12.2
During polymerization, monomers join together to form long polymer chains. But these chains do not all reach the same length.
As a result, a polymer sample contains molecules with different molar masses.
So, we use average molar masses to describe the distribution of chain sizes in the sample.
First is the number-average molar mass, written as M̅n. It equals the summation of ni times Mi, divided by the summation of ni.
Here, ni is the number of molecules with a specific molar mass, and Mi is their molar mass. This average treats each molecule equally.
Next is the weight-average molar mass, written as M̅w. It equals the summation of ni times Mi squared, divided by the summation of ni times Mi.
Since the contribution of molar mass is greater, larger polymer chains with higher molar mass contribute more to this average.
The ratio of these two averages defines dispersity, written as Đ.
A value of one means all polymer chains have the same length. However, most polymers have dispersity greater than one, indicating chains of different sizes.
Polymerization produces macromolecules with a range of chain lengths due to the random nature of molecular growth processes. As chains form and terminate at different stages, a single polymer sample contains molecules of varying sizes rather than a uniform structure. This variability is described using average molar masses and distribution-related parameters, which together provide a comprehensive understanding of polymer characteristics.
The distribution of molar masses plays a critical role in determining the physical behavior of polymers. Samples with a narrow distribution exhibit more consistent thermal and mechanical properties, while broader distributions introduce a combination of short and long chains that influence flexibility, strength, and viscosity. Shorter chains typically enhance flow properties, whereas longer chains contribute to entanglement and mechanical stability.
Dispersity serves as an indicator of how uniform or varied the polymer chains are within a sample. Values close to one suggest a highly uniform system, often associated with controlled synthesis methods. Higher values indicate a wider range of chain lengths, which is common in conventional polymerization techniques. This variation can be advantageous or disadvantageous depending on the intended application, as it affects crystallinity, durability, and processing behavior.
The method used to synthesize polymers strongly influences the resulting distribution. Conventional methods generally produce broader distributions due to less control over chain growth. In contrast, advanced techniques such as controlled radical polymerization allow for more uniform chain formation, leading to narrower distributions and more predictable material properties.
During polymerization, monomers join together to form long polymer chains. But these chains do not all reach the same length.
As a result, a polymer sample contains molecules with different molar masses.
So, we use average molar masses to describe the distribution of chain sizes in the sample.
First is the number-average molar mass, written as M̅n. It equals the summation of ni times Mi, divided by the summation of ni.
Here, ni is the number of molecules with a specific molar mass, and Mi is their molar mass. This average treats each molecule equally.
Next is the weight-average molar mass, written as M̅w. It equals the summation of ni times Mi squared, divided by the summation of ni times Mi.
Since the contribution of molar mass is greater, larger polymer chains with higher molar mass contribute more to this average.
The ratio of these two averages defines dispersity, written as Đ.
A value of one means all polymer chains have the same length. However, most polymers have dispersity greater than one, indicating chains of different sizes.
From Chapter 12:
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