Dissipative Particle Dynamics Simulations of Polymersomes Vanessa Ortiz,* ,‡,§,| Steven O. Nielsen, ‡,| Dennis E. Discher, §,| Michael L. Klein, ‡,| Reinhard Lipowsky, ² and Julian Shillcock ² Max Planck Institute of Colloids and Interfaces Golm, D-14424 Potsdam, Germany, Center for Molecular Modeling, Department of Chemistry, Biophysical Engineering Lab, Department of Chemical & Biomolecular Engineering, and Laboratory for Research on the Structure of Matter, UniVersity of PennsylVania, Philadelphia, PennsylVania 19104-6202 ReceiVed: March 11, 2005; In Final Form: July 25, 2005 A DPD model of PEO-based block copolymer vesicles in water is developed by introducing a new density based coarse graining and by using experimental data for interfacial tension. Simulated as a membrane patch, the DPD model is in excellent agreement with experimental data for both the area expansion modulus and the scaling of hydrophobic core thickness with molecular weight. Rupture simulations of polymer vesicles, or “polymersomes”, are presented to illustrate the system sizes feasible with DPD. The results should provide guidance for theoretical derivations of scaling laws and also illustrate how spherical polymer vesicles might be studied in simulation. I. Introduction Membranes composed of pure phospholipid have been studied since the 1960s 1,2 and simulated in atomistic detail for about a decade. 3 Membranes composed of purely synthetic polymer have been studied experimentally for less than a decade 4-10 and, because of the higher molecular weight (M) of the amphiphilic polymers (>kDa) compared to lipids (<kDa), polymer mem- branes have only recently been simulated. 11-13 In practice, polymer vesicles appear to have advantages over lipid vesicles because the physicochemical properties of “polymersomes” are more widely tunable. Specifically, the membrane elasticity, stability, permeability, and thickness are easily controlled by varying the molecular weight of the blocks. In addition, controlled degradability can be incorporated by the addition of hydrolyzable monomers. Sufficiently hydrophilic monomers can form blocks with variable hydrophobicity based on the molecular weight, namely at low M the block will be water soluble but at high M it can form the hydrophobic core of diblock (self- assembling) vesicles. 14 As with lipids, the more hydrophobic segments of amphiphilic block copolymers exclude water and form a melt whereas the hydrophilic chains hydrate. This aqueous environment alters the behavior from diblock melts, which historically have been the focus of theoretical efforts. Although theoretical discussions of polymer membranes and property scaling 15 predate even the first experiments, 10 these have always been based on the melt derivations. Indeed, now that the variability in structure and properties of polymer membranes with M is beginning to be elucidated experimentally, 16-21 it has become apparent that the theory does not adequately describe aqueous systems. The essential physical properties of these systems are due to the balance between the tendency of the components to phase separate into a hydrated component and a melt, and the chemical bond attaching the blocks together. A simple model that only incorporates these effects and is still capable of capturing the experimental scaling relations would be of great value in developing a theoretical description. Recent simulations of polymer membranes have exploited coarse grained molecular dynamics (CGMD) 12,13 but have proven unable to span much of the M range of experiments let alone demonstrate vesicle formation. Simulations of systems whose natural length scales far exceed those of traditional atomistic computations is perhaps better met today by the method of dissipative particle dynamics (DPD). 22 The interaction parameters for DPD simulations consist of one parameter for each species that determines the single component fluid’s compressibility, an intramolecular part capturing the connectiv- ity, and an intermolecular part that uses a single parameter for each pair of species to describe their mutual solubility. The link between the tendency of the species to phase separate and their mutual solubility is provided by the liquid-liquid interfacial tension that can be used directly as a fitting parameter. 23 While a CGMD model with a mapping of approximately three heavy atoms for every coarse grained site offers a speedup of 10 5 over fully atomistic molecular dynamics (AAMD), 24 the same mapping in the DPD framework provides an increase in efficiency of 10 6 largely because the interactions have a shorter cutoff. Figure 1 illustrates the length scales accessible to the different techniques with the above mapping at reasonable computational cost for a moderate molecular weight diblock copolymer. In DPD, this copolymer can make a closed vesicle. Here we have constructed a model in the DPD framework for aqueous poly(ethylene oxide)-polyethylethylene (PEO- PEE) diblock copolymer vesicles by incorporating intramolecu- lar data from atomistic simulations and intermolecular data from experimental interfacial tensions. Elastic properties of the membrane were used to evaluate two coarse graining schemes for DPD. The conventional coarse graining of three water molecules and one monomer per interaction site gave unphysical results, but elasticities obtained with a new mapping based on * Address correspondence to this author. E-mail: vaortiz@seas.upenn.edu. ² Max Planck Institute of Colloids and Interfaces Golm. ‡ Center for Molecular Modeling, Department of Chemistry, University of Pennsylvania. § Biophysical Engineering Lab, Department of Chemical & Biomolecular Engineering, University of Pennsylvania. | Laboratory for Research on the Structure of Matter, University of Pennsylvania. 17708 J. Phys. Chem. B 2005, 109, 17708-17714 10.1021/jp0512762 CCC: $30.25 © 2005 American Chemical Society Published on Web 08/30/2005