Intraglobular structures in multiblock copolymer chains from a Monte Carlo simulation

Multiblock copolymer chains in implicit nonselective solvents are studied by using a Monte Carlo method, which employs a parallel tempering algorithm. Chains consisting of $120\hspace{0.5em}A$ and $120\hspace{0.5em}B$ monomers, arranged in three distinct microarchitectures: $(10-10){}_{12},\hspace{0.5em}(6-6){}_{20}$, and $(3-3){}_{40}$, collapse to globular states upon cooling, as expected. By varying both the reduced temperature $T^{*}$ and the compatibility between monomers $\omega$, numerous intraglobular structures are obtained: diclusters (handshake, spiral, torus with a core, etc.), triclusters, and $n$ clusters with $n>3$ (lamellar and other), which are reminiscent of the block copolymer nanophases for spherically confined geometries. Phase diagrams for various chains in the ($T^{*},\omega$) space are mapped. The structure factor $S(k)$, for a selected microarchitecture and $\omega$, is calculated. Since $S(k)$ can be measured in scattering experiments, it can be used to relate simulation results to an experiment. Self-assembly in those systems is interpreted in terms of competition between minimization of the interfacial area separating different types of monomers and minimization of contacts between chain and solvent. Finally, the relevance of this model to the protein folding is addressed.

Figure 1

Results for the $(10-10){}_{12}$ chain (error bars are also shown): (a) reduced energy per monomer $E^{*}/N$ as a function of reduced temperature $T^{*}$, (b) specific heat $C_v$ as a function of $T^{*}$, (c) squared radius of gyration $R_g^2$ as a function of $T^{*}$.

Figure 2

Representative snapshots of the $(10-10){}_{12}$ chain with compatibility $\omega =0.1$ in different temperatures: (a) swollen state at $T^{*}=1.2$, (b) coil-to-globule transition at $T_{\mathit{CG}}^{*}=0.85$, (c) four-cluster structure at $T^{*}=0.75$, (d) tricluster structure at $T^{*}=0.62$, and (e) dicluster structure at $T^{*}=0.5$.

Figure 3

Probability of finding the $n$-cluster structure $p_n$ as a function of reduced temperature $T^{*}$ for the $(10-10){}_{12}$ chain with compatibility $\omega =0.1$. For clarity, only selected $p_n$ lines are shown.

Figure 4

Probability of finding the $n$-cluster structure $p_n$ as a function of reduced temperature $T^{*}$ for the $(10-10){}_{12}$ chain with compatibility: (a) $\omega =0.6$, (b) $\omega =0.7$, (c) $\omega =0.8$, and (d) $\omega =1.0$. For clarity, only selected $p_n$ lines are shown.

Figure 5

Phase diagram for the $(10-10){}_{12}$ chain in $(T^{*},\omega$) space. The dashed line shows coil-globule transition. The solid lines divide regions with the greatest probability of finding $n$-cluster structures. The many-cluster region consists of structures with $n>5$ clusters.

Figure 6

Variety of dicluster structures for the $(10-10){}_{12}$ chain at $T^{*}=0.5$ for compatibility: (a) $\omega =0.5$, (b) $\omega =0.8$, (c) $\omega =0.8$ (without $B$ monomers), (d) $\omega =0.9$, (e) $\omega =0.95$, and (f) $\omega =1$.

Figure 7

Structure factor $S(k)$ for the $(10-10){}_{12}$ chain with $\omega =0.1$ at $T^{*}=1.4$, $0.9$, $0.8$, $0.7$, $0.6$, and 0.5. The scattering profiles are offset vertically by factors of 10, ${10}^2,\hspace{0.5em}{10}^3,\hspace{0.5em}{10}^4$, and ${10}^5$, for clarity.

Figure 8

Phase diagram for the $(6-6){}_{20}$ chain in $(T^{*},\omega$) space. The dashed line shows coil-globule transition. The solid lines divide regions with the greatest probability of finding $n$-cluster structures. The many-cluster region consists of structures with $n>5$ clusters.

Figure 9

Phase diagram for the $(3-3){}_{40}$ chain in $(T^{*},\omega$) space. The dashed line shows coil-globule transition. The solid lines divide regions with the greatest probability of finding $n$-cluster structures. The many-cluster region consists of structures with $n>5$ clusters. In the 5/4/3 region, the probabilities of finding five, four, and triclusters is almost equal.

Figure 10

Variety of structures for the $(6-6){}_{20}$ chain at $T^{*}=0.3$ for compatibility: (a) $\omega =0.1$ (tricluster), (b) $\omega =0.7$ (at $T^{*}=0.5$, dicluster), (c) $\omega =0.7$ (at $T^{*}=0.5$, without $B$ monomers, dicluster), (d) $\omega =0.7$ (tricluster), (e) $\omega =0.9$ (dicluster), (f) $\omega =0.8$ (dicluster), and (g) $\omega =0.8$ (without $B$ monomers, dicluster).

Figure 11

Variety of structures for the $(3-3){}_{40}$ chain at $T^{*}=0.3$ for compatibility: (a) $\omega =0.1$ (five cluster, lamellar), (b) $\omega =0.1$ (without $B$ monomers, five cluster, lamellar), (c) $\omega =0.31$ (four cluster, lamellar), (d) $\omega =0.5$ (at $T^{*}=0.5$, tricluster), (e) $\omega =0.51$ (tricluster), and (f) $\omega =0.51$ (without $B$ monomers, tricluster).