Structural surface charge heterogeneity

The scientific interest in solid surfaces whether in the context of heterogeneous catalysis, solid state electronics, or corrosion is a direct consequence of the fact that their properties are unique with relation to the corresponding properties of the bulk solid. This is not difficult to appreciate since at the surface there is a breakdown of translational symmetry, extreme gradients of chemical composition are feasible, and perturbation of both bulk structure and charge are possible. There are, therefore, formidable problems to overcome if we are to arrive at a situation where surface structure, electronic... 

Furthermore, the surface structure exhibits discontinuities in slope, i.e., it is not smooth but has kinks. Both points eliminate the possibility of a perturbation study. The two-dimensional nature of the system means that we can use Eq. (107) and need only evaluate one-dimensional integrals in the terms appearing in the matrices A and B. For the calculations performed here we assume that the surfactant cylinders have circular cross-section of radius a and have a uniform surface charge, a. The substrate we presume has zero charge (thus we also incorporate charge heterogeneity in this problem). 

The polymers should be as well characterized and as monodisperse as possible. Adsorbents should have a well-defined geometry and surface structure (planes or spheres are usually preferred). It is now possible to prepare a wide range of polymer lattices and inorganic particles for use as model surfaces. Any surface heterogeneity should be well characterized e.g., the number density and type of any surface charge should be known. 

Depending on the mechanism, endocytosis can also be classified into clathrin-mediated endocytosis [34], caveolin-mediated endocytosis [35], and clathrin- and caveolin-independent endocytosis [36]. Clathrin-mediated endocytosis is a major entry mechanism, and also the most intensely investigated mechanism among the various forms of endocytosis. Although clathrin molecules are involved in most receptor-mediated endocytosis and nonspecific endocytosis, the detailed endocytic mechanism of nonviral carriers has not been well understood yet and has been shown to vary with the size, surface charges, and other characteristics of the carriers. Many carriers use several mechanisms simultaneously, probably due to the intrinsic heterogeneity of the supramolecular structure [37]. 

As can be seen in Figure 11.9, the experimental data are well reflected by the theoretical curves calculated from Equation 11.22 for its between 3 and 4. This observation has a practical implication, proving that colloid particle deposition can be exploited as a sensitive tool for detecting the structure of the surface heterogeneities in the nanometer size range, in particular the charge heterogeneity. 

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