Tuning the selective permeability of polydisperse polymer networks

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.

Continuous Ligand-Free Catalysis Using a Hybrid Polymer Network Support

Although the pharmaceutical and fine chemical industries primarily utilize batch homogeneous reactions to carry out chemical transformations, emerging platforms seek to improve existing shortcomings by designing effective heterogeneous catalysis systems in continuous flow reactors. In this work, we present a versatile network-supported palladium (Pd) catalyst using a hybrid polymer of poly(methylvinylether-alt-maleic anhydride) and branched polyethyleneimine for intensified continuous flow synthesis of complex organic compounds via heterogeneous Suzuki-Miyaura cross-coupling and nitroarene hydrogenation reactions. The hydrophilicity of the hybrid polymer network facilitates the reagent mass transfer throughout the bulk of the catalyst particles. Through rapid automated exploration of the continuous and discrete parameters, as well as substrate scope screening, we identified optimal hybrid network-supported Pd catalyst composition and process parameters for Suzuki-Miyaura cross-coupling reactions of aryl bromides with steady-state yields up to 92% with a nominal residence time of 20 min. The developed heterogeneous catalytic system exhibits high activity and mechanical stability with no detectable Pd leaching at reaction temperatures up to 95 °C. Additionally, the versatility of the hybrid network-supported Pd catalyst is demonstrated by successfully performing continuous nitroarene hydrogenation with short residence times (<5 min) at room temperature. Room temperature hydrogenation yields of >99% were achieved in under 2 min nominal residence times with no leaching and catalyst deactivation for more than 20 h continuous time on stream. This catalytic system shows its industrial utility with significantly improved reaction yields of challenging substrates and its utility of environmentally-friendly solvent mixtures, high reusability, scalable and cost-effective synthesis, and multi-reaction successes.

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.

Dynamics of self-propelled tracer particles inside a polymer network

The transport of tracer particles through mesh-like environments such as biological hydrogels and polymer matrices is ubiquitous in nature. These tracers can be passive, such as colloids, or active (self-propelled), for example, synthetic nanomotors or bacteria. Computer simulations in principle could be extremely useful in exploring the mechanism of the active transport of tracer particles through mesh-like environments. Therefore, we construct a polymer network on a diamond lattice and use computer simulations to investigate the dynamics of spherical self-propelled particles inside the network. Our main objective is to elucidate the effect of the self-propulsion on the tracer particle dynamics as a function of the tracer size and the stiffness of the polymer network. We compute the time-averaged mean-squared displacement (MSD) and the van-Hove correlations of the tracer. On the one hand, in the case of a bigger sticky particle, the caging caused by the network particles wins over the escape assisted by the self-propulsion. This results an intermediate-time subdiffusion. On the other hand, smaller tracers or tracers with high self-propulsion velocities can easily escape from the cages and show intermediate-time superdiffusion. The stiffer the network, the slower the dynamics of the tracer, and bigger tracers exhibit longer lived intermediate time superdiffusion, since the persistence time scales as ∼σ³, where σ is the diameter of the tracer. At the intermediate time, non-Gaussianity is more pronounced for active tracers. At the long time, the dynamics of the tracer, if passive or weakly active, becomes Gaussian and diffusive, but remains flat for tracers with high self-propulsion, accounting for their seemingly unrestricted motion inside the network.

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.

Coarse-Grained Simulations of Release of Drugs Housed in Flexible Nanogels: New Insights into Kinetic Parameters

The diffusion-controlled release of drugs housed in flexible nanogels has been simulated with the help of a coarse-grained model that explicitly considers polymer chains. In these in silico experiments, the effect of its flexibility is assessed by comparing it with data obtained for a rigid nanogel with the same volume fraction and topology. Our results show that the initial distribution of the drug can exert a great influence on the release kinetics. This work also reveals that certain surface phenomena driven by steric interactions can lead to apparently counterintuitive behaviors. Such phenomena are not usually included in many theoretical treatments used for the analysis of experimental release kinetics. Therefore, one should be very careful in drawing conclusions from these formalisms. In fact, our results suggest that the interpretation of drug release curves in terms of kinetic exponents (obtained from the Ritger-Peppas Equation) is a tricky question. However, such curves can provide a first estimate of the drug diffusion coefficient.

Responsive Hyaluronic Acid–Ethylacrylamide Microgels Fabricated Using Microfluidics Technique

Volume changes of responsive microgels can probe interactions between polyelectrolytes and species of opposite charges such as peptides and proteins. We have investigated a microfluidics method to synthesize highly responsive, covalently crosslinked, hyaluronic acid microgels for such purposes. Sodium hyaluronate (HA), pre-modified with ethylacrylamide functionalities, was crosslinked in aqueous droplets created with a microfluidic technique. We varied the microgel properties by changing the degree of modification and concentration of HA in the reaction mixture. The degree of modification was determined by 1H NMR. Light microscopy was used to investigate the responsiveness of the microgels to osmotic stress in aqueous saline solutions by simultaneously monitoring individual microgel species in hydrodynamic traps. The permeability of the microgels to FITC-dextrans of molecular weights between 4 and 250 kDa was investigated using confocal laser scanning microscopy. The results show that the microgels were spherical with diameters between 100 and 500 µm and the responsivity tunable by changing the degree of modification and the HA concentration. Microgels were fully permeable to all investigated FITC-dextran probes. The partitioning to the microgel from an aqueous solution decreased with the increasing molecular weight of the probe, which is in qualitative agreement with theories of homogeneous gel networks.

Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

Unraveling the Role of Architecture in Polymer-Based Glues for Hydrogels

We investigate polymers of different architectures as potential candidates for the development of glues for hydrogels. Using a combination of coarse-grained modeling and molecular dynamics simulations, we systematically characterize the link between experimentally tunable parameters and adhesion energy. We find that, for a broad set of parameters, adhesion is controlled almost exclusively by the total amount of glue at the interface and by the glue-hydrogel affinity. Instead, it is largely independent of changes in polymer architecture and size, a conclusion that shines new light on previously observed experimental trends. Additionally, we show that the scaling behavior of the properties we measure can be explained by modeling the glue as an ensemble of ideal, noninteracting, and linear polymer segments. We expect that the fundamental insights herein provided will aid the design of new polymer-based adhesives for hydrogels.

Universal description of steric hindrance in flexible polymer gels

In this work, the long-time diffusion of a solute in a chemically crosslinked and flexible hydrogel is computed from a bead-spring model of a polymeric network to assess the effect of steric obstruction. The relative diffusivities obtained for a wide variety of systems can be described by an exponential decay depending on a parameter that differs from that employed for rigid gels. The mathematical expression derived here can approximately predict the diffusivity in flexible gels if steric hindrance is the mechanism ruling diffusion.

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.

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

The permeability of hydrogels for the selective transport of molecular penetrants (drugs, toxins, reactants, etc.) is a central property in the design of soft functional materials, for instance in biomedical, pharmaceutical, and nanocatalysis applications. However, the permeation of dense and hydrated polymer membranes is a complex multifaceted molecular-level phenomenon, and our understanding of the underlying physicochemical principles is still very limited. Here, we uncover the molecular principles of permeability and selectivity in hydrogel permeation. We combine the solution-diffusion model for permeability with comprehensive atomistic simulations of molecules of various shapes and polarities in a responsive hydrogel in different hydration states. We find in particular that dense collapsed states are extremely selective, owing to a delicate balance between the partitioning and diffusivity of the penetrants. These properties are sensitively tuned by the penetrant size, shape, and chemistry, leading to vast cancellation effects, which nontrivially contribute to the permeability. The gained insights enable us to formulate semiempirical rules to quantify and extrapolate the permeability categorized by classes of molecules. They can be used as approximate guiding ("rule-of-thumb") principles to optimize penetrant or membrane physicochemical properties for a desired permeability and membrane functionality.

Scaling Laws in the Diffusive Release of Neutral Cargo from Hollow Hydrogel Nanoparticles: Paclitaxel-Loaded Poly(4-vinylpyridine)

We study the nonequilibrium diffusive release of electroneutral molecular cargo encapsulated inside hollow hydrogel nanoparticles. We propose a theoretical model that includes osmotic, steric, and short-range polymer-cargo attractions to determine the effective cargo-hydrogel interaction, u_eff*, and the effective diffusion coefficient of the cargo inside the polymer network, D_eff*. Using dynamical density functional theory (DDFT), we investigate the scaling of the characteristic release time, τ_1/2, with the key parameters involved in the process, namely, u_eff*, D_eff*, and the swelling ratio. This effort represents a full study of the problem, covering a broad range of cargo sizes and providing predictions for repulsive and attractive polymer shells. Our calculations show that the release time through repulsive polymer networks scales with q²e^βu_eff*/D_eff* for βu_eff* ≫ 1. In this case, the cargo molecules are excluded from the shell of the hydrogel. For attractive shells, the polymer retains the cargo molecules on its internal surface and its interior, and the release time grows exponentially with the attraction strength. The DDFT calculations are compared to an analytical model for the mean first passage time, which provides an excellent quantitative description of the kinetics for both repulsive and attractive shells without fitting parameters. Finally, we apply the method to reproduce experimental results on the release of paclitaxel from hollow poly(4-vinylpyridine) nanoparticles and find that the slow release of the drug can be explained in terms of the strong binding attraction between the drug and the polymer.