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Perimeter Length and Form Factor of Two-Dimensional Polymer Melts · Around

2009

Perimeter Length and Form Factor of Two-Dimensional Polymer Melts

Meyer, H., Kreer, T., Aichele, M. et al.

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Self-avoiding polymers in two-dimensional ($d=2$) melts are known to adopt compact configurations of typical size $R(N) \sim N^{1/d}$ with $N$ being the chain length.

Using molecular dynamics simulations we show that the irregular shapes of these chains are characterized by a perimeter length $L(N) \sim R(N)^{\dpm}$ of fractal dimension $\dpm = d-\Theta_2 =5/4$ with $\Theta_2=3/4$ being a well-known contact exponent.
Due to the self-similar structure of the chains, compactness and perimeter fractality repeat for subchains of all arc-lengths $s$ down to a few monomers.
The Kratky representation of the intramolecular form factor $F(q)$ reveals a strong non-monotonous behavior with $q^2F(q) \sim 1/(qN^{1/d})^{\Theta_2}$ in the intermediate regime of the wavevector $q$.

Built on

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Similar

K. Kremer and G. Grest, J. Chem. Phys. 92
1990
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J. des Cloizeaux and G. Jannink, Polymers in Solution : their Modelling and Structure (Clarendon Press, 1990)
1990
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S. J. Plimpton, J. Comp. Phys. 117
1995
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R. Everaers, I. Graham, and M. Zuckermann, J. Phys. A: Math. Gen. 28
1995
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J. Higgins and H. Benoît, Polymers and Neutron Scattering (Oxford University Press, Oxford, 1996)
1996
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B. Maier and J. Rädler, Phys. Rev. Lett. 82
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Cited alongside, same era.

Then

A. Yethiraj, Macromolecules 36
2003
Later among the works it cites.
J. P. Wittmer, H. Meyer, J. Baschnagel, A. Johner, S. P. Obukhov, L. Mattioni, M. Müller, and A. N. Semenov, Phys. Rev. Lett. 93
2004
Later among the works it cites.
A. Cavallo, M. Müller, and K. Binder, J. Phys. Chem. B 109
2005
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J. P. Wittmer, P. Beckrich, H. Meyer, A. Cavallo, A. Johner, and J. Baschnagel, Phys. Rev. E 76
2007
Later among the works it cites.
The log-log representation choosen in Fig. 1
2007
Later among the works it cites.

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A. Semenov and A. Johner, Eur. Phys. J. E 12

2003

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We have checked that the scaling of L ⁡ ( s ) L(s) does not depend on the distance used for defining a perimeter monomer

Cited in the paper.

Since we use only the Θ 2 \Theta_{2} -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 R g ( N ) x=qR_{\mathrm{g}}(N) and, thus, by construction our formula yields correctly both the Guiner regime for x ≪ 1 x\ll 1 and the generalized Porod limit for x ≫ 1 x\gg 1 , but not necessarily the hump region at x ≈ 2 x\approx 2 . In practice, our approximation is fine for all x x as shown by Fig. 4

Cited in the paper.

An alternative derivation of Eq. ( 1

Cited in the paper.

The presented data was obtained on IBM power 6 with the LAMMPS Version 21May2008 Plimpton 1995 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 N=2048 all chains have diffused over at least 10 times their radius of gyration providing thus high precision statistics

2048

Closest in time.