A statistical theory of cosolvent-induced coil-globule transitions in dilute polymer solution

Cononsolvency of thermoresponsive polymers: where we are now and where we are going

Cononsolvency is an intriguing phenomenon where a polymer collapses in a mixture of good solvents. This cosolvent-induced modulation of the polymer solubility has been observed in solutions of several polymers and biomacromolecules, and finds application in areas such as hydrogel actuators, drug delivery, compound detection and catalysis. In the past decade, there has been a renewed interest in understanding the molecular mechanisms which drive cononsolvency with a predominant emphasis on its connection to the preferential adsorption of the cosolvent. Significant efforts have also been made to understand cononsolvency in complex systems such as micelles, block copolymers and thin films. In this review, we will discuss some of the recent developments from the experimental, simulation and theoretical fronts, and provide an outlook on the problems and challenges which are yet to be addressed.

An interplay of excluded-volume and polymer-(co)solvent attractive interactions regulates polymer collapse in mixed solvents

Cosolvent effects on the coil-globule transitions in aqueous polymer solutions are not well understood, especially in the case of amphiphilic cosolvents that preferentially adsorb on the polymer and lead to both polymer swelling and collapse. Although a predominant focus in the literature has been placed on the role of polymer-cosolvent attractive interactions, our recent work has shown that excluded-volume interactions (repulsive interactions) can drive both preferential adsorption of the cosolvent and polymer collapse via a surfactant-like mechanism. Here, we further study the role of polymer-(co)solvent attractive interactions in two kinds of polymer solutions, namely, good solvent (water)-good cosolvent (alcohol) (GSGC) and poor solvent-good cosolvent (PSGC) solutions, both of which exhibit preferential adsorption of the cosolvent and a non-monotonic change in the polymer radius of gyration with the addition of the cosolvent. Interestingly, at low concentrations, the polymer-(co)solvent energetic interactions oppose polymer collapse in the GSGC solutions and contrarily support polymer collapse in the PSGC solutions, indicating the importance of the underlying polymer chemistry. Even though the alcohol molecules are preferentially adsorbed on the polymer, the trends of the energetic interactions at low cosolvent concentrations are dominated by the polymer-water energetic interactions in both the cases. Therefore, polymer-(co)solvent energetic interactions can either reinforce or compensate the surfactant-like mechanism, and it is this interplay that drives coil-to-globule transitions in polymer solutions. These results have implications for rationalizing the cononsolvency transitions in real systems such as polyacrylamides in aqueous alcohol solutions where the understanding of microscopic driving forces is still debatable.

A cosolvent surfactant mechanism affects polymer collapse in miscible good solvents

The coil-globule transition of aqueous polymers is of profound significance in understanding the structure and function of responsive soft matter. In particular, the remarkable effect of amphiphilic cosolvents (e.g., alcohols) that leads to both swelling and collapse of stimuli-responsive polymers has been hotly debated in the literature, often with contradictory mechanisms proposed. Using molecular dynamics simulations, we herein demonstrate that alcohols reduce the free energy cost of creating a repulsive polymer-solvent interface via a surfactant-like mechanism which surprisingly drives polymer collapse at low alcohol concentrations. This hitherto neglected role of interfacial solvation thermodynamics is common to all coil-globule transitions, and rationalizes the experimentally observed effects of higher alcohols and polymer molecular weight on the coil-to-globule transition of thermoresponsive polymers. Polymer-(co)solvent attractive interactions reinforce or compensate this mechanism and it is this interplay which drives polymer swelling or collapse.

A Poromechanical Model for Sorption Hysteresis in Nanoporous Polymers

Sorption hysteresis in nanoporous polymer is an intriguing phenomenon that involves coupling between sorption and deformation. Based on the mechanism revealed at the microscopic level by use of molecular simulation, a poromechanical model is developed capturing all relevant physics and yielding a quantitative description. In this model, the coupling between sorption and deformation is described by a poromechanics framework. More in detail, an upscaling process from the molecular mechanism is implemented to model the hysteresis through the state change of each element upon deformation. We provide two solutions of the model: a numerical one based on the finite element method and an analytical one based on uniform strain assumption. The results from both solutions agree well with the molecular simulation and experimental results, therefore capturing and describing adequately sorption hysteresis. The developed model illustrates that water forms different structural distributions upon adsorption and desorption. A parametric study shows that sorption hysteresis is influenced by material properties. We find that a softer material with stronger adsorbent-adsorbate interaction tends to exhibit more profound sorption hysteresis. The developed model, which relies on the concepts of sorption-deformation coupling and multiscale modeling from atomistic simulations to domain dependent theory, paves the way for a new direction of modeling sorption hysteresis.

Many-chain effects on the co-nonsolvency of polymer brushes in a good solvent mixture

Polymer brushes normally swell in a good solvent and collapse in a poor solvent. An abnormal response of polymer brushes, so-called co-nonsolvency, is the phenomenon where the brush counter-intuitively collapses in a good solvent mixture. In this work, we employed molecular dynamics simulations to investigate the structural properties of the grafted polymers in the occurrence of co-nonsolvency. Brushes with various grafting densities were considered to study the effect of topologically excluded volumes on the co-nonsolvency. We found that the brush height follows a novel scaling behavior of the grafting density h ∼ σg0.71 in the co-nonsolvent mixture. Using the scaling exponent and Alexander-de Gennes theory, an analytic function that predicts the monomer density was obtained. The many-chain effects in the co-nonsolvent lead to the formation of both intermolecular and intramolecular bridging structures. Increasing the grafting density entails lower looping events occuring because of the intermolcular bridging, causing diverse structural properties. We report how the average thickness, the polymer orientation, and the looping probability vary as the grafting density increases. Based on these observations, we constructed a phase diagram of the polymer brush system using the average thickness and orientation as order parameters. Our simulations and analytical results reveal the nature of co-nonsolvency in polymer brushes in an explicit way and will help to provide practical guidelines for applications such as drug delivery and sensor devices.

Cross-linker mediated compaction and local morphologies in a model chromosome

Chromatin and associated proteins constitute the highly folded structure of chromosomes. We consider a self-avoiding polymer model of the chromatin, segments of which may get cross-linked via protein binders that repel each other. The binders cluster together via the polymer mediated attraction, in turn, folding the polymer. Using molecular dynamics simulations, and a mean field description, we explicitly demonstrate the continuous nature of the folding transition, characterized by unimodal distributions of the polymer size across the transition. At the transition point the chromatin size and cross-linker clusters display large fluctuations, and a maximum in their negative cross-correlation, apart from a critical slowing down. Along the transition, we distinguish the local chain morphologies in terms of topological loops, inter-loop gaps, and zippering. The topologies are dominated by simply connected loops at the criticality, and by zippering in the folded phase.

Tuning the collapse transition of weakly charged polymers by ion-specific screening and adsorption

The experimentally observed swelling and collapse response of weakly charged polymers to the addition of specific salts displays quite convoluted behavior that is not easy to categorize. Here we use a minimalistic implicit-solvent/explicit-salt simulation model with a focus on ion-specific interactions between ions and a single weakly charged polyelectrolyte to qualitatively explain the observed effects. In particular, we demonstrate ion-specific screening and bridging effects cause collapse at low salt concentrations whereas the same strong ion-specific direct interactions drive re-entrant swelling at high concentrations. Consistently with experiments, a distinct salt concentration at which the salting-out power of anions inverts from the reverse to direct Hofmeister series is observed. At this so called isospheric point, the ion-specific effects vanish. Furthermore, with additional simplifying assumptions, an ion-specific mean-field model is developed for the collapse transition which quantitatively agrees with the simulations. Our work demonstrates the sensitivity of the structural behavior of charged polymers to the addition of specific salt beyond simple screening and shall be useful for further guidance of experiments.

Cosolvent Effects on Polymer Hydration Drive Hydrophobic Collapse

Water-mediated hydrophobic interactions play an important role in self-assembly processes, aqueous polymer solubility, and protein folding, to name a few. Cosolvents affect these interactions; however, the implications for hydrophobic polymer collapse and protein folding equilibria are not well-understood. This study examines cosolvent effects on the hydrophobic collapse equilibrium of a generic 32-mer hydrophobic polymer in urea, trimethylamine- N-oxide (TMAO), and acetone aqueous solutions using molecular dynamics simulations. Our results unveil a remarkable cosolvent-concentration-dependent behavior. Urea, TMAO, and acetone all shift the equilibrium toward collapsed structures below 2 M cosolvent concentration and, in turn, to unfolded structures at higher cosolvent concentrations, irrespective of the differences in cosolvent chemistry and the nature of cosolvent-water interactions. We find that weakly attractive polymer-water van der Waals interactions oppose polymer collapse in pure water, corroborating related observations reviewed by Ben-Amotz ( Annu. Rev. Phys. Chem. 2016, 67, 617-638). The cosolvents studied in the present work adsorb at the polymer/water interface and expel water molecules into the bulk, thereby effectively removing the dehydration energy penalty that opposes polymer collapse in pure water. At low cosolvent concentrations, this leads to cosolvent-induced stabilization of collapsed polymer structures. Only at sufficiently high cosolvent concentrations, polymer-cosolvent interactions favor polymer unfolding.

Statistical description of co-nonsolvency suppression at high pressures

We present an application of Flory-type theory of a flexible polymer chain dissolved in a binary mixture of solvents to theoretical description of co-nonsolvency. We show that our theoretical predictions are in good quantitative agreement with the recently published MD simulation results for the conformational behavior of a Lennard-Jones flexible chain in a binary mixture of the Lennard-Jones fluids. We show that our theory is able to describe co-nonsolvency suppression through pressure enhancement to extremely high values recently discovered in experiments and reproduced by full atomistic MD simulations. By analysing the co-solvent concentration in the internal polymer volume at different pressure values, we speculate that this phenomenon is caused by the suppression of the co-solvent preferential solvation of the polymer backbone at the rather high pressure imposed. We show that when the co-solvent-induced coil-globule transition takes place, the entropy and enthalpy contributions to the solvation free energy abruptly decrease, while the solvation free energy remains continuous.

Statistical theory of polarizable target compound impregnation into a polymer coil under the influence of an electric field

The paper presents a theoretical approach for describing the influence of an electric field on the conformation of an electrically neutral dielectric polymer chain dissolved in a dielectric solvent with an admixture of a target compound. Each monomer and each molecule of the target compound carries positive excess polarizability and the solvent is described as a continuous dielectric medium. The model is based on the Flory-type mean-field theory. We demonstrate non-monotonic dependences of the expansion factor and the concentration of the target compound on the strength of the electric field and molecular polarizability. Namely, the target compound concentration in the internal polymer volume as a function of electric field strength has pronounced maxima if the molecules are polarizable. In addition, the expansion factor of the non-polarizable polymer chain can be controlled by the electric field. The dependences of the expansion factor and target compound concentration on the monomer polarizability exhibit minima and intersection points. The intersection points correspond to the equality of dielectric permittivities in the bulk solution and in the internal polymer volume.

Polymer chain collapse induced by many-body dipole correlations

We present a simple analytical theory of a flexible polymer chain dissolved in a good solvent, carrying permanent freely oriented dipoles on the monomers. We take into account the dipole correlations within the random phase approximation (RPA), as well as a dielectric heterogeneity in the internal polymer volume relative to the bulk solution. We demonstrate that the dipole correlations of monomers can be taken into account as pairwise ones only when the polymer chain is in a coil conformation. In this case the dipole correlations manifest themselves through the Keesom interactions of the permanent dipoles. On the other hand, the dielectric heterogeneity effect (dielectric mismatch effect) leads to the effective interaction between the monomers of the polymeric coil. Both of these effects can be taken into account by renormalizing the second virial coefficient of the monomer-monomer volume interactions. We establish that in the case when the solvent dielectric permittivity exceeds the dielectric permittivity of the polymeric material, the dielectric mismatch effect competes with the dipole attractive interactions, leading to polymer coil expansion. In the opposite case, both the dielectric mismatch effect and the dipole attractive interaction lead to the polymer coil collapse. We analyse the coil-globule transition caused by the dipole correlations of monomers within the many-body theory. We demonstrate that accounting for the dipole correlations higher than the pairwise ones smooths this pure electrostatics driven coil-globule transition of the polymer chain.

Polarizable polymer chain under external electric field: Effects of many-body electrostatic dipole correlations

We present a new simple self-consistent field theory of a polarizable flexible polymer chain under an external constant electric field with account for the many-body electrostatic dipole correlations. We show the effects of electrostatic dipole correlations on the electric-field-induced globule-coil transition. We demonstrate that only when the polymer chain is in the coil conformation, the electrostatic dipole correlations of monomers can be considered as pairwise. However, when the polymer chain is in a collapsed state, the dipole correlations have to be considered at the many-body level.

Mechanism of Polymer Collapse in Miscible Good Solvents

We propose a physical mechanism for co-nonsolvency of a stimulus-responsive polymer in water/methanol mixed solution based on results obtained with molecular simulations. Even though the phenomenon is well known, the mechanism behind co-nonsolvency is still under debate. Herein, we study co-nonsolvency of poly(N-isopropylacrylamide) (PNiPAM) in methanol aqueous solutions, the most widely studied and experimentally well-characterized system. Our results show that at low alcohol content of the solution methanol preferentially binds to the PNiPAM globule and drives polymer collapse. The energetics of electrostatic, hydrogen bonding, or bridging-type interactions with the globule is found to play no role. Instead, preferential methanol binding results in a significant increase in the globule's configurational entropy, stabilizing methanol-enriched globular structures over wet globular structures in neat water. This mechanism drives the reduction of the lower critical solution temperature with increasing methanol content in the co-nonsolvency regime and eventually leads to polymer collapse. The globule-to-coil re-entrance at high methanol concentrations is instead driven by changes in solvent-excluded volume of the coil and globular states imparted by a decrease in solvent density with increasing methanol content of the solution: with increasing proportion of larger solvent particles (methanol), the entropic (cavity formation) cost of redistributing solvent molecules upon polymer re-entrance becomes smaller. This effect provides a natural explanation for the experimentally observed dependence of the re-entrance transition on chain molecular weight.