Star polymers diffusion

Figure 13 Volume fraction composition profiles for a thin film of deuterated polystyrene star polymer diffusing into a hydrogenous polystyrene star polymer film. Reprinted with permission from Clarke, N. Colley, F. R. Collins, S. A. etal. Macromolecules 2906,39,1290. Copyright 2006 American...

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

The observations above can be rapidly turned into a semi-quantitative theory for star-polymer stress-relaxation [24] which is amenable to more quantitative refinement [25]. The key observation is that the diffusion equation for stress-re-lease, which arises in linear polymers via the passage of free ends out of deformed tube segment, is now modified in star polymers by the potential of Eq. (16). Apart from small displacements of the end, the diffusion to any position s along the arm will now need to be activated and so is exponentially suppressed. Each position along the arm, s, will possess its own characteristic stress relaxation time T(s) given approximately by... 

The properties of the surplus segment probability p and the effective constraint coordination number z are less well established. It seems possible that p will dep d on polymer species to some extent, since loop projection may be easier for a more locally flexible chain. Weak dependences on concentration and temf rature are likely for the same reason. On the other hand, z characterizes the topology on a fairly large scale and therefore may be virtually a universal constant. Diese however are only some speculations. Values of p and z can be established by various experiments, p from the elastic properties of networks and also from the relaxation of star polymers, z from relative relaxation rates of linear and star molecules in liquids and networks and also from measurements of diffusion rates of stars in linear chain liquids. The adequacy of the... 

Sikorski and Romiszowski455 study confined branched star polymers by on-lattice MC simulation. Attractive forces are excluded and only excluded volume accounted for, thus making the simulations relevant for chains in a good solvent. Contrary to expectation, they find that the diffusion constant is very similar for either moderate or highly confined chains and scales approximately as A 1, though a more accurate representation is suggested by... 

Entangled star polymers relax by arm retractions with relaxation times and viscosities exponentially large in the number of entanglements per arm NJNg [Eqs (9.58) and (9.61)]. This leads to exponentially small diffusion coefficients [Eq. (9.62)] for entangled star polymers. 

Figured displays simulated form factors for a multiarm star polymer of varying functionality and a hard sphere [41], The high-g asymptotic behavior, characteristic of the coil structure, is absent in the latter case. A handicap in the experimental determination of P(g) is often the narrow-g range accessible by the scattering techniques that can be overcome through the combination of low-g light scattering and high-g X-ray and/or neutron scattering (utilized on the same system). Size and shape also determine the translational diffusion Dq of the nanoparticles in dilute solution, and hence Dq can prove the consistency of the scattering results.

The adsorption kinetics, studied by time-ressolved ellipsometry show two processes. At the initial stages the adsorption is diffusion controled. At longer times the polymers must penetrate the barrier formed by the initially adsorpted chains. It was found that the star polymers penetrate this barrier faster than the linear chains, due to the different conformations adopted by the stars. 

It should also be noted that a similar treatment is possible for the translational hydrodynamic radius, Rhj, obtained from measurements of translational diffusion coefficients or sedimentation coefficients of branched polymers. One may define a parameter gn = Rh,fb/Rhji - the ratio of the hydrodynamic radius of the branched polymer relative to that of a linear polymer of the same molecular weight. Again, it is expected that gH < 1. For star polymers with uniform subchain lengths having... 

Discriminating branched and star polymers from linear ones can always be achieved by measuring the properties in dilute solution. In fact, molecules having the same molar mass but different macromolecular architectures exhibit different transport and light scattering properties. More specifically, a branched macromolecule is more compact than a linear molecule having the same molar mass, and therefore it will display less friction and will diffuse more easily in the solvent. Viscometry can be used to detect branched structures, since the Mark-Houwink-Sakurada exponent (Eq. 2.23) for branched and star-shaped polymers is lower tiian that for the corresponding linear chain. Unfortunately, in order to measure the difference, one must have a sample made exclusively... 

Polystyrene supported versions of catalyst Id have been reported/ In addition, Frechet and coworkers demonstrated that catalyst Id can be encapsulated in the core of a soluble star polymer, which enables reagents to diffuse, allowing catalysis to take place/ Interestingly, the concurrent mixing of different chiral and achiral catalysts encapsulated in a similar manner onto different star polymers enabled one-pot multicomponent asymmetric cascade reactions of otherwise incompatible catalysts. 

Correlations of the scaling parameters with polymer molecular weight, concentration, and size are examined, a increases markedly with polymer molecular weight, namely a for r 1. r/ is 0.5 for large polymers (M larger than 400 kDa or so), but increases toward 1.0 or so at smaller M. Scaling parameters for the diffusion of star polymers do not differ markedly from scaling parameters for the diffusion of linear chains of equal size. 

Figure 37 Relative zero-shear viscosity (normalized to the solvent tis) as a function of the effective volume fraction

The diffusion constant Dc of the star polymers is estimated by the following argument. For the central segment to move to the next stable point, the polymer has to withdraw (f — 7) arms to the brandling pmnt. The activation ener required for such a process is... 

Dynamic light scattering from dilute solutions provides the value of the diffusion coefficient, which can be converted to hydrodynamic radius J h,star of the star polymer. The ratio Rh/(Rg) characterizes the compactness of the macromolecule for the uniform hard sphere impenettable for the flow, it is Rb/Rg= (5/3) 1.29, whereas for the Gaussian coil, Rh/(Rg) = 3a- / /8 0.66. For ideal stars (without excluded-volume interactions), the ratio Rh/(Rg) can be derived within the Kirkwood-Riseman approximation, which gives the value of Rh/(Rg) 0.93. Reported experimental values of the Rh/(Rg) ratio for star polymers and starlike block copolymer micelles are usually found close... 

The force of this reaction comes from the catalytic integrity of the active star polymers 113 and 115, as they cannot penetrate each other s core. In contrast to that, small molecules and catalysts can freely diffuse to the core of the star polymers 113 to form the desired salt 114, which will then react as optimal iminium catalyst. 

Poly(N,N-dimethylacrylamide) (PDMA) star polymers with 2, 3, and 4 arms and with dodecyl chains as hydrophobic end-caps were obtained in high yield with narrow polydis-persities by means of the RAFT technique. At sufficiently high concentration they form interconnected hydrophobic domains, i.e., a transient network. SANS experiments show that these hydrophobic domains contain about 20 dodecyl chains and they interact repulsively due to the PDMA chains that separate them. While the static structure is only very little affected by the number of arms this applies not at all to the dynamic properties as observed by DLS and rheology. Here one observes in DLS a complex, trimodal relaxation process, where the slower modes become more pronounced with increasing munber of arms. The fast mode corresponds to the diffusion of the hydrophobic domains while the second mode shows no q-dependence and corresponds in its values to the time deduced from the cross-over of G and G" in the oscillatory rheological experiments. Finally the slowest motion shows a rather pronounced q-dependence and is pre-stunably linked to a more complex relaxation mechanism of... 

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