Adsorption 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-... 

Loeser and Harkins (45) have made a critical comparison of the Brunauer-Emmett-Teller and Harkins-Jura methods of calculating the surface area of graphite by adsorption of n-heptane at 25° C. The lower limit of surface area which can be measured by the Harkins-Jura method using n-heptane is given as 2500 sq. cm. 

Figure 2. Dependencies of the adsorption potential on the pore width calculated according to the equations (3) (SF curve), (4) (curve KJSe) and (5) (curve KJSc). The KJSc curve was calculated via equation (5) using the Harkins-Jura-type expression for the statistical film thickness t, which gives a good representation of the experimental t-curve only in the range of relative pressures from 0.1 to 0.95. Therefore, this curve deviates from points at high values of A, which correspond to low values of p/po. Data for the ZLZ curve are from Zhu et al. [29].

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. 

Measured by atomic absorption spectrometry. Reference untreated NaY. c).d) Low pressure argon adsorption. t-Plot method of Lippens-De Boer, Harkins-Jura equation. 

As an example of a high boiling adsorbate, adsorption data for n-heptane on graphite may be considered. Harkins, Jura, and Loeser [43] reported afilm pressure at saturation of 63 dynes per cm.for this system. For comparison, we may cite the value for monolayer coverage given by Chessick, Zettlemoyer, and Wu [20], which was 27.6 dynes per cm. Thus, the relative contributions of monolayer adsorption and multilayer adsorption to the film pressures at saturation are quite comparable... 

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 ... 

The surface areas of all the samples were measured using the B.E.T. method with nitrogen adsorption at 77 K and a Micromeritics ASAP 2000 for the determination of the pore size distribution for the most interesting ones. Mesopore size distributions were calculated using the Barrett, Joyner and Halenda (BJH) method, assuming a cylindrical pore model (IS). In the analysis of micropore volume and area, the t-plot method is used in conjunction with the Harkins-Jura thickness equation (16). 

A more recent investigation has revealed that this problem can be overcome by using water as the liquid since two molecular layers are sufficient to effectively screen the underlying surface of many adsorbents. These results have led to a modification of the original Harkins-Jura "absolute method for surface area determination and they make it possible to apply the technique to mesoporous solids (by avoiding the complication of capillary condensation). Obviously, the approach cannot be used in isolation to study micropore filling, activated entry or molecular sieving, but it becomes a powerful tool when combined with gas adsorption. 

Equation (2.65) involves only the quantities P and V which are measured directly in the experimental determination of adsorption. Harkins and Jura reported that this simple equation was valid over more than twice the pressure range of any other two-constant adsorption isotherm equation. 

Make a numerical estimate, with an explanation of the assumptions involved, of the specific surface area that would be found by (a) a rate of dissolving study, (b) Harkins and Jura, who find that at the adsorption of water vapor is 6.5 cm STP/g (and then proceed with a heat of immersion measurement), and (c) a measurement of the permeability to liquid flow through a compacted plug of the powder. 

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. 

Harkins, W. D. and Jura, G. J. Chem. Phys. 11 (1943) 431. An adsorption method for the determination of the area of a solid without the assumption of a molecular area and the area occupied by nitrogen molecules on the surface of solids. J. Amer. Chem. Soc. 66 (1944) 1366. Surface of solids. Part XIII. 

A great deal of adsorption work has been carried out using titanium dioxide as an adsorbent, following extensive work with this material by Harkins and Jura 169). In one series of accurate calorimetric experiments, the initial temperature of evacuation was 300° C. 96). Any grease present on the rutile before degassing would not have been removed by this treatment. Recent work 170) has shown that it is possible that rutile may be subject to hydrocarbon contamination. 

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. 

It has long been realized that the heat of adsorption can be calculated more accurately from determinations of heats of immersion than from equilibrium vapor pressures of adsorbates. Harkins and Boyd (8) and Jura and Harkins (10) have discussed the emersion process and have developed an expression for the enthalpy of desorption that is the negative of the one above. That the immersion process is equivalent to the process we are discussing can readily be shown with the aid of the following two-step process ... 

The total surface area needs to be known to determine the change of internal surface energy from the heat of immersion. This is often done by adsorption measurements [94,83]. An alternative method was suggested by Harkins and Jura 92. They proposed not to immerse a clean solid but to expose the solid first to the vapor of the liquid. If the liquid wets the solid at the saturating vapor... 

Whilst the use of the Kelvin equation can be questioned in the case of smaller mesopores, this is not the case in the present case where, on the contrary, the pores are situated in the upper mesopore range. However, use of the BJH method implies the use of a t-curve. On commercial adsorption equipment, the software proposes the use of several equations to fit the t-curve. In the present case, the Harkins and Jura equation or Halsey equation is proposed. Unfortunately neither of these fit the original t-curve data of de Boer very well. 

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]. 

The heat measured in step (3) corresponds to the adsorption of an unknown amount of vapor on the carbon surface. Now, in case of a wetting system, we know that the conditions are then fulfilled to have a multilayer adsorbed. This means that the heat measured in step (4) corresponds to the immersion energy of a precovered solid, so that it can be used for the surface area determination by the modified Harkins and Jura method [7]. The addition of the heats measured in steps (3) and (4) after suitable correction leads to the usual immersion energy. If the full wetting is not reached at saturation pressure it is then needed to proceed to step (5). More details about this procedure and the way to get experimental data are described elsewhere [9]. 

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