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Abstract The structure and dynamics of polystyrene (PS)‐b‐poly(ethylene oxide) block copolymers (BCPs) are studied. The BCPs exhibit microphase‐separated cylindrical and lamellar morphologies. Structural dynamics are measured with X‐ray photon correlation spectroscopy in the small‐angle regime. Morphologies and domain sizes are evaluated using small‐angle X‐ray scattering (SAXS), scanning electron microscopy, and atomic force microscopy. Different solvent processing conditions are investigated. Grain sizes evaluated using SAXS are found to depend on processing only for the rubbery majority BCP. The structural relaxation times are examined as a function of PS volume fraction, temperature, morphology, and structural sizes. Well above the glass transition temperature (Tg) of PS, all samples exhibit stretched autocorrelation decays and diffusive dynamics. NearTgof PS, the dynamics of all samples are anomalous with compressed autocorrelation decays and hyperdiffusive dynamics. This transition occurs at 153 °C or 1.13Tgof PS. In the diffusive regime (at high temperature), structural relaxation times are dependent on the processing method. Near PSTg(at low temperature), structural relaxation times scale with the PS volume fraction. Structural relaxation times do not correlate with grain size, indicating that the out‐of‐equilibrium state of PS dominates the structural dynamics of these strongly phase‐segregated BCPs.
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Fluctuation exponents of the KPZ equation on a large torus
Abstract We study the one‐dimensional KPZ equation on a large torus, started at equilibrium. The main results are optimal variance bounds in the super‐relaxation regime and part of the relaxation regime.
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- PAR ID:
- 10420624
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Communications on Pure and Applied Mathematics
- ISSN:
- 0010-3640
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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