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Recent developments of microscopic mechanical experiments allow themanipulation of individual polymer molecules in two main ways: \textit{uniform}stretching by external forces and \textit{non-uniform} stretching by externalfields. Many results can be thereby obtained for specific kinds of polymers andspecific geometries. In this work we describe the non-uniform stretching of asingle, non-branched polymer molecule by an external field (e.g. fluid inuniform motion, or uniform electric field) by a universal physical frameworkwhich leads to general conclusions on different types of polymers. We deriveanalytical results both for the freely-jointed chain and the worm-like chainmodels based on classical statistical mechanics. Moreover, we provide a MonteCarlo numerical analysis of the mechanical properties of flexible andsemi-flexible polymers anchored at one end. The simulations confirm theanalytical achievements, and moreover allow to study the situations where thetheory can not provide explicit and useful results. In all cases we evaluatethe average conformation of the polymer and its fluctuation statistics as afunction of the chain length, bending rigidity and field strength.

Theory and Monte Carlo simulations for the stretching of flexible and semi-flexible single polymer chains under external fields