Implicit Side-Chain Model and Experimental Characterization of Bottlebrush Block Copolymer Solution Assembly

Abstract

Bottlebrush polymers are a class of macromolecules with linear backbones and densely grafted side chains, possessing unique physical properties due to strong steric interactions between the side chains. These interactions serve to both stiffen the molecular contour and impart a molecular width, leading to material properties distinct from linear counterparts. This is especially important for the case of diblock bottlebrush copolymers, where side-chain-induced stiffness leads to assembly on large length scales while simultaneously suppressing molecular entanglements that would otherwise hinder self-assembly. The resulting microphase-separated structure is thus ideal for photonic crystals, due to the formation of long-range order with features on length scales commensurate with the wavelength of visible light. Despite the usefulness of block copolymer bottlebrush materials, it remains challenging to model their self-assembly in solution due to the additional side-chain degrees of freedom, which are computationally expensive to resolve. In this paper, we develop a simulation model for bottlebrush block copolymer solution selfassembly that adapts a recently developed implicit side-chain model, accounting for the effect of side chains within a simplified, beadrod polymer model. We further extend this model by deriving an intermolecular interaction potential from scaling arguments and show that we can predict bottlebrush self-assembly over a range of block fractions and polymer concentrations. For all architectures studied, we observe an order−disorder transition to lamellar morphologies and regions of significant compositional fluctuations in the disordered phase. We compare computational predictions of self-assembly to experiments, using diblock bottlebrush copolymers synthesized with poly(norbornene) backbones and polystyrene side chains and poly(lactic acid) side chains on each block. We show that the simulation structure factors match well with experimental scattering and indicate the emergence of self-assembly at high concentrations.

Concentration-Driven Self-Assembly of PS-b-PLA Bottlebrush Diblock Copolymers in Solution

“…27 In addition, we used a scaling-based, soft pairwise potential to capture bottlebrush−bottlebrush interactions. 43 We used a relatively slim (noncubic) simulation box to minimize structural defect formation and obtain a better lamellar morphology in cases where it is a preferred thermodynamic state. For further details of the model, we direct readers to refer to our previous paper.…”

“…For further details of the model, we direct readers to refer to our previous paper. 43 In this work, we focused on the systems where the degrees of polymerization of the PS and PLA side chains were 45 and 60 repeat units, respectively. In this case, all interaction parameters were identical to what we used in our prior work.…”

“…In this case, all interaction parameters were identical to what we used in our prior work. 43 To explore a wider spectrum of the backbone length, here, we simplified the model by fixing the ratio of the number of coarse-grained beads between two blocks at 1:1. This would result in a slightly asymmetric block architecture since the coarse-grained beads have a small difference in their sizes, but it is much easier to control the total N bb in this way rather than choosing discretization differently for all backbone lengths.…”

“…To quantify the phases of the equilibrated state of each simulation, we used the quantity and the degree of mixing ⟨f A f B ⟩, as the criteria, which we also introduced in our prior work. 43 We will discuss the details of classifying phases in the Results and Discussion section.…”

“…The χN parameter in classic block copolymer systems serves as a useful analogue since microphase separation is more likely to happen when the two chemically different blocks become longer. In distinguishing the uniformly mixed phase and the disordered, compositionally fluctuating phase, we first applied the same criteria as in our prior work 43 (degree of mixing ⟨f A f B ⟩ equals to ∼0.85). Here, however, we find that some cases that show the characteristic scattering function of compositional fluctuations in experiments are not classified correctly.…”