Comparisons of a Polymer in Confinement versus Applied Force

The similarities and differences between geometric and tensile constraints on polymers have not been fully investigated. Here we use theory (blob models) and simulations to present a comprehensive comparison between polymers in these two situations. For a polymer in good solvent, the effect of tensile force f on extension in the Pincus regime is similar to the effect of cylindrical confinement in the de Gennes regime after mapping the characteristic length k_BT/f to the cylindrical diameter D, where k_BT is the thermal energy. However, the comparison of the effects of tension and confinement on extension is lacking when k_BT/f and D are less than the thermal blob size b, referred to as extended Pincus regime and extended de Gennes regime, respectively. In the extended Pincus regime, force can still segregate the ideal-coils with the size of ∼k_BT/f, resulting in the scaling of extension L_∥ ∼ (k_BT/f)^-1. In the extended de Gennes regime, excluded volume interaction is not sufficient to segregate the ideal-coils with the size of D, resulting in the scaling L_∥ ∼ D^-2/3 different from the scaling in the extended Pincus regime. In addition to the scaling of extension, the scaling of fluctuation in extension σ is also compared in the extended Pincus or extended de Gennes regime. It is found that σ is independent of f and D, which reflects the ideal-chain behavior. All of the above scaling relations are validated by Monte Carlo simulations. Simulation and scaling results are also used to determine the experimental conditions needed to access the extended de Gennes and de Gennes regimes in various single molecule experiments.