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

more »

... ) 02392-2] PACS numbers: 61.41. + e, 61.10.Yh Block 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 8.2 keV and a bandwidth of Dl͞l 0.013 [10] . A mirror deflected these x rays out of the undulator central cone onto the sample. The source, 46 m upstream, was 54 mm in the vertical direction. Horizontal slits, 28 m upstream, were adjusted to 250 mm to set the effective horizontal source size. For XIFS studies several criteria must be met: The beam size should be smaller than the transverse coherence length ͑ld͞2R͒, where l is the x-ray wavelength, d is the source size, and R is the distance to the source. A pinhole aperture of diameter d p 7 mm (85 mm upstream of the sample) met this condition, yielding ϳ2 3 10 9 x rays per second. In addition, the maximum optical path length difference should be less than the longitudinal coherence length ͑l 2 ͞Dl͒, requiring that Dl͞l , l͞2W sin 2 u and Dl͞l , l͞d p sin 2u, where W is the sample thickness and 2u is the scattering angle. These conditions were satisfied for wave vectors up to ϳ0.03 Å 21 . Scattered x rays were collected using a Princeton Instruments CCD array detector, 1.25 m from the sample. The CCD pixel size was 22 3 22 mm 2 . Each data set was acquired as a series of 1000 1.00 s exposures, separated by 0.24 s for readout. Measurements to determine the static scattering cross section were carried out at beam line X20A at the National Synchrotron Light Source using a point detector. On initial exposure to the beam at ID10A, the overall scattered intensity was observed to decrease by a factor of ϳ2 over a period of ϳ200 s. Subsequently, the intensity remained constant in time. We do not understand this 0031-9007͞ 97͞78(7)͞1275(4)$10.00