Isotherms Harkin-Jura

Physical adsorption of nitrogen was carried out on an ASAP 2400 Micromeritics apparatus. Before measurements, samples were evacuated overnight at 350 °C at vacuum of 2 Pa. For all samples the same adsorption data table was used. Collected adsorption data were treated by BET-isotherm in the range 0.05 < P/micropore volume and mesopore + external surface, t-plot method, with master isotherm of nonporous alumina (Harkins-Jura) was used, t-plot was linearized in the range of 0.35 < t < 0.6 nm. 

Although it may give satisfactory values for Asp, the Harkins-Jura equation leaves something to be desired at the molecular level. For example, the linear 7r versus o equation of state —the starting point of the derivation of the Harkins-Jura isotherm —represents the relatively incompressible state of the surface phase (i.e., 6 = 0.7 in Fig. 9.6b). (This equation is obtained in analogy with the approximately linear ir versus a equation for insoluble mono-layers discussed in Chapter 7.) However, in most instances of physical adsorption, no satura-... 

What is the Harkins-Jura isotherm What assumption does it make concerning the nature of the surface phase Is the assumption consistent with the experimental observations ... 

The derived values of specific surface area, a, and micropore volume, Vp, have been obtained from t-plots, as-plots and DA plots by the well known procedures described in the literature [1,3]. The Harkins-Jura (HJ) form of standard multilayer thickness curve was used to construct the t-plots. In our view, this approach is of limited value since it does not make allowance for the dependence of the standard isotherm on the surface structure of the adsorbent. For this reason, we prefer to adopt the empirical as-method, but this still leaves open the choice of the standard isotherm for nitrogen on an appropriate type of nonporous carbon. 

The N2 adsorption-desorption isotherms were collected on an ASAP 2010 analyser (Micromeritics). Prior to analysis, the samples were degassed (palumina-based materials) during 5 h. The contributions of microporosity to the overall surface area were estimated fi om a t-plot (Harkin-Jura) analysis of the adsorption curve (0.3 nm < t < 0.5 nm, with t being the statistical thickness). The pore size distribution was calculated from the desorption branch of the isotherm using the B JH model. 

Nitrogen physisorption measurements were performed on a Micromeritics Tristar 3000 apparatus at -196 °C. Prior to analysis the samples were dried in a helium flow for 14 horns at 120 °C. Surface areas (St), and micropore (Vmicro) and mesopore (Vmeso) volumes were determined using the t-method [13] with the Harkins-Jura thickness equation. There is no standard method for the determination of blocked mesopore volume (Vmeso,bi)- For this we used the pore size distribution from the desorption branch of the isotherm calculated using BJH theory [14]. The total amoimt of Vmeso,bi was determined considering that the volume in pores with a diameter of 2 - 5 run is (partially) blocked. 

We have addressed the various adsorption isotherm equations derived from the Gibbs fundamental equation. Those equations (Volmer, Fowler-Guggenheim and Hill de Boer) are for monolayer coverage situation. The Gibbs equation, however, can be used to derive equations which are applicable in multilayer adsorption as well. Here we show such application to derive the Harkins-Jura equation for multilayer adsorption. Analogous to monolayer films on liquids, Harkins and Jura (1943) proposed the following equation of state ... 

Thus, the Harkins-Jura isotherm equation can be written as... 

For the Harkins-Jura equation to describe the Type II isotherm, it must have an inflexion point occurring at the reduced pressure between 0 and 1, that is the restriction on the parameter B is ... 

We see that many isotherm equations (linear, Volmer, Hill-deBoer, Harkins-Jura) can be derived from the generic Gibbs equation (2.3-13). Other equations of state relating the spreading pressure to the surface concentration can also be used, and thence isotherm equations can be obtained. The following table (Table 2.3-1) lists some of the fundamental isotherm equations from a number of equations of state (Ross and Olivier, 1964 Adamson, 1984). 

Although the BET theory is used almost regularly as a convenient tool to evaluate the surface area of a solid, other isotherms such as the Harkins-Jura equation, obtained in Chapter 2 can also be used to determine the surface area. Analogous to a monolayer film on liquids, Harkins and Jura (1943) obtained the following equation ... 

To separate contributions due to micropore filling on one hand and the formation of mono- and multilayers on the other hand which are superimposed at relative pressures below 0.2- 0.3, the f-plot or the aj-plot approach can be applied. Both methods use empirical reference isotherms to be compared with the isotherms taken for the sample under investigation. In the f-plot method, the statistical layer thickness t of a nonmicroporous material is related to the relative pressure plp. One of the most frequently used relationship for the layer thickness is the empirical Harkins-Jura equation [67] derived for metal oxides ° ... 

Fig. 5. Thickness f of the adsorbed nitrogen film as derived from SANS (frill symbols) and from the filling isotherm on the basis of Eq. (7) (open symbols and frill line). The predictions of the Dollimore-Heal (DH) and Harkins-Jura (HJ) models are indicated by dashed lines...

The Gibbs isotherm assumes that adsorbed layers behave like liquid films, aud that the adsorbed molecules are free to move over the surface. This isotherm cau be derived then using classical thermodynamics using Gibbs free energy equations. This results in an isotherm of the form given in Equation 8.10. This is known as the Harkins-Jura (HJ) equation[90]. For details of derivation please refer to (3). 

Equation 17.23 has the form of an adsorption isotherm since it relates the amount adsorbed to the corresponding pressure. This is known as the Gibbs Adsorption Isotherm. For it to be useful, an expression is required for T. Assuming an analogy between adsorbed and liquid films, Harkins and Jura(15) have proposed that ... 

Data taken from the adsorption leg of the isotherm of Figure 17.11 are listed in the first two columns of the following table. Test the applicability of the following equilibrium theories (a) Langmuir (b) infinite BET and (c) Harkins and Jura. From (a) and (b) obtain estimates of the surface area of the adsorbent and compare the values with that obtained by the point B method. One molecule of nitrogen adsorbed on alumina occupies 0.162 nm2. 

Mention should be made of an important relation first brought out by Jura and Harkins (1944). It is simply that the adsorption isotherm is closely represented by the equation... 

Method of Jura and Harkins—This adsorption method was discussed in Chapter 11 (Eqs 11-23 and 11-24). The method involves use of the same procedure as the Brunauer technique—that is, the determination of the isotherm. Thereafter,. the linear plot of data in accordance with Eq (11-23) yields the constant necessary to determine the surface of a mass of particles. This method is comparable to that of Brunauer and his associates just described, and may be used as a check. 

Textural Parameters. Adsorption-desorption isotherms of N2 at 77K were determined in a Micromeritics ASAP 2010 with a micropore system. Prior to measurement, the samples were outgassed at 140 C for at least 16 h. The specific surface area was determined by the BET method, assuming that the area of a nitrogen molecule is 0.162 nm [12]. Micropore volume was calculated by the t-plot method using the Harkins and Jura [13] thickness. We used model isotherms calculated from density functional theory (DFT) to determine the pore size distributions and cumulative pore volume of the pillared samples by taking the adsorption branch of the experimental nitrogen isotherm, assuming slit-like pores [14]. 

More extensive and accurate data and additional calculations are necessary to obtain s , e , and from isotherm data over what is required to get the differential energy and entropy from the isosteric equation. The first complete calculation of ss, e and , as well as the differential quantities, has recently been made by Hill, Emmett, and Joyner (95). This paper shows in detail how the methods of this section can be applied in practice. Using heats of immersion, Harkins and Jura (96) made earlier equivalent calculations, but the relationship of their calculated quantities to the thermodynamic functions of the adsorbed molecules was not pointed out until recently by Jura and Hill (92). 

The adsorption isotherm yields the amount of gas adsorbed on the surface. Unless the molecular area occupied by the adsorbed gas is known, the adsorption isotherm yields only relative surface areas rather than the absolute values. This is the reason for using only one gas (nitrogen or krypton) to determine the surface areas of different solids. However, Harkins and Jura [45] developed an absolute method of... 

Work of Harkins and Jura IS). A distinctly different approach to the interpretation of low temperature gas adsorption isotherms has been followed by Harkins and Jura (13). By assuming that the same type of... 

Table III, Harkins and Jura, J. Am. Chem. Snc. A6, 1360 (1944) with a column of calculations for the areas by B.E.T. method using water isotherms with an assumed cross-section of 11.3 A. for the water molecule. 

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