Adsorption isotherms determination

Carbon black adsorbed OLOA 1200 very strongly, eventually picking up 5% of its weight in dispersant. The first 2% adsorbed almost instantly, but additional increments adsorbed more and more slowly (see Figure 5). Such time-dependence in adsorption of large molecules is quite common (15), but is seldom studied. The adsorption isotherms determined after 48 hours of tumbling at 25°... 

Derivation of the Gibbs adsorption isotherm. Determination of the adsorption of surfactants at liquid interfaces. Laboratory project to determine the surface area of the common adsorbent, powdered activated charcoal. 

In Figure 6.22a, the MPSD of the DAY zeolite calculated with the help of the SF method is reported. The DAY zeolite has an FAU framework, with a 12MR three-dimensional channel system with apertures of 7.4 A (see Section 2.5.1) [83], The obtained PSD for the DAY zeolite shows a clear maximum at about 7 A. In Figure 6.22b, the S-F MPSD of the SWCNT is reported [80], The calculated PSD for the SWCNT indicates that this material has a slightly heterogeneous distribution of pores with a clear, and highly populated, maximum at 13.5 A [80], The adsorption study, in both cases, was carried out using N2 adsorption at 77 K isotherms, obtained with a Quantachrome Autosorb-1 equipment for adsorption isotherm determination by the volumetric method [21],... 

The isosteric differential heats of physical adsorption of nitrogen near its boiling point on reduced and oxidized electropolishing single crystal copper surfaces can be evaluated from adsorption isotherms determined gravimetrically. 

The first step is devoted to the determination of adsorption isotherms. Several adsorption isotherm determination methods have been described [13], and we developed a laboratory apparatus allowing to determine very precise adsorption isotherms in supercritical fluids. 

In principle, this method of calculating the differential enthalpy of adsorption could be applied to two adsorption isotherms determined at different temperatures, but the following restrictions must be kept in mind ... 

A very unusual shape of adsorption isotherm has recently been obtained by Matsusita of this laboratory (46) for the adsorption of ethylene on reduced nickel. The adsorption isotherms determined at 130° and 140°C. in the range of 10 to 10 mm. Hg equilibrium pressure consist of three linear parts in the log-log plot as shown in Fig. 6. The first break occurs at the coverage 0.1, assuming that saturation corresponds, in this case, to one ethylene molecule being adsorbed for every four nickel atoms in the surface. 

Figure 1 illustrates typical N2 adsorption isotherms determined on the char samples produced from the dififerent wastes, providing information about samples larger pores, mainly macropores, mesopores and larger micropores. Nitrogen adsorbed volumes expressed in standard conditions of temperature and pressure (STP) per sample mass unit, V as a function of die relative pressure (p/po) are shown in the figure. 

The value of 120 has been calculated from the amount of charge associated with the voltammet-ric reduction of hydrogen peroxide preadsorbed at the TiOj electrode (cf. Fig. 11), using the H2O2 adsorption isotherm determined by Boonstra and Mutsaers for an anatase powder sample. 

Several methods allowing the determination of adsorption isotherms exist. The most economical one is the use of saturated salt solutions, generating known water partial pressures, followed by the measurement of the silica weight uptake. However, the time needed to obtain a suitable adsorption isotherm is excessively long (several weeks), and experimental precautions need to be taken to achieve meaningful results. Specialized equipments, quite expensive ones, have been developed for the water adsorption isotherm determination, based on highly sensitive microbalances. 

Determined by N2 adsorption isotherms. Determined by gravimetric method. 

Figure 4.22 Experimental concentration profiles in the column effluent for adsorption isotherm determination by binary frontal analysis. (Left) Bottom trace solid line, experimental UV profile dotted line reconstructed profile of 3-phenylpropanol (P) dashed line reconstructed profile of 2-phenylethanol (E). Arrows 1-5 indicate the time when the eluent sample was taken for on-line analysis. Top trace On-line analysis of the sampled eluent. Reproduced with permission from J. Zhu, A. Katti and G. Guiochon, J. Chromatogr. 552 (1991) 71 (Fig. 1). (Right) Examples of one-step binary frontal analyses for the determination of the competitive isotherms of N-benzoyl-D,L-alanine. Injection of large volumes (5 mL) of solutions of increasing concentrations of racemic mixture. Reproduced with permission from S.C. Jacobson, A. Felinger and G. Guiochon, Biotechnol. Progr., 8 (1992) 533 (Fig. 1), 1992 American Chemical Society.

Both volumetric and gravimetric techniques have been used for the determination of adsorption isotherms of gases on solids. The volumetric technique is one of the widely used methods for the adsorption isotherm determination and is based on the measurement of the pressure-volume relation to determine the... 

An illustration of the surface heterogeneity of silica, deduced from isotherm measurements, is shown in Figure 10 which indicates the variation, with the coverage degree (0), of the isosteric heat of adsorption Qst of heptane and toluene, calculated from adsorption isotherms determined at 37° and 47°C, on a talc by Jagiello et al.[19]. 

The H2O adsorption on superhigh surface area carbon was studied by the in situ X-ray diffraction technique [36]. The surface area, micropore volume, and pore width of superhigh surface area carbon were 2670 m /g, 0.97 ml/g, and 1.3 nm, respectively. The H2O adsorption isotherm determined at 303 K was of typical type V. The H2O molecules were not adsorbed below P/Po = 0.6 and then they were abundantly adsorbed above P/Pq = 0.6. Fig. 8 shows the X-ray diffraction patterns of adsorbed H2O as a function of... 

The isotherm of adsorption from solution may be determined by frontal chromatograms [6-8]. In [6] it was shown that if to take into consideration the broadening the band owing to diffusion, the adsorption isotherms determined by the column chromatography and in a batch process are coincided. This method can be used for the calculation of S-shape isotherm of adsorption. The isotherm of adsorption can be determined by frontal chromatography if the adsorbents have not fine pores [7]. 

For any method, care must be taken to define the reference state of the solute, which can be either the solution at equilibrium with the surface or the solution at infinite dilution state [4, 52]. An adsorption isotherm determined independently is needed to relate the calorimetric data with the surface excess amount. 

The specific surface area, Sbbt> of the support and of the prepared samples was evaluated by the BET method from the nitrogen adsorption isotherms determined at -1%°C in a high vacuum apparatus. 

Fig. 3. Water adsorption isotherms determined, at 40 °C, on Wacker s pyrogenic silica samples.

The water vapor [23] and nitrogen gas [24] adsorption isotherms determined by using automatic adsorption apparatus have been reported. On the other hand, the manual adsorption method for the adsorption of water vapor and nitrogen gas is discussed in Refs. 25 and 4, respectively. The amount adsorbed is determined by using a Shibata moisture and surface area apparatus. Model P-850 [Shibata Scientific Technology, Ltd., Tokyo, Japan) [25]. The amounts of water vapor and nitrogen gas adsorbed are determined by the gravimetric method [25] and volumetric method [4], respectively. 

For adsorption isotherm determination, the accurate knowledge of the dead volume is required. In most cases, the dead volume tracer method produces appropriate results. When a cross-check of the dead volume value is necessary, the density method can be used. First, the column is carefiiUy flushed and filled with methanol which has a density of 0.7914 g/cm at 20°C. It is disconnected fi om the pump and its two sides are closed to avoid evaporation. The column is weighted. Its mass is W eon- Next, the coluirm is similarly flushed and filled with chloroform, d=1.483 g/cm at 20°C, and weighted. The second mass, Wchcijj higher than the first one, allows to obtain the dead volume with a high accuracy using ... 

The form of the adsorption isotherm determines the shape of the polarization curve, influencing the magnitude of Tafel slope b, since, varying with the potential, leads to a variation in A and hence in the activation energy. This effect has been discussed at length, starting with the first work by Temkin (see, for example. Ref. 23). A most vivid illustration of the foregoing is the independence of the current on the potential. 

Specific surfaces are most often determined by measurements of adsorption capacity of a gas in a monomolecular layer. This method needs one or several points on the isotherm and the choice of an appropriate adsorx>-tion model. Then, the adsorption isotherms determined by GSC allow, in principle, the determination of specific surfaces. 

This chapter has reviewed modeling over the years and the progress that can be identified. It has been demonstrated that modelers, using modem computational systems, base their calculations on stmcture systems, usually around the graphitic microcrystallite. An objective of such modelers is the simulation of adsorption isotherms determined experimentally. Whether or not the structural models assumed for their work can be considered to be realistic is rarely a matter for discussion. Accordingly, the considerations of such modelers should not be adopted, uncritically, by those who have other interests in activated carbon. 

The adsorption of CNA and the Nd-CNA complex on a hanging mercury drop electrode (HMDE) was studied quantitatively as shown in fig. 4. Curve 1 is the adsorption isotherm determined experimentally, curves 2 and 3 are those calculated according to Langmuir and Frumkin isotherms, respectively. It may be seen that curve 1 fits curve 3 quite well, i.e., the Frumkin isotherm is satisfied. The Frumkin isotherm is represented by the following expression ... 

Fig. 8. Nitrogen, at 77K, and n-pentane, at 298K, adsorption isotherms determined on Ti-Ep-30 before and after water vapour adsorption (a.w.a.). (empty symbols adsorption, filled symbols desorption).

In the design of SMB experiments, one is mostly concerned with the projection of the four-dimensional space, (j=l,...4), onto (m2,) plane, i.e., the plane in the operating parameter space spanned by the flow rate ratios of the two key seetions of the SMB unit. From adsorption isotherm determined previously and the feed eoncentration, complete separation regions for propranolol hydroehloride separation was constructed in the (m2, m3) plane, as shown in Figure 5. It is worth noting that for proper operation of SMB to obtain desired complete separation, adsorbent and fluid should be regenerated in section 1 and 4 respectively. 

Numerous exact and approximate methods have been proposed to solve the integral equation (10) with Langmuir local adsorption isotherm. Then, an application of a given analytical equation to represent the overall adsorption isotherm determines automatically the form of energy distribution function, the parameters of which are obtained by fitting the isotherm to experimental data [6]. 

For small molecules it is often assumed that both attachment and detachment are so rapid (i.e., A and A are large) that there is almost equilibrium between the adsorbed layer and the subsurface concentration throughout the adsorption process ( local equilibrium ) [10]. This means that the equilibrium adsorption isotherm determines the value of namely, c s c, and that other kinetic factors can be entirely ignored. For polymers, however, this cannot be generally supposed. 

By using the constants, determined in the adsorption rate experiment, Brunauer et al. achieved an excellent fit to the adsorption isotherm determined experimentally with the same catalyst. 

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