Adsorption-desorption equilibria dynamic

Adhesive force, non-Brownian particles, 549 Admicelle formation, 277 Adsorption flow rate, 514 mechanism, 646-647 on reservoir rocks, 224 patterns, on kaolinite, 231 process, kinetics, 487 reactions, nonporous surfaces, 646 surface area of sand, 251 surfactant on porous media, 510 Adsorption-desorption equilibria, dynamic, 279-239 Adsorption plateau, calcium concentration, 229... 

Following mono-layer uptake, further increase in pressure results in multi-layer adsorption of N2. For this part of the isotherm, condensation-evaporation equilibrium is assumed to take place, instead of adsorption-desorption equilibrium for each individual layer other than the first layer. This dynamic equiUbria for the first and higher layers and some simplifying assumptions form the basis for the B ET treatment of the multi-layer adsorption isotherm. A lengthy derivation leads to the BET relation between adsorbed volume of N2 and relative pressure. Here relative pressure is defined as the ratio of the equilibrium pressure to the... 

The proposed structure of the complex does not assume a static distribution of the sequences. The system is of course a dynamic one, but we study it at equilibrium. A given COOH group, involved in a complex at the moment t, may be free or in the carboxylate from at t + dt. However the average number of complexed sequences remains invariant with time for a fixed composition of the system. The situation can be compared with the behaviour of macromolecules adsorbed at a solid-liquid interface their mean conformation is stable even if locally an adsorption/desorption equilibrium occurs. 

Summarizing this section it can be stated that the adsorption bonds in filled PDMS have a dynamic origin. With increasing temperature, the frequency of adsorption-desorption processes in the adsorption layer increases and the adsorption-desorption equilibrium shifts to the chain desorption. At room temperature, the lifetime for the dimethylsiloxane chain units in the adsorption state is very short chain units adhere to the filler surface only for tens of microseconds. 

The presence of the solid surface imposes new conditions onto the disposition of reactants, compared with the homogeneous case (section C2.14.4.T). Adsorption is often observed to approach a plateau, yet is irreversible with respect to dilution. The plateau must therefore arise because no more space is available for adsorption, rather than through a dynamic adsorption-desorption equilibrium and it can be inferred that the dissolved biopolymer does not adsorb to its preadsorbed congeners. This behaviour is by no means universal it has been proposed that the plaques associated with spongiform encephalopathies arise through the native, normally soluble Pr protein being partially denatured upon contact with a surface to become the pathogenic PrP form, to which the PrP can adhere to form multilayers. 

Instead of UHV conditions, a wet process was applied by Kunitake and coworkers in order to realize an equilibrium polymerization on the surface [136]. In this case, iodine-modified Au(111) substrates (I/Au(lll)) were dipped into aqueous solutions of tetraamine 64 and dialdehyde monomers 65-67 (Figure 28.28b). A dynamic adsorption-desorption equilibrium and a high lateral mobility of the adsorbed monomers on I/Au(lll) allowed for their surface polycondensation based on Schiff-base formation. The polycondensation was found to be sensitive to the solution conditions (such as pH), as well as to the choice of substrates. When the products were observed directly using STM, fragments with a periodic order were seen to have formed on the surface, although the lateral sizes still required some improvement (Figure 28.29). 

The study of the dynamics of N isotope transfer under adsorption-desorption equilibrium (NO -1- O2 + He) revealed two types of NOx complexes, and their concentrations and formation rates (depending on NO and O2 concentrations) were estimated. According to in situ diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) data, these complexes are assigned to nitrite-nitrate (1520 cm" ) and N02 species (2130 cm" ). Note that nitrite-nitrates and N02 differ clearly in the rates of their formation. Under the reaction conditions, the concentrations of both active species drop considerably. Therefore, two parallel reaction pathways were proposed that involve both active complexes. The rates of NOx complexes interaction with methane were also calculated, and the reaction with participation of N02 species was shown to proceed about 2.5 times faster than that of nitrite-nitrate. The N02 species was determined to form at the interface between CoO clusters and acid OH groups in zeolite (or at the paired Co -OH sites). This finding agrees well with in situ DRIFTS data that indicates that the N02 formation correlates with a drop in the acid OH group band intensity. 

The gases released from the primary coolant in the degasification system mainly contain the fission product noble gases which, with the sole exception of Kr, are comparatively short-lived nuclides. In order to prevent release to the environment, therefore, it is sufficient to store them for a certain time until these isotopes have decayed. In most of the US PWR plants as well as in the plants built by Frama-tome, gas decay tanks are used for this purpose. In the plants designed and built by Siemens/KWU, decay lines are employed which are equipped with a series of charcoal beds in which the noble gases are delayed relative to the carrier gas flow by a dynamic adsorption-desorption equilibrium. Under normal operation conditions, delay times on the order of 60 hours for the krypton isotopes and 60 days for the xenon isotopes are obtained, which are sufficiently long for nearly complete... 

Ce02-Zr02-La203 and Pt/Ce02-Zr02 solids was recently reported under conditions of dynamic adsorption-desorption equilibrium in a plug-flow microreactor at 1 atm in the temperature range 650-850°C... 

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 ... 

The Monte Carlo method as described so far is useful to evaluate equilibrium properties but says nothing about the time evolution of the system. However, it is in some cases possible to construct a Monte Carlo algorithm that allows the simulated system to evolve like a physical system. This is the case when the dynamics can be described as thermally activated processes, such as adsorption, desorption, and diffusion. Since these processes are particularly well defined in the case of lattice models, these are particularly well suited for this approach. The foundations of dynamical Monte Carlo (DMC) or kinetic Monte Carlo (KMC) simulations have been discussed by Eichthom and Weinberg (1991) in terms of the theory of Poisson processes. The main idea is that the rate of each process that may eventually occur on the surface can be described by an equation of the Arrhenius type ... 

Third, we assume the adsorption process is dynamic. Adsorption and desorption occur to equal and opposite extents at equilibrium, provided the mass of material adsorbed remains constant. 

Polysaccharides interfaced with water act as adsorbents on which surface accumulations of solute lower the interfacial tension. The polysaccharide-water interface is a dynamic site of competing forces. Water retains heat longer than most other solvents. The rate of accumulation of micromolecules and microions on the solid surface is directly proportional to their solution concentration and inversely proportional to temperature. As adsorbates, micromolecules and microions ordinarily adsorb to an equilibrium concentration in a monolayer (positive adsorption) process they desorb into the outer volume in a negative adsorption process. The adsorption-desorption response to temperature of macromolecules—including polysaccharides —is opposite that of micromolecules and microions. As adsorbate, polysaccharides undergo a nonequilibrium, multilayer accumulation of like macromolecules. 

Tensions of non-relaxed interfaces are sometimes known by the adjective dynamic dynamic surface tension or dynamic inteifacial tension. The term dynamic is not absolute. It depends on De (i.e. on the time scale of the measurement as compared with that of the relaxation process). Some interfacial processes have a long relaxation time (polymer adsorption-desorption), so that for certain purposes (say the measurement of y] they may be considered as being in a state of frozen equilibrium. This last notion was introduced at the end of sec. 1.2.3. Unless otherwise stated, we shall consider static tensions and interfaces which are so weakly curved that curvature energies, bending moments, etc. may be neglected. 

If the equilibrium adsorption-desorption assumption (EADA) is relaxed, then a more complicated kinetic model is obtained. The simplest way to relax this assumption is to replace it by a steady state assumption (SSA), that is assuming that the catalyst surface is at steady state. Both assumptions are strictly valid only for steady state conditions and cannot be used rigorously in the dynamic modelling of catalytic reactors. However, because of the complexity of the system and the lack of sufficient knowledge on the dynamics of the CSD processes, steady state kinetic models are usually used for dynamic modelling of catalytic reactors. 

In this chapter a lumped dynamic model of a porous catalyst pellet is developed on the basis of the active site theory and assuming equilibrium adsorption-desorption according to a linear Langmuir isotherm. This model is compared with a previous pseudo-homogeneous model due to Liu and Amundson (1962). Next, the assumption of equilibrium adsorption-desorption is relaxed and the effect of both activated as well as non-activated adsorption is presented. The rate of adsorption is treated in very simple terms under the Langmuir postulates as discussed earlier. 

Another important issue which is not included in the dynamic modelling here is the type of kinetic rate equations used. This is an important problem that still requires extensive experimental and theoretical research. From chapter 3, we notice that most kinetic rate equations for catalytic reactions are based on restrictive steady state assumption or more often the even more restrictive equilibrium adsorption-desorption assumption. Therefore, these rate equations are not necessarily valid for the description of the catalytic process under unsteady state conditions. 

Langmuir was the first to provide of a theory of the interrelation between thermodynamics and macro-kinetics. It introduces the balance of adsorption and desorption fluxes into the adsorption theory and defines the equality as the equilibrium state of the adsorption layer. A disturbance of the adsorption equilibrium leads to a net adsorption or net desorption flux. This idea serves as a bridge from thermodynamics to macro-kinetics and allows a deeper understanding of the equilibrium state of adsorption as a dynamic process as demonstrated by de Boer in his monograph "Dynamic Character of Adsorption". 

The equation derived for the transport of surfactant ions through the DL describes the adsorption kinetics as a reversible process. The qualitatively new result in the theory of ionic adsorption kinetics is the incorporation of electrostatic retardation for both the adsorption and desorption process, which is of essential importance for processes close to equilibrium. Such a situation exists at harmonically disturbed surfaces, used in investigations of adsorption dynamics like the damping of capillary waves or oscillating bubbles. At sufficiently high frequencies the diffusion layer becomes very thin and the adsorption-desorption exchange is controlled only by the ion transport through the DL, i.e. by the electrostatic retardation. At... 

Some consequences which result from the proposed models of equilibrium surface layers are of special practical importance for rheological and dynamic surface phenomena. For example, the rate of surface tension decrease for the diffusion-controlled adsorption mechanism depends on whether the molecules imdergo reorientation or aggregation processes in the surface layer. This will be explained in detail in Chapter 4. It is shown that the elasticity modulus of surfactant layers is very sensitive to the reorientation of adsorbed molecules. For protein surface layers there are restructuring processes at the surface that determine adsorption/desorption rates and a number of other dynamic and mechanical properties of interfacial layers. 

In order to describe the evolution of the surface pressure during the adsorption process, the three involved dynamic processes have to be considered, i.e. the diffusion process in the bulk, the adsorption-desorption exchange between the surface and the subsurface, and the change in the orientation of the adsorbed molecules. In the present model, adsorption is considered to proceed in the following way. The molecules, which are randomly oriented in the bulk, adsorb either in the state 1 or 2, with the respective probabilities x and 1-x. The diffusion sets in when there is a concentration gradient established in the bulk. As the distribution of the freshly adsorbed molecules between the two states is out of equilibrium, a re-orientation process is induced. The time evolution of the partial adsorptions T1 and T2 is described then by... 

By applying an appropriate perturbation to a relevant parameter of a system under equilibrium, various frequency modulation methods have been used to obtain kinetic parameters of chemical reactions, adsorption-desorption constants on surfaces, effective diffusivities and heat transfer within porous solid materials, etc., in continuous flow or batch systems [1-24]. In principle, it is possible to use the FR technique to discriminate between all of the kinetic mechanisms and to estimate the kinetic parameters of the dynamic processes occurring concurrently in heterogeneous catalytic systems as long as a wide enough frequency range of the perturbation can be accessed experimentally and the theoretical descriptions which properly account for the coupling of all of the dynamic processes can be derived. 

Ebner, A.D., Reynolds, S.P. and Ritter, J.A. (2006) Understanding the adsorption and desorption behavior of CO2 on a K-promoted hydrotalcite-like compound (HTlc) through non equilibrium dynamic isotherms. Industrial Engineering Chemistry Research, 45, 6387-6392. 

The desorption feature provides information on the reaction taking place at the surface. The velocity and angular distributions of desorbed species are measured by using a special setup with a rotating chopper with slits for a time-of-flight (TOF) measurement and a rotatable detector. A psuedorandom chopper is often used to perform time-resolved measurements efficiently that reflect the dynamical behavior of the surface reaction. The mechanism can be discussed on the basis of the detailed balance of desorption and adsorption. In the case of the absence of an activation barrier for adsorption, desorption shows the behavior for thermal equilibrium... 

---