Interfaces of glassy materials such as thin films, blends, and composites create strong unidirectional gradients to the local heterogeneous dynamics that can be used to elucidate the length scales and mechanisms associated with the dynamic heterogeneity of glasses. We focus on bilayer films of two different polymers with very different glass transition temperatures ( ) where previous work has demonstrated a long-range (∼200 nm) profile in local is established between immiscible glassy and rubbery polymer domains when the polymer–polymer interface is formed to equilibrium. Here, we demonstrate that an equally long-ranged gradient in local modulus is established when the polymer–polymer interface ( 5 nm) is formed between domains of glassy polystyrene (PS) and rubbery poly(butadiene) (PB), consistent with previous reports of a broad profile in this system. A continuum physics model for the shear wave propagation caused by a quartz crystal microbalance across a PB/PS bilayer film is used to measure the viscoelastic properties of the bilayer during the evolution of the PB/PS interface showing the development of a broad gradient in local modulus spanning 180 nm between the glassy and rubbery domains of PS and PB. We suggest these broad profiles in and arise from a coupling of the spectrum of vibrational modes across the polymer–polymer interface as a result of acoustic impedance matching of sound waves with nm during interface broadening that can then trigger density fluctuations in the neighboring domain.
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Optical spectral weight, phase stiffness, and T c bounds for trivial and topological flat band superconductors
We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D) . We focus on on-site attraction on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight with , where n is the flat-band density and Ω is the Marzari–Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for linear in . We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.
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- Award ID(s):
- 2011876
- PAR ID:
- 10288041
- Publisher / Repository:
- Proceedings of the National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 118
- Issue:
- 34
- ISSN:
- 0027-8424
- Page Range / eLocation ID:
- Article No. e2106744118
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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