Bicontinuous Materials Research Articles

Microstructural and transport characteristics of triply periodic bicontinuous materials

Three-dimensional (3D) bicontinuous two-phase materials are increasingly gaining interest because of their unique multifunctional characteristics and advancements in techniques to fabricate them. Because of their complex topological and structural properties, it still has been nontrivial to develop explicit microstructure-dependent formulas to predict accurately their physical properties. A primary goal of the present paper is to ascertain various microstructural and transport characteristics of five different models of triply periodic bicontinuous porous materials at a porosity ϕ1=1/2: those in which the two-phase interfaces are the Schwarz P, Schwarz D and Schoen G minimal surfaces as well as two different pore-channel structures. We ascertain their spectral densities, pore-size distribution functions, local volume-fraction variances, and hyperuniformity order metrics and then use this information to estimate certain effective steady-state as well as time-dependent transport properties via closed-form microstructure–property formulas. Specifically, the recently introduced time-dependent diffusion spreadability is determined exactly from the spectral density. Moreover, we accurately estimate the fluid permeability of such porous materials from a closed-form formula that depends on the second moment of the pore-size function and the formation factor, a measure of the tortuosity of the pore space, which is exactly obtained for the three minimal-surface structures. We also rigorously bound the permeability from above using the spectral density. For the five models with identical cubic unit cells, we find that the permeability, inverse of the specific surface, hyperuniformity order metric, pore-size second moment and long-time spreadability behavior are all positively correlated and rank order the structures in exactly the same way. We also conjecture what structures maximize the fluid permeability for arbitrary porosities and show that this conjecture must be true in the extreme porosity limits by identifying the corresponding optimal structures.

Elastic microphase separation produces robust bicontinuous materials.

Bicontinuous microstructures are essential to the function of diverse natural and synthetic systems. Their synthesis has been based on two approaches: arrested phase separation or self-assembly of block copolymers. The former is attractive for its chemical simplicity and the latter, for its thermodynamic robustness. Here we introduce elastic microphase separation (EMPS) as an alternative approach to make bicontinuous microstructures. Conceptually, EMPS balances the molecular-scale forces that drive demixing with large-scale elasticity to encode a thermodynamic length scale. This process features a continuous phase transition, reversible without hysteresis. Practically, EMPS is triggered by simply supersaturating an elastomeric matrix with a liquid, resulting in uniform bicontinuous materials with a well-defined microscopic length scale tuned by the matrix stiffness. The versatility of EMPS is further demonstrated by fabricating bicontinuous materials with superior mechanical properties and controlled anisotropy and microstructural gradients. Overall, EMPS presents a robust alternative for the bulk fabrication of homogeneous bicontinuous materials.

Controlling structure of materials derived from spinodally decomposing liquids

Arresting morphological evolution of spinodally decomposing heterogeneous mixtures via the addition of colloidal particles has resulted in the discovery of new classes of bicontinuous materials, viz., bicontinuous interfacially jammed emulsion gels (bijels) and most recently bicontinuous intraphase jammed emulsion gels (bipjels). Here, we demonstrate how the extent of particle wettability and particle–particle interactions govern the ultimate structure formed. We present the multi-phase lattice Boltzmann method (LBM) integrated with a discrete particle model with two particle–particle collision models, the classic hard-sphere model and a new bonding collision model, to predict the final state of spinodally decomposing fluid mixtures containing solid particles. We show that the elastic collision model yields either the formation of emulsions or bijels, while only the bonding collision model on particles with preferential wettability for one phase can predict bipjels formation. In the case of bipjels, a delicate balance between the dynamics of evolving interface and the strength of particle–particle aggregates is required to restrict the interfacial motion. These results are consistent with experimental findings, suggesting that the presence of smaller particles with high particle–particle interactions can yield the formation of bipjels and consequent isolation of hierarchically porous materials.

Comment to “Skeletonization-based beam finite element models for stochastic bicontinuous materials: Application to simulations of nanoporous gold” by C. Soyarslan et al. [J. Mater. Res. 33(20), 3371 (2018)

Abstract

Engineering bicontinuous polymeric monoliths through high internal phase emulsion templating

Preparation of two-component materials having morphologies with bicontinuous minor and major components is challenging. An innovative method has been developed to synthesize bicontinuous polymeric monoliths based on high internal phase emulsion (HIPE) templating. This work demonstrated a protocol of dual-hydrophobic bicontinuous material of glassy polystyrene (PS) and elastic poly(butyl acrylate) (PBA). The PS scaffold was prepared through polymerizing styrene (St) as the external phase of HIPE with an aqueous free radical initiator, in the presence of divinylbenzene (DVB) as a crosslinker. The resulting PS scaffolds were then employed as templates to absorb butyl acrylate (BA) mixed with ethylene glycol dimethylacrylate (EGDMA). Results suggested that the polymeric monoliths possessed a bicontinuous structure and good compatibility in the bulk state. This work provides a new approach for the synthesis of bicontinuous two-component materials.

A Green operator-based elastic modeling for two-phase pantographic-inspired bi-continuous materials

We propose an estimate for the effective elastic properties of a new imagined two-phase bi-continuous composite material type with a so-called ``pantographic-inspired” (P-I) architecture in the sense of a matrix reinforcement which is a 3D fiber network capable of large, pantographic-like, deformations, owing to particular properties carried by the fiber interconnections. Such fiber networks co-continuous with the matrix are described from an assemblage of inter-penetrated planar alignments of parallel infinite, identical and equally distant, rods or beams that we call fiber layers or FPAs for ``fiber planar alignments”. Piece-wise linear deformation of such a structure is constrained, as 2D pantographs are, by the specific relations that link the evolutions of the FPA misorientations, of the fiber inter distance and concentration within each FPA, and of the given characteristics to the through-layer interconnections. We derive effective properties within a well defined first gradient elastic homogenization scheme for macro-homogeneous composite structures, based on explicating the involved mean Green operator (mGO) for the representative pattern of such a P-I networked reinforcement in an isotropic matrix. This mGO for P-I composites is built in making use of previously derived and presented mGOs for rod and beam FPAs. Comparisons with Young and shear modulus variations during numerical homogeneous extension simulations show that the proposed modeling provides relevant effective property evolutions with the advantage of being analytical. Comparing so estimated force-displacement curves with numerical ones for 2D pantographs enables to identify ways to further account in the modeling for the specific strengthening effects of the FPA interconnections in pantographs. This tends to prove such P-I composite structures, still to be manufactured, to possibly also behave similarly to pantograph ones.

Skeletonization-based beam finite element models for stochastic bicontinuous materials: Application to simulations of nanoporous gold

An efficient representative volume element generation strategy is developed in modeling nanoporous materials. It uses periodic 3D beam finite element (FE) models derived from skeletonization of spinodal-like stochastic microstructures produced by a leveled random field. To mimic stiffening with agglomeration of the mass at junctions, an increased Young’s modulus is assigned to the elements within the junction zone. The effective Young’s modulus, Poisson’s ratio, and universal anisotropy index are computed. A good agreement of the Young’s modulus predictions with those obtained from experimental results for phase volume fractions 0.20<{phi _{cal B}}<0.50 is observed. Moreover, the elastic anisotropy index of the generated beam networks shows sufficient proximity to isotropy. Finally, it is demonstrated that, as compared to the simulation statistics of voxel-FE models, for the beam-FE models over 500-fold computational acceleration with 250-fold less memory requirement is provided.

Jammed Limit of Bijel Structure Formation.

Over the past decade, methods to control microstructure in heterogeneous mixtures by arresting spinodal decomposition via the addition of colloidal particles have led to an entirely new class of bicontinuous materials known as bijels. Herein, we present a new model for the development of these materials that yields to both numerical and analytical evaluation. This model reveals that a single dimensionless parameter that captures both chemical and environmental variables dictates the dynamics and ultimate structure formed in bijels. We demonstrate that this parameter must fall within a fixed range in order for jamming to occur during spinodal decomposition, as well as show that known experimental trends for the characteristic domain sizes and time scales for formation are recovered by this model.

Nanostructured Thermal Responsive Materials Synthesized by Soft Templating.

We capitalized herein the inherent tortuosity of bicontinuous microemulsion to conceive nanostructured drug-delivery devices. First, we show that it is possible to synthesize bicontinuous materials with continuous hydrophilic domains of the poly(N-isopropylacrylamide) (PNIPAM) network entangled with continuous hydrophobic polymer domains, with dual-phase continuity being imposed by the bicontinuous microemulsions used as a soft template. Particular attention is paid to the microemulsion formulations using a surfmer to preserve the one-to-one replication of the bicontinuous nanostructure after polymerization. These materials keep a volume phase transition with temperature that allows considering them as drug carriers for controlled release. PNIPAM, which plays the role of the active ingredient reservoir, is confined in the bicontinuous structure. As expected, the PNIPAM enclosure limits the surface area in contact with the releasing aqueous solution and thus slows down the desorption of aspirin, which is used as a model drug. The hydrophobic polymers play the role of in situ-created transport barriers without hindering it as all the loaded aspirin in this bicontinuous structure still remains available.

3D printing of self-assembling thermoresponsive nanoemulsions into hierarchical mesostructured hydrogels.

Spinodal decomposition and phase transitions have emerged as viable methods to generate a variety of bicontinuous materials. Here, we show that when arrested phase separation is coupled to the time scales involved in three-dimensional (3D) printing processes, hydrogels with multiple length scales spanning nanometers to millimeters can be printed with high fidelity. We use an oil-in-water nanoemulsion-based ink with rheological and photoreactive properties that satisfy the requirements of stereolithographic 3D printing. This ink is thermoresponsive and consists of poly(dimethyl siloxane) droplets suspended in an aqueous phase containing the surfactant sodium dodecyl sulfate and the cross-linker poly(ethylene glycol) dimethacrylate. Control of the hydrogel microstructure can be achieved in the printing process due to the rapid structural recovery of the nanoemulsions after large strain-rate yielding, as well as the shear thinning behavior that allows the ink to conform to the build platform of the printer. Wiper operations are used to ensure even spreading of the yield stress ink on the optical window between successive print steps. Post-processing of the printed samples is used to generate mesoporous hydrogels that serve as size-selective membranes. Our work demonstrates that nanoemulsions, which belong to a class of solution-based materials with flexible functionalities, can be printed into prototypes with complex shapes using a commercially available 3D printer with a few modifications.

Bijel reinforcement by droplet bridging: a route to bicontinuous materials with large domains

Bijels are non-equilibrium solid-stabilized emulsions with bicontinuous arrangement of the constituent fluid phases. These multiphase materials spontaneously form through arrested spinodal decomposition in mixtures of partially miscible liquids and neutrally wetting colloids. Here, we present a new solid-stabilized emulsion with an overall bicontinuous morphology similar to a bijel, but with one continuous phase containing a network of colloid-bridged droplets. This dual morphology is the result of combined spinodal decomposition and nucleation and growth in a binary liquid mixture containing colloidal particles with off-neutral wetting properties and partial affinity for one liquid phase. The rheology of these systems, which we call bridged bijels, is nearly identical to their simple bijel counterparts, with a unique exponential dependence of the zero-shear elastic modulus on the colloid volume fraction. However, partitioning of the colloids between the spinodal surface and the fluid domains delays the onset of structural arrest, providing access to domain sizes much larger than available in simple bijels without loss of mechanical stability. This ability greatly expands the potential technological applications of these unique materials. In addition, our findings reveal new strategies for tuning the rheology of bijels and outline new directions for future fundamental research on this unique class of soft materials.

Synthesis of Mesoporous Gadolinium Doped Ceria - Platinum Composite

ABSTRACTOxygen reduction in SOFC cathodes has long been the rate determining step in SOFC operations, mixed ionic-electronic conductors (MIECs) and/or forming composite between cathode and electrolyte materials have been common strategies in order to aid the cathode kinetics. We demonstrate here a viable synthesis route to impregnate mesopores with high loading of platinum towards a mesoscale bicontinuous material that composed of channels of a fast ionic conductor, i.e. gadolinium doped ceria (GDC) intertwined with channels of a good electronic conductor, i.e. Pt. This highly structural composite material holds the promise of a high performing cathode in SOFC.

Synthesis of mesoporous silicas in alkaline and acidic media using the systems cetyltrimethylammonium tosylate (CTAT)–Pluronic F127 triblock copolymer and CTAT–Pluronic F68 triblock copolymer as templates

Mesoporous silica materials were synthesized in alkaline and acidic media, using cetyltrimethylammonium tosylate (CTAT), Pluronic triblock copolymers F127 and F68, and mixtures of CTAT with each copolymer in order to investigate the effects of pH, surfactant concentration, and CTAT/triblock copolymer molar ratios on the morphology and texture of the synthesized materials. The results show that the kind of mesoporous materials and their pore size can be tuned by changing not only the pH but also the proportion of components and the nature of the copolymer. In alkaline synthesis, microscopic bicontinuous materials are obtained, which are composed by nanoscopic plate-like particles having slit-shaped pores. In acidic synthesis, on the contrary, monolithic silicas are obtained. These materials are also composed by nanoscopic plate-like particles having slit-shaped pores, although in some cases, the microscopic structures are formed by fused spherical particles. The inclusion of the triblock copolymer in the template composition causes a transformation from a bimodal to a monomodal pore size distribution, leading to small and nearly round pores which are probably formed by copolymer or copolymer-CTAT mixed micelles. The differences between the systems synthesized by CTAT–Pluronic F127 and CTAT–Pluronic F68 are explained on the basis of the different interactions between each copolymer and CTAT.

Elastic property prediction by finite element analysis with random distribution of materials for tungsten/silver composite

In the present numerical study, we introduce a finite element analysis for heterogeneous materials via a random distribution of materials to predict effective elastic properties. With this random distributing strategy, a large scale parametric analysis via finite element becomes feasible for the multi-phase heterogeneous solids. Taking a well-documented tungsten–silver bi-continuous material as an example, the numerical prediction provided here for the effective properties is checked by experimental testing data available in open publication. Discussions on the present finite element prediction and other approaches are also made by comparing with Hashin and Shtrikman (J Mech Phys Solids 11:127–140, 1963) bounds in the composite mechanics.

Elastic property prediction by finite element analysis with random distribution of materials for heterogeneous solids

In the present paper, finite element method is employed to predict the effective material properties of heterogeneous materials via random distributions of the constituent materials. With the random distributing strategy, massive parametric analysis via finite element becomes feasible for multi-phase heterogeneous solids. Using a two-phase bi-continuous material as an example, the effects of the specimen size with respect to the characteristic size of the micro-structural size and the element density on the predicted effective properties are considered. The numerical predictions of the effective properties are checked by two analytical bounds which were proposed by Hashin and Shtrikemn (1963) through the principle of variation and the matrix-fiber model. Some discussions on the finite element prediction are also made to clarify the status of the present work in the composite mechanics research.

Developing macroporous bicontinuous materials as scaffolds for tissue engineering

Calcareous skeletal elements (ossicles) isolated from the seastar, Pisaster giganteus, were characterized and tested as potential biocompatible substrates for cellular attachment. These ossicles have a remarkably robust open-framework architecture with an interconnected network of ca. 10 μm diameter pores. Scanning electron and confocal microscopy was used to characterize the cell-substrate interaction. Cell culturing experiments revealed that the cells firmly attach to the ossicle surface, forming cell aggregates of several layers thick. The anchored cells extended to form ‘bridges’ between the openings in the bicontinuous framework and the degree of coverage increased as culture time progressed. Osteoblasts grown on the ossicles were found to be viable up to 32 days after initial seeding, as proven by assaying with AlamarBlue™ and FDA/PI staining indicating the ossicle's potential as an alternative highly effective tissue scaffold. Given the limitation in availability of this natural material, the results presented here should be seen as offering guidelines for future development of synthetic materials with physical and chemical properties strongly conducive to bone repair and restoration.