| Summary: | We compute desorption rates for isolated polymers adsorbed to a solid wall with a rare event sampling technique called multilevel splitting, also known as forward flux sampling. We interpret computed rates with theories based on the conjecture that the product <inline-formula><math display="inline"><semantics><mrow><mfrac><mrow><msub><mi>t</mi><mrow><mi>des</mi></mrow></msub><mi>D</mi></mrow><mrow><msubsup><mi>R</mi><mi>g</mi><mn>2</mn></msubsup></mrow></mfrac></mrow></semantics></math></inline-formula> of the desorption time <inline-formula><math display="inline"><semantics><mrow><msub><mi>t</mi><mrow><mi>des</mi></mrow></msub></mrow></semantics></math></inline-formula> and diffusivity <inline-formula><math display="inline"><semantics><mi>D</mi></semantics></math></inline-formula> divided by squared radius of gyration <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>g</mi></msub></mrow></semantics></math></inline-formula> scales with exp(<i>h/R<sub>g</sub></i>) where <i>h</i> is the equilibrium ratio of adsorbed surface concentration of polymer <inline-formula><math display="inline"><semantics><mi>Γ</mi></semantics></math></inline-formula> to bulk concentration of polymer <inline-formula><math display="inline"><semantics><mi>c</mi></semantics></math></inline-formula>. As the polymer–wall interaction energy is increased, the slope of <inline-formula><math display="inline"><semantics><mrow><mi>l</mi><mi>n</mi><mfenced><mrow><mfrac><mrow><msub><mi>t</mi><mrow><mi>des</mi></mrow></msub><mi>D</mi></mrow><mrow><msubsup><mi>R</mi><mi>g</mi><mn>2</mn></msubsup></mrow></mfrac></mrow></mfenced></mrow></semantics></math></inline-formula> vs. <inline-formula><math display="inline"><semantics><mrow><mfrac><mrow><mi>N</mi><msub><mi>V</mi><mrow><mi>M</mi><mi>F</mi></mrow></msub></mrow><mrow><msub><mi>k</mi><mi>B</mi></msub><mi>T</mi></mrow></mfrac></mrow></semantics></math></inline-formula> nearly approaches unity, as expected for strongly-adsorbing chains, where <i>N</i> is the degree of polymerization and <inline-formula><math display="inline"><semantics><mrow><msub><mi>V</mi><mrow><mi>M</mi><mi>F</mi></mrow></msub></mrow></semantics></math></inline-formula> is the height-averaged monomer–wall interaction energy for a strongly adsorbed chain. However, we also find that this scaling law is only accurate when adsorption strength per monomer exceeds a threshold value on the order of 0.3–0.5 k<sub>B</sub>T for a freely jointed chain without or with excluded volume effects. Below the critical value, we observe that <inline-formula><math display="inline"><semantics><mrow><mfrac><mrow><msub><mi>t</mi><mrow><mi>des</mi></mrow></msub><mi>D</mi></mrow><mrow><msubsup><mi>R</mi><mi>g</mi><mn>2</mn></msubsup></mrow></mfrac></mrow></semantics></math></inline-formula> becomes nearly constant with <i>N</i>, so that <inline-formula><math display="inline"><semantics><mrow><msub><mi>t</mi><mrow><mi>des</mi></mrow></msub><mo>∝</mo><msup><mi>N</mi><mi>α</mi></msup></mrow></semantics></math></inline-formula>, with <inline-formula><math display="inline"><semantics><mrow><mi>α</mi><mo>≈</mo><mn>2</mn></mrow></semantics></math></inline-formula>. This suggests a crossover from “strong” detachment-controlled to a “weak” diffusion-controlled desorption rate as <i>V</i><sub>MF</sub>/k<sub>B</sub>T drops below some threshold. These results may partially explain experimental data, that in some cases show “strong” exponential dependence of desorption time on chain length, while in others a “weak” power-law dependence is found. However, in the “strong” adsorption case, our results suggest much longer desorption times than those measured, while the reverse is true in the weak adsorption limit. We discuss possible reasons for these discrepancies.
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