Probability of Successful Translocation

When the polymer gets caught at the pore entrance, it may subsequently penetrate through the barrier into the receiver compartment or it may return to the donor compartment. Let n+(xo) be the probability of successful transit through the barrier, if the polymer is initially at the location x = xq. This problem is discussed in Section 6.6 as a general problem of a stochastic process with finite boundaries. With the polyelectrolyte concentration being very low in the 

The probability distribution of the first passage time and its moments can be obtained from the Fokker-Planck equation for general situations of F x) and i/f (x), by following the standard procedures given in Section 6.6. In the present context, the average translocation time is the mean first passage time, which can be calculated by choosing the appropriate boundary conditions for P(x,t). 

Substitution of Equations 9.50 and 9.51 into Equations 9.67 and 6.68 gives the expression for the probability of successful translocation in terms of the barrier height, 

This result is derived for the initial position of the polymer on the left-hand side of the barrier peak. Analogous result can be derived if polymer is on the right-hand side of the barrier peak. 

The above predictions on the successful capture rate remain untested, except for some preliminary experimental results (Wong and Muthukumar 2010). 

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The above equations for the probability of successful translocation are general for the polymer transit, addressing the conformational attributes and the charged nature of the polyelectrolyte chains. The consequences of these equations for the specific model of Figure 9.7 are the following. 

Figure 9.12 Dependence of the probability of successful translocation on voltage difference. (From Muthukumar, M., J. Chem. Phys., 132, 195101, 2010. With permission.)...

The probability of successful translocation by exiting through the boundary at m = A, without ever reaching the other boundary at m = 0, follows from... 

Hydroprene has proven to be the juvenoid of choice for the control of the major domestic cockroach species. Its success appears to be due to its very high intrinsic activity as compared with most other juvenoids and probably also to its volatility which may allow for a penetration of vapor in inaccessible cockroach harborages. It is likely that hydroprene vapors readily translocate between many household surface materials and thus remain accessible to resident cockroach populations. This volatility of hydroprene could also be a liability for persistence in places with high air displacement. In this case, hydroprene formulated for slow release in a dust (RF 10%) could provide a very persistent residue, albeit without the vapor benefits. 

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