Microparticles theory

Following the intrusion branch with increasing pressure (Fig. 1.16A), the steep initial rise at low pressures is caused by the filling of interparticle spaces. The breakthrough pressure, i.e. the pressure when the voids between the particles are filled, follows in principle the theory of Mayer and Stowe [94], and is inversely proportional to the particle size [95]. The demarcation between interparticle spaces and actual intraparticle pores may be unclear for microparticles, but in the case of polymer beads from suspension polymerization having particle sizes between 50-500 pm, usually no interference occurs. The second rise of the intrusion branch is caused by pores inside the particles. Shown in Fig. 1.16A is a porous material of rather narrow pore size distribution. 

Figure 4.15 Triphasic drug release kinetics from PLGA-based microparticles in phosphate buffer pH 7.4 experimental data (symbols) and fitted theory (curve). Reprinted from [91] with permission from Springer.

A sophisticated enhancement of metal vapor deposition involves silver deposition over an ordered array of polystyrene spheres with submicron diameters (41-43). The Ag atoms deposit both on the spheres and on the flat substrate below the spheres. After deposition, the spheres may be removed to leave an ordered array of microscopic Ag pyramids with regular size and shape. The pyramids have dimensions of a few hundred nanometers, in the range required for EM field enhancement. These arrays of Ag microparticles have provided a direct test of EM field enhancement theory (44), and have been modified with platinum and organic thin films (45). 

Description of electrocatalytic processes in such modified electrodes can be derived from the intersection between the theory of Andrieux and Saveant (1980, 1988) for mediated electrocatalysis in redox polymers and those for metal oxide electrocatalysis (Lyons et al., 1992,1994 Attard, 2001 Pleus and Schulte, 2001) and the recent models for the voltammetry of microparticles given by Lovric and Scholz (1997, 1999) and Oldham (1998) and combined by Schroder et al. (2000). 

The voltammetric behavior of surface-immobilized microparticles of redox active solid materials has been extensively studied by the groups of Scholz (Greifswald, Germany), Bond (Melbourne, Australia), Grygar (Rez, Czech Republic), Komorsky-Lovric and Lovric (Zagreb, Croatia), Domenech-Carbo (Valencia, Spain), Marken (Bath, UK), and others. Theoretical aspects, however, have been addressed only in some reports. Recently, the Compton group (Oxford, UK) made several reports on the theory of microparticle-modified electrodes, and these will mainly be discussed at this point. 

The following results are applicable to any electrode modified with a sparse distribution of microparticles. The mass transport to a single, diffusionally independent microparticle can (in theory) be treated on an equal basis as a microparticle within an independent diffusional zone in the experimental time scale with respect to its neighbors. Therefore, many theoretical results produced for microparticle arrays of diffusional categories 1 and 2 (see Section 6.3.2.2.2) are also valid for single particles. 

Since its introduction in 1989 [3,4], the voltammetry of (immobilized) microparticles (earlier termed abrasive stripping voltammetry) has attracted considerable attention and initiated a wide range of experimental and theory-based studies. As outlined in Section 6.1, the first decade of investigations has been vell reviewed [5-8], while a recent monograph [9] has included the details of any diverse applications up until late 2004. Consequently, whilst the following sections will focus on the period between 2005 and the present, any earlier contributions deemed relevant to an understanding of the current investigations will also be cited or discussed. 

The dimension estimation can be carried out with the help of the Eq. (4) and the value (p can be calculated according to the Eq. (7). The results of dimension theoretical calculation according to the Eq. (29) are adduced in (Table 6.2), from which a theory and experiment good correspondence follows. The Eq. (29) indicates unequivocally to the cause of a filler in nano- and microcomposites different behavior. The high (close to 3, see Table 6.2) values d for nanoparticles and relatively small d=2. l for graphite [4]) values d for microparticles at comparable values (p is such cause for composites of the indicated classes [3, 4]. 

Dust explosions [1.33] present an industrial hazard in the grain milling and other industries where combustible airborne particles are produced. Describing in detail the conditions under which these explosions can occur requires the aerosol microphyiscs of heterogeneous processes, kinetic theory, and microparticle microphysics. 

The history, theory, and application of the voltammetry of adhered microparticles in contact with both bulk and thin-layer forms of ionic liquids have been reviewed. In the short time since its introduction, the technique has enhanced the range of studies possible for a wide variety of compounds. For example, new insights have now become available when electroactive molecules undergo kinetically slow dissolution (e.g., for oxidation of Fc in an ionic liquid). Using this method, the... 

Siepmann J, Faisant N, Akiki J, Richard J, Benoit JP. Effect of the size of biodegradable microparticles on drug release experiment and theory. J Control Release 2004 96(1) 123-34. 

Atom production in flames is an extremely complex process consisting of many stages and involving numerous sides processes. A quantitative theory of analyte atomization in flames is absent. Qualitatively, the process can be described as follows the solution droplets sprayed into the flame are first dried, the resulting solid microparticles become molten and vaporize or thermally decompose to produce gaseous molecules that are finally dissociated into free atoms. The atoms may further be excited and ionized and form new compounds. These processes are dependent upon the temperature and the reducing power of the flame and occur within a few milliseconds - the time required by the sample to pass through the... 

---