Can Polymer Helicity Affect Topological Chirality of Polymer Knots?

We investigate the effect of helicity in isolated polymers on the topological chirality of their knots with computer simulations. Polymers are described by generic worm-like chains (WLC), where helical conformations are promoted by chiral coupling between segments that are neighbors along the chain contour. The sign and magnitude of the coupling coefficient u determine the sense and strength of helicity. The corrugation of the helix is adjusted via the radius R of a spherical, hard excluded volume around each WLC segment. Open and compact helices are, respectively, obtained for R that is either zero or smaller than the length of the WLC bond, and R that is a few times larger than the bond length. We use a Monte Carlo algorithm to sample polymer conformations for different values of u, spanning the range from achiral polymers to chains with well-developed helices. Monitoring the average helix torsion and fluctuations of chiral order as a function of u, for two very different chain lengths, demonstrates that the coil-helix transition in this model is not a phase transition but a crossover. Statistical analysis of conformations forming the simplest chiral knots, 3₁, 5₁, and 5₂, demonstrates that topological mirror symmetry is broken─knots formed by helices with a given sense prefer one handedness over the other. For the 3₁ and 5₁ knots, positive helical sense favors positive handedness. Intriguingly, an opposite trend is observed for 5₂ knots, where positive helical sense promotes negative handedness. We argue that this special coupling between helicity and topological chirality stems from a generic mechanism: conformations where some of the knot crossings are found in "braids" formed by two tightly interwoven sections of the polymer.

Grafting-Induced Structural Ordering of Lactide Chains

The structure of a grafted layer of lactide chains in the “dry brush” regime immersed in a melt of chemically similar polymer was examined while varying graft lengths. To this end, microsecond atomistic molecular dynamics simulations were performed. Almost no influence of graft length on the fraction of the grafted chains backfolded to the grafting surface was found. However, a structural ordering was unexpectedly observed in the system when the length of the grafted lactide chains was close to approximately 10 Kuhn segments. This ordering of the grafts is characterized by the formation of helical fragments whose structure is in good agreement with the experimental data for the α crystal of the lactide chains. Both the backfolding and the structural ordering may be viewed as the initial stage of the crystallization of the layer of grafted lactide chains. In contrast to the known behavior for conventional polymer brushes in the “dry brush” regime, the structure of the grafted lactide chains can be either amorphous or ordered, depending on the graft length N and the grafting density σ when their product Nσ is fixed.

Induced liquid-crystalline ordering in solutions of stiff and flexible amphiphilic macromolecules: Effect of mixture composition

Impact of mixture composition on self-organization in concentrated solutions of stiff helical and flexible macromolecules was studied by means of molecular dynamics simulation. The macromolecules were composed of identical amphiphilic monomer units but a fraction f of macromolecules had stiff helical backbones and the remaining chains were flexible. In poor solvents the compacted flexible macromolecules coexist with bundles or filament clusters from few intertwined stiff helical macromolecules. The increase of relative content f of helical macromolecules leads to increase of the length of helical clusters, to alignment of clusters with each other, and then to liquid-crystalline-like ordering along a single direction. The formation of filament clusters causes segregation of helical and flexible macromolecules and the alignment of the filaments induces effective liquid-like ordering of flexible macromolecules. A visual analysis and calculation of order parameter relaying the anisotropy of diffraction allow concluding that transition from disordered to liquid-crystalline state proceeds sharply at relatively low content of stiff components.