Confinement of a Gaussian Chain

2 Confinement of a Gaussian Chain We leam here how a Gaussian chain changes npon confinement by varions geometries such as a slit, a square tube, and a cylindrical tnbe. It is possible to obtain a formula for the partition coefficient in each of the three geometries. 

We first recall that the Ganssian transition probability G(r, r ) given by Eq. 1.34 can be factored into three independent components G Gy, and G, where G is given by 

The partition coefficient is then calcnlated as the average of G z, z N) with respect to z and z  

It is now clear that decreases sharply as / g increases and becomes comparable to d. 

Becanse there is no confinement in the jc and y directions, and Gy do not change. The mean square end-to-end distance does not change its jc and y components. Thns, the chain dimension along the slit wall is given by 

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