Surface on the solid

In the pharmaceutical industry, surface area is becoming more important in the characterization of materials during development, formulation, and manufacturing. The surface area of a solid material provides information about the void spaces on the surfaces of individual particles or aggregates of particles [5], This becomes important because factors such as chemical activity, adsorption, dissolution, and bioavailability of the drug may depend on the surface on the solid [3,5]. Handling properties of materials, such as flowability of a powder, can also be related to particle size and surface area [4],... 

When a solid is dried experimentally, data relating moisture content to time are usually obtained. These data are then plotted as moisture content (dry basis) W versus time 0, as shown in Fig. 12-41a. This curve represents the general case when a wet solid loses moisture first by evaporation from a saturated surface on the solid, followed in turn by a period of evaporation from a saturated surface of gradually decreasing area, and, finally, when the latter evaporates in the interior of the solid. 

As has been pointed out byBangham and Razouk [3], this is the work required to strip the liquid from the solid so as to leave a surface on the solid which is identically the equilibrium surface on the solid in a vacuum. This work of adhesion is different from the work of adhesion required to strip the liquid from the solid so as to leave the equilibrium adsorbed film of vapor V2 on the solid surface. This latter work of adhesion is... 

Clearly, it is important that there be a large contact angle at the solid particle-solution-air interface. Some minerals, such as graphite and sulfur, are naturally hydrophobic, but even with these it has been advantageous to add materials to the system that will adsorb to give a hydrophobic film on the solid surface. (Effects can be complicated—sulfur notability oscillates with the number of preadsoibed monolayers of hydrocarbons such as n-heptane [76].) The use of surface modifiers or collectors is, of course, essential in the case of naturally hydrophilic minerals such as silica. 

Since solids do not exist as truly infinite systems, there are issues related to their temiination (i.e. surfaces). However, in most cases, the existence of a surface does not strongly affect the properties of the crystal as a whole. The number of atoms in the interior of a cluster scale as the cube of the size of the specimen while the number of surface atoms scale as the square of the size of the specimen. For a sample of macroscopic size, the number of interior atoms vastly exceeds the number of atoms at the surface. On the other hand, there are interesting properties of the surface of condensed matter systems that have no analogue in atomic or molecular systems. For example, electronic states can exist that trap electrons at the interface between a solid and the vacuum [1]. 

The potential energy 0(z) depends not only on the distance z hut also on the position of the gas molecule in the xy plane parallel to the surface of the solid and distant z from it. For any given position, the adsorption energy will be equal to the value of 0 = 0o minimum of the potential curve (cf. Fig. 1.2), which of course represents the equilibrium position. 

A Type II isotherm indicates that the solid is non-porous, whilst the Type IV isotherm is characteristic of a mesoporous solid. From both types of isotherm it is possible, provided certain complications are absent, to calculate the specific surface of the solid, as is explained in Chapter 2. Indeed, the method most widely used at the present time for the determination of the surface area of finely divided solids is based on the adsorption of nitrogen at its boiling point. From the Type IV isotherm the pore size distribution may also be evaluated, using procedures outlined in Chapter 3. 

The physical adsorption of gases by non-porous solids, in the vast majority of cases, gives rise to a Type II isotherm. From the Type II isotherm of a given gas on a particular solid it is possible in principle to derive a value of the monolayer capacity of the solid, which in turn can be used to calculate the specific surface of the solid. The monolayer capacity is defined as the amount of adsorbate which can be accommodated in a completely filled, single molecular layer—a monolayer—on the surface of unit mass (1 g) of the solid. It is related to the specific surface area A, the surface area of 1 g of the solid, by the simple equation... 

The BET treatment is based on a kinetic model of the adsorption process put forward more than sixty years ago by Langmuir, in which the surface of the solid was regarded as an array of adsorption sites. A state of dynamic equilibrium was postulated in which the rate at which molecules arriving from the gas phrase and condensing on to bare sites is equal to the rate at which molecules evaporate from occupied sites. 

In general there are two factors capable of bringing about the reduction in chemical potential of the adsorbate, which is responsible for capillary condensation the proximity of the solid surface on the one hand (adsorption effect) and the curvature of the liquid meniscus on the other (Kelvin effect). From considerations advanced in Chapter 1 the adsorption effect should be limited to a distance of a few molecular diameters from the surface of the solid. Only at distances in excess of this would the film acquire the completely liquid-like properties which would enable its angle of contact with the bulk liquid to become zero thinner films would differ in structure from the bulk liquid and should therefore display a finite angle of contact with it. 

The strength of dispersion interaction of a solid with a gas molecule is determined not only by the chemical composition of the surface of the solid, but also by the surface density of the force centres. If therefore this surface density can be sufficiently reduced by the pre-adsorption of a suitable substance, the isotherm may be converted from Type II to Type III. An example is rutile, modified by the pre-adsorption of a monolayer of ethanol the isotherm of pentane, which is of Type II on the unmodified rutile (Fig. 5.3, curve A), changes to Type III on the treated sample (cf. Fig. 5.3 curve B). Similar results were found with hexane-l-ol as pre-adsorbate. Another example is the pre-adsorption of amyl alcohol on a quartz powder... 

If the isotherm of G on the solid under test is identical in shape with that on the reference sample, then its x,-plot will be a straight line passing through the origin, and having a slope equal to the ratio >4(test solid)/>4(reference solid). Since >4(reference solid) is known, the specific surface of the test solid is obtainable at once. 

In rotary devices, reradiation from the exposed shelf surface to the solids bed is a major design consideration. A treatise on furnaces, including radiative heat-transfer effects, is given by Ellwood and Danatos [Chem. Eng., 73(8), 174 (1966)]. For discussion of radiation heat-transfer computational methods, heat fliixes obtainable, and emissivity values, see Schornshort and Viskanta (ASME Paper 68-H 7-32), Sherman (ASME Paper 56-A-III), and the fohowing subsection. 

Specific. surface of solid spheres of 0.1 mm (0.0039 in) dia is 0.06 mVml (18,300 ftVfF) and a porous activated alumina pellet has about 600 mVml (1.83 X 10 ftVfF). Other considerations aside, a large surface is desirable because the rate of reaction is proportional to the accessible surface. On the other hand, large specific surface means pores of small diameter. 

Adsorbents, and activated carbon in particular, are typically characterized by a highly porous structure. Adsorbents with the highest adsorption capacity for gasoline or fuel vapors have a large pore volume associated with pore diameters on the order of 50 Angstroms or less. When adsorption occurs in these pores, the process is comparable to condensation in which the pores become filled with hquid adsorbate. Fig. 5 depicts the adsorption process, including transfer of adsorbate molecules through the bulk gas phase to the surface of the solid, and diffusion onto internal surfaces of the adsorbent and into the pores. 

Eq. 3 may also be derived heuristically by making a balance of horizontal forces on a small section of the interline as shown in Fig. 4. This treats the solid surface and the solid-liquid interface as though they were in states of tension given by their respective surface energies. The vertical force ytsin in such a construction is balanced by stresses in the underlying solid. 

Many of the most widely used methods are based on measuring the contact angles of a series of test liquids on the solid surface, and evaluating the surface energies via Young s equation, Eq. 4 above. 

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