Heterodispersity

In applying this concept, the factor of particle size must be continuously borne in mind. A heterodisperse system can reach a steady state wherein the smaller particles are agglomerated and the larger particles are dispersed, giving the apparent effect of an equiUbrium. In ideal monodisperse systems under steady conditions, however, no such effects are noted. 

It must also be emphasized that the major mass of a heterodispersed aerosol may be contained in a few relatively large particles, since the mass of a particle is proportional to the cube of its diameter. Therefore, the particle-size distribution and the concentration of the drug particles in the exposure atmosphere should be sampled using a cascade impactor or membrane filter sampling technique, monitored using an optical or laser particle-size analyzer, and analyzed using optical or electron microscopy techniques. 

Heterodisperse Suspensions. The rate laws given above apply to monodisperse colloids. In polydisperse systems the particle size and the distribution of particle sizes have pronounced effects on the kinetics of agglomeration (O Melia, 1978). For the various transport mechanisms (Brownian diffusion, fluid shear, and differential settling), the rates at which particles come into contact are given in Table 7.2. 

Transport mechanism Rate constant for heterodisperse suspensions Rate constant Ifdi =d2b) ... 

Next, consider a polymer sample which is heterodisperse both in molecular weight and composition. In the limit of vanishing concentration. Equation 1 gives, for independent scatterers, i ... 

The light scattering equation for molecular weight-heterodisperse samples which are compositionally homogeneous simplifies if dn/dc is constant for all species ... 

Nonionic surfactants, as mentioned previously, have been widely adopted due to their characteristics and properties and, in particular, because they do not require the presence of undesirable phosphate or caustic builders in detergent formulation. However, the relatively lesser degree of biodegradability is an important disadvantage of the nonionic surfactants compared to the ionic ones. Adsorption on activated carbon and various types of clay particles is, therefore, one of the processes that has been effective in removing heterodisperse nonionic... 

A monodisperse aerosol is one with a narrow size distribution, which, for log-normal-distributed particles, usually means a geometric standard deviation of about 1.2 or smaller. Monodisperse particles are expected to have simple shapes and uniform composition with respect to size. A polydisperse aerosol, on the other hand, is one containing a wide range of particle sizes, but which may otherwise be homogeneous in terms of the basic physical and chemical properties that are not related to size. The term heterodisperse is also used occasionally this describes aerosols varying widely in physical and chemical characteristics, as well as size. 

According to this kinetic model the collision efficiency factor p can be evaluated from experimentally determined coagulation rate constants (Equation 2) when the transport parameters, KBT, rj are known (Equation 3). It has been shown recently that more complex rate laws, similarly corresponding to second order reactions, can be derived for the coagulation rate of polydisperse suspensions. When used to describe only the effects in the total number of particles of a heterodisperse suspension, Equations 2 and 3 are valid approximations (4). 

A colloidal dispersion in which all the dispersed species (droplets, particles) have the same size. Otherwise, the system is heterodisperse (paucidisperse or poly disperse). See Static Mixer. 

The geometric standard deviation (GSD) is defined as the size ratio at 84.2% on the cumulative frequency curve to the median diameter. This assumes that the distribution of particle sizes is lognormal. A monodisperse, i.e. ideal aerosol, has a GSD of 1, although in practice an aerosol with a GSD of <1.22 is described as monodisperse while those aerosols with a GSD >1.22 are referred to as poly dispersed or heterodispersed. 

Tihe theory of free-radical addition polymerization, described in numer-ous publications (2, 3, 4, 17, 21), makes it clear that radical chain-growth reactions of polymers are regulated by statistical laws. Because of their statistical character the products from these reactions must be heterodisperse. The ranges extend from a single unit upward, depending upon kinetic details of the reactions. 

Data on the effects of surfactants on the hydrolysis of aryl sulfate esters have become available only recently. A non-ionic heterodisperse polyoxyethylene sorbitan monooleate surfactant, Polysorbate 80, was found to increase the observed rate constant for the acid-catalyzed hydrolysis of potassium 2,4-dichloronaphthyl sulfate by a factor of 16-3 at a surfactant concentration of 8 g/1, but an additional 5-fold increase... 

The use of surfactants to modify the surface tension of an aerosol and alter its droplet size distribution has shown that their influence depends strongly on the characteristics of the solution to be aerosoled. The span, defined as 90% undersize —10% undersize/50% undersize, gives a measure of the width of the volume distribution relative to the median diameter of the droplets formed in the aerosoling process. Comparative studies performed with commercial air-jet and US nebulizers have shown that, under similar working conditions, the latter provide less heterodispersed aerosols, with span values ranging from 1.50 to 1.75, which are similar for aqueous drug solutions in the presence and absence of surfactants [156]. 

Figure 3.62. ionic components of charge for the double layer on haematite. Electrolyte. 10 > M KCi. Drawn curves homodis-perse sol dashed curves purified heterodisperse sol. (Redrawn from N.H.G. Fenners. L.K. Koopal and J. Lyklema. Colloids Surf. 21 (1986) 457.)... 

In more applied veins, -potentials are not measured for their own sake, but to assess particle interaction, as is for instance required in rheology and colloid stability. These measurements have to be carried out for particles that are often ill-defined the shapes may be known from electron microscopy, but they may be heterodisperse and heterogeneous and the surface composition may be unknown. For those cases the following summary may be helpful. 

When all chains of a polymer or polyelectrolyte are equally long, the macromolecules are called homodisperse or monodisperse. If this condition Is not met the system is heterodisperse or polydisperse. Synthetic polymers and polyelectro-l)Ttes usually have a certain molar mass distribution and. hence, are to some extent polydisperse. This polydlsperslty has Important implications for the adsorption behaviour because fractionation will occur upon adsorption. 

The steady-state compliance shows a strong dependence on the molecular heterodispersity. Thus the value of for a mixture of two fractions of the same polymer, one of low and the other of high molecular weight, may be up to 10 times as high as that of each component. This behavior can be explained by taking into account that 4 is the total recoverable deformation per unit of shear stress. The chains of high molecular weight have a very... 

Molecular Weight, Molecular Heterodispersity, and Molecular Topology... 

The influence of molecular heterodispersity (or molecular weight distribution) on the evolution of viscosity with shear rate is shown (41) in Figure 13.23. As the width of the distribution increases, the flow departs from Newtonian behavior at lower values of than would occur in a nearly... 

We have approached the subject in such a way that the book will meet the requirements of the beginner in the study of viscoelastic properties of polymers as well as those of the experienced worker in other type of materials. With this in mind. Chapters 1 and 2 are introductory and discuss aspects related to chemical diversity, topology, molecular heterodispersity, and states of aggregation of polymers (glassy, crystalline, and rubbery states) to familiarize those who are not acquainted with polymers with molecular parameters that condition the marked viscoelastic behavior of these materials. Chapters 1 and 2 also discuss melting processes and glass transition, and factors affecting them. 

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