Intensity-weighted particle size

Results of the data-analysis of the simulated autocorrelation functions, corresponding to an intensity-weighted particle size distribution with an average diameter of 50 nm and with a variable standard deviation (SD). The noise level was fixed at 0.0002, and the analysis range was 5. 

Data Transformation. The raw size distribution obtained in PCS is intensity weighted. Most particle sizing results are either mass, area, or number weighted. Therefore, to compare results, the PCS measurements would have to be transformed. If the ratio of the concentrations in each peak is desired, then a transformation is also necessary. The intensity of light scattered by a sphere is given by... 

Not all results agree this well. Before corrections are applied it is important to verify that peak positions and intensity-weighted ratios are repeatable. Also note that a particle property, index of refraction, was needed to transform an intensity-weighted size distribution into a mass- or number-weighted one. For monodisperse and narrow distributions this is not the case. For distributions where... 

Data Transformations. The deconvolution of correlation functions yields the intensity-weighted diffusion coefficient distribution. Transformation to a size distribution requires division by the diameter raised to a high power and by an angular dependent function which oscillates over several orders of magnitude for particles larger than a half a micron. Given the artifacts from the primary deconvolution, extreme caution is advised when transforming data. 

The particle size distribution, X(s), above is, unfortunately, not in a form which is useful for most applications. This is because it is a scattered intensity weighted distribution (for brevity, intensity distribution ) rather than a size distribution based on the volume (weight) or number of particles. The difference between distributions weighted in different ways can be most easily explained by relating the various distributions to a number distribution. 

The aim of this paper is to describe the experimental and numerical techniques that, when combined, provide a procedure that enables full particle-size distribution studies of sub-micrometer emulsion systems. We then present distribution results for several oil/water emulsions to demonstrate the ability of these techniques to monitor the effect of processing variables (such as surfactant concentration) on the final emulsion. Finally, we discuss some of the problems of converting the intensity weighted distribution to a mass weighted distribution and suggest methods for minimizing or eliminating some of these problems. 

The distribution obtained from the inversion of Equation 4 is an intensity weighted distribution. That is, it displays the percentage of light scattered from each particle size in the population. What is desired is the amount of mass at each particle size (mass distribution), or the number of particles at each particle size (number or frequency distribution). In principle, once any distribution is known, the others can be calculated. Because of finite detection limits and noise in actual experimental data, however, it is not that straightforward. 

If we restrict our attention to particles having identical shapes, /(TJ is the intensity-weighted PSD. In the limit of a continuous size distribution, Eq. (42) has the form of a Laplace transform... 

It is noted that the phonon wavefunction is a superposition of plane waves with q vectors centered at In the literature, several weighting functions such as Gaussian functions, sine, and exponential functions have been extensively used to describe the confinement functions. The choice of type of weighting function depends upon the material property of nanoparticles. Here, we present a brief review about calculated Raman spectra of spherical nanoparticle of diameter D based on these three confinement functions. In an effort to describe the realistic Raman spectrum more properly, particle size distribution is taken into account. Then the Raman intensity 7(co) can be calculated by ... 

Macromolecular or particulate samples fractionated by the FFF are usually not uniform but exhibit a distribution of the concerned extensive or intensive parameter [8] or, in other words, a polydispersity. Molar mass distribution (MMD), sometimes called molecular weight distribution (MWD), or particle size distribution (PSD) describes the relative proportion of each molar mass (molecular weight), M, or particle size (diameter), d, species composing the sample. This proportion can be expressed as a number of the macromolecules or particles of a given molar mass or diameter, respectively, relative to the number of aU macromolecules or particles in the sample ... 

A built-in microcomputer system performs rapid quadratic least squares fit to the data, yielding D, R, a (normalized standard deviation of the intensity weighted distribution of diffusion constants) and x squares goodness of fit. The greater the value of a the larger the degree of polydispersity present in the particle sizes -a values less than 0.2 are generally considered to correspond to pure monodisperse systems. A typical result obtained for 4 x 10 3M CdS-SDS is 5= 7.25 x 10"8 cm2/s, R = 300 A, a = 0.60 and y2... 

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