The entropic force is one of the most elusive interaction in macromolecules. Theoretically, this quantity is clearly defined, but practically it is difficult to evaluate, thus restricting our knowledge of it often to a qualitative level. In this work, we derive an entropic force formula for partly confined polymers and demonstrate its mathematical equivalence with the well-known chemical potential formula for solutions. It leads to an interesting cross-disciplinary correspondence between polymer physics, granular chains, and chemistry. In analytical studies, the magnitudes of the recoiling, tension, and drift entropic forces are derived for 2D strips, 3D tubes, and 3D slits, with both hard and soft boundaries. In numerical experiments, the force magnitudes extracted by the Jarzynski equality and a recursion formula highly coincide with those obtained from the analytical study. With this formalism, the strengths of various polymer entropic forces are systematically evaluated for different polymers and confinements. Remarkably, the result clarifies the force magnitudes inferred in several recent granular and polymer experiments, including the confined granular chains on a vibrating platform and DNA recoiling and tug-of-war in nanochannels, nanopillar arrays, and nanoslits. More generally, it predicts the yet-unknown force strengths in a variety of biological confined polymers and polymers in single-molecule or microfluidic experiments. According to this analysis, 20 pN seems to be close to the maximum entropic force one can observe in nature for a recoiling polymer. On the one hand, the proposed force formalism reduces the difficulty of a quantitative description on the elusive entropic force in scientific discussions and enables experimentalists to instantaneously estimate some entropic forces, without waiting for heavy numerical computations for justification. On the other hand, the success of extending the application of the reference-based strategy from the chemical potential of solutions to the entropic force of confined polymers paves the way for using the same strategy to tackle other complex problems beyond physical chemistry and polymer physics.

Reference:

Hong-Qing Xie & Cheng-Hung Chang, Chemical potential formalism for polymer entropic forces, Communications Physics 2, 24 (2019).

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