  The tube-like cages of stiff polymers in entangled solutions have been shown
to exhibit characteristic spatial heterogeneities. We explain these
observations by a systematic theory generalizing previous work by D. Morse
(Phys. Rev. E 63:031502, 2001). With a local version of the binary collision
approximation (BCA), the distribution of confinement strengths is calculated,
and the magnitude and the distribution function of tube radius fluctuations are
predicted. Our main result is a unique scaling function for the tube radius
distribution, in good agreement with experimental and simulation data.
