Decisive test of the ideal behavior of tetra-PEG gels

Effect of Polymer Gel Elasticity on Complex Coacervate Phase Behavior

Gels are key materials in biological systems such as tissues and may control biocondensate formation and structure. To further understand the effects of elastic environments on biomacromolecular assembly, we have investigated the phase behavior and radii of complex coacervate droplets in polyacrylamide (PAM) networks as a function of gel modulus. Poly-l-lysine (PLL) and sodium hyaluronate (HA) complex coacervate phases were prepared in PAM gels with moduli varying from 0.035 to 15.0 kPa. The size of the complex coacervate droplets is reported from bright-field microscopy and confocal fluorescence microscopy. Overall, the complex coacervate droplet volume decreases inversely with the modulus. Fluorescence microscopy is also used to determine the phase behavior and concentration of fluorescently tagged HA in the complex coacervate phases as a function of ionic strength (100-270 mM). We find that the critical ionic strength and complex coacervate stability are nonmonotonic as a function of the network modulus and that the local gel concentration can be used to control phase behavior and complex coacervate droplet size scale. By understanding how elastic environments influence simple electrostatic assembly, we can further understand how biomacromolecules exist in complex, crowded, and elastic cellular environments.

Dynamics of underwater microparticle adhesion to soft hydrated surfaces: Modeling and analysis by time-dependent AFM force spectroscopy

HYPOTHESIS

Understanding the attachment and detachment of microparticles and living cells to surfaces is crucial for developing antifouling strategies. Hydrogel coatings have shown promise in reducing fouling and particle adhesion due to their softness and high water content, yet the mechanisms involved are dynamic and complex, and relevant parameters are not easily accessible. AFM-based force spectroscopy (FS) experiments with colloidal probe particles is a direct way of evaluating adhesive and mechanical relaxational dynamics, yet their interpretation and modeling has been challenging. The present study proposes and examines several dynamic models, suitable for quantitative analysis of FS results with model probe particle on hydrogels surfaces.

EXPERIMENTS

FS were performed using polyethylene glycol (PEG) hydrogels and polystyrene microspheres including particle attachement to the hydrogel surface (loading), holding the particle on the surface with a constant force for variable times (dwell) and pulling the particle away from the surface (unloading) FINDINGS: It was found that a viscoelastic extension of the classical JKR model with energy of adhesion unevenly distributed over the contact area and vanishing at its circumferences accurately described all FS experiments and yielded physically consistent viscoelastic and adhesive dynamic parameters, steadily changing with dwell time and applied force. The observed time evolution and force dependence were rationalized as combination of osmotic and osmo-mechnical relaxation in the contact region.

Ion-induced changes in DNA gels

Small angle neutron scattering (SANS) measurements are reported for DNA gels under near physiological conditions in which the concentration of monovalent and divalent counter-ions and the pH are varied. The scattering intensity I(q) is described by a two-term equation, one due to osmotic concentration fluctuations and the other coming from static inhomogeneities frozen in by the cross-links. SANS in the low q range indicates the presence of large clusters and the size of which exceeds the resolution of the experiment. In the intermediate q-range, the intensity increases with the CaCl2 concentration and the slope approaches -1, corresponding to linear (rod-like) scatterers. In the highest q region, the scattering response is governed by the local chain geometry. Screening of electrostatic interactions by sodium chloride causes a moderate increase in the SANS intensity that is accompanied by an increase in the mesh size L of the network. Addition of calcium chloride, or a decrease in pH, produces similar trends, and ultimately leads to phase separation. The scattering intensity at q = 0, estimated from independent measurements of the osmotic pressure Π, is in excellent agreement with I(0) from the SANS measurements. Anomalous small angle X-ray scattering (ASAXS) measurements on the uncross-linked DNA show that the monovalent ion cloud is only weakly influenced by the addition of divalent ions. Conversely, the divalent counter-ion cloud tightly follows the contour of polymer chains.

Influence of solvent quality on the swelling and deswelling and the shear modulus of semi-dilute solution cross-linked poly(vinyl acetate) gels

We systematically examine the influence of varying temperature (T) over a large range in model poly(vinyl acetate) gels swollen in isopropyl alcohol. The theta temperature Θ, at which the second virial coefficient A2 vanishes, is found to be equal to within numerical uncertainty to the corresponding high molecular mass polymer solution value without cross-links, and we quantify the swelling and deswelling of our model gels relative to their size at T = Θ, as customary for individual flexible polymer chains in solutions. We also quantify the "solvent quality" dependence of the shear modulus G relative to G(T = Θ) and compare to the hydrogel swelling factor, α. We find that all our network swelling and deswelling data can be reduced to a scaling equation of the same general form as derived from renormalization group theory for flexible linear polymer chains in solutions so that it is not necessary to invoke either the Flory-Huggins mean field theory or the Flory-Rehner hypothesis that the elastic and mixing contributions to the free energy of network swelling are separable to describe our data. We also find that changes of G relative to G(T = Θ) are directly related to α. At the same time, we find that classical rubber elasticity theory describes many aspects of these semi-dilute solution cross-linked networks, regardless of the solvent quality, although the prefactor clearly reflects the existence of network defects whose concentration depends on the initial polymer concentration of the polymer solution from which the networks were synthesized.

Structure and conformational properties of ideal nanogel particles in athermal solutions

We investigate the conformational properties of "ideal" nanogel particles having a lattice network topology by molecular dynamics simulations to quantify the influence of polymer topology on the solution properties of this type of branched molecular architecture. In particular, we calculate the mass scaling of the radius of gyration (Rg), the hydrodynamic radius, as well as the intrinsic viscosity with the variation of the degree of branching, the length of the chains between the branched points, and the average mesh size within these nanogel particles under good solvent conditions. We find competing trends between the molecular characteristics, where an increase in mesh size or degree of branching results in the emergence of particle-like characteristics, while an increase in the chain length enhances linear polymer-like characteristics. This crossover between these limiting behaviors is also apparent in our calculation of the form factor, P(q), for these structures. Specifically, a primary scattering peak emerges, characterizing the overall nanogel particle size. Moreover, a distinct power-law regime emerges in P(q) at length scales larger than the chain size but smaller than Rg of the nanogel particle, and the Rg mass scaling exponent progressively approaches zero as the mesh size increases, the same scaling as for an infinite network of Gaussian chains. The "fuzzy sphere" model does not capture this feature, and we propose an extension to this popular model. These structural features become more pronounced for values of molecular parameters that enhance the localization of the branching segments within the nanogel particle.

Neutralization and Salt Effect on the Structure and Mechanical Properties of Polyacrylic Acid Gels under Equivolume Conditions

The effects of neutralization and salt on the structure and mechanical properties of polyacrylic acid (PAA) gels under equivolume conditions were investigated by small-angle X-ray scattering (SAXS) measurements and tensile tests. We attained the equivolume condition by immersing a piece of PAA gel sample in an ion reservoir containing linear PAA, NaOH, and NaCl at prescribed concentrations (post-ion-tuning). The volume fraction of the linear polymer was set to be the same as that of the gel so as to satisfy the iso-osmotic pressure at the reference state. Various types of reservoirs were prepared by adding NaOH and/or NaCl with different concentrations to the reference reservoir, followed by immersing a PAA gel piece. In the SAXS measurements, a scattering peak appeared, and the scattering intensity at q = 0 decreased by neutralization, while the addition of salt increased the scattering intensity. On the other hand, Young’s modulus measured with the tensile test decreased with neutralization; however, it scarcely changed with the addition of salt. The newly developed equivolume post-ion-tuning technique may serve as a new standard scheme to study polyelectrolyte gels.

Theory of Charged Gels: Swelling, Elasticity, and Dynamics

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.

Jones R, Lou J, Xia Y. Systematic investigation of synthetic polyelectrolyte bottlebrush solutions by neutron and dynamic light scattering, osmometry, and molecular dynamics simulation

There is a great interest in the synthesis and characterization of polyelectrolytes that mimic naturally occurring bottlebrush polyelectrolytes to capitalize on the unique properties of this class of macromolecules. Charged bottlebrush polymers form the protective mucus layer in the lungs, stomach, and orifices of animals and provide osmotic stabilization and lubrication to joints. In the present work, we systematically investigate bottlebrush poly(sodium acrylates) through a combination of measurements of solution properties (osmometry, small-angle neutron scattering, and dynamic light scattering) and molecular dynamics simulations, where the bottlebrush properties are compared in each case to their linear polymer counterparts. These complementary experimental and computational methods probe vastly different length- and timescales, allowing for a comprehensive characterization of the supermolecular structure and dynamics of synthetic polyelectrolyte bottlebrush molecules in solution.

Structural properties of contractile gels based on light-driven molecular motors: a small-angle neutron and X-ray study

The detailed structure of active polymer gels built by integrating light-driven rotary molecular motors as reticulation units in polymer networks is discussed as a function of gel composition. Upon light-irradiation, the collective rotation of molecular motors is translated into the macroscopic contraction of the gels through polymer chains twisting. The major role of the characteristic ratio c/c* (c* being the overlap concentration of the polymer-motor conjugates before crosslinking) on the contraction efficiency is exploited. Combined small-angle neutron and X-ray scattering experiments reveal the importance of heterogeneities in the macroscopic contraction process: the mesh size of the network increases under irradiation in the whole range of c/c*, an increase that is maximal for c/c* = 1; i.e. at higher contraction efficiency. Furthermore, the mesh size of the network reaches equilibrium within a short period of time, while the heterogeneities increase in size untill the end of the contraction process. Finally, the significant motorized twisting of polymer chains within the network allows to foresee the design of new storage energy systems.

Effects of mono- and divalent cations on the structure and thermodynamic properties of polyelectrolyte gels

Measurements are reported on the effect of monovalent and divalent salts on the swelling behavior and supramolecular structure of sodium polyacrylate gels (NaPA) made by osmotic swelling pressure and small angle neutron scattering measurements. The swelling response of the gels in solutions of ten different monovalent salts is found to be practically identical indicating that the principal effect of monovalent ions is screening the electrostatic repulsion among the charged groups on the polyelectrolyte chains; i.e., chemical differences between the monovalent ions do not play a significant role. Introducing Ca2+ ions into the equilibrium NaCl solution results in a sharp volume transition of the gels. The threshold Ca2+ ion concentration at which the transition occurs increases with increasing NaCl concentration in the surrounding bath. It is demonstrated that the swelling behavior of NaPA gels exhibits universal properties in solutions containing both NaCl and CaCl2. Osmotic swelling pressure measurements reveal that both the second and third virial coefficients decrease with increasing CaCl2 concentration until the volume transition is reached. The macroscopic measurements are complemented by small angle neutron scattering that reveals the variation of the thermodynamic length scales as the volume transition is approached. The thermodynamic correlation length L increases with increasing CaCl2 concentration.

Stretching PEO-PPO Type of Star Block Copolymer Gels: Rheology and Small-Angle Scattering

Cross-linked Tetronic star block copolymer gels, based on poly(ethylene oxide) and poly(propylene oxide), behave quite regular with respect to mechanical properties, but exhibits unusual absence of structural response to strain. The elastic response is linear up to more than 100% strain, with a steady-state modulus of the order of 0.01 MPa after an initial stress relaxation. Neutron and X-ray scattering experiments show a consistent but unexpected response to uniaxial strain, with no changes in characteristic molecular dimensions. Upon strain beyond about 100%, that is, when the stress-strain curve is no longer linear, structural texture appears and becomes even more pronounced upon further strain, thus, indicating alignment of the self-assembled hexagonally ordered cylindrical micelles with the cylinder-axis perpendicular to the strain. It is proposed that the main structural response to large-amplitude strain is related to a layer-dominated structure of cross-linked star molecules.

Ultra-tough injectable cytocompatible hydrogel for 3D cell culture and cartilage repair

In this work, we developed a very facile strategy, i.e. dual dynamic crosslinking, to prepare a high performance injectable hydrogel. Poly(vinyl alcohol) (PVA) was crosslinked by 4-carboxyphenylboronic acid (CPBA) through the generation of borate bonding and ionic interaction to bridge the polymer chains in the presence of calcium ions. The dynamic gathering of CPBA could induce a self-reinforcing effect inside the hydrogel matrix, leading to high tensile and compressive moduli of the hydrogel over 1.0 MPa including the highest compressive modulus up to 5.6 MPa. Meanwhile, the mechanical properties of the hydrogel can be broadly and accurately tuned. And owing to the flexible PVA network, the hydrogel is ultra-tough, showing maximum tensile strain, tensile and compressive fracture energies up to 1600%, 600 kJ m^-2 and 25 kJ m^-2, respectively. Besides, the dynamic bonding overcomes the barriers to forming an injected strong hydrogel, e.g. to obtain a modulus and a fracture energy exceeding 1.0 MPa and 40 kJ m^-2, by using a commercial dual-syringe kit under physiological conditions. Such a mild gelation procedure benefits the administration, 3D encapsulation and proliferation of cells of the hydrogels. The application of the PVA hydrogel was demonstrated by effective cartilage repair.