Towards the realistic computer model of precipitation polymerization microgels

Interplay of Spatial and Topological Defects in Polymer Networks

Polymer networks are widely used in applications, and the formation of a network and its gel point can be predicted. However, the effects of spatial and topological heterogeneity on the resulting network structure and ultimately the mechanical properties, are less understood. To address this challenge, we generate in silico random networks of cross-linked polymer chains with controlled spatial and topological defects. While all fully reacted networks investigated in this study have the same number of end-functionalized polymer strands and cross-linkers, we vary the degree of spatial and topological heterogeneities systematically. We find that spatially heterogeneous cross-linker distributions result in a reduction in the network's primary loops with increased spatial heterogeneity, the opposite trend as observed in homogeneous networks. By performing molecular dynamics simulations, we investigated the mechanical properties of the networks. Even though spatially heterogeneous networks have more elastically active strands and cross-linkers, they break at lower extensions than the homogeneous networks and sustain slightly lower maximum stresses. Their shear moduli are higher, i.e., stiffer, than theoretically predicted, and higher than their homogeneous gel counterparts. Our results highlight that topological loop defects and spatial heterogeneities result in significantly different network structures and, ultimately, different mechanical properties.

Peculiarities of Emulsions Stabilized by Stimuli-Responsive Interpenetrating Polymeric Network Microgels

Emulsions have become a crucial product form in various industries in modern times. Expanding the class of substances used to stabilize emulsions can improve their stability or introduce new properties. Particularly, the use of stimuli-responsive microgels makes it possible to create "smart" emulsions whose stability can be controlled by changing any of the specified stimuli. Thus, finding new ways to stabilize emulsions may broaden their application. In this work, for the first time, we applied microgels based on interpenetrating polymeric networks (IPNs) of poly(N-isopropylacrylamide) (PNIPAM) and poly(acrylic acid) (PAA) as stabilizing agents for "oil-in-water" emulsions. We have demonstrated that emulsions stabilized by such soft particles can remain colloidally stable for an extended period, even after being heated up to 40 °C, which is above the lower critical solution temperature (LCST) of PNIPAM. On the contrary, the emulsions stabilized by PNIPAM homopolymer microgels were broken upon heating. To understand the stabilization mechanism of the emulsions, mesoscopic computer simulations were performed to study the IPN microgels at the liquid-liquid interface. The simulations demonstrated that when the first subnetwork (PNIPAM) collapses, the particle adopts a flattened core-shell morphology with a highly swollen PAA-rich shell and a collapsed PNIPAM-rich core. Unlike its PNIPAM homopolymer counterpart, the IPN microgel maintains its three-dimensional shape, which provides stability to the microgel-based emulsions over a wide range of temperatures. Our combined findings could be useful in developing new approaches to emulsions' storage, biphasic catalysis, and lubrication of mechanisms in various operating and climatic conditions.

Long-range ordering of velocity-aligned active polymers

In this work, we study the effect of covalent bonding on the behavior of non-equilibrium systems with the active force acting on particles along their velocity. Self-ordering of single particles does not occur in this model. However, starting from some critical polymerization degree, the ordered state is observed. It is homogeneous and exhibits no phase separation. In the ordered state, the chains prefer a near-two-dimensional configuration and all move in one direction. Importantly, the self-ordering is obtained only at intermediate active force magnitudes. At high magnitudes, the transition from the disordered to ordered state is suppressed by the swelling of the chains during the transition, as we show by the transition kinetics analysis. We demonstrate the bistable behavior of the system in a particular range of polymerization degrees, amplitudes of active force, densities, and thermostat temperatures. Overall, we show that covalent bonding greatly aids the self-ordering in this active particle model, in contrast to active Brownian particles.

Charge Transfer Kinetics of Redox-Active Microgels

Polymer microgel particles decorated with redox-active functional groups are a new and promising object for electrochemical applications. However, the process of charge exchange between an electrode and a microgel particle carrying numerous redox-active centers differs fundamentally from charge exchange involving only molecular species. A single act of contact between the microgel and the electrode surface may not be enough to fully discharge the microgel, and partial charge states are to be expected. Understanding the specifics of this process is crucial for the correct analysis of the data obtained from electrochemical experiments with redox-active microgel solutions. In this study, we employed coarse-grained molecular dynamics to investigate in detail the act of charge transfer from a microgel particle to a flat electrode. The simulations take into account both the mobility of functional groups carrying the charge, which depend on the microgel architecture and the charge exchange between the groups, which can accelerate the propagation of charge within the microgel volume. A set of different microgel systems were simulated in order to reveal the impact of their characteristics: fraction of redox-active groups, microgel molecular mass, cross-linker content, cross-linking topology, and solvent quality. We have found trends in microgel composition leading to the most efficient charge transfer kinetics. The obtained results would be useful for understanding experimental results and for optimizing the design of redox-active microgel particles aimed at faster discharge rates.

Theoretical Study of Microgel Functional Groups' Mobility

Polymer microgels, micrometer-sized cross-linked polymer particles, are considered to be a promising type of advanced materials for a wide range of applications. To enhance the microgels' applicability, it is essential to incorporate various functional groups into a microparticle polymer network. Yet, the availability of functional groups for the interaction with surroundings depends strongly on the properties of the polymer network and has a great impact on further effective usage. In this theoretical study, we address this question and, with the help of coarse-grained molecular dynamics computer simulations, assess the segmental mobility and accessibility of functional groups bound to polymer network depending on microgel architecture and solvent quality. Additionally, we evaluate the minimum number of functional groups needed to facilitate the hopping mechanism between the functional groups (i.e., charge transfer). As an example of practical implementation of the obtained results, we estimate the optimal network topology for redox-active microgels to provide the maximum charge capacity for the dispersion electrolyte in redox-flow batteries.

Molecular Dynamics Simulations of Ideal Living Polymerization: Terminal Model and Kinetic Aspects

Living polymerization is an important synthetic approach to achieving precise control of synthesized polymers, which is crucial for their applications. The molecular weight distribution (MWD) prescribes the macroscopic properties of polymers and hence is a key feature to characterize polymerization. In this work, we present a systematic molecular dynamics simulation study of ideal living polymerization in bulk and surface-initiated systems based on a terminal stochastic reaction model. The evolution of polymer dispersity and MWD along with the polymerization process is examined. We demonstrate that MWD is generally well captured by the Schulz-Zimm distribution for bulk and surface-initiated systems with low grafting densities. However, as the grafting density in the surface-initiated case increases, heterogeneity in chain growth emerges due to the kinetic trapping of reactive sites, which causes the starving of short chains and the thriving of minority long chains such that a shoulder region shows up in MWD. This effect can be enhanced by kinetic compressing induced by polymerization. In addition, the interplay of bonding reaction kinetics and other kinetic properties (e.g., mass transfer and polymer relaxation) is further explored, alongside the influences of bonding probability and reactant concentration. We expect that this investigation will aid in our understanding of typical kinetic aspects of living polymerization.

Ionisation and swelling behaviour of weak polyampholyte core-shell networks - a Monte Carlo study

The network charge of polyampholyte microgels can be tuned by varying the pH of the surrounding solution, and a charge reversal from a positively charged microgel at low pH to a negatively charged microgel at high pH can be achieved. In a titration experiment, it is difficult to tell apart the ionisation of the acidic and basic monomers in the network and to determine the distribution of charges in the network, whereas using Metropolis Monte Carlo simulations, both the degree of ionisation and the distribution of ionised monomers can be determined separately for both species. Building on our earlier work on alternating polyampholyte microgels, we now investigated the pH-dependent ionisation and the swelling behaviour of polyampholyte core-shell microgels under good solvent conditions. For this purpose, we performed Metropolis Monte Carlo simulations for a bead-spring model using the constant-pH method. As in our previous study on alternating microgels, the width of the U-shaped curve of the microgels volume as a function of pH depends on the relative dissociation constants of acid and base, and the microgel volume can be approximated by a linear function of the total network charge. Due to the spatial separation of acid and base in core-shell systems, the ionisation is less enhanced compared to a microgel with an alternating distribution of the two species. Nevertheless, we still see an influence of the presence of one species on the ionisation behaviour of the other species under good solvent conditions. Furthermore, the isoelectric point is shifted towards higher pH, which is caused by a higher charge density in the core compared to that in the shell. Added salt changes the Donnan equilibrium, which determines the counterion distribution within and outside of the microgel. At the same time, it contributes to the electrostatic screening of the network charges, leading to a narrowing of the U-shaped volume transition curve.

Swelling and Collapse of Cylindrical Polyelectrolyte Microgels

In this study, we propose computer simulations of charged cylindrical microgels. The effects of cross-linking density, aspect ratio, and fraction of charged groups on the microgel swelling and collapse with a variation in the solvent quality were studied. The results were compared with those obtained for equivalent neutral cylindrical microgels. The study demonstrated that microgels' degree of swelling strongly depends on the fraction of charged groups. Polyelectrolyte microgels under adequate solvent conditions are characterized by a larger length and thickness than their neutral analogues: the higher the fraction of charged groups, the longer their length and greater their thickness. Microgels' collapse upon solvent quality decline is characterized by a decrease in length and non-monotonous behavior of its thickness. First, the thickness decreases due to the attraction of monomer units (beads) upon collapse. The further thickness increase is related to the surface tension, which tends to reduce the anisotropy of collapsed objects (the minimum surface energy is known to be achieved for the spherical objects). This reduction is opposed by the network elasticity. The microgels with a low cross-linking density and/or a low enough aspect ratio reveal a cylinder-to-sphere collapse. Otherwise, the cylindrical shape is preserved in the course of the collapse. Aspect ratio as a function of the solvent quality (interaction parameter) demonstrates the maximum, which is solely due to the electrostatics. Finally, we plotted radial concentration profiles for network segments, their charged groups, and counterions.

Effect of network topology and crosslinker reactivity on microgel structure and ordering at liquid-liquid interface

Polymer microgels synthesized in silico were studied at a liquid-liquid interface via mesoscopic computer simulations and compared to microgels with ideal (diamond-like) structure. The effect of crosslinkers reactivity ratio on the single particle morphology at the interface and monolayer behavior was examined. It was demonstrated that single particles deform into an explicit core-corona morphology when adsorbed at the interface. An increase in the crosslinker reactivity ratio decreased both the deformation ratio and the ratio between the core and corona sizes. Meanwhile, the compression of microgel monolayers revealed the existence of five distinct interparticle contact regimes, which have been observed experimentally in the literature. The crosslinker reactivity ratio appeared to define the compression range in these regimes and the sharpness of the transition between them. In particular, the higher the crosslinker reactivity ratio, the smaller the corona, and in turn, the narrower the range of the intermediate regime comprising both core-core and corona-corona contacts. The obtained results demonstrate that the more realistic model of microgels synthesized via precipitation polymerization allows for a more accurate prediction of the properties of the microgels at a liquid-liquid interface in comparison to the conventional diamond-like lattice model.

Copolymerization Kinetics of Dopamine Methacrylamide during PNIPAM Microgel Synthesis for Increased Adhesive Properties

Combining stimuli-responsive properties of gels with adhesive properties of mussels is highly interesting for a large field of applications as, e.g., in life science. Therefore, the present paper focuses on the copolymerization of poly(N-isopropylacrylamide) (PNIPAM) microgels with dopamine methacrylamide (DMA). A detailed understanding of reaction kinetics is crucial to figure out an optimized synthesis strategy for tailoring microgels with adhesive properties. The present study addresses the influence of relevant synthesis parameters as the injection time of DMA during the microgel synthesis and the overall reaction time of the microgel. Reaction kinetics were studied by mass spectrometry of time samples taken during the microgel synthesis. This allowed us to determine the monomer consumption of NIPAM, the cross-linker N,N'-methylenebisacrylamide (BIS), and DMA. A second-order reaction kinetics was found for DMA incorporation. The amount of DMA incorporated in the resulting microgel was successfully determined by a combination of UV-vis and NMR spectroscopy to level off limitations of both methods. The dependence of the hydrodynamic radius on temperature was determined by DLS measurements for the microgels. While an early injection of DMA stops the PNIPAM polymerization due to scavenging, it greatly enhances the reaction speed of DMA. The faster reaction of DMA and the incomplete NIPAM and BIS conversion also compensate for shorter reaction times with respect to the incorporated amount of DMA. On the contrary, a later injection of DMA leads to a full NIPAM monomer and BIS cross-linker consumption. An overall reaction time of 60 min ensures the DMA incorporation. Longer reaction times lead to clumping. First adhesion tests show an increased adhesion of P(NIPAM-co-DMA) microgels compared to pure PNIPAM microgels, when mechanical stress is applied.

Microgels react to force: mechanical properties, syntheses, and force-activated functions

Microgels are colloidal polymer networks with high molar mass and properties between rigid particles, flexible macromolecules, and micellar aggregates. Their unique stimuli-responsiveness in conjunction with their colloidal phase behavior render them useful for many applications ranging from engineering to biomedicine. In many scenarios either the microgel's mechanical properties or its interactions with mechanical force play an important role. Here, we firstly explain microgel mechanical properties and how these are measured by atomic force microscopy (AFM), then we equip the reader with the synthetic background to understand how specific architectures and chemical functionalities enable these mechanical properties, and eventually we elucidate how the interaction of force with microgels can lead to the activation of latent functionality. Since the interaction of microgels with force is a multiscale and multidisciplinary subject, we introduce and interconnect the different research areas that contribute to the understanding of this emerging field in this Tutorial Review.

The fuzzy sphere morphology is responsible for the increase in light scattering during the shrinkage of thermoresponsive microgels

Thermoresponsive microgels undergo a volume phase transition from a swollen state under good solvent conditions to a collapsed state under poor solvent conditions. The most prominent examples of such responsive systems are based on poly-(N-isopropylacrylamide). When cross-linked with N,N'-methylenebisacrylamide, such microgels typically possess a fuzzy-spherelike morphology with a higher cross-linked core and a loosely cross-linked fuzzy shell. Despite the efforts devoted to understanding the internal structure of microgels and their kinetics during collapse/swelling, the origins of the accompanying changes in light scattering intensity have barely been addressed. In this work, we study core-shell microgels that contain small gold nanoparticle cores with microgel shells of different thicknesses and cross-linker densities. All microgels are small enough to fulfill the Rayleigh-Debye-Gans criterion at all stages of swelling. Due to the high X-ray contrast of the gold cores, we can use absolute intensity small-angle X-ray scattering to determine the number density in the dilute dispersions. This allows us to extract polymer volume fractions of the microgels at different stages of swelling from form factor analysis of small-angle neutron scattering data. We match our findings to results from temperature-dependent absorbance measurements. The increase in absorbance during the shrinkage of the microgels is related to the transition from fuzzy spheres to hard sphere-like scattering objects with a rather homogeneous density profile. We provide a first attempt to model experimental spectra using finite difference time domain simulations that take into account the structural changes during the volume phase transition. Our findings significantly contribute to the understanding of the optical properties of thermoresponsive microgels. Further, we provide polymer volume fractions and microgel refractive indices as a function of the swelling state.

Microphase separation of stimuli-responsive interpenetrating network microgels investigated by scattering methods

Polymer stimuli-responsive microgels find their use in various applications. The knowledge of its internal structure is of importance for further improvement and expanding the scope. Interpenetrating network (IPN) microgels may possess a remarkable feature of strongly non-uniform inner architecture, even microphase separation, in conditions of a selective solvent. In this research, we, for the first time, use a combination of static light scattering (SLS) and small-angle X-ray scattering (SAXS) techniques to collect the structure factors of aqueous dispersions of poly(N-isopropylacrylamide)-polyacrylic acid IPN microgels on the broad scale ofqvalues. We study the influence of solvent quality on microgel conformations and show that in a selective solvent, such a system undergoes microphase separation: the sub-network in a poor solvent conditions forms dense small aggregates inside the large swollen sub-network in a good solvent. We propose the microstructured sphere model for the IPN microgel structure factor interpretation and perform additional analysis and verification through coarse-grained molecular dynamics computer simulations.

Microstructured Macromaterials Based on IPN Microgels

This study investigates the formation of microstructured macromaterials from thermo- and pH-sensitive microgels based on interpenetrating networks of poly-N-isopropylacrylamide (PNIPAM) and polyacrylic acid (PAA). Macromaterials are produced as a result of the deposition of microgel particles and subsequent crosslinking of polyacrylic acid subnetworks to each other due to the formation of the anhydride bonds during annealing. Since both PNIPAM and PAA are environment-sensitive polymers, one can expect that their conformational state during material development will affect its resulting properties. Thus, the influence of conditions of preparation for annealing (pH of the solution, the temperature of preliminary drying) on the swelling behavior, pH- and thermosensitivity, and macromaterial inner structure was investigated. In parallel, the study of the effect of the relative conformations of the IPN microgel subnetworks on the formation of macromaterials was carried out by the computer simulations method. It was shown that the properties of the prepared macromaterials strongly depend both on the temperature and pH of the PNIPAM-PAA IPN microgel dispersions. This opens up new opportunities to obtain materials with pre-chosen characteristics and environmental sensitivity.

Nanostructures, Thermoresponsiveness, and Assembly Mechanism of Hydrogel Microspheres during Aqueous Free-Radical Precipitation Polymerization

Although techniques to produce uniformly sized hydrogel microspheres (microgels) by aqueous free-radical precipitation polymerization are well established, the details of the polymerization process remain mysterious. In the present study, the structural evolution and thermoresponsiveness of the developing microgels during the polymerization were evaluated by temperature-controlled high-speed atomic force microscopy. This analysis clarified that the swelling properties of the precursor microgels formed in the early stages of the polymerization are quite low due to the high incorporation of cross-linkers and that non-thermoresponsive deca-nanosized spherical domains are already present in the precursor microgels. Furthermore, we succeeded in tracking the formation of nuclei and their growth process, which has never been fully understood, in aqueous solution by real-time observations. These findings will help us to design functional microgels with the desired nanostructures via precipitation polymerization.

Simulation of interpenetrating networks microgel synthesis

In this paper, we have implemented the sequential template synthesis of interpenetrating network (IPN) microgels in computer simulations and studied the behavior of such particles. We explored the influence of the interaction between the components of primary and secondary networks on the polymerization process and determined the necessary conditions for IPN particle formation. The interconnection between the parameters of synthesis and topological properties of the resulting microgels was investigated. We studied the morphologies of microgels in "good", "poor" and "selective" solvents. For the first time, we demonstrated the possibility of the formation of shell-corona structures in IPN microgels obtained by in silico synthesis from monomers and exposed to a selective solvent. These results allow for the better understanding of the required experimental conditions and data interpretation such as static structure factors.

Compression and Ordering of Microgels in Monolayers Formed at Liquid-Liquid Interfaces: Computer Simulation Studies

Monolayers of polymer microgels adsorbed at the liquid interfaces were studied by dissipative particle dynamics simulations. The results demonstrated that the compressibility of the monolayers can be widely tuned by varying the cross-linking density of the microgels and their (in)compatibility with the immiscible liquids. In particular, the compression of the monolayers (increase of 2D concentration of the microgels) leads to the decrease of their lateral size. Herewith, the shape of the individual soft particles gradually changes from oblate (diluted 2D system) to nearly spherical (compressed monolayer). The polymer concentration profiles plotted along the normal to the interface reveal a nonmonotonous shape with a sharp maximum at the interface. This is a consequence of the shielding effect: saturation of the interface by monomer units of the subchains is driven by minimization of unfavorable contacts between the immiscible liquids and is opposed by elasticity of the network. The decrease of the interfacial tension upon concentration (compression) of the monolayer is quantified. It has been demonstrated that the interfacial tension significantly differs if the solubility of the polymer chains of the microgel network in the liquids changes. These results correlate well with experimental data. The examination of the microgels' crystalline ordering in monolayers demonstrated a nonmonotonous dependency on the compression degree (microgel concentration). Finally, the worsening of the solvent quality leads to the collapse of the microgels in monolayer and nonmonotonous behavior of the interfacial tension.

Coarsening Kinetics of Complex Macromolecular Architectures in Bad Solvent

This study reports a general scenario for the out-of-equilibrium features of collapsing polymeric architectures. We use molecular dynamics simulations to characterize the coarsening kinetics, in bad solvent, for several macromolecular systems with an increasing degree of structural complexity. In particular, we focus on: flexible and semiflexible polymer chains, star polymers with 3 and 12 arms, and microgels with both ordered and disordered networks. Starting from a powerful analogy with critical phenomena, we construct a density field representation that removes fast fluctuations and provides a consistent characterization of the domain growth. Our results indicate that the coarsening kinetics presents a scaling behaviour that is independent of the solvent quality parameter, in analogy to the time-temperature superposition principle. Interestingly, the domain growth in time follows a power-law behaviour that is approximately independent of the architecture for all the flexible systems; while it is steeper for the semiflexible chains. Nevertheless, the fractal nature of the dense regions emerging during the collapse exhibits the same scaling behaviour for all the macromolecules. This suggests that the faster growing length scale in the semiflexible chains originates just from a faster mass diffusion along the chain contour, induced by the local stiffness. The decay of the dynamic correlations displays scaling behavior with the growing length scale of the system, which is a characteristic signature in coarsening phenomena.