The effects of solvent quality and core wetting on the circularization of star polymers

Abstract

We simulate the formation of cyclical arms in star polymers, focusing on the effects of solvent quality on their resulting linking complexity and gyration radius. We find that polymers circularized in bad solvent present a higher degree of linking among arms with respect to those circularized in good solvent. When both are transported to good solvent, this results in a smaller gyration radius of the former with respect to the latter. This effect is magnified when the polymers present a sufficiently small number of arms (or functionality $f$): in this case, in bad solvent, all arms tend to clump together on one side of the central core, due to circularization, and can hence all interact with each other. Instead, when $f$ is large enough, the whole surface of the core is wetted by the arms, whose distribution becomes radially symmetric. This hinders interactions between faraway arms and reduces the probability of inter-arm linking. Interestingly, we find that both the critical $f_c$ at which the clump transition happens and the minimal arm length $n_c$ for which the transition appears depend on the core size: the grafting density of the arms must be larger than a certain constant $ρ_g^c$, while their length must be sufficient to stretch for, at least, half of the core's circumference.

Figures (8)

• Figure 1: (a-b) Sketch of circularization driven by click chemistry. The core is shown in red, the inert arm beads are blue, while the functionalized ones are yellow. The arms of a linear star (a) attach to each other via their functionalized ends, forming a circularized star (b). We define the angle formed by the grafting points of two attached arms as $\alpha$. (c-e) Sketch of bond exchange via three-body potential. Thanks to this potential, the bonding energy over the whole process (c,d,e) does not change, making a bond among three functionalized beads unlikely and at the same time allowing bond exchange. (f-g) Simulation snapshots of star polymers with core diameter $\sigma_c=6\sigma$ and number of beads per arm $n=40$ in different setups. (f) Star polymer with number of arms $f=32$ in good solvent. (g) Star in bad solvent with $f=64$.
• Figure 2: (a) Gyration radius $R_g$ as a function of $f$. The different symbols represent star polymers in different setups: linear, i.e., not circularized (dark yellow stars), circularized in good solvent (red squares), bad solvent (green circles) and finally circularized in bad solvent and then simulated in good solvent (blue triangles). The insets show simulation snapshots of star polymers in various conditions: good solvent with $f=32$ (upper left), bad solvent with $f=8$ (lower left) and bad solvent with $f=64$ (lower right). The vertical dotted line represents the value of $f$ at which the stars in bad solvent show a discontinuity, $f_c$. The solid black lines indicate the $\propto f^{.206}$ regime of $R_g$ for the stars in good solvent and the $\propto f^{1/3}$ one for those in bad solvent. (b) Ratio $R_g^*$ between the $R_g$ of bad-good stars and good ones as a function of $f$. The dashed line at $R_g^*=1$ marks the good solvent case, serving as a reference. (c) Asphericity as a function of $f$. The solid black line highlights the $\propto f^{-1.5}$ behavior typical of star polymers in good solvent. All quantities are measured for star polymers with $n=40$ and $\sigma_c=6\sigma$.
• Figure 3: Ratio $R_g/R_g^l$, where $R_g^l$ is the gyration radius of the linear star with the same values of $n$ and $f$, as a function of the average separation angle between circularized arms $\overline{\alpha}$ for good (squares) and bad-to-good (triangles) star polymers. The color gradient indicates the average linking number per arm $\overline{|Lk|}$ divided by $f$.
• Figure 4: Simulation snapshots of star polymers with core diameter $\sigma_c=6\sigma$ and number of beads per arm $n=40$ in different setups; the color gradient indicates the relative linking for each arm $|Lk|/f$, while the core is colored in blue. In the first two panels we see star polymers with number of arms $f=32<f_c$ (a) in good and (b) bad-to-good setups. (c) Star with $f=40>f_c$ in bad-to-good conditions. The snapshots highlight that the amount of relative linking is much smaller if circularization happens in good solvent with respect to bad solvent. If circularization happens in bad solvent, the $|Lk|/f$ is heavily influenced by $f$: for $f<f_c$ (b) we observe significantly more relative linking than for $f>f_c$ (c).
• Figure 5: Asphericity $A$ of star polymers in bad solvent with $\sigma_c/\sigma\equiv c=6$ as a function of $f$ for different values of $n$. In (a) we show arms with $n< n_c$, while in (b) we show arms with $n\geq n_c$. The insets show simulation snapshots for the cases $n=10$, $f=16$ (a) and $n=40$, $f=8$ (b).