Activated barrier crossing of macromolecules at a submicron-size entropic trap

Abstract

We study the thermally activated barrier crossing by long chain molecules, initially confined to one side of an entropic trap. The entropic barrier is assumed to be of Kramers type. The barrier width is considered to be larger than the chain. The latter is in turn assumed to be long enough, so that a continuum description of the chain is applicable throughout the space. The barrier crossing rate is calculated using multidimensional Kramers theory and the functional integral method. For chains having the same total number of segments, the activation energy itself remains constant. However, the preexponential factor depends on the structure of the polymer. Polymers with the same molecular weight but having longer arms can effect larger fluctuations, thereby increasing its chance to cross the barrier. This leads to an almost exponential increase of the rate prefactor with the radius of gyration. The difference in the barrier crossing rates could be effectively exploited for the separation of molecules having architectural differences, for example, DNA of same length but different degrees of supercoiling. This is illustrated by considering star polymers. The Rouse-Ham model is used to analyze the mechanism of the barrier crossing. We show how the rate expression of the Arrhenius type is affected by the long arms of the star chain.

Efficient dynamical correction of the transition state theory rate estimate for a flat energy barrier

“…[20][21][22][23][24][25][26][27] Experimental examples of systems of this sort include polymer translocation, 28,29 where a polymer is crossing a membrane through a pore 30 or narrow µm-scale channels with traps. 31 Recent experiments by Liu et al involve the escape of a DNA molecule from an entropic cage.…”

Force applied to a single molecule at a single nanogate molecule filter

“…[1][2][3][4] Molecular separation systems based on this unique molecular motion have recently received considerable attention because of their higher performance, novel separation mechanism and possibility of miniaturizing a separation device driven by ultra-small energy. [5][6][7] The Brownian ratchet, [7][8][9] entropic trap 5,6,10 and Ogston sieve 11,12 are typical examples that have been proposed based on molecular manipulation in small spaces. However, the fact that they are based on electrophoresis is an important disadvantage to these procedures because an uncharged molecule cannot be manipulated.…”