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Driven by synthetic advances combined with the ability of processing and characterization methods, multi-stimulus responsive (MSR) polymers offer technological opportunities with significant societal impacts. The purpose of this perspective is not to itemize every possible MSR polymer system but instead to highlight recent advances along with current and future trends that redefined modern polymer science. In the context of spatiotemporal and energetic requirements, this perspective explores multi-stimulus responses driven by compositional, structural, and hierarchical macromolecular arrangements, where multi-stimulus may be achieved by combining mechano-responsiveness, pH changes, electromagnetic radiation, magnetic/electric fields, redox reactions, humidity and temperature changes, solvents and gases, or biologically triggered responses. Multi-stimulus responses may be orthogonal, competitive, or synergistic and governed by the redefined principles in developing polymers with signaling and communications, encoding phenotypic properties with precisely defined sequences, programmable assembly/disassembly, and recognition attributes, and MSR materials will pave the next generations of ingenious technological advances with living-like attributes. 

Abstract We develop a new finite difference method for the wave equation in second order form. The finite difference operators satisfy a summation-by-parts (SBP) property. With boundary conditions and material interface conditions imposed weakly by the simultaneous-approximation-term (SAT) method, we derive energy estimates for the semi-discretization. In addition, error estimates are derived by the normal mode analysis. The proposed method is termed as energy-based because of its similarity with the energy-based discontinuous Galerkin method. When imposing the Dirichlet boundary condition and material interface conditions, the traditional SBP-SAT discretization uses a penalty term with a mesh-dependent parameter, which is not needed in our method. Furthermore, numerical dissipation can be added to the discretization through the boundary and interface conditions. We present numerical experiments that verify convergence and robustness of the proposed method. 

Abstract Although dipolar forces between copolymer chains are relatively weak, they result in ubiquitous inter‐ and/or intramolecular interactions which are particularly critical in achieving the mechanical integrity of polymeric materials. In this study, a route is developed to obtain self‐healable properties in thermoplastic copolymers that rely on noncovalent dipolar interactions present in essentially all macromolecules and particularly fluorine‐containing copolymers. The combination of dipolar interactions between C─F and C═O bonds as well as CH₂/CH₃entities facilitates self‐healing without external intervention. The presence of dipole‐dipole, dipole‐induced dipole, and induced‐dipole induced dipole interactions leads to a viscoelastic response that controls macroscopic autonomous multicycle self‐healing of fluorinated copolymers under ambient conditions. Energetically favorable dipolar forces attributed to monomer sequence and monomer molar ratios induces desirable copolymer tacticities, enabling entropic energy recovery stored during mechanical damage. The use of dipolar forces instead of chemical or physical modifications not only eliminates additional alternations enabling multiple damage‐repair cycles but also provides further opportunity for designing self‐healable commodity thermoplastics. These materials may offer numerous applications, ranging from the use in electronics, ion batteries, H₂fuel dispense hoses to self‐healable pet toys, packaging, paints and coatings, and many others. 

Abstract Electrically accelerated self‐healable poly(ionic liquids) copolymers that exhibit resistor‐capacitor (RC) circuit properties are developed. At low alternating current (AC) frequencies these materials behave as a resistor (R), whereas at higher frequencies as a capacitor (C). These properties are attributed to a combination of dipolar and electrostatic interactions in (1‐[(2‐methacryloyloxy)ethyl]‐3‐butylimidazolium bis(trifluoromethyl‐sulfonyl)imide) copolymerized with methyl methacrylate (MMA) monomers to form p(MEBIm‐TSFI/MMA)] copolymers. When the monomer molar ratio (MEBIm‐TSFI:MMA) is 40/60, these copolymers are capable of undergoing multiple damage‐repair cycles and self‐healing is accelerated by the application of alternating 1.0–4.0 V electric field (EF). Self‐healing in the absence of EFs is facilitated by van der Waals (vdW) interactions, but the application of AC EF induces back and forth movement of charges against the opposing force that result in dithering of electrostatic dipoles giving rise to interchain physical crosslinks. Electrostatic inter‐ and intrachain interactions facilitated by copolymerization of ionic liquid monomers with typically dielectric acrylic‐based monomers result in enhanced cohesive energy densities that accelerate the recovery of vdW forces facilitating self‐healing. Incorporating ionic liquids into commodity polymers offers promising uses as green conducting solid polyelectrolytes in self‐healable energy storage, energy‐harvesting devices, and many other applications. 

Abstract Known for their adaptability to surroundings, capability of transport control of molecules, or the ability of converting one type of energy to another as a result of external or internal stimuli, responsive polymers play a significant role in advancing scientific discoveries that may lead to an array of diverge applications. This review outlines recent advances in the developments of selected commodity polymers equipped with stimuli‐responsiveness to temperature, pH, ionic strength, enzyme or glucose levels, carbon dioxide, water, redox agents, electromagnetic radiation, or electric and magnetic fields. Utilized diverse applications ranging from drug delivery to biosensing, dynamic structural components to color‐changing coatings, this review focuses on commodity acrylics, epoxies, esters, carbonates, urethanes, and siloxane‐based polymers containing responsive elements built into their architecture. In the context of stimuli‐responsive chemistries, current technological advances as well as a critical outline of future opportunities and applications are also tackled. 

Abstract An explicit spectrally accurate order-adaptive Hermite-Taylor method for the Schrödinger equation is developed. Numerical experiments illustrating the properties of the method are presented. The method, which is able to use very coarse grids while still retaining high accuracy, compares favorably to an existing exponential integrator – high order summation-by-parts finite difference method.