Copolymer Brownian

Theory for the self- and tracer-diffusion of a diblock copolymer in a weakly ordered lamellar phase was developed by Fredrickson and Milner (1990). They modelled the interactions between the matrix chains and a labelled tracer molecule as a static, sinusoidal, chemical potential field and considered the Brownian dynamics of the tracer for small-amplitude fields. For a macroscopically-oriented lamellar phase, they were able to account for the anisotropy of the tracer diffusion observed experimentally. The diffusion parallel and perpendicular to the lamellae was found to be sensitive to the mechanism assumed for the Brownian dynamics of the tracer. If the tracer has sufficiently low molecular weight to be unentangled with the matrix, then its motion can be described by a Rouse model, with an added term representing the periodic potential (Fredrickson and Bates 1996) (see Fig. 2.50). In this case, motion parallel to the lamellae does not change the potential on the chains, and Dy is unaffected by... 

Fig. 3.27 Schematic of the Monle Carlo moves in the lattice simulations of micellization and adsorption of block copolymers by Mattice and co-workers, (a) Brownian moton of a chain (b) end flip of an end bead (c) two types of kink jump (d) reptalion of a chain (Zhan et at. 1993d).

To exhibit an equilibrium elastic stress, it is necessary for the collection of linear polymer chains in an elastomer to be tied together into an infinite network. Otherwise the Brownian motions of the macromolecules will cause them to move past each other, thus exhibiting flow. Chemical crosslinking reactions to form covalent bonds are many and varied. In addition, microphase separation of parts of the chain (e.g., a chemically different sequence in a block copolymer) can provide a strong tie. It suffices for our purposes to consider a crosslink to be a permanent tie-point between two chains (Figure 6-2). 

Dispersion or plastisol resins are made exclusively by emulsion polymerization techniques. A vinyl latex is a colloidal suspension (emulsion) of the homo-copolymer particle in water. (The 0.2 )jm average particle size is small enough to be in Brownian movement.) Soaps are generally used to form a protective colloid around the particle, and they are surrounded by a negative electrical charge. In some cases air-dry film-forming systems are possible. 

Apparent mean square radius of Brownian block copolymers The linear block copolymers are made of different successive subchains a — 1,2,. . . and so on. For the Brownian case, Benoit and Wippler16 obtained an expression of °ka2pp(x) in terms of rather simple contrast parameters. Their result can be recovered as follows. First, let us write (7.3.46) in the form... 

Nanoscopic particles, dispersed in a block copolymer, have dimensions that are appropriate for Brownian dynamics simulations (268). Clay composites have a range of length scales, but if the gallery spacing between the layers is not large, MD methods can be used (269) with periodicity in the directions parallel to the clay platelets. However, continuum mechanical models need to be invoked for the description of exfoliated clay systems (270). These materials have so much interfacial area that adhesion properties are very important (271). Traditional continuum bounds methods (130) usually ignore the interphases on the grounds that they comprise a very small volume fraction of the total material, and so are not expected to be very accurate for exfoliated clay systems. 

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