Multilayer sphere

I he field scattered by any spherically symmetrical particle composed of materials described by the constitutive relations (2.7)-(2.9) has the same form as that scattered by the homogeneous sphere considered in Chapter 4. However, the functional form of the coefficients an and bn depends on the radial variation of e and ju. In this section we consider the problem of scattering by a homogeneous sphere coated with a homogeneous layer of uniform thickness, the solution to which was first obtained by Aden and Kerker (1951). This is one of the simplest examples of a particle with a spatially variable refractive index, and it can readily be generalized to a multilayered sphere. 

To describe the concentration profiles and release kinetics of fluorescein from single NP-shelled capsules, Munoz Tavera et al. solved a mathematical model that describes unsteady-state transport from multilayered spheres using the Sturm-Liouville approach [92], Several aspects of dye release, such as the asymptotic plateau effect of diffusive release and the effects of capsule diameter and shell thickness distribution on dye release, were captured by the model and confirmed by experimental data. 

The spray head configuration is an interesting aspect of EHDA. The nozzle varies from a simple hypodermic needle of different diameters to highly technologically advanced multiplex nozzles (Figure 22.8). The coaxial needle shown increases the number of centered nozzles to four and is mainly used to fabricate multilayer spheres. In coaxial setups, the most commonly used is the coaxial two-capillary nozzle used to fabricate core-shell spheres (capsules). The inner needle is supplied by a solution of active substance and the outer needle is filled with shell material.In this process, parameters are used as adjusting switches to control the diameter of the capsules, thickness of the shell, and number of inner cores. The two solvents used in the coaxial setup are immiscible and wettable, and the inner one has a higher surface tension. 

The Mie theory [1] and the T-matrix method [4] are very efficient for (multilayered) spheres and axisymmetric particles (with moderate aspect ratios), respectively. Several methods, applicable to particles of arbitrary shapes, have been used in plasmonic simulations the boundary element method (BEM) [5, 6], the DDA [7-9], the finite-difference time-domain method (FDTD) [10, 11], the finite element method (FEM] [12,13], the finite integration technique (FIT) [14] and the null-field method with discrete sources (NFM-DS) [15,16]. There is also quasi-static approximation for spheroids [12], but it is not discussed here. 

The computation of Lorenz-Mie coefEcients for concentrically layered spheres has been considered by Kerker [115], Toon and Ackerman [222], and Fuller [76], while recursive algorithms for multilayered spheres have been developed by Bhandari [13] and Mackowski et al. [154]. 

R. Bhandri, Scattering coefficients for a multilayered sphere Analytic expressions and algorithms, Appl. Opt. 24, 1960 (1985)... 

The LB technique was chosen for covering the spheres because it was shown to provide enhanced thermal stability of many types of proteins in deposited layers (Nicolini et al. 1993, Erokhin et al. 1995, Antolini et al. 1995), which no other technique is able to achieve. Since only the upper protein layer is involved in the catalytic activity, no special attention was paid to check whether the deposited layer is a monolayer or multilayer. However, the samples were thoroughly washed to remove protein molecnles not bound covalently to the sphere surface, since during the functional test these molecules could contribute to the measured apparent catalytic activity. 

The described procedure allows one to deposit protein, in particular, enzyme, LB films onto the surface of small spheres. Deposited multilayer film was washed in order to leave at the surface only a layer covalently attached to the activated surface. The enzyme... 

The multilayer shells can also provide a protective barrier for the loaded enzyme in environments where enzyme-degrading substrates such as proteases may be present [67]. Dissolved catalase was inactivated immediately by protease, losing its entire activity within 60 min in solution. For catalase loaded in BMS spheres, inactivation is slower, with an activity loss of about 20 % in 60 min. Notably, a negligible decrease in... 

Caruso, R.A., Susha, A. and Caruso, F. (2001) Multilayered titania, silica, and laponite nanopartides coating on polystyrene colloidal templates and resulting inorganic hollow spheres. Chemistry of Materials, 13, 400—409. 

Encapsulation via the layer-by-layer assembly of multilayered polyelectrolyte (PE) or PE/nanoparticle nanocomposite thin shells of catalase in bimodal mesoporous silica spheres is also described by Wang and Caruso [198]. The use of a bimodal mesoporous structure allows faster immobilization rates and greater enzyme immobilization capacity (20-40 wt%) in comparison with a monomodal structure. The activity of the encapsulated catalase was retained (70 % after 25 successive batch reactions) and its stability enhanced. 

Chemists have synthesized a spectacular array of submicron- and nano-particles with well-defined size and atomic structure and very special properties. Examples include CdSe quantum dots and novel spheres and rods. Transport enters the picture via fundamental studies of the physical processes that affect the synthesis, which must be understood for even modest scale-up from the milligram level. Likewise, processes for assembling fascinating face-centered-cubic crystals or ordered multilayers must concentrate on organizing the particles via flow, diffusion, or action of external fields. Near-perfection is possible but requires careful understanding and control of the forces and the rates. 

Gauging catalysis by reference to an electrode where electrons are delivered (or eaten up) in an outer-sphere manner, redox catalysis is not expected to operate at a monolayer coated electrode (Figure 4.10), since, as discussed in Section 4.2.1, redox catalysis results from the three-dimensional dispersion of the catalyst. In contrast, there is no reason that chemical catalysis could not be operative at a monolayer coated electrode. For the same reasons, both redox catalysis and chemical catalysis are expected to function at multilayer electrode coatings (Figure 4.10). 

Based on the above general principles, quite a number of models have been developed to estimate pore size distributions.29,30,31-32,33 They are based on different pore models (cylindrical, ink bottle, packed sphere,. ..). Even the so-called modelless calculation methods do need a pore model in the end to convert the results into an actual pore size distribution. Very often, the exact pore shape is not known, or the pores are very irregular, which makes the choice of the model rather arbitrary. The model of Barett, Joyner and Halenda34 (BJH model) is based on calculation methods for cylindrical pores. The method uses the desorption branch of the isotherm. The desorbed amount of gas is due either to the evaporation of the liquid core, or to the desorption of a multilayer. Both phenomena are related to the relative pressure, by means of the Kelvin and the Halsey equation. The exact computer algorithms35 are not discussed here. The calculations are rather tedious, but straightforward. 

Watanabe and Regen 81 reported the construction of ordered, dendritic multilayers (10) via a bridged, outer sphere —outer sphere mode of assembly (Figure 9.5) whereby the transition metal Pt was used as a connector moiety. Although amine-terminated PAMAM-type dendrimers 76 were employed for this particular example, this process could easily be extended to other types of macromolecules. 

Abstract In this paper we report on AFM force spectroscopy measurements on hollow polymeric spheres of colloidal dimensions made from polyelectrolyte multilayers of polyal-lylamine and polystyrenesulfonate in water. We find that the shells show a linear force-deformation characteristic for deformations of the order of the shell wall thickness. This experimental outcome is discussed in terms of analytical results of continuum mechanics, in particular the scaling behaviour of the shell spring constant with wall thickness, shell radius and speed of the deformation is analysed. The experimental results agree well with the predictions of Reissner for thin shells and allow... 

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