Extremely asymmetric phase diagram of homopolymer-monotethered nanoparticles: Competition between chain conformational entropy and particle steric interaction

Abstract

The phase behaviors of homopolymer-monotethered nanoparticles (HMNs) in melt are investigated via a theoretical method combining self-consistent field theory for polymers and density functional theory for hard spheres. An extremely asymmetric phase diagram is observed: (i) microphases are only possible for the volume fraction of the tethered polymer f > 0.35; (ii) in addition to lamellar phase, the system can only self-assemble into various morphologies with a polymer-rich matrix, including gyroid phase, cylindrical phase, and spherical phase. In the frame of this theory, the critical point for HMNs' microphase separation is significantly lower than that of linear diblock copolymers. Furthermore, the characteristic length of microphase-separated structures of HMNs is much smaller than that of linear diblock copolymers with the same molecular weight. Our calculation results on morphologies and characteristic length agree well with recent simulations and experimental observations.

Phase Behaviors and Bridging Properties of Bolaform Tethered Nanoparticles

“…Although the geometry of P 1 -H-P 1 is symmetric to the center segment, the phase diagram of P 1 -H-P 1 is extremely asymmetric due to the strong geometric difference between the spherical hard particles and the linear flexible polymer, as the same to H-Ps. 9 With the increase of f A , we found L, G, C, and S phases, which sequence is similar to the phase-separation morphology sequence of AB diblock copolymers. 19 The double-layer L phase (observed in experiments 16,32 ) and the perforated lamellae phase are metastable for symmetric P 1 -H-P 1 in our calculation.…”

“…19 This is interpreted in the same way as that for the extraordinarily low critical point of the ODT for H-Ps. 9 Although the free energy of the disordered state in the SCFT/ DFT method is inaccurate, the acceptable deviation does not change the qualitative properties of the phase diagram. Under the weak-segregation limit, the orientational entropy of nanoparticles is much less than the conformational entropy of the A blocks of the corresponding ABA triblock copolymer.…”

“…In our previous work, 9 we investigated the phase behavior of H-P melt by employing a theoretical method combining the self-consistent field theory (SCFT) for the polymers and the density functional theory (DFT) for the nanoparticles. The SCFT/DFT method, first developed by Thompson et al, 37 gives precise free energy at the mean-field level and has predicted the morphologies and phase diagram of linear diblock copolymer/nanoparticle mixtures 38,39 as well as polymer tethered nanoparticles.…”

“…The SCFT/DFT method, first developed by Thompson et al, 37 gives precise free energy at the mean-field level and has predicted the morphologies and phase diagram of linear diblock copolymer/nanoparticle mixtures 38,39 as well as polymer tethered nanoparticles. 6,9,40 Furthermore, this method has successfully described binary hard-sphere mixtures in copolymer melts. 41,42 Thus, the SCFT/DFT method is an extremely straightforward and powerful approach for studying the equilibrium behavior of particle/polymer systems.…”

Computer simulation study on the self-assembly of tethered nanoparticles with tunable shapes

“…15,16 It is not surprising that many exotic self-assembled structures of TNPs have been reported by using simulations. 1,17,18 Glotzer and coworkers pioneeringly performed a series of Brownian dynamics simulations about self-assembly of TNPs. Specically, TNP with different shapes of head groups such as sphere, cube, rod, and triangle, as well as functionalized with different number or topology of chains, has been investigated.…”