Modelling realistic microgels in an explicit solvent

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.

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.

The effect of monomer polarizability on the stability and salt partitioning in model coacervates

Coacervation of charged polymer chains has been a topic of major interest in both polymer and biological sciences, as it is a subset of a phenomenon called liquid-liquid phase separation (LLPS). In this process the polymer-rich phase separates from the polymer-lean supernatant while still maintaining its liquid-like properties. LLPS has been shown to play a crucial role in cellular homeostasis by driving the formation of membraneless organelles. It also has the potential to be harnessed to aid in novel therapeutical applications. Recent studies have demonstrated that there is no one simple mechanism which drives LLPS, which is instead a result of the combined effect of electrostatic, dipolar, hydrophobic, and other weak interactions. Using coarse-grained polymer simulations we investigate the relatively unexplored effects of monomer polarizability and spatially varying dielectric constant on LLPS propensity, and these factors affect the properties of the resulting condensates. In order to produce spatial variations in the dielectric constant, all our simulations include explicit solvent and counterions. We demonstrate that polarizability has only a minor effect on the bulk behaviour of the condensates but plays a major role when ion partitioning and microstructure are considered. We observe that the major contribution comes from the nature of the neutral blocks as endowing them with an induced dipole changes their character from hydrophobic to hydrophilic. We hypothesize that the results of this work can aid in guiding future studies concerned with LLPS by providing a general framework and by highlighting important factors which influence LLPS.

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.

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.

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.

Viscoelastic necking dynamics between attractive microgels

HYPOTHESIS

Microgels can deform and interpenetrate and display colloid/polymer duality. The effective interaction of microgels in the collapsed state is governed by the interplay of polymer-solvent interfacial tension and bulk elasticity. A connecting neck is shown to mediate microgel interaction, but its temporal evolution has not been addressed. We hypothesize that the necking dynamics of attractive microgels exhibits liquid-like or solid-like behavior over different time and length scales.

EXPERIMENTS

We simulate the merging and pinching of attractive microgels with different crosslinking densities in explicit solvent using dissipative particle dynamics. The temporal coalescence dynamics of microgels is investigated and compared with simple liquid and polymeric droplets. We model the neck growth on long time scales using Maxwell model of polymer relaxation and compare the theoretical prediction with simulation data. The mechanical strength of the neck is characterized systematically via simulated pinch-off of microgels by steered molecular dynamics.

FINDINGS

We evidence a crossover in the coalescence dynamics reflecting the viscoelastic signature of microgels. In contrast to the common knowledge that viscoelastic materials respond elastically on short time scales, the early expansion of the microgel neck exhibits a linear behavior, similar to the viscous coalescence of liquid droplets. However, the late regime with arrested dynamics resembles sintering of solid particles. Through an analytical model relating microgel dynamics to neck growth, we show that the long-term behavior is governed by stress relaxation of the polymers in the neck region and predict an exponential decay in the rate of growth, which agrees favorably with the simulation. Different from coalescence, the thread thinning in microgel breakup primarily highlights its polymeric characteristics.

Generalized energy-based fragmentation approach for calculations of solvation energies of large systems

A generalized energy-based fragmentation (GEBF) approach has been combined with a universal solvation model based on solute electron density (SMD) to compute the solvation energies of general large systems (such as protein molecules) in solutions. In the GEBF-SMD method, the solvation energy of a target system could be combined by the corresponding solvation energies of various subsystems, each of which is embedded in the background point charges and surface charges on the surface of solute cavity at the positions of its atoms and neighbouring atoms outside of the subsystem. Our results show that the GEBF-SMD model could reproduce the conventional SMD solvation energies quite well for various proteins in solutions, and could significantly reduce the computational costs for the SMD calculations of large proteins. In addition, the GEBF-SMD approach is almost independent of the basis sets and the types of solvents (including protic, polar, and nonpolar ones). Also, the GEBF-SMD approach could reproduce the relative energies of various conformers of large systems in solutions. Therefore, the GEBF-SMD method is expected to be applicable for computing the solvation energies of a broad range of large systems.

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.

Interface-induced hysteretic volume phase transition of microgels: simulation and experiment

Thermo-responsive microgel particles can exhibit a drastic volume shrinkage upon increasing the solvent temperature. Recently we found that the spreading of poly(N-isopropylacrylamide) (PNiPAm) microgels at a liquid interface under the influence of surface tension hinders the temperature-induced volume phase transition. In addition, we observed a hysteresis behavior upon temperature cycling, i.e. a different evolution in microgel size and shape depending on whether the microgel was initially adsorbed to the interface in expanded or collapsed state. Here, we model the volume phase transition of such microgels at an air/water interface by monomer-resolved Brownian dynamics simulations and compare the observed behavior with experiments. We reproduce the experimentally observed hysteresis in the microgel dimensions upon temperature variation. Our simulations did not observe any hysteresis for microgels dispersed in the bulk liquid, suggesting that it results from the distinct interfacial morphology of the microgel adsorbed at the liquid interface. An initially collapsed microgel brought to the interface and subjected to subsequent swelling and collapsing (resp. cooling and heating) will end up in a larger size than it had in the original collapsed state. Further temperature cycling, however, only shows a much reduced hysteresis, in agreement with our experimental observations. We attribute the hysteretic behavior to a kinetically trapped initial collapsed configuration, which relaxes upon expanding in the swollen state. We find a similar behavior for linear PNiPAm chains adsorbed to an interface. Our combined experimental - simulation investigation provides new insights into the volume phase transition of PNiPAm materials adsorbed to liquid interfaces.

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.

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.

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.

Numerical insights on ionic microgels: structure and swelling behaviour

Recent progress has been made in the numerical modelling of neutral microgel particles with a realistic, disordered structure. In this work we extend this approach to the case of co-polymerised microgels where a thermoresponsive polymer is mixed with acidic groups. We compare the cases where counterions directly interact with microgel charges or are modelled implicitly through a Debye-Hückel description. We do so by performing extensive numerical simulations of single microgels across the volume phase transition (VPT) varying the temperature and the fraction of charged monomers. We find that the presence of charges considerably alters the microgel structure, quantified by the monomer density profiles and by the form factors of the microgels, particularly close to the VPT. We observe significant deviations between the implicit and explicit models, with the latter comparing more favourably to available experiments. In particular, we observe a shift of the VPT temperature to larger values as the amount of charged monomers increases. We also find that below the VPT the microgel-counterion complex is almost neutral, while it develops a net charge above the VPT. Interestingly, under these conditions the collapsed microgel still retains a large amount of counterions inside its structure. Since these interesting features cannot be captured by the implicit model, our results show that it is crucial to explicitly include the counterions in order to realistically model ionic thermoresponsive microgels.

Coil-Globule Transition Thermodynamics of Poly(N-isopropylacrylamide)

Thermosensitive polymers such as poly(N-isopropylacrylamide) (PNIPAM) undergo a phase transition in aqueous solution from a random-coil structural ensemble to a globule structural ensemble at the lower critical solution temperature (LCST). Above this temperature, PNIPAM agglomerates and becomes insoluble, whereas it is soluble below the temperature. Thus, thermosensitive polymers represent essential targets for several applications, e.g., in drug delivery. Although their ability to change structure in response to a temperature alteration is highly relevant for industrial processes, their thermodynamic properties are mostly qualitatively understood, and the quantitative thermodynamic picture is still elusive. In this study, we used a combined atomistic molecular dynamics and well-tempered metadynamics simulation approach to estimate coil-globule transition thermodynamics. An isotactic 30-mer of PNIPAM was investigated over a broad temperature range between 200 and 360 K. The transition from the globule to the random-coil structure was observed with well-tempered metadynamics. For the first time, the free energy surface of PNIPAM was estimated and it is shown that the simulation results are in line with the experimentally observed thermosensitive behavior. Below the LCST, the random-coil ensemble represents the global energy minimum and is thermodynamically favored by 21 ± 9 kJ/mol compared to the globule ensemble; both are separated by a barrier of 49 ± 14 kJ/mol. In contrast, above the LCST, the globule ensemble is thermodynamically favored by 21 ± 8 kJ/mol over the random-coil ensemble. The barrier from random-coil to globule is 17 ± 10 kJ/mol.

Microgels Adsorbed at Liquid-Liquid Interfaces: A Joint Numerical and Experimental Study

Soft particles display highly versatile properties with respect to hard colloids and even more so at fluid-fluid interfaces. In particular, microgels, consisting of a cross-linked polymer network, are able to deform and flatten upon adsorption at the interface due to the balance between surface tension and internal elasticity. Despite the existence of experimental results, a detailed theoretical understanding of this phenomenon is still lacking due to the absence of appropriate microscopic models. In this work, we propose an advanced modeling of microgels at a flat water/oil interface. The model builds on a realistic description of the internal polymeric architecture and single-particle properties of the microgel and is able to reproduce its experimentally observed shape at the interface. Complementing molecular dynamics simulations with in situ cryo-electron microscopy experiments and atomic force microscopy imaging after Langmuir-Blodgett deposition, we compare the morphology of the microgels for different values of the cross-linking ratios. Our model allows for a systematic microscopic investigation of soft particles at fluid interfaces, which is essential to develop predictive power for the use of microgels in a broad range of applications, including the stabilization of smart emulsions and the versatile patterning of surfaces.

Numerical modelling of non-ionic microgels: an overview

Microgels are complex macromolecules. These colloid-sized polymer networks possess internal degrees of freedom and, depending on the polymer(s) they are made of, can acquire a responsiveness to variations of the environment (temperature, pH, salt concentration, etc.). Besides being valuable for many practical applications, microgels are also extremely important to tackle fundamental physics problems. As a result, these last years have seen a rapid development of protocols for the synthesis of microgels, and more and more research has been devoted to the investigation of their bulk properties. However, from a numerical standpoint the picture is more fragmented, as the inherently multi-scale nature of microgels, whose bulk behaviour crucially depends on the microscopic details, cannot be handled at a single level of coarse-graining. Here we present an overview of the methods and models that have been proposed to describe non-ionic microgels at different length-scales, from the atomistic to the single-particle level. We especially focus on monomer-resolved models, as these have the right level of details to capture the most important properties of microgels, responsiveness and softness. We suggest that these microscopic descriptions, if realistic enough, can be employed as starting points to develop the more coarse-grained representations required to investigate the behaviour of bulk suspensions.