https://doi.org/10.1007/s100510050576
Dynamics of polymeric manifolds in melts: the Hartree approximation
1
Max-Planck-Institut für Polymerforschung,
Postfach 3148, 55021 Mainz, Germany
2
Chemical Physics, Russian Academy of
Science, 142432, Chernogolovka, Moscow
region, Russia
Corresponding author: a rostiash@mpip-main.mpg.de
Received:
22
May
1998
Revised:
31
August
1998
Accepted:
8
September
1998
Published online: 15 December 1998
The Martin-Siggia-Rose functional technique and
the selfconsistent Hartree approximation is applied to the
dynamics of a D-dimensional manifold in a melt of similar manifolds. The generalized Rouse
equation is derived and its static and dynamic properties are studied. The
static upper critical dimension, 
, discriminates between
Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical
counterpart, 
, discriminates between Rouse- and
renormalized-Rouse behavior. The Rouse modes correlation function in a
stretched exponential form and the dynamical
exponents are calculated explicitly. The special case of linear chains D=1
shows agreement with Monte-Carlo simulations.
PACS: 05.20.-y – Statistical mechanics / 83.10.Nn – Polymer dynamics / 02.40.Vh – Global analysis and analysis on manifolds
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998
