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Forces on an attractive surface generated from a thermoresponsive polymer gel
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25.Note1, the fact that is implied by the condition that the pole does not exist. The condition holds by assumption which is possible only if .
26.Note2, we used the Mathematica software to establish that the series has a form of . This implies that A1 term has to be omitted from the analysis since it corresponds to the delta function term. The expansion is valid if the first term is much larger than the third term. The ratio between the third term and the first term is given by . The condition in the text follows by requiring that this ratio is much smaller than 1.
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Interaction between polymers and soft-matter surfaces in the biological cell is a common yet incompletely understood phenomenon. This work investigates a generic situation where a thermoresponsive polymer gel is placed in the vicinity of an adsorbing surface, and starts contracting. The force is mediated by polymer chains that partially attach to the surface and partially to the contracting gel. The main goal was to understand how the force generated by the transforming polymer gel depends on key parameters that describe the system, most importantly, the concentration of the polymer, the length of the force-mediating polymer, and the the distance between the surface and the outer border of the contracting polymer gel. The key result of the paper is the Laplace transform (with regard to the polymer length) of the pulling force expression. Analytical approximations for the force have been obtained, and the exact expression for the pulling force is presented for the situation when the gel starts contracting. In depth analysis of the force behavior revealed several phases adopted by the polymer during the gel contraction.
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