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Different from conventional single-network hydrogels, double-network (DN) hydrogels have attracted great research interest due to their ultra-high toughness; however, the working principles behind their complex mechanochemical coupling have not been fully understood. In this study, an extended potential well model is formulated to investigate the host-guest chemistry and the free-energy trap effect, coupled in DN hydrogels undergoing mechanochemical toughening. According to the Morse potential and mean field model, the newly established potential well model can describe the coupled binding of the host brittle network and guest ductile network in the DN hydrogels. A free-energy equation is further proposed to describe the working principles of the mechanochemical coupling and toughening mechanisms using the depth, width, and trap number of potential wells, which determine the barrier energy of the host brittle network, the mesh size of guest ductile network, and the mechanochemical host-guest interactions of these two networks, respectively. Finally, the effectiveness of the proposed model is verified using finite-element analysis (FEA) and experimental results of various DN hydrogels reported in the literature. Using the potential well model, which has host-guest chemistry from both brittle and ductile networks, this study clarifies the linking of mechanochemical coupling and toughening mechanisms in DN hyrdogels. [ABSTRACT FROM AUTHOR]

Polyampholyte (PA) hydrogels are incorporated of many internally charged polymer chains, which play an important role to influence the fractal networks and dynamic elasticity of the PA hydrogels owing to their different exchange and correlation charge-densities. Many properties of the PA hydrogels, such as mechanical strength and deformation, are significantly dependent on their fractal networks. However, working principles of chemo-mechanical coupling between the fractal networks and the elasticity of PA hydrogels have not been fully understood. In this study, a self-consistent fractal geometry model integrated with a complex function is proposed to understand the constitutive relationship between dynamic networks and tailorable mechanics in the PA hydrogels. The newly developed model is uniquely incorporated with the mechanochemistry, and describes the chemical polarization reactions of charged networks and their mechanical behaviors using complex fractal functions. Based on the rubber elasticity theory, constitutive stressâ€"strain relationships of fractal networks have been described using their elastic, conformational, repulsive and polarization free-energy functions. Finally, effectiveness of the proposed model has been verified using both finite element analysis and experimental results of the PA hydrogels reported in literature. [ABSTRACT FROM AUTHOR]

Polyampholyte (PA) hydrogels have attracted significant attention for their superior mechanical strength and toughness compared with other conventional hydrogels. In this study, we present a novel thermodynamic approach to understanding the mechano-chemo-electrotaxis coupling and interfacial dynamics in PA hydrogels. Flory–Huggins theory, carried out through an interfacial free-energy model, is the foundation for the quantitative study of the mechanically constitutive relationship of the PA gels. The proposed free-energy model is further extended to describe the mechano-chemo-electrotaxis switching and interfacial dynamics by co-relating the Williams–Landel–Ferry equation and scaling laws. It was concluded that the interfacial bonding strength is the key factor influencing the mechanical strength and reconstruction reversibility of the PA macromolecular gel system. The resulting analytical outcomes showed good agreement with the reported experimental data. We opine that the proposed model will guide the future application of PA hydrogels. [ABSTRACT FROM AUTHOR]

Abstract We present a phenomenological model for dynamic deformation and mechanical response of double-network (with short-chained ionic network and long-chained covalent network) hydrogel composite based on theory of transient networks. Molecular structures and stress-strain relations of the hydrogel composite were investigated based on thermomechanical properties of the individual network. Constitutive relations were derived for its nonlinear viscoelastic responses and annihilation/reformation rates of active short chains were determined by means of Eyring formula. An extended Volokh model was proposed to separate effects of large strain hysteresis and anomalous viscoelastic relaxation on the hydrogel composite after strain reversal. Experimental results from rate-independent tests are well in agreement with that of the numerical simulations. This study provides a fundamental simulation tool for modelling and predicting mechanics and mechanisms of viscoelastic response and mechanical responses in double-network hydrogel composite. [ABSTRACT FROM AUTHOR]

Molecular network plays a critical role in determining dynamic elasticity of soft condensed polymers, e.g., their varied cross-linking densities and end-to-end distances with changed Young's moduli. Although it has been studied for decades, the coupling relationship between vertices and edges of molecular networks is not well understood, mainly because the degree of the crosslinking points and asymmetry molecular networks have not been considered in the previously models. In this study, a graph theory was employed to formulate an undirected graphical model and describe the coupling between vertices and edges in molecular networks, based on which the dynamic elasticity of polyelectrolyte hydrogel was modeled. From the Kirchhoff graph theory and bead-spring model, the coupling relationship between vertices and edges was obtained using end-to-end distance and viscosity parameters. Combining the Watts–Strogatz model and kinetic probability, the coupling between vertices and edges for the polyelectrolyte network was studied. Furthermore, an adjacency matrix with eigenvalue, number of vertices and mean degree was proposed to formulate constitutive relationships including dynamic elasticity and stress-strain, according to rubber elasticity theory and Mooney-Rivlin model, respectively. The linking between the vertices and edges determines the network structure and dynamic elasticity of the polyelectrolyte hydrogel. Based on the graph theory, the vertices and edges are encoded by adjacency matrix, which is proposed to describe the dynamic elasticity of symmetric and asymmetric network structures using the crosslinking density and end-to-end distance. Finally, effectiveness of the undirected graphical model was verified using both finite element analysis and experimental results of polyelectrolyte hydrogels reported in literature. Constitutive stress-elongation ratio curves for the polyelectrolyte hydrogel, of which the graph network is determined by the mean degree of d = 2, d = 3, d = 4, d = 5, d = 6 and d = 7, at the same vertex number of N = 8 in molecular network. [Display omitted] • An undirected graphical model and describe the coupling between vertices and edges in molecular networks. • Dynamic elasticity of polyelectrolyte hydrogel has been modeled using the adjacency matrix. • A constitutive relationship is developed to understand the molecular networks and their dynamic elasticities. [ABSTRACT FROM AUTHOR]

Mechanical robustness is one of the challenges for soft hydrogels, which are difficult to repair once fractured, mainly because of their chemical bonds and large binding energies required to heal the fractured surfaces within a reasonable time scale. In this study, an extended Maxwell model is proposed to describe intra-chain ionic bonds and inter-chain hydrogen bonds, coupled in physical hydrogels undergoing self-assembly and mechanical toughening, during both of which the intra-chain and inter-chain bonds are working as sub-entanglement and physical crosslink, respectively. According to the rubber elastic theory, a topology model is formulated to identify the working principle of intra-chain and inter-chain coupled binding in the physical hydrogels. Furthermore, a constitutive stress-strain relationship is developed to understand their self-assembling topology signatures and topological transitions. Finally, effectiveness of the proposed model is verified using molecular dynamic simulations and experimental results of physical hydrogels reported in literature. Illustration of dependence of mechanical behaviors on topology signature in terms of intra-chain and inter-chain coupled binding in a hydrogel, where topological geometry is determined by the number of chains and the number of crosslinks. [Display omitted] • An extended Maxwell model is proposed for the physical hydrogels. • A topology model is formulated to identify the working principle of coupled binding. • A constitutive relationship is developed to understand the self-assembly and topological transition. [ABSTRACT FROM AUTHOR]

In this study, a cooperative model has been proposed for the double network (DN) hydrogel, which synchronously undergoes heuristic swelling and inhibitive micellization by the ionic dissociation of polyelectrolyte. Flory-Huggins solution theory is initially employed to identify the working mechanism of dielectric constants on swelling behavior of the DN hydrogel. Then a free-energy function is introduced to formulate the constitutive relationship of the DN hydrogels, in which the first hydrotropic network undergoes a heuristic swelling and the second hydrophobic network undergoes an inhibitive micellization. Finally, the proposed model has been verified using the experimental results reported in the literature. A good agreement between the theoretical results and experimental ones has been achieved. This study provides a fundamental approach to formulate the constitutive relationship and to understand the cooperative dynamics of two types of networks in DN hydrogels induced by the polyelectrolyte. A new cooperative model was proposed to explore the working mechanism of double network (DN) hydrogel undergoes heuristic swelling and inhibitive micellization, synchronously, by the ionic dissociation of polyelectrolyte. Image 10787 • A cooperative model has been proposed for the heuristic swelling and inhibitive micellization. • A free-energy function is introduced to formulate the constitutive relationship of the DN hydrogels. • This study provides a fundamental approach to formulate the cooperative dynamics in DN hydrogels. [ABSTRACT FROM AUTHOR]

Smart materials with self-growing and tailorable mechanical strength have wide-range potential applications in self-healing, self-repairing, self-assembly, artificial muscle, soft robots and intelligent devices. However, their working mechanisms and principles are not fully understood yet and mathematically and physical modeling is a huge challenge, as traditionally synthesized materials cannot self-grow and reconstruct themselves once formed or deformed. In this study, a phenomenological constitutive model was developed to investigate the working mechanisms of self-growing and tailorable mechanical strength in double-network (DN) hydrogel composites, induced by mechanochemical transduction of dynamic-modal mechanophore. An extended Maxwell model was firstly employed to characterize the mechanical unzipping of hydrogel composites, and then mechanochemically induced destruction and reconstruction processes of brittle network in the hydrogel composite were formulated. The enhanced mechanical strength of brittle network has been identified as the key driving force to generate self-growing and tailorable mechanical strength in the hydrogel composite. Finally, a stress-strain constitutive relationship was developed for the dynamic-modal mechanophorein the hydrogel composite. Simulation results obtained from the proposed model were compared with the experimental data, and a good agreement has been achieved. This study provides an effective strategy for modelling and exploring the working mechanism in the mechanoresponsive DN hydrogel composites with self-growing and tailorable mechanical strength. [ABSTRACT FROM AUTHOR]