Theory 007/Physics & Matter /Thermal transport
Interfaces Block at One Wavelength Ratio
Smooth interfaces are assumed to conduct better. At the wrong scale, smoothness may reflect phonons back.
Interface thermal resistance is maximal when the roughness scale matches a fixed ratio of the dominant phonon wavelength, so smoothing an interface can increase resistance and roughening can decrease it.
01The evidence
Interface thermal conductance varies non-monotonically with roughness in several material systems, which contradicts the assumption that smoother is better.
02The tension
Models treat roughness as a scatterer that always reduces transmission, which predicts monotonic behaviour and cannot explain the reported improvement with roughness.
03The mechanism
Phonons are waves with a dominant wavelength set by temperature. When roughness matches that wavelength, scattering is diffusive and transmission falls; when roughness is much smaller, the interface behaves as if it were smooth.
That produces a maximum in resistance at a specific roughness-to-wavelength ratio, which shifts with temperature as the dominant wavelength changes.
04What this is not
Scatterer models predict monotonic loss. This predicts a resonance in resistance at a specific ratio.
05Predictions
- P1Resistance should peak at a fixed roughness-to-wavelength ratio.
- P2The peak should move with temperature.
- P3Roughening below the ratio should improve conductance.
06Refutation
Monotonic resistance with roughness would leave the scatterer model adequate.
07What it changes
It would change interface engineering for thermal management.