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In this chapter, we explore the fitting of molecular weight distribution data with normal, lognormal, and Weibull distributions. We will identify the preferred coefficients and select the optimal model for our data set. Moreover, we will calculate the zeroth, first, second, and third moments of the lognormal and Weibull distributions, using these to derive Mn, Mw, and Mz. An assessment of the sample's polydispersity will also be conducted. Additionally, for extra credit, we will deconvolute a dataset from titania nanoparticles, utilizing either lognormal or Weibull models to estimate particle size distributions.
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Molecular weight distributions Chapter 6
Problems. Chapter 6 • Fit the data in Fig. 6.3 with normal, lognormal, and Weibull distributions. Report the preferred coefficients and select the model that best fits the data. • Generate the zeroth, 1st, 2nd and 3rd moments of the lognormal and Weibull distributions and use these to compute Mn, Mw, and Mz. What is the polydispersity of this sample?
Extra credit • Sample H data are for the primary particle size distribution of a titania nanoparticle sample. Deconvolute the cdf of sample H using either the lognormal or Weibull models, find the parameters for each fraction, and estimate the number fraction of particles of each mode.
