Determination of the adsorbed mass

Several methods are available for the determination of the adsorbed mass. One is the radio-tracer method pioneered by Horanyi and Kazarinov and Andreev. Experimental details are found in the literature. 

The most effective method to measure the adsorbed mass is the quartz crystal microbalance (QCMB). This method goes back to the work of Sauerbrey. ° The apphcation of this method is based on the following equation relating the shift A/of the resonance frequency /o of a quartz crystal to the change of the mass of the crystal Am divided by A (area) 

The application of this method is not as simple as previously assumed. - Secondary effects accompany the change of the mass, e.g., increase of roughness or changing viscosity 

To determine frequency shift and damping a frequency analyzer is used. The additional damping can be represented by a complex frequency shift, determined by the change of the full width at half maximum (FWHM) Am. 

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Recently, Keller published a method allowing for the absolute determination of the adsorbed mass m of porous materials [5]. It consists of a combination of calorimetric and impedance spectroscopic measurements. Unfortunately, that method is experimentally difficult and needs improvements for practical applications [6]. 

Figure 4.30 Determination of the adsorbed mass of lead with the twin electrode thin-layer method descrihed in Figure 4.15. Pb UPD on (a) Ag(lll) and (b) Ag(lOO). Concentrations as given in Figures 4.27 and 4.28. (Reproduced with permission from Ref. [60], 1978, Elsevier.)...

In order to study the kinetics of adsorption or desorption with flow eells as described above, an in situ method is needed for the determination of the adsorbed mass or another property of the adsorbed moleeules. A survey of the different methods is given in Seetion III.D. 

The column void volume, Vo, is dehned as the total volume of the liquid phase in the column and could be measured independently [18]. Total adsorbent surface area in the column, S, is determined as the product of the adsorbent mass and specific surface area. 

While the two coating materials, Si02 and PDMS, have different thicknesses and refractive indexes, the change of the refractive index, which is the basis for tbe determination of adsorbed mass, was observed to be nearly identical by testing with polymer-free aqueous solutions with different bulk refractive indexes, which validates the comparison of the adsorbed mass of the polymers onto both surfaces. 

Quartz Microbalance and Direct Microbalance Techniques. These methods provide direct measurements of the adsorbed mass. The vibration frequency of a quartz single crystal is very sensitive to the mass of the crystal. Upon adsorption, the vibration frequency shifts to lower values and the changes in the frequency can be related to the adsorbed mass. The surface excess can be determined by dividing the adsorbed mass by the surface area (6). Another method to directly measure the surface excess is the microbalance technique. In this technique, the... 

A simple way for the determination of the polymer mass per unit area is through gravimetric analysis. Usually the porous membranes that are used for the preparation of concave brushes have a very large surface area, so the formation of a polymer brush inside the pores produces an easily measurable change of the sample s weight. Precise knowledge of the membrane porosity and pore size permits the straightforward calculation of the polymer mass per unit area, which for the case of self-assembled brushes is the adsorbed amount P. 

In addition to separation by functionality, applications of LCCC involve the determination of the molar-mass distribution of one component in polymer blends. This is achieved by selecting critical conditions for one blend component (A), such that the other blend component (B) is adsorbed less and consequently elutes in SEC-like elution order before the solvent peak. Thus, it is possible to determine the molar-mass distribution of component B in the blend by calibration with suitable standards of t)q5e B. The amounts of both blend components can be quantified at the same time. 

Different time-dependent properties of flie adsorbed polymer layer ean be used to study the dynamie behavior of polymer adsorption. In most investigations only the inerease or decrease of the adsorbed mass with time is determined. However, these experiments do not give sufficient information with respect to rearrangement processes taking place within the adsorbed layer. For characterizing these rearrangements, measurements of the bound fraetion, train densities, or the layer thickness, are indispensable. 

Quartz Crystal Microbalance (QCM) and Direct Microbalance Techniques provide measurements of the adsorbed mass. In the QCM technique, adsorbed mass is determined from the shifts of vibration frequency of a quartz single crystal to lower values as a result of pol3rmer adsorption (80). In the microbalance technique, microbalances with sensitivity of 10 " mg are used to determine the change in mass of a substrate due to adsorption (81). 

There are two effects from the adsorbent bed depth on mass transfer. First, it is important that the bed be deeper than the length of the transfer zone which is unsaturated. The second is that any multiplication of the minimum bed depth gives more than a proportionally increased capacity. Generally, it is advantageous to size the adsorbent bed to the maximum length allowed by pressure-drop considerations. The determination of the depth of the MTZ or unsaturated depth may be determined experimentally, and applying the following relationship ... 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

We express the altered concentration in terms of the adsorption excess. If all the adsorbed substance were contained to the extent of k gr. per cm.2 on a superficial layer of zero thickness and surface total mass present in the volume Y would be m = V + kto. The layer of altered concentration must, however, have a certain thickness. We will therefore imagine a plate 2 placed in front of the surface and parallel to it, and define the adsorption excess as the concentration in the included layer minus the concentration in the free liquid. That this result is independent of the arbitrarily chosen thickness is easily proved when we remember that the problem is exactly the same as that of finding the change of concentration around an electrode in the determination of the transport number of an ion by Hittorf s method. 

SEC-GC-FID, according to Figure 7.40, has been used to carry out the simultaneous determination of the polymer average molecular masses and molar mass distribution and the concentration of additives [984]. The effluent was split and adsorbed on PTV packing material before GC analysis. The choice of PTV... 

The three remaining steps (chemisorption of reactants, reaction on the surface, and desorption of adsorbed products) are all chemical in nature. It is convenient to employ the concept of a rate limiting step in the treatment of these processes so that the reaction rate becomes equal to that of the slowest step. The other steps are presumed to be sufficiently rapid that quasiequilibrium relations may be used. The overall rate of conversion will then be determined by the interaction of the rate of the process that is rate limiting from a chemical point of view with the rates of the physical mass transfer processes discussed above. 

The model is most vulnerable in the way it accounts for the number of particles that collide with the electrode [50, 115], In the model, the mass transfer of particles to the cathode is considered to be proportional to the mass transfer of ions. This greatly oversimplifies the behavior of particles in the vicinity of an interface. Another difficulty with the model stems from the reduction of the surface-bound ions. Since charge transfer cannot take place across the non-conducting particle-electrolyte interface, reduction is only possible if the ion resides in the inner Helmholtz layer [116]. Therefore, the assumption that a certain fraction of the adsorbed ions has to be reduced, implies that metal has grown around the particle to cover an identical fraction of the surface. Especially for large particles, it is difficult to see how such a particle, embedded over a substantial fraction of its diameter, could return to the plating bath. Moreover, the parameter itr, that determines the position of the codeposition maximum, is an artificial concept. This does not imply that the bend in the polarisation curve that marks the position of itr is illusionary. As will be seen later on, in the case of copper, the bend coincides with the point of zero-charge of the electrode. 

The determination of adsorption isotherms at liquid-solid interfaces involves a mass balance on the amount of polymer added to the dispersion, which requires the separation of the liquid phase from the particle phase. Centrifugation is often used for this separation, under the assumption that the adsorption-desorption equilibrium does not change during this process. Serum replacement (6) allows the separation of the liquid phase without assumptions as to the configuration of the adsorbed polymer molecules. This method has been used to determine the adsorption isotherms of anionic and nonionic emulsifiers on various types of latex particles (7,8). This paper describes the adsorption of fully and partially hydrolyzed PVA on different-size PS latex particles. PS latex was chosen over polyvinyl acetate (PVAc) latex because of its well-characterized surface PVAc latexes will be studied later. 

Adsorption is often studied using powders or porous materials because the total surface area is large even for small amounts of adsorbent. In a typical experiment the volume (V) or the mass (to = V/p) adsorbed per gram of adsorbent, is measured. Theoretical models always describe an adsorption per surface area. In order to compare theoretical isotherms to experimentally determined adsorption results, the specific surface area needs to be known. The specific surface area (in m2/kg) is the surface area per kg of adsorbent. Once the specific surface area is known, the area can be calculated by A = madT, where mad is the mass of the adsorbent. 

The most common method used for the determination of surface area and pore size distribution is physical gas adsorption (also see 1.4.1). Nitrogen, krypton, and argon are some of the typically used adsorptives. The amount of gas adsorbed is generally determined by a volumetric technique. A gravimetric technique may be used if changes in the mass of the adsorbent itself need to be measured at the same time. The nature of the adsorption process and the shape of the equilibrium adsorption isotherm depend on the nature of the solid and its internal structure. The Brunauer-Emmett-Teller (BET) method is generally used for the analysis of the surface area based on monolayer coverage, and the Kelvin equation is used for calculation of pore size distribution. 

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