We have used the Marti-Siggia-Rose functional technique as well as the self-consistent Hartree approximation to investigate the dynamics of a chain in the melt of similar chains. The integration over the collective variables of the melt can be implemented in the framework of the dynamical random phase approximation. The resulting effective action functional of the test chain is treated by making use of the self-consistent Hartree approximation. As an outcome the generalized non-Markovian Rouse-Langevin equation of the test chain is derived and its static and dynamic properties are studied. It was found that the static upper critical dimension, d = 2, discriminates between Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical counterpart, d = 4, distinguishes between the simple Rouse and renormalized Rouse behavior. We have found that the Rouse mode correlation function has a stretched exponential form. The subdiffusional exponents for this regime are calculated explicitly. The theoretical results are in good agreement with Monte-Carlo simulation.
Relevant publications:
- V.G. Rostiashvili, M. Rehkopf and T.A. Vilgis: "The Hartree approximation in dynamics of polymeric manifolds in the melt", J. Chem. Phys. 110 (1999) 639-651. here
- V.G. Rostiashvili, M. Rehkopf and T.A. Vilgis: "Langevin dynamics of the glass forming polymer melt: Fluctuation around the random phase approximation", Eur. Phys.J. B6 (1998) 233-243. here
- V.G. Rostiashvili, M. Rehkopf and T.A. Vilgis: "Dynamics of polymeric manifolds in melts: the Hartree approximation", Eur. Phys.J. B6 (1998) 497-501. here
- V.G. Rostiashvili, M. Rehkopf and T.A. Vilgis: "Langevin dynamics of polymeric manifolds in melts", J. Phys.: Condens. matter 11(1999) A307 - A315. here
- M. Rehkopf, V.G. Rostiashvili and T.A. Vilgis: "Dynamics of a polymer test chain in a glass forming matrix", J.Phys. II (France) 7 (1997) 1469-1487. here
- V.G. Rostiashvili, N-K. Lee and T.A. Vilgis: "Collapse or swelling dynamics of homopolymer rings: Self - consistent Hartree approach", J. Chem. Phys. 118, (2003), 937. here