SEB: a computational tool for symbolic derivation of the small-angle scattering from complex composite structures.

Analysis of small-angle scattering (SAS) data requires intensive modeling to infer and characterize the structures present in a sample. This iterative improvement of models is a time-consuming process. Presented here is Scattering Equation Builder (SEB), a C++ library that derives exact analytic expressions for the form factors of complex composite structures. The user writes a small program that specifies how the sub-units should be linked to form a composite structure and calls SEB to obtain an expression for the form factor. SEB supports e.g. Gaussian polymer chains and loops, thin rods and circles, solid spheres, spherical shells and cylinders, and many different options for how these can be linked together. The formalism behind SEB is presented and simple case studies are given, such as block copolymers with different types of linkage, as well as more complex examples, such as a random walk model of 100 linked sub-units, dendrimers, polymers and rods attached to the surfaces of geometric objects, and finally the scattering from a linear chain of five stars, where each star is built up of four diblock copolymers. These examples illustrate how SEB can be used to develop complex models and hence reduce the cost of analyzing SAS data.

Multiscale equilibration of highly entangled isotropic model polymer melts.

We present a computationally efficient multiscale method for preparing equilibrated, isotropic long-chain model polymer melts. As an application, we generate Kremer-Grest melts of 1000 chains with 200 entanglements and 25 000-2000 beads/chain, which cover the experimentally relevant bending rigidities up to and beyond the limit of the isotropic-nematic transition. In the first step, we employ Monte Carlo simulations of a lattice model to equilibrate the large-scale chain structure above the tube scale while ensuring a spatially homogeneous density distribution. We then use theoretical insight from a constrained mode tube model to introduce the bead degrees of freedom together with random walk conformational statistics all the way down to the Kuhn scale of the chains. This is followed by a sequence of simulations with carefully parameterized force-capped bead-spring models, which slowly introduce the local bead packing while reproducing the larger-scale chain statistics of the target Kremer-Grest system at all levels of force-capping. Finally, we can switch to the full Kremer-Grest model without perturbing the structure. The resulting chain statistics is in excellent agreement with literature results on all length scales accessible in brute-force simulations of shorter chains.

Dynamics of dense hard sphere colloidal systems: A numerical analysis.

The applicability to dense hard sphere colloidal suspensions of a general coarse-graining approach called Record Dynamics (RD) is tested by extensive molecular dynamics simulations. We reproduce known results as logarithmic diffusion and the logarithmic decay of the average potential energy per particle. We provide quantitative measures for the cage size and identify the displacements of single particles corresponding to intermittent cage breakings. We then partition the system into spatial domains and show that, within each domain, a subset of such intermittent events called quakes constitutes a log-Poisson process, as predicted by RD. Specifically, quakes are shown to be statistically independent and Poisson distributed with an average depending on the logarithm of time. Finally, we discuss the nature of the dynamical barriers surmounted by quakes and link RD to the phenomenology of aging hard sphere colloids.

Multiscale approach to equilibrating model polymer melts.

We present an effective and simple multiscale method for equilibrating Kremer Grest model polymer melts of varying stiffness. In our approach, we progressively equilibrate the melt structure above the tube scale, inside the tube and finally at the monomeric scale. We make use of models designed to be computationally effective at each scale. Density fluctuations in the melt structure above the tube scale are minimized through a Monte Carlo simulated annealing of a lattice polymer model. Subsequently the melt structure below the tube scale is equilibrated via the Rouse dynamics of a force-capped Kremer-Grest model that allows chains to partially interpenetrate. Finally the Kremer-Grest force field is introduced to freeze the topological state and enforce correct monomer packing. We generate 15 melts of 500 chains of 10.000 beads for varying chain stiffness as well as a number of melts with 1.000 chains of 15.000 monomers. To validate the equilibration process we study the time evolution of bulk, collective, and single-chain observables at the monomeric, mesoscopic, and macroscopic length scales. Extension of the present method to longer, branched, or polydisperse chains, and/or larger system sizes is straightforward.

Generating minimal living systems from non-living materials and increasing their evolutionary abilities.

We review lessons learned about evolutionary transitions from a bottom-up construction of minimal life. We use a particular systemic protocell design process as a starting point for exploring two fundamental questions: (i) how may minimal living systems emerge from non-living materials? and (ii) how may minimal living systems support increasingly more evolutionary richness? Under (i), we present what has been accomplished so far and discuss the remaining open challenges and their possible solutions. Under (ii), we present a design principle we have used successfully both for our computational and experimental protocellular investigations, and we conjecture how this design principle can be extended for enhancing the evolutionary potential for a wide range of systems.This article is part of the themed issue 'The major synthetic evolutionary transitions'.

A formalism for scattering of complex composite structures. II. Distributed reference points.

Recently, we developed a formalism for the scattering from linear and acyclic branched structures build of mutually non-interacting sub-units. [C. Svaneborg and J. S. Pedersen, J. Chem. Phys. 136, 104105 (2012)] We assumed each sub-unit has reference points associated with it. These are well-defined positions where sub-units can be linked together. In the present paper, we generalize the formalism to the case where each reference point can represent a distribution of potential link positions. We also present a generalized diagrammatic representation of the formalism. Scattering expressions required to model rods, polymers, loops, flat circular disks, rigid spheres, and cylinders are derived, and we use them to illustrate the formalism by deriving the generic scattering expression for micelles and bottle-brush structures and show how the scattering is affected by different choices of potential link positions and sub-unit choices.

A formalism for scattering of complex composite structures. I. Applications to branched structures of asymmetric sub-units.

We present a formalism for the scattering of an arbitrary linear or acyclic branched structure build by joining mutually non-interacting arbitrary functional sub-units. The formalism consists of three equations expressing the structural scattering in terms of three equations expressing the sub-unit scattering. The structural scattering expressions allow composite structures to be used as sub-units within the formalism itself. This allows the scattering expressions for complex hierarchical structures to be derived with great ease. The formalism is generic in the sense that the scattering due to structural connectivity is completely decoupled from internal structure of the sub-units. This allows sub-units to be replaced by more complex structures. We illustrate the physical interpretation of the formalism diagrammatically. By applying a self-consistency requirement, we derive the pair distributions of an ideal flexible polymer sub-unit. We illustrate the formalism by deriving generic scattering expressions for branched structures such as stars, pom-poms, bottle-brushes, and dendrimers build out of asymmetric two-functional sub-units.

Stress relaxation in entangled polymer melts.

We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, G(t), into the plateau regime for chains with Z=40 entanglements and into the terminal relaxation regime for Z=10. Using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the microscopic topological state of our systems, we have performed parameter-free tests of several different tube models. We find excellent agreement for the Likhtman-McLeish theory using the double reptation approximation for constraint release, if we remove the contribution of high-frequency modes to contour length fluctuations of the primitive chain.

Microphase separation in cross-linked polymer blends. Efficient replica RPA post-processing of simulation data for homopolymer networks.

We investigate the behaviour of randomly cross-linked (co)polymer blends using a combination of replica theory and large-scale molecular dynamics simulations. In particular, we derive the analogue of the random phase approximation for systems with quenched disorder and show how the required correlation functions can be calculated efficiently. By post-processing simulation data for homopolymer networks we are able to describe neutron scattering measurements in heterogeneous systems without resorting to microscopic detail and otherwise unphysical assumptions. We obtain structure function data which illustrate the expected microphase separation and contain system-specific information relating to the intrinsic length scales of our networks.

Rheology and microscopic topology of entangled polymeric liquids.

The viscoelastic properties of high molecular weight polymeric liquids are dominated by topological constraints on a molecular scale. In a manner similar to that of entangled ropes, polymer chains can slide past but not through each other. Tube models of polymer dynamics and rheology are based on the idea that entanglements confine a chain to small fluctuations around a primitive path that follows the coarse-grained chain contour. Here we provide a microscopic foundation for these highly successful phenomenological models. We analyze the topological state of polymeric liquids in terms of primitive paths and obtain parameter-free, quantitative predictions for the plateau modulus, which agree with experiment for all major classes of synthetic polymers.

Strain-dependent localization, microscopic deformations, and macroscopic normal tensions in model polymer networks.

We use molecular dynamics simulations to investigate the microscopic and macroscopic response of model polymer networks to uniaxial elongations. By studying networks with strand lengths ranging from N(s)=20 to 200 we cover the full crossover from cross-link to entanglement dominated behavior. Our results support a recent version of the tube model which accounts for the different strain dependence of chain localization due to chemical cross-links and entanglements.