Lecture

Chromatographic Models: Theory and Applications

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In course

CH-301: Analytical separation methods

Les étudiants comprennent les bases physico-chimiques des méthodes de séparation chromatographiques et électrophorétiques. ...

Description

This lecture covers chromatographic models, discussing the thermodynamic and kinetic parameters associated with the equilibrium distribution of solutes between stationary and mobile phases. Various models are presented, such as the Gaussian model for ideal systems, the Craig model for strongly retained solutes, and the binomial distribution model for solute separation units. The lecture also explores the characteristics of distribution functions, including the average advancement distance and the height equivalent to a theoretical plateau. Additionally, it delves into the convergence of binomial distributions to Poisson and normal distributions, providing insights into chromatographic signals and mass distributions in planar and elution chromatography.

Instructor

Christophe Roussel

Habilitation à Diriger les Recherches (HDR) in chemistry at the Ecole Normale Supérieure Paris-Saclay (Cachan, France)PhD Thesis in physical organic chemistry at the University of Bourgogne Franche-Comté (Besançon, France) / Ecole Normale Supérieure Paris-Saclay (Cachan, France)

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable , or just distribution function of , evaluated at , is the probability that will take a value less than or equal to . Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) satisfying and .

Negative binomial distribution

In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted ) occurs. For example, we can define rolling a 6 on a dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success ().

Poisson distribution

In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.

Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.

Empirical distribution function

In statistics, an empirical distribution function (commonly also called an empirical cumulative distribution function, eCDF) is the distribution function associated with the empirical measure of a sample. This cumulative distribution function is a step function that jumps up by 1/n at each of the n data points. Its value at any specified value of the measured variable is the fraction of observations of the measured variable that are less than or equal to the specified value.

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