Interdiffusion of chains

Fig. 7. Different types of interphases. (a) Contact interphases, as produced for example by transcrystalline growth or enhanced adlayer crosslinking in the adhesive phase, (b) Diffusion interphases, as produced by interdigitation or interdiffusion of chains from either or both phases.

In studying contact between films of polyethylene (PE) and polyethylene terephthalate (PET) bonded to quartz cylinders, they observed an increase in adhesion energy with contact time for a PE/PE pair, but not for PE/PET or PET/PET combinations. They interpreted this as evidence for the development of nanoscale roughness due to the interdiffusion of chains across the PE/PE interface [84],... 

Dwell times generally increase the adherence force, and Fig. 10 shows the increase of w with contact time between glass and polyurethane (26). Between two polymers (auto-hesion ) this effect is ascribed to interdiffusion of chains by reptation theory and experiments (27-29) lead to a (hence a Dupre energy of adhesion, see below)... 

For understanding of the properties of pol5rmeric alloys, it is essential that a limited interdiffusion of chains in a very small region is possible at the interface between two immiscible components, A and B. It is in this region that the interactions of components A and B, characterized by parameter %ab, are accomplished. 

As mentioned earlier, adhesive bond formation is governed by interfacial processes occurring between the adhering surfaces. These interfacial processes, as summarized by Brown [13] include (1) van der Waals or other non-covalent interactions that form bonds across the interface (2) interdiffusion of polymer chains across the interface and coupling of the interfacial chains with the bulk polymer and (3) formation of primary chemical bonds between chains or molecules at or across the interface. 

The interdiffusion of polymer chains occurs by two basic processes. When the joint is first made chain loops between entanglements cross the interface but this motion is restricted by the entanglements and independent of molecular weight. Whole chains also start to cross the interface by reptation, but this is a rather slower process and requires that the diffusion of the chain across the interface is led by a chain end. The initial rate of this process is thus strongly influenced by the distribution of the chain ends close to the interface. Although these diffusion processes are fairly well understood, it is clear from the discussion above on immiscible polymers that the relationships between the failure stress of the interface and the interface structure are less understood. The most common assumptions used have been that the interface can bear a stress that is either proportional to the length of chain that has reptated across the interface or proportional to some measure of the density of cross interface entanglements or loops. Each of these criteria can be used with the micro-mechanical models but it is unclear which, if either, assumption is correct. 

Step I. The time dependent structure of the interface is determined. Relevant properties may be characterized by a general function H(t), which for the ca.se of polymer melts can usually be described in terms of the static and dynamic properties of the polymer chains. For example, with symmetric (A = B) amorphous melt interfaces, H(t) describes the average molecular properties developed at the interface by the interdiffusion of random coil chains as [ 1,6J... 

In which X is the average monomer interpenetration distance, L is the contour length of interdiffused chains and n(t) is the number of chains diffused at time t. The time and molecular weight dependence of these molecular properties are given in Table 1. 

Total interpenetration of chains (X approaches Rg) is not necessary to achieve complete strength when M > M and x < 7). However, a word of caution while complete strength may be obtained in terms of critical fracture measures such as G c and A lc, the durability, measured in sub-critical fracture terms, such as the fatigue crack propagation rate da/AN, may be very far from its fully healed state at r. We have shown that while the weld toughness A lc increases linearly with interdiffusion depth X as K f. X, the fatigue crack propagation behavior of partially healed welds behaves as [1]... 

For the EPDM/NR joint, the modification of the EPDM rubber increases its cure compatibility with NR. This, thus, increases with radiation dose up to 50 kGy beyond which a drop in the absorbance values due to predominant chain scission of the rubber also lowers the bond strength. Besides, interdiffusion of the mbber molecules across the interface also contributes to the formation of the bond. 

Electron Beam Lithography. LB PMMA films with thicknesses of 6.3 nm (7 layers) are sufficient for patterning a Cr film suitable for photomask fabrication. For ultrathin PMMA films the resolution (see Fig. 1) is limited by the smallest spot diameter available on MEBES I (1/8 pm). However, it is not possible to obtain this resolution if a thicker resist (>100 nm) is used under the same exposure and development conditions, which demonstrates that ultrathin resists are able to minimize the proximity effect. Also, since the radius of gyration of 188,100 Mw PMMA is about 10 nm in the bulk, and the thickness of the 7 layer film (6.3 nm) is less than 10 nm, it is reasonable to assume there must be an alteration of chain configuration in the ultrathin films. This will be particularly true when the post-deposition baking temperature of the multilayer films is less than the glass transition temperature (115°C), as is the case for the present experiments. In such a case, interdiffusion of PMMA chains between the deposited layers may not result in chain configurations characteristic of the bulk. 

Polymers interpenetration of polymer chains, phase separation, compatibility between polymers, interdiffusion of latex particles, interface thickness in blends of polymers, light-harvesting polymers, etc. 

The above description is of a thermally propagating steady-state wave. It must be emphasized, however, that the basic feature of a thermal mechanism is not altered by the superposition of molecular diffusion onto the diffusional transport of heat. This applies not only to interdiffusion of reactants and products but also to the diffusion of chain carriers participating in the chemical reaction, provided that the chains are unbranched. The reason for this is that in a wave driven by a diffusion process, the source strength of an entering mass element must continue to grow despite the drain by the adjacent sink region. This growth can occur only if the reaction rate is increased by a product of the reaction, which may be temperature as well as a material product. 

Bradford and Vanderhoff (20) have also prepared films from crosslinked latex particles. These authors studied a 65 35 styrene-butadiene copolymer crosslinked with varying amounts of divinylbenzene and found that although the incorporation of divinylbenzene retarded the coalescence of latex particles, these particles did indeed coalesce, presumably due to a similar interdiffusion of polymer chain ends. 

The diffusion law of Eq. (2.73) holds for the welding of polymers at an interface which can be explained by reptation. When two blocks of the same polymer are brought and held at a temperature just above the Tg for a short time f, interdiffusion of the chains takes place from each block across the interface thereby joining the blocks together. The strength of the junction formed will depend on time t. 

An area of intensive research involves the interfacial aspects of diverse polymer systems. Multidisciplinary programs on the interfacial characteristics of polymers are in progress as various academic institutions e.g., Center for Interfacial Engineering at the University of Minnesota, NSF Center on Interfacial Science at Lehigh University). The projects under investigation involve the nature of interfacial adhesion, interdiffusion of diverse polymer chains, and adsorption of polymers from solution on polymer surfaces. A recent textbook on polymer blends and composites has several chapters dedicated to polymer surfaces and interfaces [Sperling, 1997]. 

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