Structural transitions and magnetic response of supramolecular magnetic polymerlike structures with bidisperse monomers

Supramolecular magnetic polymerlike (SMP) structures are nanoscaled objects that combine the flexibility of polymeric conformations and controllability of magnetic nanoparticles. The advantage provided by the presence of permanent cross-linkers is that even at high temperature, a condition at which entropy dominates over magnetic interactions, the length and the topology of the SMP structures are preserved. On cooling, however, preexistent bonds constrain thermodynamically equilibrium configurations, making a low-temperature regime for SMP structures worth investigating in detail. Moreover, making SMP structures with perfectly monodisperse monomers has been a challenge. Thus, the second open problem in the application of SMP structures is the missing understanding of the polydispersity impact on their structural and magnetic properties. Here extensive Langevin dynamics simulations combined with parallel tempering method are used to investigate SMP structures of four different types, i.e., chainlike, $\mathsf{Y}$-like, $\mathsf{X}$-like, and ringlike, composed of monomers of two different sizes. Our results show that the presence of small particles in SMP structures can qualitatively change the magnetic response at low temperature, making those structures surprisingly more magnetically responsive than their monodisperse counterparts.

Figure 1

Sketch of all investigated topologies: (a) open chains, (b) $\mathsf{Y}$'s, (c) $\mathsf{X}$'s, and (d) rings.

Figure 2

Springs attached to the surface of the particles for different types of connections. In the case of a $\mathsf{Y}$-like SMP structure (left), the junction has an opening of ${120}^{\circ }$, while for an $\mathsf{X}$-like SMP structure (right) the opening angle is ${90}^{\circ }$; linear segments are cross-linked head to tail.

Figure 3

Magnetic moment as a function of $T$: (a) chainlike SMP structures, (b) $\mathsf{Y}$-like SMP structures, (c) $\mathsf{X}$-like SMP structures, and (d) ringlike SMP structures. The content and the positioning of small monomers are provided in the legend.

Figure 4

Radius of gyration as a function of $T$: (a) chainlike SMP structures, (b) $\mathsf{Y}$-like SMP structures, (c) $\mathsf{X}$-like SMP structures, and (d) ringlike SMP structures. The content and the positioning of small monomers are provided in the legend.

Figure 5

Microstate probability histogram for a monodisperse linear SMP structure at (a) $T=0.20$, (b) $T=0.70$, (c) $T=1.00$, and (d) $T=1.50$. Arrows from the configurations sketched in the middle point to corresponding bins.

Figure 6

Microstate probability histogram for a linear SMP structure with one small particle in the middle at (a) $T=0.20$, (b) $T=0.80$, (c) $T=1.00$, and (d) $T=2.00$. Particles are numbered as shown in the legend. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation. Arrows from the conformations point to corresponding bins along the horizontal axes.

Figure 7

Microstate probability histogram for a linear SMP structure with one small particle at the end at (a) $T=0.20$, (b) $T=0.35$, (c) $T=0.60$, and (d) $T=1.00$. Particles are numbered as shown in the legend. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation. Arrows from the conformations point to corresponding bins along the horizontal axes.

Figure 8

Microstate probability histogram for a linear SMP structure with four small particle at the end at (a) $T=0.20$, (b) $T=0.35$, (c) $T=0.47$, and (d) $T=1.00$. Particles are numbered as shown in the legend. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation. Arrows from the conformations point to corresponding bins along the horizontal axes.

Figure 9

Microstate probability histogram for a linear SMP structure with four small particle in the middle of the chain at (a) $T=0.20$, (b) $T=0.80$, (c) $T=1.20$, and (d) $T=1.60$. Particles are numbered as shown in the legend. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation. Arrows from the conformations point to corresponding bins along the horizontal axes.

Figure 10

Microstate probability histogram for a linear SMP structure with two small particles at the ends at (a) $T=0.20$, (b) $T=0.50$, (c) $T=0.80$, and (d) $T=1.00$. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation. Arrows from the conformations point to corresponding bins along the horizontal axes.

Figure 11

Microstate probability histogram for a linear SMP structure with three small particles, two at the ends and one in the middle, at (a) $T=0.20$, (b) $T=0.50$, (c) $T=0.80$, and (d) $T=1.00$. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation. Arrows from the conformations point to corresponding bins along the horizontal axes.

Figure 12

Microstate probability histogram for a $\mathsf{Y}$-like SMP structure with no small particles at (a) $T=0.20$, (b) $T=0.40$, (c) $T=0.70$, and (d) $T=1.00$. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation. Arrows from the conformations point to corresponding bins along the horizontal axes.

Figure 13

Microstate probability histogram for a $\mathsf{Y}$-like SMP structure with a small particle arm at (a) $T=0.20$, (b) $T=0.60$, (c) $T=1.00$, and (d) $T=1.50$. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation. Arrows from the conformations point to corresponding bins along the horizontal axes.

Figure 14

Microstate probability histogram for an $\mathsf{X}$-like SMP structure with no small particles at (a) $T=0.20$, (b) $T=0.35$, (c) $T=0.60$, and (d) $T=1.00$. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation. Arrows from the conformations point to corresponding bins along the horizontal axes.

Figure 15

Microstate probability histogram for an $\mathsf{X}$-like SMP structure with a small particle arm at (a) $T=0.20$, (b) $T=0.35$, (c) $T=0.60$, and (d) $T=1.00$. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation. Arrows from the conformations point to corresponding bins along the horizontal axes.

Figure 16

Microstate probability histogram for a ringlike SMP structure with a small six-particle segment at (a) $T=0.20$, (b) $T=0.50$, (c) $T=1.00$, and (d) $T=1.50$. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation.

Figure 17

Microstate probability histogram for a ringlike SMP structure with alternating small and large three-particle segments at (a) $T=0.20$, (b) $T=0.50$, (c) $T=1.00$, and (d) $T=2.00$. Each microstate is characterized by the set of nonpermanent bonds provided next to the actual conformation.