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The entire atomic weight of a molecule is its molecular weight (MW). The MW of a molecule is calculated by adding the masses of all the constituent atoms in the molecule.
When it comes to polymers, molecular weights are usually given as average values like Mn (number average molar mass), Mw (weight average molar mass), and Mz (weight average molar mass) (the z-average molar mass). Because polymer samples comprise a combination of chains of atoms of various lengths, the molecular weight of a polymer is expressed as an average rather than an absolute value.
Polymers
Polymers are materials that are made up of long, repeating chains of molecules. The properties of the materials vary depending on the type of molecules bound and how they are attached. Rubber and polyester are two examples of polymers that bend and stretch. Others, like epoxies and glass, are robust and durable.
Polymerisation
Polymerization is the process of making synthetic polymers by joining smaller molecules, known as monomers, into a chain held together by covalent bonds.
Certain chemical reactions, such as those generated by heat and pressure, modify the chemical bonds that hold monomers together. Polymers are formed as a result of the process, which leads the molecules to link in a linear, branching, or network structure.
These monomer chains are also known as macromolecules.
Molecular Weight
Repetitive units make up a polymer. These repetitive units were originally the monomer molecules. When polymer chains form their lengths and thus their weights differ. It is important to be able to characterize the polymer structure. Determining the weight-average molecular weight or the number-average molecular weight is a part of any polymer characterization.
The molecular weight of a polymer is defined as the sum of the atomic weight of each of the atoms in the molecules, which is present in the polymer.
Number-average molecular weight
It is just the total weight of all the polymer molecules in a sample, divided by the total number of polymer molecules in a sample
Where,
n = Moles of molecules i.e., weight
(w)/molecular weight (M)
w = Weight of individual molecules
M = The molecular weight of each molecule
Molecular Weight
The Number Average Molecular Weight is the total weight of the polymer molecules divided by the total number of polymer molecules.
Generalization of concept
Total number of molecules ( n ) id given by
The number fraction of each molecule is
Number average weight contribution of each entity is
Number average weight molecular weight is
For synthetic polymers Mw is greater than the Mn . If they are equal then they will be considered perfectly homogeneous. (Each molecule has the same molecular weight).
The Weight Average Molecular Weight takes into account that the larger molecules contain a much higher amount of the molecular mass of the polymer. The Weight Average Molecular Weight is almost always higher than the Number of Average Molecular Weight
Degree of polymerisation (DP)
The number of the repeating unit in a polymer is called the degree of polymerisation (DP). DP provides the indirect method of expressing the molecular weight and the relation is as follows;
Where, M is the molecular weight of the polymer, DP is the degree of polymerisation and m is the molecular weight of the monomer
Each of these averages can be related to the corresponding molecular weight average by the following two equations;
Methods to calculate molecular weight of polymers
Gel permeation chromatography (GPC) or size exclusion chromatography (SEC), in combination with a refractive index or UV detector, is commonly used to estimate a polymer’s molecular weight.
This approach not only provides average molecular weight numbers but also information on molecular weight distribution in the polymer sample. Additional detectors (such as a light scattering or viscometric detector) can be used with GPC or SEC to provide information on molecular architecture and size in solution.
Conclusion
When we speak of molecular weight in the context of polymers, we are referring to the length of the individual chains. The average weight of the molecules that make up a polymer is the molecular weight, which indicates the length of the polymer chains.
Because the polymerization process is variable, there is no one chain length; instead, there is a wide range of lengths, therefore when we talk about molecular weight, we truly mean the material’s average molecular weight. This average is calculated by taking samples of the material as it is being manufactured.
