Monodisperse, definition

Electrochemistry provides routes to directly prepare nanostructures both delocalized in a random or organized way and localized at predefined surface sites with adjustable aspect ratios. Purity, monodispersity, ligation, and other chemical properties and treatments are definitely important in most cases. By delocalized electrodeposition it is possible to decorate large areas of metal or semiconductor surfaces with structures of a narrow size distribution stable nuclei-clusters can be... 

In the derivation of eqn. (7) it was assumed that n (number of equivalent random links) is the same for all chains. For our samples (B2 system, Mw/Mn=1.45), this assumption is definitely not correct. Therefore, it is desirable to obtain birefringence results on networks prepared from monodisperse polymer (in that n is constant), before the validity of n itself is questioned. 

However, the choice of c as reference is not advisable, because R is a z-average while is a weight average. Even for monodisperse samples the various definitions are not equivalent. Therefore c is a quantity that strictly de-... 

The behaviour of the Q-tensor in shear gives directly the damping function from its definition in Eq. (42) so that h(y)=(l5l4 )Q (Y)ly. This function is plotted in the usual convention in Fig. 17. It is very close to results on monodisperse entangled solutions and melts [64]. 

The second equation, with the third (constant) term discarded, is the standard result [compare Eqs. (5), (6) and (Al)]. However, the first expression appears more natural, and is retained, within the combinatorial derivation it embodies the intuitively reasonable prescription that entropy is best measured relative to the parent distribution (°)( t). This was also an essential ingredient of the projection method, as described in Section n.A, where the prior in the entropy expression was likewise identified with the parent. Retaining the parent as prior also avoids subtleties with the definition of the integrals in Eq. (36) in the case where the phases contain monodisperse components, corresponding to 5-peaks in the density distributions [8]. 

Only a minority of systems of industrial interest contain powders with a uniform particle size, i.e. monodisperse. Most systems generally show a distribution of sizes (polydisperse) and it is then necessary to define the average dimension. There are many different definitions of particle size,1 2 the most commonly used, particularly in fluidisation, is the so called volume-surface mean or the Sauter mean diameter. This is the... 

Unsteady state diffusion in monodisperse porous solids using a Wicke-Kallenbach cell have shown that non-equimolal diffusion fluxes can induce total pressure gradients which require a non-isobaric model to interpret the data. The values obtained from this analysis are then suitable for use in predicting effectiveness factors. There is evidence that adsorption of the non-tracer component can have a considerable influence on the diffusional flux of the tracer and hence on the estimation of the effective diffusion coefficient. For the simple porous structures used in these tests, it is shown that a consistent definition of the effective diffusion coefficient can be obtained which applies to both the steady and unsteady state and so can be used as a basis of examining the more complex bimodal pore size distributions found in many catalysts. 

The ratio Mw/ Mn must by definition be greater than unity for a polydisperse polymer and is known as the polydispersity or heterogeneity index. Its value often is used as a measure of the breadth of the molar mass distribution, though it is a poor substitute for knowledge of the complete distribution curve. Typically Mw/ Mn is in the range 1.5-2, though there are many polymers which have smaller or very much larger values of polydispersity index. A perfectly monodisperse polymer would have Mw/ Mn = 1.00. 

The edges of this dodecahedron sized a - 8.5 cm. When the volume of the rubber balloon at inflation became bigger than the volume of the sphere inscribed in the dodecahedron, the balloon was deformed by the dedecahedron faces and took a shape close to the respective shape of a bubble in a monodisperse dodecahedral foam with a definite expansion ratio. The expansion ratio of the foam was determined by the volume of liquid (surfactant solution or black ink in the presence of sodium dodecylsulphate) poured into the dodecahedron. An electric bulb fixed in the centre of the balloon was used to take pictures of the model of the foam cell obtained. The film shape and the projection of the borders and vertexes on the dodecahedron face are clearly seen in Fig. 1.10. 

We take the Mark-Houwink-Sakurada equation (Eq. 3-44) as given. We assume also that the same values of K and a will apply to all species in a polymer mixture dissolved in a given solvent. Consider a whole polymer to be made up of a series of I monodisperse macromolecules each with concentration (weight/volume) c, and molecular weight A/,. From the definition of [r ] in Eq. (3-37),... 

Although it is simple to understand what a dendrimer is just by looking at the beautiful chemical structures drawn in the literature, there is at present no rigorous definition of the term dendrimer . It is generally agreed that monodispersity is an essential characteristic of dendrimers, which are thus sets of molecules all having the same identical constitution (and thus the same molecular weight), differently from hyperbranched polymers [1], which are a mixture of different, even if chemically similar, macromolecules. 

Consider a monodispersed latex, where water-phase termination is negligible and termination is instantaneous when a radical enters a polymer particle containing one radical. By definition, IV2 = IV3 = — = 0 and the total radical entry rate per liter of latex equals p. Application of the stationary-state hypothesis gives... 

A second principle applying to these model systems is derived from their colloidal nature. With the usual thermodynamic parameters fixed, the systems come to a steady state in which they are either agglomerated or dispersed. No dynamic equilibrium exists between dispersed and agglomerated states. In the solid-soil systems, the particles (provided they are monodisperse, i.e., all of the same size and shape) either adhere to the substrate or separate from it. In the liquid-soil systems, the soil assumes a definite contact angle with the substrate, which may be anywhere from 0° (complete coverage of the substrate) to 180° (complete detachment). The governing thermodynamic parameters include pressure, temperature, concentration of dissolved... 

If we assume that the molecules in each slice, /, following separation by SEC, are monodisperse, the mass moments of each sample peak selected are calculated from the conventional definitions [3,5] by... 

The light scattering methods provide statistically averaged quantities when applied to polydisperse samples (e.g., micellar or polymer solutions). The case of independent scatterers can be rigorously treated 2 by using the mass distribution function of the particles, f M). By definition, dm =f(M)dM is the mass of particles in the range between M and (M + dM), scaled by the total particle mass. As shown by Zimm, the scattering law in such a system can be presented similarly to the case of monodisperse particles (see Equation 5.405) ... 

It is difficult to define precisely the term aqueous silica sols and thereby contrast them with other forms of silica (colloidal silica, colloidal quartz, pyrogenic silica, and so forth). Bulk chemical distinctions are not very useful. The definition chosen here follows Iler s terminology (I). Aqueous silica sols are characteristically composed of spherical particles nucleated and grown by alkaline hydrolysis of sodium silicate solutions. They are often monodisperse systems and have particle diameters in the range 1-100 nm (density, —2.2 g/cm3) that lead to sols that vary from optically transparent to opalescent. 

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