Modeling Microgels with a Controlled Structure across the Volume Phase Transition

Unified Understanding of the Structure, Thermodynamics, and Diffusion of Single-Chain Nanoparticle Fluids

Single-chain nanoparticles (SCNPs) are a fascinating class of soft nano-objects with promising properties and relevance to protein condensates, polymer nanocomposites, nanomedicine, bioimaging, catalysis, and drug delivery. We combine molecular dynamics simulations and equilibrium and time-dependent statistical mechanical theory to construct a unified understanding of how the internal conformational structure of SCNPs, of both a simple fractal globule-like form and more complex objects with multiple internal intermediate length scales, determines nm-scale intermolecular packing correlations, thermodynamic properties, and center-of-mass diffusion over a wide range of concentrations up to dense melts. The intermolecular pair correlations generically exhibit a distinctive deep correlation hole form due to SCNP internal connectivity structure and repulsive interparticle interactions associated with a globular-like conformation on the macromolecular scale, with concentration-dependent deviations at small separations. Unanticipated exponential-like dependences of the equation-of-state, osmotic compressibility, and center-of-mass diffusion constant on SCNP macromolecular packing fraction are theoretically predicted and confirmed via simulations. System-specific behaviors are found associated with SCNP internal structure, but overarching regularities are identified and understood based on a generalized effective globule conformation on macromolecular scales. Diffusivity slows down by 2-3 decades with increasing concentration and is understood as a consequence of a nonactivated excluded volume-driven weak-caging process associated with space-time correlated intermolecular forces experienced by the SCNP. Good agreement between the theory and simulations is established, testable predictions are made, and a quantitative comparison with viscosity measurements on a specific SCNP fluid is carried out. The basic theoretical approach can potentially be extended to treat the chemical and physical consequences of varying the structure of other classes of soft nanoparticles with distinctive internal nanoscale organization relevant in nanotechnology and nanomedicine, and the possible emergence of macromolecular kinetically arrested glasses.

Softness matters: effects of compression on the behavior of adsorbed microgels at interfaces

Deformable colloids and macromolecules adsorb at interfaces as they decrease the interfacial energy between the two media. The deformability, or softness, of these particles plays a pivotal role in the properties of the interface. In this study, we employ a comprehensive in situ approach, combining neutron reflectometry with molecular dynamics simulations, to thoroughly examine the profound influence of softness on the structure of microgel Langmuir monolayers under compression. Lateral compression of both hard and soft microgel particle monolayers induces substantial structural alterations, leading to an amplified protrusion of the microgels into the aqueous phase. However, a critical distinction emerges: hard microgels are pushed away from the interface, in stark contrast to the soft ones, which remain firmly anchored to it. Concurrently, on the air-exposed side of the monolayer, lateral compression induces a flattening of the surface of the hard monolayer. This phenomenon is not observed for the soft particles as the monolayer is already extremely flat even in the absence of compression. These findings significantly advance our understanding of the key role of softness on both the equilibrium phase behavior of the monolayer and its effect when soft colloids are used as stabilizers of responsive interfaces and emulsions.

Auxetic polymer networks: The role of crosslinking, density, and disorder

Low-crosslinked polymer networks have recently been found to behave auxetically when subjected to small tensions, that is, their Poisson's ratio ν becomes negative. In addition, for specific state points, numerical simulations revealed that diamond-like networks reach the limit of mechanical stability, exhibiting values of ν = -1, a condition that we define as hyper-auxeticity. This behavior is interesting per se for its consequences in materials science but is also appealing for fundamental physics because the mechanical instability is accompanied by evidence of criticality. In this work, we deepen our understanding of this phenomenon by performing a large set of equilibrium and stress-strain simulations in combination with phenomenological elasticity theory. The two approaches are found to be in good agreement, confirming the above results. We also extend our investigations to disordered polymer networks and find that the hyper-auxetic behavior also holds in this case, still manifesting a similar critical-like behavior as in the diamond one. Finally, we highlight the role of the number density, which is found to be a relevant control parameter determining the elastic properties of the system. The validity of the results under disordered conditions paves the way for an experimental investigation of this phenomenon in real systems, such as hydrogels.

Toward a Unified Description of the Electrostatic Assembly of Microgels and Nanoparticles

The interplay of soft responsive particles, such as microgels, with nanoparticles (NPs) yields highly versatile complexes that show great potential for applications, ranging from plasmonic sensing to catalysis and drug delivery. However, the microgel-NP assembly process has not been investigated so far at the microscopic level, thus hindering the possibility of designing such hybrid systems a priori. In this work, we combine state-of-the-art numerical simulations with experiments to elucidate the fundamental mechanisms taking place when microgel-NP assembly is controlled by electrostatic interactions and the associated effects on the structure of the resulting complexes. We find a general behavior where, by increasing the number of interacting NPs, the microgel deswells up to a minimum size after which a plateau behavior occurs. This occurs either when NPs are mainly adsorbed to the microgel corona via the folding of the more external chains or when NPs penetrate inside the microgel, thereby inducing a collective reorganization of the polymer network. By varying microgel properties, such as fraction of cross-linkers or charge, as well as NP size and charge, we further show that the microgel deswelling curves can be rescaled onto a single master curve, for both experiments and simulations, demonstrating that the process is entirely controlled by the charge of the whole microgel-NP complex. Our results thus have a direct relevance in fundamental materials science and offer novel tools to tailor the nanofabrication of hybrid devices of technological interest.

Colloidal Clusters and Networks Formed by Oppositely Charged Nanoparticles with Varying Stiffnesses

Colloidal clusters and gels are ubiquitous in science and technology. Particle softness has a strong effect on interparticle interactions; however, our understanding of the role of this factor in the formation of colloidal clusters and gels is only beginning to evolve. Here, we report the results of experimental and simulation studies of the impact of particle softness on the assembly of clusters and networks from mixtures of oppositely charged polymer nanoparticles (NPs). Experiments were performed below or above the polymer glass transition temperature, at which the interaction potential and adhesive forces between the NPs were significantly varied. Hard NPs assembled in fractal clusters that subsequently organized in a kinetically arrested colloidal gel, while soft NPs formed dense precipitating aggregates, due to the NP deformation and the decreased interparticle distance. Importantly, interactions of hard and soft NPs led to the formation of discrete precipitating NP aggregates at a relatively low volume fraction of soft NPs. A phenomenological model was developed for interactions of oppositely charged NPs with varying softnesses. The experimental results were in agreement with molecular dynamics simulations based on the model. This work provides insight on interparticle interactions before, during, and after the formation of hard-hard, hard-soft, and soft-soft contacts and has impact for numerous applications of reversible colloidal gels, including their use as inks for additive manufacturing.

Impact of polyelectrolyte adsorption on the rheology of concentrated poly(N-isopropylacrylamide) microgel suspensions

We explore the impact of three water-soluble polyelectrolytes (PEs) on the flow of concentrated suspensions of poly(N-isopropylacrylamide) (PNIPAm) microgels with thermoresponsive anionic charge density. By progressively adding the PEs to a jammed suspension of swollen microgels, we show that the rheology of the mixtures is remarkably influenced by the sign of the PE charge, PE concentration and hydrophobicity only when the temperature is increased above the microgel volume phase transition temperature T_c, namely when microgels collapse, they are partially hydrophobic and form a volume-spanning colloidal gel. We find that the original gel is strengthened close to the isoelectric point, attained when microgels are mixed with cationic PEs, while PE hydrophobicity rules the gel strengthening at very high PE concentrations. Surprisingly, we find that polyelectrolyte adsorption or partial embedding of PE chains inside the microgel periphery occurs also when anionic polymers of polystyrene sulfonate with a high degree of sulfonation are added. This gives rise to colloidal stabilization and to the melting of the original gel network above T_c. Contrastingly, the presence of polyelectrolytes in suspensions of swollen, jammed microgels results in a weak softening of the original repulsive glass, even when an apparent isoelectric condition is met. Our study puts forward the crucial role of electrostatics in thermosensitive microgels, unveiling an exciting new way to tailor the flow of these soft colloids and highlighting a largely unexplored path to engineer soft colloidal mixtures.

Concentration and temperature dependent interactions and state diagram of dispersions of copolymer microgels

We investigate by means of small angle neutron scattering experiments and numerical simulations the interactions and inter-particle arrangements of concentrated dispersions of copolymer poly(N-isopropylacrylamide)-poly(ethylene glycol methyl ether methacrylate) (PNIPAM-PEGMA) microgels across the volume phase transition (VPT). The scattering data of moderately concentrated dispersions are accurately modeled at all temperatures by using a star polymer form factor and static structure factors calculated from the effective potential obtained from simulations. Interestingly, for temperatures below the VPT temperature (VPTT), the radius of gyration and blob size of the particles significantly decrease with increasing the effective packing fraction in the non-overlapping regime. This is attributed to the presence of charges in the system associated with the use of an ionic initiator in the synthesis. Simulations using the experimentally corroborated interaction potential are used to explore the state diagram in a wide range of effective packing fractions. Below and slightly above the VPTT, the system undergoes an arrest transition mainly driven by the soft repulsion between the particles. Only well above the VPTT the system is found to phase separate before arresting. Our results highlight the versatility and potential of copolymer PNIPAM-PEGMA microgels to explore different kinds of arrested states balancing attraction and repulsion by changing temperature and packing fraction.

Buckling and Interfacial Deformation of Fluorescent Poly(N-isopropylacrylamide) Microgel Capsules

Hollow microgels are fascinating model systems at the crossover between polymer vesicles, emulsions, and colloids as they deform, interpenetrate, and eventually shrink at higher volume fraction or when subjected to an external stress. Here, we introduce a system consisting of microgels with a micrometer-sized cavity enabling a straightforward characterization in situ using fluorescence microscopy techniques. Similarly to elastic capsules, these systems are found to reversibly buckle above a critical osmotic pressure, conversely to smaller hollow microgels, which were previously reported to deswell at high volume fraction. Simulations performed on monomer-resolved in silico hollow microgels confirm the buckling transition and show that the presented microgels can be described with a thin shell model theory. When brought to an interface, these microgels, that we define as microgel capsules, strongly deform and we thus propose to utilize them to locally probe interfacial properties within a theoretical framework adapted from the Johnson-Kendall-Roberts (JKR) theory. Besides their capability to sense their environment and to address fundamental questions on the elasticity and permeability of microgel systems, microgel capsules can be further envisioned as model systems mimicking anisotropic responsive biological systems such as red blood and epithelial cells thanks to the possibility offered by microgels to be synthesized with custom-designed properties.

Structure and elasticity of model disordered, polydisperse, and defect-free polymer networks

The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly cross-linked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the cross-links and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density and connect the cross-link localization length to the shear modulus of the system.

Probing Temperature Responsivity of Microgels and Its Interplay with a Solid Surface by Super-Resolution Microscopy and Numerical Simulations

Super-resolution microscopy has become a powerful tool to investigate the internal structure of complex colloidal and polymeric systems, such as microgels, at the nanometer scale. An interesting feature of this method is the possibility of monitoring microgel response to temperature changes in situ. However, when performing advanced microscopy experiments, interactions between the particle and the environment can be important. Often microgels are deposited on a substrate, since they have to remain still for several minutes during the experiment. This study uses direct stochastic optical reconstruction microscopy (dSTORM) and advanced coarse-grained molecular dynamics simulations to investigate how individual microgels anchored on hydrophilic and hydrophobic surfaces undergo their volume phase transition with temperature. We find that, in the presence of a hydrophilic substrate, the structure of the microgel is unperturbed and the resulting density profiles quantitatively agree with simulations performed under bulk conditions. Instead, when a hydrophobic surface is used, the microgel spreads at the interface and an interesting competition between the two hydrophobic strengths,monomer-monomer vs monomer-surface,comes into play at high temperatures. The robust agreement between experiments and simulations makes the present study a fundamental step to establish this high-resolution monitoring technique as a platform for investigating more complex systems, these being either macromolecules with peculiar internal structure or nanocomplexes where molecules of interest can be encapsulated in the microgel network and controllably released with temperature.

In situ imaging of the three-dimensional shape of soft responsive particles at fluid interfaces by atomic force microscopy

The reconfiguration of individual soft and deformable particles upon adsorption at a fluid interface underpins many aspects of their dynamics and interactions, ultimately regulating the properties of monolayers of relevance for applications. In this work, we demonstrate that atomic force microscopy can be used for the in situ reconstruction of the three-dimensional conformation of model poly(N-isopropylacrylamide) microgels adsorbed at an oil-water interface. We image the particle topography from both sides of the interface to characterize its in-plane deformation and to visualize the occurrence of asymmetric swelling in the two fluids. In addition, the technique enables investigating different fluid phases and particle architectures, as well as studying the effect of temperature variations on particle conformation in situ. We envisage that these results open up an exciting range of possibilities to provide microscopic insights into the single-particle behavior of soft objects at fluid interfaces and into the resulting macroscopic material properties.

In-situ study of the impact of temperature and architecture on the interfacial structure of microgels

The structural characterization of microgels at interfaces is fundamental to understand both their 2D phase behavior and their role as stabilizers that enable emulsions to be broken on demand. However, this characterization is usually limited by available experimental techniques, which do not allow a direct investigation at interfaces. To overcome this difficulty, here we employ neutron reflectometry, which allows us to probe the structure and responsiveness of the microgels in-situ at the air-water interface. We investigate two types of microgels with different cross-link density, thus having different softness and deformability, both below and above their volume phase transition temperature, by combining experiments with computer simulations of in silico synthesized microgels. We find that temperature only affects the portion of microgels in water, while the strongest effect of the microgels softness is observed in their ability to protrude into the air. In particular, standard microgels have an apparent contact angle of few degrees, while ultra-low cross-linked microgels form a flat polymeric layer with zero contact angle. Altogether, this study provides an in-depth microscopic description of how different microgel architectures affect their arrangements at interfaces, and will be the foundation for a better understanding of their phase behavior and assembly.

How Softness Matters in Soft Nanogels and Nanogel Assemblies

Softness plays a key role in determining the macroscopic properties of colloidal systems, from synthetic nanogels to biological macromolecules, from viruses to star polymers. However, we are missing a way to quantify what the term "softness" means in nanoscience. Having quantitative parameters is fundamental to compare different systems and understand what the consequences of softness on the macroscopic properties are. Here, we propose different quantities that can be measured using scattering methods and microscopy experiments. On the basis of these quantities, we review the recent literature on micro- and nanogels, i.e. cross-linked polymer networks swollen in water, a widely used model system for soft colloids. Applying our criteria, we address the question what makes a nanomaterial soft? We discuss and introduce general criteria to quantify the different definitions of softness for an individual compressible colloid. This is done in terms of the energetic cost associated with the deformation and the capability of the colloid to isotropically deswell. Then, concentrated solutions of soft colloids are considered. New definitions of softness and new parameters, which depend on the particle-to-particle interactions, are introduced in terms of faceting and interpenetration. The influence of the different synthetic routes on the softness of nanogels is discussed. Concentrated solutions of nanogels are considered and we review the recent results in the literature concerning the phase behavior and flow properties of nanogels both in three and two dimensions, in the light of the different parameters we defined. The aim of this review is to look at the results on micro- and nanogels in a more quantitative way that allow us to explain the reported properties in terms of differences in colloidal softness. Furthermore, this review can give researchers dealing with soft colloids quantitative methods to define unambiguously which softness matters in their compound.

Influence of the interfacial tension on the microstructural and mechanical properties of microgels at fluid interfaces

Microgels are soft colloidal particles constituted by cross-linked polymer networks with a high potential for applications. In particular, after adsorption at a fluid interface, interfacial tension provides two-dimensional (2D) confinement for microgel monolayers and drives the reconfiguration of the particles, enabling their deployment in foam and emulsion stabilization and in surface patterning for lithography, sensing and optical materials. However, most studies focus on systems of fluids with a high interfacial tension, e.g. alkanes/ or air/water interfaces, which imparts similar properties to the assembled monolayers. Here, instead, we compare two organic fluid phases, hexane and methyl tert-butyl ether, which have markedly different interfacial tension (γ) values with water and thus tune the deformation of adsorbed microgels. We rationalize how γ controls the single-particle morphology, which consequently modulates the structural and mechanical response of the monolayers at varying interfacial compression. Specifically, when γ is low, the microgels are less deformed within the interface plane and their polymer networks can rearrange more easily upon lateral compression, leading to softer monolayers. Selecting interfaces with different surface energy offers an additional control to customize the 2D assembly of soft particles, from the fine-tuning of particle size and interparticle spacing to the tailoring of mechanical properties.

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.

Onset of criticality in hyper-auxetic polymer networks

Against common sense, auxetic materials expand or contract perpendicularly when stretched or compressed, respectively, by uniaxial strain, being characterized by a negative Poisson's ratio ν. The amount of deformation in response to the applied force can be at most equal to the imposed one, so that ν = - 1 is the lowest bound for the mechanical stability of solids, a condition here defined as "hyper-auxeticity". In this work, we numerically show that ultra-low-crosslinked polymer networks under tension display hyper-auxetic behavior at a finite crosslinker concentration. At this point, the nearby mechanical instability triggers the onset of a critical-like transition between two states of different densities. This phenomenon displays similar features as well as important differences with respect to gas-liquid phase separation. Since our model is able to faithfully describe real-world hydrogels, the present results can be readily tested in laboratory experiments, paving the way to explore this unconventional phase behavior.

Thermoresponsivity of poly(N-isopropylacrylamide) microgels in water-trehalose solution and its relation to protein behavior

HYPOTHESES

Additives are commonly used to tune macromolecular conformational transitions. Among additives, trehalose is an excellent bioprotectant and among responsive polymers, PNIPAM is the most studied material. Nevertheless, their interaction mechanism so far has only been hinted without direct investigation, and, crucially, never elucidated in comparison to proteins. Detailed insights would help understand to what extent PNIPAM microgels can effectively be used as synthetic biomimetic materials, to reproduce and study, at the colloidal scale, isolated protein behavior and its sensitivity to interactions with specific cosolvents or cosolutes.

EXPERIMENTS

The effect of trehalose on the swelling behavior of PNIPAM microgels was monitored by dynamic light scattering; Raman spectroscopy and molecular dynamics simulations were used to explore changes of solvation and dynamics across the swelling-deswelling transition at the molecular scale.

FINDINGS

Strongly hydrated trehalose molecules develop water-mediated interactions with PNIPAM microgels, thereby preserving polymer hydration below and above the transition while drastically inhibiting local motions of the polymer and of its hydration shell. Our study, for the first time, demonstrates that slowdown of dynamics and preferential exclusion are the principal mechanisms governing trehalose effect on PNIPAM microgels, at odds with preferential adsorption of alcohols, but in full analogy with the behavior observed in trehalose-protein systems.

How the interplay of molecular and colloidal scales controls drying of microgel dispersions

Bringing an aqueous dispersion or solution into open air leads to water evaporation. The resulting drying process initiates the buildup of spatial heterogeneities, as nonvolatile solutes and colloids concentrate. Such composition gradients associate with mesostructure gradients, which, in turn, impact flows within these multicomponent systems. In this work, we investigate the drying of microgel dispersions in respect to two reference systems, a colloidal dispersion and a polymer solution, which, respectively, involve colloidal and molecular length scales. We evidence an intermediate behavior in which a film forms at the air/liquid interface and is clearly separated from bulk by a sharp drying front. However, complex composition and mesostructure gradients develop throughout the drying film, as evidenced by Raman and small-angle X-ray scattering mapping. We show that this results from the soft colloidal structure of microgel, which allows them to interpenetrate, deform, and deswell. As a result, water activity and water transport are drastically decreased in the vicinity of the air/liquid interface. This notably leads to diffusional drying kinetics that are nearly independent on the air relative humidity. The interplay between water fraction, water activity, and mesostructure on water transport is generic and, thus, shown to be pivotal in order to master evaporation in drying complex fluids.

Thermoresponsive Chitosan-Grafted-Poly(N-vinylcaprolactam) Microgels via Ionotropic Gelation for Oncological Applications

Microgels can be considered soft, porous and deformable particles with an internal gel structure swollen by a solvent and an average size between 100 and 1000 nm. Due to their biocompatibility, colloidal stability, their unique dynamicity and the permeability of their architecture, they are emerging as important candidates for drug delivery systems, sensing and biocatalysis. In clinical applications, the research on responsive microgels is aimed at the development of "smart" delivery systems that undergo a critical change in conformation and size in reaction to a change in environmental conditions (temperature, magnetic fields, pH, concentration gradient). Recent achievements in biodegradable polymer fabrication have resulted in new appealing strategies, including the combination of synthetic and natural-origin polymers with inorganic nanoparticles, as well as the possibility of controlling drug release remotely. In this review, we provide a literature review on the use of dual and multi-responsive chitosan-grafted-poly-(N-vinylcaprolactam) (CP) microgels in drug delivery and oncological applications.

Two-step deswelling in the Volume Phase Transition of thermoresponsive microgels

Microgels, colloidal-scale polymer networks, are the prototype soft colloids. When the constituent polymers are thermoresponsive, they undergo a volume phase transition (VPT) from a swollen to a collapsed state at a characteristic temperature, close to ambient one, of great appeal for several applications. To describe this phenomenon, microgels are usually treated as neutral, but here we show that electrostatics needs to be taken into account. In particular, deswelling occurs via a two-step, rather than a homogeneous, particle collapse, mainly driven by peripheral charges located on the microgel corona, for which we also establish a unifying framework encompassing all studied microgels. Our work thus provides a change of perspective to describe these fascinating systems.

Thermoresponsive microgels are one of the most investigated types of soft colloids, thanks to their ability to undergo a Volume Phase Transition (VPT) close to ambient temperature. However, this fundamental phenomenon still lacks a detailed microscopic understanding, particularly regarding the presence and the role of charges in the deswelling process. This is particularly important for the widely used poly(N-isopropylacrylamide)–based microgels, where the constituent monomers are neutral but charged groups arise due to the initiator molecules used in the synthesis. Here, we address this point combining experiments with state-of-the-art simulations to show that the microgel collapse does not happen in a homogeneous fashion, but through a two-step mechanism, entirely attributable to electrostatic effects. The signature of this phenomenon is the emergence of a minimum in the ratio between gyration and hydrodynamic radii at the VPT. Thanks to simulations of microgels with different cross-linker concentrations, charge contents, and charge distributions, we provide evidence that peripheral charges arising from the synthesis are responsible for this behavior and we further build a universal master curve able to predict the two-step deswelling. Our results have direct relevance on fundamental soft condensed matter science and on applications where microgels are involved, ranging from materials to biomedical technologies.

Effect of Internal Architecture on the Assembly of Soft Particles at Fluid Interfaces

Monolayers of soft colloidal particles confined at fluid interfaces are at the core of a broad range of technological processes, from the stabilization of responsive foams and emulsions to advanced lithographic techniques. However, establishing a fundamental relation between their internal architecture, which is controlled during synthesis, and their structural and mechanical properties upon interfacial confinement remains an elusive task. To address this open issue, which defines the monolayer's properties, we synthesize core-shell microgels, whose soft core can be chemically degraded in a controlled fashion. This strategy allows us to obtain a series of particles ranging from analogues of standard batch-synthesized microgels to completely hollow ones after total core removal. Combined experimental and numerical results show that our hollow particles have a thin and deformable shell, leading to a temperature-responsive collapse of the internal cavity and a complete flattening after adsorption at a fluid interface. Mechanical characterization shows that a critical degree of core removal is required to obtain soft disk-like particles at an oil-water interface, which present a distinct response to compression. At low packing fractions, the mechanical response of the monolayer is dominated by the outer polymer chains forming a corona surrounding the particles within the interfacial plane, regardless of the presence of a core. By contrast, at high compression, the absence of a core enables the particles to deform in the direction orthogonal to the interface and to be continuously compressed without altering the monolayer structure. These findings show how fine, single-particle architectural control during synthesis can be engineered to determine the interfacial behavior of microgels, enabling one to link particle conformation with the resulting material properties.

Soft Particles at Liquid Interfaces: From Molecular Particle Architecture to Collective Phase Behavior

Soft particles such as microgels can undergo significant and anisotropic deformations when adsorbed to a liquid interface. This, in turn, leads to a complex phase behavior upon compression. To date, experimental efforts have predominantly provided phenomenological links between microgel structure and resulting interfacial behavior, while simulations have not been entirely successful in reproducing experiments or predicting the minimal requirements for the desired phase behavior. Here, we develop a multiscale framework to link the molecular particle architecture to the resulting interfacial morphology and, ultimately, to the collective interfacial phase behavior. To this end, we investigate interfacial morphologies of different poly(N-isopropylacrylamide) particle systems using phase-contrast atomic force microscopy and correlate the distinct interfacial morphology with their bulk molecular architecture. We subsequently introduce a new coarse-grained simulation method that uses augmented potentials to translate this interfacial morphology into the resulting phase behavior upon compression. The main novelty of this method is the possibility to efficiently encode multibody interactions, the effects of which are key to distinguishing between heterostructural (anisotropic collapse) and isostructural (isotropic collapse) phase transitions. Our approach allows us to qualitatively resolve existing discrepancies between experiments and simulations. Notably, we demonstrate the first in silico account of the two-dimensional isostructural transition, which is frequently found in experiments but elusive in simulations. In addition, we provide the first experimental demonstration of a heterostructural transition to a chain phase in a single-component system, which has been theoretically predicted decades ago. Overall, our multiscale framework provides a phenomenological bridge between physicochemical soft-particle characteristics at the molecular scale and nanoscale and the collective self-assembly phenomenology at the macroscale, serving as a stepping stone toward an ultimately more quantitative and predictive design approach.

Effect of Chain Polydispersity on the Elasticity of Disordered Polymer Networks

Due to their unique structural and mechanical properties, randomly cross-linked polymer networks play an important role in many different fields, ranging from cellular biology to industrial processes. In order to elucidate how these properties are controlled by the physical details of the network (e.g., chain-length and end-to-end distributions), we generate disordered phantom networks with different cross-linker concentrations C and initial densities ρinit and evaluate their elastic properties. We find that the shear modulus computed at the same strand concentration for networks with the same C, which determines the number of chains and the chain-length distribution, depends strongly on the preparation protocol of the network, here controlled by ρinit. We rationalize this dependence by employing a generic stress-strain relation for polymer networks that does not rely on the specific form of the polymer end-to-end distance distribution. We find that the shear modulus of the networks is a nonmonotonic function of the density of elastically active strands, and that this behavior has a purely entropic origin. Our results show that if short chains are abundant, as it is always the case for randomly cross-linked polymer networks, the knowledge of the exact chain conformation distribution is essential for correctly predicting the elastic properties. Finally, we apply our theoretical approach to literature experimental data, qualitatively confirming our interpretations.

Glass and Jamming Rheology in Soft Particles Made of PNIPAM and Polyacrylic Acid

The phase behaviour of soft colloids has attracted great attention due to the large variety of new phenomenologies emerging from their ability to pack at very high volume fractions. Here we report rheological measurements on interpenetrated polymer network microgels composed of poly(N-isopropylacrylamide) (PNIPAM) and polyacrylic acid (PAAc) at fixed PAAc content as a function of weight concentration. We found three different rheological regimes characteristic of three different states: a Newtonian shear-thinning fluid, an attractive glass characterized by a yield stress, and a jamming state. We discuss the possible molecular mechanisms driving the formation of these states.

Charge affinity and solvent effects in numerical simulations of ionic microgels

Ionic microgel particles are intriguing systems in which the properties of thermo-responsive polymeric colloids are enriched by the presence of charged groups. In order to rationalize their properties and predict the behaviour of microgel suspensions, it is necessary to develop a coarse-graining strategy that starts from the accurate modelling of single particles. Here, we provide a numerical advancement of a recently-introduced model for charged co-polymerized microgels by improving the treatment of ionic groups in the polymer network. We investigate the thermoresponsive properties of the particles, in particular their swelling behaviour and structure, finding that, when charged groups are considered to be hydrophilic at all temperatures, highly charged microgels do not achieve a fully collapsed state, in favorable comparison to experiments. In addition, we explicitly include the solvent in the description and put forward a mapping between the solvophobic potential in the absence of the solvent and the monomer-solvent interactions in its presence, which is found to work very accurately for any charge fraction of the microgel. Our work paves the way for comparing single-particle properties and swelling behaviour of ionic microgels to experiments and to tackle the study of these charged soft particles at a liquid-liquid interface.

Mechanochemical Cellular Membrane Internalization of Nanohydrogels: A Large-Scale Mesoscopic Simulation

By combining large-scale dissipative particle dynamics and steered molecular dynamics simulations, we investigate the mechanochemical cellular internalization pathways of homogeneous and heterogeneous nanohydrogels and demonstrate that membrane internalization is determined by the crosslink density and encapsulation ability of nanohydrogels. The homogeneous nanohydrogels with a high crosslink density and low encapsulation ability behave as soft nanoparticles partially wrapped by the membrane, while those with a low crosslink density and high encapsulation ability permeate into the membrane. Regardless of the crosslink density, the homogeneous nanohydrogels undergo typical dual morphological deformations. The local lipid nanodomains are identified at the contacting region between the membrane and nanohydrogels because of different diffusion behaviors between lipid and receptor molecules during the internalization process. The yolk@shell heterogeneous nanohydrogels present a different mechanochemical cellular internalization pathway. The yolk with strong affinity is directly in contact with the membrane, resulting in partial membrane wrapping, and the contacting area is much reduced when compared to homogenous nanohydrogels, leading to a smaller lipid nanodomain and thus avoiding related cellular toxicity. Our findings provide a critical mechanism understanding of the biological pathways of nanohydrogels and may guide the molecular design of the hydrogel-based materials for controlled release drug delivery, tissue engineering, and cell culture.

Pathways and challenges towards a complete characterization of microgels

Due to their controlled size, sensitivity to external stimuli, and ease-of-use, microgel colloids are unique building blocks for soft materials made by crosslinking polymers on the micrometer scale. Despite the plethora of work published, many questions about their internal structure, interactions, and phase behavior are still open. The reasons for this lack of understanding are the challenges arising from the small size of the microgel particles, complex pairwise interactions, and their solvent permeability. Here we describe pathways toward a complete understanding of microgel colloids based on recent experimental advances in nanoscale characterization, such as super-resolution microscopy, scattering methods, and modeling.

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.

Poly-N-isopropylacrylamide Nanogels and Microgels at Fluid Interfaces

The confinement of colloidal particles at liquid interfaces offers many opportunities for materials design. Adsorption is driven by a reduction of the total free energy as the contact area between the two liquids is partially replaced by the particle. From an application point of view, particle-stabilized interfaces form emulsions and foams with superior stability. Liquid interfaces also effectively confine colloidal particles in two dimensions and therefore provide ideal model systems to fundamentally study particle interactions, dynamics, and self-assembly. With progress in the synthesis of nanomaterials, more and more complex and functional particles are available for such studies. In this Account, we focus on poly(N-isopropylacrylamide) nanogels and microgels. These are cross-linked polymeric particles that swell and soften by uptaking large amounts of water. The incorporated water can be partially expelled, causing a volume phase transition into a collapsed state when the temperature is increased above approximately 32 °C. Soft microgels adsorbed to liquid interfaces significantly deform under the influence of interfacial tension and assume cross sections exceeding their bulk dimensions. In particular, a pronounced corona forms around the microgel core, consisting of dangling chains at the microgel periphery. These polymer chains expand at the interface and strongly affect the interparticle interactions. The particle deformability therefore leads to a significantly more complex interfacial phase behavior that provides a rich playground to explore structure formation processes. We first discuss the characteristic "fried-egg" or core-corona morphology of individual microgels adsorbed to a liquid interface and comment on the dependence of this interfacial morphology on their physicochemical properties. We introduce different theoretical models to describe their interfacial morphology. In a second part, we introduce how ensembles of microgels interact and self-assemble at liquid interfaces. The core-corona morphology and the possibility to force these elements into overlap upon compression results in a complex phase behavior with a phase transition between microgels with extended and collapsed coronae. We discuss the influence of the internal particle architecture, also including core-shell microgels with rigid cores, on the phase behavior. Finally, we present new routes for the realization of more complex structures, resulting from multiple deposition protocols and from engineering the interaction potential of the individual particles.