Chain entanglements and fracture energy in interfaces between immiscible polymers

Entanglements are the ultimate source of toughness in glassy polymers, in fact at molecular weights lower than the critical molecular weight for entanglements they become quite brittle. Similarly, the strength of an interface between two immiscible glassy polymers is determined by the density of entangled strands that cross it, usually denoted by Σeff. This is a microscopic quantity that cannot be measured or controlled directly, except in very special cases, and therefore it is important to relate it to some significative macroscopic parameter characterizing the interface. In recent years many experimental works proved that there is a clear correlation between the toughness of an interface between glassy polymers and its width, so that models of entanglements at interfaces have become necessary to interpret the data. Some theoretical approaches have been proposed in the last few years, but their agreement with experimental data cannot be considered completely satisfactory. In this thesis we propose a new model to describe entanglements at interfaces, that relates the fracture energy of an interface between immiscible polymers to its width [1]. The role of other important parameters, first of all the molecular weight of the polymers, is also investigated. The starting point is a study of the interfaces between immiscible polymers at thermodynamical equilibrium. To this end we use a Self Consistent Field approach, which is suitable for the strong and intermediate segregation regime, to numerically derive concentration profiles and mean fields. The central part of this work is devoted to the calculation of Σeff, with a method, based on a mean field approximation, that it is a generalization of the stochastic ii approach successfully applied by Mikos and Peppas [2] to symmetric interfaces. Numerical results are obtained using the Self Consistent mean fields and the dependence of Σeff on the interface width and polymers molecular weights is shown. Following previous literature descriptions, possible fracture mechanisms, depending on the values of Σeff, are then discussed and a new fracture regime is introduced, called “partial crazing”, to account for the intermediate situation in which a craze starts in one of the two materials but it cannot fully develop. Numerical results for the fracture energy as a function of interface width and polymers molecular weights are compared with literature experimental data, showing good agreement. In the case of PMMA/P(S-r-MMA) interfaces, the dependence of the fracture energy on the interfacial width could be reproduced very well over the whole range of investigated widths, more satisfactory than in previous literature works. The last chapter of this work is focused on the calculation of the molecular weight of entanglements Me, which influences greatly the value of Σ eff. This quantity has been measured in bulk polymers, but, to our knowledge, never at a polymer-polymer interface. Moreover, theories that clarify the nature of entanglements and allow speculations on the value of M e in inhomogeneous systems, have been proposed only recently. In this work the packing model for entanglements is adopted to estimate the value of M e at polymer-polymer interfaces and in thin polymer films. Our numerical results show that the molecular weight of entanglement of chains near an interface is larger than in the bulk, leading to appreciable corrections in the Σ eff and fracture energy calculations. We also compute the average molecular weight of entanglements in thin films, and predict that it should increase as the thickness of the film decreases below the entanglement length.