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Long Range Bond-Bond Correlations in Dense Polymer Solutions

J. P. Wittmer, H. Meyer, J. Baschnagel, A. Johner, S. Obukhov, L. Mattioni, M. Müller, and A. N. Semenov
Phys. Rev. Lett. 93, 147801 – Published 29 September 2004
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    Abstract

    The scaling of the bond-bond correlation function P1(s) along linear polymer chains is investigated with respect to the curvilinear distance s along the flexible chain and the monomer density ρ via Monte Carlo and molecular dynamics simulations. Surprisingly, the correlations in dense three-dimensional solutions are found to decay with a power law P1(s)∼s−ω with ω=3/2 and the exponential behavior commonly assumed is clearly ruled out for long chains. In semidilute solutions, the density dependent scaling of P1(s)≈g−ω0(s/g)−ω with ω0=2−2ν=0.824 (ν=0.588 being Flory's exponent) is set by the number of monomers g(ρ) in an excluded volume blob. Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains caused by the chain connectivity and the incompressibility of the melt.

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    • Received 11 March 2004

    DOI:https://doi.org/10.1103/PhysRevLett.93.147801

    ©2004 American Physical Society

    Authors & Affiliations

    J. P. Wittmer1,*, H. Meyer1, J. Baschnagel1, A. Johner1, S. Obukhov1,2, L. Mattioni3, M. Müller4, and A. N. Semenov1

    • 1Institut Charles Sadron, 6 Rue Boussingault, 67083 Strasbourg, France
    • 2Department of Physics, University of Florida, Gainesville, Florida 32611, USA
    • 3LPMCN, Université Claude Bernard & CNRS, Lyon, France
    • 4Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 7, D-55099 Mainz, Germany

    • *Electronic address: jwittmer@ics.u-strasbg.fr

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    Vol. 93, Iss. 14 — 1 October 2004

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    • Figure 1
      Figure 1
      Sketch of the bond-bond correlation 〈ln·lm=n+s〉 of the bond vectors li=ri+1−ri, ri being the position vector of monomer i. The bond-bond correlation function is defined as the first Legendre polynomial P1(s)=〈ln·ln+s〉n/l2 over all possible bond pairs with curvilinear distance s=m−n≥0 normalized by the mean squared bond length l2=〈ln2〉. The typical size of the corresponding chain segments is R(s)=〈rnm2〉n1/2 with rnm=rm=n+s−rn. The dashed lines show the four relevant graphs of the analytical perturbation calculation. The numerical factors indicate the relative weights of the leading 1/s3/2 contributions to P1(s).Reuse & Permissions
    • Figure 2
      Figure 2
      The bond-bond correlation function P1(s) for BFM systems of different densities as indicated in the legend. The two lines indicate power laws corresponding to the asymptotic regime for dilute (ω0≈0.824, dashed line) and dense (ω=3/2, bold lines) solutions, respectively. The observation of the second power-law regime is the central result of this work. For systems in the so-called semidilute regime where the excluded volume is sufficiently large both exponents can be seen. The curvilinear distance at the crossover corresponds to the number of monomers per blob g(ρ).Reuse & Permissions
    • Figure 3
      Figure 3
      Crossover scaling for P1(s) for the BFM (N=2048) for different densities. In the main panel, the rescaled bond-bond correlation function f(x)=P1(s)g(ρ)ω0 is plotted versus the natural scaling variable x=s/g(ρ). Note that for large s/N the final cutoff [see Eq. (4)] becomes visible. In the inset we explicitly verify the density dependence of the amplitude ca(ρ) obtained from P1(s) (spheres) and R(s) (squares) using Eqs. (2, 3), respectively. The prediction for the melt regime, Eq. (2), is indicated by the dashed line, the scaling for the semidilute regime by the bold line.Reuse & Permissions
    • Figure 4
      Figure 4
      P1(s) at melt densities for different N for the BFM (ρ=0.5/8) and the bead-spring model (ρ=0.83) for N=256. The bold line indicates Eq. (2) with ca≈0.09 for long BFM chains. The dash-dotted curve P1(s)≈exp(−s/1.5) shows that exponential behavior is compatible with the small N data. The dashed lines correspond to the complete theoretical prediction Eq. (4) for finite chain lengths N=16,32,64, and 256. In the inset we check (bold line) the recursion relation Eq. (5) by plotting K(s) versus U(s)=s/R(s)3ρ (same symbols as in main figure).Reuse & Permissions
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