Gaussian polymer chains in a harmonic potential: the path integral approach

Paradezhenko, G. V.; Connor, Gascoigne,; Brilliantov, Nikolai V.

doi:10.1088/1751-8121/abb0c2

Cited by 2 publications

(6 citation statements)

References 25 publications

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“…Inspection of equations ( 25) and ( 26) reveals the exact same relation in the case of a 3D polymer confined by a soft and symmetric field centered at the origin, indicating agreement in the results of the two different approaches. Finally, Paradezhenko et al [9] derive the probability density function of the squared radius of gyration for a symmetric harmonic field. In order to compare the results of the Paradezhenko model with the R 2 g predictions of the current model, the PDF of the former and its mean value were obtained via numerical integration.…”

Section: Comparison Of Theoretical Results With Other Theories and Si...mentioning

confidence: 99%

“…The harmonic potential in their work was described as an approximation for the case of confinement between two walls, as in Casassa; however, the case of a harmonic potential is more broadly applicable in the vicinity of any local minimum of a potential (assuming the expansion about the minimum is quadratic to leading order). Later work established integral forms for the probability density functions (PDFs) of potential energy [8] and squared radius of gyration [9] of continuous Gaussian chains in a harmonic potential, following a formulation proposed by Fixman [10] for discrete chains, with asymptotic behavior corrected in work by Fujita and Norisuye [11]. In these works, the external potential was generalized to be multidimensional, albeit isotropic.…”

Section: Introductionmentioning

confidence: 99%

“…x , and values of the Paradezhenko model [9]. The objective of these derivations is to have a functional form for the root mean squared (RMS) radius of gyration as a function of confinement that is able to describe both weak and strong confinement and smoothly connect the two extreme limits.…”

Section: Introductionmentioning

confidence: 99%

“…Although the path-integral formulation of the partition function in this work is similar to that found in [8,9], the method of solution is different and allows for further generalization of the model. Here, the partition function is solved directly rather than left in open form as a step in computing the characteristic function for the PDFs.…”

Section: Introductionmentioning

confidence: 99%

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Statistics of Gaussian polymer chains in harmonic applied fields

Mikhail,

Rutledge

2024

J. Phys.: Condens. Matter

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The model of an ideal polymer chain in a harmonic applied field has broad applicability in situations involving polymer confinement and deformation due to applied stress. In this work we (1) formulate a general analytical model for a continuous Gaussian chain under a harmonic applied potential and (2) evaluate the statistical mechanics of this model given the potential, obtaining partition functions and moment generating functions that describe the chain configurations. Closed-form expressions for the squared radius of gyration, potential energy, partition function, and moment generating function for the center of mass are obtained for a general and multidimensional harmonic field. The expressions are compared with results of Monte Carlo simulations of a discrete Gaussian chain as well as results for related systems obtained from the literature. The theory derived here is used to test the applicability of the current model assumptions to relations from the literature describing polymer confinement and deformation in experiment, theory, and simulations.

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Section: Comparison Of Theoretical Results With Other Theories and Si...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Statistics of Gaussian polymer chains in harmonic applied fields

Mikhail,

Rutledge

2024

J. Phys.: Condens. Matter

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“…Then it is necessary to calculate the path integral in equation (10). Using the saddle-point method [4,7,8], we obtain…”

Section: Star Polymermentioning

confidence: 99%

On gyration radius distributions of star-like macromolecules

Budkov¹,

Kolesnikov²

2021

J. Stat. Mech.

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Using the path integral approach, we obtain the characteristic functions of the gyration radius distributions for Gaussian star and Gaussian rosette macromolecules. We derive the analytical expressions for cumulants of both distributions. Applying the steepest descent method, we estimate the probability distribution functions (PDFs) of the gyration radius in the limit of a large number of star and rosette arms in two limiting regimes: for strongly expanded and strongly collapsed macromolecules. We show that in both cases, in the regime of a large gyration radius relative to its mean-square value, the PDFs can be described by the Gaussian functions. In the shrunk macromolecule regime, both distribution functions tend to zero faster than any power of the gyration radius. Based on the asymptotic behavior of the distribution functions and the behavior of statistical dispersions, we demonstrate that the PDF for the rosette is more densely localized near its maximum than that for the star polymer. We construct the interpolation formula for the gyration radius distribution of the Gaussian star macromolecule which can help to take into account the conformational entropy of the flexible star macromolecules within the Flory-type mean-field theories.

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Gaussian polymer chains in a harmonic potential: the path integral approach

Cited by 2 publications

References 25 publications

Statistics of Gaussian polymer chains in harmonic applied fields

Statistics of Gaussian polymer chains in harmonic applied fields

On gyration radius distributions of star-like macromolecules

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