Random sequential adsorption models

FIGURE 15.6 Excluded interfacial area for deposition of molecules that adsorb according to the random sequential adsorption model. 

FIGURE 15.7 Available interfacial area for adsorption of spheres as a function of surface coverage, according to the random sequential adsorption model. The fuU-line curve represents c )(9) calculated using (15.9) whereas the other curves are calculated using Equation 15.10 taking two, three, and four terms of the series into account. 

The non-equilibrium problem is even more complicated. The large particles can have surface binding energy much larger than kT and in this case they neither diffuse nor desorb from the surface. The Random Sequential Adsorption (RSA) model [9] assumes that a particle, which arrives at a random location on a surface, is adsorbed only if there is... 

The RSA model received renewed attention after Feder [12] observed that the adsorption on the surface of apo-ferritin molecules (large iron-storage proteins with a diameter of about 10 nm), which adsorb irreversibly, reached saturation at a coverage (k = 0.518. Monte Carlo simulations of Random Sequential Adsorption of disks on a surface last prohibitively long in the vicinity of the jamming point however Feder [12] noted that in the vicinity of the jamming coverage, 9 has a power-law dependence on time ... 

On the basis of the model of a heterogeneous membrane, it is possible to create a simulation scheme based on dynamic Monte Carlo computer simulations of the adsorption and desorption process on heterogeneous surfaces to extract the involved rate constants as a function of the calcium ion concentration. A simple simulation based on a modified, partly reversible, random sequential adsorption (RSA) algorithm provides very good accordance between experiment and measurement. Figure 8 schematically depicts the assumed model. 

Most theories for polymer adsorption kinetics start from (combinations of) the models discussed earlier. Other theories, often proposed for (bio)polymer adsorption, are based on the random sequential adsorption (RSA) model. According to this model, the adsorbate molecules arrive randomly at the interface and they stick where they hit. It implies that both desorption and tangential motion of the adsorbate at the interface are absent. Because the center of a newly arriving spherical molecule cannot be accommodated within the shaded areas enclosed by the dashed circles shown in Figure 15.6, only the unshaded fraction < ) of the surface is available for adsorption. It is obvious that ( ) is a function of 0, the fraction of the surface that is covered by the adsorbate. For sphere-like molecules, 0 = niUi (R being the radius of the molecule). The following expressions for the available surface function < )(0) can be derived from the RSA theory ... 

When adsorption is completely irreversible, the particle description reduces to the random sequential adsorption (RSA) model (87-89). An RSA process is one in which hard objects are added randomly and sequentially to a surface at a given rate and in which any object placed in a position so as to overlap with another object is immediately removed. The governing kinetic equation is... 

The theoretical approaches aimed at a description of nonlinear adsorption regimes are discussed next—in particular the elassieal, random sequential adsorption (RSA) model. The role of polydispersity, particle shape, orientation, and electrostatic interactions is elucidated. Then, the generalized RSA model is presented, which reflects the coupling of the surface transport with the bulk transfer step governed by external force or diffusion. 

Different models have been used to fit the interfacial protein adsorption data [76] and include, but are not hm-ited to, Langmuir [56, 58, 71, 73, 77], Freundlich [78, 79], and random sequential adsorption (RSA) [80, 81] models. Equilibrium adsorption of different proteins at the silicone oil/water interface, under different solution conditions, has been seen to occur in a monolayer as indicated by the Langmuir [51,55] (Figure 25.6) or RSA model [30,54]. 

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