Effect of ion distribution on stress relaxation in polyelectrolyte complex gels.

Solutions of polyelectrolytes consisting of polycations and polyanions in equal proportions were studied in the present work. Due to the physical cross-links formed by the charged groups, physical gels were formed in such systems. The mechanical properties and structure of the obtained gels depending on the charge arrangement along the backbone and the dimensionless Bjerrum length λ were investigated. The response of the systems to a uniaxial affine deformation was studied first. It was found that the systems can be divided into three groups depending on the charge arrangement: showing an almost elastic response; showing a viscoelastic response with a very long relaxation time; and showing a weak viscoelastic response with a short relaxation time. Interestingly, no stable aggregates were formed in the systems with the charges located on spacers, probably because of the increased mobility of the charges in such systems. The obtained stress relaxation curves had different functional forms, indicating that the relaxation has at least two characteristic times, which are different for different systems. In order to understand the molecular nature of the observed mechanical response, the temporal evolution of the network structure of a system showing a viscoelastic response with a very long relaxation time was studied; the aggregates were found to be dynamic, which leads to the relaxation of the "subchains" conformation.

Conformational transitions and helical structures of a dipolar chain in external electric fields.

The conformational behavior of a single dipolar chain in a uniform electric field is investigated by molecular dynamics simulations. The dipolar chain is modeled as a backbone bead-on-spring chain of equally charged beads, each connected by a rigid spring with an oppositely charged side bead that can freely rotate around the backbone bead. In the strong coupling regime, when the dipolar chain is in the globular state due to a strong electrostatic correlational attraction, the application of an electric field causes the chain swelling and elongation along the field direction. In the weak coupling regime, a qualitatively new regime is found when the swollen dipolar chain shrinks along the field direction adopting flattened conformations due to the field-induced anisotropy of the chain rigidity and the head-to-tail attraction of the dipoles orienting along the field lines. A novel helical conformation is detected for low-polar media and strong electric fields. An increasing rigidity of the backbone chain leads to some stabilization of the helical conformation and the formation of double and triple helices as well as flat spread springs. Fine tuning of the interplay between dipolar and volume interactions by external electric fields induces re-orientation of rod-like dipolar chains in dilute solutions. The obtained results can provide new ways to control dipolar polymer conformations and design materials with responsive properties.

The effect of explicit polarity on the conformational behavior of a single polyelectrolyte chain.

In this work using dissipative particle dynamics simulations with explicit treatment of polar species we demonstrate that the molecular nature of dielectric media has a significant impact on swelling and collapse of a polyelectrolyte chain in a dilute solution. We show that the small-scale effects related to the presence of polar species lead to the intensification of the electrostatic interactions when the charges are close to each other and/or their density is high enough. As a result, the electrostatic strength , usually regarded as the main parameter governing the polyelectrolyte chain collapse, does not have a universal meaning: the value of λ at which the coil-to-globule transition occurs is found to be dependent on the specific fixed value of the solvent bulk permittivity ε while varying the monomer unit charge Q and vice versa. This effect is observed even when the backbone and the counterions have the same polarity as the solvent beads, i.e. no dielectric mismatch is present. The reason for such behavior is rationalized in terms of the "effective" dielectric permittivity εeff which depends on the volume fraction φ of charged units inside the polymer chain volume; using εeff instead of ε collapses all data onto one master curve describing the chain shrinking with λ. Furthermore, it is shown that a polar chain adopts less swollen conformations in the polyelectrolyte regime and collapses more easily compared to a non-polar chain.

Two contributions to the dielectric response of polar liquids.

In this Note, we study the total conservative force {instead of pure electrostatic force as it was carried out in the work by Gavrilov [J. Chem. Phys. 152, 164101 (2020)]} acting on two charges in a polar liquid using dissipative particle dynamics and coarse-grained molecular dynamics simulations. We show that such force (instead of the electrostatic force) obeys Coulomb's law at large distances between the charges. Apparently, the dielectric response of a polar liquid (at least, within such coarse-grained models) can be decomposed into two contributions: the reorientation of the dipoles (i.e., electrostatic contribution) and the density redistribution (i.e., volume interaction contribution).

Effects of generation number, spacer length and temperature on the structure and intramolecular dynamics of siloxane dendrimer melts: molecular dynamics simulations.

The structure and properties of polysiloxane dendrimer melts are studied by extensive atomistic molecular dynamics simulations. Two homologous series differing in the spacer length are considered. In the first series the dendrimer spacers are the shortest ones, comprising only one oxygen atom, while in the second series the spacers consist of two oxygen atoms with the silicon atom in between. Melts of the dendrimers from the 3rd up to the 6th generation number are modelled in a wide temperature range from 273 to 600 K. A comparative study of the macroscopic melt characteristics such as the melt density and thermal expansion coefficients is performed for the two series. Analysis of the dendrimer structure in melts and in the isolated state shows that intermolecular interactions and interpenetration of dendrimer molecules in melts hardly affect the dendrimer interior organization. However, the presence of neighboring molecules significantly slows down their intramolecular dynamics in melts in comparison with that of isolated dendrimers. An increasing generation number causes an increase of the radius of the dendrimer interior region unavailable for neighboring molecules, which starts to exceed the length of the peripheral interpenetration layer for high-generation dendrimers; this fact could lead to different mechanisms of melt dynamics for lower and higher generation dendrimers.

Conformational behavior of a semiflexible dipolar chain with a variable relative size of charged groups via molecular dynamics simulations.

The conformational behavior of an isolated semiflexible dipolar chain has been studied by molecular dynamics simulations. The dipolar chain was modeled as a backbone chain of charged beads, each containing an oppositely charged unit connected to it by a rigid spring. The main focus was on the effect of the backbone chain rigidity and the size of the charged groups on the morphology of the collapsed states of the chain formed in low-polar media where the electrostatic interactions are essential. It has been found that the stable globular conformations of the long chain of N = 256 backbone beads are a toroid and an elliptical globule. The macroscopic parameters (such as the radius of gyration and shape factors) as well as the local characteristics of these conformations (radial density distributions of ions, orientational correlations of chain segments, dipoles etc.) are studied depending on the chain stiffness. The regions of stability of a torus and an elliptical globule are found for the dipolar chains with variable dipole length and stiffness, which depend on the strength of electrostatic interactions. It has been shown that a size asymmetry of oppositely charged beads destabilizes globular states favoring elongated chain conformations. A coexistence of various metastable states was demonstrated for shorter chains of N = 128, 64, and 32.

Surface relief of magnetoactive elastomeric films in a homogeneous magnetic field: molecular dynamics simulations.

The structure of a thin magnetoactive elastomeric (MAE) film adsorbed on a solid substrate is studied by molecular dynamics simulations. Within the adopted coarse-grained approach, a MAE film consists of magnetic particles modeled as soft-core spheres, carrying point dipoles, connected by elastic springs representing a polymer matrix. MAE films containing 20, 25 and 30 vol% of randomly distributed magnetic particles are simulated. Once a magnetic field is applied, the competition between dipolar, elastic and Zeeman forces leads to the restructuring of the layer. The distribution of the magnetic particles as well as elastic strains within the MAE films are calculated for various magnetic fields applied perpendicular to the film surface. It is shown that the surface roughness increases strongly with growing magnetic field. For a given magnetic field, the roughness is larger for the softer polymeric matrix and exhibits a nonmonotonic dependence on the magnetic particle concentration. The obtained results provide a better understanding of the MAE surface structuring as well as possible guidelines for fabrication of MAE films with a tunable surface topology.

Magnetodielectric Response of Soft Magnetoactive Elastomers: Effects of Filler Concentration and Measurement Frequency.

The magnetodielectric response of magnetoactive elastomers (MAEs) in its dependence on filler concentration, magnetic field, and test frequency is studied experimentally. MAEs are synthesized on the basis of a silicone matrix filled with spherical carbonyl iron particles characterized by a mean diameter of 4.5 µm. The concentration of the magnetic filler within composite materials is equal to 70, 75, and 80 mass%. The effective lossless permittivity ε' as well as the dielectric loss tanδ grow significantly when the magnetic field increases. The permittivity increases and the dielectric loss decreases with increasing filler concentration. In the measurement frequency range between 1 kHz and 200 kHz, the frequency hardly affects the values of ε' and tanδ in the absence of a magnetic field. However, both parameters decrease considerably with the growing frequency in a constant magnetic field. The more strongly the magnetic field is applied, the larger the change in permittivity and loss tangent at the same test frequency is observed. An equivalent circuit formulation qualitatively describes the main tendencies of the magnetodielectric response.

Effect of counterion excluded volume on the conformational behavior of polyelectrolyte chains.

Conformational behavior of a single strongly charged polyelectrolyte chain in a dilute solution is studied by molecular dynamics simulations. The novel feature of the model is variation of the excluded volume of counterions for investigating its effect on the chain conformation, especially in low-polar media. It has been confirmed that the chain with conventional counterions collapses into a dense globule with increasing electrostatic interactions. However, if the counterions are bulky enough, they prevent the chain collapse even in media with strong electrostatic interactions. They stay bound in the vicinity of the backbone of the chain that adopts a swollen conformation. In this conformation, the scaling relation for the polymer dimensions with the chain length is the same as for neutral macromolecules in a good solvent, however the polyelectrolyte chain complexed with bulky counterions has a larger gyration radius than its uncharged analogue due to the excluded volume of the counterions contributing to the chain rigidity. Study of the counterion mobility has shown that, similar to the conventional counterions, the bulky counterions do not form stable ion pairs with ions on the polymer chain even in media with strong electrostatic interactions, but rather freely move along the chain backbone. In solutions containing mixtures of counterions with a bimodal size distribution, the conformations of linear polyelectrolytes depend considerably on the fraction of bulky counterions. Furthermore, a kind of intramolecular microphase separation can take place within a polyelectrolyte globule with the formation of a core-shell particle: the smaller counterions concentrate within the globular core while the bulkier counterions form a shell on the globule surface. The stability of the core-shell globule depends on the relative size of the counterions as well as their fractions in the solution. Thus, fine tuning of the balance between the counterion excluded volume and the electrostatic interactions opens new ways for controlling the conformational behavior of polyelectrolytes.

Two regions of microphase separation in ion-containing polymer solutions.

The phenomenon of spinodal decomposition in weakly charged polyelectrolyte solutions is studied theoretically within the random phase approximation. A novel feature of the theoretical approach is that it accounts for the effects of ionic association, i.e. ion pair and multiplet formation between counterions and ions in polymer chains, as well as the dependence of local dielectric permittivity on the polymer volume fraction Φ. The main focus is on the spinodal instability of polyelectrolyte solutions towards microscopic phase separation. It has been shown that increasing the binding energy of ions decreases the classical microphase separation region (possible at low polymer concentrations) due to the effective neutralization of the chains. A qualitatively new type of microphase separation is found in the presence of a dielectric mismatch between polymer and solvent. This new branch of microphase separation is realized at high polymer concentrations where ion association processes are the most pronounced. Typical microstructures are shown to have a period of a few nanometers like in ionomers. The driving force for the microphase formation of a new type is more favourable ion association in polymer-rich domains where ionomer-type behavior takes place. Effective attraction due to ion association promotes microscopic as well as macroscopic phase separation, even under good solvent conditions for uncharged monomer units of polymer chains. Polyelectrolyte-type behavior at low Φ and ionomer-type behavior at high Φ result in the presence of two critical points on the phase diagrams of polyelectrolyte solutions as well as two separate regions of possible microscopic structuring. Our predictions on the new type of microphase separation are supported by experimental data on polymer solutions, membranes and gels.

Communication: Light driven remote control of microgels' size in the presence of photosensitive surfactant: Complete phase diagram.

Here we report on a light triggered remote control of microgel size in the presence of photosensitive surfactant. The hydrophobic tail of the cationic surfactant contains azobenzene group that undergoes a reversible photo-isomerization reaction from a trans- to a cis-state accompanied by a change in the hydrophobicity of the surfactant. We have investigated light assisted behaviour and the complex formation of the microgels with azobenzene containing surfactant over the broad concentrational range starting far below and exceeding several times of the critical micelle concentration (CMC). At small surfactant concentration in solution (far below CMC), the surfactant in the trans-state accommodates within the microgel causing its compaction, while the cis-isomer desorbs out of microgel resulting in its swelling. The process of the microgel size change can be described as swelling on UV irradiation (trans-cis isomerization) and shrinking on irradiation with blue light (cis-trans isomerization). However, at the surfactant concentrations larger than CMC, the opposite behaviour is observed: the microgel swells on blue irradiation and shrinks during exposure to UV light. We explain this behaviour theoretically taking into account isomer dependent micellization of surfactant within the microgels.

Transient magnetorheological response of magnetoactive elastomers to step and pyramid excitations.

Transient rheological response of magnetoactive elastomers is experimentally studied using dynamic torsion at a fixed oscillation frequency in temporally stepwise changing magnetic fields and oscillation amplitudes. For step magnetic-field excitations, at least three exponential functions are required to reasonably describe the time behavior of the storage shear modulus over long time scales (>10(3) s). The deduced characteristic time constants of the corresponding rearrangement processes of the filler network differ approximately by one order of magnitude: τ1 ≲ 10(1) s, τ2 ∼ 10(2) s, and τ3 ∼ 10(3) s. The sudden imposition of the external magnetic field activates a very fast rearrangement process with the characteristic time under 10 s, which cannot be determined more precisely due to the measurement conditions. Even more peculiar transient behavior has been observed during pyramid excitations, when either the external magnetic field was first stepwise increased and then decreased in a staircase manner at a fixed strain amplitude γ or the strain amplitude γ was first stepwise increased and then decreased in a staircase manner at a fixed magnetic field. In particular, the so-called "cross-over effect" has been identified in both dynamical loading programs. This cross-over effect seems to be promoted by the application of the external magnetic field. The experimental results are discussed in the context of the specific rearrangement of the magnetic filler network under the simultaneous action of the external magnetic field and shear deformation. Striking similarities of the observed phenomena to the structural relaxation processes in glassy materials and to the jamming transition of granular materials are pointed out. The obtained results are important for fundamental understanding of material behavior in magnetic fields as well as for the development of devices on the basis of magnetoactive elastomeric materials.

Photosensitive microgels containing azobenzene surfactants of different charges.

We report on light sensitive microgel particles that can change their volume reversibly in response to illumination with light of different wavelengths. To make the anionic microgels photosensitive we add surfactants with a positively charged polyamine head group and an azobenzene containing tail. Upon illumination, azobenzene undergoes a reversible photo-isomerization reaction from a trans- to a cis-state accompanied by a change in the hydrophobicity of the surfactant. Depending on the isomerization state, the surfactant molecules are either accommodated within the microgel (trans-state) resulting in its shrinkage or desorbed back into water (cis-isomer) letting the microgel swell. We have studied three surfactants differing in the number of amino groups, so that the number of charges of the surfactant head varies between 1 and 3. We have found experimentally and theoretically that the surfactant concentration needed for microgel compaction increases with decreasing number of charges of the head group. Utilization of polyamine azobenzene containing surfactants for the light triggered remote control of the microgel size opens up a possibility for applications of light responsive microgels as drug carriers in biology and medicine.

Polymer gels with associating side chains and their interaction with surfactants.

Conformational behaviour of hydrophobically modified (HM) polymer gels in solutions of nonionic surfactants is studied theoretically. A HM gel contains hydrophobic side chains (stickers) grafted to its subchains. Hydrophobic stickers are capable to aggregate into joint micelles with surfactant molecules. Micelles containing more than one sticker serve as additional physical cross-links of the network, and their formation causes gel shrinking. In the proposed theoretical model, the interior of the gel/surfactant complex is treated as an array of densely packed spherical polymer brushes consisting of gel subchains tethered to the surface of the spherical sticker/surfactant micelles. Effect of stickers length and grafting density, surfactant concentration and hydrophobicity on gel swelling as well as on hydrophobic association inside it is analyzed. It is shown that increasing surfactant concentration can result in a gel collapse, which is caused by surfactant-induced hydrophobic aggregation of stickers, and a successive gel reswelling. The latter should be attributed to a growing fraction of surfactants in joint aggregates and, hence, increasing number of micelles containing only one sticker and not participating in gel physical cross-linking. In polyelectrolyte (PE) gels hydrophobic aggregation is opposed by osmotic pressure of mobile counterions, so that at some critical ionization degree hydrophobic association is completely suppressed. Hydrophobic modification of polymers is shown to open new ways for controlling gel responsiveness. In particular, it is discussed that incorporation of photosensitive groups into gel subchains and/or surfactant tail could give a possibility to vary the gel volume by light. Since hydrophobic aggregation regularities in gels and solutions are common, we hope our findings will be useful for design of polymer based self-healing materials as well.

Experimental study of the magnetic field enhanced Payne effect in magnetorheological elastomers.

The dynamic modulus and the loss factor of magnetorheological elastomers (MREs) of various compositions and anisotropies are studied by dynamic torsion oscillations performed in the absence and in the presence of an external magnetic field. The emphasis is on the Payne effect, i.e. the dependence of the elastomer magnetorheological characteristics on the strain amplitude and their evolution with cyclically increasing and decreasing strain amplitudes. MREs are based on two silicone matrices differing in storage modulus (soft, G' ∼ 10(3) Pa, and hard, G' ∼ 10(4) Pa, matrices). For each matrix, the concentration of carbonyl iron particles with diameters of 3-5 µm was equal to 70 and 82 mass% (22 and 35 vol%, respectively) in the composite material. Samples for each filler content, isotropic and aligned-particles, are investigated. It is found that the Payne effect significantly increases in the presence of an external magnetic field and varies with the cyclical loading which reaches saturation after several cycles. The results are interpreted as the processes of formation-destruction-reformation of the internal filler structure under the simultaneously applied mechanical force and magnetic field. Impacts of matrix elasticity and magnetic interactions on the filler alignment are elucidated.

Effects of Filler Anisometry on the Mechanical Response of a Magnetoactive Elastomer Cell: A Single-Inclusion Modeling Approach.

A finite-element model of the mechanical response of a magnetoactive elastomer (MAE) volume element is presented. Unit cells containing a single ferromagnetic inclusion with geometric and magnetic anisotropy are considered. The equilibrium state of the cell is calculated using the finite-element method and cell energy minimization. The response of the cell to three different excitation modes is studied: inclusion rotation, inclusion translation, and uniaxial cell stress. The influence of the magnetic properties of the filler particles on the equilibrium state of the MAE cell is considered. The dependence of the mechanical response of the cell on the filler concentration and inclusion anisometry is calculated and analyzed. Optimal filler shapes for maximizing the magnetic response of the MAE are discussed.

Structure and Mechanical Response of Polybutylcarbosilane Dendrimers Confined in a Flat Slit: Effect of Molecular Architecture and Generation Number.

Due to the absence of specific interactions, carbosilane dendrimers are ideal models to study the effect of a hyperbranched regular structure on the molecular response to external influences. In this work, we have studied the conformational behavior of single polybutylcarbosilane dendrimers under confinement between impermeable flat surfaces using atomistic molecular dynamics simulations. Dendrimers of different generations belonging to two homologous series with a tetra-functional core and three- and four-functional branches were simulated. The analysis of the dependence of the internal energy of the dendrimers on the wall distance allowed us to determine the critical degree of compression at which the dendrimers are able to change their shape without energy loss. The effects of generation number and branching functionality on the number of wall contacts, density distribution and shape changes were elucidated. It was found that for high generation dendrimers, the inner layers are not accessible for external interaction. It was shown that the excess stresses occurring at high compressions are concentrated in the structural center of the dendrimer. The nature of the elastic response, which is strongly nonlinear, was analyzed at different compressions depending on the dendrimer architecture and generation. We believe that our results are useful for further studies of dendrimer films under compression and can also serve as a basis for developing model concepts to describe the dynamics of dendrimer melts.

Programming and Reprogramming the Viscoelasticity and Magnetic Response of Magnetoactive Thermoplastic Elastomers.

We present a novel type of magnetorheological material that allows one to restructure the magnetic particles inside the finished composite, tuning in situ the viscoelasticity and magnetic response of the material in a wide range using temperature and an applied magnetic field. The polymer medium is an A-g-B bottlebrush graft copolymer with side chains of two types: polydimethylsiloxane and polystyrene. At room temperature, the brush-like architecture provides the tissue mimetic softness and strain stiffening of the elastomeric matrix, which is formed through the aggregation of polystyrene side chains into aggregates that play the role of physical cross-links. The aggregates partially dissociate and the matrix softens at elevated temperatures, allowing for the effective rearrangement of magnetic particles by applying a magnetic field in the desired direction. Magnetoactive thermoplastic elastomers (MATEs) based on A-g-B bottlebrush graft copolymers with different amounts of aggregating side chains filled with different amounts of carbonyl iron microparticles were prepared. The in situ restructuring of magnetic particles in MATEs was shown to significantly alter their viscoelasticity and magnetic response. In particular, the induced anisotropy led to an order-of-magnitude enhancement of the magnetorheological properties of the composites.

Polymer micelles with hydrophobic core and ionic amphiphilic corona. 1. Statistical distribution of charged and nonpolar units in corona.

Polymer micelles with hydrophobic polystyrene (PS) core and ionic amphiphilic corona from charged N-ethyl-4-vinylpyridinium bromide (EVP) and uncharged 4-vinylpyridine (4VP) units spontaneously self-assembled from PS-block-poly(4VP-stat-EVP) macromolecules in mixed dimethylformamide/methanol/water solvent. The fraction of statistically distributed EVP units in corona-forming block is ß = [EVP]/([EVP]+[4VP]) = 0.3-1. Micelles were transferred into water via dialysis technique, and pH was adjusted to 9, where 4VP is insoluble. Structural characteristics of micelles were investigated both experimentally and theoretically as a function of corona composition ß. Methods of dynamic and static light scattering, electrophoretic mobility measurements, sedimentation velocity, transmission electron microscopy, and UV spectrophotometry were applied. All micelles possessed spherical morphology. The aggregation number, structure, and electrophoretic mobility of micelles changed in a jumplike manner near ß ~ 0.6-0.75. Below and above this region, micelle characteristics were constant or insignificantly changed upon ß. Theoretical dependencies for micelle aggregation number, corona dimensions, and fraction of small counterions outside corona versus ß were derived via minimization the micelle free energy, taking into account surface, volume, electrostatic, and elastic contributions of chain units and translational entropy of mobile counterions. Theoretical estimations also point onto a sharp structural transition at a certain corona composition. The abrupt reorganization of micelle structure at ß ~ 0.6-0.75 entails dramatic changes in micelle dispersion stability in the presence of NaCl or in the presence of oppositely charged polymeric (sodium polymethacrylate) or amphiphilic (sodium dodecyl sulfate) complexing agents.

Polymer micelles with hydrophobic core and ionic amphiphilic corona. 2. Starlike distribution of charged and nonpolar blocks in corona.

Mixed polymer micelles with hydrophobic polystyrene (PS) core and ionic amphiphilic poly(4-vinylpyridine)/poly(N-ethyl-4-vinylpyridinium bromide) corona (P4VP/PEVP) spontaneously self-assembled from mixtures of PS-b-PEVP and PS-b-P4VP macromolecules in dimethylformamide/methanol/water selective solvent. The fraction of PEVP units in corona was ß = [PEVP]/([PEVP] + [P4VP]) = 0.05-1.0. Micelles were transferred into pure water via dialysis technique and pH was adjusted to 9, where P4VP blocks are insoluble. Structural characteristics of micelles as a function of corona composition ß were investigated. Methods of dynamic and static light scattering, electrophoretic mobility measurements, sedimentation velocity, transmission electron microscopy, and UV spectrophotometry were applied. Spherical morphology with core (PS)-shell (P4VP)-corona (PEVP) organization was postulated. Micelles demonstrated a remarkable inflection in structural characteristics near ß ~ 0.5-0.7. Above this region, aggregation number (m), core and corona radii of mixed micelles coincided with those of individual PS-b-PEVP micelles. When ß decreased below 0.5, dramatic growth of aggregation number was observed, accompanied by growth in micelle size and stretching PEVP chains. At ß below 0.2, dispersions of mixed micelles were unstable and easily precipitated upon addition of NaCl. Scaling relationships between micelle characteristics and ß were obtained via minimization the micelle free energy, taking into account electrostatic, osmotic, volume, and surface contributions. Theoretical estimations predicted dramatic influence of ß on aggregation number, m ~ ß(-3). This result is in general agreement with experimental data and confirms the correctness of the core-shell-corona model. The inflection in micelle characteristics entails drastic changes in micelle dispersion stability in the presence of oppositely charged polymeric (sodium polymethacrylate) or amphiphilic (sodium dodecyl sulfate) complexing agents.