Polydispersity in particle size

Figure 16 may also be used to illustrate the problem of polydispersity. For simplicity, consider a small polydispersity in particle size at constant refractive index. The theoretical surface shown in Figure 16 must be modified with a running integration over the size distribution which tends to fill in the minima and round off the maxima so that some of the structure is averaged out. Graphical illustrations of the effect have been reported (9) and the effect has been exploited to obtain both particle size and distribution width (10). It should be realized that both very narrow or very broad distributions tend... 

In this chapter, intermolecular forces that are the basis of self-assembly are considered in Section 1.2. Section 1.3 outlines common features of structural ordering in soft materials. Section 1.4 deals similarly with general considerations concerning the dynamics of macromolecules and colloids. Section 1.5 focuses on phase transitions along with theories that describe them, and the associated definition of a suitable order parameter is introduced in Section 1.6. Scaling laws are defined in Section 1.7. Polydispersity in particle size is an important characteristic of soft materials and is described in Section 1.8. Section 1.9 details the primary experimental tools for studying soft matter and Section 1.10 summarizes the essential features of appropriate computer simulation methods. 

The slight polydispersity in particle size allows the system to avoid the crystalline phase and reach the metastable glass state. Above ( ) = 0.58, the system is metastable with polydispersity, the random close-packing volume fraction shifts to higher values. 

Even when carefully prepared, model colloids are almost never perfectly monodisperse. The spread in particle sizes, or polydispersity, is usually expressed as the relative widtli of tire size distribution,... 

Instead of poly lysine, commercially available oligolysine of dp 19, which is less polydisperse than poly lysine, has been used to condense pDNA. A minimal repeating lysine chain of 18 residues followed by a tryptophan and an alkylated cysteine (AlkCWK18) has been found to condense plasmid DNA into small particles of 78 nm that mediated efficient in vitro transfection (Wadhwa et al., 1997) (Table 16.4). Compared to a commercially available K19, AlkCWK18 induced a 40-fold reduction in particle size and a 1000-fold increase in transfection efficiency. 

The three samples statistically were very different, both in particle size and polydispersity. In the case of the particle size determination, the two-factor interactions involving the SAMPLE were all significant, including the SAMPLE-METHOD interaction. Running the samples individually does not indicate why this might be. However, as noted below, the effects observed may be the result of different operator training, especially in determining the baselines. Yet, from practical considerations, the final variations are still acceptably small. 

Equations (16) and (18) discriminate between intraparticle and interparticle interference effects embodied in bj(q. t) and exp rq- ry(/)—r/(/) ), respectively. The amplitude function bj(q.t) contains information on the internal structure, shape, orientation, and composition of individual particles. Variations of bj(q.t) across the particle population reflect the polydispersity of particle size, shape, orientation, and composition. The phase function expjrq (ry (r) — r/(/)]( carries information on the random motion of individual particles, the collective motion of many particles, and the equilibrium arrangement of particles in the suspension medium. 

Figures 19 and 20 show experimental data recently obtained by Siebenburger et al. [33] on polydisperse dispersions of the thermosensitive core-shell particles introduced in Sect. 3.1.2 [31]. In all cases stationary states were achieved after shearing long enough, proving that ageing could be neglected even for glassy states. Because of the appreciable poyldispersity in particle size (standard deviation 17%) crystallization could efficiently be prevented and flow curves over extremely wide windows could be obtained. Two flow curves from their work can be used to test the asymptotic results.

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]. 

Particle size distributions have been reported with another new method, quasi-elastic light scattering. This method is most useful for the average particle size of monodisperse systems. Mathematical transforms are used to resolve polydisperse distributions, but no physical separation takes place. This method seems to work satisfactorily if the dispersion around each maximum in the polydisperse sol is narrow and the peaks are well separated in particle size. 

We have investigated theoretically film-thickness stability and structure formation inside a liquid film by Monte Carlo numerical simulations and analytical methods, using the Omstein-Zemicke (0-Z) statistical mechanics theory (21-24). The formation of longrange, ordered microstructures (giving rise to an oscillating force) within the liquid film leads to a new mechanism of stabilization of emulsions (3,4,25). In addition to the effective volume of micelles or other colloidal particles and polydispersity in micelle size, the film size is also found to be flic main parameter governing emulsion stability (15). 

It is even harder to prepare catalysts with a narrow Ag particle size distribution supported on alumina with a small surface. In all cases, the preparation of Ag catalysts on a-Al203 via conventional deposition and drying produces a polydisperse Ag particle size distribution. Probably, this results from a weak metal-support interaction. Indeed, Ag particles are known to migrate over dumina surface even under rather mild conditions [8]. 

Hosemann [156] developed a method of SANS data analysis, which accounts for polydispersity in the sizes of the scattering particles. This analysis assumes that the distribution of sizes of scattering particles is of a Maxwell type ... 

Rowell and co-workers [62-64] have developed an electrophoretic fingerprint to uniquely characterize the properties of charged colloidal particles. They present contour diagrams of the electrophoretic mobility as a function of the suspension pH and specific conductance, pX. These fingerprints illustrate anomalies and specific characteristics of the charged colloidal surface. A more sophisticated electroacoustic measurement provides the particle size distribution and potential in a polydisperse suspension. Not limited to dilute suspensions, in this experiment, one characterizes the sonic waves generated by the motion of particles in an alternating electric field. O Brien and co-workers have an excellent review of this technique [65]. 

The diametei of average mass and surface area are quantities that involve the size raised to a power, sometimes referred to as the moment, which is descriptive of the fact that the surface area is proportional to the square of the diameter, and the mass or volume of a particle is proportional to the cube of its diameter. These averages represent means as calculated from the different powers of the diameter and mathematically converted back to units of diameter by taking the root of the moment. It is not unusual for a polydispersed particle population to exhibit a diameter of average mass as being one or two orders of magnitude larger than the arithmetic mean of the diameters. In any size distribution, the relation ia equation 4 always holds. 

Natural latex is polydisperse (size of individual particles may vary from 0.01 to 5 p.m). Flowever, synthetic latex has a relatively narrow particle size, and therefore the viscosity at a given rubber content is higher in synthetic rubber (polyisoprene) solutions. The average molecular weight is typically about I million g/mol, although it depends on the gel content. 

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