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Structural and conformational dynamics of supercooled polymer melts: Insights from first-principles theory and simulations

Song-Ho Chong, Martin Aichele, Hendrik Meyer, Matthias Fuchs, and Jörg Baschnagel
Phys. Rev. E 76, 051806 – Published 30 November 2007
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  • INTRODUCTION
  • MODEL
  • SUMMARY OF STATIC PROPERTIES
  • THEORY
  • RESULTS AND DISCUSSION
  • SUMMARY AND CONCLUDING REMARKS
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    Abstract

    We report on quantitative comparisons between simulation results of a bead-spring model and mode-coupling theory calculations for the structural and conformational dynamics of a supercooled, unentangled polymer melt. We find semiquantitative agreement between simulation and theory, except for processes that occur on intermediate length scales between the compressibility plateau and the amorphous halo of the static structure factor. Our results suggest that the onset of slow relaxation in a glass-forming melt can be described in terms of monomer caging supplemented by chain connectivity. Furthermore, a unified atomistic description of glassy arrest and of conformational fluctuations that (asymptotically) follow the Rouse model emerges from our theory.

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    • Received 16 July 2007

    DOI:https://doi.org/10.1103/PhysRevE.76.051806

    ©2007 American Physical Society

    Authors & Affiliations

    Song-Ho Chong1, Martin Aichele2,3, Hendrik Meyer3, Matthias Fuchs4, and Jörg Baschnagel3

    • 1Institute for Molecular Science, Okazaki 444-8585, Japan
    • 2Institut für Physik, Johannes Gutenberg–Universität, 55099 Mainz, Germany
    • 3Institut Charles Sadron, 6 rue Boussingault, 67083 Strasbourg, France
    • 4Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany

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    Issue

    Vol. 76, Iss. 5 — November 2007

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    Images

    • Figure 1
      Figure 1
      (Color online) Collective static structure factor S(q) of the melt as a function of the modulus of the wave vector q for temperatures T=0.47 (solid line), 0.70 (dashed line), and 1 (dotted line). S(q) exhibits a maximum around q∗=6.9 whose position is indicated by an arrow. The inset shows SC(q), the static structure factor of the chain’s center of mass, for T=0.47, 0.70, and 1. There is practically no temperature dependence in SC(q), and the three curves cannot be distinguished from each other. SC(q) exhibits a weak maximum at qC=3.4 whose position is indicated by an arrow.Reuse & Permissions
    • Figure 2
      Figure 2
      (Color online) Comparison of the static structure factor S(q) (circles) with the site-dependent static structure factors S̃a(q) for a=1 (dashed line), 2 (solid line), and 5 (dotted line). The inset compares S(q) (circles) with 1/S̃a−1(q) for a=1 (dashed line), 2 (solid line), and 5 (dotted line). (The dotted lines for a=5 in the main panel and in the inset are not clearly visible since they almost agree with the solid lines for a=2.) S̃a(q) and S̃a−1(q) are defined by the first equality of Eqs. (19, 20), respectively. S(q), S̃a(q), and S̃a−1(q) are taken from the simulation at T=0.47.Reuse & Permissions
    • Figure 3
      Figure 3
      (Color online) (a) Glass form factors fc(q) of the coherent density correlators ϕ(q,t) versus q. The circles represent the result from the simulation at T=0.47, and the solid line that from MCT. The dashed line denotes the extrapolated S(q) (multiplied by 0.1) at TcMCT≈0.277. The arrows indicate the peak positions q∗ and qC of S(q) and SC(q) (see Fig. 1). The inset depicts the extrapolated S(q) at TcMCT (dashed line), and the simulated S(q) at T=0.47 (solid line), 0.48 (dotted line), and 1 (long-dashed line) around the peak q∗. (b) Rescaled α relaxation times τq/τq∗ (main panel) and the stretching exponent βq (inset) of ϕ(q,t) versus q. The circles represent the result from the simulation at T=0.47, and the solid line that from MCT.Reuse & Permissions
    • Figure 4
      Figure 4
      (Color online) (a) ϕ(q,t) as a function of t/τq∗ for q=4.0 (left scale), 6.9 (right scale), and 12.8 (right scale). τq∗ is the α relaxation time at q∗. The circles refer to the simulation results at T=0.47, the solid lines to the MCT α master curves, and the dashed lines to the MCT curves at the distance parameter εMCT=−0.046. (b) ϕ(q,t) as a function of t/τq∗ for q=6.9 and 12.8. The circles and the dashed lines are the same as in (a), but here the dotted lines denoting the MCT curves at the distance parameter εMCT=−0.022 are included as well.Reuse & Permissions
    • Figure 5
      Figure 5
      (Color online) Glass form factors fsc(q) of the correlators ϕs(q,t) (a) and fpc(q) of the correlators ϕp(q,t) (b) as functions of the wave number q. The circles represent the result from the simulation at T=0.47, and the solid line that from MCT. The dash-dotted line in (a) denotes fGsc(q) based on the Gaussian approximation (64) with the value rMc=0.098 taken from the theoretical calculation. The dashed line in (b) shows the simulated w(q) (multiplied by 0.1) at T=0.47.Reuse & Permissions
    • Figure 6
      Figure 6
      (Color online) Single-chain density correlators ϕs(q,t) (a) and ϕp(q,t) (b) as functions of t/τq∗ for q=4.0, 6.9, and 12.8. τq∗ is the α relaxation time of the coherent density correlator ϕ(q,t) at q=q∗. The circles refer to the simulation results at T=0.47, the solid lines to the MCT α master curves, and the dashed lines to the MCT curves at the distance parameter εMCT=−0.046.Reuse & Permissions
    • Figure 7
      Figure 7
      (Color online) (a) Normalized Rouse-mode correlators cp(t)=Cpp(t)/Cpp(0) as a function of t/τq∗ for p=1, 2, 3, 5, and 9 (from right to left). τq∗ is the α relaxation time of the coherent density correlator ϕ(q,t) at q=q∗. The circles refer to the simulation results at T=0.47, and the solid lines to the MCT α master curves. (b) Enlargement of the β region in (a); the results for p=9 are omitted. Here, dashed lines represent the MCT curves at the distance parameter εMCT=−0.046.Reuse & Permissions
    • Figure 8
      Figure 8
      (Color online) The plateau heights fpc (a), the ratio τp/τq∗ of the α relaxation times (b), and the stretching exponent βp (c) of the Rouse-mode correlators cp(t) as a function of the mode index p. The circles represent the result from the simulation at T=0.47, and the solid line that from MCT. The dotted line in each panel refers to pure Rouse behavior predicted by our theory in the asymptotic limit of large N (see Appendix ): fpc=1, τp∝[sin(pπ/2N)]−2, and βp=1.Reuse & Permissions
    • Figure 9
      Figure 9
      (Color online) Double-logarithmic presentation of the MSDs gM(t) (labeled M, left scale) and gC(t) (labeled C, right scale) as a function of Dt. The inset exhibits the ratio g1(t)/g5(t) (end over middle monomer MSD). The circles refer to the simulation results at T=0.47, the solid lines to the MCT α master curves, and the dashed lines to the MCT curves at the distance parameter εMCT=−0.046. The dash-dotted lines indicate the diffusion law 6Dt, while the dotted line shows the power law ∼t0.63.Reuse & Permissions
    • Figure 10
      Figure 10
      (Color online) Double-logarithmic presentation of gM(t) (labeled M) and gC(t) (labeled C) versus Dt at T=1. The upper inset exhibits gMC(t)≡gM(t)−gC(t), whereas the lower inset shows the q dependence of the ratio τq/τq∗ of the α relaxation times of the coherent density correlators ϕ(q,t) at T=1. The circles represent the result from the simulation, and the solid line that from MCT. The dotted line in the main panel and the upper inset denotes the power law ∼t0.63.Reuse & Permissions
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