Perimeter length and form factor in two-dimensional polymer melts

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 5, 2009, Pages

  Meyer, H ^a   Kreer, T ^a   Aichele, M ^a   Cavallo, A ^a   Johner, A ^a   Baschnagel, J ^a   Wittmer, J P ^a  

^a INSTITUT CHARLES SADRON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FORM FACTORS; FRACTALITY; INTERMEDIATE REGIMES; IRREGULAR SHAPE; MOLECULAR DYNAMICS SIMULATIONS; SELF-AVOIDING POLYMERS; SELF-SIMILAR; SUBCHAINS; TWO-DIMENSIONAL POLYMERS; WAVE VECTOR;

APPROXIMATION THEORY; FRACTAL DIMENSION; TWO DIMENSIONAL;

POLYMER MELTS;

EID: 67549134406     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.050802     Document Type: Article

References (23)

1. P. G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, New York, 1979).
2. B. Duplantier, J. Stat. Phys. 54, 581 (1989). 10.1007/BF01019770
3. A. Semenov and A. Johner, Eur. Phys. J. E 12, 469 (2003). 10.1140/epje/e2004-00019-2
4. I. Carmesin and K. Kremer, J. Phys. (France) 51, 915 (1990). 10.1051/jphys:019900051010091500
5. A. Cavallo, M. Müller, and K. Binder, J. Phys. Chem. B 109, 6544 (2005). 10.1021/jp0458506
6. A. Yethiraj, Macromolecules 36, 5854 (2003). 10.1021/ma025907r
7. J. Higgins and H. Benoît, Polymers and Neutron Scattering (Oxford University Press, Oxford, 1996).
8. B. Maier and J. O. Radler, Phys. Rev. Lett. 82, 1911 (1999). 10.1103/PhysRevLett.82.1911
9. G. S. Grest and K. Kremer, Phys. Rev. A 33, 3628 (1986). 10.1103/PhysRevA.33.3628
10. K. Kremer and G. Grest, J. Chem. Phys. 92, 5057 (1990). 10.1063/1.458541
11. S. J. Plimpton, J. Comput. Phys. 117, 1 (1995). 10.1006/jcph.1995.1039
12. The presented data was obtained on IBM power 6 with the LAMMPS version 21 May 2008 and is part of a larger study where we have systematically varied density, system size, and friction coefficient of the Langevin thermostat to confirm the robustness of theory and simulation with respect to these parameters. Taken apart the longest chains with N=2048 all chains have diffused over at least 10 times their radius of gyration providing thus high-precision statistics.
13. J. P. Wittmer, H. Meyer, J. Baschnagel, A. Johner, S. P. Obukhov, L. Mattioni, M. Müller, and A. N. Semenov, Phys. Rev. Lett. 93, 147801 (2004). 10.1103/PhysRevLett.93.147801
14. J. P. Wittmer, P. Beckrich, H. Meyer, A. Cavallo, A. Johner, and J. Baschnagel, Phys. Rev. E 76, 011803 (2007). 10.1103/PhysRevE.76.011803
15. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986).
16. The log-log representation chosen in Fig. 1 masks deliberately corrections to the leading power law ν=1/2 due to finite segment and chain lengths which exist in two dimensions as they do in three dimensions. These are revealed, e.g., by a logarithmic-linear plot of R2 (s) /s vs s showing a nonmonotonous behavior with a sharp decay for s→N where the Θ0 exponent becomes relevant. It is ultimately due to this decay that the ratio R2 (N) / Rg2 (N) approaches a value 5.3 rather than 6.
17. We have checked that the scaling of L (s) does not depend on the distance used for defining a perimeter monomer.
18. J. des Cloizeaux and G. Jannink, Polymers in Solution: Their Modeling and Structure (Clarendon Press, Oxford, 1990).
19. R. Everaers, I. Graham, and M. Zuckermann, J. Phys. A 28, 1271 (1995). 10.1088/0305-4470/28/5/015
20. Since we use only the Θ2 exponent and in addition to this the Redner-des Cloizeaux formula there are two levels of approximation. Our final result is rephrased consistently in terms of x=q Rg (N) and, thus, by construction our formula yields correctly both the Guiner regime for x 1 and the generalized Porod limit for x 1, but not necessarily the hump region at x 2. In practice, our approximation is fine for all x as shown by Fig. 4.
21. P. Z. Wong and A. J. Bray, Phys. Rev. Lett. 60, 1344 (1988). 10.1103/PhysRevLett.60.1344
22. H. D. Bale and P. W. Schmidt, Phys. Rev. Lett. 53, 596 (1984). 10.1103/PhysRevLett.53.596
23. An alternative derivation of Eq. 1 is obtained from a scaling argument using the return probability 1/ s1+ν Θ2 measured in Fig. 3. The key point is that a monomer in a long segment cannot "distinguish" if the contact is realized through the backfolding of its own segment or by another segment. Since the probability of such a binary contact, L (s) /s, must be proportional to the return probability times the number s of monomers in the second segment this yields Eq. 1.