Anomalous chain diffusion in polymer nanocomposites for varying polymer-filler interaction strengths

Monojoy Goswami and Bobby G. Sumpter

Phys. Rev. E 81, 041801 – Published 6 April 2010

Abstract

Anomalous diffusion of polymer chains in a polymer nanocomposite melt is investigated for different polymer-nanoparticle interaction strengths using stochastic molecular dynamics simulations. For spherical nanoparticles dispersed in a polymer matrix the results indicate that the chain motion exhibits three distinct regions of diffusion, the Rouse-like motion, an intermediate subdiffusive regime followed by a normal Fickian diffusion. The motion of the chain end monomers shows a scaling that can be attributed to the formation of strong “networklike” structures, which have been seen in a variety of polymer nanocomposite systems. Irrespective of the polymer-particle interaction strengths, these three regimes seem to be present with small deviations. Further investigation on dynamic structure factor shows that the deviations simply exist due to the presence of strong enthalpic interactions between the monomers with the nanoparticles, albeit preserving the anomaly in the chain diffusion. The time-temperature superposition principle is also tested for this system and shows a striking resemblance with systems near glass transition and biological systems with molecular crowding. The universality class of the problem can be enormously important in understanding materials with strong affinity to form either a glass, a gel or networklike structures.

Received 6 October 2009

DOI:https://doi.org/10.1103/PhysRevE.81.041801

Authors & Affiliations

Monojoy Goswami^* and Bobby G. Sumpter^†

Computational Chemical Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*goswamim@ornl.gov
^†sumpterbg@ornl.gov

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Vol. 81, Iss. 4 — April 2010

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Figure 1
(Color online) Mean square displacement of the end monomers with respect to the chain center-of-mass (CM) for (a) $ε_{p c} = 0.25$ , (b) $ε_{p c} = 2.5$ . Black solid line is for $T^{*} = 0.1$ , blue dotted line is for $T^{*} = 0.3$ and red dot-dash line is for $T^{*} = 0.5$ . $R_{e}^{2}$ represents end-to-end distance square which is also the plateau value of $g_{1} (t)$ at equilibrium. The power law exponent $α = 0.5$ represents Rouse behavior which continues to a longer time-scale than a random walk chain. (c) For $ε_{p c} = 0.25$ (top dashed line) and 3.0 (bottom dashed line), the derivative (referred as $D$ ) of log of the end monomers MSD, $g_{3} (t^{*})$ is plotted at a fairly high temperature, $T^{*} = 0.45$ . Cross-over time is used to estimate entanglement length by assuming it to be the Rouse relaxation time of a subchain of length $N_{e}$ . $g_{3} (t^{*})$ is discussed in detail in Fig. 3.Reuse & Permissions
Figure 2
(Color online) Mean square displacement of chain center of mass for (a) low $ε_{p c} = 0.25$ and (b) high $ε_{p c} = 3.0$ . Red solid line (bottom line) represents $T^{*} = 0.1$ and magenta solid line (top line) represents $T^{*} = 0.5$ . The black dotted lines are power law fits to $t^{α}$ in a log-log scale for shorter times, where $α$ varies between 0.79–0.81 in this time range. The blue dotted lines (far end of the lines) are long time fits to the power law where the exponent $α = 1.0$ indicating a crossover to simple Fickian diffusion. (c) and (d), slopes for larger particles, $2 σ$ , are shown for $ε_{p c} = 0.25$ and 3.0. Note the difference in slopes for the anomalous region.Reuse & Permissions
Figure 3
(Color online) Comparison of the mean square displacements of the end monomers, $g_{3} (t)$ , at different temperature and $ε_{p c}$ . (a) $g_{3} (t)$ is plotted for different $ε_{p c}$ at $T^{*} = 0.45$ . Black, red, blue, magenta and green solid lines (from left to right) represent $ε_{p c} = 0.25$ , 0.5, 1.0, 1.5, 2.0 and 3.0 respectively. (b) Different lines represent different temperatures, red solid line: $T^{*} = 0.1$ , blue dotted line: $T^{*} = 0.2$ , magenta dot-dash line: $T^{*} = 0.3$ , green dotted line: $T^{*} = 0.4$ and black solid line: $T^{*} = 0.5$ (right to left in grayscale). In both the plots, the three short black solid lines are to guide the eye to their respective slopes.Reuse & Permissions
Figure 4
(Color online) (a) End-to-end distance square, $⟨ R_{e}^{2} ⟩$ and (b) ratio of the radius of gyration of the chain $⟨ R_{g} ⟩$ and radius of gyration of random walk chain, $⟨ R_{g 0} ⟩$ as a function of temperature for different polymer-NP interaction strengths. Black circles $ε_{p c} = 0.25$ , red square, $ε_{p c} = 0.5$ , green diamond, $ε_{p c} = 1.0$ , magenta left-triangle $ε_{p c} = 1.5$ , light blue down-triangle $ε_{p c} = 2.0$ , yellow up-triangle $ε_{p c} = 2.5$ , and blue right-triangle $ε_{p c} = 3.0$ . The red solid line in (a) shows the ideal chain $⟨ R_{e}^{2} ⟩$ of chain length 64. In the presence of NPs, around 40% swelling is observed compared to the ideal chain of length $N = 64$ and $b = 1.12 σ$ . The black dashed line in (b) shows an average $⟨ R_{g} ⟩ / ⟨ R_{g 0} ⟩ = 1.17$ which is in reasonable agreement with the experimental results by Tuteja et al. [29].Reuse & Permissions
Figure 5
(Color online) Structural relaxation time as a function of time. For all the plots, all solid lines signify $T^{*} = 0.1$ and dashed lines signify $T^{*} = 0.45$ . The blue, red and green colors (left to right) represent $ε_{p c} = 0.25$ , $ε_{p c} = 1.5$ and $ε_{p c} = 3.0$ respectively. (a) $S (q, t^{*})$ for $q σ = 1.5$ for the two temperatures and for low, intermediate and high polymer-NP interaction strengths. (b) Master curves using time-temperature superposition principle, $Φ (q, t^{*})$ plotted as a function of $log (t^{*} / τ)$ at small wavelength, $q σ = 1.5$ . All the curves fit quite well with a ‘single’ stretched exponential of the form, $exp (- {(t^{*} / τ)}^{0.8})$ . Inset plot is for long wavelength, $q σ = 0.3$ .Reuse & Permissions

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