Entanglement Density at the Interface between Two Immiscible Polymers Robert Oslanec and Hugh R. Brown* BHP Steel Institute University of Wollongong Wollongong, NSW 2522 Australia Received July 2, 2002; Revised Manuscript Received May 29, 2003 ABSTRACT: The variation of entanglement density with interface width at an interface between two polymers is calculated using the relationships between chain packing and entanglement. The chain packing is obtained by the use of self-consistent mean-field techniques to calculate the average chain conformations within the interface region. The interface width is controlled by an assumed value of Flory-Huggins interaction parameter  between the two polymers. As the value of  is increased from 0 (completely miscible) to 0.1 (immiscible with a sharp interface), the calculated entanglement density is found to decrease by about a factor of 2. These modified entanglement densities are used within an existing model of interface coupling to estimate the effect of entanglement changes on the variation of interface toughness with interface width. Introduction Entanglements of polymer chains are topological constraints to motion that have a profound effect on the mobility of the molecules. Qualitatively, they can be envisioned as crossings of polymer chains that remain intact when the material is subject to strain and so are mechanically active. They therefore strongly influence dynamic properties of polymer melts such as viscosity and diffusion. The main glassy state properties that are influenced by entanglements are the high strain proper- ties, such as natural draw ratio, craze extension ratio, and toughness. The density of entanglements, often described by the molecular weight of a chain between entanglements M e , can be obtained from the plateau modulus of a high molecular weight melt. The mean distance between entanglements serves as the tube diameter within the dominant reptation model of poly- mer dynamics. Although the precise nature of entanglements is not well understood, there is good evidence that the density of entanglements is strongly related to the chain topol- ogy. A number of authors have suggested that entangle- ments, and hence M e , are controlled by the packing of the polymer chains. 1-5 They proposed that the volume of space pervaded by a single chain of molecular weight M e is a fixed constant of order 10 times the hard core volume occupied by that chain. The actual value of the fixed constant depends on the precise definition of the pervaded volume. Their arguments, which are sup- ported by strong experimental evidence, are based on the idea that it is the chain packing that that defines the constraints, placed by surrounding chains, on the motion of a single chain. If a chain is in a more compact form, then a relatively longer length of chain is required before it interacts significantly with other chains (high M e ), whereas if the chain is extended, then a much shorter length interacts with other chains (low M e ). Entanglement in the polymer bulk is thus reasonably well understood in broad terms, but the situation at an interface or surface is much less clear. Russell and one of the current authors 6 have suggested that, as chain packing is modified close to an interface, entanglement is likely to be modified also. They argued, following Silberberg, 7,8 that chains are “reflected” at an interface and so tend to pack more densely than in the bulk, decreasing the entanglement density and increasing M e from the bulk values. The aim of the current work is to use the ideas on the relation between chain contours and entanglement to calculate the entanglement density close to an interface between immiscible polymers. The structure of the interface is controlled by the repulsion between the polymers, described by the Flory-Huggins interac- tion parameter . The mean chain contours, and hence the chain packing, will be obtained as a function of  using self-consistent mean-field theory (SCMF). Hence, the interface entanglement density will be obtained as a function of . The main motivation for this work derives from the relationship between chain entanglement and fracture. Chain entanglement controls fracture in two basically separate ways. It controls both the saturation toughness of a polymer at high molecular weight and the molecular weight at which the toughness saturates. Failure of glassy polymers normally occurs through a crazing mechanism, and craze microstructure is strongly influ- enced by the entanglement density within high molec- ular weight material and hence by the M e of the material. Thus, entanglement controls the high molec- ular weight toughness. The toughness of glassy poly- mers increases with molecular weight until it saturates at a molecular weight of about 8M e . The use of diblock coupling agents has demonstrated that this increase and saturation in toughness are related to the molecular failure mechanism. Short chain strands that cross the fracture plane can pull out, whereas longer chains tend to fail by scission. The chain length at which this transition occurs is related to M e . The use of diblock copolymers at interfaces has also demonstrated that the areal density of chains that cross the interface, and thus have to undergo pullout or scission when the interface fails, controls the toughness of an interface between polymers. Hence, it has been suggested that, for high molecular weight polymers without specific coupling agents, the areal density of coupling chain strands controls the toughness of the 5839 Macromolecules 2003, 36, 5839-5844 10.1021/ma021044q CCC: $25.00 © 2003 American Chemical Society Published on Web 06/25/2003