Scattering From Ramified Polymeric Systems

Abstract

Here, of great interest to us is a quantitative study of the scattering properties from ramified polymeric systems of arbitrary topology. We consider three types of systems, namely ramified polymers in solution, ramified polymer blends, or ternary mixtures made of two ramified polymers of different chemical nature immersed in a good solvent. To achieve the goal of the study, use is made of the Random Phase Approximation. First we determine the exact expression of the form factor of an ideal ramified polymer of any topology, from which we extract the exact expression of its gyration radius. Using the classical Zimm's formulae and the exact form factor, we determine all scattering properties of these three types of ramified polymeric systems. The main conclusion is that ramification of the chains induces drastic changes of the scattering properties.

Monte Carlo computer investigations of higher generation ideal dendrimers

“…where λ j andλ k are the non-zero eigenvalues of the Kirchhoff matrix for a dendrimer and linear polymer with N monomers. The exact 9-branch and 21-branch dendrimer S(k)'s have previously been determined [12]: We have applied the general algorithm detailed in the Appendix in combination with the Benhamou et al [15] formalism to obtain results for 45, 93 and 189-branched systems. Their method expresses S(k) as…”

“…We have applied the general algorithm detailed in the Appendix in combination with the Benhamou et al [15] formalism to obtain results for 45, 93 and 189-branched systems. Their method expresses 𝑆(𝑘) as…”

“…Figure 3 shows the variation of a Kratky plot for the MC 93-branch dendrimer 𝑆(𝑘) calculations as the total number of units in all the branches is increased from 931 to 3727. Note that we have used 𝑥 = 𝑘 2 𝑆 2 throughout this paper instead of the usual 𝑥 2 = 𝑘 2 𝑆 2 to conform to the notation employed by Benhamou et al [15]. It is clear that number dependent effects are quite small if one uses a sufficiently large number of units in the simulations.…”

Form Factor of Simple Three and Four Junction Comb Polymers

“…The corresponding form factors for an eight and an 11 branch NEV comb polymer have been computed by following the method of Benhamou . Here, Debye scattering for tree-like networks built from identical NEV linear polymer chains is investigated.…”

“…the length of the unique path between, and including, the chains involved in each contribution. If μ j denotes the number of paths within the tree-like network G involving j identical chains one defines s G ( k ) = prefix∑ j ≥ 2 μ j normale − j x Then the form factor of the network of a total of F such chains may be written as S G ( k ) = 1 F { s D false( k false) + 1 F ( e x − 1 x ) 2 s G false( k false) } …”