The fundamental attributes of charged hydrogels containing predominantly water and controllable amounts of low molar mass electrolytes are of tremendous significance in biological context and applications in healthcare. However, a rigorous theoretical formulation of gel behavior continues to be a challenge due to the presence of multiple length and time scales in the system which operate simultaneously. Furthermore, chain connectivity, the electrostatic interaction, and the hydrodynamic interaction all lead to long-range interactions. In spite of these complications, considerable progress has been achieved over the past several decades in generating theories of variable complexity. The present review presents an analytically tractable theory by accounting for correlations emerging from topological, electrostatic, and hydrodynamic interactions. Closed-form formulas are derived for charged hydrogels to describe their swelling equilibrium, elastic moduli, and the relationship between microscopic properties such as gel diffusion and macroscopic properties such as elasticity. In addition, electrostatic coupling between charged moieties and their ion clouds, which significantly modifies the elastic diffusion coefficient of gels, and various scaling laws are presented. The theoretical formulas summarized here are useful to adequately capture the essentials of the physics of charged gels and to design new hydrogels with specified elastic and dynamical properties.

Luminescence imaging techniques assume a critical role in the evaluation of the durability and lifespan of solar cells. This study presents a novel empirical approach that capitalizes on simple machine learning-based linear regression (MLLR) to prognosticate the performance of perovskite solar cells (PSCs). Three types of MLLR models were developed: (a) Full width at Half maximum (FWHM)-based MLLR Model, (b) Colour Correlated Temperature (CCT)-based MLLR Model, and (c) Hybrid or FWHM-CCT-based MLLR Model. The proposed FWHM-based MLLR model achieves the best overall performance in fitting all current-voltage (IV) parameters. The CCT-based model, while applicable to all parameters, exhibits slightly lower accuracy compared to the FWHM-based approach; however, considering standalone analysis, CCT-based MLLR model is the best fit for estimation of Voc and FF parameters. This prognostication hinges on quantitatively assessing the FWHM using electroluminescence (EL) spectroscopy data. Notably, this investigation stands out by showcasing the potential of simple yet supervised machine learning in appraising IV characteristics of PSC through EL spectroscopy. Remarkably, the study attains an average predictive accuracy of beyond 90% for IV characteristics via EL spectroscopy facilitated by a supervised machine-learning model using both continuous and discontinuous datasets. The findings of this research underscore the potential of supervised machine learning as an innovative technique for approximating IV curve parameters of PSC, utilizing EL spectroscopy. This advancement holds significant ramifications for fortifying the assessment of PSCs in terms of reliability analysis and manufacturing efficiency.

Uniformly charged polyelectrolyte molecules disperse uniformly in aqueous electrolyte solutions, due to electrostatic repulsion between them. In stark contrast to this well-established result of homogeneous polyelectrolyte solutions, we report a phenomenon where an aqueous solution of positively charged poly(L-lysine) (PLL) exhibits precipitation of similarly charged macromolecules at low ionic strength and a homogeneous solution at very high ionic strength, with a stable mesomorphic state of spherical aggregates as an interlude between these two limits. The precipitation at lower ionic strengths that is orthogonal to the standard polyelectrolyte behavior and the emergence of the mesomorphic state are triggered by the presence of a monovalent small organic anion, acrylate, in the electrolyte solution. Using light scattering, we find that the hydrodynamic radius R _h of isolated PLL chains shrinks upon a decrease in electrolyte (NaBr) concentration, exhibiting the “anti-polyelectrolyte effect.” In addition, R _h of the aggregates in the mesomorphic state depends on PLL concentration c _p according to the scaling law, R h ~ c p 1 / 6 . Furthermore, at higher PLL concentration, the mesomorphic aggregates disassemble by a self-poisoning mechanism. We conjecture that all these findings can be attributed to both intra- and interchain dipolar interactions arising from the transformation of polycationic PLL into a physical polyzwitterionic PLL at higher concentrations of acrylate. The reported phenomenon of PLL exhibiting dipole-directed assembly of mesomorphic states and the anti-polyelectrolyte effect are of vital importance toward understanding more complex situations such as coacervation and formation of biomolecular condensates.

Breaking the paradigm that polymers in crowded aqueous media obey Einstein’s law of diffusion, we report a localized nondiffusive hierarchical metastable state at intermediate confinements. Combining electrostatic and topological effects, we can tune the propensity of this new universality class in a quasicoacervate gel system consisting of guest polyamino acid chains inside an oppositely charged host hydrogel. Our observations offer strategies for controlled release and retention of macromolecules in aqueous crowded media, while opening a new direction for understanding topologically frustrated dynamics in polymers and other soft matter systems.

Hydrogel composites in an aqueous media with viscoelastic properties and elastic modulus that can be precisely tailored are desirable to mimic many biological tissues ranging from mucus, vitreous humor, and nucleus pulposus as well as build up biosensors. Without altering the chemistry, tuning the physical interactions and structures to govern the viscoelastic properties of the hydrogels is indispensable for their applications but quite limited. Here we design a complexation gel composite and utilize the physical principle of topologically frustrated dynamical state to tune the correlated structures between the guest polycation chains and negatively charged host gels. We precisely quantify the mesh size of the host gel and guest chain size. By designing various topologically correlated structures, a viscoelastic moduli map can be built up, ranging from tough to ultrasoft, and from elastic-like with low damping properties to viscous-like with high damping properties. We also tune the swelling ratio by using entropy effect and discover an Entropy-driven Topologically Isovolumetric Point. Our findings provide essential physics to understand the relationship between entropy-driven correlated structures and their viscoelastic properties of the complexation hydrogel composites and will have diverse applications in tissue engineering and soft biomaterials.

Gels comprised of dynamic bonds are important candidates for the emerging ‘intelligent’ gels due to their unique characteristics. We report a universal law of hierarchical gel dynamics arising from association-dissociation of physical crosslinks, as discerned from dynamic light scattering (DLS) on diverse sets of complex gels. It is the first experimental evidence of a stretched exponential decay with a universal exponent 1/3 in DLS for all the physical gels, complementing more than five decades of DLS studies on conventional chemical gels. Here we show that diversely different chemistries of dynamic bonds map into the observed unifying law for large-scale collective dynamical properties of physical gels. This discovery allows identification of whether physical or chemical bonds dominate the crosslinks in complex gels, as well as extraction of local energetics of the constituent physical crosslinks by their characteristic relaxation times. It also elicits large-scale functional properties applicable in smart gels.