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Comparatively Speaking—Entanglement vs. Overlap
By: Anthony J. O'Lenick Jr., Siltech LLC, and Thomas O'Lenick, PhD, SurfaTech Corp.
Posted: May 11, 2011
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The critical point at which polymer chains become large enough to entangle is called the molecular weight of entanglement (Mc), which is the point where the physical properties of the polymer change. Most commonly, the molecular weight of entanglement is determined by plotting the log of the melt viscosity versus the log of the molecular weight. As the molecular weight increases, the plot will follow a linear path. Once the molecular weight of entanglement is reached, the slope of the line will increase drastically. It is important to note that the molecular weight of entanglement only applies when in bulk or neat conditions. Also, the Mc is specific to each polymer and controlled by the properties of that polymer including chain flexibility, pendant groups and intermolecular forces.
Critical concentration of overlap: Unlike the critical molecular weight of entanglement, the critical concentration of overlap (C*) can be adjusted by the formulation. As a polymer is added into a solvent, the polymer will take a random coil conformation and take up as much space as possible. de Gennes and Daoud et al.2 described a model that defined a polymer chain in solution as a “blob.” In this model, a polymer chain is divided into several different spheres, each having an average size, which are non-interpenetrating with other blobs. The best was to describe is is a string of pearls. The blobs are the pearl beads. As you move the string, the beads cannot pass through one other (i.e., they are non-interpenetrating).
As another polymer chain is added into the same volume of solvent, the first polymer chain does not have as much solvent as before, so it has to change its shape to avoid contact with the new polymer chain. As the concentration of polymer chains (in solution) increases, the original polymer has to collapse to minimize contact with other chains. Eventually, a concentration is reached where the polymer chains cannot collapse any further so they have to entangle. This value is the concentration of overlap (C*). Much like the molecular weight of entanglement, C* is commonly measured by the plot of viscosity versus concentration. At low concentrations, the plot will follow a linear path and once the C* is reached, the slope of the line drastically increases. It is important to note that the C* of the polymer is different for each solvent and can be easily adjusted by changing the solvent or its amount in a formulation.
These two concepts are important for formulators to grasp as both deal with altering the physical properties of a finished product. The critical molecular weight of entanglement is useful to a chemist when he or she is designing a new polymer for a certain application. If a low viscosity polymer for a given application is desired, the polymerization can be stopped below the critical molecular weight of entanglement. The opposite is also true; if a material is not rigid enough, the molecular weight can be increased to increase mechanical properties.
C* is a probably the more important parameter to understand for the formulation purposes. Take a hair spray, for example. To apply a hair spray, the consumer wants a low viscosity solution that is easily sprayed onto the hair. Once the product comes into contact with the hair, the product should reach the C* rapidly (through evaporation of the solvent) so the polymer can entangle. This entanglement locks the hair into place. This concept is very important for a formulating chemist.