Adsorption blobs

The thickness ads of the adsorbed layer defines the adsorption blob size (see Fig. 3.12), This adsorption blob size is the length scale on which the cumulative interaction energy of a small section of the chain with the sur-face is of the order of the thermal energy kT. On smaller length scales, the... 

In order to calculate the size of the adsorption blob ads we need to calculate the number of monomers in contact with the surface for a chain section of size ads- The average volume fraction in a chain section of size Cads containing gads monomers is 0 ... 

The number of monomers in each adsorption blob that are in direct contact with the surface (within a layer of thickness b from it) is estimated as the product of the mean-field number density of monomers in the blob 0/6 and the volume of this layer within distance b of the surface, Cads ... 

The energy gain per monomer in contact with the surface is 6kT. Therefore, the energy gain per adsorption blob is... 

The free energy of an adsorbed chain can be estimated as the thermal energy kT per adsorption blob ... 

Both theories of single-chain adsorption, described above, ignore a very important effect—the loss of conformational entropy of a trand due to its proximity to the impenetrable surface. Each adsorption blob has jb contacts with the surface and each strand of the chain near these contacts loses conformational entropy due to the proximity effect. In order to overcome this entropic penalty, the chain must gain finite energy E er per contact between a monomer and the surface. This critical energy Ecr corresponds to the adsorption transition. For ideal chains Ecr A E. The small additional free energy gain per contact kT6 should be considered in excess of the critical value Ecr,... 

Fig. 3.13. For adsorption of real chains, the actual concentration inside each adsorption blob decays as a power law in distance from the surface. This power law decay modifies the exponent in Eqs (3.62) and (3.70) (see Problem 3.22).

The adsorption blob size decreases with increasing surface attraction 6 as for exponent i/ = 0.588. 

The concentration in the adsorbed layer decreases away from the surface as (f) (z/b) for exponent 0.588. This power law concentration profile in an adsorbed polymer layer was proposed by de Gennes and is called the de Gennes self-similar carpet. This profile of adsorbed polymer can be described by a set of layers ot correlation blobs with their size of order of their distance to the surface z (see Fig. 5.11). The self-similar concentration profile starts at the adsorption blob ads in the first layer. The self-similar profile ends either at the correlation length of the surrounding solution if it is semidilute or at the chain size Rf bN if the surrounding solution is dilute. 

The adsorbed amount T is the number of monomers adsorbed per unit area of the surface, and is controlled by the densest layet with thickness of the order of adsorption blob size ads ... 

When D is larger than unity, as mentioned above,the probe chain adopts a pancake shape along the surface for large distance scales. For shorter distances however, it remains isotropic. On a local scale, inside the isotropic blob discussed above, relation (7), it is still ideal. For intermediate distances, the interaction with the surface is not sufficiently strong to adsorb the chain, and we may define adsorption blobs, as in relation (18). These are defined by generalizing equation (27). This leads to the number giso of elements in the adsorption blobs. 

Note that while the two previous examples correspond to chains confined by cylindrical capillaries, this example is reminiscent of a chain confined to a slit. The adsorption behavior of star polymers may be analyzed in terms of such adsorption blobs. ... 

Several examples of scaling with different types of scaling blobs have already been introduced for tension, compression, and adsorption. The main idea in all scaling approaches is a separation of length scales. The... 

In order to estimate the first contribution from the elastic adsorption, a C gel picture is used, in which the gel is a collection of adjacent blobs of radius that has a characteristic relaxation time Ti / >coop, where Dcoop r/bnrji is the cooperative diffusion constant of the gel, T is temperature and t] is the viscosity of the solvent [80]. Each blob is associated with a partial polymer chain (the polymer chain between two next-neighboring cross-linking points). The scaling theory relates this molecular structure of the gel with its elastic modulus E by the equation [80]. 

Figure 4 Maps of the average density of nitrogen adsorbed in three nanotube bundles. The contours are for constant density in the x, y planes i.e., for an observer looking in the z direction parallel to the pore axes. The pore diameters are (a) 1.37mn, (b) 1.43 nm, and (c) 0.69 nm. The in-plane coordinates x, y are defined so that unit x, y= 0.07, 0.14 run, respectively. The larger blobs show density contours inside the tubes and the smaller ones are for molecules adsorbed in the interstices between the hexagonally packed tubes. The interaction potential for the Nj is diatomic thus, the approximate molecular length is 0.1 run greater than the width which is 0.35 nm. The consequence is that the tube of (c) is too small to admit the N2 molecules so that the adsorption shown there is essential all interstitial. Also, in (a) and (b), the N2 appears to lie parallel to the tube axis and is adsorbed on the tube walls. The differences between the (a) and (b) contours are at least partly due to the differences in the numbers of molecules in these systems. These amount to 334 and 199 in (a) and (b).

The adsorption model described above assumes the existence of different discrete states of protein molecules in the surface layer, with neighbouring states differing from one another by the molar area increment Aco. From the viewpoint of scaling analysis, (Aco) has to be close to the size of an electrostatic blob [132]. In adsorption layers of proteins the flexibility of chains increases due to the high concentration of both protein and inorganic electrolyte [133]. This allows to consider, instead of discrete states, an infinitesimal change do in the molar area. To perform the transition from the discrete to the continuous model one has to replace formally the summations in Eqs. (2.126)-(2.128) by an integration [86]. 

These and others experimental facts have been theoretically analyzed with the use of the methods of the self-consistent field and scaling [7i-17], The results of an analysis can be lined in the following simplified model in the flocculent adsorption layer (a distance between the centers of the adsorptive molecules I > 2Rj, the polymeric chain is in practically the same conformational state as in the solution in dripless adsorptive layer (/ < 27 an interaction between the adsorbed chains compresses the pol5mieric bdls in the adsorption plate and stretches them in a form of the chain by blobs [76], cylinders [72] or rotation ellipsoids [75] along the normal to the surface. 

Blob Type screening collapse electrostatic Pincus adsorption confinement... 

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