Accounting for Cooperativity in the Thermotropic Volume Phase Transition of Smart Microgels
A full quantitative description of the swelling of smart microgels is still problematic in many cases. The original approach of Flory and Huggins for the monomer–solvent interaction parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline&quo...
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MDPI AG
2021-04-01
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| author | Simon Friesen Yvonne Hannappel Sergej Kakorin Thomas Hellweg |
| author_facet | Simon Friesen Yvonne Hannappel Sergej Kakorin Thomas Hellweg |
| author_sort | Simon Friesen |
| collection | DOAJ |
| description | A full quantitative description of the swelling of smart microgels is still problematic in many cases. The original approach of Flory and Huggins for the monomer–solvent interaction parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>χ</mi></semantics></math></inline-formula> cannot be applied to some microgels. The reason for this obviously is that the cross-linking enhances the cooperativity of the volume phase transitions, since all meshes of the network are mechanically coupled. This was ignored in previous approaches, arguing with distinct transition temperatures for different meshes to describe the continuous character of the transition of microgels. Here, we adjust the swelling curves of a series of smart microgels using the Flory–Rehner description, where the polymer–solvent interaction parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>χ</mi></semantics></math></inline-formula> is modeled by a Hill-like equation for a cooperative thermotropic transition. This leads to a very good description of all measured microgel swelling curves and yields the physically meaningful Hill parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>. A linear decrease of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> is found with increasing concentration of the cross-linker <i>N,N</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>′</mo></msup></semantics></math></inline-formula>-methylenebisacrylamide in the microgel particles p(NIPAM), p(NNPAM), and p(NIPMAM). The linearity suggests that the Hill parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> corresponds to the number of water molecules per network chain that cooperatively leave the chain at the volume phase transition. Driven by entropy, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> water molecules of the solvate become cooperatively “free” and leave the polymer network. |
| first_indexed | 2024-03-10T12:30:09Z |
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| spelling | doaj.art-a772e0d9f8e446acb33593399758ebeb2023-11-21T14:45:34ZengMDPI AGGels2310-28612021-04-01724210.3390/gels7020042Accounting for Cooperativity in the Thermotropic Volume Phase Transition of Smart MicrogelsSimon Friesen0Yvonne Hannappel1Sergej Kakorin2Thomas Hellweg3Department of Chemistry, Physical and Biophysical Chemistry, Bielefeld University, Universitätsstr. 25, 33615 Bielefeld, GermanyDepartment of Chemistry, Physical and Biophysical Chemistry, Bielefeld University, Universitätsstr. 25, 33615 Bielefeld, GermanyDepartment of Chemistry, Physical and Biophysical Chemistry, Bielefeld University, Universitätsstr. 25, 33615 Bielefeld, GermanyDepartment of Chemistry, Physical and Biophysical Chemistry, Bielefeld University, Universitätsstr. 25, 33615 Bielefeld, GermanyA full quantitative description of the swelling of smart microgels is still problematic in many cases. The original approach of Flory and Huggins for the monomer–solvent interaction parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>χ</mi></semantics></math></inline-formula> cannot be applied to some microgels. The reason for this obviously is that the cross-linking enhances the cooperativity of the volume phase transitions, since all meshes of the network are mechanically coupled. This was ignored in previous approaches, arguing with distinct transition temperatures for different meshes to describe the continuous character of the transition of microgels. Here, we adjust the swelling curves of a series of smart microgels using the Flory–Rehner description, where the polymer–solvent interaction parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>χ</mi></semantics></math></inline-formula> is modeled by a Hill-like equation for a cooperative thermotropic transition. This leads to a very good description of all measured microgel swelling curves and yields the physically meaningful Hill parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>. A linear decrease of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> is found with increasing concentration of the cross-linker <i>N,N</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>′</mo></msup></semantics></math></inline-formula>-methylenebisacrylamide in the microgel particles p(NIPAM), p(NNPAM), and p(NIPMAM). The linearity suggests that the Hill parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> corresponds to the number of water molecules per network chain that cooperatively leave the chain at the volume phase transition. Driven by entropy, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> water molecules of the solvate become cooperatively “free” and leave the polymer network.https://www.mdpi.com/2310-2861/7/2/42Flory–Rehner theorymicrogelHill cooperativityFlory–Huggins parameterswelling behaviorNNPAM |
| spellingShingle | Simon Friesen Yvonne Hannappel Sergej Kakorin Thomas Hellweg Accounting for Cooperativity in the Thermotropic Volume Phase Transition of Smart Microgels Gels Flory–Rehner theory microgel Hill cooperativity Flory–Huggins parameter swelling behavior NNPAM |
| title | Accounting for Cooperativity in the Thermotropic Volume Phase Transition of Smart Microgels |
| title_full | Accounting for Cooperativity in the Thermotropic Volume Phase Transition of Smart Microgels |
| title_fullStr | Accounting for Cooperativity in the Thermotropic Volume Phase Transition of Smart Microgels |
| title_full_unstemmed | Accounting for Cooperativity in the Thermotropic Volume Phase Transition of Smart Microgels |
| title_short | Accounting for Cooperativity in the Thermotropic Volume Phase Transition of Smart Microgels |
| title_sort | accounting for cooperativity in the thermotropic volume phase transition of smart microgels |
| topic | Flory–Rehner theory microgel Hill cooperativity Flory–Huggins parameter swelling behavior NNPAM |
| url | https://www.mdpi.com/2310-2861/7/2/42 |
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