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The authors formulate the first first-principles microscopic derivation of the empirical two-branch Baumgärtel-Schausberger-Winter (BSW) relaxation spectrum by modeling chain segments moving relative to a screened, dynamically responding multichain environment. Combining Gaussian-chain preaveraging with longitudinal primitive-path contour-length fluctuations analytically reproduces both scaling branches—$H(\tau)\sim\tau^{-2/3}$ and $H(\tau)\sim\tau^{1/4}$—and matches experimental $G'(\omega)$ and $G''(\omega)$ spectra for polybutadiene melts without fitting exponents or modal weights. This work bridges entangled polymers and nonpolymeric disordered systems under a unified framework of two-sector caged dynamics.
Decades of empirical viscoelastic modeling are resolved from pure microphysics, deriving the two-branch BSW relaxation spectrum and its exact power-law exponents without fitting modal parameters.
Entangled polymer melts exhibit the robust two-branch Baumg\"artel-Schausberger-Winter (BSW) relaxation spectrum, while related spectra occur in nonpolymeric monodisperse disordered systems. In spite of the successful application of BSW to many different materials, a molecular derivation of these spectra is lacking. We construct a molecular theory in which a chain segment moves relative to a screened, dynamically responding multichain environment. Gaussian-chain preaveraging gives $M_{\rm seg}(\Delta m)\sim(\Delta m)^{-1/2}$, hence $\lambda_p\sim p^{3/2}$ and, after stress projection, $H(\tau)\sim\tau^{-2/3}$. Independently, longitudinal primitive-path diffusion gives contour-length fluctuations with $H(\tau)\sim\tau^{1/4}$. A molecular-weight-constrained implementation is tested simultaneously against experimental $G'(\omega)$ and $G''(\omega)$ data for four monodisperse polybutadiene (PBD) melts, without fitting spectral exponents or individual modal weights. The resulting BSW spectrum exhibits a continuous transfer from the fast cooperative to the slow constraint-renewal cascade before a finite-chain terminal edge. A common two-sector caged dynamics then connects polymers to particle rafts without assuming identical microscopic mechanisms.