Fundamental Hydrodynamic Characteristics of Polymers with Star and Comb Macromolecular Structures

Abstract

Using the theoretical results published previously (Beier 1973), experimental data of the scattering of 'Li*-ions at Ar are evaluated. From the diffraction effect detailed statements about the repulsive term oftheinteraction potentialaregiven. The simple Yukawa type screened Coulomb potential is very well suited for describing the small angle scattering between ions and atoms. A modification of this potential can be clearly excepted. The evaluation method for determining the potential parameters is described in detail and gives for 'Li+-Ar the parameters R , = 0.289 A and Zaeff = 54.In the region of the first undulation maximum the influence of the attractive potential term is found experimentally. Certainly the experiments show with decreasing scattering angle a shape of approximately 1/02 which is caused by inelastic scattering. Because of the covered elastic scattering in the region of very small angles at the present time no results about the attractive potential term can be given. For this purpose the clastic scattering alone below the undulation region has to be measured.

Lignin. Structural organisation and fractal properties

“…It is noteworthy that these values do not coincide with the values obtained in terms of the SARW model for linear chains (a = 0.78, d f = 1.67). Although the results of the theoretical simulation of star polymers remain debatable, they are still consistent with the known statement 63,64 that the Mark ± Kuhn ± Houwink parameter a (and, hence, d f ) for these polymers does not depend on the quality of the solvent. Since the d f values of the hardwood lignins studied differ insignificantly from the value 2.0, which was found for the clusters formed according to the model of `lattice animals', ultimate determination of the fractal structure of the macromolecules of guaiacyl-syringyl lignins requires further investigations.…”

“…62 According to this model, one-centre star tri-and tetrafunctional macromolecules form impermeable coils with a Mark ± Kuhn ± Houwink diffusional parameter b close to 70.5 and a fractal dimension d f equal to 2. } It is pertinent to recall that Flory 63 has shown theoretically that the viscosimetric parameters a for star and linear macromolecules coincide. Later, this result was confirmed experimentally 64 in relation to polystyrenes.…”

Stable Freestanding Thin Films of Copolymer Melts Far from the Glass Transition

“…As a consequence, the side-chains see each other and they minimize their interactions by forcing the backbone to stretch. Thus we hypothesize that the copolymers form dense combs 41,42 . Moreover, since we consider melt properties, we assume that individual chains are in a -solvent.…”

“…The macromolecular conformation of branched polymers depends on the polymerization degrees N b and N s of the backbone and side chain, respectively, and on the number of backbone units n between consecutive side-chain grafting points. We are in the limit of short non-Gaussian side chains ( N s < 100) , and of a Gaussian backbone . The spacers l s between branching points are approximately four siloxane units long on average, that is, l s ≈ 1.3 nm considering that the distance between two silicon atoms in the backbone is given by 2 l Si‑O , with l Si‑O = 0.164 nm and assuming that the monomers are linearly arranged.…”

“…As a consequence, the side chains see each other and they minimize their interactions by forcing the backbone to stretch. Thus, we hypothesize that the copolymers form dense combs. , Moreover, since we consider melt properties, we assume that individual chains are in a θ-solvent. Assuming that only steric interactions matter in setting the macromolecular conformation and neglecting bond length differences, the radius of gyration R g of the copolymer may be estimated using the following scaling law …”