Equilibrium Gel Research Articles

Networks of Limited-Valency Patchy Particles.

Equilibrium gels provide physically attractive counterparts of nonequilibrium gels, allowing statistical understanding and design of the equilibrium gel structure. Here, we assemble two-dimensional equilibrium gels from limited-valency "patchy" colloidal particles and follow their evolution at the particle scale to elucidate cluster-size distributions and free energies. By finely adjusting the patch attraction with critical Casimir forces, we let a mixture of two-valent and pseudo-three-valent patchy particles approach the percolated network state through a set of equilibrium states. Comparing this equilibrium route with a deep quench, we find that both routes approach the percolated state via the same equilibrium states, revealing that the network topology is uniquely set by the particle bond angles, independent of the formation history. The limited-valency system follows percolation theory remarkably well, approaching the percolation point with the expected universal exponents.

Gelation Time of Network-Forming Polymer Solutions with Reversible Cross-Link Junctions of Variable Multiplicity.

The gelation time tg necessary for a solution of functional (associating) molecules to reach its gel point after a temperature jump, or a sudden concentration change, is theoretically calculated on the basis of the kinetic equation for the stepwise cross-linking reaction as a function of the concentration, temperature, functionality f of the molecules, and multiplicity k of the cross-link junctions. It is shown that quite generally tg can be decomposed into the product of the relaxation time tR and a thermodynamic factor Q. They are functions of a single scaled concentration x≡λ(T)ϕ, where λ(T) is the association constant and ϕ is the concentration. Therefore, the superposition principle holds with λ(T) as a shift factor of the concentration. Additionally, they all depend on the rate constants of the cross-link reaction, and hence it is possible to estimate these microscopic parameters from macroscopic measurements of tg. The thermodynamic factor Q is shown to depend on the quench depth. It generates a singularity of logarithmic divergence as the temperature (concentration) approaches the equilibrium gel point, while the relaxation time tR changes continuously across it. Gelation time tg obeys a power law tg-1∼xn in the high concentration region, whose power index n is related to the multiplicity of the cross-links. The retardation effect on the gelation time due to the reversibility of the cross-linking is explicitly calculated for some specific models of cross-linking to find the rate-controlling steps in order for the minimization of the gelation time to be easier in the gel processing. For a micellar cross-linking covering a wide range of the multiplicity, as seen in hydrophobically-modified water-soluble polymers, tR is shown to obey a formula similar to the Aniansson-Wall law.

Mechanistic insight into the structure, thermodynamics and dynamics of equilibrium gels of multi-armed DNA nanostars.

The unique sequence specificity rule of DNA makes it an ideal molecular building block for constructing periodic arrays and devices with nanoscale accuracy and precision. Here, we present the self-assembly of DNA nanostars having three, four and five arms into a gel phase using a simplistic coarse-grained bead-spring model developed by Z. Xing, C. Ness, D. Frenkel and E. Eiser (Macromolecules, 2019, 52, 504-512). Our simulations show that the DNA nanostars form a thermodynamically stable fully bonded gel phase from an unstructured liquid phase with the lowering of temperature. We characterize the phase transition by calculating several structural features such as the radial distribution function and structure factor. The thermodynamics of gelation is quantified by the potential energy and translational pair-entropy of the system. The phase transition from an arrested gel phase to an unstructured liquid phase has been modelled using a two-state theoretical model. We find that this transition is enthalpy driven, and loss of configuration and translational entropy is counterpoised by enthalpic interaction of the DNA sticky-ends, which gives rise to a gel phase at low temperature. The absolute rotational and translational entropy of the systems, measured using a two-phase thermodynamic model, also substantiates the gel transition. The slowing down of the dynamics upon approaching the transition temperature from a high temperature demonstrates the phase transition to a gel phase. A detailed numerical simulation study of the morphology, dynamics and thermodynamics of DNA gelation can provide guidance for future experiments, is easily extensible to other polymeric systems, and is expected to help in understanding the physics of self-assembly.

Correlation between effective charge density and crosslinking efficiency of dicarboxylic acid containing highly anionic networks

By investigating the relationship between the swelling and deformation properties, an attempt was made to establish a correlation between microstructure and charge density of anionic polyacrylamide/itaconic acid (PAAm/ITA) hydrogels. The effective charge density of network dominated the microstructure of PAAm/ITA hydrogels. The porosity of anionic hydrogels increased with addition of diprotic ITA, and resulting microstructure determined the swollen state deformation. Based on effective charge density, the swelling gradually increased and maximum swelling was achieved with 14% ITA, while there was a 24-fold increase in gel volume relative to homopolymer network. The relationship between elasticity and crosslinking density was explained using Rubber elasticity theory on deformation behavior. A variety of factors that affect swelling and elasticity was explored such as effective charge density, crosslink density of anionic network as well as pH of solution and surfactant type. The equilibrium volume swelling ratio in water scales with network charge density by the relation φV ∝ feff1.17, while the dependence of reduced modulus with equilibrium gel volume was found to be Gr≈(φV)−0.28 indicating that equilibrium swollen PAAm/ITA hydrogels are in Gaussian regime. An empirical relationship has been found implying that by varying amount of ITA, the crosslinked structure and crosslinking density can be effectively controlled. PAAm/ITA hydrogels showed good reversible characteristics during repeated oscillations between pH 11.2 and 2.1, which is important for controlled drug delivery system. Rapid water penetration of PAAm/ITA hydrogels with internal morphology and high swelling resulting from the presence of ITA revealed internal adsorption sites for methyl violet and methylene blue. The adsorption kinetics followed a pseudo-second order and showed a two-stage intra-particle diffusion model. The results will contribute to the determination of correlation between anionic structure and properties for efficient and economical design of anionic materials for specific uses and industrial scale-up.

Preparation, characterization and application of gamma irradiated some water soluble polymers/natural rubber latex blends

AbstractThis work mainly depends on the assumption or hypothesis which exploits the tendency of natural rubber latex (NRL) to cross‐link under irradiation in the presence of Alginate and CMC biopolymer and form (ALG/NRL and CMC/NRL) films containing polar/charged functional groups which offer them hydrophilicity, and consequently water absorption capacity. CMC/NRL and ALG/NRL (v/v) blend films prepared first by latex compounding followed by casting technique. The prepared ALG/NRL and CMC/NRL blend films characterized then, by various techniques such as IR, scanning electron microscopy (SEM), and thermogravimetric analysis (TGA). Equilibrium swelling properties and gel percent GF% of prepared films also studied in details. GF% studies revealed that the GF% increased with increasing both NRL content and irradiation dose for both ALG/NRL and CMC/NRL. Thermal analysis shows the increased thermal stability of the irradiated samples due cross‐linking effect of NRL. The improved gel content percentage obtained paved the way for the application of various films in the removal of toxic dyes such as acidic, direct, and basic dyes from waste water where in this study, the films exhibited high affinity toward basic blue dye.

Dynamics of equilibrium-linked colloidal networks

Colloids that attractively bond to only a few neighbors (e.g., patchy particles) can form equilibrium gels with distinctive dynamic properties that are stable in time. Here, we use a coarse-grained model to explore the dynamics of linked networks of patchy colloids whose average valence is macroscopically, rather than microscopically, constrained. Simulation results for the model show dynamic hallmarks of equilibrium gel formation and establish that the colloid-colloid bond persistence time controls the characteristic slow relaxation of the self-intermediate scattering function. The model features re-entrant network formation without phase separation as a function of linker concentration, centered at the stoichiometric ratio of linker ends to nanoparticle surface bonding sites. Departures from stoichiometry result in linker-starved or linker-saturated networks with reduced connectivity and shorter characteristic relaxation times with lower activation energies. Underlying the re-entrant trends, dynamic properties vary monotonically with the number of effective network bonds per colloid, a quantity that can be predicted using Wertheim's thermodynamic perturbation theory. These behaviors suggest macroscopic in situ strategies for tuning the dynamic response of colloidal networks.

Percolation in binary mixtures of linkers and particles: Chaining vs branching.

Equilibrium gels of colloidal particles can be realized through the introduction of a second species, a linker that mediates the bonds between colloids. A gel forming binary mixture whose linkers can self-assemble into linear chains while still promoting the aggregation of particles is considered in this work. The particles are patchy particles with fC patches of type C and the linkers are patchy particles with 2 patches of type A and fB patches of type B. The bonds between patches of type A (AA bonds) promote the formation of linear chains of linkers. Two different ways (model A and model B) of bonding the linkers to the particles-or inducing branching-are studied. In model A, there is a competition between chaining and branching, since the bonding between linkers and particles takes place through AC bonds only. In model B, the linkers aggregate to particles through bonds BC only, making chaining and branching independent. The percolation behavior of these two models is studied in detail, employing a generalized Flory-Stockmayer theory and Monte Carlo simulations. The self-assembly of linkers into chains reduces the fraction of particles needed for percolation to occur (models A and B) and induces percolation when the fraction of particles is high (model B). Percolation by heating and percolation loops in temperature-composition diagrams are obtained when the formation of chains is energetically favorable by increasing the entropic gain of branching (model A). Chaining and branching are found to follow a model dependent relation at percolation, which shows that, for the same composition, longer chains require less branching for percolation to occur.

Interpenetrating gels in binary suspensions of DNA nanostars.

We experimentally investigate the equilibrium gel formation in a binary mixture of DNA nanostars. The binding rules, encoded in the DNA sequence of the nanostar binding ends, are such that each component is able to form only intra-species bonds. Reducing the excluded volume by properly designing the DNA nanostars, we show that two interpenetrating unconnected gels form in the sample on cooling, each of the two forms at a temperature controlled by the selected binding DNA sequence. The dynamic light scattering correlation functions show a non-common three-step relaxation process due to the splitting of the slow relaxation into two distinct decays, each of them reflecting the relaxation dynamics of one of the two networks.

Entropy-Driven Thermo-gelling Vitrimer.

Thermo-gelling polymers have been envisioned as promising smart biomaterials but limited by their weak mechanical and thermodynamic stabilities. Here, we propose a new thermo-gelling vitrimer, which remains at a liquid state because of the addition of protector molecules preventing the crosslinking, and with increasing temperature, an entropy-driven crosslinking occurs to induce the sol–gel transition. Moreover, we find that the activation barrier in the metathesis reaction of vitrimers plays an important role, and experimentally, one can use catalysts to tune the activation barrier to drive the vitrimer to form an equilibrium gel at high temperature, which is not subject to any thermodynamic instability. We formulate a mean-field theory to describe the entropy-driven crosslinking of the vitrimer, which agrees quantitatively with computer simulations and paves the way for the design and fabrication of novel vitrimers for biomedical applications.

Protein Binding in Translational Antimicrobial Development-Focus on Interspecies Differences.

Background/Introduction: Plasma protein binding (PPB) continues to be a key aspect of antibiotic development and clinical use. PPB is essential to understand several properties of drug candidates, including antimicrobial activity, drug-drug interaction, drug clearance, volume of distribution, and therapeutic index. Focus areas of the review: In this review, we discuss the basics of PPB, including the main drug binding proteins i.e., Albumin and α-1-acid glycoprotein (AAG). Furthermore, we present the effects of PPB on the antimicrobial activity of antibiotics and the current role of PPB in in vitro pharmacodynamic (PD) models of antibiotics. Moreover, the effect of PPB on the PK/PD of antibiotics has been discussed in this review. A key aspect of this paper is a concise evaluation of PPB between animal species (dog, rat, mouse, rabbit and monkey) and humans. Our statistical analysis of the data available in the literature suggests a significant difference between antibiotic binding in humans and that of dogs or mice, with the majority of measurements from the pre-clinical species falling within five-fold of the human plasma value. Conversely, no significant difference in binding was found between humans and rats, rabbits, or monkeys. This information may be helpful for drug researchers to select the most relevant animal species in which the metabolism of a compound can be studied for extrapolating the results to humans. Furthermore, state-of-the-art methods for determining PPB such as equilibrium dialysis, ultracentrifugation, microdialysis, gel filtration, chromatographic methods and fluorescence spectroscopy are highlighted with their advantages and disadvantages.

Phase separation of chemically crosslinked poly(n-butyl methacrylate-co-methacrylic acid) in mixtures of N,N-dimethyl formamide and water

When a copolymer network of chemically crosslinked poly( n -butyl methacrylate- co -methacrylic acid) was immersed into a bath of N,N -dimethylformamide (DMF) and water, the swollen network underwent phase separation depending on the fraction x w of water in the bath. Swelling ratio, light transmittance, thermomechanics, dynamical mechanical spectra, and tensile property of the gels in baths of different x w 's were investigated. A ternary phase diagram of this system was calculated from theory for comparison of the experimental data. A glass line was also provided in the ternary phase diagram from the estimation by the diluent effect on glass temperature. The results indicated that the polymer-rich phase after phase separation became glassy as the bath composition x w was above 0.75. This resulted in a fundamental change in the thermomechanical behavior of the gel from one of a typical rubber to one a typical glassy polymer. Meanwhile a dynamical gel-to-glass transition was observed in the time-temperature superposition (TTS) master curves. The transition temperature T 0 decrease with increasing x w . A weak-to-tough transition was observed at T − T 0 ≈ 0 K, while a tough-to-brittle transition occurs at T − T 0 ≈ −50 K. A conceptual scheme was proposed to clarify the interplay of phase separation, glass transition in the present work. This scheme could also explain some of the previous work. An example of application in shape memory materials was provided. Highlights • Phase separation inside a gel in equilibrium with solvent/nonsolvent is calculated. • Glass transition line and the Berghmans point is added to the phase diagram. • Thermoelasticity of gel swollen in solvent/nonsolvent is eccentric. • The calculated phase diagram explains the window of mechanical toughening.

Empty liquid state and re-entrant phase behavior of the patchy colloids confined in porous media.

Patchy colloids with three and four equivalent patches, confined in an attractive random porous medium, undergo re-entrant gas-liquid phase separation with the liquid phase density approaching zero at low temperatures. The (bonding) colloid-colloid interaction causes the liquid-gas phase separation, which is modulated by the presence of the randomly distributed hard-sphere obstacles, attracting the colloids via Yukawa potential. Due to this interaction, a layer of mutually bonded colloids around the obstacles is formed. The network becomes nonuniform, with colloid particles locally centered on the obstacles. Features described in this article may open possibilities to produce equilibrium gels with predefined nonuniform distribution of particles and indicate how complicated the phase behavior of biological macromolecules in a crowded environment may be.

Spatially uniform dynamics in equilibrium colloidal gels.

Gels of DNA nanostars, besides providing a compatible scaffold for biomedical applications, are ideal model systems for testing the physics of equilibrium colloidal gels. Here, using dynamic light scattering and photon correlation imaging (a recent technique that, by blending light scattering and imaging, provides space-resolved quantification of the dynamics), we follow the process of gel formation over 10 orders of magnitude in time in a model system of tetravalent DNA nanostars in solution, a realization of limited-valence colloids. Such a system, depending on the nanostar concentration, can form either equilibrium or phase separation gels. In stark contrast to the heterogeneity of concentration and dynamics displayed by the phase separation gel, the equilibrium gel shows absence of aging and a remarkable spatially uniform dynamics.

Programmable Anisotropy and Percolation in Supramolecular Patchy Particle Gels.

Patchy particle interactions are predicted to facilitate the controlled self-assembly and arrest of particles into phase-stable and morphologically tunable "equilibrium" gels, which avoids the arrested phase separation and subsequent aging that is typically observed in traditional particle gels with isotropic interactions. Despite these promising traits of patchy particle interactions, such tunable equilibrium gels have yet to be realized in the laboratory due to experimental limitations associated with synthesizing patchy particles in high yield. Here, we introduce a supramolecular metal-coordination platform consisting of metallic nanoparticles linked by telechelic polymer chains, which validates the predictions associated with patchy particle interactions and facilitates the design of equilibrium particle hydrogels through limited valency interactions. We demonstrate that the interaction valency and self-assembly of the particles can be effectively controlled by adjusting the relative concentration of polymeric linkers to nanoparticles, which enables the gelation of patchy particle hydrogels with programmable local anisotropy, morphology, and low mechanical percolation thresholds. Moreover, by crowding the local environment around the patchy particles with competing interactions, we introduce an independent method to control the self-assembly of the nanoparticles, thereby enabling the design of highly anisotropic particle hydrogels with substantially reduced percolation thresholds. We thus establish a canonical platform that facilitates multifaceted control of the self-assembly of the patchy nanoparticles en route to the design of patchy particle gels with tunable valencies, morphologies, and percolation thresholds. These advances lay important foundations for further fundamental studies of patchy particle systems and for designing tunable gel materials that address a wide range of engineering applications.

On the Role of Competing Interactions in Charged Colloids with Short-Range Attraction

In this review, we discuss recent advances in the investigation of colloidal systems interacting via a combination of short-range attraction and long-range repulsion. The prototypical examples of this phenomenology are charged colloids with depletion interactions, but the results apply, to a large extent, also to suspensions of globular proteins, clays, and, in general, to systems with competing attractive (hydrophobic) and repulsive (polar) contributions. After a brief introduction to the problem, we focus on the three disordered states that characterize these systems: equilibrium cluster phase, equilibrium gel, and Wigner glass of clusters. We provide a comparison of their static and dynamic observables, mainly by means of numerical simulations. Next, we discuss the few available studies on their viscoelastic properties and on their response to an external shear. Finally, we provide a summary of the current findings and also raise the main open questions and challenges for the future in this topic.

Volume Transition and Phase Coexistence in Polyelectrolyte Gels Interacting with Amphiphiles and Proteins.

Polyelectrolyte gels have the capacity to absorb large amounts of multivalent species of opposite charge from aqueous solutions of low ionic strength, and release them at elevated ionic strengths. The reversibility offers the possibility to switch between “storage” and “release” modes, useful in applications such as drug delivery. The review focuses on systems where so-called volume phase transitions (VPT) of the gel network take place upon the absorption and release of proteins and self-assembling amphiphiles. We discuss the background in terms of thermodynamic driving forces behind complex formation in oppositely charged mixtures, the role played by cross-links in covalent gels, and general aspects of phase coexistence in networks in relation to Gibbs’ phase rule. We also briefly discuss a gel model frequently used in papers covered by the review. After that, we review papers dealing with collapse and swelling transitions of gels in contact with solution reservoirs of macroions and surfactants. Here we describe recent progress in our understanding of the conditions required for VPT, competing mechanisms, and hysteresis effects. We then review papers addressing equilibrium aspects of core–shell phase coexistence in gels in equilibrium. Here we first discuss early observations of phase separated gels and results showing how the phases affect each other. Then follows a review of recent theoretical and experimental studies providing evidence of thermodynamically stable core–shell phase separated states, and detailed analyses of the conditions under which they exist. Finally, we describe the results from investigations of mechanisms and kinetics of the collapse/swelling transitions induced by the loading/release of proteins, surfactants, and amphiphilic drug molecules.

Amnion and collagen-based blended hydrogel improves burn healing efficacy on a rat skin wound model in the presence of wound dressing biomembrane.

A burn wound is one of the most frequent and devastating injuries for patients which requires extensive care. Early treatment of burn wounds improves healing significantly. This study was designed to investigate the efficacy of amnion and collagen-based hydrogels on cutaneous burn wound healing in rats with covering membrane. We prepared a novel cell free hydrogel comprising human amnion, rabbit collagen, carboxymethyl cellulose sodium salt, citric acid, methyl paraben, propyl paraben, glycerin and triethanol amine. The wound covering membrane was developed from rabbit collagen and prawn shell chitosan. Beside swelling ratio, water absorption, equilibrium water content, gel fraction and spreadability analysis, in vitro cytotoxicity and biocompatibility tests were performed for the formulated hydrogels. Following the skin irritation study, second-degree burns were created on the dorsal region of the rats and the gels were applied with/without covering membrane to study the wound contraction and re-epithelialization period. The formulated hydrogels were observed non-cytotoxic and compatible with human blood cells. No erythema and edema were found in skin irritation assay confirming the safety and applicability. Hydrogel consisting in a combination of amnion and collagen demonstrated significantly rapid wound healing, driven by complete re-epithelialization (16.75 ± 0.96 days) and closure by wound contraction (72 ± 3.27%, P < 0.0000009) when wound dressing membrane was used, whereas this gel alone healed about 62.5 ± 4.43% (P < 0.00001) and required 18.75 ± 0.50 days to complete re-epithelialization. Additionally, the gel with covering membrane treated group had maximum average body weight, food and water intake. The amnion and collagen-based blended gel offers alternative possibilities to treat skin wounds when covered with film, which could overcome the limitations associated with modern therapeutic products such as high costs, long manufacturing times, complexities, storing, and presence of living biomaterials.

Glass transition and reversible gelation in asymmetric binary mixtures: A study by mode coupling theory and molecular dynamics.

The glass transition and the binodals of asymmetric binary mixtures are investigated from the effective fluid approach in the mode coupling theory and by molecular dynamics. Motivated by previous theoretical predictions, the hard-sphere mixture and the Asakura-Oosawa models are used to analyze experimental results from the literature, relative to polystyrene spheres mixed either with linear polymers or with dense microgel particles. In agreement with the experimental observations, the specificity of the depletant particles is shown to favor lower density gels. It further favors equilibrium gelation by reducing also the tendency of the system to phase separate. These results are confirmed by a phenomenological modification of the mode coupling theory in which the vertex functions are computed at an effective density lower than the actual one. A model effective potential in asymmetric mixtures of hard particles is used to further check this phenomenological modification against molecular dynamics simulation.

Structure and phase behavior of polymer-linked colloidal gels

Low-density "equilibrium" gels that consist of a percolated, kinetically arrested network of colloidal particles and are resilient to aging can be fabricated by restricting the number of effective bonds that form between the colloids. Valence-restricted patchy particles have long served as one archetypal example of such materials, but equilibrium gels can also be realized through a synthetically simpler and scalable strategy that introduces a secondary linker, such as a small ditopic molecule, to mediate the bonds between the colloids. Here, we consider the case where the ditopic linker molecules are low-molecular-weight polymers and demonstrate using a model colloid-polymer mixture how macroscopic properties such as the phase behavior as well as the microstructure of the gel can be designed through the polymer molecular weight and concentration. The low-density window for equilibrium gel formation is favorably expanded using longer linkers while necessarily increasing the spacing between all colloids. However, we show that blends of linkers with different sizes enable wider variation in microstructure for a given target phase behavior. Our computational study suggests a robust and tunable strategy for the experimental realization of equilibrium colloidal gels.

Slow dynamics and equilibrium gelation in fractionated montmorillonite nanoplatelet dispersions

Spontaneous temporal evolution of self-assembled phases of high aspect ratio (~ 250) fractionated nanoplatelets of Na Montmorillonite (FMMT) dispersions is systematically studied using rheology, light scattering, dilution, and electron microscopy experiments. Age-dependent viscosity of the suspensions shows a power-law behavior with the waiting time and scaled concentrations, beyond a threshold concentration, cg, below which phase separation occurs on long waiting times. The slow dynamics was monitored for more than 5 years which revealed the system evolved into different self-assembled phases, namely phase separation and equilibrium gels. Scanning electron microscope images show the highly porous nature of the gels. Gelation kinetics in the aging dispersion was modeled through percolation formalism which suggested that slow dynamics was responsible for the growth of the network. The formation of equilibrium gels was observed similar to the low aspect ratio (~ 25) Laponite® dispersions and the patchy particles. Thus, the present study provides experimental evidence of patchy nature of MMT clays, equilibrium, gelation, and empty liquids, which do not require an underlying phase separation to form as was predicted for the low-valance colloidal particles and multi-valent DNA nanostars.