Microphase separation of weakly charged block polyelectrolyte solutions: Donnan theory for dynamic polymer morphologies

A mean-field dynamic density functional theory for the phase behavior of concentrated weakly charged block polyelectrolyte solutions is developed, using the Donnan membrane equilibrium approach to account for electrostatic interactions. In this limit all long-range electrostatic interactions are canceled and the net charge density in any region on a coarse-grained scale is zero. The phase diagram of a model triblock polyelectrolyte in solution as a function of the charge of the solvophilic block and the solvent concentration is established. Different mesoscopic structures (lamellar, bicontinuous, hexagonal, micellar, and dispersed coexisting phases) are formed depending on the copolymer charge asymmetry. It is found that upon changing the charge of the solvophilic copolymer block the polyelectrolyte solution does not follow the lyotropic sequence of phases of this polymer. Upon increase in the charge of the solvophilic blocks, changes in copolymer morphology take place by means of change in curvature of polymeric domains.     

Structure formation in films of weakly charged block polyelectrolyte solutions

A mean-field dynamic density functional theory is used to describe a phase diagram of concentrated solutions of weakly charged flexible block polyelectrolytes in a film. Electrostatics is taken into account by applying the local electroneutrality constraint (the Donnan membrane equilibrium approach). In the Donnan limit it is assumed that a salt added to the solution perfectly screens long-range electrostatic interactions. The phase diagram of a solution of a triblock polyelectrolyte in a film as a function of the solvent concentration and the charge of the polyelectrolyte (solvophilic) block is calculated for a given film thickness. The phase behavior of the block polyelectrolyte film arises from the interplay between surface-induced alignment and the electrostatically-driven structure formation. The observed mesoscopic structures (lamellar, perforated lamellar, cylindrical, micellar, and mixed phases) are oriented parallel to the surfaces for the considered case of morphologies unfrustrated by the film thickness. Structures with connections between parallel layers (bicontinuous, etc.) are not formed. As a result of surface-induced ordering, the region of ordered phases in a film is wider than in bulk and the phase boundary between ordered and disordered phases is more diffuse. As in the case of unconfined block polyelectrolyte solution, the solution in a film does not follow the lyotropic sequence of phases of such a block copolymer upon increase in the charge of the polyelectrolyte block. Upon changing the charge of the solvophilic copolymer block, transformations of copolymer morphology take place via change in curvature of polymeric domains. Due to confinement of a polyelectrolyte film, no swelling of solvophilic domains is observed.     

Stress State of an Orthotropic Electroelastic Medium with an Arbitrarily Oriented Elliptic Inclusion*

International Applied Mechanics - The problem of electric and stress state in an orthotropic electroelastic space containing an arbitrarily oriented ellipsoidal inclusion under homogeneous force...     

Simulations of Electric Field Induced Lamellar Alignment in Block Copolymers in the Presence of Selective Electrodes

Computer simulations have been performed for electric field induced parallel‐perpendicular lamellar phase transition in the presence of electrodes. The simulations are based on the dynamic density functional theory. Here we provide the extension of earlier work in two dimensions (2D) to three dimensions (3D). The result is a vivid picture of the transitions through defect creation and collision.

Observed change in lamellar alignment with applied electric field.     

Electric field versus surface alignment in confined films of a diblock copolymer melt

The dynamics of alignment of microstructure in confined films of diblock copolymer melts in the presence of an external electric field was studied numerically. We consider in detail a symmetric diblock copolymer melt, exhibiting a lamellar morphology. The method used is a dynamic mean-field density functional method, derived from the generalized time-dependent Ginzburg-Landau theory. The time evolution of concentration variables and therefore the alignment kinetics of the morphologies are described by a set of stochastic equations of a diffusion form with Gaussian noise. We investigated the effect of an electric field on block copolymers under the assumption that the long-range dipolar interaction induced by the fluctuations of composition pattern is a dominant mechanism of electric-field-induced domain alignment. The interactions with bounding electrode surfaces were taken into account as short-range interactions resulting in an additional term in the free energy of the sample. This term contributes only in the vicinity of the surfaces. The surfaces and the electric field compete with each other and align the microstructure in perpendicular directions. Depending on the ratio between electric field and interfacial interactions, parallel or perpendicular lamellar orientations were observed. The time scale of the electric-field-induced alignment is much larger than the time scale of the surface-induced alignment and microphase separation.     

Predicting the Morphology of Metallo‐Supramolecular Block Copolymers with Bulky Counter Ions

Summary: The phase behavior of metallo‐supramolecular block copolymers with bulky counter ions is theoretically studied within the framework of a mean‐field dynamic density functional theory and compared with recent experiments on a polystyrene–poly(ethylene oxide) metallo‐supramolecular diblock copolymer, PS₂₀‐[Ru]‐PEO₇₀, with tetraphenylborate counter ions. The copolymer is modeled as a triblock polyelectrolyte, in which the metal complex is treated as the polyelectrolyte block. The topology and kinetics of the formation of the observed three‐domain lamellar morphology in which the polyelectrolyte blocks and bulky counter ions are located together to form electroneutral complexes, are in good agreement with experimental results. In addition, the model predicts the existence of core–shell morphologies. The agreement with and variations from the experimental phase diagram are discussed in detail.

Morphological transformations in a metallo‐supramolecular block copolymer with bulky counter ions upon increasing the temperature.