Dynamics of Block Copolymer Micelles Revealed by X-Ray Intensity Fluctuation Spectroscopy

Abstract

We report x-ray intensity fluctuation spectroscopy measurements of the equilibrium dynamics of polymer micelle liquids, composed of polystyrene-polyisoprene block copolymer micelles within a polystyrene homopolymer matrix. The equilibrium dynamics were investigated for times between one and several hundred seconds, and for wave vectors from 0.003 to 0.015 Å 21 , far beyond wave vectors that can be studied with visible light. A wave-vector-dependent diffusion coefficient is found.[S0031-9007 (97)02392-2] PACS numbers: 61.41. + e, 61.10.YhBlock copolymers show a variety of microstructures as a result of their amphiphilic molecular architectures [1], motivating continuing investigations of their structure, thermodynamics, and rheology. However, it has not generally been possible to study the molecular-scale dynamics of block copolymer melts, because the length scale of the microstructure is several tens of nanometers-determined by the size of the polymers-and is thus inaccessible to light scattering techniques; while the relevant time scales are slower than can be easily studied by neutron scattering [2].The introduction of high-brilliance synchrotron sources now allows for intensity fluctuation spectroscopy measurements using coherent x rays (XIFS), enabling investigations of molecular-scale dynamics [3][4][5][6]. XIFS was recently demonstrated in small-angle scattering studies of the diffusion of dilute gold [5] and palladium [6] colloidal particles, suspended in glycerol. In the present paper, we report an XIFS study of the dynamics of mixtures of polystyrene-polyisoprene block copolymers with polystyrene homopolymer. The mixtures lie in a micellar region of the phase diagram, forming either spherical or wormlike micelles [7][8][9]. There are correlations among the micelles, which give rise to a peak in the static scattering function at ϳ0.012 Å 21 , corresponding to liquidlike micellar order. The glass transition of the homopolymer matrix occurs at ϳ360 K. It follows that the micelles are mobile only above ϳ360 K. We have investigated the dynamics of these polymer micelle liquids for times between one and several hundred seconds, and for wave vectors from 0.003 to 0.015 Å 21 , extending far above what can be achieved with visible light and including the peak in the static structure factor.Copolymer synthesis was performed via anionic polymerization under inert gas, yielding P (S-b-I) with a styrene number fraction of f s 0.5,M w 89.1k, andM w M n 1.02. (M w andM n are the weight-and numberaveraged molecular weights, respectively.) The mixtures were prepared by dissolution in toluene, followed by methanol precipitation. After drying, samples were hot pressed into 1 mm diameter, 0.5 mm thick Al sample holders and vacuum annealed at 150 ± C. For the x-ray studies, the samples were held under vacuum, and at constant temperature to within 60.1 ± C. The XIFS experiments were carried out at beam line ID10A (TROIKA) at the European Synchrotron Radiation Facility (ESRF) and employed undulator radiation with an energy of ...

Statistical Analysis of X-ray Speckle at the NSLS

“…Evidently, (4) provides a fair description of the wavevector dependence of the experimental data. It is worthwhile to compare the current result with earlier discussions (Dierker et al, 1995;Thurn-Albrecht et al, 1996;Mochrie et al, 1997;Abernathy et al, 1998;Mainville et al, 1997), which suggests that the maximum optical path-length difference should be less than the longitudinal coherence length. This notion, in turn, leads to the conditions k2/Ak > dvQ/k and k2/Ak >_ WQ2/lfl.…”

“…Insertion-device-based synchrotron X-ray sources present us with the exciting opportunity to carry out X-ray intensityfluctuation spectroscopy (XIFS) measurements to investigate the dynamics of condensed matter on molecular length scales (Brauer et al, 1995: Dierker, Pindak, Fleming, Robinson & Berman, 1995Thurn-Albrecht et al, 1996;Mochrie et al, 1997). The success of these experiments, and others requiring coherent X-rays, depends crucially on being able to employ X-ray beams of the highest possible brilliance.…”

Imaging by parabolic refractive lenses in the hard X-ray range

“…Laterally coherent secondary source. Coherent X-ray scattering is a new spectroscopy for studying dynamical processes, which extends speckle spectroscopy with laser light from the mm length scale to the nm range (Brauer et al, 1995;Thurn-Albrecht et al, 1996;Mochrie et al, 1997). The spectroscopy needs a laterally coherent X-ray beam.…”

Submillisecond X-ray photon correlation spectroscopy from a pixel array detector with fast dual gating and no readout dead-time

“…The prevalence of high intensity, partially coherent synchrotron X-ray sources worldwide has led to great advances in the development of coherent X-ray scattering techniques, including transmission and Bragg geometry X-ray ptychography (Rodenburg et al, 2007;Hruszkewycz et al, 2012), coherent diffraction imaging (Robinson & Harder, 2009) and X-ray photon correlation spectroscopy (XPCS) (Dierker et al, 1995;Mochrie et al, 1997). XPCS measures fluctuations at the mesoscale via changes in the coherent scattering patterns from samples.…”