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Langevin dynamics simulations of double-knotted DNA molecules in a nanochannel reveal that the interactions between the two knots differ with the degree of channel confinement. In relatively wide channels, the two knots can intertwine with each other, forming a persistently intertwined knot. Moreover, the two knots can pass through each other in large channels. In contrast, for small channel sizes, the knots tend to remain separated, and their crossing is inhibited. The change in knot–knot interactions as the channel size decreases is rationalized through an analysis of the magnitude of the transverse fluctuations, which must be large enough to allow one knot to swell to accommodate the intertwined state. 

Block polymers are an attractive platform for uncovering the factors that give rise to self-assembly in soft matter owing to their relatively simple thermodynamic description, as captured in self-consistent field theory (SCFT). SCFT historically has found great success explaining experimental data, allowing one to construct phase diagrams from a set of candidate phases, and there is now strong interest in deploying SCFT as a screening tool to guide experimental design. However, using SCFT for phase discovery leads to a conundrum: How does one discover a new morphology if the set of candidate phases needs to be specified in advance? This long-standing challenge was surmounted by training a deep convolutional generative adversarial network (GAN) with trajectories from converged SCFT solutions, and then deploying the GAN to generate input fields for subsequent SCFT calculations. The power of this approach is demonstrated for network phase formation in neat diblock copolymer melts via SCFT. A training set of only five networks produced 349 candidate phases spanning known and previously unexplored morphologies, including a chiral network. This computational pipeline, constructed here entirely from open-source codes, should find widespread application in block polymer phase discovery and other forms of soft matter. 

Block copolymers at homopolymer interfaces are poised to play a critical role in the compatibilization of mixed plastic waste, an area of growing importance as the rate of plastic accumulation rapidly increases. Using molecular dynamics simulations of Kremer–Grest polymer chains, we have investigated how the number of blocks and block degree of polymerization in a linear multiblock copolymer impacts the interface thermodynamics of strongly segregated homopolymer blends, which is key to effective compatibilization. The second virial coefficient reveals that interface thermodynamics are more sensitive to block degree of polymerization than to the number of blocks. Moreover, we identify a strong correlation between surface pressure (reduction of interfacial tension) and the spatial uniformity of block junctions on the interface, yielding a morphological framework for interpreting the role of compatibilizer architecture (number of blocks) and block degree of polymerization. These results imply that, especially at high interfacial loading, the choice of architecture of a linear multiblock copolymer compatibilizing surfactant does not greatly affect the modification of interfacial tension. 

We used Langevin dynamics simulations without hydrodynamic interactions to probe knot diffusion mechanisms and the time scales governing the evolution and the spontaneous untying of trefoil knots in nanochannel-confined DNA molecules in the extended de Gennes regime. The knot untying follows an “opening up process,” wherein the initially tight knot continues growing and fluctuating in size as it moves toward the end of the DNA molecule before its annihilation at the chain end. The mean knot size increases significantly and sub-linearly with increasing chain contour length. The knot diffusion in nanochannel-confined DNA molecules is subdiffusive, with the unknotting time scaling with chain contour length with an exponent of 2.64 ± 0.23 to within a 95% confidence interval. The scaling exponent for the mean unknotting time vs chain contour length, along with visual inspection of the knot conformations, suggests that the knot diffusion mechanism is a combination of self-reptation and knot region breathing for the simulated parameters.