A Small-Angle Neutron and X-ray Contrast Variation Scattering Study of the Structure of Block Copolymer Micelles:  Corona Shape and Excluded Volume Interactions

Abstract

Small-angle neutron and X-ray scattering data have been obtained for micelles of d-polystyrene−polyisoprene (d-PS−PI) of relatively high molecular weight in n-decane. Contrast variation was performed using mixtures of hydrogenated and deuterated decane. Three samples were investigated with d-polystyrene and polyisoprene molar masses of, respectively, 12 000 and 48 000, 40 000 and 40 000, and 40 000 and 80 000. For the two latter samples, the concentration of the polymer was also varied. The data obtained at relatively high resolution were analyzed together with small-angle X-ray scattering data using scattering functions recently derived from Monte Carlo simulations for a model with a spherical core and a corona of semiflexible chains interacting with a hard-core potential. The scattering from the model can be generated by assuming an analytical form of the radial distribution of the corona and an effective single chain form factor of the random-phase approximation type. In the analysis of the experimental scattering data intermicellar interactions were modeled by an effective hard-sphere model. The analysis of the experimental data provides information on shape, aggregation number, polydispersity, core size, core solvation, corona shape/size, and the interactions between the chains in the corona, which are significant for these micelles. The shape of the corona profile depends on the surface coverage of the micelles as well as the curvature of the core−corona interface. For high curvatures the profile is in agreement with a power-law behavior as predicted by scaling theory. For low curvatures the profile is more compact. The profiles and scattering curves are very well reproduced by Monte Carlo simulations based on the parameters for the structures determined in the analysis of the experimental scattering data. The study shows that two parameters are decisive for the profile shape and internal correlations, namely the reduced surface coverage and the curvature.

Surface and Interface Analyses of Polymer Brushes by Synchrotron Radiation

“…3. We estimated the radius of gyration of the polymer layer, s, of SiNP-PMAPS and SiNP-PMPC from the SAXS profile using a core-shell model analysis, taking the interacting excluded-volume chains into consideration 23) and assuming the corona chains as infinitely thin perturbed wormlike chains. 24) Figure 4 shows the C s -dependence of s and R H,brush for SiNP-PMAPS ( ) and SiNP-PMPC ( ) in aqueous NaCl solutions, where R H,brush were obtained by DLS measurements.…”

Modeling of Intermediate Structures and Chain Conformation in Silica–Latex Nanocomposites Observed by SANS During Annealing

“…In this section, it will be shown that the phenomenological evolution of the SANS data can be quantitatively reproduced with an additive model of free chains (RPA) and of an adaptation of the Pedersen model for hairy micelles 60,61 . The form factor of the latter is mimicked by a sphere with Gaussian chains on the surface.…”

Structural Observation and Kinetic Pathway in the Formation of Polymeric Micelles

“…This model describes the detailed structural features of the starlike micelles considering both the internal PEP core and the outer PEO shell. In order to account for some slight structure factor effects at the highest concentration, we employed Percus-Yevick structure factor which is shown to give good results for dilute block copolymer micelles [24]. Some fit results are shown in Fig.…”