Molar mass distribution

The molecular weight distribution ( MWD often, molecular weight distribution ) referred for a given substance, the distribution, ie the proportional division of the molar mass of the molecules contained. The term is usefully be applied only in polymers, since their degrees of polymerization (and thus their molecular weights ) over a more or less wide area distributed. In particular biopolymers, there is only a defined molar mass. Widespread is the term molecular weight distribution, but this is not correct ( see note here).

Distribution functions

In accordance with the distribution of features from the mathematics or the physico-chemical conditions during the production of the polymer to various possible distribution functions obtained:

  • Gaussian distribution
  • Schulz- Zimm distribution
  • Poisson

In practice, of course, can also emerge from these theoretical models differing distributions. Often one finds the names:

  • Narrow molecular weight distribution
  • Broad molecular weight distribution

Molecular weight of polymers

Various means defined in order to describe the statistical sample:

  • Number average molecular weight

The molar mass of the i -mer is the relative number of share that has this polymer, weighted. The number average molecular weight indicates, therefore, which has a random molecular weight be taken from the sample molecule on average. Here, the number of macromolecules in the sample corresponds exactly i repeating units.

  • Weight average molecular weight

The molar mass of the i -mer is the relative mass fraction, the polymer has this weighted. If one were to select a random monomer unit and determine the molecular weight of the corresponding polymer would be obtained as the average of the weight-average molecular weight.

  • Centrifuges average molecular weight (number-average )

=

  • Viscosity- average molecular weight

Can take values ​​between 0 and 1.

[ ] = Amount [ mass ] of the i- mer; [] = Sum of [ ]   = Mole fraction of i- mers   = Molar mass of the i -mer, =   [] = Average molar mass [ mole ] of a monomeric unit   = Mass fraction of the i -mer

Determination methods

The following analytical methods have been proven to determine the molecular weight distribution:

  • Gel permeation chromatography ( GPC)
  • Sedimentation analysis for the determination of the centrifuge agent
  • Mass spectrometry (MALDI -TOF)
  • Viscometry, ie rheological behavior in solution
  • Rheology
  • Light scattering
  • At very low vapor pressure osmometry molecular weight (up to about 50,000 g / mol)
  • Osmometry at low molecular weight (up to about 10,000 g / mol)
  • NMR spectroscopy for determination of Mn (up to about 3104 g · mol -1).

GPC and centrifugation can also be used for preparative polymer fractionation.

Polydispersity

Physical, mechanical and rheological properties are often determined by the polydispersity (the ratio of weight average to number average). This ratio is also known as polydispersity and is a measure of Q, the width of a molecular weight distribution (MMV). The larger Q is, the wider the MMV. In the case that it holds that: Applying this is when the macromolecules of biological origin, such as Proteins, polysaccharides, DNA, all of which have the same molecular weight. However, applies to synthetic polymers:

The ratio of the number average and the average molecular weight of a monomeric unit indicates the degree of polymerization. It describes how many monomeric units react to form a polymer.

Average degree of polymerization

In general we obtain the average degree of polymerization by dividing the average molar mass by the molar mass of the monomer.

For non free-radical polymerization has to be considered whether and which groups are split off in the binding of the monomers, and this must be taken into account in the calculations.

Similarly, the following formulas shall not apply to copolymerizations.

Number average

Weight average

Viscosity-average

Molecular heterogeneity

The molecular non-uniformity U is a mathematical measure of the polydispersity of a polymer, or for the width of molecular weight distribution.

The smaller this value, the more uniform is the polymer, the narrower the molecular weight distribution.

Digital Object Identifier Krzysztof Matyjaszewski
578592
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