Speeding-up particle simulations of multicomponent polymer systems by coupling to continuum descriptions Marcus M ¨ uller 1 Institute for Theoretical Physics, Georg-August University, 37077 G¨ ottingen, Germany E-mail: mmueller@theorie.physik.uni-goettingen.de The simulation of structure formation by particle-based simulations poses a computational chal- lenge because of (i) the wide spread of time scales or (ii) the presence of free-energy barriers along the transformation path. A prototypical example of the former difficulty of multiple disparate time scales is the simultaneous presence of stiff bonded interactions, defining the molecular architecture of polymer systems and the weak non-bonded interactions, giving rise to macrophase separation or self-assembly in dense multicomponent systems. A characteris- tic illustration of the latter problem are nucleation barriers or metastable intermediate states in the course of morphology transformation. Continuum models, in turn, describe the system by a collective order-parameter field, e.g., the composition, rather than particle coordinates, and often do not suffer from these limitations because (i) the stiff molecular degrees of freedom have been integrated out and (ii) advanced numerical techniques, like the string method, exist that identify free-energy barriers and most probable transition paths. Using field-theoretic um- brella sampling, we determine an approximation of the continuum free-energy functional for a specific particle-based model. We illustrate how (i) the on-the-fly string method can identify the minimal free-energy path for the formation of an hourglass-shaped passage (stalk) between two apposing bilayer membranes and (ii) the continuum free-energy functional can be used in conjunction with a heterogeneous multiscale method (HMM) to speed-up the simulation of Lifshitz-Slyozov coarsening in a binary polymer blend by two orders of magnitude. 1 Soft, coarse-grained particle-based models 1.1 Length, time, and energy scales in multicomponent polymer melts Soft matter and in particular multicomponent polymer systems are characterized by (i) widely disparate time, length and energy scales, (ii) responsiveness to small driving forces, (iii) a multitude of metastable states, and (iv) structural and chemical complexity of the materials. These challenges require a multiscale approach that often relies on the develop- ment and validation of coarse-grained models and the development of new computational strategies. The length, time, and energy scales on the atomic scale, e.g. associated with a cova- lent bond along the backbone of a polymer, are on the order of Angstrom (bond length), sub-picoseconds (molecular vibrations), and electron Volts (bond energy). The scales as- sociated with a polymer molecule are its root mean-squared end-to-end distance, R e that is on the order of tens of nanometers, the time scale to diffuse its own molecular ex- tension, τ ∼ seconds, and the repulsive interaction free energy between different poly- mers in a blend, χNk B T ∼ k B T , where k B T denotes the thermal energy scale, χ the Flory-Huggins parameter, and N the number of effective coarse-grained interactions cen- ters along the molecular contour. Length and time scales associated with the collective dynamics of structure formation, i.e. phase separation in a binary homopolymer blend 1