Effect of the contour length fluctuation on reptation

If the contour length fluctuation is neglected, the disengagement time is estimated as the time necessary for the chain to move the distance L, 

Precise calculation of requires the first passage problem in multidimensional phase space. A variational calculation for the Rouse model shows that X is larger that 1.47. Hence the effect of the contour length fluctuation is significant even if Z is as large as 100. 

The effect of the contour length fluctuation has been studied for slightly different models and it has been reported that the effect is less significant than in the case of the Rouse model. The discrepancy is perhaps due to the difference in the dynamics of the fluctuation, especially the short-time dynamics, which is quite important in the first passage time problem. 

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