How the Shape and Chemistry of Molecular Penetrants Control Responsive Hydrogel Permeability

Anisotropic Liesegang pattern for the nonlinear elastic biomineral-hydrogel complex

The Liesegang pattern is a beautiful natural anisotropic patterning phenomenon observed in rocks and sandstones. This study reveals that the Liesegang pattern can induce nonlinear elasticity. Here, a Liesegang-patterned complex with biomineral-hydrogel repetitive layers is prepared. This Liesegang-patterned complex is obtained only when the biomineralization is performed under the supersaturated conditions. The Liesegang-patterned complex features a nonlinear elastic response, whereas a complex with a single biomineral shell shows a linear behavior, thus demonstrating that the Liesegang pattern is essential in achieving nonlinear elasticity. The stiff biomineral layers have buffered the concentrated energy on behalf of soft hydrogels, thereby exposing the hydrogel components to reduced stress and, in turn, enabling them to perform the elasticity continuously. Moreover, the nonlinear elastic Liesegang-patterned complex exhibits excellent stress relaxation to the external loading, which is the biomechanical characteristic of cartilage. This stress relaxation allows the bundle of fiber-type Liesegang-patterned complex to endure greater deformation.

Penetrant shape effects on activated dynamics and selectivity in polymer melts and networks based on self-consistent cooperative hopping theory

We generalize and apply the microscopic self-consistent cooperative hopping theory for activated penetrant dynamics in polymer melts and crosslinked networks to address the role of highly variable non-spherical molecular shape. The focus is on vastly different shaped penetrants that have identical space filling volume in order to isolate how non-spherical shape explicitly modifies dynamics over a wide range of temperature down to the kinetic glass transition temperature. The theory relates intramolecular and intermolecular structure and kinetic constraints, and reveals how different solvation packing of polymer monomers around variable shaped penetrants impact penetrant hopping. A highly shape-dependent penetrant activated relaxation, including alpha time decoupling and trajectory level cooperativity of the hopping process, is predicted in the deeply supercooled regime for relatively larger penetrants which is sensitive to whether the polymer matrix is a melt or heavily crosslinked network. In contrast, for smaller size penetrants or at high/medium temperatures the effect of isochoric penetrant shape is relatively weak. We propose an aspect ratio variable that organizes how penetrant shape influences the activated relaxation times, leading to a (near) collapse or master curve. The relative absolute values of the penetrant relaxation time (inverse hopping rate) in polymer melts versus in crosslinked networks are found to be opposite when compared at a common absolute temperature versus when they are compared at a fixed value of distance from the glass transition based on the variable Tg/T with Tg the glass transition temperature. Quantitative comparison with recent diffusion experiments on chemically complex molecular penetrants of variable shape but fixed volume in crosslinked networks reveals good agreement, and testable new predictions are made. Extension of the theoretical approach to more complex systems of high experimental interest are discussed, including applications to realize selective transport in membrane separation applications.

Synergistic chemomechanical dynamics of feedback-controlled microreactors

The experimental control of synergistic chemomechanical dynamics of catalytically active microgels (microreactors) is a key prerequisite for the design of adaptive and biomimetic materials. Here, we report a minimalistic model of feedback-controlled microreactors based on the coupling between the hysteretic polymer volume phase transition and a volume-controlled permeability for the internal chemical conversion. We categorize regimes of mono- and bistability, excitability, damped oscillations, as well as sustained oscillatory states with tunable amplitude, as indicated by experiments and representable by the FitzHugh-Nagumo dynamics for neurons. We summarize the features of such a "colloidal neuron" in bifurcation diagrams with respect to microgel design parameters, such as permeability and relaxation times, as a guide for experimental synthesis.

Ce(IV)-coordinated organogel-based assay for on-site monitoring of propyl gallate with turn-on fluorescence signal

Propyl gallate (PG) is a commonly used synthetic phenolic antioxidant in foodstuffs and industrial products. Due to the potential health risk of PG, rapid and on-site detection in food and environment samples are important to guarantee human health. Herein, we demonstrated rapid monitoring of PG by a fluorescence turn-on strategy based on a specific fluorogenic reaction between PG and polyethyleneimine (PEI). Specifically, Ce4+ with oxidase-mimicking activity oxidized PG to its oxides, which then reacted with PEI through the Michael addition to generate the fluorescent compound. The proposed fluorogenic reaction had good specificity for PG, which could distinguish PG from other phenolic antioxidants and interferences. Furthermore, portable and low-cost organogel test kits were prepared using poly(ethylene glycol) diacrylate for quantitative and on-site detection of PG via a smartphone-based sensing platform. The organogel-based assay detection limit was 1.0 μg mL-1 with recoveries ranging from 80.2% to 106.2% in edible oils and surface water. Suitability of the developed assay was also validated by high-performance liquid chromatography. Our study provides an effective fluorescent approach to rapid, specific, and convenient monitoring of PG, which is useful for diminishing the risk of PG exposure.

How Segmental Dynamics and Mesh Confinement Determine the Selective Diffusivity of Molecules in Cross-Linked Dense Polymer Networks

The diffusion of molecules ("penetrants") of variable size, shape, and chemistry through dense cross-linked polymer networks is a fundamental scientific problem broadly relevant in materials, polymer, physical, and biological chemistry. Relevant applications include separation membranes, barrier materials, drug delivery, and nanofiltration. A major open question is the relationship between transport, thermodynamic state, and penetrant and polymer chemical structure. Here we combine experiment, simulation, and theory to unravel these competing effects on penetrant transport in rubbery and supercooled polymer permanent networks over a wide range of cross-link densities, size ratios, and temperatures. The crucial importance of the coupling of local penetrant hopping to polymer structural relaxation and the secondary importance of mesh confinement effects are established. Network cross-links strongly slow down nm-scale polymer relaxation, which greatly retards the activated penetrant diffusion. The demonstrated good agreement between experiment, simulation, and theory provides strong support for the size ratio (penetrant diameter to the polymer Kuhn length) as a key variable and the usefulness of coarse-grained simulation and theoretical models that average over Angstrom scale structure. The developed theory provides an understanding of the physical processes underlying the behaviors observed in experiment and simulation and suggests new strategies for enhancing selective polymer membrane design.

Feedback-controlled solute transport through chemo-responsive polymer membranes

Polymer membranes are typically assumed to be inert and nonresponsive to the flux and density of the permeating particles in transport processes. Here, we theoretically study the consequences of membrane responsiveness and feedback on the steady-state force-flux relations and membrane permeability using a nonlinear-feedback solution-diffusion model of transport through a slab-like membrane. Therein, the solute concentration inside the membrane depends on the bulk concentration, c₀, the driving force, f, and the polymer volume fraction, ϕ. In our model, the solute accumulation in the membrane causes a sigmoidal volume phase transition of the polymer, changing its permeability, which, in return, affects the membrane's solute uptake. This feedback leads to nonlinear force-flux relations, j(f), which we quantify in terms of the system's differential permeability, P_sys ^Δ∝dj/df. We find that the membrane feedback can increase or decrease the solute flux by orders of magnitude, triggered by a small change in the driving force and largely tunable by attractive vs repulsive solute-membrane interactions. Moreover, controlling the inputs, c₀ and f, can lead to the steady-state bistability of ϕ and hysteresis in the force-flux relations. This work advocates that the fine-tuning of the membrane's chemo-responsiveness will enhance the nonlinear transport control features, providing great potential for future (self-)regulating membrane devices.

Phenol release from pNIPAM hydrogels: scaling molecular dynamics simulations with dynamical density functional theory

We employed molecular dynamic simulations (MD) and the Bennett's acceptance ratio method to compute the free energy of transfer, ΔG_trans, of phenol, methane, and 5-fluorouracil (5-FU), between bulk water and water-pNIPAM mixtures of different polymer volume fractions, ϕ_p. For this purpose, we first calculate the solvation free energies in both media to obtain ΔG_trans. Phenol and 5-FU (a medication used to treat cancer) attach to the pNIPAM surface so that they show negative values of ΔG_trans irrespective of temperature (above or below the lower critical solution temperature of pNIPAM, T_c). Conversely, methane switches the ΔG_trans sign when considering temperatures below (positive) and above (negative) T_c. In all cases, and contrasting with some theoretical predictions, ΔG_trans maintains a linear behavior with the pNIPAM concentration up to large polymer densities. We have also employed MD to compute the diffusion coefficient, D, of phenol in water-pNIPAM mixtures as a function of ϕ_p in the diluted limit. Both ΔG_trans and D as a function of ϕ_p are required inputs to obtain the release halftime of hollow pNIPAM microgels through Dynamic Density Functional Theory (DDFT). Our scaling strategy captures the experimental value of 2200 s for 50 μm radius microgels with no cavity, for ϕ_p ≃ 0.83 at 315 K.

Supramolecular Structure and Mechanical Performance of κ-Carrageenan-Gelatin Gel

In this work, by means of complex physicochemical methods the structural features of a composite κ-carrageenan–gelatin system were studied in comparison with initial protein gel. The correlation between the morphology of hydrogels and their mechanical properties was demonstrated through the example of changes in their rheological characteristics. The experiments carried out with PXRD, SAXS, AFM and rheology approaches gave new information on the structure and mechanical performance of κ-carrageenan–gelatin hydrogel. The combination of PXRD, SAXS and AFM results showed that the morphological structures of individual components were not observed in the composite protein–polysaccharide hydrogels. The results of the mechanical testing of initial gelatin and engineered κ-carrageenan–gelatin gel showed the substantially denser parking of polymer chains in the composite system due to a significant increase in intermolecular protein–polysaccharide contacts. Close results were indirectly followed from the SAXS estimations—the driving force for the formation of the common supramolecular structural arrangement of proteins and polysaccharides was the increase in the density of network of macromolecular chains entanglements; therefore, an increase in the energy costs was necessary to change the conformational rearrangements of the studied system. This increase in the macromolecular arrangement led to the growth of the supramolecular associate size and the growth of interchain physical bonds. This led to an increase in the composite gel plasticity, whereas the enlargement of scattering particles made the novel gel system not only more rigid, but also more fragile.

Elucidation of the physical factors that control activated transport of penetrants in chemically complex glass-forming liquids

Understanding the activated transport of penetrant or tracer atoms and molecules in condensed phases is a challenging problem in chemistry, materials science, physics, and biophysics. Many angstrom- and nanometer-scale features enter due to the highly variable shape, size, interaction, and conformational flexibility of the penetrant and matrix species, leading to a dramatic diversity of penetrant dynamics. Based on a minimalist model of a spherical penetrant in equilibrated dense matrices of hard spheres, a recent microscopic theory that relates hopping transport to local structure has predicted a novel correlation between penetrant diffusivity and the matrix thermodynamic dimensionless compressibility, S₀(T) (which also quantifies the amplitude of long wavelength density fluctuations), as a consequence of a fundamental statistical mechanical relationship between structure and thermodynamics. Moreover, the penetrant activation barrier is predicted to have a factorized/multiplicative form, scaling as the product of an inverse power law of S₀(T) and a linear/logarithmic function of the penetrant-to-matrix size ratio. This implies an enormous reduction in chemical complexity that is verified based solely on experimental data for diverse classes of chemically complex penetrants dissolved in molecular and polymeric liquids over a wide range of temperatures down to the kinetic glass transition. The predicted corollary that the penetrant diffusion constant decreases exponentially with inverse temperature raised to an exponent determined solely by how S₀(T) decreases with cooling is also verified experimentally. Our findings are relevant to fundamental questions in glassy dynamics, self-averaging of angstrom-scale chemical features, and applications such as membrane separations, barrier coatings, drug delivery, and self-healing.

Modeling Solution Behavior of Poly(N-isopropylacrylamide): A Comparison between Water Models

Water is known to play a fundamental role in determining the structure and functionality of macromolecules. The same crucial contribution is also found in the in silico description of polymer aqueous solutions. In this work, we exploit the widely investigated synthetic polymer poly(N-isopropylacrylamide) (PNIPAM) to understand the effect of the adopted water model on its solution behavior and to refine the computational setup. By means of atomistic molecular dynamics simulations, we perform a comparative study of PNIPAM aqueous solution using two advanced water models: TIP4P/2005 and TIP4P/Ice. The conformation and hydration features of an atactic 30-mer at infinite dilution are probed at a range of temperature and pressure suitable to detect the coil-to-globule transition and to map the P–T phase diagram. Although both water models can reproduce the temperature-induced coil-to-globule transition at atmospheric pressure and the polymer hydration enhancement that occurs with increasing pressure, the PNIPAM–TIP4P/Ice solution shows better agreement with experimental findings. This result can be attributed to a stronger interaction of TIP4P/Ice water with both hydrophilic and hydrophobic groups of PNIPAM, as well as to a less favorable contribution of the solvent entropy to the coil-to-globule transition.

Theory of the effect of external stress on the activated dynamics and transport of dilute penetrants in supercooled liquids and glasses

We generalize the self-consistent cooperative hopping theory for a dilute spherical penetrant or tracer activated dynamics in dense metastable hard sphere fluids and glasses to address the effect of external stress, the consequences of which are systematically established as a function of matrix packing fraction and penetrant-to-matrix size ratio. All relaxation processes speed up under stress, but the difference between the penetrant and matrix hopping (alpha relaxation) times decreases significantly with stress corresponding to less time scale decoupling. A dynamic crossover occurs at a critical "slaving onset" stress beyond which the matrix activated hopping relaxation time controls the penetrant hopping time. This characteristic stress increases (decreases) exponentially with packing fraction (size ratio) and can be well below the absolute yield stress of the matrix. Below the slaving onset, the penetrant hopping time is predicted to vary exponentially with stress, differing from the power law dependence of the pure matrix alpha time due to system-specificity of the stress-induced changes in the penetrant local cage and elastic barriers. An exponential growth of the penetrant alpha relaxation time with size ratio under stress is predicted, and at a fixed matrix packing fraction, the exponential relation between penetrant hopping time and stress for different size ratios can be collapsed onto a master curve. Direct connections between the short- and long-time activated penetrant dynamics and between the penetrant (or matrix) alpha relaxation time and matrix thermodynamic dimensionless compressibility are also predicted. The presented results should be testable in future experiments and simulations.

Tuning the permeability of regular polymeric networks by the cross-link ratio

The amount of cross-linking in the design of polymer materials is a key parameter for the modification of numerous physical properties, importantly, the permeability to molecular solutes. We consider networks with a diamond-like architecture and different cross-link ratios, concurring with a wide range of the polymer volume fraction. We particularly focus on the effect and the competition of two independent component-specific solute-polymer interactions, i.e., we distinguish between chain-monomers and cross-linkers, which individually act on the solutes and are altered to cover attractive and repulsive regimes. For this purpose, we employ coarse-grained, Langevin computer simulations to study how the cross-link ratio of polymer networks controls the solute partitioning, diffusion, and permeability. We observe different qualitative behaviors as a function of the cross-link ratio and interaction strengths. The permeability can be tuned ranging over two orders of magnitude relative to the reference bulk permeability. Finally, we provide scaling theories for the partitioning and diffusion that explicitly account for the component-specific interactions as well as the cross-link ratio and the polymer volume fraction. These are in overall good agreement with the simulation results and grant insight into the underlying physics, rationalizing how the cross-link ratio can be exploited to tune the solute permeability of polymeric networks.

Activated penetrant dynamics in glass forming liquids: size effects, decoupling, slaving, collective elasticity and correlation with matrix compressibility

We employ the microscopic self-consistent cooperative hopping theory of penetrant activated dynamics in glass forming viscous liquids and colloidal suspensions to address new questions over a wide range of high matrix packing fractions and penetrant-to-matrix particle size ratios. The focus is on the mean activated relaxation time of smaller tracers in a hard sphere fluid of larger particle matrices. This quantity also determines the penetrant diffusion constant and connects directly with the structural relaxation time probed in an incoherent dynamic structure factor measurement. The timescale of the non-activated fast dissipative process is also studied and is predicted to follow power laws with the contact value of the penetrant-matrix pair correlation function and the penetrant-matrix size ratio. For long time penetrant relaxation, in the relatively lower packing fraction metastable regime the local cage barriers are dominant and matrix collective elasticity effects unimportant. As packing fraction and/or penetrant size grows, much higher barriers emerge and the collective elasticity associated with the correlated matrix dynamic displacement that facilitates penetrant hopping becomes important. This results in a non-monotonic variation with packing fraction of the degree of decoupling between the matrix and penetrant alpha relaxation times. The conditions required for penetrant hopping to become slaved to the matrix alpha process are determined, which depend mainly on the penetrant to matrix particle size ratio. By analyzing the absolute and relative importance of the cage and elastic barriers we establish a mechanistic understanding of the origin of the predicted exponential growth of the penetrant hopping time with size ratio predicted at very high packing fractions. A dynamics-thermodynamics power law connection between the penetrant activation barrier and the matrix dimensionless compressibility is established as a prediction of theory, with different scaling exponents depending on whether matrix collective elasticity effects are important. Quantitative comparisons with simulations of the penetrant relaxation time, diffusion constant, and transient localization length of tracers in dense colloidal suspensions and cold viscous liquids reveal good agreements. Multiple new predictions are made that are testable via future experiments and simulations. Extension of the theoretical approach to more complex systems of high experimental interest (nonspherical molecules, semiflexible polymers, crosslinked networks) interacting via variable hard or soft repulsions and/or short range attractions is possible, including under external deformation.