Stretch transition in a polymer brush

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Abstract
The behavior of a grafted chain of length K inside an otherwise monodispersed (of length N) polymer brush is investigated. For the case of K≤N, the stretching of the chain increases abruptly as K approaches N, analogous to the coil-stretch transition. By generalizing previous results, we derive the scaling forms for the stretching parameter and its mean square fluctuations. We also extend our investigation to the K>N regime and obtain results for the stretching parameter by scaling calculations. We show that the chain is maximally stretched as K→N from above. Furthermore, we perform a Monte Carlo simulation using the bond-fluctuation model to study the chain end position and its fluctuations. Our data indicate that both the stretching of the chain and its fluctuation are maximal at K=N and the system exhibits a first-order phase transition. The scaling form for the stretching parameter is verified and the scaling function is obtained.