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4D printing of smart materials is a viable field of research for fabricating dynamic structures for various biomedical applications. 4D printing of hydrogel structures is challenging due to poor printability of hydrogels and poor shape fidelity of printed patterns when direct-ink writing-based 3D printers are used. In this study, chitosan (CS) hydrogel ink cross-linked with citric acid (CA) was made printable, exhibiting a shape-morphing behaviour when exposed to solvent as an external trigger. As one side of a printed structure is exposed to solvent, the solvent diffuses in and a concentration gradient is developed across the section. This concentration gradient results in displacement field, which finally leads to out-of-plane bending of the structure. This actuation is irreversible in nature since the concentration gradient is maintained between hydrophilic chitosan and hydrophobic silane layers. The reversibility of the morphed structures was achieved by dipping them in ethanol, which takes up solvent over time and thus diminishes the concentration gradient.The optimized CS/CA ink exhibited excellent rheological properties, with good extrudability and shape fidelity of printed structures. The chitosan ink was printed into various complex 3D architectures and was modified by hydrophobic coating of trimethyl silane (TMS). These hydrophobic patterns were coated on printed structures with varied interspacing, angles, and hinges to generate programmable designs. A printed soft gripper was demonstrated as an application that could lift an object seven times its weight. The shape morphing CS/CA hydrogel with excellent printability exhibits potential for 4D printing that has wide applications in soft robots, actuators, grippers, and sensors.

We demonstrate the formation of a versatile luminescent organo-inorganic layered hybrid material, composed of bovine serum albumin (BSA)-protected Au30clusters and aminoclay sheets. X-ray diffraction revealed the intercalation of Au30@BSA in the layered superstructure of aminoclay sheets. Coulombic attraction of the clusters and the clay initiates the interaction, and the appropriate size of the clusters allowed them to intercalate within the lamellar aminoclay galleries. Electron microscopy measurements confirmed the hierarchical structure of the material and also showed the cluster-attached clay sheets. Zeta potential measurement and dynamic light scattering probed the gradual formation of the ordered aggregates in solution. The hybrid material could be stretched up to 300% without fracture. The emergence of a new peak in the luminescence spectrum was observed during the course of mechanical stretching. This peak increased in intensity gradually with the degree of elongation or strain of the material. A mechanochromic luminescence response was further demonstrated with a writing experiment on a luminescent mat of the material, made by electrospinning.

Cluster-assembled solids (CASs) formed by the self-assembly of monodispersed atomically precise monolayer-protected noble metal clusters are attractive due to their collective properties. The physical stability and mechanical response of these materials remain largely unexplored. We have investigated the mechanical response of single crystals of atomically precise dithiol-protected Ag29polymorphs, monothiol-protected Ag46, and a cocrystal of the latter with Ag40(formulas of the clusters have been simplified merely with the number of metal atoms). The Ag29polymorphs crystallize in cubic and trigonal lattices (Ag29C and Ag29T, respectively), and Ag46and its cocrystal with Ag40crystallize in trigonal and monoclinic lattices (Ag46T and Ag40/46M, respectively). The time and loading-rate-dependent mechanical properties of the CASs are elucidated by measuring nanoindentation creep and stress relaxation. The obtained Young’s modulus (Er) values of the CASs were similar to those of zeolitic imidazolate frameworks (ZIFs) and show the trend Ag29T > Ag29C > Ag40/46M > Ag46T. We have also studied the viscoelastic properties of all of the four CASs and found that the value of tan δ/damping factor of monothiol-protected Ag46T was higher than that of other CASs. The unusual mechanical response of CASs was attributed to the supramolecular interactions at the surface of nanoclusters. This observation implies that the stiffness and damping characteristics of the materials can be modulated by ligand and surface engineering. These studies suggest the possibility of distinguishing between the crystal structures using mechanical properties. This work provides an understanding that is critical for designing nanocluster devices capable of withstanding mechanical deformations.

Shape-shifting solvent-responsive hydrogels have emerged as a crucial material platform for the design of soft robots, sensors, and actuators. Generally, to achieve actuation under different environments, using a layered structure with heterogeneous properties is a prevalent approach. However, the nonuniform force distribution at the interface between the layers can induce material delamination, thus greatly compromising the system’s stability and applicability. Here, we present the fabrication, design, and analysis of a reversible and structurally stable single-component functionally graded (FG) hydrogel thin film. The gradation is in terms of the modulus and diffusion coefficient. The FG film exhibits a fast actuation rate and is capable of actuating in both immersed and nonimmersed aqueous environments. The fabricated FG film can eliminate the requirement for a layered structure yet retain all its functionalities. A coupled diffusion–deformation framework using the finite element (FE) method is employed to comprehend the mechanism and understand the factors governing the actuation of a FG film. The displacement profiles obtained from the simulations are successfully compared with the experiments for a FG–chitosan–water system. The rate of concentration change in different layers of the FG film is shown to play a pivotal role in steering the direction of actuation as well as the reversibility of folding under different conditions. The differential strain obtained from the length change between the different layers of the FG films is identified as a contributing factor for different actuation rates. Additionally, the simulation curvatures from different scenarios elucidate the influence of cross-linking gradation, water diffusion, and thickness on the folding of a FG film. As a prospective application, we demonstrate the design of different underwater grippers using geometrically engineered symmetric and asymmetric FG films.

The molecular mechanism behind the process of biodegradation and consequently the loss in mechanical properties of polylactic acid (PLA) requires detailed understanding for the successful designing of various technological devices. In this study, we examine the role of free water and chain scission in this degradation process and quantify the mechanical properties of pristine and nanoparticle-reinforced PLA as it degrades over time. The in situ mechanical response of the degrading polymer is determined experimentally using nano-dynamic mechanical analysis (nanoDMA). Water present in the polymer matrix contributes to hydrolysis and subsequent scission of polymer chains. Water in excess of hydrolysis, however, alters the load transfer mechanism within the polymer chains. Molecular mechanism study applied in this work provides detailed insights into the relative role of these two mechanisms, (i) chain scission and (ii) solvation, in the reduction of mechanical properties during degradation. Functional groups such as ester (−COO−) and terminal acid (−COOH) interact with water molecules leading to the formation of water bridges and solvation shells, respectively. These are found to hinder the load transfer between polymer chains. It is observed that, compared to scission, solvation plays a more active role in the reduction of mechanical properties of degrading PLA.

Poly(vinylidine fluoride) (PVDF) is a semicrystalline polymer which is known to exist in several polymorphic phases, namely, α, β, and γ. Each one of these polymorphic phases is characterized by unique features such as spherulite formation in the case of the α and γ phases and the presence of large piezoelectric and ferroelectric activity in the β phase. Despite being widely used as thin coatings in sensors, lack of reports on nanomechanical properties suggests that investigation of mechanical properties of PVDF, let alone those of its polymorphic phases, seems to have evaded the sight of the research community. Herein, we report the nanomechanical properties of the α, β, and γ phases of PVDF. The modulus and hardness values were evaluated from nanoindentation experiments; it was found that the electroactive β phase is the softest among the three polymorphic phases. This result was further confirmed by scratch experiments. We have attempted to establish a correlation between the microstructure and nanomechanical properties of these phases. This work sheds light on the mechanisms responsible for the observed mechanical behavior and the role of tie moleculesand amorphous content in providing flexibility to the polymer.

Hydrogel-based pH-responsive bilayer actuators exhibit bidirectional actuation due to the differences in the concentration gradient developed across the thickness, the volume expansion due to swelling, and the mechanical stiffness of the layers involved. At a pH value (point), where the sum of these factors generates moments of equal magnitudes, the moments cancel each other and result in no net actuation. This pH point is termed here as a “nonmorphing point”. In this work, we present a bilayer of chitosan (CS) and carboxymethyl cellulose (CMC) cross-linked with citric acid (CA) with tunable nonmorphing points across the pH spectrum by modulating the concentration and cross-linking density of the layers involved. The standard CS/CMC bilayer films took about 40 s to completely fold (clockwise) in 0.1 M HCl and 78 s to completely fold (anticlockwise) in 0.1 M NaOH. Generally, pH-responsive actuators are designed for targeted drug delivery to a specific site inside the body as they show bidirectional (clockwise/anticlockwise) actuation around a single nonmorphing point. The same pH-responsive system cannot be applied for drug release at another site with a different functioning pH. Thus, having a pH-responsive system with multiple nonmorphing points is highly desirable. Drug release experiments were performed with FITC and EtBr as model drugs loaded in CS and CMC layers. Moreover, the clockwise/anticlockwise actuation of the bilayer around the nonmorphing point can facilitate or inhibit the release of a drug. The clockwise actuation resulted in 55% FITC release and inhibited EtBr release to 4%; anticlockwise actuation resulted in 50% EtBr release and inhibited FITC release to 5%. We demonstrated morphing induced drug release by hydrogel bilayer films with tunable nonmorphing points across the pH spectrum.

Pyrophyllite is the precursor to other smectite-group minerals which exhibit swelling. The mineral structure of pyrophyllite can lead to other minerals in the smectite group, including montmorillonite, through appropriate isomorphous substitutions. In this work, an atomic model of the pyrophyllite interlayer was constructed. The response of the interlayer was evaluated using steered molecular dynamics simulations. In steered molecular dynamics, external forces were applied to individual atoms to study the response of the model to applied forces. In this work, forces are applied to the surface clay atoms to evaluate the displacement vs.applied stress in the interlayer between clay layers. This paper describes the construction of the model, the simulation procedure, and the results of the simulations which show that under the applied loading, deformation occurs mainly in the interlayer. The clay layers show relatively little deformation. The results show that the relationship between applied stress and displacement of the interlayer is linear. The stress-deformation relationship for the interlayer is presented.

Abstract: We find self-adjoint extensions of the rational Calogero model in the presence of the harmonic interaction. The corresponding eigenfunctions may describe the near-horizon quantum states of certain types of black holes.

The importance of thesupport functionin representation, manipulation, and analysis of convex bodies can indeed be compared with that of the Fourier transform in signal processing. The support function, in intuitive terms, is the signed distance of a supporting plane of a convex body from the origin point. In this paper we show that, just as simple multiplication in the Fourier transform domain turns out to be the convolution of two signals, similarly simple algebraic operations on support functions result in a variety of geometric operations on the corresponding geometric objects. In fact, since the support function is areal-valuedfunction, these simple algebraic operations are nothing but arithmetic operations such as addition, subtraction, reciprocal, and max–min, which give rise to geometric operations such as Minkowski addition (dilation), Minkowski decomposition (erosion), polar duality, and union–intersection. Furthermore, it has been shown in this paper that a number of representation schemes (such as the Legendre transformation, the extended Gaussian image, slope diagram representation, the normal transform, and slope transforms), which appear to be very disparate at first sight, belong to the same class of the support function representation. Finally, we indicate some algebraic manipulations of support functions that lead to new and unsuspected geometric operations. Support function like representations for nonconvex objects are also indicated.

An indecomposable shape is like a prime number. It cannot be decomposed further as a Minkowski sum of two simpler shapes. With respect to Minkowski addition (dilation), therefore, the indecomposable shapes are the fundamental building blocks of all geometric shapes. However, just as it is difficult to identify whether a given number is a prime number or not, it is equally or more difficult to say whether a given shape is indecomposable or not. In this paper we take up a subdomain of binary images, called the weakly taxicab convex image domain, and show how the indecomposability problem in that shape domain can be approached in a manner closely analogous to the number theoretic way. Apart from our attempt to show that the indecomposability problem is an extremely interesting mathematical problem, our algorithmic treatment of the problem also leads to an efficient method of computing Minkowski addition and decomposition of binary images.

The resemblance between the integer number system with multiplication and division and the system of convex objects with Minkowski addition and decomposition is really striking. The resemblance also indicates a computational technique which unifies the two Minkowski operations as a single operation. To view multiplication and division as a single operation, it became necessary to extend the integer number system to the rational number system. The unification of the two Minkowski operations also requires that the ordinary convex object domain must be appended by a notion of inverse objects or negative objects. More interestingly, the concept of negative objects permits further unification. A nonconvex object may be viewed as a mixture of ordinary convex object and negative object, and thereby, makes it possible to adopt exactly the same computational technique for convex as well as nonconvex objects. The unified technique, we show, can be easily understood and implemented if the input polygons and polyhedra are represented by their slope diagram representations.

We consider a CPNmodel with the subgroup SU(r) completely gauged, where 1 < r< N+ 1. The gauge field dynamics is solely governed by a nonabelian Chern-Simons term and the global SU(N+ 1) symmetry is broken explicitly by introducing a SU(r) invariant scalar potential. We obtain self-dual equations of this gauged CPNmodel and find that the energy is bounded from below by a linear combination of the topological charge and a global U(1) charge present in the theory. We also discuss on the self-dual soliton solutions of this model.