Single-chain diffusion

This chapter examines the diffusion of mesoscopic rigid probe particles through polymer solutions. These measurements form a valuable complement to studies of polymer self- and tracer diffusion, and to studies of self- and tracer diffusion in colloid suspensions. Any properties that are common to probe diffusion and polymer self-diffusion cannot arise from the flexibility of the polymer probes or from their ability to be interpenetrated by neighboring matrix chains. Any properties that are common to probe diffusion and to colloid diffusion cannot arise from the flexibility of the matrix polymers or from the ability of matrix chains to interpenetrate each other. Conversely, phenomena that require that the probe and matrix macromolecules be able to change shape or to interpenetrate each other will reveal themselves in the differences between probe diffusion, single-chain diffusion, and colloid single-particle diffusion. 

Single chains confined between two parallel purely repulsive walls with = 0 show in the simulations the crossover from three- to two-dimensional behavior more clearly than in the case of adsorption (Sec. Ill), where we saw that the scaling exponents for the diffusion constant and the relaxation time slightly exceeded their theoretical values of 1 and 2.5, respectively. In sufficiently narrow slits, D density profile in the perpendicular direction (z) across the film that the monomers are localized in the mid-plane z = Djl so that a two-dimensional SAW, cf. Eq. (24), is easily established [15] i.e., the scaling of the longitudinal component of the mean gyration radius and also the relaxation times exhibit nicely the 2 /-exponent = 3/4 (Fig. 13). 

The bond fluctuation model not only provides a good description of the diffusion of polymer chains as a whole, but also the internal dynamics of chains on length scales in between the coil size and the length of effective bonds. This is seen from an analysis of the normalized intermediate coherent scattering function S(q,t)/S(q,0) of single chains ... 

Under good solvent conditions the crossover from single-chain relaxation to collective diffusion (many-chain behavior) can be observed by variation of the Q-value... 

Fig. 2. The tube model replaces the many-chain system left) with an effective constraint on each single chain right). The tube permits diffusion of chains along their own contours only...

This simple argument can yield the expected molecular weight dependence of both the single chain diffusion constant (in three dimensions) D and the viscosity 77. For in one reptation time the chain has moved on average one chain end-to-end distance R (N/Nj a, so... 

Fig. 3.6 Single chain structure factor from PEE melts as a function of the Rouse scaling variable. The dashed line displays the Rouse prediction for infinite chains, the solid lines incorporate the effect of translational diffusion. The different symbols relate to the spectra displayed in Fig. 3.5. (Reprinted with permission from [40]. Copyright 2003 Springer, Berlin)...

Most single-chain surfactants do not sufficiently lower the oil-water interfacial tension to form MEs, nor are they of the right molecular structure (i.e., HLB) to act as cosolvents. To overcome such a barrier, cosurfactant/cosolvent molecules are added to further lower the interfacial tension between oil and water, fluidize the hydrocarbon region of the interfacial film, and influence the curvature of the film. Typically small molecules (C3-C8) with a polar head (hydroxyl or amine) group that can diffuse between the bulk oil and water phase and the interfacial film are suitable candidates [11],... 

On the basis of monomer molecular weights (from sedimentation-equilibrium and sedimentation—diffusion studies, amino acid sequences and compositions), the a-lactalbumins, with one exception (rat a-lactalbumin, 140 residues, see Section VII,B), have a single chain of — 123 residues and values of —14,000. The mammalian lysozymes have 128-130 residues and values of —14,400, except echidna lysozyme, which has —125 residues. The c-type hen egg-white lysozymes have -127—131 residues, in contrast to the g type, which has —185 residues. 

Although the electrical conductivity is enhanced by the relatively high mobility associated with intra-chain transport, one must have the possibility of inter-chain charge transfer to avoid the localization inherent to systems with a one-dimensional electronic structure [237,238]. The electrical conductivity becomes three-dimensional (and thereby truly metallic) only if there is high probability that an electron will have diffused to a neighboring chain prior to traveling between defects on a single chain. For well-ordered crystalline material in which the chains have precise phase order, the interchain diffusion is a... 

The morphological changes discussed in Section 15.4.1.2 were obtained for monolayers at assembled states in 2D. In such an assembled state, secondary effects such as generation of 3D collapse are accompanied on the solid surface. This should be ascribed to the limited allowance of lateral diffusion compared to the rate of the photoisomerization process. For observation of intrinsic photoresponse of the monolayer, separation of the polymer chain is highly desired, ideally on a single-chain level. 

Consider a molecule made out of two /-arm stars with Kuhn segments per arm with junction points connected by a central linear strand of Abb Kuhn monomers. This molecule is called a pom-pom polymer. If/= 1, this molecule is linear, while the H-polymer corresponds to /=2. Estimate the /-dependence of relaxation time and diffusion coefficient of a melt of monodisperse pom-pom polymers for /> 1. Consider only single-chain modes and assume that the coordination number of an entanglement network is z. 

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