Adhesion

Many people know that most polymers are not mutually compatible - they will phase separate given enough time and temperature. They then mistakenly think that at a polymer-polymer interface you cannot get much useful intermingling and entanglement "because polymers are incompatible".

This view happens to be wrong because you can get significant adhesion across an interface as long as the polymers are reasonably compatible.

The distance, d, by which the chains can intermingle is calculated very simply via the Helfand formula which depends on the effective length, b, of each segment of the polymer (the Kuhn length) and the Flory-Huggins χ parameter.

d = b/(6χ)^0.5

The χ parameter is related to the HSP Distance, D, via D²=4RTχ/100 where the 100 is a nominal molar volume of a monomer unit. So for good adhesion across a polymer interface, the lower D, the better.

In adhesion science terms, if d is small then adhesion is proportional to d. But once d is large enough to create entanglement, then adhesion is proportional to 100x d! Because entanglement takes place above a critical value of d, a relatively small decrease in D (giving a larger d) can lead to a large increase in adhesion. Or, to be more pessimistic, a small change in formulation which increases D and decreases d can lead to a catastrophic loss of adhesion.