Self-Assembly of Symmetric Copolymers in Slits with Inert and Attractive Walls.

Although the behavior of the confined semi-dilute solutions of self-assembling copolymers represents an important topic of basic and applied research, it has eluded the interest of scientists. Extensive series of dissipative particle dynamics simulations have been performed on semi-dilute solutions of A5B5 chains in a selective solvent for A in slits using a DL-MESO simulation package. Simulations of corresponding bulk systems were performed for comparison. This study shows that the associates in the semi-dilute bulk solutions are partly structurally organized. Mild steric constraints in slits with non-attractive walls hardly affect the size of the associates, but they promote their structural arrangement in layers parallel to the slit walls. Attractive walls noticeably affect the association process. In slits with mildly attractive walls, the adsorption competes with the association process. At elevated concentrations, the associates start to form in wide slits when the walls are sparsely covered by separated associates, and the association process prevents the full coverage of the surface. In slits with strongly attractive walls, adsorption is the dominant behavior. The associates form in wide slits at elevated concentrations only after the walls are completely and continuously covered by the adsorbed chains.

Changes in Ion Concentrations upon the Binding of Short Polyelectrolytes on Phospholipid Bilayers: Computer Study Addressing Interesting Physiological Consequences.

This computer study was inspired by the experimental observation of Y. Qian et al. published in ACS Applied Materials and Interfaces, 2018 that the short positively charged ß-peptide chains and their oligomeric analogues efficiently suppress severe medical problems caused by antimicrobial drug-resistant bacteria despite them not penetrating the bacterial membrane. Our coarse-grained molecular dynamics (dissipative particle dynamics) simulations confirm the tentative explanation of the authors of the experimental study that the potent antimicrobial activity is a result of the entropically driven release of divalent ions (mainly magnesium ions essential for the proper biological function of bacteria) into bulk solution upon the electrostatic binding of ß-peptides to the bacterial membrane. The study shows that in solutions containing cations Na+, Ca2+ and Mg2+, and anions Cl-, the divalent cations preferentially concentrate close to the membrane and neutralize the negative charge. Upon the addition of positively charged oligomer chains (models of ß-peptides and their analogues), the oligomers electrostatically bind to the membrane replacing divalent ions, which are released into bulk solvent. Our simulations indicate that the entropy of small ions (which controls the behavior of synthetic polyelectrolyte solutions) plays an important role in this and also in other similar biologically important systems.

Modeling the Phase Equilibria of Associating Polymers in Porous Media with Respect to Chromatographic Applications.

Associating copolymers self-assemble during their passage through a liquid chromatography (LC) column, and the elution differs from that of common non-associating polymers. This computational study aims at elucidating the mechanism of their unique and intricate chromatographic behavior. We focused on amphiphilic diblock copolymers in selective solvents, performed the Monte Carlo (MC) simulations of their partitioning between a bulk solvent (mobile phase) and a cylindrical pore (stationary phase), and investigated the concentration dependences of the partition coefficient and of other functions describing the phase behavior. The observed abruptly changing concentration dependences of the effective partition coefficient demonstrate the significant impact of the association of copolymers with their partitioning between the two phases. The performed simulations reveal the intricate interplay of the entropy-driven and the enthalpy-driven processes, elucidate at the molecular level how the self-assembly affects the chromatographic behavior, and provide useful hints for the analysis of experimental elution curves of associating polymers.

DPD Modelling of the Self- and Co-Assembly of Polymers and Polyelectrolytes in Aqueous Media: Impact on Polymer Science.

This review article is addressed to a broad community of polymer scientists. We outline and analyse the fundamentals of the dissipative particle dynamics (DPD) simulation method from the point of view of polymer physics and review the articles on polymer systems published in approximately the last two decades, focusing on their impact on macromolecular science. Special attention is devoted to polymer and polyelectrolyte self- and co-assembly and self-organisation and to the problems connected with the implementation of explicit electrostatics in DPD numerical machinery. Critical analysis of the results of a number of successful DPD studies of complex polymer systems published recently documents the importance and suitability of this coarse-grained method for studying polymer systems.

Phase equilibria and conformational behavior of dendrimers in porous media: Towards chromatographic analysis of dendrimers.

HYPOTHESIS: The intricate entropy-enthalpy interplay of dendrimers confined in pores affects their conformation and retention in the porous stationary phase. This work aims at providing important insights into its impacts on partitioning and chromatographic separation in both size-exclusion chromatography (SEC) and interaction chromatography (IC) regimes. SIMULATIONS: Using Monte Carlo (MC) simulations, we investigated the bulk-pore phase equilibria and the conformational behavior of flexible dendrimers differing in generation, in spacer length and in fraction of modified terminal groups interacting differently with pore walls than the majority building units. FINDINGS: With increasing interaction strength, a distinct transition from a roughly spherical shape caused by simultaneous interactions with two walls to an ellipsoidal (or even disklike) conformation tenaciously adhering to only one wall was observed for moderately confined dendrimers. The strongly deformed dendrimers subjected to severe confinement gain high energy and the samples differing in the degree of modification become chromatographically discernable thanks to large energy differences. Consequently, our results suggest that the column fillings with fairly narrow pores which are ineffective in SEC, are highly efficient separation media for dendrimer studies by IC above the critical adsorption point (CAP). Overall, our simulations reveal useful information for advancing and optimizing experimental liquid chromatography studies of dendrimers.

Solubilization of Charged Porphyrins in Interpolyelectrolyte Complexes: A Computer Study.

Using coarse-grained dissipative particle dynamics (DPD) with explicit electrostatics, we performed (i) an extensive series of simulations of the electrostatic co-assembly of asymmetric oppositely charged copolymers composed of one (either positively or negatively charged) polyelectrolyte (PE) block A and one water-soluble block B and (ii) studied the solubilization of positively charged porphyrin derivatives (P+) in the interpolyelectrolyte complex (IPEC) cores of co-assembled nanoparticles. We studied the stoichiometric mixtures of 137 A10+B25 and 137 A10-B25 chains with moderately hydrophobic A blocks (DPD interaction parameter aAS=35) and hydrophilic B blocks (aBS=25) with 10 to 120 P+ added (aPS=39). The P+ interactions with other components were set to match literature information on their limited solubility and aggregation behavior. The study shows that the moderately soluble P+ molecules easily solubilize in IPEC cores, where they partly replace PE+ and electrostatically crosslink PE- blocks. As the large P+ rings are apt to aggregate, P+ molecules aggregate in IPEC cores. The aggregation, which starts at very low loadings, is promoted by increasing the number of P+ in the mixture. The positively charged copolymers repelled from the central part of IPEC core partially concentrate at the core-shell interface and partially escape into bulk solvent depending on the amount of P+ in the mixture and on their association number, AS. If AS is lower than the ensemble average ⟨AS⟩n, the copolymer chains released from IPEC preferentially concentrate at the core-shell interface, thus increasing AS, which approaches ⟨AS⟩n. If AS>⟨AS⟩n, they escape into the bulk solvent.

Partitioning of polymers between bulk and porous media: Monte Carlo study of the effect of pore size distribution.

In this paper we investigated the partitioning of polymer chains between bulk solvent and porous stationary phase under conditions appropriate for the chromatography under critical conditions (LCCC) close to the critical adsorption point (CAP). We addressed the concentration effect and the thermodynamic effect of pore-size dispersity (PSD) and their impacts on chromatography, i.e., the topics which surprisingly escaped from the interest of scientists in spite that the hydrodynamic effect of PSD has been a subject of numerous studies. The phase equilibria in narrow pores (as compared with the size of polymer coil) with attractive pores are complex and the enthalpy-to-entropy interplay is very intricate. The chains are attracted into pores and the partition coefficients are larger than 1, which corresponds to the interaction chromatography (IC), but they are strongly confined and deformed. The entropy plays important role and the elution volumes of chains differing in molar mass correspond to the size-exclusion chromatography (SEC). The study thus reveals a new chromatography regime which could be easily overlooked without the awareness of its existence. The unexpected findings are important not only for chromatography, but for understanding the phase equilibria of polymers in porous systems in general.

Pore size effect on the separation of polymers by interaction chromatography. A Monte Carlo study.

When the polymers are studied by interaction chromatography (IC) in porous media, the IC separation mechanism competes with the size-exclusion chromatography (SEC) mechanism and under specific conditions close to the critical adsorption point (CAP), the elution times of monodisperse polymer samples nonmonotonically depend on pore sizes. We performed Monte Carlo (MC) simulations to elucidate this intriguing effect. By analyzing the behavior of self-avoiding and intersecting chains in two-dimensionally (2D)-confining square pores and in 1D-confining slits in good and Θ-solvents, we confirmed that the dimensionality of the confinement, more specifically, pore geometry, controls the chromatographic behavior. The nonmonotonic dependence of chromatographic characteristics on pore sizes occurs only in separations of self-avoiding chains on stationary phases composed of 2D-confining pores with strongly interacting walls. In agreement with experimental observations, the partition coefficient, K, increases with pore size, D, in narrow pores, peaks and then decreases in wider pores. The combination of thermodynamic and conformational analyses clearly showed that a complex interplay between enthalpy and entropy in 2D-confined media explains the nonmonotonic pore size dependence observed in the IC regime. The study specifies the region of conditions which endanger unambiguous interpretation of elution curves. Because the interplay of steric and adsorption effects takes place not only in chromatography, but also in other separation techniques (e.g., gel electrophoresis, nanofluidic techniques), the conclusions are generally relevant for all separations of large molecules in porous media.

Computer study of the solubilization of polymer chains in polyelectrolyte complex cores of polymeric nanoparticles in aqueous media.

The formation and structure of nanoparticles containing non-polar polymer chains solubilized in interpolyelectrolyte complex (IPC) cores and the partitioning of non-polar chains between bulk solvent and IPC cores were studied by coarse-grained computer simulations. The choice of the model system was inspired by experimental results published by van der Burgh et al. (Langmuir, 2004, 20, 1073-1084). The dissipative particle dynamics (DPD) simulations reproduced the structure and basic features of co-assembled nanoparticles described by experimentalists well at the semi-quantitative coarse-grained level and revealed new properties of co-assembled particles. The simulated co-assemblies were used as reference systems for the solubilization studies. Their results show that non-polar polymers (electrically neutral and compatible with core-forming chains) solubilize easily in IPC cores. They intermix with polyelectrolyte blocks in cores and do not hinder, but, on the contrary, they slightly promote the electrostatic co-assembly.

Adsorption of amphiphilic graft copolymers in solvents selective for the grafts on a lyophobic surface: a coarse-grained simulation study.

The sorption of graft copolymers on surfaces attractive only for the backbone and its effect on the conformational behavior of adsorbed/desorbed chains in solvents good for the grafts and poor for the backbone was studied by coarse-grained computer simulations. It was found that the sorption and conformational behavior are very complex and are results of an intricate interplay of solvent quality (polymer-solvent interactions) and solvent strength (polymer-surface vs. solvent-surface interactions). Increasing grafting density and length of grafts protect the backbone against adsorption, but the behavior is non-trivial. A decrease in solvent quality promotes the adsorption, because it lowers the overall solubility, but the backbone collapses and the probability of backbone-surface contacts decreases, which simultaneously hinders the adsorption. The results of simulations are presented in the form of phase diagrams depicting the decisive features of the conformational and sorption behavior.

Local pH and Effective pK of a Polyelectrolyte Chain: Two Names for One Quantity?

In recent experiments, the "local pH" near polyelectrolyte chains was determined from the shift in the effective acidity constant of fluorescent pH indicators attached to the macromolecules. This indirect determination raises the question if the analyzed quantity was indeed the "local pH" and what this term actually means. In this study, we combined experiments and simulations to demonstrate that the shift in ionization constant is slightly lower than the difference between the pH and the "local pH". This offset is caused by correlations between fluctuations in chain conformation, small-ion distribution, and fluorophore ionization.

The electrostatic co-assembly in non-stoichiometric aqueous mixtures of copolymers composed of one neutral water-soluble and one polyelectrolyte (either positively or negatively charged) block: a dissipative particle dynamics study.

The electrostatic co-assembly in non-stoichiometric aqueous mixtures of diblock copolymers composed of a neutral water-soluble block and an either positively or negatively charged polyelectrolyte (PE) block has been studied by dissipative particle dynamics (DPD) simulations. The employed DPD variant includes explicit electrostatics and enables the investigation of the role of small ions in the co-assembly. The properties of core-shell associates containing insoluble interpolyelectrolyte complex cores and protective neutral shells were investigated as functions of the ratio of positive-to-negative charges in the system. This ratio was varied by increasing the number of positively charged PE chains of the same length as those of negatively charged chains, and by changing the PE length and charge density. The simulation results show that the associates formed in non-stoichiometric mixtures differ from those formed in stoichiometric mixtures: their association numbers are lower, their cores are charged and a fraction of excess chains remain free in the non-associated state. The study demonstrates the important role of the compatibility of the counterions with the polymer blocks. It simultaneously emphasizes the necessity of including the electrostatic interaction of all the charged species in the DPD computational scheme.

The self-assembly of copolymers with one hydrophobic and one polyelectrolyte block in aqueous media: a dissipative particle dynamics study.

The reversible self-assembly of symmetrical block copolymers consisting of one hydrophobic block and one ionizable polyelectrolyte block of the same length has been studied in aqueous solutions by dissipative particle dynamics simulations. In addition to three standard dissipative particle dynamics forces (conservative soft repulsion, dissipative and stochastic forces), explicit interaction between smeared charges on ions and on ionized polymer beads described by the electrostatic potential with appropriately localized charges was taken into account. The self-assembly and properties of formed core-shell micelles were investigated as functions of the degree of ionization for systems differing in the hydrophobicity of the non-ionized polyelectrolyte block and in the compatibility of the polymer blocks. This study shows that micelles undergo massive dissociation with increasing degree of ionization. The simulation data compare well with the predictions of scaling theories for systems with soluble polyelectrolytes on a semi-quantitative level and broaden the knowledge of systems in poor solvents.

Influence of Corona Structure on Binding of an Ionic Surfactant in Oppositely Charged Amphiphilic Polyelectrolyte Micelles.

Interaction of polystyrene-block-poly(methacrylic acid) micelles (PS-PMAA) with cationic surfactant N-dodecylpyridinium chloride (DPCl) in alkaline aqueous solutions was studied by static and dynamic light scattering, SAXS, cryogenic transmission electron microscopy (cryo-TEM), isothermal titration calorimetry (ITC), and time-resolved fluorescence spectroscopy. ITC and fluorescence measurements show that there are two distinct regimes of surfactant binding in the micellar corona (depending on the DPCl content) caused by different interactions of DPCl with PMAA in the inner and outer parts of the corona. The compensation of the negative charge of the micellar corona by DPCl leads to the aggregation of PS-PMAA micelles, and the micelles form colloidal aggregates at a certain critical surfactant concentration. SAXS shows that the aggregates are formed by individual PS-PMAA micelles with intact cores and collapsed coronas interconnected with surfactant micelles by electrostatic interactions. Unlike polyelectrolyte-surfactant complexes formed by free polyelectrolyte chains, the PMAA/DPCl complex with collapsed corona does not contain surfactant micelles.

Polyelectrolyte-surfactant complexes of poly[3,5-bis(dimethylaminomethyl)-4-hydroxystyrene]-block-poly(ethylene oxide) and sodium dodecyl sulfate: anomalous self-assembly behavior.

Polyelectrolyte-surfactant complexes (PE-S) formed by double hydrophilic cationic polyelectrolyte poly[3,5-bis(dimethylaminomethyl)-4-hydroxystyrene]-block-poly(ethylene oxide) (NPHOS-PEO) and anionic surfactant sodium dodecyl sulfate (SDS) in acidic aqueous solutions were studied by light scattering, SAXS, and scanning transmission electron microcopy in the environmental mode (wet-STEM) for various stoichiometric ratios between the numbers of SDS anions and dimethylaminomethyl groups of NPHOS in the complex. The obtained results show that the NPHOS-PEO/SDS system behaves differently from other systems of double hydrophilic block polyelectrolyte and oppositely charged ionic surfactant because it forms water-insoluble PE-S for compositions close to the zero net charge of the complex. This phase separation occurs, instead of the PE-S rearrangement to core-shell particles, which is hindered due to conformational rigidity of the NPHOS blocks. For the surfactant amounts below and above the precipitation region, large spherical aggregates and their clusters are present in the solution. SAXS measurements indicate that although the NPHOS-PEO/SDS system does not form the core-shell particles with the NPHOS/SDS core and the PEO shell as other PE-S of double hydrophilic polyelectrolytes, the aggregates contain domains of closely packed surfactant micelles which bind to both NPHOS polyelectrolyte blocks and PEO blocks.

Association of poly(4-hydroxystyrene)-block-poly(ethylene oxide) in aqueous solutions: block copolymer nanoparticles with intermixed blocks.

Association behavior of diblock copolymer poly(4-hydroxystyrene)-block-poly(ethylene oxide) (PHOS-PEO) in aqueous solutions and solutions in water/tetrahydrofuran mixtures was studied by static, dynamic, and electrophoretic light scattering, (1)H NMR spectroscopy, transmission electron microscopy, and cryogenic field-emission scanning electron microscopy. It was found that, in alkaline aqueous solutions, PHOS-PEO can form compact spherical nanoparticles whose size depends on the preparation protocol. Instead of a core/shell structure with segregated blocks, the PHOS-PEO nanoparticles have intermixed PHOS and PEO blocks due to hydrogen bond interaction between -OH groups of PHOS and oxygen atoms of PEO and are stabilized electrostatically by a fraction of ionized PHOS units on the surface.

Polyelectrolyte-surfactant complexes formed by poly[3,5-bis(trimethylammoniummethyl)4-hydroxystyrene iodide]-block-poly(ethylene oxide) and sodium dodecyl sulfate in aqueous solutions.

Formation of polyelectrolyte-surfactant (PE-S) complexes of poly[3,5-bis(trimethylammoniummethyl)-4-hydroxystyrene iodide]-block-poly(ethylene oxide) (QNPHOS-PEO) and sodium dodecyl sulfate (SDS) in aqueous solution was studied by dynamic and electrophoretic light scattering, small-angle X-ray scattering (SAXS), atomic force microscopy, and fluorometry, using pyrene as a fluorescent probe. SAXS data from the QNPHOS-PEO/SDS solutions were fitted assuming contributions from free copolymer, PE-S aggregates described by a mass fractal model, and densely packed surfactant micelles inside the aggregates. It was found that, unlike other systems of a double hydrophilic block polyelectrolyte and an oppositely charged surfactant, PE-S aggregates of the QNPHOS-PEO/SDS system do not form core-shell particles and the PE-S complex precipitates before reaching the charge equivalence between dodecyl sulfate anions and QNPHOS polycationic blocks, most likely because of conformational rigidity of the QNPHOS blocks, which prevents the system from the corresponding rearrangement.

Micelle-like nanoparticles of block copolymer poly(ethylene oxide)-block-poly(methacrylic acid) incorporating fluorescently substituted metallacarboranes designed as HIV protease inhibitor interaction probes.

We prepared nanoparticles differing in morphology from double-hydrophilic block copolymer poly(ethylene oxide)-block-poly(methacrylic acid), PEO-PMA, and two types of fluorescein-[3-cobalt(III) bis(1,2-dicarbollide)] conjugates, GB176 and GB179, in alkaline buffer. GB176 molecule consists of fluorescein attached to the metallacarborane anion. In GB179 molecule, the fluorescein moiety connects two metallacarborane anions. The self-assembly is based on the unusual interaction of metallacarborane clusters with PEO blocks which form insoluble micellar cores. The GB176 containing nanoparticles are loose and irregular, while the GB179 ones are rigid and spherical. The structure of nanoparticles depends to some extent on a procedure of preparation. The micelles were studied by static and dynamic light scattering, fluorometry and atomic force microscopy. Since the metallacarborane conjugates act as potent inhibitors of HIV protease, the presented system is important from the point of view of drug delivery.

Self-assembly of poly(4-methylstyrene)-g-poly(methacrylic acid) graft copolymer in selective solvents for grafts: scattering and molecular dynamics simulation study.

Poly(4-methylstyrene)-g-poly(methacrylic acid) (P4MS-g-PMAA) graft copolymer was synthesized by the grafting-onto method from poly(4-methylstyrene), selectively brominated on methyl groups, and "living" poly(tert-butyl methacrylate). The average degree of polymerization of the backbone and the grafts and the average number of grafts per backbone were 251, 21, and 25, respectively. The self-assembly of P4MS-g-PMAA was studied in methanol and aqueous buffers (selective solvents for grafts). Micelles of P4MS-g-PMAA in methanol were studied by a combination of static and dynamic light scattering, TEM and SAXS. It was found that their spherical core/shell morphology resembles that of diblock copolymer micelles but they have a very low aggregation number (approximately 3) and a high cmc (approximately 0.8 mg/mL). The spherical core-shell structure revealed by SAXS was confirmed by the molecular dynamics study emulating an associate of comblike copolymers with structural parameters close to those of the experimentally studied system. Because P4MS-g-PMAA was not directly soluble in water, its aqueous solutions had to be prepared by dialysis of the methanolic solutions. In aqueous solutions, unlike in methanol, small P4MS-g-PMAA micelles (approximately 20 nm in diameter) form large secondary aggregates (approximately 100-400 nm).

Interaction of fluorescently substituted metallacarboranes with cyclodextrins and phospholipid bilayers: fluorescence and light scattering study.

We prepared two fluorescein-[3-cobalt(III) bis(1,2-dicarbollide)](-) conjugates. They are sparingly soluble in water and form large aggregates in aqueous solutions. An extensive study on their spectral and aggregation behavior was carried out. To prepare their well-defined dispersion in aqueous systems, we studied the interaction of both probes with two biocompatible amphiphilic systems, cyclodextrins, which are frequently used in drug-delivery systems, and phospholipid membranes, which are the major constituents of cell barriers in living organisms. The presence of fluorescein in both conjugates allows us to study their behavior in detail by steady-state and time-resolved fluorometry, fluorescence correlation spectroscopy, and fluorescence lifetime imaging. The self-assembly of these metallacarboranes in aqueous solutions was studied by dynamic light scattering. The study shows that the compounds interact with cyclodextrins that increases their solubility in water, and they solubilize easily in phospholipid bilayers.