Vertical Phase Segregation Induced by Dipolar Interactions in Planar Polymer Brushes

Chains Stiffness Effect on the Vertical Segregation of Mixed Polymer Brushes in Selective Solvent

The microstructure of the binary polymer brushes in the selective solvent was studied using the numerical lattice self-consisting field approach. The case was considered when the selectivity to the solvent (the Flory-Huggins parameter χ) was varied only for one type of chains (responsive chains) while the others (non-responsive chains) remained hydrophilic (χ = 0). In such a brush, with an increase in the hydrophobicity of the responsive chains, a transition occurs between two two-layer microstructures. In the initial state the ends of the longer responsive chains are located near the external surface of the brush and those of non-responsive chains are inside the brush. When the hydrophobicity of the responsive chains becomes high enough then the reversed two-layer microstructure is formed, when the ends of non-responsive chains are located near the brush surface and the responsive chains collapse on the brush bottom. In contrast to previous works, the stiffness parameter (Kuhn segment length p) for one or for both types of chains was varied and its effect on the mechanism and characteristics of the transition was studied. If the stiffness of only responsive chains increases, then the transition occurs with the formation of an intermediate three-layer microstructure, where a layer of responsive chains is located between layers formed by non-responsive ones. If both types of chains have the same p, then the transition occurs gradually without the formation of an intermediate three-layer microstructure. For both cases, the effect of p on the critical value of χ*, corresponding to the transition point and on the steepness of the transition was investigated.

The Structure of Dipolar Polymer Brushes and Their Interaction in the Melt. Impact of Chain Stiffness

By using the numerical lattice Scheutjens-Fleer self-consistent field (SF-SCF) method we have studied the effect of the restricted flexibility of grafted chains on the structure and mutual interaction of two opposing planar conventional and A-type dipolar brushes. Brushes are immersed in the solvent consisting of chains similar to the grafted ones. The increase of the chain rigidity enhances the segregation of grafted chains in a A-type dipolar brush into two populations: backfolded chains with terminal monomers near the grafting surface and chains with the ends at the brush periphery. The fraction of backfolded chains grows by an increase of the Kuhn segment length. It is shown that two opposite A-type dipolar brushes from semi-rigid chains are attracted to each other at short distances. The attraction becomes more pronounced and begins at larger distances for more rigid chains with the same brush characteristics: polymerization degree, grafting density, and dipole moments of monomer units. This attraction is connected with the dipole-dipole interactions between chains of oncoming brushes with oppositely directed dipoles penetrating deeply into each other upon contact. This effect of the chain rigidity is opposite to that for conventional brushes without dipoles in the chains. For such brushes, an increase in the chain rigidity leads to the enhanced repulsion between them.

Real-Time Measurement of Polymer Brush Dynamics Using Silicon Photonic Microring Resonators: Analyte Partitioning and Interior Brush Kinetics

Polymer brushes are found in biomedical and industrial technologies, where they exhibit functionalities considerably dependent on polymer brush-solvent-analyte interactions. It remains a difficult challenge to quickly analyze solvent-swollen polymer brushes, both at the solvent-polymer brush interface and in the brush interior, as well as to monitor the kinetics of interaction of solvent-swollen brushes with key analytes. Here, we demonstrate the novel use of silicon photonic microring resonators to characterize in situ swollen polymer brush-analyte interactions. By monitoring resonant wavelength shifts, we find that brush-solvent-analyte interaction parameters can be extracted from a single set of data or from successive analyte introductions using a single brush-coated sensor. The partition coefficient of three industrially relevant plasticizers into hydrophobic and hydrophilic brushes was determined and found to be in agreement with known solubility trends. We found that the diffusion coefficient of the plasticizer into the brush decreases as brush thickness increases, supporting a model of a dense inner brush layer and diffuse outer layer. pK_a's of pH-sensitive brushes were determined on the microring resonator platform; upon increasing the dry brush thickness, the pK_a for poly(2-dimethylamino ethyl methacrylate) decreased from 8.5 to approach the bulk material pK_a of 7.3 and showed dependence on the presence and concentration of salt. These proof-of-concept experiments show how the surface-sensitive nature of the microring resonator detection platform provides valuable information about the interaction of the polymer brushes with the solvents and analytes, not easily accessed by other techniques.

Surface Tension of Dielectric-Air Interfaces

Analytical and semianalytical expressions for the surface tension of dielectric-air interfaces are presented after considering local and nonlocal dielectric effects near interfaces. It is shown that the nonlocal effects of dielectrics are significant for highly polar dielectric fluids such as water. Far from the interface, nonlocal dielectric effects are shown to cause not only the oscillatory potential of the mean force but also a reversal of sign at intermediate distances.

A statistical field theory of salt solutions of 'hairy' dielectric particles

In this paper, we formulate a field-theoretical model of dilute salt solutions of electrically neutral spherical colloid particles. Each colloid particle consists of a 'central' charge that is situated at the center and compensating peripheral charges (grafted to it) that are fixed or fluctuating relative to the central charge. In the framework of the random phase approximation, we obtain a general expression for electrostatic free energy of solution and analyze it for different limiting cases. In the limit of infinite number of peripheral charges, when they can be modelled as a continual charged cloud, we obtain an asymptotic behavior of the electrostatic potential of a point-like test charge in a salt colloid solution at long distances, demonstrating the crossover from its monotonic decrease to damped oscillations with a certain wavelength. We show that the obtained crossover is determined by certain Fisher-Widom line. For the same limiting case, we obtain an analytical expression for the electrostatic free energy of a salt-free solution. In the case of nonzero salt concentration, we obtain analytical relations for the electrostatic free energy in two limiting regimes. Namely, when the ionic concentration is much higher than the colloid concentration and the effective size of charge cloud is much bigger than the screening lengths that are attributed to the salt ions and the central charges of colloid particles. The proposed theory could be useful for theoretical description of the phase behavior of salt solutions of metal-organic complexes and polymeric stars.

Enhanced scattering induced by electrostatic correlations in concentrated solutions of salt-free dipolar and ionic polymers

We present a generalized theory for studying the static monomer density-density correlation function (structure factor) in concentrated solutions and melts of dipolar as well as ionic polymers. The theory captures effects of electrostatic fluctuations on the structure factor and provides insights into the origin of experimentally observed enhanced scattering at ultralow wavevectors in salt-free ionic polymers. It is shown that the enhanced scattering can originate from a coupling between the fluctuations of electric polarization and monomer density. Local and non-local effects of the polarization resulting from finite sized permanent dipoles and ion-pairs in dipolar and charge regulating ionic polymers, respectively, are considered. Theoretical calculations reveal that, similar to the salt-free ionic polymers, the structure factor for dipolar polymers can also exhibit a peak at a finite wavevector and enhanced scattering at ultralow wavevectors. Although consideration of dipolar interactions leads to attractive interactions between monomers, the enhanced scattering at ultralow wavevectors is predicted solely on the basis of the electrostatics of weakly inhomogeneous dipolar and ionic polymers without considering the effects of any aggregates or phase separation. Thus, we conclude that neither aggregation nor phase separation is necessary for observing the enhanced scattering at ultralow wavevectors in salt-free dipolar and ionic polymers. For charge regulating ionic polymers, it is shown that electrostatic interactions between charged monomers get screened with a screening length, which depends not only on the concentration of "free" counterions and coions, but also on the concentration of "adsorbed" ions on the polymer chains. Qualitative comparisons with the experimental scattering curves for ionic and dipolar polymer melts are presented using the theory developed in this work.

Understanding the effects of symmetric salt on the structure of a planar dipolar polymer brush

The effects of added salt on a planar dipolar polymer brush immersed in a polar solvent are studied using a field theoretic approach. The field theory developed in this work provides a unified framework for capturing effects of the inhomogeneous dielectric function, translational entropy of ions, crowding due to finite sized ions, ionic size asymmetry, and ion solvation. In this paper, we use the theory to study the effects of ion sizes, their concentration, and ion-solvation on the polymer segment density profiles of a dipolar brush immersed in a solution containing symmetric salt ions. The interplay of crowding effects, translational entropy, and ion solvation is shown to exhibit either an increase or decrease in the brush height. Translational entropy and crowding effects due to finite sizes of the ions tend to cause expansion of the brush as well as uniform distribution of the ions. By contrast, ion-solvation effects, which tend to be stronger for smaller ions, are shown to cause shrinkage of the brush and inhomogeneous distribution of the ions.

Response of a Permanently Charged Polyelectrolyte Brush to External Ions: The Aspects of Structure and Dynamics

Structure and dynamics inside permanently charged polyelectrolyte brushes, sodium polystyrene sulfonate brushes, during their response to the introduction of external ions (NaCl) are investigated by neutron reflectivity and dielectric spectroscopy. Neutron reflectivity measurements show that the segmental density of the inner part of the brushes decreases and that of the outer part increases when the salt level is tuned from the salt-free condition to a moderate level (<10^-2 M)-the brushes swell further compared with the salt-free condition. This is attributed to the breakup of the multiplets formed by dipole-dipole pairs, and by this process, the previously constrained chain segments by the multiplets are released. Dielectric spectroscopy discovers a giant dipole by the charge separation of the adsorbed counterions and the PSS^- chains, induced by electric field. The dynamics of the induced giant dipole is accelerated with the increase of external salt, as a result of the charge regularization by elevated salt level. At high-enough salt level, the screening effect reduces the electrostatic repulsion between the neighboring chains and makes the brushes shrink.

An interplay of electrostatic and excluded volume interactions in the conformational behavior of a dipolar chain: theory and computer simulations

The effect of an interplay between electrostatic and excluded volume interactions on the conformational behavior of a dipolar chain has been studied theoretically and by means of molecular dynamics simulations. Every monomer unit of the dipolar chain comprises a dipole formed by a charged group of the chain and an oppositely charged counterion. The counterion is assumed to freely move around the chain but keeping the distance between oppositely charged ions (the dipole length) fixed. The novelty of the developed mean-field theory is that variations of the dipole parameters (the dipole length and the counterion size) have been accounted for in both electrostatic and excluded volume contributions to the total free energy of the dipolar chain. It has been shown that conformational transitions between swollen and collapsed states of the chain can be induced by fine-tuning the balance between electrostatic and excluded volume interactions. In particular, in low-polar media not only globule but also extended coil conformations can be realized even under strong electrostatic attraction. The results of MD simulations of a dipolar chain with variable dipolar length support theoretical conclusions.

Flory-type theories of polymer chains under different external stimuli

In this Review, we present a critical analysis of various applications of the Flory-type theories to a theoretical description of the conformational behavior of single polymer chains in dilute polymer solutions under a few external stimuli. Different theoretical models of flexible polymer chains in the supercritical fluid are discussed and analysed. Different points of view on the conformational behavior of the polymer chain near the liquid-gas transition critical point of the solvent are presented. A theoretical description of the co-solvent-induced coil-globule transitions within the implicit-solvent-explicit-co-solvent models is discussed. Several explicit-solvent-explicit-co-solvent theoretical models of the coil-to-globule-to-coil transition of the polymer chain in a mixture of good solvents (co-nonsolvency) are analysed and compared with each other. Finally, a new theoretical model of the conformational behavior of the dielectric polymer chain under the external constant electric field in the dilute polymer solution with an explicit account for the many-body dipole correlations is discussed. The polymer chain collapse induced by many-body dipole correlations of monomers in the context of statistical thermodynamics of dielectric polymers is analysed.

Molecular dynamics simulations of oligoester brushes: the origin of unusual conformations

We present results from all-atom molecular dynamics simulations for the structural properties of oligomeric lactic acid chains (OLA) grafted to the surface of cellulose nanocrystals (CNCs) and immersed in the melt of polylactic acid (PLA). Earlier, we have found that the distribution of free ends of OLA molecules is bimodal [Glova et al., Polym. Int., 2016, 65(8), 892]. The results cannot be explained within the standard picture of uncharged polymer brushes exposed to the melt of a chemically identical polymer. Although the oligomeric brushes of the OLA chains are uncharged, they have partial polarization charges producing a non-zero dipole moment of the monomeric chain unit. We study the influence of partial charges on the structure of the layer of OLA chains grafted to the CNC surface. A detailed analysis of the conformations of the grafted chains shows that interaction of partial charges in the models causes bending of the OLA molecules toward the cellulose surface, forming a hairpin structure. The observed separation of the grafted chains into two populations increases with grafting density. We demonstrate that hydrogen bonds can be formed between the free ends of the grafted chains and the CNC surface, but they do not affect the brush structure significantly. Thus, dipole-dipole interactions turn out to be the key factor governing the unusual conformations of grafts.

Attraction between Opposing Planar Dipolar Polymer Brushes

We use a field theory approach to study the effects of permanent dipoles on interpenetration and free energy changes as a function of distance between two identical planar polymer brushes. Melts (i.e., solvent-free) and solvated brushes made up of polymers grafted on nonadsorbing substrates are studied. In particular, the weak coupling limit of the dipolar interactions is considered, which leads to concentration-dependent pairwise interactions, and the effects of orientational order are neglected. It is predicted that a gradual increase in the dipole moment of the polymer segments can lead to attractive interactions between the brushes at intermediate separation distances. Because classical theory of polymer brushes based on the strong stretching limit (SSL) and the standard self-consistent field theory (SCFT) simulations using the Flory's χ parameter always predicts repulsive interactions at all separations, our work highlights the importance of dipolar interactions in tailoring and accurately predicting forces between polar polymeric interfaces in contact with each other.

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.

Effects of counterion size and backbone rigidity on the dynamics of ionic polymer melts and glasses

Backbone rigidity, counterion size and the static dielectric constant affect the glass transition temperature, segmental relaxation time and decoupling between counterion and segmental dynamics in significant manners.