Dilute Semiflexible Polymers with Attraction: Collapse, Folding and Aggregation

Zierenberg, Johannes; Marenz, Martin; Janke, Wolfhard

doi:10.3390/polym8090333

Cited by 40 publications

(47 citation statements)

References 138 publications

(195 reference statements)

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“…Hairpins and toroids exist at high stiffness, but they are no longer the ground state, which is a knotted structure, ideally the trefoil knot as for L=0.51 and N=40. The knotted structures in general have moved to the high stiffness region (they occur for L≤0.6) and are not found in the intermediate stiffness region, like in [22,23], where the high stiffness region is dominated by hairpins and folded chains. This comparison thus confirms our claim from the introduction: not all stiffnesses are created equal [7], and this is true even for models exhibiting the persistent mechanism of flexibility.…”

Section: Discussionmentioning

confidence: 99%

“…While these studies were performed for chains of lengths N=40−256, a Wang–Landau Monte Carlo [19,20] study of such semi-flexible bead-spring chains in the continuum, performed for chains of length N=13−55 [21] later confirmed the occurrence of these morphologies. Recently a similar model was studied by multi-canonical simulations [22,23], and it was shown that ground states at different stiffness can also be characterized by their knottedness (here, knots are defined by joining the two ends of the chain by an additional long bond).…”

Section: Introductionmentioning

confidence: 99%

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On the Pseudo Phase Diagram of Single Semi-Flexible Polymer Chains: A Flat-Histogram Monte Carlo Study

et al. 2017

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Local stiffness of polymer chains is instrumental in all structure formation processes of polymers, from crystallization of synthetic polymers to protein folding and DNA compactification. We present Stochastic Approximation Monte Carlo simulations-a type of flat-histogram Monte Carlo method-determining the density of states of a model class of single semi-flexible polymer chains, and, from this, their complete thermodynamic behavior. The chains possess a rich pseudo phase diagram as a function of stiffness and temperature, displaying non-trivial ground-state morphologies. This pseudo phase diagram also depends on chain length. Differences to existing pseudo phase diagrams of semi-flexible chains in the literature emphasize the fact that the mechanism of stiffness creation matters.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Pseudo Phase Diagram of Single Semi-Flexible Polymer Chains: A Flat-Histogram Monte Carlo Study

et al. 2017

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“…Bonds are modelled between neighbouring monomers by the FENE potential V FENE ( r )=−( KR 2 /2)ln[1−( r − r 0 ) 2 / R 2 ] with K =40, R =0.3 and r 0 =0.7. Non-bonded monomers interact with the same Lennard-Jones potential as above but with σ = r 0 2 −1/6 such that r min = r 0 18 19 20 . The total number of monomers is 13 N , which yields 3 × 13 N total momentum degrees of freedom in equation (5) and successive relations.…”

Section: Methodsmentioning

confidence: 99%

“…Importantly, we consider a setup at fixed density with varying temperature—an intuitive approach from a condensed matter perspective. We focus on aggregation of polymers in a dilute setup 18 19 20 guided by the canonical case of droplet formation in a particle gas. For the canonical case, we analyse a two-dimensional free-energy landscape and identify the energy as a suitable reaction coordinate.…”

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confidence: 99%

Canonical free-energy barrier of particle and polymer cluster formation

2017

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A common approach to study nucleation rates is the estimation of free-energy barriers. This usually requires knowledge about the shape of the forming droplet, a task that becomes notoriously difficult in macromolecular setups starting with a proper definition of the cluster boundary. Here we demonstrate a shape-free determination of the free energy for temperature-driven cluster formation in particle as well as polymer systems. Combined with rigorous results on equilibrium droplet formation, this allows for a well-defined finite-size scaling analysis of the effective interfacial free energy at a fixed density. We first verify the theoretical predictions for the formation of a liquid droplet in a supersaturated particle gas by generalized-ensemble Monte Carlo simulations of a Lennard-Jones system. Going one step further, we then generalize this approach to cluster formation in a dilute polymer solution. Our results suggest an analogy with particle condensation, when the macromolecules are interpreted as extended particles.

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“…The sum of the FENE and the non-bonded potential provides a total interaction between two connected monomers showing a deep minimum at r ∼ 0.95, which guarantees uncrossability and prevents violation of the topological constraints. In the case of the semiflexible linear chains the bending stiffness was implemented through the worm-like model [29,30]. Thus, the interaction for the polymer bending has the form:…”

Section: Model and Simulation Detailsmentioning

confidence: 99%

Coarsening Kinetics of Complex Macromolecular Architectures in Bad Solvent

2020

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This study reports a general scenario for the out-of-equilibrium features of collapsing polymeric architectures. We use molecular dynamics simulations to characterize the coarsening kinetics, in bad solvent, for several macromolecular systems with an increasing degree of structural complexity. In particular, we focus on: flexible and semiflexible polymer chains, star polymers with 3 and 12 arms, and microgels with both ordered and disordered networks. Starting from a powerful analogy with critical phenomena, we construct a density field representation that removes fast fluctuations and provides a consistent characterization of the domain growth. Our results indicate that the coarsening kinetics presents a scaling behaviour that is independent of the solvent quality parameter, in analogy to the time–temperature superposition principle. Interestingly, the domain growth in time follows a power-law behaviour that is approximately independent of the architecture for all the flexible systems; while it is steeper for the semiflexible chains. Nevertheless, the fractal nature of the dense regions emerging during the collapse exhibits the same scaling behaviour for all the macromolecules. This suggests that the faster growing length scale in the semiflexible chains originates just from a faster mass diffusion along the chain contour, induced by the local stiffness. The decay of the dynamic correlations displays scaling behavior with the growing length scale of the system, which is a characteristic signature in coarsening phenomena.

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Dilute Semiflexible Polymers with Attraction: Collapse, Folding and Aggregation

Cited by 40 publications

References 138 publications

On the Pseudo Phase Diagram of Single Semi-Flexible Polymer Chains: A Flat-Histogram Monte Carlo Study

On the Pseudo Phase Diagram of Single Semi-Flexible Polymer Chains: A Flat-Histogram Monte Carlo Study

Canonical free-energy barrier of particle and polymer cluster formation

Coarsening Kinetics of Complex Macromolecular Architectures in Bad Solvent

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