“Gradient method” for surface area estimation by benzene vapour adsorption at temperatures below the freezing point

“Gradient method” for surface area estimation by benzene vapour adsorption at temperatures below the freezing point

207 CaHoids and S~~jaces, 62 f 1992) 207-2 i 3 Elscvicr Science Publishers B.V., Amsterdam “Gradient method” for surface area estimation by benzene ...

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207

CaHoids and S~~jaces, 62 f 1992) 207-2 i 3 Elscvicr Science Publishers B.V., Amsterdam

“Gradient method” for surface area estimation by benzene vapour adsorption at temperatures below the freezing point Akira Nonaka Institute

of Applied

Physics,

University

of Tsukuba.

Tsukuba

305, Japan

(Received 24 June 1991; accepted 30 August 1991) Abstract it was found that benzene vapour, as welt as low alkylbenzcne vapours, might bc applicable to the “gradient method” of surl&c arca estimation in which the gradient of the linear portion in Type II adsorption isotherms obtained for most samples is equal to the morolnycr capacity of adsorption. This was ascertained by compuring the surface areas estimated by the method with N,/BET arcas, using several typical solid samples. Although it is :heoretically necessary that the adsorbed molecules used for the method are liquid-!ikc on the multiadsorption layer, the benzene vapour could be used at 0 C, ix. below the freezing point, 5S”C. To clarify this discrepancy, the adsorption experiments for benzene vapour wcrc carried OUI at temperatures much lower than the ireezing point, i.e. down IO -45°C using typical solid samples (gold and silicate glass). The experiment-l results showed that in the relative pressure range 0.2-0.4, where the saturation vapour prcssurc of the supercooled benzene calculated from the Antoine equation was adopted as the relative pressure standard, the adsorbed benzene molecules might be in a supercooled liquid state, because it was found that the isotherms at various temperatures below the freezing point coincided with each other in the relative pressure range 0.2-0.4, and that the isosteric heats of adsorption wcrc nearly equal to the heat of liquefaction of benzene vapour. Kqw~rris:

Bcnzcne

vapocr;

grudicnt

method;

supercooling

liquid; surface area estimation.

Introduction

The “gradient method” for the estimation of solid surface areas, which involves the adsorption of the vapour of low alkylbenzenes, such as toluene, n-butylbenzene, ethylbenzene, and has been reported [l-5]. In this method, the monolayer volumes of adsorption were taken to be equal to the gradient of the linear portion [du/d(P/P,), where D is the amount adsorbed, P the vapoul pressure, and PO the saturation pressure] found in Type II adsorption isotherms [6] exhibited by these adsorbates on most solid surfaces. The applicability of benzene vapour itself has only been fully tested for two solid samples: mica plates and aluminium foil; in both cases benzene vapour was found to be applicable in practice (Table 1). In this 0 I66-6622/92/SO5.00

(cj 1992 -

Elscvicr

Science

Publishers

study of the adsorption of benzene vapour on several other types of solid samples, it was found that benzene vapour might be applicable to the gradient method for most solid samples. This fact was verified by comparing surface areas from the gradient method with standard N,/BET surface areas [7]. This adsorption experi;::-nt for verifying the effectiveness of the gradient meihod when using benzene vapour was carried out at O”C, as in the case of low alkylbenzene vapours, although the temperature was lower than the freezing temperature of benzene. In the method with benzene vapour, however, when the vapour pressure of supercooled liquid benzene estimated by the Antoine equation [S], which has been generally used for obtaining liquid vapour pressures, is used as the relative pressure standard instead of the B.V. All rights

reserved.

208

frozen benzene vapour pressure at 0°C the estimation of the surface areas might be improved. The theory for the gradient method claims that, on a multimolecular adsorption layer, represented by the linear portion of Type II isotherms, the adsorbed molecules used for the gradient method must have molecular kinetic freedom almost similar to that of the corresponding liquid surface molecules [2]. Under this theoretical assumption, the gradient values might be equal to the monolayer volumes and the surface areas could be calculated from the monolayer volumes and the cross-sectional molecular area calculated from the density of the adsorbate liquid. In fact it was found that the heat of adsorption of the alkylbenzene vapours in the region of the linear pcrtion of the isotherms for most samples was very similar to the heat of liquefaction of the vapour, from the experimental finding that the gradients at the linear portion of the isotherms were constant with a change in the adsorption temperature near 0°C. It may be because the alkylbenzenes hitherto used for the gradient method have a comparatively high boiling point (about l OO-200°C) and a low freezing point (about - 100°C) and were used at a temperature of O”C, which is near the midpoint between the boiling and freezing points. The applicability of benzene vapour for the gradient method at O”C, which is lower than the freezing point, suggests that benzene molecules adsorbed on the solid surface in the region of the linear portion of the multilayer adsorption maintain their liquid state in a supercooled condition. To verify this assumption, experiments involving the adsorption of benzene vapour were carried out from room temperature to temperatures well below the freezing point of benzene, i.e. -40 to -45”C, using fine crystalline powdered gold and porous silicate glass as typical solid samples. The experiments showed that from the estimated isosteric heat of adsorption, which was nearly equal to the heat of liquefaction, the benzene molecules adsorbed in the region of the linear portion (a relative pressure of 0.2-0.4) of Type IT isotherms maintain a supercooled liquid state even at temper-

atures much lower than the freezing point. This fact made us understand that benzene vapour also could be applied to the gradient method for estimating solid surface areas. The fact that adsorbed molecules at temperatures below the freezing point may maintain a supercooled liquid state has been reported for several substances, e.g. argon [9], ni?rogen [IO], and water [l I,1 2-J. Benzene has also been reported to be in a supercooled liquid state under adsorptive conditions on some solids, e.g. silica gel at temperatures below the normal freezing point [ 131. In this paper, however, the existence of a supercooled liquid state of the benzene adsorbate on nonporous solids such as crystalline gold !.s shown in connection with the gradient method for surface area estimation, in the region of multilayer adsorption. Experimental

For the measurements of the adsorption of both nitrogen and benzene vapour, an apparatus similar to that used in a previous study C4,5] for low alkylbenzene vapour adsorptions was employed (Fig. 1). It was constructed from metals only, such as stainless steel, with copper or nickel gaskets. The volume of the gas burette, made of a metal bellows, was able to be changed by 200 ml from the outside by using a handle, in order to maintain a constant pressure so as to measure the amount adsorbed (or desorbed) when the adsorbate vapour is introduced from (or into) the gas burette into (or from) the sample tube. The volume change was measured by weighing the volume of liquid (ethylene glycol) transferred between the vessel and the inside of the bellows, on an electrobalance, with a precision of + 1 ~1. By using the bellows as a gas burette, the amount adsorbed on the inside surface was constant, or cancelled out under constant vapour pressure. The pressure gauges used were the T-Series/l 37 I-22 (Sensotec-Sokken, Tokyo) at higher pressures (for nitrogen adsorption) and the SSP/806 (Sensotec-Sokken, Tokyo) with a

A. Nonnka/Colloids

Srtrjaccs 62 (1992) 207-213

209

Solid samples

T[ il 7

13d

.:, L 2

I

J!2+,

p6-1

The powdered solid samples used in this experiment are shown in Table 1. Sodium chloride and calcium carbonate samples were prepared by miliing lar,$e-scrik single crystals. Aiuminium oxide and zirconium oxide were of reagent grade and were commeici~ily available. C-22 was a diatoma~01:s firebrick powder (SO- 100 mesh, Johns Manvilie, NY, E.J%). The porous glass sample was a powder of C’FG- IO- 1000 (Electra-nucieonics, NJ, USA), having uniformly controlled pores of about 1000 A [ :4]. The gold sample was a fine, dry powder crystdliized in the form of platelets, prepared by reducing an aqueous solution of hydrochloroauric acid with a salicyiic acid solution [15]. Sample arear over 5 m2 and 3 m2 were used for nitrogen adsorption and benzene vapour adsorption, respectively. These soiid samples were outgassed in the sample tubes in vacua at 150-200” C, llsually overnight.

r

w

1

Fig. 1. Schematic diagram of adsorption mcasurcment apparatus. I, gas burette: 2. clcctrobalancc; 3 and 4, pressure gauges; 5, air bath: 6, sample tube; 7. adsorbate boiler; 8 and 9, liquid baths; 10 and 11, thernzccia!s; 12 and 13, gas cylinders (Hc and N,); 14, liquid nitiogcn trap; 15, turbo-molecular pump; IG. rotary pump.

precision of + 5 - 10e4 Torr, at lower pressures (for benzene vapour adsorption}. The gas burette, pressure gauges, connection valves, etc. were maintained at 30°C in an air bath. The liquid benzene boiler and the sample tube were thermostatted between room temperature and -5Q*C with a liquid (ethanol) bath ( f O.O2”C), or at 77 K with a liquid nitrogen bath. In the vacuum line, a turbomolecular pump (50 1 s- ‘) was used.

Adsorbates

Benzene was distilled twice, dehydrated with sodium wire, introduced into the boiler with 10 g

TABLE I Comparison

of BET surface arcas (SDET) with gradient method surface arcas (Sprld) using benzene and low alkylbcnzcne her

(m*g- ‘1

Sample

N2

Aluminium oxide Zirconium oxide Porous glass c-22 Calcium carbonate Sodium chloride Gold Aluminium (foil) Mica (ptates)

0.647 22.7 22.6 3.74 1.53 0.306 0.789

“Average value. bRatio to geometrical area. values for nitrogen. =&ET values for benzene. dGlET

181) 143) 129) (68) (50) (90) (38)’

vapours

SErad (mZg- ’ 1

SOr.dlSE;IET

Benzcnc

Benzene

Benzcnc

Low alkylbenzenc”

0.429 (38 l)d 13.0 (114)d 14.2 (2Ud 2.18 (3OY 0.844 (49)d 0.085 (4.3)d G.433 (24)d

0.595 22.5 27.0 3.61 1.64 0.291 0.839

0.92 0.99 I.19 0.97 1.07 0.95 1.06 0.96 1.OSb

0.99 1.16 0.80 0.99 I .oo 1.20 I.12

1.oo

210

of anhydrous calcium sulphate under a helium atmosphere, and after solidifying iii a liquid niirogen bath was degassed until the vapour pressure at 0°C became constant (24.3 Torr). The purities of helium and nitrogen used were 99.9999% and 99.9995%, respectively. Results and discussion Comparison of N,/ LL ‘I .- 1- surface area with a benzene vapourjgradieut method surface area

Aii the adsorption isotherms of benzene vapour for solid samples tested al 0°C were Type II (similar to Type III [6] for some samples, i.e. sodium chloride), having a linear portion at relative pressures from about 0.2 to 0.4, where the relative pressure standard was the presumed saturation pressure of supercooled liquid benzene at 0°C (Pp). The monolayer capacities of adsorption (V,) were assumed to be equal to the gradients of the linear portion, i.e. V,=dv/d(P/PF), where v is the amount adsorbed and P is the adsorbate pressure. The surface areas were estimated using the monolayer capacities and the molecular cross-section, calculated from the density of liquid benzene, 30.4 A2 [ 161 (gradient method). A comparison of N,/BET surface areas with benzene vapourlgradient method surface areas is shown in Table 1. The table also shows the CsEr values [7] for nitrogen and benzene vapour as well as a comparison of their SnET values. A large amount of benzene vapour adsorptive data and the appiications of the BET method have been reported by many authors [!6]. From the table, it can be seen that the benzene vapour/gradient method surface areas coincide with the N,/BET surface areas with a difference of up to f20% at most, although the N,/BET surface areas are thought to have a fairly large error, -1_10% or more in some cases [ 161. The vapour pressure of benzene at 0°C which is the temperature of the adsorption measurement, is 24.3 Torr, i.e. that measured in equilibrium with solid benzene. However, the vapour pressure of

A. NorrakalColloids SurJaces 62 ( 1992) 207-2 I3

supercooled liquid benzene at 0°C (Pp) is estimated in be 26.4 Torr by using the Antoine vapour pressure equation [S]. As mentioned later, since the molecules adsorbed at the linear portion of the isotherm may be in a liquid state, the supercooled liquid vapour pressure was adopted as the relative pressure standard for the estimation of surface areas by benzene vapour. The deviations of the benzene vapour/gradient method surface areas from the N,/BET surface areas for various solid samples were similar to those obtained using low alkylbenzene vapours. Although the gradient method surface area for porous glass was somewhat larger than the N,/ BET surface area, it has been found that the gradient method surface area for a glass plate sample using toluene [2], or n-butylbenzene vapour [4] agreed very well with the geometrical surface area. For a C-22 (diatomaceous firebrick) sample, which was thought to have micropores on the surface, benzene vapour brought the gradient surface area nearer to the N,/BET area than low alkylbenzenes, perhaps because of the difference in the sizes of the molecules used, since the gradient method surface area might measure an external surface area [16]. For sodium chloride samples, other than the sample in the table which was prepared by milling at fairly high temperatures, the ratio of the gradient surface area to the N2/BET surface area was found to be very low, i.e. 0.65. It was found, however, that by the as-plots analysis [16,17], in which the sodium chloride sample in the table was used as the standard, these samples had fine micropores on the surface and the external surface area was very simiiar to the gradient surface area estimated. The micropores were so fine that preadsorption by benzene vapour for these samples did not lower the NJBET surface area. The details for the anomalous sodiutn chloride samples wili be reported later. Saturation pressure and heat of liquefaction (or solidijcation) of benzene vapour below 0” C

Prior to the adsorption experiments, the saturation pressures of benzene at 10 to -45°C were

A. Nonaka/Colloids Surf&s

62(1992)207-211

measured with use of the adsorption measurement apparatus by thermostatting the benzene adsorbate boiler at the temperature to be measured. When the temperature of the boiler wds lowered gradually from the higher temperature, supercooling of liquid benzene was observed do-wn to about 2”C, although the solidifying temperature was determined to be about 55°C by extrapolating the saturation pressure-temperature curve upward. In Fig. 2, the plots of In P, vs. I/T (P, is saturation pressure and T the temperature) are shown with the adsorption isosteric curves of crystalhne gold samples. However, the vapour pressures of supercooled

3.6

211

liquid benzene, PI, up to -45°C were estimated from the Antoine vapour-pressure equation, In P, = A - B/( T -t C), where A = 15.9008, J3= 27SS.51, and C = - 52.36 for benzene, since the benzene molecules adsorbed on solid surfaces in a multilayer were considered to be in a supercooled liquid state even at a temperature lower than the solidifying temperature, as discussed later. Although the values of P, were also calculated by using the Wagner vapour-pressure equation [18], the values of PI obtained by this method were very similar to those obtained by using the Antoine equation with differences of no more than a few per cent. In Fig. 2, the plot of In P, vs. l/T is also shown. Heats of liquefaction and solidification at 0°C were estimated to be 34.9 and 44.3 kJ mol-’ respectively from the Clausius-Clapeyron equation using the plots of In P,, or In P, vs. 1/T. For each, the values at temperatures lower than 0°C were similar to the values of 0°C. Adsorption of benzene vapour at temperatures the solidifying temper&u-e

-24 ‘:L Fig. 2. Equilibrium vapour pressure of supercooled !iquid (P,) and solid (P,)of benzene [In P, vs.I/T (M) and In PI vs.l/T (a)], and adsorption isosteres of benzene on gold (0. 0) at relative pressures, P/P,,of about 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 from the bottom. (0) represents the portion of 0.2-0.4 of relative pressure.

below

In Figs 3 and 4, the adsorption isotherms of benzene vapour on gold and porous glass samples at temperatures below the solidifying temperature down to -40 or -45°C are shown. In the isotherms shown in region (a) of the figures, the vapour pressures measured for solid benzene at temperatures below 5.5”C are adopted as the standard of the relative pressure of the ordinate. However, in region (b) of the figures, the standards of the relative pressure are the saturation pressures of the supercooied liquid benzene estimated from the Antoine equation. The isotherms in region (a) in both figures show that the gradients at the linear portions over point B [19] are lowered more and more as the temperature decreases. However, the isotherms in region (b) show that all the gradients of the linear portions agree with each other in the relative pressure range 0.2-0.4, although with a decrease in temperature the adsorptions become infinite at the relative pressure corresponding to the real saturation pressure of solid benzene. At

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the temperature of - 45 aC (e.g. for the gold sample) the gradient value becomes somewhat larger than those at higher temperatures, probably because the relative pressure for infinite adsorption by condensation is lower than 0.4 and uoveradsorptionn, associated with a sort of capillary condensation, may be brought about near the condensation pressure of the vapour. The almost perfect agreement between the isotherms expressed by the standard of saturated liquid vapour pressure suggests that the isosteric heats of adsorption should be nearly equal to the heats of Iiquefaction, and the molecules adsorbed in this range may be in a supercooled liquid state. In Fig. 2, the adsorption isosteres of the crystalline gold sample are shown by the plots of In P vs. l/T. For the adsorption isosteres in the relative pressure range 0.2-0.4 it is found that .;le gradients of the isosteres agree with the gradient of the plots of In Pi vs. l/T over the experimental temperatures. From the agreement between the gradients, the isosteric heat of adsorption is estimated to be almost equal to the heat of liquefaction of benzene, 34.9 kJ mol”, which is much lower than the heat of solidification, 44.3 kJ mol’i. For the glass sample, the same results are found as the gold sample. From the above discussion, it may be concluded that the benzene molecules adsorbed on the solid surface in the multilayer range are in a liquid state, even at temperatures much lower than the freezing temperature, down to -45°C. It has been thought theoretically that in the estimation of monolayer capacity by equalizing the gradient of the linear portion of Type II adsorption isotherms for the low alkylbenxene vapours (gradient method), the molecules adsorbed on the solid in the range of the linear portion must be in the liquid state and have freedom similar to the molecules on the surface of the corresponding liquid [2]. It is seen from this study that benzene vapour also can be used in the gradient method for surface area estimation, as well as other low alkylbenzene vapours at 0°C or at room temperature. Since the molecules physisorbed on a solid surface up to the monolayer range may be as much

affected by the molecular constituent of the surface as the molecules chemisorbed, and may have adsorption energies characteristic of the solid and the adsorbate molecules, it may be very difficult to estimate various types of surface areas with only one type of probe adsorption gas. Therefore, surface area measurement making use of adsorption in the multilayer range may be more reasonable because the molecules adsorbed in this range are less affected by the surface than the molecules adsorbed directly on the surface. The estimation of the external surface arca obtained by the gradient method, where the somewhat indefinite part of the surface area associated with fine micropores on the surface (which is questionable as the real area of the surface) is properly omitted, also may make the gradient method very reasonable. References

9

10 II 12 I3 14 IS 16 17

18

19

A. Nonaka, J. Colloid Interface Sei, 99 (1984) 335. A. Nonaka, J. Colloid Interface Sci, II2 (1986) 548. A. Nonaka, J. Colloid Interface Sci.. I 17 (1987) 355. A. Nonaka, Colloids Surfaces. 36 (1989) 49. A. Nonaka, Hyomen Gijutsu, 41 (1990) 670. S. Brunauer. L.S. Deming, W.E. Deming and E.Tellcr. J. Am. Chem. Sot., 62 (1940) 1723. S. Brunauer. P.H. Emmett and E.Teller. J. Am. Chem. See., 60 (1938) 389. R.C. Reid, J.M. Prausnitz and T.K. Sherwood, The Properties of Gases and Liquids, 3rd edn, MeGraw-Hill. New York, 1977, p. 184. J.A. Morrison and L.E. Drain, J. Chcm. Phys., 19 (1951) 1063. J.A. Morrison, LE. Drain and J.S. DugdaIe, Can. J. Chem, 30 (1952) 890. EW. Sidebottom and G.G. Litvan, Trans. Faraday See., 67 (1971) 2726. A. Tsugita, T. Takei, M. Chikazawa and T. Kanazawa, Langmuir, 6 (1990) 1461. G.I. Berain, A.V. Kiselev and A.A. Koalov, J. Colloid Interface Sci, 45 (1973) 1%. W. Halter, J. Chem. Phys., 42 (1965) 686. S. Okamoto and S. Hachisu, J. Colloid Interface Sci., 62 (1977) 172. SJ. Gregg and K.S.W. Sing, Adsorption, Suriace Ama and Porosity, Academic Press, London, 1982, pp. 41-105. K.S.W. Sing, Surface Area Determination, in D.H. Everett and R.H. Ottewill (Ed& Proc. Int. Syrnp. 1%9. Butterworthq London, 1970, p. 25. RC. Raid, J.M. Prausnitz and BE. Poling, The Properties of Gases and Liquids, 4th aln, McGraw-Hill, New York, 1988, p. 212. P.H. Emmett and S. Brunauer, J. Am. Chem. Sot., 59 (1937) 1553.