We present a study of equilibrium chain-exchange kinetics of a well-defined model system for starlike polymeric micelles. The results show that the kinetics follows a logarithmic time dependence. The same feature has been confirmed for two other micellar systems. This is in sharp contrast to theoretical predictions and hints towards strongly coupled chain dynamics within the micellar cores induced by geometrical constraints. DOI: 10.1103/PhysRevLett.96.068302 PACS numbers: 82.70.Uv, 61.12.Ex, 61.25.Hq, 82.35.Lr Polymeric micelles are macromolecular analogues of well-known low-molecular surfactant micelles. As a consequence of random stochastic forces, the constituting chains will continuously exchange between the micelles. From the theory of Halperin and Alexander (HA), this exchange kinetics is expected to be dominated by a simple expulsion or insertion mechanism where single chains (unimers) are required to overcome a defined potential barrier [1]. Higher order kinetics including fusion and fission is not expected to take place since these mechanisms are neither favored energetically nor entropically [1,2]. Experimentally, relatively few studies have been devoted to the exchange kinetics of polymeric micelles in equilibrium. This is most likely related to the associated experimental difficulties. Two principal types of methods have mainly been used: fluorescence quench spectroscopy [3][4][5] and temperature jump techniques [6]. However, both types of experiments generally require a significant perturbation to the equilibrium as either bulky chemical labels or strong temperature jumps are required. Nevertheless, results from fluorescence quench experiments seem to indicate a distribution of rate constants which is in contradiction to the single expulsion rate predicted in the HA model. The reason for these deviations is unknown, but speculations include the presence of bulky labels [3,5] and several kinetic mechanisms such as micellar fusion or fission [4,7] or concerted chain insertion [7]. However, since the latter mechanisms would occur in parallel, it is not immediately clear why this should lead to a large separation in the time scale.In this Letter we demonstrate that the equilibrium exchange kinetics of starlike poly(ethylene-propylene)-poly(ethylene oxide) (PEP1-PEO20, the numbers indicate the molecular weight in kg=mol) micelles can be described by a logarithmic time dependence. Logarithmic relaxation has been encountered in several physical situations such as in relaxation experiments on glasses [8], friction experiments [9], protein folding [10], and local dynamics of DNA [11]. In all cases the behavior is attributed to either a broadly distributed single mode or strongly coupled dynamics. Here we will show that such logarithmic relaxation can also be found for two further micellar systems, suggesting a general phenomenon. This behavior most likely stems from strong chain correlations within the confinement of the micellar cores.In this study we used a newly developed time resolved small angle ne...