Semi-flexible compact polymers in two dimensional nonhomogeneous confinement

Marčetić, Dušanka; Elezović-Hadžić, Sunčica; Adžić, Nataša; Živić, Ivan

doi:10.1088/1751-8121/ab04e7

Cited by 6 publications

(3 citation statements)

References 59 publications

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“…Persistence length of semi-flexible HWs is independent of stiffness and equal to 3 2 on 3-simplex lattice. On other fractal lattices, although stiffness dependent, l p of semi-flexible HWs is finite even in the infinite stiffness limit [53,54]. Since Hamiltonian walks visit all lattice sites and are enumerated on larger and larger lattices with boundaries always present, they are bounded by definition, which may reflect on l p .…”

Section: Results and Discussion 0 < S ≤mentioning

confidence: 99%

Interacting semi-flexible self-avoiding walks studied on a fractal lattice

Marčetić¹

2023

Preprint

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Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, non-homogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between non-consecutively visited pairs of nearest-neighboring sites (contacts). It captures the main features of a semi-flexible polymer subjected to variable solvent conditions. Hierarchical structure of the fractal lattice enabled determination of the exact recurrence equations for the generating function, through which universal and local properties of the model were studied. Analysis of the recurrence equations showed that for all finite values of the considered energies and non-zero temperatures, polymer resides in an expanded phase. Critical exponents of the expanded phase are universal and the same as those for ordinary self-avoiding walks on the same lattice found earlier. As a measure of local properties, the mean number of contacts per mean number of steps as well as persistence length, are calculated as functions of Boltzmann weights associated with bending energies and attractive interactions between contacts. Both quantities are monotonic functions of stiffness weights for fixed interaction, and in the limit of infinite stiffness the number of contacts decreases to zero, while the persistence length increases unboundedly.

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Section: Results and Discussion 0 < S ≤mentioning

confidence: 99%

Interacting semi-flexible self-avoiding walks studied on a fractal lattice

Marčetić¹

2023

Preprint

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“…The persistence length of semi-flexible HWs is independent of stiffness and equal to 3 2 on the 3-simplex lattice. On other fractal lattices, although stiffness dependent, l p of semi-flexible HWs is finite even in the infinite stiffness limit [63,64]. Since Hamiltonian walks visit all lattice sites and are enumerated on larger and larger lattices with boundaries, they are bounded by definition, which may reflect on l p .…”

Section: Results and Discussion 0 < Smentioning

confidence: 99%

Interacting semi-flexible self-avoiding walks studied on a fractal lattice

Marčetić

2023

Phys. Scr.

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Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, nonhomogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between nonconsecutively visited pairs of nearest-neighboring sites (contacts). It captures the main features of a semi-flexible polymer subjected to variable solvent conditions. A hierarchical structure of the fractal lattice enabled determination of the exact recurrence equations for the generating function, through which universal and local properties of the model were studied. An analysis of the recurrence equations showed that for all finite values of the considered energies and nonzero temperatures, the polymer resides in an expanded phase. Critical exponents of the expanded phase are universal and the same as those for ordinary self-avoiding walks on the same lattice found earlier. As a measure of local properties, the mean number of contacts per mean number of steps as well as the persistence length, are calculated as functions of Boltzmann weights associated with bending energies and attractive interactions between contacts. Both quantities are monotonic functions of stiffness weights for fixed interaction, and in the limit of infinite stiffness the number of contacts decreases to zero, while the persistence length increases unboundedly.

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“…Also, we numerically find the corresponding entropies per dimer in the thermodynamic limit. Although for some lattice models it was possible to find exact set of recurrence equations on the whole MR family [25], in this case we were not able to do so for the reason that would be explained in the appendix A. Secondly, we apply the same method on 4-simplex lattice and determine the entropy.…”

Section: Recursive Enumerative Methods For Dimer Coverings On Fractal...mentioning

confidence: 99%

Statistics of close-packed dimers on fractal lattices

Marčetić

Elezović-Hadžić

Živić

2020

Physica A: Statistical Mechanics and its Applications

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We study the model of close-packed dimers on planar lattices belonging to the family of modified rectangular (MR) fractals, whose members are enumerated by an integer p ≥ 2, as well as on the non-planar 4-simplex fractal lattice. By applying an exact recurrence enumeration method, we determine the asymptotic forms for numbers of dimer coverings, and numerically calculate entropies per dimer in the thermodynamic limit, for a sequence of MR lattices with 2 ≤ p ≤ 8 and for 4-simplex fractal. We find that the entropy per dimer on MR fractals is increasing function of the scaling parameter p, and for every considered p it is smaller than the entropy per dimer of the same model on 4-simplex lattice. Obtained results are discussed and compared with the results obtained previously on some translationally invariant and fractal lattices.

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Semi-flexible compact polymers in two dimensional nonhomogeneous confinement

Cited by 6 publications

References 59 publications

Interacting semi-flexible self-avoiding walks studied on a fractal lattice

Interacting semi-flexible self-avoiding walks studied on a fractal lattice

Interacting semi-flexible self-avoiding walks studied on a fractal lattice

Statistics of close-packed dimers on fractal lattices

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