Aggregate size polydispersity

The anomalous static structure factor of the aggregates associated with a relatively small size polydispersity could produce the observed behaviour of /2K. The latter parameter is given by ... 

Polydispersity arises in systems composed of particles characterized by a property (e.g., particle diameter) that spans a continuum of values. Small molecules exhibit discrete properties, so they do not form polydisperse mixtures. Only at the level of macromolecules and colloidal aggregates does polydispersity become an issue. Here variations in particle size are known to influence the ordering into a solid phase. Experimentally it has been observed that colloidal systems will not form a solid phase if the size polydispersity (as measured by the standard deviation of the particle-size distribution) is greater than about 5% to 10% of the average diameter [252]. 

The variation of this standard ehemical potential with aggregate size is important in determining whether micelles or aggregates will form. This reference potential also determines polydispersity and aggregate shape. For the sake of discussion we consider the formation of (one-dimensional aggregates) linear ehains of surfactants. We approximate the pairwise binding energy (relative to separated speeies) as akT. The standard reference potential is then written ... 

It is appropriate to consider the multiphase systems as composed of a matrix and concentration-dependent dynamic clusters or aggregates characterized by specific strength, a, the aggregate relaxation time, Xy, and the cluster size polydispersity index, w w 0.2 — 1.0 [44]. Thus the apparent shear stress may he expressed as ... 

Ultrasonication is a common tool for the preparation and processing of polymer nanoparticles. It is particularly effective in breaking up aggregates and in reducing the size and polydispersity of nanoparticles. The physical stability and in vivo distribution of nanoparticles are affected by their mean size, polydispersity, and surface charge density. Despite the widespread applications of ultrasonication in nanotechnology, its effects on chitosan nanoparticles are not well understood. 

DLS is an established technique for protein characterization. For example, to And optimum protein crystalhzation conditions, DLS is used as a prescreening tool to identify critical parameters of the process such as the hydrodynamic size, polydispersity, and aggregation factors. DLS is also used as a method to characterize the hydrodynamic properties of globular proteins in electrolyte solutions. However, applications of DLS to characterize charged protein solutions, just as any other charged molecules in solution, could face certain difficulties in subsequent data treatment. 

Thus, by measuring the dynamics of the scattered light it is possible to measure the size of spherical particles in dilute solution. It is also important to mention that the effect of polydispersity can be accounted for by introducing a distribution in the diffusion constants. In this way, gi(s,t) then becomes a sum over different sizes and the way to deal with this problem is to either assume a functional form, i.e. model-dependent, cf. the discussion above on the interpretation of SANS data (one often used distribution of aggregate sizes is the log-normal distribution function), or by performing a numerical inverse Laplace transform of g (s,t) to obtain the distribution in diffusion coefficients (33). 

A growth in micelle size, and consequently an increase in aggregation number, with the surfactant concentration was inferred from SANS study of the nonionic surfactant [Q], X = OH with x = 12 and 16 in D2O [100]. The size of the micelles formed by surfactant with x = 12 was close to that for the surfactant with x = 16, i.e., with an aggregation number of 95 at 5 wt % and 116 at 10 wt %. The results also indicated that the micelles remained spherical with only a slight size polydispersity that did not vary significantly upon surfactant concentration. 

Conversion of this flexible hydrophobic moiety into a rigid planar structure can, in some cases, lead to a non-micellar association pattern in which the mean aggregate size increases continuously with increase in concentration. Such systems have no CMC and exhibit a considerable degree of polydispersity in the aggregate size. This topic is dealt with in detail in Chapter 4. 

The time dependence of birefringence is affected by intermicellar interaction, electrolytes, and polydispersity. If the aggregates are polydisperse, the time dependence of birefringence deviates from a single exponential relationship. The size distribution function must be known, because the deviation depends on the width of the distribution function [243]. In spite of these limitations, Shorr and... 

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