Spatially Resolved Tracer Diffusion in Complex Responsive Hydrogels

Multiscale homogenisation of diffusion in enzymatically-calcified hydrogels

Hydrogels are a promising class of material in biomedical and industrial applications, where both the mechanical and diffusion properties play an important role. The wide range of polymers that can be used and the different production methods allows these properties to be specifically tuned to a high degree for their application. Producing tough hydrogels with high stiffness has been a long-standing challenge that has recently been addressed by mineralisation methods. Those methods modify the hydrogel into one with a supporting mineral microstructure that is highly heterogeneous. This work investigates methods to determine the macroscopic diffusion behaviour of heterogeneous gels by a homogenisation method implemented in a finite element framework. This is applied to two recently developed materials by calcifying poly-dimethyl-acrylamide (PDMA) and polyacrylamide hydrogels (PAAm). The former has porous, spherical inclusions obstructing diffusion, while the latter has spherical pores enabling it. For both gels the unobstructed volume can be used as the primary parameter to tune the diffusivity. In PDMA the porosity of the obstructions is shown by multiscale analysis to give a strong, non-linear dependence of the diffusivity on the solute molecule radius. The framework is extended to other materials and comparisons are made to experimental works from the literature.

Spatially Resolving Size Effects on Diffusivity in Nanoporous Extracellular Matrix-like Materials with Fluorescence Correlation Spectroscopy Super-Resolution Optical Fluctuation Imaging

It is well documented that the nanoscale structures within porous microenvironments greatly impact the diffusion dynamics of molecules. However, how the interaction between the environment and molecules influences the diffusion dynamics has not been thoroughly explored. Here, we show that fluorescence correlation spectroscopy super-resolution optical fluctuation imaging (fcsSOFI) can be used to accurately measure the diffusion dynamics of molecules within varying matrices such as nanopatterned surfaces and porous agarose hydrogels. Our data demonstrate the robustness of fcsSOFI, where it is possible not only to quantify the diffusion speeds of molecules in heterogeneous media but also to recover the matrix structure with resolution on the order of 100 nm. Using dextran molecules of varying sizes, we show that the diffusion coefficient is sensitive to the change in the molecular hydrodynamic radius. fcsSOFI images further reveal that smaller dextran molecules can freely move through the small pores of the hydrogel and report the detailed porous structure and local diffusion heterogeneities not captured by the average diffusion coefficient. Conversely, bigger dextran molecules are confined and unable to freely move through the hydrogel, highlighting only the larger pore structures. These findings establish fcsSOFI as a powerful tool to characterize spatial and diffusion information of diverse macromolecules within biorelevant matrices.

Hydrogels as Drug Delivery Systems: A Review of Current Characterization and Evaluation Techniques

Owing to their tunable properties, controllable degradation, and ability to protect labile drugs, hydrogels are increasingly investigated as local drug delivery systems. However, a lack of standardized methodologies used to characterize and evaluate drug release poses significant difficulties when comparing findings from different investigations, preventing an accurate assessment of systems. Here, we review the commonly used analytical techniques for drug detection and quantification from hydrogel delivery systems. The experimental conditions of drug release in saline solutions and their impact are discussed, along with the main mathematical and statistical approaches to characterize drug release profiles. We also review methods to determine drug diffusion coefficients and in vitro and in vivo models used to assess drug release and efficacy with the goal to provide guidelines and harmonized practices when investigating novel hydrogel drug delivery systems.

Tracer Diffusion in Tightly-Meshed Homogeneous Polymer Networks: A Brownian Dynamics Simulation Study

We report Brownian dynamics simulations of tracer diffusion in regularly crosslinked polymer networks in order to elucidate the transport of a tracer particle in polymer networks. The average mesh size of homogeneous polymer networks is varied by assuming different degrees of crosslinking or swelling, and the size of a tracer particle is comparable to the average mesh size. Simulation results show subdiffusion of a tracer particle at intermediate time scales and normal diffusion at long times. In particular, the duration of subdiffusion is significantly prolonged as the average mesh size decreases with increasing degree of crosslinking, for which long-time diffusion occurs via the hopping processes of a tracer particle after undergoing rattling motions within a cage of the network mesh for an extended period of time. On the other hand, the cage dynamics and hopping process are less pronounced as the mesh size decreases with increasing polymer volume fractions. The interpretation is provided in terms of fluctuations in network mesh size: at higher polymer volume fractions, the network fluctuations are large enough to allow for collective, structural changes of network meshes, so that a tracer particle can escape from the cage, whereas, at lower volume fractions, the fluctuations are so small that a tracer particle remains trapped within the cage for a significant period of time before making infrequent jumps out of the cage. This work suggests that fluctuation in mesh size, as well as average mesh size itself, plays an important role in determining the dynamics of molecules and nanoparticles that are embedded in tightly meshed polymer networks.

Evidence of superdiffusive nanoscale motion in anionic polymeric hydrogels: Analysis of PGSE- NMR data and comparison with drug release properties

Polymeric hydrogels are promising candidates for drug delivery applications, thanks to their ability to encapsulate, transport and release a wide range of chemicals. The successful application of these materials requires a deep understanding of the mechanisms governing solute transport at the nanoscale and its impact on release kinetics. In this work, we investigate the translational diffusion of ibuprofen loaded in anionic agarose-carbomer (AC) hydrogels by ¹H high resolution magic angle spinning (HR-MAS) NMR spectroscopy, and compare it to its macroscopic release kinetics. The analysis of the experimental NMR data provides the first evidence of superdiffusion for ibuprofen in AC hydrogels. Superdiffusive transport is observed in the majority of our samples, especially those with the smallest mesh size (7 nm) and highest ibuprofen concentrations (90-120 mg/mL). This outcome is rationalized in terms of heavy-tailed distributions of spatial displacements (Lèvy flights) and of waiting times, which depend on the nanoscopic structural heterogeneity of the gels and the strong but reversible association between ibuprofen and the agarose matrix.

Droplet-Assisted Microfluidic Fabrication and Characterization of Multifunctional Polysaccharide Microgels Formed by Multicomponent Reactions

Polysaccharide-based microgels have broad applications in multi-parametric cell cultures, cell-free biotechnology, and drug delivery. Multicomponent reactions like the Passerini three-component and the Ugi four-component reaction are shown in here to be versatile platforms for fabricating these polysaccharide microgels by droplet microfluidics with a narrow size distribution. While conventional microgel formation requires pre-modification of hydrogel building blocks to introduce certain functionality, in multicomponent reactions one building block can be simply exchanged by another to introduce and extend functionality in a library-like fashion. Beyond synthesizing a range of polysaccharide-based microgels utilizing hyaluronic acid, alginate and chitosan, exemplary in-depth analysis of hyaluronic acid-based Ugi four-component gels is conducted by colloidal probe atomic force microscopy, confocal Brillouin microscopy, quantitative phase imaging, and fluorescence correlation spectroscopy to elucidate the capability of microfluidic multicomponent reactions for forming defined polysaccharide microgel networks. Particularly, the impact of crosslinker amount and length is studied. A higher network density leads to higher Young's moduli accompanied by smaller pore sizes with lower diffusion coefficients of tracer molecules in the highly homogeneous network, and vice versa. Moreover, tailored building blocks allow for crosslinking the microgels and incorporating functional groups at the same time as demonstrated for biotin-functionalized, chitosan-based microgels formed by Ugi four-component reaction. To these microgels, streptavidin-labeled enzymes are easily conjugated as shown for horseradish peroxidase (HRP), which retains its activity inside the microgels.

How gold nanoparticles can be used to probe the structural changes of a pH-responsive hydrogel

Gold nanoparticles (GNPs) have UV-visible absorption spectra that are highly sensitive to their local environment due to their surface plasmon resonance (SPR). Furthermore, GNPs are able to quench the fluorescence of suitable dyes depending on the GNP-dye separation. Both of these features have led to the use of GNPs as spectroscopic rulers. In this study we sought to use GNPs as spectroscopic probes to investigate the local structural changes associated with the macroscopic pH-triggered swelling/de-swelling transitions of a pH-responsive hydrogel. The hydrogel used in this study comprised covalently inter-linked pH-responsive poly(ethylacrylate-co-methacrylic acid-co-divinyl benzene) microgel particles (MGs). MGs are crosslinked polymer colloids that swell when the pH approaches the pK_a of the constituent polymer. The interlinked MG hydrogels are termed doubly crosslinked microgels (DX MGs) and are a new family of hydrogels. They had polymer volume fractions (ϕ_p) that strongly decreased as the pH increased. UV-visible spectra showed that the wavelength of the SPR absorption (λ_max) for the DX MG/GNP gels was pH-responsive. A linear relationship was found between λ_max and ϕ_p for ϕ_p values up to ∼0.80. The inclusion of Rhodamine 6G within the DX MG/GNP hydrogels resulted in metal-induced fluorescence quenching which was studied using photoluminescence (PL) spectroscopy. The extent of quenching was pH-dependent and was also proportional to ϕ_p. The results of the study showed that the pH-triggered changes of the nanoscale and macroscopic swelling for the DX MGs were similar and imply that affine swelling occurred, which is a new observation. The data suggest that UV-visible or PL spectroscopy could be used to study the swelling of pH-responsive hydrogels containing GNPs remotely.

Brownian motion of a circle swimmer in a harmonic trap

We study the dynamics of a Brownian circle swimmer with a time-dependent self-propulsion velocity in an external temporally varying harmonic potential. For several situations, the noise-free swimming paths, the noise-averaged mean trajectories, and the mean-square displacements are calculated analytically or by computer simulation. Based on our results, we discuss optimal swimming strategies in order to explore a maximum spatial range around the trap center. In particular, we find a resonance situation for the maximum escape distance as a function of the various frequencies in the system. Moreover, the influence of the Brownian noise is analyzed by comparing noise-free trajectories at zero temperature with the corresponding noise-averaged trajectories at finite temperature. The latter reveal various complex self-similar spiral or rosette-like patterns. Our predictions can be tested in experiments on artificial and biological microswimmers under dynamical external confinement.

Correlation between collective and molecular dynamics in pH-responsive cyclodextrin-based hydrogels

The joint use of UV Raman and Brillouin scattering experiments is employed to explore phase evolutions in pH-responsive polysaccharide hydrogels.

Transport Properties of Ibuprofen Encapsulated in Cyclodextrin Nanosponge Hydrogels: A Proton HR-MAS NMR Spectroscopy Study

The chemical cross-linking of β-cyclodextrin (β-CD) with ethylenediaminetetraacetic dianhydride (EDTA) led to branched polymers referred to as cyclodextrin nanosponges (CDNSEDTA). Two different preparations are described with 1:4 and 1:8 CD-EDTA molar ratios. The corresponding cross-linked polymers were contacted with 0.27 M aqueous solution of ibuprofen sodium salt (IP) leading to homogeneous, colorless, drug loaded hydrogels. The systems were characterized by high resolution magic angle spinning (HR-MAS) NMR spectroscopy. Pulsed field gradient spin echo (PGSE) NMR spectroscopy was used to determine the mean square displacement (MSD) of IP inside the polymeric gel at different observation times td. The data were further processed in order to study the time dependence of MSD: MSD = f(td). The proposed methodology is useful to characterize the different diffusion regimes that, in principle, the solute may experience inside the hydrogel, namely normal or anomalous diffusion. The full protocols including the polymer preparation and purification, the obtainment of drug-loaded hydrogels, the NMR sample preparation, the measurement of MSD by HR-MAS NMR spectroscopy and the final data processing to achieve the time dependence of MSD are here reported and discussed. The presented experiments represent a paradigmatic case and the data are discussed in terms of innovative approach to the characterization of the transport properties of an encapsulated guest within a polymeric host of potential application for drug delivery.

Diffusion of macromolecules in a polymer hydrogel: from microscopic to macroscopic scales

To gain insight into the fundamental processes determining the motion of macromolecules in polymeric matrices, the dynamical hindrance of polymeric dextran molecules diffusing as probe through a polyacrylamide hydrogel is systematically explored. Three complementary experimental methods combined with Brownian dynamics simulations are used to study a broad range of dextran molecular weights and salt concentrations. While multi-parameter fluorescence image spectroscopy (MFIS) is applied to investigate the local diffusion of single molecules on a microscopic length scale inside the hydrogel, a macroscopic transmission imaging (MTI) fluorescence technique and nuclear magnetic resonance (NMR) are used to study the collective motion of dextrans on the macroscopic scale. These fundamentally different experimental methods, probing different length scales of the system, yield long-time diffusion coefficients for the dextran molecules which agree quantitatively. The measured diffusion coefficients decay markedly with increasing molecular weight of the dextran and fall onto a master curve. The observed trends of the hindrance factors are consistent with Brownian dynamics simulations. The simulations also allow us to estimate the mean pore size for the herein investigated experimental conditions. In addition to the diffusing molecules, MFIS detects temporarily trapped molecules inside the matrix with diffusion times above 10 ms, which is also confirmed by anisotropy analysis. The fraction of bound molecules depends on the ionic strength of the solution and the charge of the dye. Using fluorescence intensity analysis, also MTI confirms the observation of the interaction of dextrans with the hydrogel. Moreover, pixelwise analysis permits to show significant heterogeneity of the gel on the microscopic scale.

Temperature-Controlled Diffusion in PNIPAM-Modified Silica Inverse Opals

We report a new strategy for the preparation of well-defined and mechanically stable porous nanostructures with tunable porosity. Silica inverse opals, which are known as a model system for a porous periodic nanostructure, were grafted with brushes of the thermoresponsive poly(N-isopropylacrylamide) grown via atom transfer radical polymerization. By tuning the temperature, the swelling state of the brush layer is reversibly altered, and with this we were able to control the overall porosity of the system and, thus, the mobility of small penetrants. Fluorescence correlation spectroscopy, a method combining single molecule sensitivity with small probing volume (<1 μm³), was used to directly monitor and quantify in situ the changes in the penetrants' mobility.

Engineering Systems with Spatially Separated Enzymes via Dual-Stimuli-Sensitive Properties of Microgels

This work examines the adsorption regime and the properties of microgel/enzyme thin films deposited onto conductive graphite-based substrates. The films were formed via two-step sequential adsorption. A temperature- and pH-sensitive poly(N-isopropylacrylamide)-co-(3-(N,N-dimethylamino)propylmethacrylamide) microgel (poly(NIPAM-co-DMAPMA microgel) was adsorbed first, followed by its interaction with the enzymes, choline oxidase (ChO), butyrylcholinesterase (BChE), or mixtures thereof. By temperature-induced stimulating both (i) poly(NIPAM-co-DMAPMA) microgel adsorption at T > VPTT followed by short washing and drying and then (ii) enzyme loading at T < VPTT, we can effectively control the amount of the microgel adsorbed on a hydrophobic interface as well as the amount and the spatial localization of the enzyme interacted with the microgel film. Depending on the biomolecule size, enzyme molecules can (in the case for ChO) or cannot (in the case for BChE) penetrate into the microgel interior and be localized inside/outside the microgel particles. Different spatial localization, however, does not affect the specific enzymatic responses of ChO or BChE and does not prevent cascade enzymatic reaction involving both BChE and ChO as well. This was shown by the methods of electrochemical impedance spectroscopy (EIS), atomic force microscopy (AFM), and amperometric analysis of enzymatic responses of immobilized enzymes. Thus, a novel simple and fast strategy for physical entrapment of biomolecules by the polymeric matrix was proposed, which can be used for engineering systems with spatially separated enzymes of different types.

Swelling and mechanical properties of hydrogels composed of binary blends of inter-linked pH-responsive microgel particles

We show that a new type of hydrogel can be prepared by covalently inter-linking binary blends of microgel (MG) particles and that the swelling ratio and modulus of the gels can be predicted from their composition. In previous work we established that physical gels of glycidyl methacrylate (GMA) functionalised poly(methyl methacrylate-co-methacrylic acid-co-ethyleneglycol dimethacrylate) microgel particles (GMA-MG) could be covalently inter-linked to give hydrogels, termed doubly crosslinked microgels, DX MGs. We build on this concept here by investigating the properties of DX MGs containing binary blends of GMA-MG particles and glycidyl oligo(ether ester) acrylate-functionalised microgel particles (GOE-MG). These new hydrogels were assembled by inter-linking nanoscale MG building blocks in the absence of small molecule monomers or crosslinkers. The volume fraction of GMA-MG particles used to prepare the GOE-GMA DX MGs was systematically varied. Rheology data showed that inclusion of GMA-MG and GOE-MG within the GOE-GMA DX MGs increased the modulus and yield strain, respectively, compared to the values measured for the respective physical gels. The data for the covalent GOE-GMA DX MG gels showed that the ductility increased with increasing GOE-MG content. GOE provided covalent inter-linking of the MG particles and also acted as a lubricant between particles due to its low Tg. By demonstrating compositionally determined swelling and mechanical properties for DX MG gels prepared using binary blends of MG particles, this study introduces a new, widely applicable, hydrogel construction assembly concept that is not available for conventional hydrogels.

A study of physical and covalent hydrogels containing pH-responsive microgel particles and graphene oxide

In this study we mixed low concentrations of graphene oxide (GO) with microgel (MG) particles and formed composite doubly cross-linked microgels (DX MG/GO) gels. The MG particles comprised poly(ethyl acrylate-co-methacrylic acid-co-1,4-butanediol diacrylate) with pendant glycidyl methacrylate units. The MG/GO mixed dispersions formed physical gels of singly cross-linked MGs (termed SX MG/GO), which were subsequently heated to produce DX MG/GO gels by free-radical reaction. The influence of the GO concentration on the mechanical properties of the SX MG/GO and DX MG/GO gels was investigated using dynamic rheology and static compression measurements. The SX MG/GO physical gels were injectable and moldable. The moduli for the DX MG/GO gels increased by a factor of 4-6 when only ca. 1.0 wt % of GO was included. The isostrain model was used to describe the variation of modulus with DX MG/GO composition. Inclusion of GO dramatically altered the stress dissipation and yielding mechanisms for the gels. GO acted as a high surface area, high modulus filler and played an increasing role in load distribution as the GO concentration increased. It is proposed that MG domains were dispersed within a percolated GO network. Comparison of the modulus data with those published for GO-free DX MGs showed that inclusion of GO provided an unprecedented rate of modulus increase with network volume fraction for this family of colloid gels. Furthermore, the DX MG/GO gels were biocompatible and the results imply that there may be future applications of these new systems as injectable load supporting gels for soft tissue repair.

Diffusion of guest molecules within sensitive core-shell microgel carriers

The diffusion of payloads within core-shell carrier particles is of major relevance for drug-delivery applications. We use spatially resolved two-focus fluorescence correlation spectroscopy to quantify the diffusivity of different dextran molecules and colloids within carrier particles composed of a temperature-responsive poly(N-isopropylacrylamide) (PNIPAM) shell that surrounds a temperature-insensitive polyacrylamide core. The deswelling of the shell that occurs upon heating above the lower critical solution temperature of PNIPAM slightly slows down the diffusion of these tracer oligomers near the core-shell interface. By contrast, the mobility of the tracers inside the core is not affected by deswelling of the shell. This finding assures absence of artifacts such as adsorption of the guests to the amphiphilic shell polymer, supporting the utility of these microgel carriers in encapsulation and controlled release applications.

Gel architectures and their complexity

Gels have made the transition from brittle materials with few potential applications to high performance systems with mechanical properties approaching that of rubber. They have a wide variety of structures and provide the opportunity to tailor these structures to achieve well-controlled properties over a range of length scales. In this review we consider and compare the structures and properties of a range of gels that have been studied in recent years. In comparing these gels we highlight the importance of key structural parameters in defining gel mechanical properties. It is hoped that this article will provide authors who discover new gels a resource that will easily enable them to determine the differences of their new gels to existing gels.

Modulation of the deswelling temperature of thermoresponsive microgel films

We demonstrate fine-tuning of the deswelling temperatures of thermoresponsive microgels within a biologically relevant range (30-40 °C). This was achieved by copolymerizing N-isopropylacrylamide and N-isopropylmethacrylamide (NIPAm and NIPMAm, respectively) in varying ratios; the parent homopolymers are well-known thermoresponsive polymers. Polyelectrolyte layer-by-layer (LbL) assemblies of these microgels retain the temperature response properties as demonstrated by temperature-dependent light scattering. Furthermore, films composed of more than one type of microgel building block were shown to have multiple temperature responses similar to those observed for the individual building blocks, permitting further tailoring of the temperature responsive interface. Additional experiments with mixed composition films, investigating multiple assembly processes, show that the location of the microgels within the film does not interfere with the temperature response. This suggests that microgels within the polyelectrolyte assembly behave independently of neighboring microgels with respect to their thermally induced deswelling.