Mass-weighted distributions

The observation of molecular size or polydispersity and the subsequent determination of relative molecular mass, (MJ or molecular mass (weight) distribution (MWD), is the most common analytical application of SEC. The goal of these types of experiments is to either observe the solvated size of one or more molecular species or to observe the distribution of sizes present in a mixture... 

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. 

Molecular weightjmass detectors include light scattering detectors and viscosity detectors. When SEC is used in the characterisation of polymer systems, its main aim will be the production of a molecular mass/weight distribution and where possible absolute molecular weights. Mass calibration is a complicated matter (section 9.3.5.1) in that calibration curves differ for different polymer types, and for many commercial polymers, direct molar mass calibration is not possible because of the lack of suitable, known molecular weight standards. 

Having calibrated the system, the calculation of the molecular mass/weight distribution curve and molecular weight averages requires a number of data treatment steps (Evans, 1973). 

Simple models have only one coimter and size level circuit (and so are called single-channel models) more complex instruments can obtain number and/or mass (weight) distributions automatically in up to 256 size channels within a few seconds. Counting and sizing rates of up to some 10,000 particles per second are possible, with each pulse height being... 

Another common way to introduce the distribution is by weighting. Imagine that we sort all particles according to their size into bins as discussed before, but instead of counting the individual particles, we weigh all the particles within each bin with a balance. This process leads to the mass-weighted distribution. This distribution is simply proportional to R N(R), since the volume of a particle (and thereby its mass at constant particle density) is proportional to R. The quantity R N R)dR is proportional to the mass fraction between R and R- -dR. The unknown proportionality constant can be obtained through an appropriate normalization and the distribution reads as follows ... 

For n = 0, we recover the number-weighted distribution, namely po(R) — p R), while for n = 3 the mass-weighted distribution is obtained. Of course, other weights can be introduced, for example, n = 2 corresponds to the area-weighted distribution, while n = 6 is sometimes referred to as the intensity-weighted distribution for reasons to be discussed later. 

The particle size distribution of a given dust or mist can be reported as a number, length, surface, volume or mass (weight) distribution. Figure 2.3.3 shows number and volume distribution curves for a sample powder. The curves in the figure are density curves the function values /(x) represent the fraction of particles in a given interval divided by the width of that interval. The definition of the number density distribution fN x) is thus ... 

The MEP is defined as the path of steepest descent in mass-weighted Cartesian coordinates. This is also called intrinsic reaction coordinate (IRC). In reality, we know that many other paths close to the IRC path would also lead to a reaction and the percentage of the time each path is taken could be described by the Boltzmann distribution. 

Range of molecular weight distribution (mass/molar). 

A common error is to confuse the GPC distribution with the weight distribution. The response of a refractive index detector is proportional to the mass of polymer. The GPC elution volume (V) typically scales according to the logarithm of the degree of polymerization (or the logarithm of the molecular... 

The molecular weights and molecular weight distributions (MWD) of phenolic oligomers have been evaluated using gel permeation chromatography (GPC),23,24 NMR spectroscopy,25 vapor pressure osmometry (VPO),26 intrinsic viscosity,27 and more recently matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS).28... 

These parameters are used calculate the site and mass distribution functions assuming a Schulz-Zimm molecular weight distribution. The Schulz-Zimm parameters are calculated in lines 930-950. The weight fraction of diluent (as a fraction of the amount of polymer) is then sought. If there is no diluent enter 0. If there is a diluent, the functionality and molecular weight of the diluent is requested (line 1040). The necessary expectation values are computed (lines 1060-1150). 

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