Surface area/volume ratios, particle

The pore size of the membrane could also be controlled independently of the porosity by altering the size of the salt particles (Fig. 5a). Membranes with high surface area/volume ratios were produced and the ratio was dependent on both salt weight fraction and particle size (Fig. 5b). In addition, the crystallinity of PLLA membranes can be tailored to that desired for each application. These characteristics are all desirable properties of a scaffold for organ regeneration. The major disadvantage of this technique is that it can only be used to produce thin wafers or membranes (up to 2 mm in thickness). A three-dimensional scaffold cannot be directly constructed. This problem may be circumvented however, by membrane lamination. 

Nanomaterials can be in the form of fibers (one-dimensional), thin films (two-dimensional), or particles (three-dimensional). A nanomaterial is any material that has at least one of its dimensions in the size range 1 to 100 nm (Figure 6.1). Many physical and chemical properties are determined by the very large surface area/volume ratio associated with such ultrasmall particles. There are two major categories into which all nanomaterial preparative techniques can be grouped the physical, or top-down, approach and the chemical, or bottom-up, approach. In this chapter, our primary focus is on chemical synthesis. Nevertheless, we discuss the physical methods briefly, as they have received a great deal more interest in the industrial sector because of their promise to produce large volumes of nanostructured solids. 

Figure 6.4. Comparison of the surface area/volume ratio of macroscopic particles (marbles) and nanoscopic aluminum oxide particles. Since nanoparticules contain a proportionately large number of surface atoms, there are a significantly greater number of adsorption/reaction sites that are available to interact with the surrounding environment. Further, whereas bending of a bulk metal occurs via movement of grains in the >100nm size regime, metallic nanostructures will have extreme hardness, with significantly different malleability/ductility relative to the bulk material.

Solutions consist of individual particles, molecules and ions dispersed through a solvent. The lumps of solute therefore have to be split up into individual particles. The act of dissolving takes place at the surface of the lump and smaller lumps have a larger surface area volume ratio. The smaller the lumps are to start with, the faster they will dissolve. So powdered salt will dissolve faster than salt with coarse grains. The effect of particle size on the rate of a chemical reaction is discussed in Section 5.3.4. 

Specific surface area. The higher the specific surface area (surface area volume ratio) of silica particles, the greater their dissolution rate will be in general, it is also true that smaller particles will dissolve more rapidly than larger particles (as much as 50-75% of biogenic silica in soils may be in the <5/im size fraction). 

The main approach to reach higher sensor sensitivity is based on maximization of the electron depletion layer compared with the semiconducting core this can be realized by decreasing the particle size down to the scale of the depletion layer thickness.6-8 Oxide semiconductors in the form of nanocrystalline powders,9-11 nanorods,12 nanowires,13-15 nanotubes,1617 and nanobelts18 with a high surface area/ volume ratio have been studied intensively as highly sensitive materials. 

According to the above equations, we can estimate the performance of a particle bed cathode that treats a 667 ppm (667 mg/1) Cu aqueous waste stream and generates a product effluent containing 1 ppm Cu, as was done in [125]. The cathode bed particles in the reactor are assumed to have a surface area/volume ratio of 25 cm" with a bed porosity of 0.3. The reactor operates with a superficial solution velocity of 0.0036 cm/sec and a 0.2 V potential variation in the cathode bed, i.e., the front face potential of the cathode is 0.2 V more negative (more cathodic) than the back of the bed. For these conditions, the cathode bed thickness should be 5.0 cm. The length and width of the bed are determined by the volumetric feed flow rate into the reactor, hence, the flow... 

External surface area/volume ratio for adsorbent particle Sorbate concentration in fluid phase Initial steady value of c Heat capacity of adsorbent Diffusivity... 

At the scales involved, electrodynamics, chemistry, and fluid mechanics are inextricably intertwined electric fields can create fluid flow, and fluid flow can create electric fields, with the surface chemistry driving the degree of coupling. The flow coupling effect can be described by electrostatic source terms in the Navier-Stokes equations or particle transport equations. Boundary conditions become an issue in microsystems, due to high surface area-volume ratios. Boundary conditions that are taken for granted at the macroscale (e.g., the no-sUp condition) can often fail in these systems. 

A morphological characteristic, which is of fundamental importance to the understanding of the structure-property relationship of nanocomposites, is the surface area/volume ratio of the fillers [37]. As illustrated in Fig. 1, the change in particle diameter, layer thickness, or fibrous material diameter from micrometer to nanometer changes the surface area/volume ratio by three orders of magnitude. At this scale, there often is a distinct size dependence of the material properties. In addition, the properties of the composite became dominated by the properties of the interface or interphase when the interfacial area drastically increased. 

The transition from macro- through micro-, and finally to nanoscales for filler particles introduces increased surface area/volume ratios [increased fraction of atoms at the surface of the material], as well as length/diameter ratios [also called the aspect ratio). These dimensional changes can alter certain properties of the nano-filler itself, as well as the behavior of the filler within the matrix. 

Figure 1.1 Common particle reinforcements and their respective surface area/volume ratios [4],...

Figure 20.2 The dimensions, surface areas, and volumes of three different-sized cubes, which schematically represent particles, are compared here to show how surface area/volume ratio increases as the dimensions decrease.

Sphericity. Sphericity, /, is a shape factor defined as the ratio of the surface area of a sphere the volume of which is equal to that of the particle, divided by the actual surface area of the particle. 

One general benefit of subunit association is a favorable reduction of the protein s surface-to-volume ratio. The surface-to-volume ratio becomes smaller as the radius of any particle or object becomes larger. (This is because surface area is a function of the radius squared and volume is a function of the radius cubed.) Because interactions within the protein usually tend to stabilize the protein energetically and because the interaction of the protein surface with... 

It will be noted that the relevant characteristic dimension in the Biot number is defined as the ratio of the volume to the external surface area of the particle (V/Ae), and the higher the value of V/Ae, then the slower will be the response time. With the characteristic dimension defined in this way, this analysis is valid for particles of any shape at values of the Biot number less than 0.1... 

Since sorption is primarily a surface phenomenon, its activity is a direct function of the surface area of the solid as well as the electrical forces active on that surface. Most organic chemicals are nonionic and therefore associate more readily with organic rather than with mineral particles in soils. Dispersed organic carbon found in soils has a very high surface-to-volume ratio. A small percentage of organic carbon can have a larger adsorptive capacity than the total of the mineral components. 

When mixtures of substances are investigated, e.g. in solid state reactions, the mixture should be completely homogeneous and of uniform particle size. Smaller particle size, i.e. higher ratio surface area/volume, are important for such types of reaction ... 

The two factors are seldom completely independent most times they are interdependent. A typical example is the effect of particle size. A decrease in particle size produces an increase in surface area at constant amount of material. At the same time, as the particle size decreases the surface-to-volume ratio increases, which may lead to modifications of the electronic properties of surface atoms. 

---