Effect of the Counterion Valence on the Behavior of Thermo-Sensitive Gels and Microgels: A Monte Carlo Simulation Study

Triggering doxorubicin release from responsive hydrogel films by polyamine uptake

Polyamines such as putrescine, spermidine and spermine are required in many inter- and intra-cellular processes. There is, however, evidence of anomalously high concentrations of these polyamines around cancer cells. Furthermore, high polyamine concentrations play a key role in accelerating the speed of cancer proliferation. Some current therapies target the reduction of the polyamine concentration to delay the cancer advance. In this study, we use a molecular theory to prove the concept that poly(methacrylic acid) (PMAA) hydrogels can play the dual role of incorporating and retaining polyamines as well as releasing preloaded drugs in response. Towards such a goal, we have developed a molecular model for each of the chemical species, which includes the shape, size, charge, protonation state, and configuration. Our results indicate that PMAA hydrogel films can incorporate significant amounts of polyamines; this absorption increases with the solution concentration of the polyamines. Doxorubicin was chosen as a model drug for this study, which can be successfully incorporated within the film; the optimal encapsulation conditions occur at low salt concentrations and pH values near neutral. Polyamine absorption within the film results in the desorption of the drug from the hydrogel. An increase in the concentration of the polyamines enhances the drug release. To validate our theoretical findings, poly(methacrylic acid) hydrogel thin films were synthesized by atom transfer radical polymerization. Absorption/desorption experiments followed by UV-Vis spectroscopy demonstrate doxorubicin encapsulation within these films and polyamine-dependent drug release.

Self-assembly of polyelectrolyte diblock copolymers within mixtures of monovalent and multivalent counterions

In this study, the self-assembly behavior of polyelectrolyte (PE) diblock copolymers in solutions containing mixtures of monovalent and multivalent counterions was investigated using molecular dynamics simulation. The properties of the assembled micelles and counterion condensations at different charge fractions of multivalent ions have been discussed. The bridging effect of multivalent ions induces the electrostatic correlations of the PE chains, leading to the fusion of large micelles and the formation of bulky aggregates. Notably, lamellar and well-organized face-centered cubic (FCC) arrangements of the assembled micelles were observed in the mixture of monovalent and trivalent ions. At large fractions of multivalent ions, cylindrical and lamellar precipitates composed of the assembled micelles were formed owing to the inter-connecting coronas. The mixtures of monovalent and multivalent counterions allow the regulation of the electrostatic interactions and tuning of the properties in assembled micelles.

Interactions of star-like polyelectrolyte micelles with hydrophobic counterions

Hydrophobicity of a counterion has a profound effect on the interaction with polyelectrolytes similar to that of multivalency. Specifically, understanding this interaction in weak polyelectrolyte micelles might assist in developing nanocarriers for pH-controlled encapsulation and release. We used star-like weak polyelectrolyte micelles of polystyrene-block-poly(2-vinyl pyridine) (PS-P2VP) with fixed aggregation number as a model polyelectrolyte, and cobalt bis(1,2-dicarbollide) (COSAN) as a model hydrophobic anion. We used NMR to assess the mobility of the polymer segments in the presence of varying amounts of COSAN, and at varying protonation degrees of the polyelectrolyte. Same experiments with indifferent electrolyte (NaCl) were used as a control. Furthermore, we used coarse-grained simulations to obtain a detailed picture of the effect of hydrophobic counterions on the conformation of the micelles. A small amount of hydrophobic counterions causes morphological changes within the micelles, whereas a bigger amount causes precipitation. This was confirmed both in simulations and in experiments. Furthermore, adsorption of the counterions induces ionization of the collapsed segments of the polyelectrolyte. Although the COSAN/P2VP system is rather specific, the generic model used in the coarse-grained simulations shows that the observed behavior is a consequence of synergy of hydrophobic and electrostatic attraction between polyelectrolytes and hydrophobic counterions. Our study provides general insights into the molecular mechanisms of these interactions.

Self-assembly of polyelectrolyte diblock copolymers at monovalent and multivalent counterions

In this work, the self-assembly behaviors of diblock copolymers consisting of one hydrophobic block and one ionizable polyelectrolyte (PE) block in the presence of monovalent and multivalent counterions are systematically discussed through molecular dynamics simulation. Copolymers are molded as bead-spring chains and the ions are explicitly considered. First, the self-assembled structures of symmetrical block copolymers at different charge fractions are analyzed in detail. Spherical hydrophobic cores are favored by all of the micelles. The effect of counterion valence is much more noticeable at high values of charge fraction. When the PE blocks are fully charged, the presence of multivalent counterions preferably provokes the formation of macroscopic structures. A precipitant spherical micelle is generated in the presence of divalent counterions. Special shapes of coronas are created in the presence of trivalent ions, and a remarkable one dimensional macroscopic cylindrical aggregation of micelles forms; the whole assembly is not typical core-shell micelles, but rather a cylinder with alternating spherical micelles arranged perpendicular to the cylinder axis. The self-assemblies with different lengths of fully charged PE blocks are also discussed. Surprisingly, in the presence of divalent counterions, two dimensional in-plane macroscopic aggregation of micelles is realized when the proportion of PE blocks is larger than 1/2; the self-assembled spherical micelles locate approximately in the same plane to form an inter-linked network. One dimensional aggregation of micelles in the presence of trivalent counterions is maintained with an increased proportion of the PE block. Owing to the dominant intra- and inter-condensation of divalent and trivalent counterions, respectively, two and one dimensional macroscopic aggregation of the micelles is achieved. Our findings indicate that varying the counterion valence is a powerful mechanism to tune the properties of self-assemblies, and the bridging effect introduced by multivalent counterions is the key parameter for the aggregation of the micelles.

Using Polymer Hydrogels for Glyphosate Sequestration from Aqueous Solutions: Molecular Theory Study of Adsorption to Polyallylamine Films

A molecular theory has been applied to study the equilibrium conditions of glyphosate and aminomethylphosphonic acid (AMPA) adsorption from aqueous solutions to hydrogel films of cross-linked polyallylamine (PAH). This theoretical framework allows for describing the size, shape, state of charge/protonation, and configurational freedom of all chemical species in the system. Adsorption of glyphosate is a nonmonotonic function of the solution pH, which results from the protonation behavior of both the adsorbate and adsorbent material. Glyphosate and chloride ions compete for adsorption to neutralize the polymer charge; lowering the solution salt concentration enhances the partition of glyphosate inside the hydrogel film. AMPA adsorption is qualitatively similar to that of glyphosate but orders of magnitude smaller under the same conditions. AMPA is less charged than glyphosate, which unbalances the competition for adsorption with salt counter ions. In mixed solutions, glyphosate presence can significantly hinder AMPA adsorption. A higher pH establishes inside the film than in the bulk solution, which has important implications for the herbicide biodegradation because microbial activity is pH-dependent. Thus, PAH hydrogel films can be considered as functional materials that combine glyphosate sequestration and in situ degradation. In devising these materials, the polymer density is an important variable of design; polymer networks with high density of titratable units can enhance adsorption; this density can also be used to modify the pH inside the material.

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.

Gels with sense: supramolecular materials that respond to heat, light and sound

Advances in the field of supramolecular chemistry have made it possible, in many situations, to reliably engineer soft materials to address a specific technological problem. Particularly exciting are "smart" gels that undergo reversible physical changes on exposure to remote, non-invasive environmental stimuli. This review explores the development of gels which are transformed by heat, light and ultrasound, as well as other mechanical inputs, applied voltages and magnetic fields. Focusing on small-molecule gelators, but with reference to organic polymers and metal-organic systems, we examine how the structures of gelator assemblies influence the physical and chemical mechanisms leading to thermo-, photo- and mechano-switchable behaviour. In addition, we evaluate how the unique and versatile properties of smart materials may be exploited in a wide range of applications, including catalysis, crystal growth, ion sensing, drug delivery, data storage and biomaterial replacement.

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.

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.

Self-organization of hydrophobic-capped triblock copolymers with a polyelectrolyte midblock: a coarse-grained molecular dynamics simulation study

We present the results of a Langevin dynamics simulation study of micellar organization and hydrogel formation in the solutions of coarse-grained ABA copolymer chains. Polymer chains are modeled as bead-spring chains of Lennard-Jones particles by explicit treatment of ionic species in implicit solvent. The studied copolymer is composed of a polyelectrolyte midblock flanked by two hydrophobic endblocks. We explore the self-assembly of copolymer solutions at a fixed polymer concentration and temperature upon systematic variation of the midblock charge fraction, valency of neutralizing counterions, and the stiffness and length of hydrophobic endblocks. Minimization of the surface energy, conformational entropy of the midblock chains, electrostatic repulsion of midblock charges, and the translational entropy of counterions are found to play central roles in controlling the self-organization features of copolymer solutions. Flower-like micelles with A-blocks forming the core of spherical aggregates and B-blocks constituting the micelle corona are established for the neutral midblocks. Increasing the charge content of B chains lowers the fraction of loop conformations and yields a spanning hydrogel network with midblocks bridging the hydrophobic clusters. Counterion valence is shown to exert a strong effect on the micelle size and network structure. The increase in the rigidity of terminal A-blocks increases the fraction of bridging chains and results in the formation of a hydrogel network with bundle-like hydrophobic domains. Longer endblocks are shown to increase the hydrophobic cluster size and enhance the bridged midblock fraction. The qualitative agreement between the experimental and theoretical studies is also discussed. The comprehensive molecular picture provides a framework for the future studies of stimuli-responsive copolymer systems.

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.

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

In this work, coarse-grained simulations of two charged thermo-shrinking nanogels (with degrees of ionization of 0.125 and 0.250) in the presence of 1:1 and 3:1 electrolytes have been explicitly performed through the bead-spring model of polyelectrolyte. In a first set of simulations, salt concentrations for 1:1 and 3:1 electrolytes ranged from 1 to 100 mM and from 0.167 to 16.7 mM, respectively, whereas temperature remained fixed at a value for which hydrophobic forces were negligible in our case (288 K). The sizes of swollen nanogels are smaller when trivalent cations are present, but they do not change significantly in the range of concentrations of 3:1 electrolyte studied here. It should be also stressed that trivalent cations neutralize the nanogel charge more efficiently. According to these results the electrostatic repulsion plays an important role. In a second set of simulations, the temperature varied from 288 to 333 K to study the effect of salt on the thermal response when hydrophobic forces are not negligible. For the nanogels with the lowest degree of ionization, the behavior of the radius with increasing the temperature can be described by a sigmoid function, which shifts towards lower temperatures in the presence of salt. This shift is more clearly observed for trivalent cations, even at low concentrations. For the nanogels with the highest degree of ionization, the effect of additional electrolyte is also noticeable. In this case, hydrophobic forces are not the only responsible for their shrinkage in the presence of trivalent cations. The surface electrostatic potential and the concentration of salt cations inside the nanogel have been computed from simulations and a modified Poisson-Boltzmann (PB) cell model. The thermosensitivity in size have certain influence on the sensitivity of these properties to temperature changes. The rich behavior of the surface electrostatic potential and the uptake of salt cations are successfully predicted by the modified PB cell model proposed (at least qualitatively). Particularly, the model is able to predict how the retention of salt cations depends on their charge and the ionic valence when nanogels shrink.

A cosolvency effect on tunable thermosensitive core-shell nanoparticle gels

The influence of co-solvents on the swelling behavior of tunable thermosensitive core-shell nanoparticle gels was investigated. The poly(methyl methacrylate) (PMMA) core and poly(2-hydroxyethyl methacrylate) (PHEMA) shell network in 1-propanol reacted differently upon the addition of three co-solvents (cyclohexane (CHX), 1,3-propanediol (PDO), and water), resulting in highly controllable swelling properties of the core-shell gels. In particular, a strongly enhanced solvation effect, called the cosolvency phenomenon, occurred even with a very small amount of water (1-3 wt%). To examine the tunability, thermo-optical analysis (TOA) and photon correlation spectroscopy (PCS) were employed. The results show that a small addition of CHX, PDO, or water induced the "lower/upper," "even/upper," and "lower/lower" volume transition temperatures (VTTs) of the core-shell networks, respectively. For theoretical treatment, a multi-component lattice theory of mixing was combined with the Flory-Rehner (F-R) chain model to calculate the net free energy of mixing. The required interaction parameters were obtained from the binary and ternary phase diagrams of the linear polymer solutions and were applied directly to the swelling calculation of the cross-linked core-shell network solutions. The calculated results corresponded well with the experimental swelling data without further adjustment.

Ion permeation inside microgel particles induced by specific interactions: from charge inversion to overcharging

In this work we have performed a theoretical study of a system formed by ionic microgels in the presence of monovalent salt with the help of Ornstein-Zernike integral equations within the hypernetted-chain (HNC) approximation. We focus in particular on analysing the role that the short-range specific interactions between the polymer fibres of the microgel and the incoming ions have on the equilibrium ion distribution inside and outside the microgel. For this purpose, a theoretical model based on the equilibrium partitioning effect is developed to determine the interaction between the microgel particle and a single ion. The results indicate that when counterions are specifically attracted to the polymer fibres of the microgel, an enhanced counterion accumulation occurs that induces the charge inversion of the microgel and a strong increase of the microgel net charge (or overcharging). In the case of coions, the specific attraction is also able to provoke the coion adsorption even though they are electrostatically repelled, and so increasing the microgel charge (true overcharging). Moreover, we show that ion adsorption onto the microgel particle is very different in swollen and shrunken states due to the competition between specific attraction and steric repulsion. In particular, ion adsorption occurs preferentially in the internal core of the particle for swollen states, whereas it is mainly concentrated in the external shell for de-swollen configurations. Finally, we observe the existence of a critical salt concentration, where the net charge of the microgels vanishes; above this inversion point the net charge of the microgels increases again, thus leading to reentrant stability of microgel suspensions.