Lecture

Polymer Molecular Weights: Distributions and Measurements

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In course

MSE-437: Polymer chemistry and macromolecular engineering

Know modern methods of polymer synthesis. Understand how parameters, which determine polymer structure and properties, such as molecular weight, molecular weight distribution, topology, microstructure can be controlled by proper choice of polymerization me ...

Description

This lecture covers the concept of polymer molecular weights and weight distributions, emphasizing the variability in polymer molecules due to statistical variations in the polymerization process. The instructor explains the importance of both average molecular weight and molecular weight distribution in characterizing a polymer. Various techniques for measuring polymer molecular weights, such as number-average and weight-average molecular weights, are discussed. The lecture also delves into the impact of molecular weight on properties like mechanical strength and processability, highlighting the trade-offs involved in selecting the desired polymer molecular weight.

Instructor

Harm-Anton Klok

Expertise Polymer design at nanoscaleBiologically-inspired polymers Mission Research at the Laboratory of Polymer (LP) focuses on the development of novel advanced polymeric materials with potential applications in optics, electronics or medicine. The philosophy is that precise control over nanoscale structure is an important prerequisite to tailor polymer properties. To this end, a “bottom-up” approach is followed, which starts with designing a new material at the molecular level, in order to be able to pr

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Related concepts (23)

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

Cauchy distribution

The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution is the distribution of the x-intercept of a ray issuing from with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero.

F-distribution

In probability theory and statistics, the F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA) and other F-tests. The F-distribution with d1 and d2 degrees of freedom is the distribution of where and are independent random variables with chi-square distributions with respective degrees of freedom and .

Ratio distribution

A ratio distribution (also known as a quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. Given two (usually independent) random variables X and Y, the distribution of the random variable Z that is formed as the ratio Z = X/Y is a ratio distribution. An example is the Cauchy distribution (also called the normal ratio distribution), which comes about as the ratio of two normally distributed variables with zero mean.

Stable distribution

In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).

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