Effect of Entanglement on Nucleation Rate of Polyethylene

Abstract

Recently, present authors found a power law of nucleation rate (I) of single crystals of polyethylene (PE), I ∝ M−H, where M is molecular weight and H is a constant.1, 2 This indicates that the topological nature of polymer chain plays an important role on nucleation of polymers. Topological nature is related to the chain entanglement and chain sliding diffusion.3, 4 Polymer chains should be disentangled within interface between the melt and a nucleus during nucleation. Therefore, if number density of entanglement (νe) is small, it is expected that I becomes large. This expectation was confirmed in our preliminary study5 that I decreases with increase of keeping time at a temperature above melting temperature (∆t). This result was speculated that when the melt is kept above melting temperature, νe gradually increases with increase of ∆t and approaches to thermal equilibrium νe (νe = 1), which can be regarded as “melt relaxation”. However, any experimental evidence of the expectation has not been reported yet, therefore it is important to show the evidence. Purpose of this work is to show an experimental evidence that I increases with decrease of νe within the melt. It is reasonable that a giant extended chain single crystals (ECSCs) includes little entanglement (νe ∼ 0), while thin lamellae of folded chain crystals (FCCs) do a lot of entanglements. Therefore, when the giant ECSC and thin FCCs are melted, the melt should have small νe and large νe, respectively for small ∆t, because the above “melt relaxation” process takes long time, i.e., we showed that it takes about several hours or a few days depending on the conditions and molecular weight.5 This suggests that νe should decrease with increase of lamellar thickness (l). In the case of polyethylene, l can be changed easily from several nm to several μm by changing crystallization conditions, such as degree of supercooling (∆T ) and pressure. According to classical nucleation theory by Becker and Doring and Turnbull and Fisher, I is expressed by two competing factors as