Adsorption of Wormlike Chains onto Partially Permeable Membranes
Reversible adsorption of a single stiff wormlike macromolecule to flat membranes with various permeabilities is considered theoretically. It is shown that the adsorbed layer microstructure is significantly different from either a flexible chain or a stiff chain adsorption at a solid surface. Close t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Polymers |
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| Online Access: | https://www.mdpi.com/2073-4360/15/1/35 |
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| author | Alexander Semenov Irina Nyrkova |
| author_facet | Alexander Semenov Irina Nyrkova |
| author_sort | Alexander Semenov |
| collection | DOAJ |
| description | Reversible adsorption of a single stiff wormlike macromolecule to flat membranes with various permeabilities is considered theoretically. It is shown that the adsorbed layer microstructure is significantly different from either a flexible chain or a stiff chain adsorption at a solid surface. Close to the critical point, the adsorbing wormlike chain forms a strongly anisotropic proximal layer near the membrane in addition to a nearly isotropic distal layer. The proximal layer is characterized by the algebraic monomer concentration profile, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>∝</mo><msup><mfenced open="|" close="|"><mi>x</mi></mfenced><mrow><mo>−</mo><mi>β</mi></mrow></msup></mrow></semantics></math></inline-formula>, due to the self-similar distribution of aligned polymer loops. For a perfectly penetrable membrane, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> which is different from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><mn>4</mn><mo>/</mo><mn>3</mn></mrow></semantics></math></inline-formula> obtained for semiflexible chain adsorption at a solid surface. Moreover, we establish that the critical exponent for a partially permeable membrane depends on its properties (porosity <i>w</i>) and propose an asymptotically exact theory (based on the generalized Edwards equation) predicting this dependence, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><mi>β</mi><mo>(</mo><mi>w</mi><mo>)</mo></mrow></semantics></math></inline-formula>. We also develop a scaling theory elucidating, in particular, an intricate competition of loops and tails in both proximal and distal sublayers. |
| first_indexed | 2024-03-09T09:43:10Z |
| format | Article |
| id | doaj.art-f0066c1cd9f54cca9a2df4c60e857b0a |
| institution | Directory Open Access Journal |
| issn | 2073-4360 |
| language | English |
| last_indexed | 2024-03-09T09:43:10Z |
| publishDate | 2022-12-01 |
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| series | Polymers |
| spelling | doaj.art-f0066c1cd9f54cca9a2df4c60e857b0a2023-12-02T00:48:48ZengMDPI AGPolymers2073-43602022-12-011513510.3390/polym15010035Adsorption of Wormlike Chains onto Partially Permeable MembranesAlexander Semenov0Irina Nyrkova1Institut Charles Sadron, CNRS-UPR 22, University of Strasbourg, CEDEX 2, 67034 Strasbourg, FranceInstitut Charles Sadron, CNRS-UPR 22, University of Strasbourg, CEDEX 2, 67034 Strasbourg, FranceReversible adsorption of a single stiff wormlike macromolecule to flat membranes with various permeabilities is considered theoretically. It is shown that the adsorbed layer microstructure is significantly different from either a flexible chain or a stiff chain adsorption at a solid surface. Close to the critical point, the adsorbing wormlike chain forms a strongly anisotropic proximal layer near the membrane in addition to a nearly isotropic distal layer. The proximal layer is characterized by the algebraic monomer concentration profile, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>∝</mo><msup><mfenced open="|" close="|"><mi>x</mi></mfenced><mrow><mo>−</mo><mi>β</mi></mrow></msup></mrow></semantics></math></inline-formula>, due to the self-similar distribution of aligned polymer loops. For a perfectly penetrable membrane, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> which is different from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><mn>4</mn><mo>/</mo><mn>3</mn></mrow></semantics></math></inline-formula> obtained for semiflexible chain adsorption at a solid surface. Moreover, we establish that the critical exponent for a partially permeable membrane depends on its properties (porosity <i>w</i>) and propose an asymptotically exact theory (based on the generalized Edwards equation) predicting this dependence, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><mi>β</mi><mo>(</mo><mi>w</mi><mo>)</mo></mrow></semantics></math></inline-formula>. We also develop a scaling theory elucidating, in particular, an intricate competition of loops and tails in both proximal and distal sublayers.https://www.mdpi.com/2073-4360/15/1/35adsorptionpolymersmembranes |
| spellingShingle | Alexander Semenov Irina Nyrkova Adsorption of Wormlike Chains onto Partially Permeable Membranes Polymers adsorption polymers membranes |
| title | Adsorption of Wormlike Chains onto Partially Permeable Membranes |
| title_full | Adsorption of Wormlike Chains onto Partially Permeable Membranes |
| title_fullStr | Adsorption of Wormlike Chains onto Partially Permeable Membranes |
| title_full_unstemmed | Adsorption of Wormlike Chains onto Partially Permeable Membranes |
| title_short | Adsorption of Wormlike Chains onto Partially Permeable Membranes |
| title_sort | adsorption of wormlike chains onto partially permeable membranes |
| topic | adsorption polymers membranes |
| url | https://www.mdpi.com/2073-4360/15/1/35 |
| work_keys_str_mv | AT alexandersemenov adsorptionofwormlikechainsontopartiallypermeablemembranes AT irinanyrkova adsorptionofwormlikechainsontopartiallypermeablemembranes |