We analyze exact analytical partition functions for Gaussian chains near surfaces and interfaces. These partition functions contain the possibility of conformational first-order phase transitions. Such transitions occur when chains are tethered in space and exposed to a local perturbing field. Then the chain can partially escape from the field: the chain transforms from the confined coil to an inhomogeneous flower conformation. The flower consists of a strongly stretched stem and a very weakly deformed crown. A generic phase diagram including one binodal and two spinodal lines is found for three related systems. The height of the barrier between stable and metastable states as well as the dynamics of barrier crossings is discussed.
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