Temperature-sensitive nanogels in the presence of salt: explicit coarse-grained simulations

Zwitterion-Modified Nanogel Responding to Temperature and Ionic Strength: A Dissipative Particle Dynamics Simulation

The self-assembly and stimuli-responsive properties of nanogel poly(n-isopropylacrylamide) (p(NIPAm)) and zwitterion-modified nanogel poly(n-isopropylacrylamide-co-sulfobetainemethacrylate) (p(NIPAm-co-SBMA)) were explored by dissipative particle dynamics simulations. Simulation results reveal that for both types of nanogel, it is beneficial to form spherical nanogels at polymer concentrations of 5-10%. When the chain length (L) elongates from 10 to 40, the sizes of the nanogels enlarge. As for the p(NIPAm) nanogel, it shows thermoresponsiveness; when it switches to the hydrophilic state, the nanogel swells, and vice versa. The zwitterion-modified nanogel p(NIPAm-co-SBMA) possesses thermoresponsiveness and ionic strength responsiveness concurrently. At 293 K, both hydrophilic p(NIPAm) and superhydrophilic polysulfobetaine methacrylate (pSBMA) could appear on the outer surface of the nanogel; however, at 318 K, superhydrophilic pSBMA is on the outer surface to cover the hydrophobic p(NIPAm) core. As the temperature rises, the nanogel shrinks and remains antifouling all through. The salt-responsive property can be reflected by the nanogel size; the volumes of the nanogels in saline systems are larger than those in salt-free systems as the ionic condition inhibits the shrinkage of the zwitterionic pSBMA. This work exhibits the temperature-responsive and salt-responsive behavior of zwitterion-modified-pNIPAm nanogels at the molecular level and provides guidance in antifouling nanogel design.

Structure of swollen hollow polyelectrolyte nanogels with inhomogeneous cross-link distribution

HYPOTHESIS

Recently, it has become possible to synthesize hollow polyelectrolyte nano- and microgels. The shell permeability can be controlled by external stimuli, while the cavity can serve as a storage place for guest molecules. However, there is a lack of a detailed understanding at the molecular level regarding the role of the network topology, inhomogeneities of the distribution of cross-links, and the impact of the electrostatics on the structural response of hollow microgel to external stimuli. To bridge these gaps, molecular dynamics (MD) of computer simulations are used.

EXPERIMENTS

Here, we propose a fresh methodology to create realistic hollow microgel particles in silico. The technique involves a gradual change in the average local length of subchains depending on the distance to the center of mass of the microgel particles resulting in the microgels with a non-uniform distribution of cross-linking species. In particular, a series of microgels with (i) a highly cross-linked inner part of the shell and gradually decreased cross-linker concentration towards the periphery, (ii) microgels with loosely cross-linked inner and outer parts, as well as (iii) microgels with a more-or-less homogeneous structure, have been created and validated. Counterions and salt ions are taken into account explicitly, and electrostatic interactions are described by the Coulomb potential.

FINDINGS

Our studies reveal a strong dependence of the microgel swelling response on the network topology. Simple redistribution of cross-links plays a significant role in the structure of the microgels, including cavity size, microgel size, fuzziness, and extension of the inner and outer parts of the microgels. Our results indicate the possibilities of qualitative justification of the structure of the hollow microgels in the experiments by measuring the relative change in the size of the sacrificial core to the size of the cavity and by estimation of a power law function, [Formula: see text] , of the hydrodynamic radius of the hollow microgels as a function of added salt concentration.

Temperature sensitive nanogels for real-time imaging during transcatheter arterial embolization

Several vascular embolization materials are commonly used in clinical practice, however, having application defects of varying degrees, such as poor intraoperative imaging and easy recanalization of embolized blood vessels, they are challenging for application during Transcatheter arterial embolization (TAE). Thus, an intraoperative visible vascular embolization material with good embolization effect and biocompatibility can improve transcatheter arterial embolization clinical efficacy to some extent. Our study aimed to synthesize a novel vascular embolization material that can achieve complete embolization of arterial trunks and peripheral vessels, namely poly (N-isopropyl acrylamide)-co-acrylic acid nanogel (NIPAM-co-AA). Iohexol 200 mg/mL was co-assembled with 7 wt% NIPAM-co-AA nanogel to create an intelligent thermosensitive radiopaque nanogel (INCA), which achieves a good intraoperative imaging effect and is convenient for transcatheter arterial bolus injection due to its good fluidity and temperature-sensitive sol-gel phase transition. The normal rabbit kidney embolism model further confirmed that INCA could effectively use Digital subtraction angiography (DSA) to achieve intraoperative imaging, and real-time monitoring of the embolization process could avoid mis-embolization and leakage. Meanwhile, in a 42-day study, INCA demonstrated an excellent embolization effect on the right renal artery of New Zealand white rabbits, with no vascular recanalization and ischemic necrosis and calcification remaining. As a result, this radiopaque thermosensitive nanogel has the potential to be an intelligent thermosensitive medical vascular embolization material, providing dual benefits in TAE intraoperative imaging and long-term postoperative embolization while effectively addressing the shortcomings and challenges of commonly used clinical vascular embolization agents.

Monte Carlo simulations of weak polyampholyte microgels: pH-dependence of conformation and ionization

We performed Metropolis Monte Carlo simulations to investigate the impact of varying acid and base dissociation constants on the pH-dependent ionization and conformation of weak polyampholyte microgels under salt-free conditions and under explicit consideration of the chemical ionization equilibria of the acidic and basic groups and their electrostatic interaction. Irrespective of their relative acid and base dissociation constant, all of the microgels undergo a pH-dependent charge reversal from positive to negative with a neutral charge at the isoelectric point. This charge reversal is accompanied by a U-shaped swelling transition of the microgels with a minimum of their size at the point of charge neutrality. The width of the U-shaped swelling transition, however, is found to depend on the chosen relative acid and base dissociation constants through which the extent of the favorable electrostatic intramolecular interaction of the ionized acidic and basic groups is altered. The pH-dependent swelling transition of the microgels is found to become broader, the stronger the intramolecular electrostatic interaction of the oppositely charged ionized species is. In addition, the intramolecular charge compensation of the acidic and basic groups of the microgels allows their counterions to abandon the microgel and the associated gain in translational entropy further amplifies the broadening of the pH-dependent swelling transition. The analysis of the radial ionization profiles of the acidic and basic groups of the differently composed microgels reveals a variety of radial ionization patterns with a dependence on the overall charge of the microgels.

Not only in silico drug discovery: Molecular modeling towards in silico drug delivery formulations

The use of methods at molecular scale for the discovery of new potential active ligands, as well as previously unknown binding sites for target proteins, is now an established reality. Literature offers many successful stories of active compounds developed starting from insights obtained in silico and approved by Food and Drug Administration (FDA). One of the most famous examples is raltegravir, a HIV integrase inhibitor, which was developed after the discovery of a previously unknown transient binding area thanks to molecular dynamics simulations. Molecular simulations have the potential to also improve the design and engineering of drug delivery devices, which are still largely based on fundamental conservation equations. Although they can highlight the dominant release mechanism and quantitatively link the release rate to design parameters (size, drug loading, et cetera), their spatial resolution does not allow to fully capture how phenomena at molecular scale influence system behavior. In this scenario, the "computational microscope" offered by simulations at atomic scale can shed light on the impact of molecular interactions on crucial parameters such as release rate and the response of the drug delivery device to external stimuli, providing insights that are difficult or impossible to obtain experimentally. Moreover, the new paradigm brought by nanomedicine further underlined the importance of such computational microscope to study the interactions between nanoparticles and biological components with an unprecedented level of detail. Such knowledge is a fundamental pillar to perform device engineering and to achieve efficient and safe formulations. After a brief theoretical background, this review aims at discussing the potential of molecular simulations for the rational design of drug delivery systems.

Coarse-grained Monte Carlo simulations of nanogel-polyelectrolyte complexes: electrostatic effects

Coarse-grained Monte-Carlo simulations of nanogel-polyelectrolyte complexes have been carried out. The results presented here capture two phenomena reported in experiments with real complexes: (i) the reduction in size after absorbing just a few chains and (ii) the charge inversion detected through electrophoretic mobility data. Our simulations reveal that charge inversion occurs if the polyelectrolyte charge is large enough. In addition, the distribution of chains inside the nanogel strongly depends on whether charge inversion takes place. It should also be stressed that the chain topology has little influence on most of the properties studied here.

Ionic equilibria and swelling of soft permeable particles in electrolyte solutions

We discuss osmotic equilibria between soft permeable particles, of radius R and volume charge density ρ, and bulk electrolyte solutions of inverse Debye length κ. Existing models are based on a simplified assumption of weakly charged particles. Here we derive analytical approximations for the distribution of potentials, ions and pressure in a system, suitable even when ρ is quite large. Our theory is valid not only for "large" particles (κR≫ 1), where the central part is fully screened, but also for weakly screened "small" particles (κR≤ 1) with overlapping inner diffuse layers. Besides, we present novel coarse-grained simulations to validate the analysis and illustrate the variation of potential/ion profiles in response to changes in κR and ρ. Our simulations also allow us to argue that swelling of both "large" and "small" particles is uniform, although their inner non-uniform local pressure profiles are essentially and qualitatively different. These results are directly relevant for a variety of permeable charged objects, from polymer micro- and nanogels to more rigid porous colloids.

From Microscale to Macroscale: Nine Orders of Magnitude for a Comprehensive Modeling of Hydrogels for Controlled Drug Delivery

Because of their inherent biocompatibility and tailorable network design, hydrogels meet an increasing interest as biomaterials for the fabrication of controlled drug delivery devices. In this regard, mathematical modeling can highlight release mechanisms and governing phenomena, thus gaining a key role as complementary tool for experimental activity. Starting from the seminal contribution given by Flory-Rehner equation back in 1943 for the determination of matrix structural properties, over more than 70 years, hydrogel modeling has not only taken advantage of new theories and the increasing computational power, but also of the methods offered by computational chemistry, which provide details at the fundamental molecular level. Simulation techniques such as molecular dynamics act as a "computational microscope" and allow for obtaining a new and deeper understanding of the specific interactions between the solute and the polymer, opening new exciting possibilities for an in silico network design at the molecular scale. Moreover, system modeling constitutes an essential step within the "safety by design" paradigm that is becoming one of the new regulatory standard requirements also in the field-controlled release devices. This review aims at providing a summary of the most frequently used modeling approaches (molecular dynamics, coarse-grained models, Brownian dynamics, dissipative particle dynamics, Monte Carlo simulations, and mass conservation equations), which are here classified according to the characteristic length scale. The outcomes and the opportunities of each approach are compared and discussed with selected examples from literature.

Simulations of ionization equilibria in weak polyelectrolyte solutions and gels

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

Monte Carlo simulations of weak polyelectrolyte microgels: pH-dependence of conformation and ionization

In this study, we investigated the effect of pH on single weak acidic polyelectrolyte microgels under salt-free conditions with (i) varying microgel concentration, (ii) varying content of acidic groups and (iii) different crosslinking densities using Monte Carlo simulations under explicit consideration of the protonation/deprotonation reaction. We assessed both global properties, such as the degree of ionization, the degree of swelling and the counterion distribution, and local properties such as the radial network ionization profile and the ionization along the polymer chains as a function of pH. We found a pronounced suppression of the pH-dependent ionization of the microgels, as compared to the ideal titration behavior and a shift of the titration curve to a higher pH originating in the proximity of acidic groups in the microgel. In contrast to macroscopic gels, counterions can leave the microgel, resulting in an effective charge of the network, which hinders the ionization. A decreasing microgel concentration leads to an increased effective charge of the microgel and a more pronounced shift of the titration curve. The number of acidic groups showed only a weak effect on the ionization behavior of the microgels. For two different microgels with different crosslinking densities, similar scaling of the gel size was observed. A distinct transition from an uncharged and unswollen to a highly charged and expanded polymer network was observed for all investigated microgels. The degree of swelling mainly depends on the degree of ionization. An inhomogeneous distribution of the degree of ionization along the radial profile of the microgel was found.

Direct determination of forces between charged nanogels through coarse-grained simulations

In this work, electrostatic forces between charged nanogels are explored through coarse-grained simulations. These simulations allow us to explicitly consider the complex topology of these nanoparticles and provide reliable force values to examine highly charged nanogels of a few tens of nanometers. The results obtained here clearly reveal that the electrostatic interactions between these nanoparticles are not governed by the net charge of the nanogel, which includes not only the charge of the polymer network but also the charge of ions inside. Thus two theoretical procedures for predicting effective charges are also proposed and investigated. Both provide predictions of the same order and capture the behavior found for the effective charge obtained from simulations.

Computer Simulations of Static and Dynamical Properties of Weak Polyelectrolyte Nanogels in Salty Solutions

We investigate the chemical equilibria of weak polyelectrolyte nanogels with reaction ensemble Monte Carlo simulations. With this method, the chemical identity of the nanogel monomers can change between neutral or charged following the acid-base equilibrium reaction HA ⇌ A- + H⁺. We investigate the effect of changing the chemical equilibria by modifying the dissociation constant K a . These simulations allow for the extraction of static properties like swelling equilibria and the way in which charge-both monomer and ionic-is distributed inside the nanogel. Our findings reveal that, depending on the value of K a , added salt can either increase or decrease the gel size. Using the calculated mean-charge configurations of the nanogel from the reaction ensemble simulation as a quenched input to coupled lattice-Boltzmann molecular dynamics simulations, we investigate dynamical nanogel properties such as the electrophoretic mobility μ and the diffusion coefficient D.

Solvent Induced Inversion of Core-Shell Microgels

The morphology of core-shell microgels under different swelling conditions and as a function of the core-shell thickness ratio is systematically characterized by mesoscale hydrodynamic simulations. With increasing hydrophobic interaction of the shell polymers, we observe drastic morphological changes from a core-shell structure to an inverted microgel, where the core is turned to the outside, or a microgel with a patchy surface of core polymers directly exposed to the environment. We establish a phase diagram of the various morphologies. Moreover, we characterize the polymer and microgel conformations. For sufficiently thick shells, the changes of the shell size upon increasing hydrophobic interactions are well described by the Flory-Rehner theory. Additionally, this theory provides a critical line in the phase diagram separating core-shell structures from the distinct two other phases. The appearing new phases provide a novel route to nano- and microscale functionalized materials.

Polymer Conformations in Ionic Microgels in the Presence of Salt: Theoretical and Mesoscale Simulation Results

We investigate the conformational properties of polymers in ionic microgels in the presence of salt ions by molecular dynamics simulations and analytical theory. A microgel particle consists of coarse-grained linear polymers, which are tetra-functionally crosslinked. Counterions and salt ions are taken into account explicitly, and charge-charge interactions are described by the Coulomb potential. By varying the charge interaction strength and salt concentration, we characterize the swelling of the polyelectrolytes and the charge distribution. In particular, we determine the amount of trapped mobile charges inside the microgel and the Debye screening length. Moreover, we analyze the polymer extension theoretically in terms of the tension blob model taking into account counterions and salt ions implicitly by the Debye–Hückel model. Our studies reveal a strong dependence of the amount of ions absorbed in the interior of the microgel on the electrostatic interaction strength, which is related to the degree of the gel swelling. This implies a dependence of the inverse Debye screening length κ on the ion concentration; we find a power-law increase of κ with the Coulomb interaction strength with the exponent 3/5 for a salt-free microgel and an exponent 1/2 for moderate salt concentrations. Additionally, the radial dependence of polymer conformations and ion distributions is addressed.

Defined pH-sensitive nanogels as gene delivery platform for siRNA mediated in vitro gene silencing

An advanced cationic carrier system which combines high transfection efficiency with low cytotoxicity and a control over the release of the encapsulated genetic material by the reduction of the multivalent architecture upon pH triggered degradation was developed.

Competition between excluded-volume and electrostatic interactions for nanogel swelling: effects of the counterion valence and nanogel charge

The equilibrium distribution of monovalent and trivalent ions within a thermo-responsive charged nanogel is investigated using Monte Carlo simulations and Ornstein–Zernike equations.

Thermoresponsive microgels at the air-water interface: the impact of the swelling state on interfacial conformation

Poly(N-vinylcaprolactam) (PVCL) is a new temperature-responsive type of polymer microgel with improved biocompatibility as compared to more commonly used poly(N-isopropylacrylamide) (PNIPAM). Both polymers swell at low temperatures and collapse at high ones, showing a volume phase transition temperature (VPTT) around the physiological temperature. Exploring the interfacial characteristics of thermoresponsive microgels is important due to their potential application in emulsion based systems with tailored stabilities and controlled degradation profiles. In this work, we study the properties of charged PVCL particles at the air-water interface by a combination of adsorption, dilatational rheology and Langmuir monolayers. Although PVCL particles adsorb spontaneously at the air-water interface in both, swollen and collapsed conformations, the interfacial properties show significant differences depending on the swelling state. In particular, the total amount of adsorbed microgels and the rigidity of the monolayer increase as the temperature increases above the VPTT, which is connected to the more compact morphology of the microgels in this regime. Dilatational rheology data show the formation of a very loose adsorbed layer with low cohesivity. In addition, collapsed microgels yield a continuous increase of the surface pressure, whereas swollen microgels show a phase transition at intermediate compressions caused by the deformation of the loose external polymer shell of the particles. We also provide a qualitative interpretation for the surface pressure behavior in terms of microgel-microgel effective pair potentials, and correlate our experimental findings to recent rescaling models that take into account the importance of the internal polymer degrees of freedom in the rearrangement of the conformation of the microgel particles at the interface.

Universal conformational properties of polymers in ionic nanogels

Polyelectrolyte gels are known to undergo significant conformational changes in response to external stimuli such as pH, temperature, or the dielectric constant. Specifically, an increase of the degree of ionization associated with an increasing number of counterions leads to swelling of the network. For a macroscopically large gel, which is electrostatically neutral in its interior, swelling is no longer governed by electrostatic interactions, but rather by the osmotic pressure of counterions. However, this electrostatic neutrality is typically violated for nanogels, because counterions are free to leave a gel particle. Although nanogel-swelling exhibits similar features as swelling of micro- and macrogels, another mechanism has to be relevant. Here, we use molecular dynamics simulations and scaling theory to unravel the structural properties of nanogels upon changing the electrostatic interactions. We demonstrate that the swelling of nanogels is governed by screened electrostatic interactions without a relevant contribution by the counterion osmotic pressure.

Swelling of ionic microgel particles in the presence of excluded-volume interactions: a density functional approach

In this work a new density functional theory framework is developed to predict the salt-concentration dependent swelling state of charged microgels and the local concentration of monovalent ions inside and outside the microgel.