Adsorption excess isotherms

The retention of analyses in RP-HPLC markedly depends on the adsorption of the organic constituent of the mobile phase on the surface of the stationary phase. The excess adsorption isotherms of ACN, THF and methanol were measured on silica support modified with C, C6, C8, C10, C12 and C18 monomeric phase and a model was developed for the description of the retention of solutes from the binary mobile phase. The dependence of the retention factor on the partition coefficient can be described by... 

Y.V. Kazakevich, R. LoBrutto, F. Chan and T. Patel, Interpretation of the excess adsorption isotherms of organic components on the surface of reversed-phase adsorbents. Effect on the analyte retention. J. Chromatogr.A 913 (2001) 75-87. 

FIGURE 9.11 Classification of excess adsorption isotherms for binary solutions with o° solubility. After Kipling [39]. Reproduced by permission from Quantitative Review by Ripling Royal Society of Chemistry, Cambridge, UK, 1951. 

FIGURE 9.12 Excess adsorption isotherms for ideal bindary solution with infinite solubility for different values of K the adsorption distribution constant given by equation 9.44. 

Figure 2.2 Typical shapes of the absolute adsorption isotherm and excess absorption isotherm. The inflection of the excess adsorption isotherm can occur at high pressures.

In case of injection of a very small amount of analyte, its concentration is in the linear region of adsorption isotherm (Henry region of linear variation of adsorption with the equilibrium concentration of the analyte) and the derivative could be substituted with the slope of excess adsorption isotherm, also known as Henry constant, Kh, to get... 

It is essential that while setting the conditions for the differential mass-balance equation we did not define the function of the excess adsorption isotherm. We can now use the expression (2-46) for measurement of the model independent excess adsorption values. It is convenient to use it for the study of the adsorption behavior of binary eluents [22]. 

Since the measurement of the excess adsorption isotherm of a component in the binary system does not require a priori introduction of any model, it is possible to consider the excess adsorption isotherm as being model-independent (within a framework of adsorption process) and it is possible to derive the properties of the adsorbed layer on the basis of consideration of... 

Figure 2-8. Typical excess adsorption isotherm of acetonitrile from water on the surface of reversed-phase silica.

In another words, the negative slope of the excess adsorption isotherm in the linear region is equal to the volume of adsorbed layer, which was derived from the consideration of the adsorption process and not from a prior introduction of the model. A similar expression was derived by Everett [27]. 

The analysis of experimental excess adsorption isotherms using equation (2-50) had shown unusual results [22]. The adsorbed layer thickness of acetonitrile adsorbed from water on different types of reversed-phase adsorbents calculated as the ratio of adsorbed layer volume and adsorbent surface area appears to be on average equal to 14 A, which is equivalent to approximately five monolayers of acetonitrile molecules adsorbed on the hydrophobic surface. At the same time, the adsorbed layer thickness of methanol adsorbed from water on the same adsorbents is equal to only 2.5 A, which is equivalent to the monolayer-type adsorption. 

Equation (2-79) is the general form describing retention of ionizable analytes. Since it was derived with the assumption that injected analyte does not noticeably disturb the eluent adsorption equilibrium in the column, it is only applicable for very low analyte concentrations. At these low analyte concentrations, the slope of the excess adsorption isotherm is assumed to be constant and we can substitute the derivatives of the excess adsorption functions for both forms of the analyte with corresponding Henry constants (K and bh) ... 

Peak tailing is the most commonly observed effect of sample overloading. In essence, in most cases this effect is associated with nonlinear adsorption isotherms. In Chapter 2 the relationship of the retention volume and the derivative of the excess adsorption isotherm of the analyte on given stationary phase surface was derived. If the isotherm is linear within the injected concentration region, all components of the chromatographic zone are moving... 

Figure 4-52. Acetonitrile excess adsorption isotherm from water on Zorbax Eclipse XDB-C8 adsorbent (left) normalized filling of adsorbed layer (right). (Reprinted from reference 165, with permission.)...

A. Dabrowskl, M. Jaronlec, Excess Adsorption Isotherms for Solid-Liquid Systems and Their Analysis to Determine the Surface Phase Capacity, Adv. Colloid Interface Set, 31 (1990) 155. (Essential an attempt to obtain and define surface areas by adsorption from binary mixtures.)... 

We used excess adsorption isotherms for N2, CH4, Ar, CgHg and n-C4Hio on an activated carbon (F30-470 from Chemviron Carbon) at 303, 323, 343, 363 and 383 K. These data have been measured using a magnetic suspension balance specially instrumented to perform simultaneous high pressure and high temperature adsorption isotherms measurements. The experimental apparatus and the data are presented elsewhere [11,12,13]. 

M. Frere and G. De Weireld, High pressure and high temperature excess adsorption isotherms of Ni, CH4 and CsHg on activated carbon, J. Chem Eng. Data, accepted for publication in Chem. Eng. Data. 

The absolute aulsorption isotherms for —30°C and TO C were calculated from the 20°C isotherm using the integrated form of Eq. (1) and the differential enthalpy plotted on Fig. 2. The reasonable approximation was made that the differentiaJ enthaJpy is independent of temperature. No other assumptions were needed to calculate the excess adsorption isotherms on Fig. 3. 

Fig. 1 A comparison of the absolute with the excess adsorption isotherms of CH4 on activated carbon... 

The mole fraction was evaluated from the experimentally measured excess adsorption isotherms according to the following equation ... 

Figure 2. Excess adsorption isotherms for Figure 3. Excess adsorption isotherms for benzene (1) + n-heptane (2) on the carbons benzene (1) + 2-propanol (2) on the carbons AC-2 and AC-4 at 293K, AC-2 and AC-4 at 293K,...

In all these cases a system of non-linear equations is obtained, the numerical solution of which yields the concentration profile near a solid surface. From that concentration profile the (excess) adsorption isotherm is calculated next. Thus, although more accurate, this theoretical treatment does not lead to simple compact expressions which are so much preferred in practical interpretation of experimental data. 

In this work the independent method for determining the parameter n is presented. The main idea of this method is supported by a new form of the so - called exponential adsorption isotherm [2] and takes into account both heterogeneity of the solids and the nonideality of the liquid mixtures. One ought stress that this method in contrast to aforementioned is suitable for analyzing all types of the excess adsorption isotherms. 

Figure 1. Excess adsorption isotherm nj " vs. x of n-butanol (1) from benzene (2) on silica gel at 298 K 0-experimental points, — theoretical isotherm according to Eqs. (7) and (8).

An efficient model for the excess adsorption isotherms of microporous adsorbents should rely on a minimum number of parameters with a clear... 

Current measurements show that under ambient conditions, pure SWNTs adsorb little hydrogen (<1 wt%,) and their excess adsorption isotherms are linear, exhibiting classic Henry s law behavior. Under cryogenic conditions (77 K and 1 atmosphere), however, an excess adsorbed density of up to 2.5... 

The step in this development is the recognition that a Type I adsorption equation like Eq. (1) applies to absolute adsorption n. Absolute adsorption refers to the actual number of molecules present in the micropores and increases monotonically with pressure to an asymptote called the saturation capacity m. Experimental excess adsorption isotherms pass through a maximum and then decrease with pressure. 

The maximum in the excess adsorption isotherm occurs at the point where the densities in the micropore and the bulk gas are increasing at the same rate with respect to pressure, so... 

Serpinski, V.V., and Jakubov, T.S., Dubinin-Radushkevich equation as the equation for the excess adsorption isotherm, Adsorpt. Sci. Technol., 10, 85-92 (1994). 

Figure 3.10. Gibbs excess adsorption isotherms of (CO2, CH4, CO, N2) on activated carbon NORIT R1 EXTRA at T = 298.15 K, [3n.27], Data have been correlated using an isotherm of the generalized Langmuir type (3.38).

Figure 6.26. Gibbs excess adsorption isotherm (mQE(p)) and reduced molar polarizability (aj, /s ) of CH4 on DAY-zeolite (Degussa, Hanau) at T = 298 K for pressures up to 2 MPa, [6.41].

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