arXiv subjects

Friederike Schmid

Publications and source records attributed to Friederike Schmid.

At least 55 records · Page 3Linked to original sources

arXiv2018

Generalized Langevin dynamics: Construction and numerical integration of non-Markovian particle-based models

We propose a generalized Langevin dynamics (GLD) technique to construct non-Markovian particle-based coarse-grained models from fine-grained reference simulations and to efficiently integrate them. The proposed GLD model has the form of a discretized generalized Langevin equation with distance-dependent two-particle contributions to the self- and pair-memory kernels. The memory kernels are iteratively reconstructed from the dynamical correlation functions of an underlying fine-grained system. We develop a simulation algorithm for this class of non-Markovian models that scales linearly with the number of coarse-grained particles. Our GLD method is suitable for coarse-grained studies of systems with incomplete time scale separation, as is often encountered, e.g., in soft matter systems. We apply the method to a suspension of nanocolloids with frequency-dependent hydrodynamic interactions. We show that the results from GLD simulations perfectly reproduce the dynamics of the underlying fine-grained system. The effective speedup of these simulations amounts to a factor of about $10^4$. Additionally, the transferability of the coarse-grained model with respect to changes of the nanocolloid density is investigated. The results indicate that the model is transferable to systems with nanocolloid densities that differ by up to one order of magnitude from the density of the reference system.

cond-mat.soft↗

arXiv2018

Frequency-dependent Hydrodynamic Interaction Between Two Solid Spheres

Hydrodynamic interactions play an important role in many areas of soft matter science. In simulations with implicit solvent, various techniques such as Brownian or Stokesian dynamics explicitly include hydrodynamic interactions a posteriori by using hydrodynamic diffusion tensors derived from the Stokes equation. However, this equation assumes the interaction to be instantaneous which is an idealized approximation and only valid on long time scales. In the present paper, we go one step further and analyze the time-dependence of hydrodynamic interactions in a compressible fluid on the basis of the linearized Navier-Stokes equation. The theoretical results show that the compressibility of the fluid has a significant impact on frequency-dependent pair interactions. The predictions of the hydrodynamic theory are compared to molecular dynamics simulations of two solid spheres in a Lennard-Jones fluid. For this system we reconstruct memory functions by extending the inverse Volterra technique. The simulation data agree very well with the theory, therefore, the theory can be used to implement dynamically consistent hydrodynamic interactions in the increasingly popular field of non-Markovian modeling.

cond-mat.soft↗

arXiv2018

Poly-Sarcosine and Poly(ethylene-glycol) interactions with proteins investigated using molecular dynamics simulations

Nanoparticles coated with hydrophilic polymers often show a reduction in unspecific interactions with the biological environment, which improves their biocompatibility. The molecular determinants of this reduction are not very well understood yet, and their knowledge may help improving nanoparticle design. Here we address, using molecular dynamics simulations, the interactions of human serum albumin, the most abundant serum protein, with two promising hydrophilic polymers used for the coating of therapeutic nanoparticles, poly(ethylene-glycol) and poly-sarcosine. By simulating the protein immersed in a polymer-water mixture, we show that the two polymers have a very similar affinity for the protein surface, both in terms of the amount of polymer adsorbed and also in terms of the type of amino acids mainly involved in the interactions. We further analyze the kinetics of adsorption and how it affects the polymer conformations. Minor differences between the polymers are observed in the thickness of the adsorption layer, that are related to the different degree of flexibility of the two molecules. In comparison poly-alanine, an isomer of poly-sarcosine known to self-aggregate and induce protein aggregation, shows a significantly larger affinity for the protein surface than PEG and PSar, which we show to be related not to a different patterns of interactions with the protein surface, but to the different way the polymer interacts with water.

cond-mat.soft↗

arXiv2018

Curvature as a guiding field for patterns in thin block copolymer films

Experimental data on thin films of cylinder-forming block copolymers (BC) -- free-standing BC membranes as well as supported BC films -- strongly suggest that the local orientation of the BC patterns is coupled to the geometry in which the patterns are embedded. We analyze this phenomenon using general symmetry considerations and numerical self-consistent field studies of curved BC films in cylindrical geometry. The stability of the films against curvature-induced dewetting is also analyzed. In good agreement with experiments, we find that the BC cylinders tend to align along the direction of curvature at high curvatures. At low curvatures, we identify a transition from perpendicular to parallel alignment in supported films, which is absent in free standing membranes. Hence both experiments and theory show that curvature can be used to manipulate and align BC patterns.

cond-mat.soft↗

arXiv2018

Simulating Copolymeric Nanoparticle Assembly in the Co-solvent Method: How Mixing Rates Control Final Particle Sizes and Morphologies

The self-assembly of copolymeric vesicles and micelles in micromixers is studied by External Potential Dynamics (EPD) simulations -- a dynamic density functional approach that explicitly accounts for the polymer architecture both at the level of thermodynamics and dynamics. Specifically, we focus on the co-solvent method, where nanoparticle precipitation is triggered by mixing a poor co-solvent into a homogeneous copolymer solution in a micromixer. Experimentally, it has been reported that the flow rate in the micromixers influences the size of the resulting particles as well as their morphology: At small flow rates, vesicles dominate; with increasing flow rate, more and more micelles form, and the size of the particles decreases. Our simulation model is based on the assumption that the flow rate mainly sets the rate of mixing of solvent and co-solvent. The simulations reproduce the experimental observations at an almost quantitative level and provide insight into the underlying physical mechanisms: First, they confirm an earlier conjecture according to which the size control takes place in the earliest stage of the particle self-assembly, during the spinodal decomposition of polymers and solvent. Second, they reveal a crossover between different morphological regimes as a function of mixing rate. Hence they demonstrate that varying the mixing rate in a co-solvent setup is an effective way to control two key properties of drug delivery systems, their mean size and their morphology.

cond-mat.soft↗

arXiv2018

Self-assembly of polymeric particles in Poiseuille flow: A hybrid Lattice Boltzmann / External Potential Dynamics simulation study

We present a hybrid simulation method which allows one to study the dynamical evolution of self-assembling (co)polymer solutions in the presence of hydrodynamic interactions. The method combines an established dynamic density functional theory for polymers that accounts for the nonlocal character of chain dynamics at the level of the Rouse model, the external potential dynamics (EPD) model, with an established Navier-Stokes solver, the Lattice Boltzmann (LB) method. We apply the method to study the self-assembly of nanoparticles and vesicles in two-dimensional copolymer solutions in a typical microchannel Poiseuille flow profile. The simulations start from fully mixed systems which are suddenly quenched below the spinodal line. In order to isolate effects caused by walls, we use a reverse Poiseuille flow geometry with periodic boundary conditions. We identify three stages of self assembly, i.e., initial spinodal decomposition, particle nucleation, and particle growth (ripening). We find that (i) In the presence of shear, the nucleation of droplets is delayed by an amount roughly proportional to the shear rate, (ii) Shear flow greatly increases the rates of particle fusions, (iii) in later stages of self-assembly, stronger shear flows may induce irreversible shape transformation {\em via} finger formation, in particular in vesicle systems. The combination of these effects lead to an accumulation of particles close to the center of the Poiseuille flow profile, and the polymeric matter has a double peak distribution centered around the flow maximum.

cond-mat.soft↗

arXiv2018

Modeling size controlled nanoparticle precipitation with the co-solvency method by spinodal decomposition

The co-solvency method is a method for the size controlled preparation of nanoparticles like polymersomes, where a poor co-solvent is mixed into a homogeneous copolymer solution to trigger precipitation of the polymer. The size of the resulting particles is determined by the rate of co-solvent addition. We use the Cahn-Hilliard equation with a Flory-Huggins free energy model to describe the precipitation of a polymer under changing solvent quality by applying a time dependent Flory-Huggins interaction parameter. The analysis focuses on the characteristic size R of polymer aggregates that form during the initial spinodal decomposition stage, and especially on how R depends on the rate s of solvent quality change. Both numerical results and a perturbation analysis predict a power law dependence $R \sim s^{-1/6}$, which is in agreement with power laws for the final particle sizes that have been reported from experiments and molecular dynamics simulations. Hence, our model results suggest that the nanoparticle size in size-controlled precipitation is essentially determined during the spinodal decomposition stage.

cond-mat.soft↗

arXiv2018

Anomalous Critical Slowdown at a First Order Phase Transition in Single Polymer Chains

Using Brownian Dynamics, we study the dynamical behavior of a polymer grafted onto an adhesive surface close to the mechanically induced adsorption-stretching transition. Even though the transition is first order, (in the infinite chain length limit, the stretching degree of the chain jumps discontinuously), the characteristic relaxation time is found to grow according to a power law as the transition point is approached. We present a dynamic effective interface model which reproduces these observations and provides an excellent quantitaive description of the simulations data. The generic nature of the theoretical model suggests that the unconventional mixing of features that are characteristic for first-order transitions (a jump in an order parameter) and features that are characteristic of critical points (anomalous slowdown) may be a common phenomenon in force-driven phase transitions of macromolecules.

cond-mat.soft↗

arXiv2018

Phase transitions in single macromolecules: loop-stretch transition versus loop adsorption transition in end-grafted polymer chains

We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. One is the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter $\varepsilon$, and the other is the loop-stretch transition in a chain with one end attached to a repulsive substrate, driven by an external end-force $F$ applied to the free end. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption transition, and the mean position of the chain end in the case of the loop-stretch transition. Close to the transition points, both the static and the dynamic behavior of chains with different length $N$ are very well described by a scaling Ansatz with the scaling parameters $(\varepsilon - \varepsilon^*) N^ϕ$ (adsorption transition) and $(F-F^*) N^ν$ (loop-stretch transition), respectively, where $ϕ$ is the crossover exponent of the adsorption transition, and $ν$ the Flory exponent. We show that both the loop-stretch and the loop adsorption transitions provide an exceptional opportunity to construct explicit analytical expressions for the crossover functions which perfectly describe all simulation results on static properties in the finite-size scaling regime. Explicit crossover functions are based on the Ansatz for the analytical form of the order parameter distributions at the respective transition points. In contrast to the close similarity in equilibrium static behavior, the dynamic relaxation at the two transitions shows qualitative differences, especially in the strongly ordered regimes.

cond-mat.soft↗

arXiv2017

Critical behavior of active Brownian particles

We study active Brownian particles as a paradigm for genuine non-equilibrium phase transitions. Access to the critical point in computer simulations is obstructed by the fact that the density is conserved. We propose a modification of sampling finite-size fluctuations and successfully test this method for the 2D Ising model. Using this model allows us to determine accurately the critical point of two dimensional active Brownian particles at $\text{Pe}_{\text{cr}}=40(2)$, $ϕ_{\text{cr}}=0.597(3)$. Based on this estimate, we study the corresponding critical exponents $β$, $γ/ν$, and $ν$. Our results are incompatible with the 2D-Ising exponents, thus raising the question whether there exists a corresponding non-equilibrium universality class.

cond-mat.soft↗

arXiv2017

Dynamic density functional theories for inhomogeneous polymer systems compared to Brownian dynamics simulations

Dynamic density functionals (DDFs) are popular tools for studying the dynamical evolution of inhomogeneous polymer systems. Here, we present a systematic evaluation of a set of diffusive DDF theories by comparing their predictions with data from particle-based Brownian dynamics (BD) simulations for two selected problems: Interface broadening in compressible A/B homopolymer blends after a sudden change of the incompatibility parameter, and microphase separation in compressible A:B diblock copolymer melts. Specifically, we examine (i) a local dynamics model, where monomers are taken to move independently from each other, (ii) a nonlocal "chain dynamics" model, where monomers move jointly with correlation matrix given by the local chain correlator, and (iii,iv) two popular approximations to (ii), namely (iii) the Debye dynamics model, where the chain correlator is approximated by its value in a homogeneous system, and (iv) the computationally efficient "external potential dynamics" (EPD) model. With the exception of EPD, the value of the compressibility parameter has little influence on the results. In the interface broadening problem, the chain dynamics model reproduces the BD data best. However, the closely related EPD model produces large spurious artefacts. These artefacts disappear when the blend system becomes incompressible. In the microphase separation problem, the predictions of the nonlocal models (ii-iv) agree with each other and significantly overestimate the ordering time, whereas the local model (i) underestimates it. We attribute this to the multiscale character of the ordering process, which involves both local and global chain rearrangements. To account for this, we propose a mixed local/nonlocal DDF scheme which quantitatively reproduces all BD simulation data considered here.

cond-mat.soft↗

arXiv2017

Iterative Reconstruction of Memory Kernels

In recent years, it has become increasingly popular to construct coarse-grained models with non-Markovian dynamics to account for an incomplete separation of time scales. One challenge of a systematic coarse-graining procedure is the extraction of the dynamical properties, namely, the memory kernel, from equilibrium all-atom simulations. In this article, we propose an iterative method for memory reconstruction from dynamical correlation functions. Compared to previously proposed noniterative techniques, it ensures by construction that the target correlation functions of the original fine-grained systems are reproduced accurately by the coarse-grained system, regardless of time step and discretization effects. Furthermore, we also propose a new numerical integrator for generalized Langevin equations that is significantly more accurate than the more commonly used generalization of the velocity Verlet integrator. We demonstrate the performance of the above-described methods using the example of backflow-induced memory in the Brownian diffusion of a single colloid. For this system, we are able to reconstruct realistic coarse-grained dynamics with time steps about 200 times larger than those used in the original molecular dynamics simulations.

cond-mat.soft↗

arXiv2017

Hybrid Particle-Continuum Simulations Coupling Brownian Dynamics and Local Dynamic Density Functional Theory

We present a multiscale hybrid particle-field scheme for the simulation of relaxation and diffusion behavior of soft condensed matter systems. It combines particle-based Brownian dynamics and field-based local dynamics in an adaptive sense such that particles can switch their level of resolution on the fly. The switching of resolution is controlled by a tuning function which can be chosen at will according to the geometry of the system. As an application, the hybrid scheme is used to study the kinetics of interfacial broadening of a polymer blend, and is validated by comparing the results to the predictions from pure Brownian dynamics and pure local dynamics calculations.

cond-mat.soft↗

arXiv2016

Protein corona composition of PEGylated nanoparticles correlates strongly with amino acid composition of protein surface

Extensive molecular dynamics simulations reveal that the interactions between proteins and poly(ethylene glycol)(PEG) can be described in terms of the surface composition of the proteins. PEG molecules accumulate around non-polar residues while avoiding polar ones. A solvent-accessible-surface-area model of protein adsorption on PEGylated nanoparticles accurately fits a large set of data on the composition of the protein corona recently obtained by label-free proteomic mass spectrometry.

physics.bio-ph↗

arXiv2016

Polydisperse polymer brushes: internal structure, critical behavior, and interaction with flow

We study the effect of polydispersity on the structure of polymer brushes by analytical theory, a numerical self-consistent field approach, and Monte Carlo simulations. The polydispersity is represented by the Schulz-Zimm chain-length distribution. We specifically focus on three different polydispersities representing sharp, moderate and extremely wide chain length distributions and derive explicit analytical expressions for the chain end distributions in these brushes. The results are in very good agreement with numerical data obtained with self-consistent field calculations and Monte Carlo simulations. With increasing polydispersity, the brush density profile changes from convex to concave, and for given average chain length $N_n$ and grafting density $σ$, the brush height $H$ is found to scale as $(H/H_{\mathrm{mono}}-1)\propto(N_w/N_n-1)^{1/2}$ over a wide range of polydispersity indices $N_w/N_n$ (here $H_{\mathrm{mono}}$ is the height of the corresponding monodisperse brush. Chain end fluctuations are found to be strongly suppressed already at very small polydispersity. Based on this observation, we introduce the concept of the brush as a near-critical system with two parameters (scaling variables), $(N_{n}σ^{2/3})^{-1}$ and $(N_w/N_n-1)^{1/2}$, controlling the distance from the critical point. This approach provides a good description of the simulation data. Finally we study the hydrodynamic penetration length $l_\mathrm{p}$ for brush-coated surfaces in flow. We find that it generally increases with polydispersity. The scaling behavior crosses over from $l_\mathrm{p}\sim N_\mathrm{n}^{1/2}σ^{-1/6}$ for monodisperse and weakly polydisperse brushes to $l_\mathrm{p}\sim N_{n}^{2/3}$ for strongly polydisperse brushes.

cond-mat.soft↗

arXiv2016

Physical mechanisms of micro- and nanodomain formation in multicomponent lipid membranes

This article summarizes a variety of physical mechanisms proposed in the literature, which can generate micro- and nanodomains in multicomponent lipid bilayers and biomembranes. It mainly focusses on lipid-driven mechanisms that do not involve direct protein-protein interactions. Specifically, it considers (i) equilibrium mechanisms based on lipid-lipid phase separation such as critical cluster formation close to critical points, and multiple domain formation in curved geometries, (ii) equilibrium mechanisms that stabilize two-dimensional microemulsions, such as the effect of linactants and the effect of curvature-composition coupling in bilayers and monolayers, and (iii) non-equilibrium mechanisms induced by the interaction of a biomembrane with the cellular environment, such as membrane recycling and the pinning effects of the cytoplasm. Theoretical predictions are discussed together with simulations and experiments. The presentation is guided by the theory of phase transitions and critical phenomena, and the appendix summarizes the mathematical background in a concise way within the framework of the Ginzburg-Landau theory.

physics.bio-ph↗

arXiv2016

A hybrid particle-continuum resolution method and its application to a homopolymer solution

We discuss in detail a recently proposed hybrid particle-continuum scheme for complex fluids and evaluate it at the example of a confined homopolymer solution in slit geometry. The hybrid scheme treats polymer chains near the impenetrable walls as particles keeping the configuration details, and chains in the bulk region as continuous density fields. Polymers can switch resolutions on the fly, controlled by an inhomogeneous tuning function. By properly choosing the tuning function, the representation of the system can be adjusted to reach an optimal balance between physical accuracy and computational efficiency. The hybrid simulation reproduces the results of a reference particle simulation and is significantly faster (about a factor of 3.5 in our application example).

cond-mat.soft↗

arXiv2016

Computing bulk and shear viscosities from simulations of fluids with dissipative and stochastic interactions

Exact values for bulk and shear viscosity are important to characterize a fluid and they are a necessary input for a continuum description. Here we present two novel methods to compute bulk viscosities by non-equilibrium molecular dynamics (NEMD) simulations of steady-state systems with periodic boundary conditions -- one based on frequent particle displacements and one based on the application of external bulk forces with an inhomogeneous force profile. In equilibrium simulations, viscosities can be determined from the stress tensor fluctuations via Green-Kubo relations; however, the correct incorporation of random and dissipative forces is not obvious. We discuss different expressions proposed in the literature and test them at the example of a dissipative particle dynamics (DPD) fluid.

cond-mat.soft↗