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The truth about number average molecular weight: Do you understand it?
In polymer chemistry, the molecular weight distribution (or molar mass distribution) describes the number of moles of each polymer species (N_i) relative to the molar mass of that species (M_i ). In linear polymers, the individual polymer chains rarely have the same degree of polymerization and molar mass, so there is always a distribution around a mean. The molar mass distribution of polymers can be modified by polymer fractionation.
Different averages can be defined according to the statistical method applied. In practice, four averages are used, representing a weighted average in terms of mole fraction and weight fraction.
Different average values of molar mass
In polymer chemistry, different measurement methods target specific molar masses. The four most frequently mentioned are:
- Number average molar mass (
M_n), also known as number average molecular weight (NAMW). - Mass average molar mass (
M_w), where w represents weight; also often called weight average or weight average molecular weight (WAMW). - Z-average molar mass (
M_z), where z stands for centrifugation (from the German Zentrifuge). - Viscosity average molar mass (
M_v).
The ratio between the number average molar mass and the mass average molar mass is called dispersion, or polydispersity index, which can indicate the distribution range of a sample.
Measurement of molar mass
These different definitions have real physical meaning because different techniques in polymer chemistry often measure only one of them. For example, permeation method measures the number-averaged molar mass, while small-angle laser light scattering measures the mass-averaged molar mass. The viscosity-average molar mass obtained from viscometry is determined by the interaction of the environment and the polymer and is typically between 0.5 and 0.8.
In a typical distribution curve, the relationship between the average values is:
M_n < M_v < M_w < M_z.
Characteristics and distribution of polymers
The molar mass distribution of a polymer sample can be affected by chemical kinetics and processing procedures. An ideal step-growing polymer would have a dispersion of 2, while an ideal living polymer reaction would form a polymer with a dispersity of 1. By dissolving the polymer, there may be an insoluble high molar mass fraction that is filtered out, causing M_w to be reduced more than M_n, thereby reducing dispersion.
The number average molar mass is determined by calculating the ordinary arithmetic mean of the molar masses of various different polymers.
The influence of quantity and mass on average molar mass
Number average molar mass (M_n) can be calculated by measuring the mass of a certain number of polymer molecules and then dividing the sum by the total number of molecules. The mass-average molar mass (M_w), on the other hand, takes into account the size of each polymer, and larger molecules will have a larger proportion than smaller molecules.
The calculation formula of mass average molar mass is:
M_w = ∑ N_i M_i^2 / ∑ N_i M_i.
Understanding of Z-average molar mass
Z-Average molar mass is the average molar mass of the third moment, or cube, and this measurement enables a better assessment of polymer performance, especially in terms of flow and viscoelastic properties.
Z-average molar mass is calculated by:
M_z = ∑ M_i^3 N_i / ∑ M_i^2 N_i.
In summary, understanding the meaning behind number average molecular weight not only helps to understand the properties of polymers, but also improves the efficiency and effectiveness of related applications. However, have you ever thought about the impact these molecular weights will have on future changes in materials science?
