Marginally compact fractal trees with semiflexibility

Dolgushev, Maxim; Hauber, Adrian L.; Pelagejcev, Philipp; Wittmer, J. P.

doi:10.1103/physreve.96.012501

Cited by 7 publications

(4 citation statements)

References 66 publications

(161 reference statements)

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“…Recent simulation studies have suggested that other molecular architectures than linear chains may have mass scaling exponents governing polymer size (e.g., Rnormalg), less than ν=1/2. For randomly branched polymers in their melt state, ν has been proposed to be exactly 1/3 [55,56,57,58], indicating that these polymers also form rather ‘compact’ structures in the melt state [59]. Ring polymers in the melt have been predicted to exhibit this same type of asymptotic scaling [52], strongly suggesting that these polymers belong to the randomly branched polymer universality class when they are in the melt state.…”

Section: Resultsmentioning

confidence: 99%

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

Chremos

Douglas

2019

Polymers

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We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius R h , packing length p, pair correlation function g ( r ) , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

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Section: Resultsmentioning

confidence: 99%

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

Chremos

Douglas

2019

Polymers

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“…Randomly branched polymers in their melt state likewise exhibit a reduction in their mass scaling exponent ν due to the excluded volume screening. Recent simulation studies have suggested that ν for randomly branched polymers in their melt state is exactly 1/3, [43][44][45][46] indicating that these polymers form rather 'compact' structures in the melt state, rather than being like randomly branched polymers at their θ-point. Screening evidently operates differently between linear chains and randomly branched polymers.…”

Section: Background On Universality Classes Of Polymers In Relatimentioning

confidence: 99%

A comparative study of thermodynamic, conformational, and structural properties of bottlebrush with star and ring polymer melts

Chremos

Douglas

2018

The Journal of Chemical Physics

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Thermodynamic, conformational, and structural properties of bottlebrush polymer melts are investigated with molecular dynamics simulations and compared to linear, regular star, and unknotted ring polymer melts to gauge the influence of molecular topology on polymer melt properties. We focus on the variation of the backbone chain length, the grafting density along the backbone, and the length of the side chains at different temperatures above the melt glass transition temperature. Based on these comparisons, we find that the segmental density, isothermal compressibility, and isobaric thermal expansion of bottlebrush melts are quantitatively similar to unknotted ring polymer melts and star polymer melts having a moderate number ( f = 5 to 6) of arms. These similarities extend to the mass scaling of the chain radius of gyration. Our results together indicate that the configurational properties of bottlebrush polymers in their melt state are more similar to randomly branched polymers than linear polymer chains. We also find that the average shape of bottlebrush polymers having short backbone chains with respect to the side chain length is also rather similar to the unknotted ring and moderately branched star polymers in their melt state. As a general trend, the molecular shape of bottlebrush polymers becomes more spherically symmetric when the length of the side chains has a commensurate length as the backbone chain. Finally, we calculate the partial static structure factor of the backbone segments and we find the emergence of a peak at the length scales that characterizes the average distance between the backbone chains. This peak is absent when we calculate the full static structure factor. We characterize the scaling of this peak with parameters characterizing the bottlebrush molecular architecture to aid in the experimental characterization of these molecules by neutron scattering.

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“…In particular, the resulting Gaussian networks [33][34][35] with (m, k)depending rigidities are often used for the description of 3D structures of proteins. In [36,37] static and dynamic properties of marginally compact trees with various fractal architectures were considered. A related hierarchical variational approach for an account of volume interactions of swollen polymer chains had been proposed in Ref.…”

Section: Fractal Brownian Motion As a Conformation Of A Polymer Cmentioning

confidence: 99%

Effective Hamiltonian of topologically stabilized polymer states

2018

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Topologically stabilized polymer conformations in melts of nonconcatenated polymer rings and crumpled globules are considered to be a good candidate for the description of the spatial structure of mitotic chromosomes. Despite significant efforts, the microscopic Hamiltonian capable of describing such systems still remains unknown. We describe a polymer conformation by a Gaussian network - a system with a Hamiltonian quadratic in all coordinates - and show that by tuning interaction constants, one can obtain equilibrium conformations with any fractal dimension between 2 (an ideal polymer chain) and 3 (a crumpled globule). Monomer-to-monomer distances in topologically stabilized states, according to available numerical data, fit very well the Gaussian distribution, giving an additional argument in support of the quadratic Hamiltonian model. Mathematically, the polymer conformations are mapped onto the trajectories of a subdiffusive fractal Brownian particle. Moreover, we explicitly show that the quadratic Hamiltonian with a hierarchical set of coupling constants provides the microscopic background for the description of the path integral of the fractional Brownian motion with an algebraically decaying kernel.

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Marginally compact fractal trees with semiflexibility

Cited by 7 publications

References 66 publications

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

A comparative study of thermodynamic, conformational, and structural properties of bottlebrush with star and ring polymer melts

Effective Hamiltonian of topologically stabilized polymer states

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