Surface area solid

Physical and Chemical Adsorption for the Measurement of Solid Surface Areas... 

One of the factors that influences the rate of dissolving of solid is the area, A, of the crystal surface that contacts the liquid. If many crystals (with large A) are dissolving simultaneously, the rate of dissolving is faster than if only a few crystals (with small A) are in the solvent. The rate of dissolving is proportional to this liquid-solid surface area, A. 

Application of this, or the equivalent statistical models, to actual polymer adsorption processes is further complicated by very imprecise knowledge of the solid surface area which is actually available for polymer adsorption. Surface roughness etc. can certainly be expected to have much more complex effects than on the adsorption of small molecules due to restrictions on... 

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. 

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. 

The terms in equation (7.3) have previously been defined asW = weight of adsorbate, M = adsorbate molecular weight, S, = solid surface area and P = equilibrium pressure. 

The rates here are number of nuclei appearing per unit time. The symbol Xht refers to the number of sites available for heterogeneous nucleation and Nhm is the number for homogeneous nucleation. The first is proportional to solid surface area, the second to liquid volume. The value 0 depends only on the contact angle for wetting. 

While the exact sorption mechanism may not be clear, the available literature suggests the following generalizations. First, coarser particles (e.g., silica sand) exhibit less binding per mass of solid than corresponding finer particles made of the same material (e.g., porous silica). This is presumably due to the influence of increased solid surface area per mass of sorbent. Thus, values of sorption coefficients for minerals (Kimm = Cimin/Ciw.Mr) are more useful if they are normalized to the solid s surface area rather than its mass. The second tendency we see is that for any... 

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. 

Sulfated zirconia is a good example of a structural Lewis acid which has been chemically treated to enhance acidity. It has been extensively studied as a solid acid catalyst for vapour phase reactions and we1112 and others14 have found that a mesoporous version of this material is a particularly effective catalyst for liquid phase Friedel-Crafts alkylation reactions and to a lesser extent Friedel-Crafts benzoylations. The commercial (MEL Chemicals Ltd) material SZ999/1 shows a nitrogen isotherm characteristic of a mesoporous solid (surface area 162 m2g, pore volume 0.22 cm3g )- Whereas microporous and mesoporous materials are capable of rapidly catalysing the alkylation of benzene with various alkenes (Table 1), on reuse only the mesoporous... 

Containing Initial Additions Of NaCl And CaCl2. All Experiments Have A Solid Surface Area To Solution Volume Ratio Of 0.75 X 10 cm /L—Continued... 

This review has been limited to studies in which solid surface areas were reported. We have not considered specific exper-... 

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. 

SA denotes the solid surface area and Fis the solution volume. 

As can be seen, the agreement between the experiments and the calculations is excellent. It is also interesting to note that the surface reactions at the solid surface area to solution volume ratios used here do not influence the bulk concentrations of aqueous radiolysis products significantly. However, this is only valid when the dose is uniformly distributed in the whole volume. Under deep repository conditions, i.e. in systems dominated by a-radiolysis, the relative impact of H202has been shown to be >99.9% Consequently, H2O2 is the only radiolytical oxidant needed to be accounted for when... 

Figure 4 compares several of these models with respect to the nature of the constants that each uses. The simplest model (linear sorption or Ai ) is the most empirical model and is widely used in contaminant transport models. values are relatively easy to obtain using the batch methods described above. The Aid model requires a single distribution constant, but the Aid value is conditional with respect to a large number of variables. Thus, even if a batch Aid experiment is carefully carried out to avoid introduction of extraneous effects such as precipitation, the Aid value that is obtained is valid only for the particular conditions of the experiment. As Figure 4 shows, the radionuclide concentration, pH, major and minor element composition, rock mineralogy, particle size and solid-surface-area/solution volume ratio must be specified for each Aid value. 

N < Njs produces a dramatic increase in the mass transfer rate primarily because the particles exposed area in Eq. (1) increases with N as more particles become fully suspended. Increasing N beyond produces only a moderate increase in the mass transfer rate, as the interfacial area. A, now corresponds to the effective solids surface area, and the mass transfer rate inereases solely because increases with P (and hence N), as quantified in the next section. This constitutes an... 

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. 

In Eq. 10.18, C is the difference between hydroxide-ion and hydrogen ion adsorption in the nnit of miliequivalents per solid surface area (m ) that is, C = Cqjj -Ch+- hydrogen exchange capacity (maximum uptake or... 

The reactive surface area S within a layer of thickness ft is a product of the solid surface area per gram, Sg, solid density, and its volume fraction ... 

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