Polyelectrolyte complexes
Polyelectrolyte complexes formed from combined water soluble and negatively charged polyelectrolytes
Rembaum, A.↗
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Novel polyelectrolytes
Cationic polyelectrolytes are formed by the polymerization in absence of oxygen of a monomer of the general formula: ##STR1## where x is 3 or more than 6 and Z is I, Br or Cl to form high charge density linear polymers. Segments of the linear polymer may be attached to or formed in the presence of polyfunctional reactive tertiary amines or halogen polymeric substrates or polyfunctional lower molecular reactive polyfunctional substrates to form branched or star polyelectrolytes by a quaternization polymerization reaction.
Rembaum, Alan↗
Anion-tethered Single Lithium-ion Conducting Polyelectrolytes through UV-induced Free Radical Polymerization for Improved Morphological Stability of Lithium Metal Anodes
Single Li + ion conducting polyelectrolytes (SICs), which feature covalently tethered counter-anions along their backbone, have the potential to mitigate dendrite formation by reducing concentration polarization and preventing salt depletion. However, due to their low ionic conductivity and complicated synthetic procedure, the successful validation of these claimed advantages in lithium metal (Li 0 ) anode batteries remains limited. In this study, we fabricated a SIC electrolyte using a single-step UV polymerization approach. The resulting electrolyte exhibited a high Li + transference number (t + ) of 0.85 and demonstrated good Li + conductivity (6.3×10 -5 S/cm at room temperature), which is comparable to that of a benchmark dual ion conductor (DIC, 9.1×10 -5 S/cm). Benefitting from the high transference number of SIC, it displayed a three-fold higher critical current density (2.4 mA/cm 2 ) compared to DIC (0.8 mA/cm 2 ) by successfully suppressing concentration polarization-induced short-circuiting. Additionally, the t + significantly influenced the deposition behavior of Li0, with SIC yielding a uniform, compact, and mosaic-like morphology, while the low t + DIC resulted in a porous morphology with Li 0 whiskers. Using the SIC electrolyte, Li 0 ||LiFePO 4 cells exhibited stable operation for 4500 cycles with 70.5 % capacity retention at 22 °C.
25 ENERGY STORAGE↗
Conjugated Polyelectrolyte-Based Complex Fluids as Aqueous Exciton Transport Networks
The ability to assemble artificial systems that mimic aspects of natural light-harvesting functions is fascinating and attractive for materials design. Given the complexity of such a system, a simple design pathway is desirable. Here, we argue that associative phase separation of oppositely charged conjugated polyelectrolytes (CPEs) can provide such a path in an environmentally benign medium: water. We find that complexation between an exciton–donor and acceptor CPE leads to formation of a complex fluid. We interrogate exciton transfer from the donor to the acceptor CPE within the complex fluid and find that transfer is highly efficient. We also find that excess molecular ions can tune the modulus of the inter-CPE complex fluid. Even at high ion concentrations, CPEs remain complexed with significantly delocalized electronic wavefunctions. In conclusion, our work lays the rational foundation for complex, tunable aqueous light-harvesting systems via the intrinsic thermodynamics of associative phase separation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Anion-tethered Single Lithium-ion Conducting Polyelectrolytes through UV-induced Free Radical Polymerization for Improved Morphological Stability of Lithium Metal Anodes
Single Li + ion conducting polyelectrolytes (SICs), which feature covalently tethered counter-anions along their backbone, have the potential to mitigate dendrite formation by reducing concentration polarization and preventing salt depletion. However, due to their low ionic conductivity and complicated synthetic procedure, the successful validation of these claimed advantages in lithium metal (Li 0 ) anode batteries remains limited. In this study, we fabricated a SIC electrolyte using a single-step UV polymerization approach. The resulting electrolyte exhibited a high Li + transference number (t + ) of 0.85 and demonstrated good Li + conductivity (6.3×10 -5 S/cm at room temperature), which is comparable to that of a benchmark dual ion conductor (DIC, 9.1×10 -5 S/cm). Benefitting from the high transference number of SIC, it displayed a three-fold higher critical current density (2.4 mA/cm 2 ) compared to DIC (0.8 mA/cm 2 ) by successfully suppressing concentration polarization-induced short-circuiting. Additionally, the t + significantly influenced the deposition behavior of Li 0 , with SIC yielding a uniform, compact, and mosaic-like morphology, while the low t + DIC resulted in a porous morphology with Li 0 whiskers. In conclusion, using the SIC electrolyte, Li 0 ||LiFePO 4 cells exhibited stable operation for 4500 cycles with 70.5 % capacity retention at 22 °C.
25 ENERGY STORAGE↗
Synergistic foam stabilization and transport improvement in simulated fractures with polyelectrolyte complex nanoparticles: Microscale observation using laser etched glass micromodels
Inaccessibility to direct pore scale observation in hydrocarbon recovery of tight shale formations poses a great challenge to water-energy nexus initiatives and necessitates the use of high throughput technologies to emulate environmentally friendly processes. Herein, we employ a precise glass micromodel fabrication and visualization method to isolate the supercritical CO 2 bubbles surrounded by CO 2 -water lamella prepared in saline produced water stabilized with molecular complexation of zwitterionic surfactants (ZS) and polyelectrolyte complex nanoparticles (PECNP). The Selective Laser Enhanced Etching (SLE) technique was selected for micromodel simulation of high-pressure flow. Two representative designs, (1) fracture/micro-crack network 28 and (2) fracture/matrix were etched on fused silica glass with a laser printing machine and scCO 2 foam was injected to study the foamability, propagation, stability, and fluid loss properties. The highly monodispersed and uniformly distributed array of scCO 2 bubbles were detected in flow of scCO 2 foam in highly saline brine containing ionic complexes of positively charged PECNPs and ZS, whereas foam flow with the lamella containing ZS in fractures offered a noticeably large and polydisperse array of scCO 2 bubbles. scCO 2 bubble motion and deformation were traced, and local description of foam flow was visually examined. The confined array of scCO 2 bubbles stabilized by ZS in microcracks was affected by bubble growth and coalescence, whereas the super-populated array of monodispersed scC O2 bubbles with lamella containing complexes of PECNP and ZS were able to fill the channels with stable configurations within the timeframe of comparative stability measurements. The ability of complex fluid to prevent the formation damage was evaluated through fluid loss visualization in micromodels. Probing scCO 2 foam transport in homogenous porous media revealed smaller volume leak-off for scCO 2 foam containing PECNP-ZS ionic complexes.
04 OIL SHALES AND TAR SANDS↗
A reactive electrochemomechanical theory for growth and remodeling of polyelectrolyte hydrogels and application to dynamic polymerization of $\text{DNA}$ hydrogels
Here this study develops a framework for growth and remodeling of active polyelectrolyte hydrogels that accounts for effects of compositional changes on the mechanical response. By developing a reactive electrochemomechanical theory, thermodynamical constraints upon reactive and remodeling processes are elucidated within a general framework that allows any number of chemical reactions to evolve the response of the gel and transfer mass and charge between constituents. Fully coupled, nonlinear constitutive relations are adopted for molar fluxes, allowing exploration of effects including cross-diffusion, electrophoresis, and electro-osmosis. A robust finite element implementation is developed in the open source FEBio software (febio.org) by exploiting an equivalence between electrochemomechanics and mixture theory. The implementation is verified against analytical solutions for free swelling, and a proper reduction to a prior chemomechanical theory is demonstrated for neutral gels swollen only by a solvent with no solutes. The theory and implementation are then applied to model the tunable large swelling achieved through dynamic polymerization of DNA crosslinkers seen in our recently developed experimental hydrogel system (Cangialosi et al., 2017). A novel constitutive model for reaction-driven evolution of the locking stretch λ L in a non-Gaussian mechanical free energy was developed, where the increasing concentration of DNA crosslinkers makes further swelling energetically favorable. With a single free parameter, excellent agreement was found between measured and predicted equilibrium swelling ratios. This study demonstrated the ability to extend the electrochemomechanical framework to include chemical reactions and composition-aware constitutive models, and showed that development of reactive models allows simulation of complex dynamic polymerization phenomena not treated before. The theoretical frame here can be further expanded in scope to incorporate additional non-ideal and nonlinear phenomena.
42 ENGINEERING↗
Overlap Concentration in Salt-Free Polyelectrolyte Solutions
For strongly charged polyelectrolytes in salt-free solutions, we use molecular dynamics simulations of a coarse-grained bead-spring model to calculate overlap concentrations c* and chain structure for polymers containing N = 10 to 1600 monomers. Over much of this range, we find that the end-to-end distance R* at c* increases faster than linearly with increasing N, as chains at the overlap concentration approach strongly extended conformations. This trend results in the overlap concentration c* decreasing as a stronger function of N than the classical prediction c* ~ N –2 . Finally, this stronger dependence can be fit either by a logarithmic correction to scaling or by an apparent scaling c* ~ N –m , with m > 2.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Computational Insights into the Salt-Induced Modulation of Electron Transporting Conjugated Polyelectrolytes
The morphological and electronic properties of conjugated polyelectrolytes (CPEs) are highly sensitive to their ionic environment and remain poorly understood. To elucidate structure–property relationships in CPEs, we investigate the role of salt concentration on CPE morphology and hole conductivity using a quantum mechanically informed coarse-grained (CG) model coupled with semiclassical rate theory. Under good solvent conditions, high salt concentration induces torsional disorder along the conjugated backbone, decreasing hole delocalization. In contrast, under poor solvent conditions, high salt concentration promotes CPE aggregation, leading to thicker fibers and increased hole mobilities. Collectively, this work characterizes the competing interactions governing CPE assembly and hole transport as a function of salt concentration, highlighting ion engineering as a powerful strategy for tailoring the properties of mixed-conducting polymers.
diseases↗
Block Polyelectrolyte Additives That Modulate the Viscoelasticity and Enhance the Printability of Gelatin Inks at Physiological Temperatures
We demonstrate the utility of block polyelectrolyte (bPE) additives to enhance viscosity and resolve challenges with the three-dimensional (3D) printability of extrusion-based biopolymer inks. The addition of oppositely charged bPEs to solutions of photocurable gelatin methacryloyl (GelMA) results in complexation-driven self-assembly of the bPEs, leading to GelMA/bPE inks that are printable at physiological temperatures, representing stark improvements over GelMA inks that suffer from low viscosity at 37 °C, leading to low printability and poor structural stability. The hierarchical microstructure of the self-assemblies (either jammed micelles or 3D networks) formed by the oppositely charged bPEs, confirmed by small-angle X-ray scattering, is attributed to the enhancements in the shear strength and printability of the GelMA/bPE inks. Varying bPE concentration in the inks is shown to enable tunability of the rheological properties to meet the criteria of pre- and postextrusion flow characteristics for 3D printing, including prominent yielding behavior, strong shear thinning, and rapid recovery upon flow cessation. Moreover, the bPE self-assemblies also contribute to the robustness of the photo-cross-linked hydrogels; photo-cross-linked GelMA/bPE hydrogels are shown to exhibit higher shear strength than photo-cross-linked GelMA hydrogels. Last, the assessment of the printability of GelMA/bPE inks indicates excellent printing performance, including minimal swelling postextrusion, satisfactory retention of the filament shape upon deposition, and satisfactory shape fidelity of the various printed constructs. We envision this study to serve as a practical guide for the printing of bespoke extrusion inks where bPEs are used as scaffolds and viscosity enhancers that can be emulated in a range of photocurable precursors.
36 MATERIALS SCIENCE↗
Antielectrophoretic Response-Driven Bending–Tilting Deformation of Cationic Polyelectrolyte Brushes Drives Nonlinear Electroosmotic Transport in Brush-Grafted Nanochannels
In this paper, we use all-atom molecular dynamics (MD) simulations to describe a non-linearly enhanced electroosmotic (EOS) flow, where, in a nanochannel grafted with cationic PMETAC ([Poly(2-(Methacryloyloxy)Ethyl) Trimethylammonium Chloride]) brushes, a two-fold increase in the electric field strength leads to a several-fold (more than two-fold) increase in the EOS flow strength and volume flow rate. The electric field enforces the PMETAC brushes to undergo a bending-tilting driven deformation with a significant portion of the brush layer becoming parallel to the grafting surface. In response, a substantial fraction of the counterions leave the brush layer (hence become more mobile), but instead of going into the bulk, accumulate at the brush-bulk interface, i.e., stay in proximity of the brush segments aligned parallel to the grafting surface. This creates an interesting situation, where the counterions are not completely within the brush layer, yet they fully screen the brush charges. Such “freer” conditions enable the counterions to achieve very high velocity, thereby ensuring that the water solvating the counterions themselves move very fast triggering the significantly augmented EOS transport. Probing deeper we can identify that the bending-tilting driven brush deformation, enforcing the brushes to align parallel to the substrate, results from the anti-electrophoretic behavior of the brushes, where despite being positively charged, the brushes move against the electric field direction. Such an anti-electrophoretic behavior of the PE brushes, which has not been reported before, can be associated with the very fast velocities of the negatively charged counterions and the electrostatic and hydrodynamic coupling of the counterions with the positive functional groups of the brushes. Here, we anticipate that the findings of this paper will shed light on strategies for nanochannel flow, the anti-electrophoretic response of charged polymer chains, and the significance of capturing the detailed chemical architecture of polyelectrolytes in nanoscale science and engineering.
36 MATERIALS SCIENCE↗
Overscreening, Coion-Dominated Electroosmosis, and Electric Field Strength Mediated Flow Reversal in Polyelectrolyte Brush Functionalized Nanochannels
Controlling the direction and strength of nanofluidic electrohydrodyanmic transport in the presence of an externally applied electric field is extremely important in a number of nanotechnological applications. Here, we employ all-atom molecular dynamics simulations to discover the possibility of changing the direction of electroosmotic (EOS) liquid flows by merely changing the electric field strength in a nanochannel functionalized with polyelectrolyte (PE) brushes. In exploring this, we have uncovered three facets of nanoconfined PE brush behavior and resulting EOS transport. First, we identify the onset of an overscreening effect: such overscreening refers to the presence of more counterions (Na + ) within the brush layer than needed to neutralize the negative brush charges. Accordingly, as a consequence of the overscreening, in the bulk liquid outside the brush layer, there is a greater number of co-ions (Cl – ) than counterions in the presence of an added salt (NaCl). Second, this specific ion distribution ensures that the overall EOS flow is along the direction of motion of the co-ions. Such co-ion-dictated EOS transport directly contradicts the notion that EOS flow is always dictated by the motion of the counterions. Finally, for large-enough electric fields, the brush height reduces significantly, causing some of the excess overscreening-inducing counterions to squeeze out of the PE brush layer into the brush-free bulk. As a result, the overscreening effect disappears and the number of co-ions and counterions outside the PE brush layer become similar. Despite that there is an EOS transport, this EOS transport, unlike the standard EOS transport that occurs due to the imbalance of the co-ions and counterions, occurs since a larger residence time of the water molecules in the first solvation shell of the counterions (Na + ) ensures a water transport in the direction of motion of the counterions. In this work, the net effect is the reversal of the direction of the EOS transport by merely changing the strength of the electric field.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Simultaneous Energy Generation and Flow Enhancement (Electroslippage Effect) in Polyelectrolyte Brush Functionalized Nanochannels
Energy generation through nanofluidics is a topic of great nanotechnological relevance. In this work, we conduct all-atom molecular dynamics (MD) simulations of the transport of water and ions in a pressure-driven flow in nanochannels grafted with charged polyelectrolyte (PE) brushes and discover the possibility of simultaneous electrokinetic energy generation and flow enhancement (henceforth denoted as the electroslippage effect). Such PE-brush-functionalized nanochannels have been recently shown to demonstrate an overscreening (OS) effect (characterized by the presence of a greater number of screening counterions within the PE brush layer than needed to screen the PE brush charges), a consequent presence of excess coions within the PE brush-free bulk, and a coion-driven electroosmotic (EOS) transport in the presence of small to moderate applied axial electric fields. Here, however, we find that the streaming current, which represents the current generated by the flow-driven downstream advection of the charge imbalance present within the electric double layer (EDL) that screen the PE brush charges, is governed by the migration of the counterions. This stems from the fact that the highest contribution to the overall streaming current arises from the region near the PE brush-water interface (where there is an excess of counterions), while the brush-free bulk yields a hitherto unreported, but small, coion-dictated streaming current. This downstream advection of the charge imbalance (and the resultant counterion-driven streaming current) eventually leads to the development of an electric field (streaming electric field) in the direction that is opposite to the direction of the counterion-driven streaming current. The streaming current and the streaming electric field interact to generate the electrokinetic energy. Equally importantly, this streaming electric field induces an EOS transport, which becomes coion-driven, due to the presence of excess coions in the brush-free bulk. For the case of nanochannels grafted with negatively charged PE brushes, the streaming electric field will be in a direction that is opposite to the pressure-driven transport, and hence the coion (or anion) driven EOS flow, will be in the same direction as the pressure-driven transport. On the other hand, for the case of nanochannels grafted with positively charged PE brushes, the streaming electric field will be in the same direction as the pressure-driven flow, and hence the coion (or cation) driven EOS flow, will again be in the same direction as the pressure-driven flow. Therefore, whenever there occurs the presence of the OS and the resulting coion-driven EOS transport in PE brush grafted nanochannels, regardless of the sign of the charges of the PE brushes, this EOS transport will always aid the pressure-driven transport and will cause the most fascinating increase in the net volume flow rate across the nanochannel cross section, which is the electroslippage effect.
overscreening↗
Structure–Transport Properties Governing the Interplay in Humidity-Dependent Mixed Ionic and Electronic Conduction of Conjugated Polyelectrolytes
Polymeric mixed ionic-electronic conductors (MIECs) are of broad interest in the field of energy storage and conversion, opto-electronics, and bioelectronics. A class of polymeric MIECs are conjugated polyelectrolytes (CPEs), which possess a p-conjugated backbone imparting electronic transport characteristics along with side chains comprised of a pendant ionic group to allow for ionic transport. Here, our study focuses on the humidity-dependent structure-transport properties of poly[3-(potassium-n-alkanoate) thiophene-2,5-diyl] (P3KnT) CPEs with varied side-chain lengths of n = 4, 5, 6, and 7. UV-Vis spectroscopy along with electronic paramagnetic resonance (EPR) spectroscopy reveal the infiltration of water leads to a hydrated, self-doped state that allows for electronic transport. The resulting humidity-dependent ionic conductivity (σ i ) of the thin films shows a monotonic increase with relative humidity (RH) while electronic conductivity (σ e ) follows a nonmonotonic profile. The values of σ e continue to rise with increasing RH reaching a local maximum after which σ e begins to decrease. P3KnTs with higher n values demonstrate greater resiliency to increasing RH before suffering decrease in σ e . This drop in σ e is attributed to two factors. First, disruption of the locally-ordered π-stacked domains observed through in situ humidity-dependent grazing incidence wide angle X-ray scattering (GIWAXS) experiments can account for some of the decrease in σ e . A second and more dominant factor is attributed to the swelling of the amorphous domains where electronic transport pathways connecting ordered domains are impeded. P3K7T is most resilient to swelling (based on ellipsometry and water uptake measurements) where sufficient hydration allows for high σ i (1.0 × 10 -1 S/cm at 95% RH) while not substantially disrupting σ e (1.7 × 10 -2 S/cm at 85% RH and 8.0 × 10 -3 S/cm at 95% RH). Overall, our study highlights the complexity of balancing electronic and ionic transport in hydrated CPEs.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Highly stretchable ionically crosslinked acrylate elastomers inspired by polyelectrolyte complexes
Dynamic bonds are a powerful approach to tailor the mechanical properties of elastomers and introduce shape-memory, self-healing, and recyclability. Among the library of dynamic crosslinks, electrostatic interactions among oppositely charged ions have been shown to enable tough and resilient elastomers and hydrogels. In this work, we investigate the mechanical properties of ionically crosslinked ethyl acrylate-based elastomers assembled from oppositely charged copolymers. Using both infrared and Raman spectroscopy, we confirm that ionic interactions are established among polymer chains. We find that the glass transition temperature of the complex is in between the two individual copolymers, while the complex demonstrates higher stiffness and more recovery, indicating that ionic bonds can strengthen and enhance recovery of these elastomers. We compare cycles to increasing strain levels at different strain rates, and hypothesize that at fast strain rates ionic bonds dynamically break and reform while entanglements do not have time to slip, and at slow strain rates ionic interactions are disrupted and these entanglements slip significantly. Further, we show that a higher ionic to neutral monomer ratio can increase the stiffness, but its effect on recovery is minimal. Lastly, taking advantage of the versatility of acrylates, ethyl acrylate is replaced with the more hydrophilic 2-hydroxyethyl acrylate, and the latter is shown to exhibit better recovery and self-healing at a cost of stiffness and strength. The design principles uncovered for these easy-to-manufacture polyelectrolyte complex-inspired bulk materials can be broadly applied to tailor elastomer stiffness, strength, inelastic recovery, and self-healing for various applications.
36 MATERIALS SCIENCE↗
Peeling back the layers: Investigating the effects of polyelectrolyte layering on surface structure and stability of oil-in-water nanoemulsions
Layer-by-layer deposition of polyelectrolytes is a useful technique for modifying surface functionalities. For drug delivery systems, alternating layers of biopolymers coat nanoemulsions, which house and protect the cargo until the time and destination of delivery. In this report we investigate molecular factors contributing to the stability and interfacial properties of nanoemulsions prepared by a co-adsorption of polymers poly(styrene sulfonate) and polyethylenimine (PEI), and surfactant dodecyltrimethylammonium bromide. We hypothesize the interplay between electrosteric and hydrophobic effects upon multi-polymer co-adsorption contributes to both macroscopic and molecular-level interfacial properties of nanoemulsions. To probe interfacial layering properties, we use vibrational sum frequency scattering spectroscopy with ζ -potential measurements to determine the adsorptive behavior and molecular conformational arrangement of the polymer layers. Complementing these interfacial studies are dynamic light scattering experiments measuring the nanoemulsion size distribution and polydispersity index over a 30-day period. Our light scattering, ζ -potential, and spectroscopic results of the nanoemulsion surface show that the duration of droplet stability and the degree of molecular orientation of adsorbed polymers can be tuned by surfactant concentration, PEI concentration, and pH. These results illustrate how molecular surface properties of multi-polymer coated nanoemulsions contribute to synergistic effects and droplet stability, enabling advancements in applications surrounding biopharmaceuticals, cosmetics, and food sciences.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Thermoosmotic Transport in Nanochannels Grafted with pH-responsive Polyelectrolyte Brushes Modelled Using Augmented Strong Stretching Theory
In this paper, we develop a theory to establish that the thermoosmotic (TOS) effects, induced by the application of an axial temperature gradient, leads to a massive enhancement in liquid transport in nanochannels grafted with charged polyelectrolyte (PE) brushes. Here, we quantify the TOS transport by quantifying the induced electric field and the induced TOS flow field. The different components of the electric field, namely the ionic component, the thermal component, and the osmotic component, as well as the contributions of different ions to these components, are quantified. Furthermore, we express the TOS velocity as a combination of chemiosmotic (COS), thermal, and electroosmotic (EOS) components. The COS and the thermal components augment each other and the overall strength and direction of the TOS flow are dictated by the direction and the relative strength of the EOS component. Most importantly, we compare the cases of brush-grafted nanochannels with those of the brush-free nanochannels of identical surface charge densities: the TOS transport is massively augmented in the brush-grafted nanochannels attributed to the combination of the localization of the EDL (and hence any body force that depends on the EDL charge density) away from the nanochannel wall (i.e., the location of the maximum drag force) and the presence of a possible molecular slip (experienced by the liquid) along the brush surface.
42 ENGINEERING↗
Specific Ion and Electric Field Controlled Diverse Ion Distribution and Electroosmotic Transport in a Polyelectrolyte Brush Grafted Nanochannel
Controlling ion distribution inside a charged nanochannel is central to using such channels in diverse applications. Here, we show the possibility of using a charged polyelectrolyte (PE) brush grafted nanochannel for triggering diverse nanoscopic ion distribution and nanofluidic electroosmotic transport by controlling the valence and size of the counterions (that screen the charges of the PE brushes) and the strength of an externally applied axial electric field. We atomistically simulate separate cases of fully charged Polyacrylic acid (PAA) brush functionalized nanochannels with Na + , Cs + , Ca 2+ , Ba 2+ , and Y 3+ counterions screening the PE charges. Four key findings emerge from our simulations. First, we find that the counterions with a greater valence and a smaller size prefer to remain localized inside the brush layer. Second, for the case where there is an added chloride salt with the same cation (as the screening counterions), there are more coions (Cl - ions) in the brush-free bulk than counterions (for counterions Na + , Ca 2+ , Ba 2+ , Y 3+ ): this is a manifestation of the overscreening (OS) of the PE brush layer. Contrastingly, the number of Cs + ions remain higher than the Cl - ions inside the brush-free bulk, ensuring that there is no OS effect for this case. Third, large applied electric field enables a few Na + , Cs + , and Ba 2+ counterions to leave the brush layer and to go to the bulk: this makes the OS of the PE brush layer disappear for the cases of PE brushes being screened by the Na+ and Ba 2+ ions. On the other hand, no such electric-field-mediated disappearance of OS is observed for the cases of Ca 2+ and Y 3+ screening counterions; we attribute this to the firm attachment of these counterions to the negatively charged monomers. Free energy associated to a counterion binding to a PE chain corroborates this diversity in the counterion-specific response to the applied electric field. Lastly, we demonstrate that such diverse ion distributions, along with specific electric-field-strength-dependent ion properties, lead to (1) EOS transport in nanochannels grafted with PAA brushes screened with Cs + ions to be always counterion dominated, (2) EOS transport in nanochannels grafted with PAA brushes screened with Ca 2+ and Y 3+ ions to be always coion dominated, and (3) EOS transport in nanochannels grafted with PAA brushes screened with Na + and Ba 2+ ions to be coion dominated for smaller electric fields and counterion dominated for larger electric fields.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗