Design of polymer nanocomposites in solution by polymer functionalization

Polymer nanocomposites, materials combining polymers and inorganic components such as nanosized crystallites or nanoparticles have attracted significant attention in recent years. A successful strategy for designing polymer nanocomposites is polymer functionalization via attaching functional groups with specific affinity for the inorganic component. In this paper, a systematic investigation by molecular dynamics of polymer functionalization for design of composites combining nanosize crystallites with multiblock polymers in solution is presented. It is shown that functionalization is an example of active self-assembly, where the resulting polymer nanocomposite exhibits a different type of order than the original pure polymer system (without inorganic components). Optimal polymer architectures and concentrations are identified appropriate for different applications, alongside an in-depth analysis on the origin and stability of the resulting phases as well as its experimental implications.

Figure 1

(Color online) Schematic representation of the polymer model highlighting the two energy scales ${\epsilon }_N$ and ${\epsilon }_F$, the respective interaction strengths of the inorganic components among themselves and with the functional end groups. $A$ beads are hydrophilic, $B$ beads are hydrophobic, and the entire system is in an implicit solvent.

Figure 2

(Color online) Phase diagram obtained from the simulation runs of $C{A}_5{B}_7{A}_{5}C$ at ${\varphi }_{\text{P}}=0.20$. A pure polymer system with no inorganic beads forms spherical micelles at this concentration. Symbols indicate points where simulations are carried out and are filled where the inorganic particles form a crystalline phase. For a legend, see Fig. 3.

Figure 3

(Color online) Phase diagrams obtained from the simulation runs of $C{A}_n{B}_m{A}_{n}C$ at ${\varphi }_{\text{P}}=0.25$. Symbols are filled where the inorganic particles form a crystalline phase. The pure polymer systems with no inorganic beads display the classical phases ranging from the hexagonal for the shorter polymers to spherical micelles with cubic symmetry for the longer ones.

Figure 4

(Color online) Plots of the density of polymer and inorganic beads along a given line. In the plot for the hexagonal phase, the line passes through three neighboring cylinders. In the square columnar phase, the line is chosen to pass diagonally from one hydrophobic cylinder through the inorganic component and on to the next nearest neighbor. The line specified for the gyroid phase passes perpendicular to the tube network and through a node. Finally, in the plot of the lamellar phase, the line chosen is perpendicular to the lamellar plates. Additionally, vertical black lines are added to the gyroid plot indicating the location of the density isosurface with a total mean curvature of 0.

Figure 5

(Color online) Snapshot of the hexagonal phase obtained in the $C{A}_5{B}_7{A}_{5}C$ simulation run at ${\varphi }_{\text{P}}=0.20$, ${\epsilon }_{\text{N}}=1.0$, and ${\epsilon }_{\text{F}}=2.0$. $B$ beads are blue (light gray) and $I$ beads are purple (dark gray). $A$ and $C$ beads area not shown to improve clarity. All snapshots in this work are created in VMD [47] and raytraced with Tachyon [48].

Figure 6

(Color online) Snapshot of the square columnar phase obtained in the $C{A}_5{B}_7{A}_{5}C$ simulation run at ${\varphi }_{\text{P}}=0.20$, ${\epsilon }_{\text{N}}=1.0$, and ${\epsilon }_{\text{F}}=4.0$. Coloration is the same as in Fig. 5, except that some whole polymers are highlighted in red (dark gray) to demonstrate the preferred U, L, and stretched orientations. Additionally, red (dark gray) lines are overlaid on top of the phase to visually indicate how the preferred orientations form.

Figure 7

(Color online) Polymer end to end distance distributions obtained from various phases found in the $C{A}_5{B}_7{A}_{5}C$ simulation runs. Data from the run at ${\epsilon }_N=1.0$, ${\epsilon }_F=4.0$, ${\varphi }_P=0.20$ is used for the square columnar line, from ${\epsilon }_N=1.0$, ${\epsilon }_F=2.5$, ${\varphi }_P=0.25$ for the gyroid line, and from ${\epsilon }_N=2.0$, ${\epsilon }_F=4.0$, ${\varphi }_P=0.25$ for the lamellar.

Figure 8

(Color online) Snapshot of the $I{4}_{1}32$ gyroid phase characteristic of those obtained in many simulation runs. Only $B$ beads are shown to improve clarity. The red (dark gray) surface is the mathematical minimal surface obtained from the Weierstrass representation.

Figure 9

(Color online) The yellow (light gray) surface is the isosurface of the hydrophobic density at which the total mean curvature is zero. The red (dark gray) surface is the same mathematical minimal surface in Fig. 8.

Figure 10

(Color online) Snapshot of the gyroid phase obtained in the $C{A}_{11}{B}_{1}4A_{11}C$ simulation run at ${\varphi }_{\text{P}}=0.25$, ${\epsilon }_{\text{N}}=1.0$, and ${\epsilon }_{\text{F}}=2.5$. Only $B$ beads are shown to improve clarity. The red (dark gray) surface is the isosurface of the hydrophobic density at which the total mean curvature is zero.

Figure 11

(Color online) Snapshot of the lamellar phase obtained in the $C{A}_5{B}_7{A}_{5}C$ simulation run at ${\varphi }_{\text{P}}=0.25$, ${\epsilon }_{\text{N}}=2.0$, and ${\epsilon }_{\text{F}}=4.0$. $B$ beads are blue (light gray) and $I$ beads are purple (dark gray). $C$ beads are orange (light gray) and are located neighboring the $I$ beads. $A$ beads area not shown to improve clarity.

Figure 12

(Color online) Snapshot of the disordered micelle phase obtained in the $C{A}_{19}{B}_7{A}_{19}C$ simulation run at ${\varphi }_{\text{P}}=0.25$, ${\epsilon }_{\text{N}}=2.0$, and ${\epsilon }_{\text{F}}=5.0$. Coloration is the same as in 11.