Adsorption isotherm experimental details

There are many methods to estimate LG parameters. One of these is comparison of MC simulations (see Sect. V) of a LG model with experimental adsorption isotherms. For detailed descriptions of this method we refer to Refs. [30,31,36-39]. Here we instead concentrate on the purely theoretical method based on quantum-mechanical DFT calculations. ... 

As stated in the introduction to the previous chapter, adsorption is described phenomenologically in terms of an empirical adsorption function n = f(P, T) where n is the amount adsorbed. As a matter of experimental convenience, one usually determines the adsorption isotherm n = fr(P), in a detailed study, this is done for several temperatures. Figure XVII-1 displays some of the extensive data of Drain and Morrison [1]. It is fairly common in physical adsorption systems for the low-pressure data to suggest that a limiting adsorption is being reached, as in Fig. XVII-la, but for continued further adsorption to occur at pressures approaching the saturation or condensation pressure (which would be close to 1 atm for N2 at 75 K), as in Fig. XVII-Ih. 

Adsorption is determined by the depletion method using a Dohrmann DC 80 carbon analyzer. The mineral is contacted with the polymer solution and agitated with a mechanical tumbler for 24 hours, a time which has been verified to be sufficient for adsorption to be complete (9). A more detailed description of experimental procedures is given elsewhere (10). All the data reported in this study are taken in the plateau region of the adsorption isotherm. 

As we have seen, an adsorption isotherm is one way of describing the thermodynamics of gas adsorption. However, it is by no means the only way. Calorimetric measurements can be made for the process of adsorption, and thermodynamic parameters may be evaluated from the results. To discuss all of these in detail would require another chapter. Rather than develop all the theoretical and experimental aspects of this subject, therefore, it seems preferable to continue focusing on adsorption isotherms, extracting as much thermodynamic insight from this topic as possible. Within this context, results from adsorption calorimetry may be cited for comparison without a full development of this latter topic. 

The packed bed breakthrough method for investigation of mass transfer phenomena in sorbent systems can in many instances offer certain advantages not found in other experimental methods. The method is especially useful when the adsorption isotherms for the principal sorbate exhibit favorable curvature (convex toward loading axis). In such a case, there is the potential for a portion of the sorption front to approach a stable wave form (shape of the front invariant with time). Given the existence of a stable or "steady-state" mass transfer zone (MTZ) and a detailed knowledge of the equilibrium loading characteristics within that zone, one can extract local values of the effective mass transfer resistance at any concentration in the zone. 

Which theory is suitable for a certain application The adsorption theory of Henry is applicable at low pressure. This, however, is natural since it can be viewed as the first term in a series of the adsorption function. A widely used adsorption isotherm equation is the BET equation. It usually fits experimental results for 0.05 < P/P0 < 0.35. For very small pressures the fit is not perfect due to the heterogeneity. For higher pressures the potential theory is more suitable at least for flat, homogeneous adsorbents. It often applies to P/Po values from 0.1 to 0.8. Practically for P/Po > 0.35 adsorption is often dominated by the porosity of the material. A more detailed description of adsorption is obtained by computer simulations [382],... 

Roginski (331) has treated the problem of determination of the distribution function p E) of activation energies by this approximate statistical method. The details are very similar to those discussed above for the determination of p(Q) from the experimental adsorption isotherm. 

For the moment it is concluded that the stable parts of /7(h) curves are experimentally accessible. Technical details will be deferred until Volume IV. It is noted that often toppled /7(h) curves are drawn, in that h is plotted as a function of 77. Plots of this type are analogous to adsorption isotherms in which the mass adsorbed is plotted as a function of relative pressure. An illustration follows in fig. 5.16. 

The high pressure-high temperature adsorption isotherms have been measured using a RUBOTHERM magnetic suspension balance The adsorption isotherms and the detail of the experimental procedure are presented elsewhere [11,12] Considering the measurement accuracy of each sensor (mass, temperature and pressure), the relative errors on the adsorbed mass and on the pressure are estimated respectively to 0 3 and 0 5 % the temperature is measured with an accuracy of 0 1 K The main cause of experimental error is not the lack of accuracy of the sensors but rather the buoyancy effect on the adsorbent sample on the one hand and on the adsorbed phase on the other hand The first contibution is taken into account by... 

The basis for thermodynamic calculations is the adsorption isotherm, which gives the amount of gas adsorbed in the nanopores as a function of the external pressure. Adsorption isotherms are measured experimentally or calculated from theory using molecular simulations. Potential functions are used to constmct a detailed molecular model for atom-atom interactions and a distribution of point charges is used to reproduce the polarity of the solid material and the adsorbing molecules. Recently, ab initio quantum chemistry has been applied to the theoretical determination of these potentials, as discussed in another chapter of this book. 

Quantum chemistry approaches to zeolites are complemented by an active research community that uses classical force-field methods to study molecular adsorption and diffusion in zeolites and similar materials. This topic was comprehensively reviewed by Keil, Krishna, and Coppens in 2000.262 For more recent examples of activity in this area, see References 263-270. Examples of impressive agreement between adsorption isotherms and molecular dilfusivities predicted with calculations of this type and experimental data are available.271,272 There appear to be many future opportunities for linking the detailed understanding of multi-component adsorption and diffusion that is now emerging from this area with detailed quantum chemistry approaches to reactivity at active sites inside zeolites. 

In contrast to the well-developed thermodynamic methods for determining gas/ liquid equilibriums the theoretical determination of adsorption isotherms is not yet feasible. Only approaches to determining multi-component isotherms from experimentally determined single-component isotherms are known. Such approaches are explained in more detail in Section 2.5.2.3. Careful experimental determination of the adsorption isotherm is therefore absolutely necessary. The different approaches for isotherm determination are discussed in Chapter 6.5.7. 

In order to calculate band profiles and compare the results with experimental profiles, we need to know the detailed experimental conditions. These conditions include (i) the adsorption isotherm, (ii) the HETP under linear conditions, (iii) the sample size, (iv) the mobile phase flow rate, (v) the hold-up volume, and (vi) the column dimensions. The column HETP can be obtained easily by injecting a very small amormt of sample and measuring the band width. The band profile im-der overloaded conditions is very sensitive to the adsorption isotherm, which is why isotherms must be measured accurately in order to achieve good agreement... 

Finally, some formulas and stability constants of (hypothetical) surface species (or Gibbs energies of adsorption) are reported in Tables 4.1-4.4. These quantities belong to adsorption models proposed by the authors of cited publications, but they are not sufficient to calculate the uptake curves or adsorption isotherms when the model involves an electrostatic factor. Adsorption models themselves are not discussed in the present chapter, their terminology is explained in detail in Chapter 5, In contrast with the directly measured quantities that represent the sorption properties at specific experimental conditions, the model parameters characterize the sorption process over a wide range of experimental conditions, although the match between experimental and theoretically calculated quantities was not always... 

There have been several improvements to the slit-pore model and the description based on the concept of a pore size distribution. These improved models are also constructed by making detailed observations of the experimental data (electron micrographs. X-ray diffraction, adsorption isotherms, etc.), extracting more relevant features of the pore topology and the structure of the pore walls, and including these features in the models. For example, a 2D distribution of pore size and pore-wall thickness may be used, instead of a pore size distribution [22]. Most of these improvements are described in detail in a recent review [1]. 

Below in Section 2.4.4. and Appendix 2B, the physical background and derivation of the most frequently used adsorption isotherms will be discussed in more detail. Examples of the application of the Langmuir and Frumkin isotherms to experimental data are summarised in Appendix 5D. 

Studies of dynamic adsorption layers require the use of equilibrium adsorption isotherms, as will be demonstrated in detail in Chapter 4. The use of Langmuir s isotherm is restricted to large molecular areas of adsorbing molecules because specific interaction is left out of his account. This isotherm is however the most frequently-used relationship because of its simple form and comparatively good agreement with many experimental data. 

Examples of experimental and simulated effluent profiles and the adsorption isotherm based on the simulated surfactant profile are shown in Figure 10. For the data discussed in this chapter, adsorption was modeled using the surface excess formalism (8—10, 115), or in some cases, the Langmuir adsorption model (8, 9, 34, 82) as discussed in detail in these references. The model used to calculate the adsorption isotherm in Figure 10 assumes that surfactant adsorption takes place from the monomer... 

Simons s pioneering efforts anticipated the need for a detailed examination of pore connectivity in carbons. This issue continues to be in need of careful experimental assessment [171-174]. For example. Figure 1.9 reproduces the approach proposed by Ldpez-Ramdn et al. [174] The smaller adsorptive species probes all the pores, and its adsorption isotherm yields the complete PSD. The larger species is excluded from the smaller pores and also from the larger pore that is shielded by the smaller pores. So the PSD obtained using the larger species is (i) zero for pores that are smaller than the molecules of that species and... 

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