(670d) Molecular Dynamics Study of Hydrophilic-Hydrophobic Diblock Copolymer Self-Assembly: Phase Diagram, Vesicle Morphogenesis, and Shear Flow Dynamics

Hydrophilic-hydrophobic diblock copolymers can self-assemble into structures such as micelles, membranes, and vesicles, which find significant applications in detergency, drug delivery, and catalysis. Lamellar and vesicular structures as well as their stability and mechanical properties are of fundamental importance in understanding several biological phenomena. An ideal bilayer of amphiphilic molecules in aqueous solution experiences energetically unfavorable hydrophobic interactions due to the adjacency of the lateral molecules along the perimeter of the lamella to surrounding water molecules. It has been hypothesized that at sufficiently large amphiphile concentrations, a flexible lamella can bend, curve and fold to form a vesicle to minimize hydrophobic interactions at the expense of gaining curvature energy: for example, see DD Lasic, Biochimica et Biophysica Acta, 692, 501 (1982). Another problem of great biological relevance is the effect of the presence of insertion of a second molecular species into on the stability of lamellae and vesicles: for example, incorporation of n-alkane molecules tends to rigidify lipid bilayers and make them more prone to rupture due to enhanced elastic stresses (Hishida et al., J. Chem. Phys. 144, 041103 (2016)) while modification of phospholipids by cyclopentane rings is observed to enhance bilayer stability to electric breakdown (Batischev et al., Soft Matter, 16, 3216 (2020). The molecular mechanisms of such phenomena remain largely unexplored. In this work, we employ coarse-grained molecular dynamics (CGMD) simulations to study the aqueous self-assembly of diblock copolymers consisting of polybutadiene (PB)-polyethylene oxide (PEO) monomers. The equilibrium phase diagram of this system has been studied extensively by experiments (Jain and Bates, Science, 300, 5618 (2003)). The simulation results are used to gain insights into the mechanisms of phase transitions as well as mechanical properties of the self-assembled structures and how they are influence by the presence of additives.

We have extended CGMD simulations models, previously developed to study self-assembly in ionic and non-ionic surfactant solutions [Sangwai and Sureshkumar, Langmuir 27, 6628 (2011); Sambasivam et al., Phys. Rev. Lett. 114, 158302; Dhakal and Sureshkumar, J. Chem. Phys. 143, 024905 (2015)] to diblock copolymer solutions. Depending on the copolymer concentration, relative composition (PB to PEO ratio), and temperature, spherical and cylindrical micelles, linear and branched wormlike micelles, rigid and flexible bilayers, vesicles, as well as topologically complex and heterogenous morphologies are observed. Structures are characterized by calculating parameters such as the aggregation number, surface to volume ratio, packing parameter, end-to-end distances, persistence length, bending modulus, and energy associated with bonded and non-bonded interactions. Various morphologies are organized into a phase diagram. Structure transitions will be explained based on considerations of geometry and energetics considerations. The influence of local (interfacial) distribution of water and copolymers on phase transitions will also be discussed.

Simulations are used to explore the pathways by which vesicles form from an initially homogeneous copolymer solution. In one such pathway, spherical micelles are observed to merge and reorganize into rigid bilayer structures. These bilayer structures grow to form flexible lamellae. Further growth, curvature development and folding of a lamella cause the formation of a vesicle. The morphogenesis of lamella to vesicle transition is understood by tracking the aggregation number, end-to-end distance, and energy of interactions as a function of time. These results will be discussed in the context of classical molecular thermodynamics theories.

We also compute the details of molecular organization (e.g. the splay/tilt angle between adjacent molecules) and mechanical properties (e.g. Poisson ratio) of the bilayer and how they are influenced by the insertion of additives. Further, the mechanical deformation of bilayers and vesicles under homogeneous shear flow are studied by non-equilibrium MD simulations. Results of these simulations will be discussed in the context of the experiments mentioned in the first paragraph above.