Effect of Barriers on Capture Rate

For sufficiently large values of N and the monomer volume fraction in the jammed state higher than about 0.1, f decreases with N, according to Equation 5.31 

The reduction in the free energy barrier with the chain length originates from the entropic pressure created by the confining region to push the chain end in the direction of the pore entrance (Kumar and Muthukumar 2009). This trend is opposite to that of fJ, associated with chain confinement inside the pore. For example, for full confinement within a cylindrical pore of diameter d, f is extensive in N as given by Equation 5.44, 

The effect of entropic barrier on the rate of capture of the polymer by the pore is given by Equation 9.7. In the absence of external flow fields, the flux in the number concentration of the polymer chains is given by the contributions from the diffusion, electrophoretic drift, and the free energy barrier as 

In writing the electrophoretic drift contribution, we have used /r=zA where z is defined in Equation 9.24, and F x) is the free energy in units of ksT (Equation 9.6). 

We now consider the consequences of the above barrier on the steady-state rate of capture of the polymer and probability of its successful transition across the barrier. 

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