Solid Surface Area Determination

As far as surface chemistry is concerned, a solid particle is a very important substance as regards its surface characteristics. In all applications where finely divided powders are used (such as talcum, cement, and charcoal powder), the property of these will depend mainly on the surface area per gram (varying from few m [talcum] to over 1000 mVg [charcoal]). For example, if one needs to use charcoal to remove some chemical (such as coloring substances or other pollutants) from wastewater, then it is necessary to know the amount of absorbent needed to fulfill the process. 

In other words, if one needs 1000 area for the adsorption when using charcoal, 1 g of solid will be required. The estimation of surface area of finely divided solid particles from solution adsorption studies is subject to many of the same considerations as in the case of gas adsorption, but with the added complication that larger molecules are involved, whose surface orientation and pore penetrability may be uncertain. The first condition is that a definite adsorption model is obeyed, which in practice means that area determination data are valid within the simple Langmuir equation relation. 

In the case of gas adsorption where the BET method is used, it is reasonable to select the van der Waals area of the adsorbate molecule moreover, being small or even monoatomic, surface orientation is not a major problem. In the case of adsorption from solution, however, the adsorption may be chemisorption. 

In another example, the adsorption of surfactants on polycarbonate indicated that, depending on the surfactant and concentration, the adsorbed molecules might be lying flat on the surface perpendicular to it, or might form a bilayer. 

A second widely used class of adsorbates is that of dyes. Methods using these are appealing because of the ease with which analysis may be made colorimetrically. The adsorption generally follows the Langmuir equation. Graham found an apparent molecular area of 19.7 A2 for methane blue on Graphon or larger than the actual 

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The Langmuir equation and the method of solid surface area determination based on it can be applied for the systems in which the adsorption process is not complicated by formation of a multilayer as well as by adsorption in micropores and capillary condensation. Adsorption of gases at the temperatures higher than the critical temperature on nonporous or wideporous adsorbents is an example of such cases. Despite this limitation, the Langmuir equation is used in technical adsorption for calculations of kinetics and dynamics of impurities uptake from the gas medium or diluted solutions. 

Perhaps the simplest case of reaction of a solid surface is that where the reaction product is continuously removed, as in the dissolving of a soluble salt in water or that of a metal or metal oxide in an acidic solution. This situation is discussed in Section XVII-2 in connection with surface area determination. 

As pointed out in Section XVII-8, agreement of a theoretical isotherm equation with data at one temperature is a necessary but quite insufficient test of the validity of the premises on which it was derived. Quite differently based models may yield equations that are experimentally indistinguishable and even algebraically identical. In the multilayer region, it turns out that in a number of cases the isotherm shape is relatively independent of the nature of the solid and that any equation fitting it can be used to obtain essentially the same relative surface areas for different solids, so that consistency of surface area determination does not provide a sensitive criterion either. 

Johnson, Christian, and Tiedemann (Ref 27) evaluated the Sorptometer vs the Micromero-graph and the microscope for particle size and surface area determinations to characterize powdered materials used in solid propints. Table 12 compares the surface area of A1 powder samples calculated from Micromerograph and microscopic data with that measured using a Sorptometer... 

The problems associated with the application of this (or any other) model have been discussed. Because of the form of the typical isotherm, which exhibits a broad plateau region, fitting of experimental results to the model requires that data be obtained over a very broad range of concentrations. This is often very difficult to accomplish in practice, especially when difference methods are used to determine the amount of polymer adsorbed. Evaluation of adsorption in real systems is further complicated by a lack of knowledge of the available solid surface area. The latter may be affected by particle size, shape and surface topography and by polymer bridging between particles. 

The intrinsic dissolution rates of pharmaceutical solids may be calculated from the dissolution rate and wetted surface area using Eq. (36) or (37). For powdered solids, two common methods are available the powder intrinsic dissolution rate method, and the disc intrinsic dissolution rate method. In the former method, the initial dissolution rate of one gram of powder is determined by a batch-type procedure as illustrated in Fig. 13A. The initial wetted surface area of one gram of powder is assumed to equal the specific surface area determined by an established dry procedure, such as monolayer gas adsorption by the Brunauer, Emmett, and Teller (BET) procedure [110]. 

In the literature, many different approaches have been proposed for estimating the surface area of a solid. Surface areas may be estimated from the exclusion of like charged ions from a charged interface. This method is intriguing in that no estimation of either site or molecular area is needed. In general, however, surface area determination by means of solution adsorption studies, while convenient experimentally, may not provide the most correct information. Nonetheless, if a solution adsorption procedure has been standardized for a given system by means of independent checks, it can be very useful determining relative areas of a series of similar materials. In all cases, it is also more real as it is what happens in real life. 

In the case of solid electrodes, knowledge of the real surface area is a prerequisite for the proper evaluation of the activity with respect to other samples from the same laboratory, or for the comparison of results from different laboratories. It is very difficult to determine the real surface area because there are no unique techniques applicable to all materials. When the surface area determination is lacking, an evaluation in terms of synergetic effects can only be ambiguous. 

Krypton adsorption at 77 K is often used for the determination of relatively low solid-surface areas. At this temperature the vapour pressure of krypton (and so the dead-space correction) is small, and a reasonable precision is attainable. 

Kaneko, K. and Ishii, C. Superhigh surface area determination of microporous solids. Colloid. Surf. 67, 1992 203-212. 

Ultrahigh vacuum techniques (basic pressure xl02 Pa) enable adsorption studies to be made on stringently clean solid surfaces whereas degassing under moderate vacuum conditions, as normally applied in surface area determinations, leave the adsorbent covered with a preadsorbed layer of impurities and/or the adsorbate. On subsequent adsorption (e.g. of N2 or noble gases) completion of the physisorbed monolayer is usually reached at p/pn 0.1 whereas on clean surfaces this state occurs at p/p° values which may be smaller by orders of magnitude. However, as mentioned above, it should be kept in mind that linearity of the BET plot does not in itself provide conclusive evidence for the validity of njj,. 

The early technological interest in anatase pigments was probably why anatase powder was for a time favoured as a non-porous adsorbent. Thus, anatase was one of the few finely divided crystalline solids used by Harkins and Jura (1944) in the development of new procedures for surface area determination. Anatase was also featured... 

In practice, the amount of solid molecules on the surface being exposed to the solution is difficult or even impossible to quantify. Instead, the solid surface area to solution volume ratio is often used to quantify the amount of solid reactant. Therefore, experimentally determined second-order rate constants for interfacial reactions have the unit m s h As the true surface area of the solid is very difficult to determine, the BET (Brunauer-Emmett-Teller) surface area is fte-quentiy used. The maximum diffusion-controlled rate constant for a particle suspension containing pm-sized particles is ca 10 m s and for mm-sized particle suspensions the corresponding value is I0 m s h Unfortunately, the discrepancy between the true surface area and the BET surface area and the non-spherical geometry of the solid particles makes it impossible to exactly determine the theoretical diffusion-controlled rate constant. 

Rate constants for interfacial reactions have mainly been determined from experiments using particle suspensions where the concentration of reactive solute is monitored as a function of time. In these experiments, the solid surface is in large excess and the consumption of reactive solute follows first order kinetics. By plotting the pseudo-first-order rate constant against the solid surface area to solution volume ratio, the second-order rate constant can be obtained (from the slope). The main limitation here is that only relatively stable solutes can be studied experimentally. It is not possible to study the reactivity of short-lived species such as radicals using this approach. 

Application of the BET equation to experimental data has become the standard method for surface area determinations. The constants are determined from data at low humidities (5-30% RH). Based on these parameters, the BET equation almost always overestimates the amount of water associated with the solid at high humidity. 

While in principle all molecules can be used for this purpose, meaningful values are only obtained if the dimensions of the sorbate are small compared to the diameter of the pores of the solid. Conventionally, most surface area determinations use the area occupied by a nitrogen molecule. The nitrogen adsorption is measured at the boiling point of nitrogen, 77.4 K. 

Most surface area determinations are based on measurements of the low temperature adsorption of nitrogen or krypton on the solid and use of the BET theory. This procedure may not give reliable results because the products are chilled well below reaction temperature, possibly resulting in the sealing of internal pores. Volumes of gases adsorbed are sometimes small, as observed for dehydrated alums [37] and decomposed ammonium perchlorate [48], where the areas are consistent with product crystallites of linear dimensions between 1 and 3 pm. The results indicate, however, that little, if any, zeolitic material is formed [36]. The surface area of a solid may also be estimated from electron micrographs. Density measurements may be used to complement area measurements. 

K. Kaneko, C. Ishii and T. Rybolt, Superhigh surface area determination of microporous carbons, in J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.), Characterization of Porous Solids III, Studies in Surface Science and Catalysis Vol. 87, Proc. of the lUPAC Symposium (COPS III), Marseille, France, May 1993, Elsevier, Amsterdam, 1994, pp. 583-592. 

Equations (33) and (34) form the theoretical basis for the absolute Harkins-Jura (HJ) method [76,94] to estimate the solid surface area. However, in the earlier calorimetric experiments applying the Harkins-Jura principle, the term QjJJ, was always neglected. Neglecting it may lead to certain discrepancies between the surface areas determined by the Harkins-Jura and BET methods in the case of water adsorbed on oxides. 

The heat measured in step (3) corresponds to the adsorption of an unknown amount of vapor on the carbon surface. Now, in case of a wetting system, we know that the conditions are then fulfilled to have a multilayer adsorbed. This means that the heat measured in step (4) corresponds to the immersion energy of a precovered solid, so that it can be used for the surface area determination by the modified Harkins and Jura method [7]. The addition of the heats measured in steps (3) and (4) after suitable correction leads to the usual immersion energy. If the full wetting is not reached at saturation pressure it is then needed to proceed to step (5). More details about this procedure and the way to get experimental data are described elsewhere [9]. 

The surface area expansion process in Figure 3.5 must obey the basic thermodynamic reversibility rules so that the movement from equilibrium to both directions should be so slow that the system can be continually relaxed. For most low-viscosity liquids, their surfaces relax very rapidly, and this reversibility criterion is usually met. However, if the viscosity of the liquid is too high, the equilibrium cannot take place and the thermodynamical equilibrium equations cannot be used in these conditions. For solids, it is impossible to expand a solid surface reversibly under normal experimental conditions because it will break or crack rather than flow under pressure. However, this fact should not confuse us surface tension of solids exists but we cannot apply a reversible area expansion method to solids because it cannot happen. Thus, solid surface tension determination can only be made by indirect methods such as liquid drop contact angle determination, or by applying various assumptions to some mechanical tests (see Chapters 8 and 9). 

The titania particles precipitate under reaction conditions very similar to those of the silica systems discussed earlier. A critical nucleation concentration of 1.5-3 times [C]eq is measured. This low supersaturation level is not reached until very late in the precipitation reaction (Figure 3). The rate of loss of soluble titania is also independent of the presence of solid surface area. Finally, on the basis of measures of particle surface potentials, nuclei of sizes less than about 20 nm are expected to be unstable and to rapidly aggregate. These results again indicate that during the precipitation of titania, nucleation may occur over much of the reaction period and final particle sizes may be determined by the aggregation of primary particles. These conclusions are supported by the transmission electron microscopy work of Diaz-Gomaz et al. (30). 

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