Coherent Dynamic Structure Factor of a Polymer Chain Confined Into a Harmonic Radial Potential

Dolgushev, Maxim; Krutyeva, Margarita

doi:10.1002/mats.201200045

Cited by 6 publications

(8 citation statements)

References 13 publications

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“…This is the expected result for a thin rod, P(Q) % Q À1 . In order to check this limiting calculation, a comparison with the model of Dolgushev and Krutyeva [3] has been done. In this model a harmonic potential with cylindrical symmetry acts as confinement.…”

Section: Two-dimensional Confinement (Channel)mentioning

confidence: 99%

“…Dolgushev and Krutyeva [3] (DK) calculate the form factor of the chain in a radially symmetric (cylindrical) harmonic potential from the t ¼ 0 value of a modified Rouse model:…”

Section: Appendix A: Continuous Chain Limit Of the Dolgushev-krutyevamentioning

confidence: 99%

“…Note that the parameter d used to express the strength of the confinement is different from the one used in ref. [3] ,d. Actually, the fundamental parameter in the DK model is the force constant in the potential. In order to convert this parameter to a length DK use the root-mean-square distance of a single segment,d ¼ 2 ffiffiffiffiffiffiffiffiffi hr 2 n i p .…”

Section: Appendix A: Continuous Chain Limit Of the Dolgushev-krutyevamentioning

confidence: 99%

“…The problem with this definition is that the action of the potential on the centre-of-mass increases with N. For a chain of given length the root-mean-square of the centre-of-mass displacement, ffiffiffiffiffiffiffiffi ffi hr 2 i p , would decrease with increasing subdivision of the chain as can be seen from Equation (10) of ref. [3] Instead, with the definition here ffiffiffiffiffiffiffiffi ffi hr 2 i p is independent of N and equal to d (Equation A6). The relation between the definition here and that of ref.…”

Section: Appendix A: Continuous Chain Limit Of the Dolgushev-krutyevamentioning

confidence: 99%

“…[2] Dolgushev and Krutyeva (DK) have recently presented a calculation of the form factor (and even the dynamical scattering function) for a polymer chain in a cylindrically symmetric potential. [3] This can be seen as a kind of confinement but the confining potential in real systems is rather box-shaped than harmonic. Nevertheless, the DK model represents actual neutron small-angle scattering data well.…”

Section: Introductionmentioning

confidence: 99%

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Closed‐Form Expressions for the Form Factor of a Polymer under Strong Confinement

Zorn

2013

Macro Theory & Simulations

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In this paper the scattering from an ideal polymer chain in strong confinement (d≪Rnormalg) is calculated. It is possible to derive analytical closed‐form expressions analogous to the Debye form factor. The results can be written in terms of one hypergeometric function 2F2 for all geometries (channel, film, unconfined). It is shown that the result is consistent with a recent calculation of the form factor for a polymer chain in a radial harmonic potential.

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Section: Two-dimensional Confinement (Channel)mentioning

confidence: 99%

“…Dolgushev and Krutyeva [3] (DK) calculate the form factor of the chain in a radially symmetric (cylindrical) harmonic potential from the t ¼ 0 value of a modified Rouse model:…”

Section: Appendix A: Continuous Chain Limit Of the Dolgushev-krutyevamentioning

confidence: 99%

Section: Appendix A: Continuous Chain Limit Of the Dolgushev-krutyevamentioning

confidence: 99%

Section: Appendix A: Continuous Chain Limit Of the Dolgushev-krutyevamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Closed‐Form Expressions for the Form Factor of a Polymer under Strong Confinement

Zorn

2013

Macro Theory & Simulations

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Insight into the Competitive Adsorption Behavior of Polymer Chains in Silica Nanopores by Small-Angle Neutron Scattering

Wang,

Lyu,

et al. 2024

Macromolecules

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Processive hydrogenolysis catalysts, in which a metal nanoparticle (e.g., Pt) embedded at the bottom of a cylindrical silica nanopore can repeatedly cleave polymer chains and produce value-added hydrocarbon products, offer a potential solution for billions of tons of waste plastics. As the chain stays longer near the Pt catalysts, it would have a higher chance of getting cut, and therefore the molecular weight distribution of the product could be affected by the adsorption behavior of virgin chains (long polymers) versus cleaved chains (short polymers) into the nanopores. This work reports a model study to understand the competitive adsorption behavior of the two different molecular weight polymers that are mixed, mimicking the reaction medium in the intermediate stage of the catalytic reaction. This study employs small-angle neutron scattering (SANS), which takes advantage of contrast differences between hydrogenous and deuterated polystyrenes to experimentally observe the relative composition of the two polymers in the silica nanopores. Our results reveal preferential adsorption of longer chains in the silica nanopores, which is consistent with the theoretical prediction in the literature for the case of the enthalpic attraction between polymers and pore walls.

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Structure and dynamics of confined flexible and unentangled polymer melts in highly adsorbing cylindrical pores

Carrillo

Sumpter

2014

The Journal of Chemical Physics

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Coarse-grained molecular dynamics simulations are used to probe the dynamic phenomena of polymer melts confined in nanopores. The simulation results show excellent agreement in the values obtained for the normalized coherent single chain dynamic structure factor, S(Q,Δt)/S(Q,0). In the bulk configuration, both simulations and experiments confirm that the polymer chains follow Rouse dynamics. However, under confinement, the Rouse modes are suppressed. The mean-square radius of gyration ⟨R(g)(2)⟩ and the average relative shape anisotropy ⟨κ(2)⟩ of the conformation of the polymer chains indicate a pancake-like conformation near the surface and a bulk-like conformation near the center of the confining cylinder. This was confirmed by direct visualization of the polymer chains. Despite the presence of these different conformations, the average form factor of the confined chains still follows the Debye function which describes linear ideal chains, which is in agreement with small angle neutron scattering experiments (SANS). The experimentally inaccessible mean-square displacement (MSD) of the confined monomers, calculated as a function of radial distance from the pore surface, was obtained in the simulations. The simulations show a gradual increase of the MSD from the adsorbed, but mobile layer, to that similar to the bulk far away from the surface.

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Coherent Dynamic Structure Factor of a Polymer Chain Confined Into a Harmonic Radial Potential

Cited by 6 publications

References 13 publications

Closed‐Form Expressions for the Form Factor of a Polymer under Strong Confinement

Closed‐Form Expressions for the Form Factor of a Polymer under Strong Confinement

Insight into the Competitive Adsorption Behavior of Polymer Chains in Silica Nanopores by Small-Angle Neutron Scattering

Structure and dynamics of confined flexible and unentangled polymer melts in highly adsorbing cylindrical pores

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