We investigate the dynamics of pore-driven polymer translocation by theoretical analysis and molecular dynamics (MD) simulations. Using the tension propagation theory within the constant flux approximation we derive an explicit equation of motion for the tension front. From this we derive a scaling relation for the average translocation time τ , which captures the asymptotic result τ ∝ N 1+ν 0 , where N0 is the chain length and ν is the Flory exponent. In addition, we derive the leading correction-to-scaling term to τ and show that all terms of order N 2ν 0

Monopolar charge disorder effects are studied in the context of fluctuation-induced interactions between neutral dielectric slabs. It is shown that quenched bulk charge disorder gives rise to an additive contribution to the net interaction force which decays as the inverse distance between the slabs and may thus completely mask the standard Casimir-van der Waals force at large separations. By contrast, annealed (bulk or surface) charge disorder leads to a net interaction force whose large-distance behavior agrees with the universal Casimir force between ideal conductors, which scales as the inverse cubic distance, and the dielectric properties enter only in the subleading corrections.

We investigate the effect of monopolar charge disorder on the classical fluctuation-induced interactions between randomly charged net-neutral dielectric slabs and discuss various generalizations of recent results [A. Naji et al., Phys. Rev. Lett. 104, 060601 (2010)] to highly inhomogeneous dielectric systems with and without statistical disorder correlations. We shall focus on the specific case of two generally dissimilar plane-parallel slabs, which interact across vacuum or an arbitrary intervening dielectric medium. Monopolar charge disorder is considered to be present on the bounding surfaces and/or in the bulk of the slabs, may be in general quenched or annealed and may possess a finite lateral correlation length reflecting possible "patchiness" of the random charge distribution. In the case of quenched disorder, the bulk disorder is shown to give rise to an additive long-range contribution to the total force, which decays as the inverse distance between the slabs and may be attractive or repulsive depending on the dielectric constants of the slabs. By contrast, the force induced by annealed disorder in general combines with the underlying van der Waals forces in a nonadditive fashion, and the net force decays as an inverse cube law at large separations. We show, however, that in the case of two dissimilar slabs, the net effect due to the interplay between the disorder-induced and the pure van der Waals interactions can lead to a variety of unusual nonmonotonic interaction profiles between the dielectric slabs. In particular, when the intervening medium has a larger dielectric constant than the two slabs, we find that the net interaction can become repulsive and exhibit a potential barrier, while the underlying van der Waals force is attractive. On the contrary, when the intervening medium has a dielectric constant between that of the two slabs, the net interaction can become attractive and exhibit a free energy minimum, while the pure van der Waals force is repulsive. Therefore, the charge disorder, if present, can drastically alter the effective interaction between net-neutral objects.

We study the driven translocation of a semi-flexible polymer through a nanopore by means of a modified version of the iso-flux tension propagation theory, and extensive molecular dynamics (MD) simulations. We show that in contrast to fully flexible chains, for semi-flexible polymers with a finite persistence length the trans side friction must be explicitly taken into account to properly describe the translocation process. In addition, the scaling of the end-to-end distance R N as a function of the chain length N must be known. To this end, we first derive a semi-analytic scaling form for R N, which reproduces the limits of a rod, an ideal chain, and an excluded volume chain in the appropriate limits. We then quantitatively characterize the nature of the trans side friction based on MD simulations. Augmented with these two factors, the theory shows that there are three main regimes for the scaling of the average translocation time τ ∝ N α. In the rod , Gaussian and excluded volume chain  ≫ 10 6 limits, α = 2, 3/2 and 1 + ν, respectively, where ν is the Flory exponent. Our results are in good agreement with available simulations and experimental data.

We found out that, in several places in our paper, the reference to the results by G. Gómez-Santos [Phys. Rev. B 80, 245424 (2009)] (Ref. 39 in the paper) is made erroneously. Table I and its captions should be corrected as follows.On p. 5, left column, the last paragraph should read: "We can gain some understanding of these regimes by comparing with various previous calculations in the two-layer geometry. For vanishing separations, the n = 5/2 regime, seen here, has also been observed between thin ideal metallic layers at zero temperature. 33,38 Our doped graphene sheet results would, thus, indicate that the dependence of the vdW-Casimir interactions' free energy on the separation could be rationalized in terms of interactions between thin ideal metallic sheets. The n = 2 regime for asymptotically large separations corresponds to the zero-frequency Matsubara term and has the same scaling form as the finite-temperature vdW-Casimir interaction between two metallic sheets at large separations and has also been detected in the case of two graphene sheets at finite temperatures 39 . . .."On p. 8, left column, the last paragraph should be replaced with: "At vanishingly small separations, the free energy shows the n = 5/2 scaling, whereas, for larger spacings, it shows a scaling exponent n = 3, approaching the n → 2 limit for asymptotically large separations. The changes in the slope appear to occur at the same values of the interlayer spacing when the electron density decreases (compare dashed and solid curves). Both the n = 5/2 scaling for small separations as well as the n = 2 scaling for large separations suggest, again, that the doped graphene sheet behaves in a similar way as an ideal metallic layer."On p. 12, left column, the second paragraph should be replaced with: "Gómez-Santos, in his paper on the thermal van der Waals interaction between graphene sheets, 39 gives several results that are consistent with our calculations where such a comparison makes sense. For two graphene sheets at zero temperature or finite temperature and small separations b ξ T , Gómez-Santos gets n = 3, which is exactly the same as derived by Dobson et al. 38 and is completely consistent with our Fig. 2 for two undoped graphene sheets. For finite temperatures and large separations b ξ T , we find n = 4 for undoped graphene, however, as noted above, finite-temperature effects are expected to play a role in this regime, and the presence of thermally excited charge carriers (electrons and holes), when accounted for, leads to an exponent similar to the doped case with n = 2 (Fig. 3) as shown by Gómez-Santos 39 and by Fialkovsky et al. 41 for a graphene layer apposed to a perfect conductor sheet."On p. 12 and in the last paragraph, the citation for Ref. 39 should be omitted. The above changes only affect the way we cite Ref. 39 in our paper and do not concern our results and conclusions. We also emphasize (as in our paper on p. 11) that our focus in this paper is ". . .on the direct temperature effects as given by the finite-temperature L...

We develop a theory for polymer translocation driven by a time-dependent force through an oscillating nanopore. To this end, we extend the iso-flux tension propagation theory [Sarabadani et al., J. Chem. Phys. 141, 214907 (2014)] for such a setup. We assume that the external driving force in the pore has a component oscillating in time, and the flickering pore is similarly described by an oscillating term in the pore friction. In addition to numerically solving the model, we derive analytical approximations that are in good agreement with the numerical simulations. Our results show that by controlling either the force or pore oscillations, the translocation process can be either sped up or slowed down depending on the frequency of the oscillations and the characteristic time scale of the process. We also show that while in the low and high frequency limits, the translocation time τ follows the established scaling relation with respect to chain length N0, in the intermediate frequency regime small periodic, fluctuations can have drastic effects on the dynamical scaling. The results can be easily generalized for non-periodic oscillations and elucidate the role of time dependent forces and pore oscillations in driven polymer translocation.

We consider the translocation dynamics of a polymer chain forced through a nanopore by an external force on its head monomer on the trans side. For a proper theoretical treatment we generalize the iso-flux tension propagation (IFTP) theory to include friction arising from the trans side subchain. The theory reveals a complicated scenario of multiple scaling regimes depending on the configurations of the cis and the trans side subchains. In the limit of high driving forces f such that the trans subchain is strongly stretched, the theory is in excellent agreement with molecular dynamics simulations and allows an exact analytic solution for the scaling of the translocation time τ as a function of the chain length N0 and f . In this regime the asymptotic scaling exponents for τ ∼ N α 0 f β are α = 2, and β = −1. The theory reveals significant correction-to-scaling terms arising from the cis side subchain and pore friction, which lead to a very slow approach to α = 2 from below as a function of increasing N0.

We review recent progress on the theory of dynamics of polymer translocation through a nanopore based on the iso-flux tension propagation (IFTP) theory. We investigate both pore-driven translocation of flexible and a semi-flexible polymers, and the end-pulled case of flexible chains by means of the IFTP theory and extensive molecular dynamics (MD) simulations. The validity of the IFTP theory can be quantified by the waiting time distributions of the monomers which reveal the details of the dynamics of the translocation process. The IFTP theory allows a parameter-free description of the translocation process and can be used to derive exact analytic scaling forms in the appropriate limits, including the influence due to the pore friction that appears as a finite-size correction to asymptotic scaling. We show that in the case of pore-driven semi-flexible and end-pulled polymer chains the IFTP theory must be augmented with an explicit trans side friction term for a quantitative description of the translocation process.