Soft Nanopolyhedra as a Route to Multivalent Nanoparticles

Computer simulations show that end-grafted immiscible homopolymers can confer multivalence to nanoparticles, resulting in soft nanopolyhedra with structures identical to those found in small clusters of colloidal microspheres. Unprecedented structure tunability is demonstrated by several structure transition sequences, including a reentrant transition, induced by varying composition, polymer lengths, or grafting patterns. These results suggest a new method for fabricating nanoparticles with precisely controlled numbers and locations of functional sites (i.e., multivalent nanoparticles).

Figure 1

A trivalent, $s{p}^2$-like, nanoparticle formed in a poor solvent when only $A$ polymers are grafted, $N_A=30$ and $f_A=8$. (a) A “world map” (abscissa: $\phi /\pi$; ordinate: $\theta /\pi$) of segment density, $r(\mathrm{\text{distance from the center of the particle}})=6$. (b) Segment density plotted on the plane $\phi =0$.

Figure 2

Structures at varying composition but fixed total grafting density, $f_A+f_B=180$. Structure labels such as ${\mathrm{L}}_{BA}$ are defined in text. (a) Free-end distributions of $A$ (left) and $B$ (right), $\phi =0$ (circle: sphere surface). (b)–(h) World maps of total segment density, $r=7$; same grid lines as in Fig. 1. Islands are $B$ rich in (b),(d), and (e) and $A$ rich in (g) and (h). In (e), 2 twofold axes are indicated (green and red symbols). Two transition sequences are obtained by varying $f_A/f_B$: For $N_A=20$ and $N_B=20$, ${\mathrm{L}}_{AB}\to \mathrm{ICO}/B\to \mathrm{R}\to \mathrm{ICO}/A\to {\mathrm{L}}_{AB}$ as $f_A/f_B=150/30\to 120/60\to 90/90\to 60/120\to 30/150$; for $N_A=30$ and $N_B=25$, ${\mathrm{L}}_{BA}\to \mathrm{ICO}/B\to \mathrm{Z}8/B\to \mathrm{R}\to \mathrm{ICO}/A\to {\mathrm{L}}_{AB}$ as $f_A/f_B=150/30\to 140/40\to 120/60\to 90/90\to 60/120\to 30/150$.

Figure 3

Free-end distributions (left: $A$; right: $B$) at various chain-length disparities. $N_A=30$, $f_A/f_B=120/60$.

Figure 4

World maps of total segment density ($r=7$) for $\{N_A,N_B,f_A/f_B\}=$ (a) $\{25,25,80/40\}$, (b) $\{30,25,30/30\}$, (c) $\{25,20,120/60\}$, (d) $\{15,15,60/60\}$, (e) $\{30,30,60/60\}$, (f) $\{30,30,30/30\}$, (g) $\{20,20,120/60\}$, (h) $\{20,20,120/60\}$. In (d)–(h) nonuniform distributions were employed: (d)–(f) and (h), ${\sigma }_A\propto 3+\cos \theta$ and ${\sigma }_B\propto 3-\cos \theta$; (g), ${\sigma }_A\propto 1$ and ${\sigma }_B\propto 3+\cos \theta$. Islands in (b) and in the southern hemispheres in (d) and (f) are $A$ rich, whereas those in (a),(c), and (g), and in the northern hemispheres in (d) and (f) are $B$ rich. In (a) and (c), two symmetric axes are indicated.