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In this edition of "Comparatively Speaking," Tony O’Lenick looks to Thomas O’Lenick, PhD, to describe the difference between critical molecular weight of entanglement (Mc) and critical concentration of overlap (C*). These concepts are important for formulators to grasp since they deal with altering the physical properties of a finished product.
Polymers differ from small molecules in many different ways. One of the most appealing is their drastic difference in physical properties. Many examples of this are seen in everyday life. For instance, ethylene, a small organic hydrocarbon, is a gas. Polyethylene is a polymer made up of repeat units of ethylene that varies from a weak stretchable solid, used in trash bags, to a hard brittle solid, used in laundry detergent containers. Polymer chemistry can provide an advantage to a formulating chemist by changing the physical properties of a product. A major component as to why polymers have such interesting properties is that the polymer chains entangle at certain concentrations and molecular weights and although this does not seem drastic, entanglement provides polymers with many unique properties.
When polymer chains entangle, the chains stop acting like individual chains and begin to act like a single unit. A good example of this is Crayola's Silly Putty product. Silly Putty is a lightly cross-linked polymer network but acts the same way as entangled polymer chains if one considers each cross-link as an entanglement. When Silly Putty is left in a ball on a table, the ball will slowly flatten out and become a flat layer of putty. On the other hand, if the ball is dropped on the table, the ball will bounce back. This is due to the rate of stress put on the system. There are two major ways to induce polymer entanglement; the first is increase the molecular weight of polymer chains and the second is to increase the concentration of the polymer in a formulation. The major difference between the two is that the molecular weight of the polymer is controlled by the polymerization and the concentration is controlled by the formula in which the polymer is used.
It is important to note that this is a brief overview of polymer chain-chain interactions. For a complete discussion, it is important to discuss the Flory-Huggins theory and the interaction parameter χ. To discuss the Flory-Huggins theory, this column would need to go into great detail about specific thermodynamic behaviors, which is a common topic in many polymer chemistry graduate school courses. Instead of going into complex physics, it would be better to go into a brief discussion of the basics; those interested in following the topic in more detail should consult a good polymer chemistry book.1
Molecular weight of entanglement: First it is important to understand the molecular weight of entanglement. Small molecules can mix together and easily pass by each other without entangling, resulting in minimal interaction with surrounding molecules. A great example of this is grains of rice. When rice is mixed together, a random mixture is formed but the rice gains are easily separated from one another. Low molecular weight polymers, much like grains of rice, do not have long enough chains to entangle. High molecular weight polymers, on the other hand, have long chains, thus they have much more difficulty passing by one another. As they try to squeeze past one another, they become entangled. This results in a higher viscosity and physical properties. A great example of this is cooked spaghetti noodles. When spaghetti noodles are mixed, a random mixture of entangled noodles results and this entanglement makes it more difficult to remove a single noodle from the entangled mass of noodles. To remove a single noodle, one needs to provide enough energy to overcome the entanglements it has with the surrounding polymer chains. High molecular weight polymers (i.e., the spaghetti noodles) do not possess the properties of a single chain, but instead possess properties of the whole bowl of noodles and one cannot change a single noodle without affecting the other noodles.