) l2 (nm)

176.8 1858.5 20.5 10.9 245.2

202.8 814.2 13.4 4.3 54.9

Cps, counts per second.

the two solids, are listed in Table 3. For Aerosil 200 the l1 value (10.9 nm) corresponds well with the primary particle diameter (12 nm). The l1 value for the Stoeber silica (4.3 nm) is much smaller than the average particle diameter (about 270 nm).

Figure 11. (a) Plot of the weight loss due to heating of Stoeber silica impregnated by cyclohexane and water. (b) Pore radius distribution calculated from TG curves due to evaporation of cyclohexane and water from the pores of Stoeber silica.

In Figure 10 and Table 2 the results of the surface fractal analysis of N2 adsorption isotherms at 77 K by the fractal FHH method32,33 are shown. On the length scale of N2 adsorption/condensation the two adsorbents show fractal surfaces with a nearly equal dimension, 2.60 for Aerosil 200 and 2.65 for the Stoeber silica. The results of thermogravimetric analysis of Stoeber silica are shown in Figure 11a,b. In the thermogravimetric curves (Figure 11a) the evaporation of bulk cyclohexane and water can be seen from the large weight loss at the boiling points of the two liquids, 80.74 °C for cyclohexane and 100 °C for water. Evaporation of the bulk cyclohexane was observed in fact at a temperature lower by 1-2 °C than the boiling point. The reason for this is not clear. By increasing the temperature, evaporation from the pores takes place. Pore size analysis according to the Kelvin equation34 showed that Stoeber silica has a narrow distribution around d ) 2 nm from water evaporation and another, wider distribution approximately from d ) 14 nm to d ) 18 nm from cyclohexane evaporation (designated as average dpore (nm) ) 2, 16 in Table 2). Except for the pores with distinct pore diameters, as it can be seen from the pore size distribution curves (Figure 11b), in Stoeber silica there are large amounts of liquid evaporating from curved surfaces with continuously increasing radius of curvature. Consequently, a continuous range of pore sizes exists possibly up to the macropore size range (designated as average dpore (nm) >16 in Table 2). Discussion As it has been shown earlier,5 the very low BET specific surface area of the Stoeber silica does not correlate with (32) Pfeifer, P.; Wu, Y. J.; Cole, M. W.; Krim, J. J. Phys. Rev. Lett. 1989, 62, 1997. (33) Ismail, I. M. K.; Pfeifer, P. Langmuir 1994, 10, 1532.

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its charging and adsorption properties in aqueous media. The surface charge density of a Stoeber silica (similar to the sample prepared in the present work) determined by potentiometric acid-base titration5 is 0.8 mmol/g, at pH ) 9 in the presence of 0.1 mol/dm3 KNO3 indifferent electrolyte. Relating this value to the BET specific surface area of 43 m2/g determined in N2 adsorption experiment at 77 K would lead to a density of charged surface silanol groups as high as 11 sites/nm2. The surface charge density data for the Stoeber silica sample described in this work is also 13 sites/m2, under the same solution conditions. Potentiometric acid-base titration (not shown here) gives 0.4 mmol/g for the amount of deprotonated OH groups on the silica at pH ) 9 and I ) 0.1 M ionic strength, and the BET surface area (Figure 1b and Table 1) is 18 m2/g. The above charge density values are comparable with the largest total (charged + noncharged) surface OH group densities among the values determined by different methods on different silica samples.35,36 For Aerosil 200 on the other hand, using the BET specific surface area leads to a reasonable result for the density of dissociated surface OH groups, about 4 sites/nm2,37 under the same titration conditions. Clearly, it is not relevant to use the standard BET surface area result for Stoeber silica particles in liquid-media dispersion. We made a series of advanced analysis of the N2/77 K adsorption isotherms by using the method of To´th to get better results using model suppositions approaching more closely the real physical system characteristics than the BET suppositions do. In Figures 3-5 it can be seen that with the use of the approach of To´th to model the adsorption systems we could describe the adsorption isotherms very well in a wide range of pressures both for the Aerosil 200 and Stoeber silica adsorbent. The analysis methods of adsorption isotherms derived by To´th resulted in higher calculated surface areas for both adsorbents, in accordance with the theory behind the To´th methods. The modifications lead to an increase in surface area by 28 % for the nonporous Aerosil 200 and by 33 % for the microporous Stoeber silica at best fits (see data in Table 1). However, even the higher surface area value for Stoeber silica is not adequate, since the resulting charge density value would be still unrealistically high, 10 sites/nm2. This means that the surface area tested by adsorption of N2 at 77 K does not correspond with the surface area relevant in the surface charging process in aqueous media for the Stoeber silica, irrespective of the analysis method used to describe the isotherm. The adsorption isotherm of N2 at high temperature was determined to apply the method of Bond and Spencer18 for specific surface area estimation of Stoeber silica. The resulting value of 670 m2/g is 30 times larger than the BET area. The adsorption behavior of N2 at 253 K is different from that at 77 K. It is much larger on Stoeber silica than on Aerosil 200 (Figure 6), in contrast to the adsorption order at the low temperature. Thus, we can suppose that parts of the Stoeber silica surface become available for the nitrogen at the higher temperature, which are unaccessible at low temperature. This effect was described earlier as the activated entry and activated diffusion effect.6-8 It can be calculated6 that at 87 K 500 times more molecules can pass the narrow sections of the (34) Dabrowsky, A.; Leboda, R.; Goworek, J.; Garbacz, J. K. In Adsorption on New and Modified Inorganic Adsorbents; Dabrowsky, A., Tertykh V. A., Eds.; Elsevier: Amsterdam, 1996; Chapter 3.1. (35) Iler, R. K. The Chemisrty of Silica; John Wiley and Sons: New York, 1979; p 631. (36) James, R. O.; Parks, G. A. Surface and Colloid Science; Matijevic, E., Ed.; Plenum: New York, 1982; Vol. 12, p 119. (37) Tomba´cz, E.; Szekeres, M.; Kerte´sz, I.; Turi, L. Prog. Colloid Polym. Sci. 1995, 98, 161.

Szekeres et al.

structure of a microporous material than do at 77 K. In the method of Bond and Spencer the adsorption is related to that on the surface of a nonporous adsorbent, the effectively available surface of which does not change with temperature. Supposing that the state of the adsorbate on the two surfaces is identical (that is, the surface density of the adsorbate is also equal), the available surface area of the microporous adsorbent can be determined relative to the known value of that of the nonporous adsorbent. However, it is not proven that the state of N2 on the flat surface of the Aerosil 200 and in the pores of Stoeber silica correspond to one another. Thus, the above result can be considered only as a strong indication of the presence of a large internal surface area in Stoeber silica, not available for nitrogen at the commonly applied isotherm temperature. Acknowledging the weaknesses of the surface area determination of microporous adsorbents by the method of Bond and Spencer, the authors “do not claim, that the reliability of their values is better than 4-fold”7). The measured heats of immersional wetting in water are approximately equal to the heats of wetting in methanol for both adsorbents: ∼32 J/g in methanol and water for Aerosil 200 and 70 J/g in methanol and water for Stoeber silica. This suggests that the energetic properties of the two surfaces may be rather similar. Thus, the specific heats of wetting for the two silicas can be supposed to be equal. For Aerosil 200, the specific heat of wetting either in water or in methanol is 160 mJ/m2, calculated for the known specific surface area. Using this value of specific heat of wetting, a specific surface area value of 452 m2/g can be calculated for the Stoeber silica (Table 1). The surface energetic similarity of the two solids can also be considered as an argument for the reliability of the method of Bond and Spencer for surface area estimation from the Henry law range part of the N2 gas adsorption isotherms. Both the Bond and Spencer method and the method of calculation from specific heats of wetting are relative methods. To apply them, measured values have to be related to ones obtained for an adsorbent with flat surface (known surface area) but with similar adsorption properties in relation to the used adsorbate. In Figure 7, from the ethanol/cyclohexane liquid mixture adsorption excess isotherm on Stoeber silica, it is seen that ethanol (x1 is the mole fraction of ethanol) adsorbs preferentially and that the isotherm has a linear part in the mole fraction range of 0.05-0.5. In this middle range of liquid mixture composition the thickness of the adsorbed layer can be considered constant, as a first approximation. More rigorous analysis of the excess isotherms shows that the linearity in the decreasing part is connected with the low accuracy of the experimental concentration determination at high solution concentration.38,39 We use the Schay-Nagy extrapolation method since it gives satisfactory approximation for the accessible surface area in liquid mixtures. If there is a need of a more exact analysis, models suitable for heterogeneous surfaces are preferable. From the adsorption excess isotherm and cross sectional area (am,1) of ethanol it is possible to calculate the equivalent specific surface area of the adsorbent: aseq ) n1,0sam,1, where n1,0s is the adsorption capacity of the pure component 1. The value of n1,0s can be found by extrapolating n1s to x1 ) 0. Our result presented in Table 1 is based on the surface coverage value extrapolated to the state when only ethanol would be present at the interface. It is likely that for ethanol molecules the inner pore space is also available (38) Rusanov, A. I. Phase Equilibria and Surface Phenomena; Izd. Khimia: Leningrad, Russia, 1967. (39) Bering B. P.; Izv. Akad. Nauk SSSR, Ser. Khim. 1970, 6, 1232.

Specific Surface Area of Stoeber Silica

at the temperature of isotherm. The Schay-Nagy linear function was used for approximate estimation of the ethanol uptake by the Stoeber silica. A more exact way of the assessment of the adsorption capacity is to use equations that are more suitable for adsorption on heterogeneous surfaces since the silica adsorbent can be regarded as heterogeneous. Small-angle X-ray scattering gives a measure of the total internal surface area in the case of porous adsorbents if the characteristic length of electron density fluctuations (l) coincides with the range of scattering angles (q), so that 0.1 e ql.40 In our SAXS experiments structural information could be obtained in the range of 1-100 nm, corresponding well with the dimensions of Aerosil 200 particles (average particle diameter is 12 nm) and the possible range of the pore dimensions inside the Stoeber silica spheres of 270 nm diameter. The specific surface area for Stoeber silica from this method corresponds well with the results of the method of Bond and Spencer, adsorption from ethanol/cyclohexane mixture, and heats of immersional wetting (Table 1), being more than 1 order of magnitude higher than the BET surface area. From SAXS results, valuable structural information could be obtained for the two silica samples. The small correlation length of the solid phase (l1 ) 4.3 nm) compared to that of the gas phase (l2 ) 54.9 nm) in the case of the Stoeber silica (Table 3) reveals that the particles have highly porous structure that is characteristic of typical mass fractal objects.40 This result agrees very well with the findings of Brinker and Scherer41 that silica particles prepared from TEOS in base-alcohol-mixed media have a structure of a random walk polymer chain or a randomly branched polymer chain. This picture corresponds well with the mass fractal dimension from SAXS, dm ) 1.73 (Table 2), showing that this adsorbent has a highly fractal structure. We tried to test the fractal structure of the surfaces of the two adsorbents by using the N2/77 K adsorption isotherms for fractal FHH analysis. This result (Figure 10 and Table 2) shows that, in contrast to the SAXS experiments, N2 adsorption isotherms at 77 K cannot be used to distinguish between Aerosil 200 and Stoeber silica concerning their structural properties. The FHH analysis of N2 adsorption isotherms at 77 K suggests that both adsorbents have fractal surface with the same fractal dimension and that their structure is not different. On the basis of the SAXS experiments, both adsorbents have nonfractal surface, but their bulk structure is very different, Aerosil 200 being nonporous, nonfractal and Stoeber silica having a solid network structure with massfractal property. The pore structure of Stoeber silica is complex, which is characteristic of mass-fractal objects. Pores of different sizes and shapes fill the space between the chains of the solid network. It can be supposed that activated entry of gas molecules at the narrow necks of such a structure is possible. The results of thermal desorption of water and cyclohexane (Figure 11a,b and Table 2) can be explained by the presence of such a complex pore structure. Cyclohexane desorbs from pores mainly of diameter of around 16 nm but not less than about 2.5 nm. Likely it does not penetrate (40) Schmidt, P. W. In The Fractal Approach to Heterogeneous Chemistry, Surfaces, Colloids, Polymers; Avnir, D., Ed.; Wiley: Chichester, U.K., 1992; Chapter 2.2. (41) Brinker, C. J.; Scherer, G. W. J. Non-Cryst. Solids 1985, 70, 301.

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into the smallest pores. Water penetrates into pores of 2 nm. Large amount of liquid desorbs continuously however from surfaces with much smaller curvature at lower temperatures. The presence of a series of pore diameters, i.e., inner surfaces of continuously changing curvature, corresponds with the picture of the inorganic polymer network structure41 of the Stoeber silica. Conclusions For Stoeber silica of the diameter of 270 nm neither the shape of the N2/77 K isotherm nor the t-plot method reveals microporous structure or a structure in which the presence of micropores would be the main characteristic feature. Thus, the indication for using experimental methods other than the standard BET method to determine the total accessible surface of the adsorbent (or the density of reactive sites at the interface of this solid with a fluid medium) is not evident. The calculated BET surface area is very small, irrespective of the analytical method applied to analyze the low-temperature N2 adsorption isotherm. Nevertheless, surface proton dissociation reaction in acidbase titration experiment gives a large value of specific charge for Stoeber silica. It must then be supposed that this amount of charge must find a place inside such pores, which cannot be accessed by nitrogen at low temperature but are open for protons in aqueous media at room temperature. Our experiments showed that there are other methods, in principle investigations conducted at higher temperatures (-20 °C and room temperature), which lead to such surface area data that can be successfully used for calculation of the charge density in aqueous medium. All the higher temperature experimental methods used by us (N2 adsorption isotherm measured at 253 K, adsorption from liquid mixture ethanol/cyclohexane at 25 °C, measuring heats of immersional wetting at 25 °C, and analysis of small-angle X-ray scattering at room temperature) lead to surface area data 20-30 times larger than those determined from the N2 adsorption isotherms at 77 K. Structural investigation of the Stoeber silica sample (pore size analysis by differential thermogravimetry and fractal analysis of small-angle X-ray scattering curve) implies that this adsorbent has a complex pore structure. The spheres are only partly microporous; other pore diameters are present too. The solid structure is mass fractal. Mass fractals are solid tubular systems, the inverse form of the classical porous systems where the pores are distributed in the bulk of the solid phase. We suppose that the behavior of Stoeber silica in conventional nitrogen adsorption experiment at 77 K, where the inner surfaces are not available for N2, can be a consequence of its inverse complex pore structure. The N2 adsorption isotherm is not characteristic of microporous systems because the micropores present only a part of the total pore structure. Considerable fraction of the pores is in the mesopore and macropore range, as it is seen from the liquid desorption experiments. In such a system it is possible that narrow necks can be present and passing them to get inside the big poles of the solid network requires high energy for the adsorbate molecules that can be achieved, for example, by increasing the temperature. The total surface area of Stoeber silica relevant at ambient temperature can be estimated from experiments at higher temperatures than the conventional BET temperature using probes corresponding in size with the range of pore sizes. LA011370J