Molecular Dynamics of Janus Nanodimers Dispersed in Lamellar Phases of a Block Copolymer

Abstract

We investigate structural and dynamical properties of Janus nanodimers (NDs) dispersed in lamellar phases of a diblock copolymer. By performing molecular dynamics simulations, we show that an accurate tuning of the interactions between NDs and copolymer blocks can lead to a close control of NDs' space distribution and orientation. In particular, NDs are preferentially found within the lamellae if enthalpy-driven forces offset their entropic counterpart. By contrast, when enthalpy-driven forces are not significant, the distribution of NDs, preferentially observed within the inter-lamellar spacing, is mostly driven by excluded-volume effects. Not only does the degree of affinity between host and guest species drive the NDs' distribution in the polymer matrix, but it also determines their space orientation. In turn, these key structural properties influence the long-time dynamics and the ability of NDs to diffuse through the polymer matrix.

Keywords: coarse-grained; copolymer; diffusion; janus; lamellar; molecular dynamics; nanoparticles; nematic; orientational order; polymer nanocomposites.

Figure 1

Model di-BCP chain with h-block beads in orange and t-block beads in cyan (top); and model nanodimers with neutral (grey), head-like (red) and tail-like (blue) beads (bottom).

Figure 2

Isothermal curves at $T=1ϵ/k_{\mathrm{B}}$ and pressure rates $\delta P/\delta t=1.5·{10}^{-2}ϵ{\sigma }^{-3}{\tau }^{-1}$ (black) and $\delta P/\delta t=3.0·{10}^{-3}ϵ{\sigma }^{-3}{\tau }^{-1}$ (red) obtained by expanding and then compressing between $P_1=1.5ϵ{\sigma }^{-3}$ and $P_2=150ϵ{\sigma }^{-3}$. The continuous vertical line marks our system’s pressure $P=11.3ϵ{\sigma }^{-3}$ and density $\rho =1.0{\sigma }^{-3}$ (magenta). (Left) Pressure vs. density plane. It contains the isotherms (continues lines) and linear regressions of the slow-rate curve at each end (dashed and dotted red lines). Their intersection ($P=8.82ϵ{\sigma }^{-3},\rho =0.95{\sigma }^{-3}$) distinguishes isotropic (light yellow area) from lamellar (yellow-purple mixed-coloured and purple areas) phases. The inset shows the same results in the low-density region. (Right) Box dimensions vs. density plane. It displays evolution of $L_{\mathrm{x}}$ (dashed lines), $L_{\mathrm{y}}$ (dashed-dotted lines) and $L_{\mathrm{z}}$ (continuous lines) at the two pressure rates. An abrupt change in $\delta L_i/\delta \rho$ is observed at $\rho =1.13{\sigma }^{-3}$.

Figure 3

Density profiles of the pristine polymer (a) and the systems with 5 wt% particle mass fraction (b) in the z direction. The density profiles of h-block, t-block, chain beads and chains’ centre of mass are, respectively, indicated by orange, cyan, solid black and dashed black curves. The density profiles of H-like, T-like and neutral ND beads are represented as solid diamonds in red, blue and grey, respectively, and those of the NDs’ centre of mass as violet solid lines.

Figure 4

Frontal view of typical equilibrated configurations of the model PNCs studied in this work. NDs’ monomers are shown as spherical beads. Most polymer chains are depicted as points for clarity. However, some of them are magnified to better appreciate their conformations across the interface. Different colours indicate h-block (orange), t-block (cyan), neutral (grey), head-like (red) and tail-like (blue) monomers. Subfigures a to m are each identified by ND type and ND mass fraction, as detailed in Table 2.

Figure 5

Probability distribution functions of polar (θ) and azimuthal (ϕ) ngles at particle mass fractions 1 wt% (purple lines), 5 wt% (yellow lines) and 10 wt% (green lines).

Figure 6

Polar ($\langle \theta \rangle$, $\langle \left|\theta \right|\rangle$) and azimuthal ($\langle \varphi \rangle$) average angle values of particles (00, H0, HH and HT) at mass fractions $1$wt% (empty purple circles), $5$wt% (yellow diamonds) and $10$wt% (green crosses).

Figure 7

Nematic order parameter at mass fraction values $1$wt% (empty purple circles), $5$wt% (yellow diamonds) and $10$wt% (green crosses).

Figure 8

Mean squared displacement of neutral and Janus NDs at 5 wt% in 3D-space (continuous lines), within the lamellar $xy$ plane (dashed-dotted lines) and along the z direction (dashed lines).

Figure 9

Time autocorrelation functions of the orientation of NDs. The inset provides a zoom at short time scales (notice the log-lin scale). Systems containing 00 (empty circles), HH (solid triangles), H0 (solid diamonds) and HT (empty squares) NDs are shown at particle mass fractions $1$wt% (purple), $5$wt% (yellow) and $10$wt% (green).

Figure 10

Translational diffusivity of NDs in the plane (left) and rotational diffusivity (right) for various particle mass fractions: $1$wt% (purple empty circles), $5$wt% (yellow full diamonds) and $10$wt% (green crosses).