Adsorption, kinetics

If the adsorption rate is high, or the additive concentration low, substantial depletion of the additive concentration occurs next to the electrode. In a supported electrolyte, the interfacial concentration of the additive, Q, is determined by mass balance between adsorption, desorption and the available diffusional flux  

The rate of adsorption comprises two steps transport of the gas or solute molecules toward the interface and interaction with the sorbent surface. These steps are considered separately in the following sections. For the sake of simplicity, a solution containing one adsorbing component is considered. The same reasoning applies to adsorption from the gas phase. In that case, the composition should be expressed in (partial) pressure instead of concentration. 

Various possible steps are involved in the transfer of an adsorbate to the adsorption layer. Transport to the surface by convection or molecular diffusion, attachment to the surface, surface diffusion, dehydration, formation of a bond with the surface constituents. 

We consider here first, the kinetics of the adsorption of metal ions on a hydrous oxide surface. 

Adsorption of Metai Ions to a Hydrous Oxide Surface 

We have argued that (inner-sphere) surface complex formation of a metal ion to the oxygen donor atoms of the functional groups of a hydrous oxide is in principle similar to complex formation in homogeneous solution, and we have used the same type of equilibrium constants. How far can we apply similar concepts in kinetics  

The Homogeneous Case. Margerum (1978) and Hering and Morel (1990) have elaborated on mechanisms and rates of metal complexation reactions in solution. In the Eigen mechanism, formation of an outer-sphere complex between a metal and a ligand is followed by a rate limiting loss of water from the inner coordination sphere of the metal, Thus, for a bivalent hexaaqua metal ion 

The final elements of the mass balances are the adsorption kinetics and equilibria. According to Equations 6.5 and 6.6, adsorption and desorption steps are modeled as reactions with finite rate. The reaction rate based on the solid volume of all particles (Equation 6.20) in the volume element is 

Like the equilibrium isotherms, the net adsorption rates V reac, can be defined in quite different ways. One example is given in Equation 6.31 where a first-order equilibrium reaction with two rate constants for the adsorption (k ds) and desorption (kdes) steps (Ma, Whitley, and Wang, 1996) is specified  

The terms ijsat,i represent again the maximum possible loadings for each component. Interaction between the different components is considered by the summation over all N -omp components. Equation 6.31 is the nonequilibrium form of the multicomponent Langmuir isotherm (Equation 2.57). 

The nonequilibrium form of the simpler linear isotherm (Equation 2.48) can be obtained by neglecting the sum in Equation 6.31, leading to 

As a fundamental method to monitor the adsorption efficiency, the adsorption kinetics are often used to predict the adsorption characteristics and mechanisms. The kinetic models involve pseudo-first-order, [17] pseudo-second-order, [18] Elovich, [19] and intraparticle [20] diffusion model, of which the pseudo-first and pseudo-second-order equations are listed as Equations (11.11) and (11.12), respectively  

The presence of H-H interactions [399] on the surface results in the formation of ordered domains at low temperatures. The kinetics of domain growth for H/Fe(l 10) has been studied by Monte Carlo simulations [400]. At 9 = 0.500 the domains grow according to an Allen-Cahn power law the size of the domains is proportional to [400]. At 0 = 0.667 the rate is lower due to diffusion limitations [400]. The diffusion and reactions of H at the surface has a number of similarities to the diffusion of H in the bulk [401]. 

For a film of Fe the rate of adsorption for H2 at low temperature is proportional to the square root of the hydrogen pressure [402] and decreases exponentially with coverage [402]. The activation energy is 3-6 kcal/mole and increases with coverage [402]. The H2 chemisorption is activated for small Fe particles on MgO [328], and for (Fe, Ir)/Al203 [365]. 

This means that the reduction of the fluid loading is low after the first stage for the given total reduction 7. - for an equilibrium favorable for adsorption (small B values). 

A countercurrent unit as illustrated in Fig. 9.4-5 can also be used for desorption processes. In this case substances are transferred from the sohd adsoibent phase into the fluid phase and the operating line is miming below the equihbiium curve. Balances of the substance transferred around the top or the bottom of the column deliver the equation of the operating hue. 

Adsorption takes place when the concentration c. or the partial pressure / , of the adsorptive i is greater than the equilibrium values c or p, which belongs to the loading X, of the adsoibent. 

In the case of a desorption process all these resistances must be overcome in the reverse order. At first the heat of desorption to be added results in a detachment of the molecules which pass then through the micro- and macroporous system and finally through the concentration boundary layer into the bulk fluid around an adsorbent pellet. The heat of adsorption (in most cases exothermic) and the heat of desorption (endothermic as a rule) lead to the result that these processes cannot be carried out in an isothermal field. The increase of temperature of the adsorbent by adsorption and the decrease of temperature of the sohd phase are the reason that the driving force is reduced and the mass transfer is retarded. It can happen that the mass transfer rates of adsorptives with great heats of adsorption result in such tem-peratrue changes that additional adsorptive can only be adsorbed after a removal of heat combined with a temperatrrre loss. The kinetics in the adsorber is limited by heat transfer (heat transfer controlled). 

In industrial adsorbers, however, often only small amormts of impurities are removed by adsorption especially in plants for the protection of the environment. The temperature changes during adsorption or desorption of gases can be so small 

There are some important general relations for a substance adsorbed from solution on an electrode. These pertain to the equilibrium state and the kinetics of the process leading to equilibrium. Adsorption kinetics receives rather intermittent attention in the electrochemical literature. One of the clearest discussions is by Mohilner (1966) see also Delahay (1966), Damaskin et al (1975), Bard and Faulkner (1980). 

If there is interaction between the particles (attractive or repulsive), the Frumkin isotherm may apply  

In order to obtain a certain surface concentration r or fractional coverage 0, the substance in question must first arrive at the electrode, by some transport process. The rate of increase of r (per unit area) is proportional to the unit area flux at the electrode 

In dimensionless form, using the transformations Eq. 2.31 as before, this is 

There is a thought experiment analogous to the electron transfer potential step experiment we arrange for an initially homogeneous solution with bulk concentration Cj, in contact with a clean electrode (r=0) to start adsorbing onto the electrode at t=0. At any time thereafter, the coverage is given by 

Technical adsorbents include active carbon, active coke, silica gel, active argillaceous earth or aluminum oxide gel, bleaching earth and molecular sieves (Table 4-6). In Tables 4-7 and 4-8, some properties of the adsorbents are deseribed. 

The design of adsorbers depends on the adsorption equilibrium (static loading capac- 

Active carbon, active coke, carbon molecular sieve, carbon fiber mat, carbon fiber paper [4.54, 4.55]. 

Active argillaceous earth, aluminum oxide gel, alumina gel 

Specific surface area a outer and inner adsorbent surface area referred to its mass unit (mVg). Experimentally determined by N2-adsorption isotherms with respect to space requirement of an N2-molecule (BET-surface area). 

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The tendency to form organized monolayers improves with chain length. This is illustrated in a study of adsorption kinetics in alkanoic acid monolayers on alumina by Chen and Frank [36]. They find that the Langmuir kinetic equation, discussed in Section XVII-3, (see Problem XI-6)... 

Fig. XI-1. Adsorption kinetics for C g alkanoic acids adsorbing onto alumina for various solution concentrations from Ref. 36. Lines are the fit to Eq. XI-IS.

If Langmuir adsorption occurs, then a plot of 9 versus p for a particular isothenn will display the fonn of equation (Al.7.3). Measurements of isothenns are routinely employed in this manner in order to detennine adsorption kinetics. 

We now consider how one extracts quantitative infonnation about die surface or interface adsorbate coverage from such SHG data. In many circumstances, it is possible to adopt a purely phenomenological approach one calibrates the nonlinear response as a fiinction of surface coverage in a preliminary set of experiments and then makes use of this calibration in subsequent investigations. Such an approach may, for example, be appropriate for studies of adsorption kinetics where the interest lies in die temporal evolution of the surface adsorbate density N. ... 

Mintz M H, Atzmony U and Shamir N 1987 Initial adsorption kinetics of oxygen on polycrystalline copper Surf. Sc/. 185 413-30... 

Ramsden J J 1994 Experimental methods for investigating protein adsorption kinetics at surfaces Q. Rev. Blophys. 27 41-105... 

Jin X, Talbot J and Wang N FI L 1994 Analysis of steric hindrance effects on adsorption kinetics and equilibria AlChE J. 40 1685-96... 

Van Tassel P R, Guemourl L, Ramsden J J, Tar]us G, VIot P and Talbot J 1998 A model for the Influence of conformational change on protein adsorption kinetics J. Colloid Interfaoe Sc/. 207 317-23... 

In contrast, physical adsorption is a very rapid process, so the rate is always controlled by mass transfer resistance rather than by the intrinsic adsorption kinetics. However, under certain conditions the combination of a diffiision-controUed process with an adsorption equiUbrium constant that varies according to equation 1 can give the appearance of activated adsorption. 

Polymeric cation-exchange resins are also used in the separation of fmctose from glucose. The UOP Sarex process has employed both 2eohtic and polymeric resin adsorbents for the production of high fmctose com symp (HFCS). The operating characteristics of these two adsorbents are substantially different and have been compared in terms of fundamental characteristics such as capacity, selectivity, and adsorption kinetics (51). 

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

Surface SHG [4.307] produces frequency-doubled radiation from a single pulsed laser beam. Intensity, polarization dependence, and rotational anisotropy of the SHG provide information about the surface concentration and orientation of adsorbed molecules and on the symmetry of surface structures. SHG has been successfully used for analysis of adsorption kinetics and ordering effects at surfaces and interfaces, reconstruction of solid surfaces and other surface phase transitions, and potential-induced phenomena at electrode surfaces. For example, orientation measurements were used to probe the intermolecular structure at air-methanol, air-water, and alkane-water interfaces and within mono- and multilayer molecular films. Time-resolved investigations have revealed the orientational dynamics at liquid-liquid, liquid-solid, liquid-air, and air-solid interfaces [4.307]. 

In contrast to the above resins, the chelating resin Amberlite IRC-718 is based upon a macroreticular matrix. It is claimed to exhibit superior physical durability and adsorption kinetics when compared to chelating resins derived from gel polymers and should also be superior for use in non-aqueous solvent systems. 

Domenek S., Petit E., Ducept F., Mezdoura S., Brambati N., Ridoux C., Guedj S., Michon C. 2008. Influence of concentration and ionic strength on the adsorption kinetics of gelatin at the air/water interface. Colloids and Surfaces A Physicochem. Eng. Aspects 331, 48-55. 

The same resin was used for the purification via downstream processing of carminic acid, the natural colorant extracted from cochineal. By a direct adsorption method, a crude extract was applied on the polymeric bed gel and the adsorption kinetics studied using elution with hydrochloric acid and ethanol. The desorbed pure carminic acid concentrated under vacuum yielded a final product that complied with Codex Alimentarius requirements and FAO/OMS norms. 

Hydrogen chemisorbs reversibly on Rh/S102 and Rh/T102 as a species which can be treated as molecular hydrogen In terms of Its adsorption kinetics. 

For potentials higher than 0.5 V vs. RHE, the formation of adsorbed oxygen species at Ru as well as at Pt will block the catalytic surface, leading to a decrease in the methanol adsorption kinetics. Therefore, in a potential range higher than 0.5 V vs. RHE, the kinetics of methanol oxidation is optimized at a Ru-poor catalyst, because methanol adsorption is not blocked and because the presence of Ru provides the extra oxygen atom needed to complete the oxidation of adsorbed CO to CO2. 

Pfniir H, Menzel D. 1983. The influence of adsorbate interactions on kinetics and equilibrium for CO on Ru(OOl). I. Adsorption kinetics. J Chem Phys 79 2400. 

In Chapter 1 we consider the physical and diemical basis of the method of semiconductor chemical sensors. The items dealing with mechanisms of interaction of gaseous phase with the surface of solids are considered in substantial detail. We also consider in this part the various forms of adsorption and adsorption kinetics processes as well as adsorption equilibria existing in real gas-semiconductor oxide adsorbent systems. We analyze the role of electron theory of chemisorption on... 

We should point out that the Langmuir kinetics given by expressions (1.11) and (1.12) which is often observed in experiment is as often violated. In numerous cases the data on adsorption kinetics follows the well-known Roginsky-Zeldovich-Elovich kinetics isotherm [47, 48]... 

S Harnisch, RH Muller. Adsorption kinetics of plasma proteins on oil-in-water emulsions for parenteral nutrition. Eur J Pharm Biopharm 49(l) 41-46, 2000. 

Winters and Lee134 describe a physically based model for adsorption kinetics for hydrophobic organic chemicals to and from suspended sediment and soil particles. The model requires determination of a single effective dififusivity parameter, which is predictable from compound solution diffusivity, the octanol-water partition coefficient, and the adsorbent organic content, density, and porosity. 

Adsorption kinetics of Zn on the untreated soil and the soils with the removal of organic matter and Fe oxides has been studied in detail by Hinz and Selim (1999) using a thin disk flow method. They reported that Zn sorption was highly concentration-dependent. When Zn concentration was... 

Adsorption Kinetics. Figure 1 shows the adsorbance, Ap, of NaPSS-3 as a function of adsorption time for two NaCl concentrations at the NaPSS concentration of 0.04 g/lOOml. Hie Ap first increases with adsorption time and then the equilibrium adsorbance is attained after 1.5 x 10J minutes. 

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