Anomalous Fluctuations of Nematic Order in Solutions of Semiflexible Polymers

Sergei A. Egorov, Andrey Milchev, and Kurt Binder

Phys. Rev. Lett. 116, 187801 – Published 5 May 2016

Abstract

The nematic ordering in semiflexible polymers with contour length $L$ exceeding their persistence length $ℓ_{p}$ is described by a confinement of the polymers in a cylinder of radius $r_{eff}$ much larger than the radius $r_{ρ}$ expected from the respective concentration of the solution. Large-scale molecular dynamics simulations combined with density functional theory are used to locate the isotropic-nematic ( $I − N$ ) transition and to validate this cylindrical confinement. Anomalous fluctuations due to chain deflections from neighboring chains in the nematic phase are proposed. Considering deflections as collective excitations in the nematically ordered phase of semiflexible polymers elucidates the origins of shortcomings in the description of the $I − N$ transition by existing theories.

Received 11 January 2016

DOI:https://doi.org/10.1103/PhysRevLett.116.187801

Physics Subject Headings (PhySH)

Nematic order

Polymers

Molecular dynamics

Polymers & Soft Matter

Authors & Affiliations

Sergei A. Egorov^1,3,*, Andrey Milchev², and Kurt Binder³

¹Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901, USA
²Institute for Physical Chemistry, Bulgarian Academia of Sciences, 1113 Sofia, Bulgaria
³Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany

^*sae6z@cms.mail.virginia.edu

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Vol. 116, Iss. 18 — 6 May 2016

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Images

Figure 1
(a) Snapshot of a system of semiflexible polymers with length $N = 32$ , stiffness $ε_{b} = 100$ , at concentration $ρ = 0.6$ (deep in the nematic phase). (b) Typical conformation of a semiflexible polymer in the nematic phase ( $N = 64$ , $ε_{b} = 16$ , $ρ = 0.4$ ). (c) Schematic description of nematic order: each chain has its own cylindrical (bent) tube of diameter $2 r_{ρ}$ defined such that it contains only monomers from the considered chain. The tube is placed inside a straight wider cylinder of diameter $2 r_{eff}$ (see text). The definition of the deflection length $λ$ is indicated.
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Figure 2
(a) Pressure vs concentration for the case $N = 32$ , $ε_{b} = 32$ according to MD (full dots) and two versions of density functional theory, the first based on the Carnahan-Starling (CS) equation of state (solid lines) [34] and the second, using the generalized Flory Dimer (GFD) [39] equation of state (broken lines) [28]. The $I − N$ transition in the simulation is rounded by finite-size effects. DFT predictions for $I − N$ coexistence are indicated by squares (DFT CS) and crosses (DFT GFD). (b) Scaled volume fraction $ρ π ℓ_{p} / (4 d)$ at the transition plotted versus $L / ℓ_{p}$ according to MD, theory [12], and typical experiments [53, 54]. The shaded stripe indicates the $I − N$ coexistence region $ρ_{i} < ρ < ρ_{n}$ , as predicted by Chen [12]. MD does not resolve $ρ_{i}$ , $ρ_{n}$ , rather $ρ_{tr}$ is the position of the maximum slope of the $S$ vs $ρ$ curve (see Fig. 3). For the experiments, namely, poly(hexyl isocyanate) (PHIC) in toluene [54] and poly(yne)-platinum (PYP) in trichloroethylene [53] $ρ_{av} = (ρ_{i} + ρ_{n}) / 2$ was taken as the transition density. The numbers in the brackets in the legend indicate $d / ℓ_{p}$ .
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Figure 3
Nematic order parameter $S$ from MD (filled circles) vs concentration $ρ$ for $N = 32$ and various choices of $ε_{b}$ , as indicated. Full curves denote corresponding predictions of DFT CS [28]. $I − N$ coexistence is indicated by diamonds and broken straight lines (lever rule). Corresponding predictions from Chen [12] are shown by squares and dotted lines.
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Figure 4
(a) Local order parameter $S_{i}$ (referring to bond vector ${\vec{a}}_{i}$ ) plotted vs $i / N$ and averaged over all equivalent bonds in the system for the case $N = 64$ and several choices of $N / ε_{b}$ , as indicated. The left inset shows a semilog plot of $S_{\infty} - S_{i}$ vs $i$ so as to demonstrate Eq. (1). From the slope, the deflection length $λ$ is extracted as $λ / ℓ_{p} = 2.36$ , 3.65, and 8.2 for $ε_{b} = 8$ , 16, and 32, respectively. (b) Variation of the confinement radius $r_{eff}$ with concentration $ρ$ for semiflexible chains with $N = 128$ and two choices of stiffness $ε_{b} = 64$ and 128 computed from Eq. (2) and from the maximum of $⟨ (r_{i, ⊥} - r_{j, ⊥})^{2} ⟩$ . The inset shows the mean-squared displacement of consecutive beads $⟨ (r_{i, ⊥} - r_{j, ⊥})^{2} ⟩$ perpendicular to the respective end-to-end vector ${\vec{R}}_{e}$ averaged over all chains in the nematic phase for $ε_{b} = 128$ and two densities.
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Figure 5
Plot of $1 - S$ vs the relative reduction $1 - ⟨ R_{e}^{2} ⟩^{1 / 2} / L$ of the end-to-end distance for three choices of $N = 32$ , 64, and 128, and three choices of the $N / ε_{b} = 1$ , 2, and 4, as indicated. Different points with the same symbol refer to different choices of the density $ρ$ . The fully stretched chain would be the origin of the plot, whereas the straight line shows Eq. (2). Rigid rods correspond to the ordinate axis here.
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