Schematic representation of the 1D random-walk model that is used to represent the polymer translocation process. This example shows a chain with monomers with size moving through a channel with length with monomers on the cis side, monomers inside the pore, and monomers on the trans side. At each MC step, the chain moves according to the probabilities given by Eqs. (1) and (2), while the time duration of that step is given by Eq. (5). The properties of monomers and can differ via the charge parameter or the friction constants , , and .
[(a)–(f)] The mean translocation times obtained for each of the 256 possible arrangements of eight monomers of type or . The linear charge density of the monomers is always set to 1, while the ratio changes for each graph. The external field is set to . The axis represents the fraction of monomers in the chain, while the axis gives the mean translocation time. The broken lines join the average translocation times for each of the nine different values of . (g) From top to bottom, the broken lines are, in order, from graph (a) to (f).
Translocation probabilities from the cis side to the trans side for each of the 256 possibles arrangements of eight monomers of type or with , , and as a function of the fraction of monomers. The broken line joins the average translocation probabilities obtained for each of the nine different values of .
(a) The 256 different mean translocation times (top) repeated from Fig. 2(e), together with the 256 corresponding standard deviations (bottom). The conditions are , , and . (b) Correlation between the mean translocation time and its standard deviation for the six conditions studied in Fig. 2. The gray circles correspond to the data of Fig. 2(a), while the five other sets are shown as small black points.
Mean translocation times for the 256 combinations of eight monomers for three different values of the external field (with and ). The broken lines are obtained as described in Fig. 2.
Mean translocation times as a function of the scaled external field for the eight possible chains of eight monomers with only one monomer . We used the conditions and . In the limit of a large external field, the fastest translocating sequence is , which is followed by .
Mean translocation times as a function of the mixing parameter for chains with length monomers, with , , and . Data for three different values of the charge density ratio are shown. The factor represents the number of bonds in the block copolymer sequence. The largest value of corresponds to the alternating sequence.
Mean translocation time for all possible chain sequences, where , , and are integers. The value is set to 0.5 while the charge density ratio is given by (the ratio of the applied forces used by Luo et al. was equal to . The solid line joins all the results for which and/or .
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