Isotherms interpretation

Nguyen, T.H., Sabbah, I. Ball, W.P. (2004) Sorption nonlinearity for organic contaminants with diesel soot method development and isotherm interpretation. Environ. Sci. Technol. 38, 3593-3603. 

K. Chinnick, C. Gibson and J.F. Griffiths, Isothermal Interpretations of Oscillatory Ignition During Hydrogen Oxidation in an Open System, 2 Numerical-Analysis, Proc. Roy. Soc. 405 (1986) 129-142. 

It must be concluded that the quantitative determination of micropore size is still an ambiguous problem new theories, models, mechanisms and simulations are still under study [56-58]. Therefore isotherm interpretations must be used carefully and can be considered as useful mainly for qualitative studies. No reliable method has been developed for the determination of the micropore size distribution. At present the most promising approach appears to be that of pre-adsorption linked with the use of various probe molecules of known size and shape [59-61]. For example, this approach has been applied successfully for silica compacts characterisation in [61] using spherical symmetrical inert molecules, such as neopentane and trimethylsiloxysilane [(CH3)3SiO]4Si with diameters of 6.5 and 11.5 A respectively. In general the limited availability of volatile probe molecules with diameters extending above 10 A puts a restriction on the applicability of this method. Furthermore effective pore sizes determined by this technique depend on the kinetic and thermodynamic properties of the... 

The concept has no relevance to processes of physical adsorption, isotherm interpretation as well as processes of activation (physical and chemical). 

Due to limitation of the pressure-sensing devices, the very low-pressure isotherms are almost never measured by the volumetric technique. The problem can be corrected by employing more than one sensor device to obtain values below 0.001 atm. Two problems are present for this technique. Firstly, the cross-calibration between the two pressure sensors must be very good to avoid large errors. Secondly, the problem of molecular flow becomes important as mentioned in a previous section. This leads to both an accounting problem and a problem in determining an important quantity for isotherm interpretation, the chemical potential of the adsorbate. Theoretically, these problems can be handled. Practically, it is easier and more certain not to use the volumetric method in this range. 

There are several isotherm interpretations available. The most widely used is the Brunauer, Emmett and Teller (BET) [1] and its various modifications including the Brunauer, Deming, Doming and Teller (BDDT) [2]. 

In this book, the simple interpretations of the physisorption experiments are presented in Chapter 1. Chapter 2 presents the important details on how to make the measurements usually associated with physical adsorption. If one already has a commercial instrument, this chapter may be irrelevant. Chapter 3 is designed to present step-by-step analysis of the isotherms by a few methods and to present other isotherm interpretations. It is generally not a good idea to rely upon manufacturers software supplied with the instruments. Although the programers are quite knowledgeable about physisorption, it is still best to examine the data carefully. Chapter 4... 

The kinetic interpretation of measured curves of reactions under non-isothermal conditions is clearly labour-intensive work and is especially very sensitive to measurement errors. Even small errors of the values q and T and the additive quantities C, kE, qst and V will cause a perceptible and momentous change in the auxiliary quantities A and B and cause an important variance in the elaborated kinetic parameters k, n and E. Eor the sake of correctness it is advisable to choose such conditions of the reaction (temperature, concentration level)—if that is somehow possible—that the reaction runs at least for a large part of the total conversion under isothermal conditions. Errors that arise by extrapolating the curve q measured under isothermal conditions during the final run rearward to the non-isothermal initial phase (Eig. 2.31) are generally smaller than those caused by the described non-isothermal interpretation method. 

The BET equation filled an annoying gap in the interpretation of adsorption isotherms, and at the time of its appearance in 1938 it was also hailed as a general method for obtaining surface areas from adsorption data. The equation can be put in the form... 

In the present study we try to obtain the isotherm equation in the form of a sum of the three terms Langmuir s, Henry s and multilayer adsorption, because it is the most convenient and is easily physically interpreted but, using more a realistic assumption. Namely, we take the partition functions as in the case of the isotherm of d Arcy and Watt [20], but assume that the value of V for the multilayer adsorption appearing in the (5) is equal to the sum of the number of adsorbed water molecules on the Langmuir s and Henry s sites ... 

Type 1 isotherms, as will be demonstrated in Chapter 4, are characteristic of microporous adsorbents. The detailed interpretation of such isotherms is controversial, but the majority of workers would probably agree that the very concept of the surface area of a microporous solid is of doubtful validity, and that whilst it is possible to obtain an estimate of the total micropore volume from a Type I isotherm, only the crudest guesses can be made as to the pore size distribution. 

To obtain the monolayer capacity from the isotherm, it is necessary to interpret the (Type II) isotherm in quantitative terms. A number of theories have been advanced for this purpose from time to time, none with complete success. The best known of them, and perhaps the most useful in relation to surface area determination, is that of Brunauer, Emmett and Teller. Though based on a model which is admittedly over-simplified and open to criticism on a number of grounds, the theory leads to an expression—the BET equation —which, when applied with discrimination, has proved remarkably successful in evaluating the specific surface from a Type II isotherm. 

Following the pioneer work of Beebe in 1945, the adsorption of krypton at 77 K has come into widespread use for the determination of relatively small surface areas because its saturation vapour pressure is rather low (p° 2Torr). Consequently the dead space correction for unadsorbed gas is small enough to permit the measurement of quite small adsorption with reasonable precision. Estimates of specific surface as low as 10 cm g" have been reported. Unfortunately, however, there are some complications in the interpretation of the adsorption isotherm. 

A further complication which not infrequently appears is the occurrence of a phase transition within the adsorbed film. Detailed investigation of a number of step-like isotherms by Rouquerol, Thorny and Duval, and by others has led to the discovery of a kink, or sub-step within the first riser, which has been interpreted in terms of a two-dimensional phase change in the first molecular layer. 

Any interpretation of the Type I isotherm must account for the fact that the uptake does not increase continuously as in the Type II isotherm, but comes to a limiting value manifested in the plateau BC (Fig. 4.1). According to the earlier, classical view, this limit exists because the pores are so narrow that they cannot accommodate more than a single molecular layer on their walls the plateau thus corresponds to the completion of the monolayer. The shape of the isotherm was explained in terms of the Langmuir model, even though this had initially been set up for an open surface, i.e. a non-porous solid. The Type I isotherm was therefore assumed to conform to the Langmuir equation already referred to, viz. 

For a second active carbon, AG, the DR plot was convex to the logio(p7p) This carbon was believed from X-ray results to have a wider distribution of pores. It was found that the isotherms of both benzene and cyclohexane could be interpreted by postulating that the micropore system consisted of two sub-systems each with its own Wq and and with m = 2 ... 

More recent results, however, throw some doubt on this interpretation. The isotherms in Fig. 5.22 were determined after successive oatgassings at (1) 25°C, (2) lOO C, (3) 150 C, (4) SOO C, and (5) 25 C, respectively. It will be noted (a) that only isotherms (4) and (5) exhibit a Point X and that they are nearly parallel at pjp° > 0-1 (b) that isotherms (2) and (3) are similarly parallel in the same range and (c) that isotherms (1) and (5), though both obtained after outgassing at 25 C, are quite different in shape. 

The first stage in the interpretation of a physisorption isotherm is to identify the isotherm type and hence the nature of the adsorption process(es) monolayer-multilayer adsorption, capillary condensation or micropore filling. If the isotherm exhibits low-pressure hysteresis (i.e. at p/p° < 0 4, with nitrogen at 77 K) the technique should be checked to establish the degree of accuracy and reproducibility of the measurements. In certain cases it is possible to relate the hysteresis loop to the morphology of the adsorbent (e.g. a Type B loop can be associated with slit-shaped pores or platey particles). 

A manual entitled Reporting Physisorption Data for Gas/Solid Systems with Special Reference to the Determination of Surface Area and Porosity has been prepared as a provisional publication by Commission 1.6 of the International Union of Pure and Applied Chemistry (lUPAC). The purpose of the manual is to draw attention to problems involved in reporting physisorption data and to provide guidance on the evaluation and interpretation of isotherm data. The general conclusions and recommendations are very similar to those contained in Chapter 6. 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

Surface areas are deterrnined routinely and exactiy from measurements of the amount of physically adsorbed, physisorbed, nitrogen. Physical adsorption is a process akin to condensation the adsorbed molecules interact weakly with the surface and multilayers form. The standard interpretation of nitrogen adsorption data is based on the BET model (45), which accounts for multilayer adsorption. From a measured adsorption isotherm and the known area of an adsorbed N2 molecule, taken to be 0.162 nm, the surface area of the soHd is calculated (see Adsorption). 

The graphical interpretation of Eq. (16-197) is shown in Fig. 16-37 for the conditions of Example 12. An operating hne is drawn from the origin to the point of the pure displacer isotherm at = cf. For displacement to occur, the operating hne must cross the pure component isotherms of the feed solutes. The product concentrations in the iso-tachic train are found where the operating hne crosses the isotherms. When this condition is met, the feed concentrations do not affect the final product concentrations. 

In previous studies, the main tool for process improvement was the tubular reactor. This small version of an industrial reactor tube had to be operated at less severe conditions than the industrial-size reactor. Even then, isothermal conditions could never be achieved and kinetic interpretation was ambiguous. Obviously, better tools and techniques were needed for every part of the project. In particular, a better experimental reactor had to be developed that could produce more precise results at well defined conditions. By that time many home-built recycle reactors (RRs), spinning basket reactors and other laboratory continuous stirred tank reactors (CSTRs) were in use and the subject of publications. Most of these served the original author and his reaction well but few could generate the mass velocities used in actual production units. 

Carbon isotherms for a pressure of 30 psia are superimposed on the ternary (Figure 3). Interpretation of the isotherms reveals that mixtures of the elements which fall above the curves are in the carbon-forming region when at chemical equilibrium. Mixtures of the elements which... 

Although there are experimental and interpretative limitations [189, 526] in the kinetic analysis of non-isothermal data, DTA or DSC observations are particularly useful in determining the temperature range of occurrence of one or perhaps a sequence of reactions and also of phase changes including melting. This experimental approach provides, in addition, a useful route to measurements of a in the study of reactions where there is no gas evolution or mass loss. The reliability of conclusions based on non-isothermal data can be increased by quantitatively determining the... 

Isothermal studies at 370—420 K have been made of the kinetics of decomposition of [Co(NH3)6](N3)3, [Co(NH3)5(N3)](N3)2 and both cis-and frarcs-[Co(NH3)4(N3)2](N3) [1120]. Results are interpreted as indicating the operation of a common reaction mechanism which is not greatly influenced by either the constituents or the stereochemistry of the complex cation. The reactions of all four compounds may yield either CoN or Co(NH3)2(N3)2 as the residual product the alternative decompositions may be represented as... 

---