Adsorbed thickness

Fig. 6. Calculated ATR spectra (angle of incidence 45°) for a monolayer adsorbate (thickness tZ3 = 3 A) on a 20-nm-thick metal film in contact with a solvent as a function of the complex refractive index of the metal film. Sohd line parallel polarized light dotted line perpendicular-polarized light. The appropriate complex refractive index n2 is given at the top of each spectrum. The vertical bars indicate the scale for the absorbance, which is different for each spectrum. Parameters ni = 4.01 (Ge), n4 = 1.4 (organic solvent), rfs = 3 A, He = 1.6, S = 280000cm , Vo = 2000cm , y = 60cm . The parameters correspond to adsorbed CO. The calculations were performed by using the formalism proposed by Hansen (76), and the results are given in terms of absorbance A = —logio(7 /7 o), where 77 is the reflectivity of the system Ge/Pt/ adsorbate/solvent and Rg is the reflectivity of the system Ge/Pt/solvent (7S).

Fig.4.a A perfectly flat wall in presence of sufficient polymer adsorption and interfacial chain entanglements, b An entangling melt under high stresses (o>oc) in contact with a molecularly smooth wall, where the adsorbed (thick) chains undergo a coil-stretch transition and the unbound chains are no longer in entanglement with the tethered chains. Here the first layer of adsorbed chains is stagnant, as the unbound chains flow by. 

Physisorption arises from the van der Waals forces, and these forces also condense gas molecules into their liquid state. Thus, in principle, there is no reason to stop upon completion of a monolayer during physisorption. Indeed, the formation of multi-layers, which are basically liquid in nature, is very common in physisorption experiments. Brunauer, Emmett and Teller developed a theory in 1938 to describe physisorption, where the adsorbate thickness exceeds a monolayer, and this isotherm equation is known by the initials of the authors (B.E.T.). The original derivation of the B.E.T. equation is an extension of Langmuir s treatment of monolayer adsorption from kinetic arguments. Later, in 1946, Hill derived this equation from statistical mechanics. In the B.E.T. isotherm, it is assumed that ... 

If an adsorbate is placed in the tunneling gap, the tunneling current will be modified by the local change in work function that the adsorbate produces. To observe a tunneling current, electrons must tunnel from one electrode (the cathode) into the adsorbate, and then conduct through the adsorbate to the other electrode (the anode). Alternately, electrons could tunnel completely through the adsorbate, but this process becomes more improbable as the thickness of the adsorbate increases. As the adsorbate thickness increases, the electrode gap that contains it must also increase. If the adsorbate is a protein molecule, the gap must be increased to tens or hundreds of nanometers. At these distances, a tunneling current could normally not be measured. 

FIG. 15 Volume of nitrogen gas adsorbed versus statistical thickness. C-0. C-IO, C-20, and C-30 are collagen fibers alkali-treated for 0, 10. 20, and 30 days, respectively. = amount adsorbed converted into liquid t = adsorbed thickness. (From Ref. 4.)... 

Fig. 2. Upper panel acJsorption kinetics for a 0.02 mg/ml PLL- -PEG solution in HEPES 2 as measured by OWLS (adsorbed mass vs time, line) and VASE (layer thickness vs time. ). 17 min is needed to reach a plateau value in the adsorption curve. Lower panel direct comparison of layer thickness from VASE and EG monomer surface daisity derived from OWLS measurem ts for different adsorption times. A good correlation was found betweai both techniques, allowing for a convCTsion of adsorbed thickness into EG monomer surface density rec-...

The question as to why, in the case of bovine albumin films, the amount of adsorbed antibodies increases with the number of underlying monolayers is of importance. First, it seems probable that the antibody molecules are piled up on top of each other in the thick layers of antibodies adsorbed on four double layers of bovine albumin. If this is true, the same process might take place in other cases. It has often been reported that undiluted immune sera gave much thicker layers of specifically adsorbed material than diluted sera. Bateman, Calkins and Chambers (19) found increments in thickness of 200 A and 60 A with undiluted and diluted serum, respectively. These variations have usually been assumed to result from a different orientation of the adsorbed antibody molecule which in the case of the rabbit antibody has approximately the dimensions of 40 X 270 A. Great variations in the thickness of adsorbed layers of antibodies have also been observed by electron microscopy. For instance, Anderson and Stanley (24) reported an adsorbed thickness of 225 A of rabbit antibodies on the surface of tobacco mosaic virus molecules but they also have observed much smaller increments. 

Nearly all of the analysis of mesoporosity starts with the Kelvin-Cohan [14] formulation. Foster [15] proposed the Kelvin equation for the effect of vapor pressure on capillary rise but did not anticipate its use for very small capillaries where the adsorbate thickness is a significant geometrical perturbation. Cohan formulation subtracts the adsorbate film thickness from the radius of the pore to yield the modified Kelvin equation... 

Problem 8.4. In order to determine an adsorbate thickness from an ellipso-metric measurement one needs to know the dielectric function of the investigated system. This function depends on temperature and thus can give rise to a large uncertainty in the measurement. 

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