Compression of a polymer chain by a small obstacle: the effect of fluctuations on the escape transition

We describe the escape transition of an ideal chain compressed between finite-sized obstacles. Three different theoretical methods are used and each provides a similar description of the escape transition, as predicted by earlier and less detailed mean-field theories. The first two methods show that thermal fluctuations near the transition can blur what was previously described as a sharp transition. The last method is an exact calculation of the partition function that shows unambiguously the character of the escape transition. This exact calculation overcomes the inherent uncertainties associated with previous theory and computer simulation.