The de Gennes' blob model is extensively used in different problems of polymer physics. This model is theoretically applicable when the number of monomers inside each blob is large enough. For confined flexible polymers, this requires the confining geometry to be much larger than the monomer size. In this paper, the opposite limit of polymer in nanoslits with one to several monomers width is studied, using molecular dynamics simulations. Extension of the polymer inside nanoslits, confinement force on the plates, and the effective spring constant of the confined polymer are investigated. Despite the theoretical limitations of the blob model, the simulation results are explained with the blob model very well. The agreement is observed for the static properties and the dynamic spring constant of the polymer. A theoretical description of the conditions under which the dynamic spring constant of the polymer is independent of the small number of monomers inside blobs is given. Our results on the limit of applicability of the blob model can be useful in the design of nanotechnology devices.

Translocation of a polymer through a nano-pore is relevant in a variety of contexts such as passage of RNAs through a nuclear pore and transportation of proteins across a membrane. An essential step in polymer translocation is for the end monomers to search the pore. This process requires a characteristic time, referred to as the “attempt time” in this work. Here, we study the attempt time τ of a confined polymer inside a spherical surface by combining a scaling approach and Langevin dynamics simulations. For a moderately to strongly confined polymer, our results suggest that τ ∼ R3.67 for R > P and τ ∼ R2.67 for R < P, where R is the radius of the spherical surface and P is the persistence length of the polymer. All simulation data obtained for an intermediate range of the volume fraction of monomers ϕ(≲ 0.2) tend to collapse onto each other. This implies that τ does not explicitly depend on ϕ, in agreement with the theoretical predictions. These results will be useful for interpreting translocation as a two-step process: the initial attempt to find the pore and eventual pore crossing.

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