Small‐Angle Scattering From Branched Polymers

Abstract

The single-polymer form factor is determined for branched polymers using a scaling argument in order to recover the low-Q Porod exponent characteristic of the overall structure. The high-Q Porod exponent characterizes the local branching structure. An alternative approach based on a high-Q expansion contains information about functionality, branch length and branch content. The specific case of a starburst dendrimer for which the form factor is known is discussed. The model predictions are compared to small-angle neutron scattering data from a dilute solution of dendrimer in D 2 O.

The microscopic network structure of mussel ( Mytilus ) adhesive plaques

“…Cylindrical network junctions displaying a q 22 decay in the mid-q regime followed by a plateau at low-q [25] are also not observed. Hammouda [26] has shown that the form factor of branched polymers exhibits a broad shoulder and a decay with q Àc , 2 c 1, again incompatible with our experimental curves. Rather, the q 24 scaling suggests the dominance of scattering from interfaces.…”

Simulating Light Scattering Behavior of Branched Molecules

“…A logical property of this comb approximation is that the longest side arm length cannot exceed half the backbone length, as a consequence of identifying the backbone as the longest end‐to‐end distance. Note finally that what we have called “backbone” here, is in fact identical to the “minimum path” as discussed by Hammouda …”

“…Here we will compare P −1 (θ) behavior of realistic ldPE topologies with the typical terminal branching topologies associated with the Zimm and Stockmayer theory. First, we explore the asymptotic behavior of P (θ), since this offers an interesting comparison to a similar exercise by Hammouda . Second, we will present scattering function results for terminally branched molecules, the topology for which Zimm and Stockmayer have derived their famous contraction factor formula.…”

“…Most comprehensive are those describing the spatial arrangement of hyperbranched (AB 2 polycondensation) during chemical growth, using lattice or bond fluctuation models . Another class of models starts at given, simple branching topologies, comprising molecular dynamics (MD) and Monte Carlo (MC) simulations, and analytical approaches . The MD study confirms the scaling law with ε = 0.2, except where “crowding” occurs in dense parts of the molecules.…”

“…Note that like Kosmas et al our model also involves exactly defined topologies, for which we employ graph theory, which the author does not mention. The most recent modeling work directly focusing at predicting scattering behavior has been performed by Hammouda . Benoit's formula was adapted for EV effects using an exponent 1 + ε in the same manner as we do in the present paper (Equation ).…”