Topological Effects Near Order–Disorder Transitions in Symmetric Diblock Copolymer Melts

Abstract

The effects of polymer chain topology on the order–disorder transition of symmetric AB diblock copolymer melts are studied using coarse-grained molecular dynamics simulations. Specifically, we compared chain conformations near the lamellar-disordered transition in melts of symmetric (i.e., 50–50) AB diblock copolymers of linear chains, rings, and trefoil knots at the same chain lengths. The order (lamellar)–disorder transition temperature and the domain sizes both shifted to lower values with the introduction of topological constraints, leading to the following sequence: linear chains > rings > trefoil knots. Investigation of the polymer chain conformations in terms of their radii of gyration, their writhe values (a measure for the degree of intertwining of a chain around itself), and their Jones polynomials (a method to measure entanglement of curves) showed that linear chains and rings remained stretched, while knots were stretched and tightened in disordered melts close to the lamellar-disorder transition. This work highlights chain topology as an important factor in affecting microphase separation in block copolymers.

Computational Study of Mechanochemical Activation in Nanostructured Triblock Copolymers

“…Block copolymers (BCPs) offer an attractive option for simultaneously controlling the network-like topology, and thus transmission of bulk forces to the molecular scale, and the overall mechanical properties of the material. − ABA triblock copolymers with long enough chain lengths ( N ) and large enough interaction parameters (χ) microphase segregate into ordered morphologies ranging from spherical to cylindrical to lamellar, depending on the volume fractions of each block type. , By choosing glassy A blocks and rubbery B blocks, the self-assembled A domains can serve as physical links that enable the B chains to behave like they are in a network. ,, Importantly, the self-assembled structures not only have different overall symmetries but also different chain conformations . Although the influence of chain conformations (i.e., tie and loop chains) in the purely mechanical behavior of triblocks − and cross-linked networks , have been studied previously, it is not clear how those conformations influence the efficiency of mechanochemical activation in the material. Changing the morphology of the self-assembled structures is expected to drive substantial changes in the activation profile.…”

“…Taking a simulation-based approach enables investigation not only of the average response of the entire sample but also of how the conformations and spatial positions of individual chains drive differences in their activation across different self-assembled morphologies. While a number of groups have modeled either the deformation of homopolymers, , purely rubbery, − or rubbery-glassy , triblock systems, they have not investigated the interplay of nanostructured morphology and mechanophore activation. Our work thus contributes to this gap in understanding force-driven activation in these materials.…”

Control of Diblock Copolyelectrolyte Morphology through Electric Field Application

“…Note that in the studies of BCPs and block copolyelectrolytes, the parameters χN are an important factor to measure the immiscibility of different blocks and dictate their phase behavior, where χ is the Flory–Huggins segment interaction parameter and N is the degree of polymerization. ,,− In our MD simulations, the effective Flory–Huggins interaction parameter for the uncharged diblock copolymers A X B Y (as the electrostatic interactions are excluded) can be estimated as χ ∼ 0.43 from the second virial coefficients, of which the details are shown in the Supporting Information. In the current work, we only consider the intermediate immiscibility between the hydrophobic blocks and the polyelectrolytes through the settings of ϵ LJ and r c in eq .…”

The Jones polynomial of collections of open curves in 3-space

“…This new framework also allowed to define Vassiliev measures of open curves in 3-space and to derive closed formulae for the second Vassiliev measure of single open curves in 3-space [17]. These advances led to immediate applications in materials and biology to obtain novel understanding of such physical systems, rigorously and without any closure scheme for the first time [18][19][20]. However, extending the Jones polynomial to collections of open curves in 3-space has not been possible, even though one would think it would be straightforward, as the definition of the classical Jones polynomial applies to both knots and links.…”