Polydispersity calculating

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. 

Compai ison with literature experimental and calculation data showed that the model proposed ensures the accurate behavior of the functional dependence of x-ray fluorescence intensity on the particle size. Its main advantage is the possibility to estimate the effect of particle size for polydispersive multicomponent substances. 

In case of a polydisperse filler with a specific surface area Sspec, it has been proposed to calculate the mesophase thickness the product Afiller volume per unit of its mass) [50,65]. 

This trend is illustrated by the curves for the micro-mixed reactor in Figures 8 through 14. Also characteristic of the seeded, micro-mixed reactor is the convergence of the polydispersity index to 2 for a high degree of polymerization. This trend is illustrated to some extent in Table VI which presents the calculated degrees of polymerizations. 

Solution Equation (13.4) is used to relate //v and at complete conversion. The polydispersity is then calculated using Equation (13.20). Some results are shown in Table 13.3. The polydispersity becomes experimentally indistinguishable from 2 at a chain length of about 10. 

Table 13.4 tabulates results at the same value of as in Table 13.3. The polydispersities are lower than when the same average chain length is prepared by a binary polycondensation going to completion. The stoichiometry-limited binary polycondensations have a higher polydispersity because the monomer in stoichiometric excess (the B monomer) is included in the calculations. This broadens the molecular weight distribution.

Find the standard deviation of the Flory distribution as given by Equation (13.26) and relate it to the polydispersity. Extend the calculations in Problem 13.5 to /X3. Find the kurtosis of the distribution in the limit of high conversion. 

A modification of the method proposed by Ishige, Lee, and Kamielec (29) has been shown to work well for calculating W(y) to compute a PSD (27). This iterative method starts with a first estimate of W(yT obtained from the polydisperse chromatogram assuming no axial dispersion. Equation (8) is then evaluated from which the computed chromatogram F (V) is obtained. From... 

Because of chromatographic dispersion, the sample fraction in the detector cell is polydisperse. The weight-average and number-average molecular weights of the polydisperse fraction are calculated as... 

The weight-average molecular weight (Mw), number-average (Mn) molecular weight, and the polydispersity ratio (P) can be calculated as 76-77... 

ESI mass spectra of mixtures are difficult to interpret, because each component produces ions with many different charge states. The most direct and reliable method to solve this problem is to use high-resolution MS and calculate the charge states by measuring the spacing of the isotope peaks. ESI mass spectrometry of (polymeric) mixtures with broad molecular weight distribution benefits from a prior separation that reduces the polydispersity of the analyte. 

Several mathematical models are available for predicting the dissolution of particles of mixed size. Some are more complex than others and require lengthy calculations. The size of polydisperse drug particles can be represented with a distribution function. During the milling of solids, the distribution of particle sizes most often results in a log-normal distribution. A log-normal distribution is positively skewed such that there can exist a significant tail on the distribution, hence a number of large particles. The basic equation commonly used to describe the particle distribution is the log-normal function,... 

From the analysis of the rate equations it can be concluded that the classical polymerization model does not apply whenever the instantaneous polydispersity is greater than 2 or smaller than 3/2. This limitation of the classical model has resulted in piecewise continuous models for high viscosity polymerizations. Preliminary calculations, on the order of magnitude of the terms contributing... 

The general inferiority of geometrical construction methods [162,163] as compared to more involved methods which consider polydispersity has first been demonstrated by Santa Cruz et al. [130], and later in many model calculations by Crist [ 165-167]. Nevertheless, in particular the first-zero method is frequently used. Thus, it appears important to assess its advantages as well as its limits. Validation can be carried out by graphical evaluation of model correlation functions [130,165],... 

A dissolution model that takes in account the change in particle number and the polydisperse nature of the powder was proposed by de Almeida et al. [25]. The following dissolution equations were used to calculate the decrease in weight of solids with time ... 

A series of bis(phenoxide) aluminum alkoxides have also been reported as lactone ROP initiators. Complexes (264)-(266) all initiate the well-controlled ROP of CL, NVL.806,807 and L-LA.808 Block copolymers have been prepared by sequential monomer addition, and resumption experiments (addition of a second aliquot of monomer to a living chain) support a living mechanism. The polymerizations are characterized by narrow polydispersities (1.20) and molecular weights close to calculated values. However, other researchers using closely related (267) have reported Mw/Mn values of 1.50 and proposed that an equilibrium between dimeric and monomeric initiator molecules was responsible for an efficiency of 0.36.809 In addition, the polymerization of LA using (268) only achieved a conversion of 15% after 5 days at 80 °C (Mn = 21,070, Mn calc 2,010, Mw/Mn = 1.46).810... 

Matveev V.V. Calculation of the Electrochemical Characteristics of Porous Electrodes with a Polydisperse Crystal Structure (Rus.), Problems of Chemistry and Chemical Technology IVoprosy Khimii i Khimicheskoy Tekhnologiil (Ukrainian Journal). 2001 3 96-111. 

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