In polymer chemistry, the molar mass distribution (or molecular weight distribution) describes the relationship between the number of moles of each polymer species () and the molar mass () of that species. In linear polymers, the individual polymer chains rarely have exactly the same degree of polymerization and molar mass, and there is always a distribution around an average value. The molar mass distribution of a polymer may be modified by polymer fractionation. Definitions of molar mass average Different average values can be defined, depending on the statistical method applied. In practice, four averages are used, representing the weighted mean taken with the mole fraction, the weight fraction, and two other functions which can be related to measured quantities: Number average molar mass (), also loosely referred to as number average molecular weight (NAMW). Mass average molar mass (), where stands for weight; also commonly referred to as weight average or weight average molecular weight (WAMW). Z-average molar mass (), where stands for centrifugation (). Viscosity average molar mass (). Here, is the exponent in the Mark–Houwink equation that relates the intrinsic viscosity to molar mass. Measurement These different definitions have true physical meaning because different techniques in physical polymer chemistry often measure just one of them. For instance, osmometry measures number average molar mass and small-angle laser light scattering measures mass average molar mass. is obtained from viscosimetry and by sedimentation in an analytical ultra-centrifuge. The quantity a in the expression for the viscosity average molar mass varies from 0.5 to 0.8 and depends on the interaction between solvent and polymer in a dilute solution. In a typical distribution curve, the average values are related to each other as follows: The dispersity (also known as the polydispersity index) of a sample is defined as divided by and gives an indication just how narrow a distribution is. The most common technique for measuring molecular mass used in modern times is a variant of high-pressure liquid chromatography (HPLC) known by the interchangeable terms of size exclusion chromatography (SEC) and gel permeation chromatography (GPC). These techniques involve forcing a polymer solution through a matrix of cross-linked polymer particles at a pressure of up to several hundred bar. The limited accessibility of stationary phase pore volume for the polymer molecules results in shorter elution times for high-molecular-mass species. The use of low dispersity standards allows the user to correlate retention time with molecular