Polymer Density Functional Theory Research Articles

Phase behavior of ionic fluid in charged confinement: An associating polymer density functional theory study

AbstractWith the rapid advancement of the new energy industry, porous electrode materials and complex electrolytes have gained widespread usage. Electrolytes exhibit distinctive phase behavior when subjected to the combined influence of confined space and electric fields. However, the measurement and prediction of such phase behavior encounter significant challenges. Consequently, numerous theoretical tools have been employed to establish models for phase equilibrium calculations. Nevertheless, current research in this field has notable limitations and fails to address the confinement of space or complex polymer electrolytes. Considering these shortcomings, an associating polymer density functional theory (PDFT) was developed by modifying excess free energy. This study examines the phase behavior of electrolytes with various chain lengths within diverse confined slits, revealing that the confinement effect and fluid tail chains can narrow the phase diagram. Additionally, a linear correlation between the electric field strength and the phase equilibrium offset has been identified, and a quantitative relationship is derived. The results of this investigation contribute to a deeper comprehension of complex fluid phase behavior and guide the design of electrochemical devices.

Enabling High-Capacitance Supercapacitors by Polyelectrolyte Brushes.

Polyelectrolyte brushes (PEBs) hold excellent potential for designing high-capacitance electrical double-layer capacitors (EDLCs), a crucial component of supercapacitors. Both experiments and computational simulations have shown their energy-storage advantage. However, the effect of PEBs on the energy storage of EDLCs is not yet fully understood. Herein, we systematically study the energy-storage effects of polyanionic (PA) and polycationic (PC) brushes using polymer density functional theory (DFT). First, the application of polymer DFT in polyelectrolyte-grafted EDLCs is successfully validated using molecular dynamics simulations. With the help of polymer DFT, an interfacial adhesion microstructure of the PA/PC brushes is observed. Most importantly, the results show that polyelectrolyte-grafted EDLCs achieve a significant increase in capacitance at low salt concentrations and surface voltages, offering an excellent energy-storage advantage over traditional EDLCs. However, this advantage is considerably diminished at high salt concentrations or surface voltages, showing unusual salt- and voltage-dependent behaviors of energy-storage capacity. Nonetheless, the PC-grafted EDLCs maintain their outstanding energy-storage performance, even at relatively high salt concentrations and surface voltages. These findings deepen our comprehension of PEBs at the molecular level and provide insights for the molecular design of high-capacitance supercapacitors.

Interfacial microstructure of neutral and charged polymer brushes: A density functional theory study.

Polymer density functional theory (PDFT) is a computationally efficient and robust statistical mechanics theory for capturing the interfacial microstructure of grafted polymer brushes (PBs). Undoubtedly, the intramolecular and intermolecular interactions in PDFT (e.g., hard-core interactions and direct Coulomb interactions) are greatly affected by the grafting behavior of PBs. However, the combination of these interactions with the physical constraints on grafting behavior remains unclear and there is a remarkable difference in the density profile of grafted PB between PDFT and simulation. Herein, we propose a PDFT to study neutral and charged grafted PBs by incorporating the physical constraints of end-grafted PBs into the excess free energies due to intramolecular and intermolecular interactions. This PDFT has been successfully validated where the density distributions of neutral and weakly charged PBs predicted by the PDFT are in excellent agreement with the results of the Monte Carlo and molecular dynamics simulations. In addition, the significant contribution of grafting behavior to the free energy of PB systems is presented. Consequently, this work provides a powerful and accurate theoretical method to reveal the interfacial microstructure of grafted PBs.

Ising density functional theory for weak polyelectrolytes with strong coupling of ionization and intrachain correlations.

We report a theoretical framework for weak polyelectrolytes by combining the polymer density functional theory with the Ising model for charge regulation. The so-called Ising density functional theory provides an accurate description of the effects of polymer conformation on the ionization of individual segments and is able to account for both the intra- and interchain correlations due to the excluded-volume effects, chain connectivity, and electrostatic interactions. Theoretical predictions of the titration behavior and microscopic structure of ionizable polymers are found to be in excellent agreement with the experiment.

Nonmonotonic adsorption behavior of semiflexible polymers

We study the adsorption behavior of semiflexible polymer chains with finite concentrations onto a structureless, planar, and impenetrable surface using polymer density functional theory based on a discretization of the Kratky-Porod wormlike chain model. Adsorption characteristics are investigated at different attractive interactions between the surface and polymers of various intrinsic stiffnesses. We analyze the density distributions in the vicinity of the surface and find, in the adsorption regime (when the surface attraction is strong: ϵw≳ϵw c, where ϵw c is the critical surface potential of adsorption transition), a nonmonotonic adsorption behavior for polymer chains with various intrinsic stiffnesses: the adsorption amount first decreases and then increases with the intrinsic stiffness, and the minimum adsorption amount (as well as the maximum critical surface potential of adsorption transition) occurs at lp ∼ Δ (Δ and lp are the attractive range of surface potential and persistence length, respectively), while in the depletion regime (ϵw≪ϵw c), the depletion depth and range are increased monotonically with the intrinsic stiffness. Furthermore, we find βϵw c∼lp/Δ-0.185 for lp ⋗ Δ and βϵw c∼lp/Δ0.366 for lp < Δ.

Development of 3D polymer DFT and its application to molecular transport through a surfactant‐covered interface

We have developed a three‐dimensional polymer density functional theory (DFT) and applied it to predict the thermodynamic and structural information of molecular transport through a surfactant‐covered interface. The green recursive function method has been employed to consider the chain conformation effect. The reference ideal gas method has been developed, extending it from molecular DFT to polymer DFT, with a universal form to calculate thermodynamic properties such as the grand potential and free energy. We have demonstrated the accuracy of the theory by comparing it to available simulations. Furthermore, we have applied the theory to predict the free energy barrier and density profile of molecular transport through a surfactant‐covered interface. The free energy profile provides reasonable predictions of the transition velocity, while the density profile gives insight into the microstructural information of the transport process, which is consistent with the available molecular simulations. © 2017 American Institute of Chemical Engineers AIChE J, 63: 238–249, 2018

Self-Assembly of Polymeric Particles in Poiseuille Flow: A Hybrid Lattice Boltzmann/External Potential Dynamics Simulation Study

We present a hybrid simulation method which allows one to study the dynamical evolution of self-assembling (co)polymer solutions in the presence of hydrodynamic interactions. The method combines an established dynamic density functional theory for polymers that accounts for the nonlocal character of chain dynamics at the level of the Rouse model, the external potential dynamics (EPD) model, with an established Navier–Stokes solver, the Lattice Boltzmann (LB) method. We apply the method to study the self-assembly of nanoparticles and vesicles in two-dimensional copolymer solutions in a typical microchannel Poiseuille flow profile. The simulations start from fully mixed systems which are suddenly quenched below the spinodal line. In order to isolate effects caused by walls, we use a reverse Poiseuille flow geometry with periodic boundary conditions. We identify three stages of self-assembly, i.e., initial spinodal decomposition, particle nucleation, and particle growth (ripening). We find that (i) in the presence of shear the nucleation of droplets is delayed by an amount roughly proportional to the shear rate, (ii) shear flow greatly increases the rates of particle fusions, and (iii) in later stages of self-assembly stronger shear flows may induce irreversible shape transformation via finger formation, in particular in vesicle systems. The combination of these effects leads to an accumulation of particles close to the center of the Poiseuille flow profile, and the polymeric matter has a double peak distribution centered around the flow maximum.

Theoretical and Experimental Investigations of Polyelectrolyte Adsorption Dependence on Molecular Weight.

This work focuses on adsorption of polyions onto oppositely charged surfaces and on responses to the addition of a simple monovalent salt as well as to the polyion length (degree of polymerization). We also discuss possible mechanisms underlying observed differences, of the adsorbed amount on silica surfaces at high pH, between seemingly similar polyions. This involves theoretical modeling, utilizing classical polymer density functional theory (DFT). We furthermore investigate how long- and short-chain versions of the polymer adsorb onto carboxymethylated cellulose, carrying a high negative charge. Interestingly enough, comparing results obtained for the two different surfaces, we observe an opposite qualitative response for the molecular weight. The large polymer adsorbs more strongly at a silica surface, but for cellulose at low salt levels, there are indications that the trend is opposite. Another difference is the very slow adsorption process observed for cellulose, particularly with short polymers; in fact, with short polymers, we were sometimes unable to establish any adsorption plateau at all. We speculate that the slow dynamics is due to a gradual diffusion of short polymers into the cellulose matrix. This phenomenon could also explain why short-chain polymers seem to adsorb more strongly than long-chain ones, at low salt concentrations, provided that the latter then are too large to enter the cellulose pores. Cellulose swelling at high salt concentrations might diminish these differences, leading to more similar adsorbed amounts or even a lower adsorption for short chains.

Density functional theory for polymeric systems in 2D

We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim’s first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.

Density functional theory of equilibrium random copolymers: application to surface adsorption of aggregating peptides

We generalize a recently developed polymer density functional theory (PDFT) for polydisperse polymer fluids to the case of equilibrium random copolymers. We show that the generalization of the PDFT to these systems allows us to obtain a remarkable simplification compared to the monodispersed polymers. The theory is used to treat a model for protein aggregation into linear filaments in the presence of surfaces. Here we show that, for attractive surfaces, there is evidence of significant enhancement of protein aggregation. This behaviour is a consequence of a surface phase transition, which has been shown to occur with ideal equilibrium polymers in the presence of sufficiently attractive surfaces. For excluding monomers, this transition is suppressed, though an echo of the underlying ideal transition is present in the sudden change in the excess adsorption.

Theoretical Predictions of Temperature-Induced Gelation in Aqueous Dispersions Containing PEO-Grafted Particles.

In this work, we utilize classical polymer density functional theory (DFT) to study gelation in systems containing colloidal particles onto which polymers are grafted. The solution conditions are such that the corresponding bulk system displays a lower critical solution temperature (LCST). We specifically compare our predictions with experimental results by Shay et al. (J. Rheol. 2001, 45, 913-927), who investigated temperature response in aqueous dispersions containing polystyrene particles (PS), with grafted 45-mer poly(ethylene oxide) (PEO) chains. Our DFT treatment is based on a model for aqueous PEO solutions that was originally developed by Karlström for bulk solutions. In this model, monomers are assumed to be in either of two classes of states, labeled A and B, where B is more solvophobic than A. On the other hand, the degeneracy of B exceeds that of A, causing the population of solvophobic monomers to increase with temperature. In agreement with experimental findings by Shay et al., we locate gelation at temperatures considerably below TΘ, and far below the LCST for such chain lengths. This gelation occurs also without any dispersion interactions between the PS particles. Interestingly, the polymer-induced interaction free energy displays a nonmonotonic dependence on the grafting density. At high grafting densities, bridging attractions between grafted layers take place (considerably below TΘ). At low grafting densities, on the other hand, the polymers are able to bridge across to the other particle surface. Shay et al. conducted their experiments at very low ionic strength, using deionized water as a solvent. We demonstrate that even minute amounts of adsorbed charge on the surface of the particles, can lead to dramatic changes of the gelation temperature, especially at high grafting densities. Another interesting prediction is the existence of elongated (chainlike) equilibrium structures, at low particle concentrations. We emphasize that our model does not rely upon any temperature-dependent interactions.

Theoretical predictions of structures in dispersions containing charged colloidal particles and non-adsorbing polymers.

We develop a theoretical model to describe structural effects on a specific system of charged colloidal polystyrene particles, upon the addition of non-adsorbing PEG polymers. This system has previously been investigated experimentally, by scattering methods, so we are able to quantitatively compare predicted structure factors with corresponding experimental data. Our aim is to construct a model that is coarse-grained enough to be computationally manageable, yet detailed enough to capture the important physics. To this end, we utilize classical polymer density functional theory, wherein all possible polymer configurations are accounted for, subject to a mean-field Boltzmann weight. We make efforts to counteract drawbacks with this mean-field approach, resulting in structural predictions that agree very well with computationally more demanding simulations. Electrostatic interactions are handled at the fully non-linear Poisson-Boltzmann level, and we demonstrate that a linearization leads to less accurate predictions. The particle charge is an experimentally unknown parameter. We define the surface charge such that the experimental and theoretical gel point at equal polymer concentration coincide. Assuming a fixed surface charge for a certain salt concentration, we find very good agreements between measured and predicted structure factors across a wide range of polymer concentrations. We also present predictions for other structural quantities, such as radial distribution functions, and cluster size distributions. Finally, we demonstrate that our model predicts the occurrence of equilibrium clusters at high polymer concentrations, but low particle volume fractions and salt levels.

Role of histidine for charge regulation of unstructured peptides at interfaces and in bulk

Histidine-rich, unstructured peptides adsorb to charged interfaces such as mineral surfaces and microbial cell membranes. At a molecular level, we investigate the adsorption mechanism as a function of pH, salt, and multivalent ions showing that (1) proton charge fluctuations are-in contrast to the majority of proteins-optimal at neutral pH, promoting electrostatic interactions with anionic surfaces through charge regulation and (2) specific zinc(II)-histidine binding competes with protons and ensures an unusually constant charge distribution over a broad pH interval. In turn, this further enhances surface adsorption. Our analysis is based on atomistic molecular dynamics simulations, coarse grained Metropolis Monte Carlo, and classical polymer density functional theory. This multiscale modeling provides a consistent picture in good agreement with experimental data on Histatin 5, an antimicrobial salivary peptide. Biological function is discussed and we suggest that charge regulation is a significant driving force for the remarkably robust activity of histidine-rich antimicrobial peptides.

Polyelectrolyte Adsorption: Electrostatic Mechanisms and Nonmonotonic Responses to Salt Addition

The main question addressed in this work is as follows: Under pure electrosorption conditions, that is, disregarding nonelectrostatic effects, how does the net adsorption of a polyelectrolyte at an oppositely charged surface respond to the addition of simple salt? Previous simulations and mean-field calculations have suggested that the polymers will desorb. However, we will demonstrate that an increased adsorption also is possible, even for pure electrosorption, at low and intermediate levels of salt. As this is a correlation-driven effect, mean field approaches will fail to capture it. Using simulations, one will in general need to simulate large systems and relatively long polymers. Also important is the presence of a proper bulk solution, with a finite and well-defined polyelectrolyte concentration. We have performed a theoretical study of polyelectrolyte adsorption, assuming screened Coulomb interactions between monomers; that is, the salt is implicit. This work focuses on the effects from ionic screening and polymer length. Specifically, the adsorption at a weakly charged colloidal particle, with a diameter of 200 nm, is monitored for various salt concentrations, in the presence of highly charged chains. Using simulations, we investigate polymers with two different degrees of polymerization: 40 and 160, respectively. These simulations are complemented by predictions from classical polymer density functional theory, utilizing a recently developed correlation-correction (Forsman, J.; Nordholm, S. Langmuir, in press). The agreement with corresponding simulations is semiquantitative, and because the calculations run many orders of magnitude faster than the simulations, longer and more realistic polymers could be studied with this approach. However, switching off the correlation-correction leads to a mean-field theory, which fails to even qualitatively reproduce the simulated response to screening.

Polydisperse Telechelic Polymers at Interfaces: Analytic Results and Density Functional Theory

We use a recently developed continuum theory to expand on an exact treatment of the interfacial properties of telechelic polymers displaying Schulz-Flory polydispersity. Our results are remarkably compact and can be derived from the properties of equilibrium, ideal polymers at interfaces. A new surface adsorption transition is identified for ideal telechelic chains, wherein the central block is an equilibrium polymer. This transition occurs in the limit of strong end adsorption. Additionally, closed expressions are derived for the ideal continuum telechelic chain in contact with two large spheres, using the Derjaguin approximation. We analyze the interactions between colloids as a function of polydispersity and molecular weight, and the results are compared with polymer density functional theory in the dilute limit. Significant variations in polymer mediated forces are observed as a function of polydispersity, molecuar weight, and chain stiffness.

Analyzing surface tension in higher alkanes and their CO2 mixtures

We have used polymer density functional theory to study the surface tension behavior of heavy hydrocarbons and their binary mixtures with CO2, for which very limited data is available in the literature. Dodecane (C12H26), tertacosane (C24H50), and hexatriacontane (C36H74), and their CO2 binary mixtures have been studied over a wide range of temperature (313–423K) and pressure (ambient to 30MPa) conditions representative of typical petroleum reservoirs. We have compared three parameterization schemes and showed that parameterization using critical constants gives surface tension results that are in very good agreement with the available experimental data. The most significant result from this study is the double crossover behavior in the surface tension of the alkane–CO2 binary mixtures, resulting from the simultaneous changes in liquid density and CO2 solubility.

Density functional theory for rod-coil polymers with different size segments

A polymer density functional theory (PDFT) for rod-coil copolymers with different size segments is proposed, in which the PDFT approach combines a modified fundamental measure theory for the excluded-volume effects, Wertheim's first-order thermodynamics perturbation theory for the chain connectivity and the mean field approximation for van der Waals attraction. First, for testing the PDFT derived, we compare the density profiles from present theory to simulation data, and find that the present theory successfully reproduces the simulation data. Therefore, we use the PDFT to further investigate the local density and solvation forces of rod-coils with different size (A(5)D(3)) and the same size (A(5)B(3)) segments. Results indicate that the excluded volume effect from the coil part determines the solvation force profiles of two rod-coil brushes at strong surface energy. In addition, owing to the vacuum effect, the weak attraction around the classical contact of the rod-coil brushes is also observed. In short, the present theory can be easily applied to the other architecture polymers containing different size segments. It is expected that the calculation results in this work could provide useful reference to select the rod-coils as stabilizer for the protection of surfaces or the colloidal stabilization.

Structure and phase behavior of a confined nanodroplet composed of the flexible chain molecules

A polymer density functional theory has been employed for investigating the structure and phase behaviors of the chain polymer, which is modelled as the tangentially connected sphere chain with an attractive interaction, inside the nanosized pores. The excess free energy of the chain polymer has been approximated as the modified fundamental measure-theory for the hard spheres, the Wertheim's first-order perturbation for the chain connectivity, and the mean-field approximation for the van der Waals contribution. For the value of the chemical potential corresponding to a stable liquid phase in the bulk system and a metastable vapor phase, the flexible chain molecules undergo the liquid-vapor transition as the pore size is reduced; the vapor is the stable phase at small volume, whereas the liquid is the stable phase at large volume. The wide liquid-vapor coexistence curve, which explains the wide range of metastable liquid-vapor states, is observed at low temperature. The increase of temperature and decrease of pore size result in a narrowing of liquid-vapor coexistence curves. The increase of chain length leads to a shift of the liquid-vapor coexistence curve towards lower values of chemical potential. The coexistence curves for the confined phase diagram are contained within the corresponding bulk liquid-vapor coexistence curve. The equilibrium capillary phase transition occurs at a higher chemical potential than in the bulk phase.

A theoretical study of colloidal forces near amphiphilic polymer brushes

Polymer-based “non-stick” coatings are promising as the next generation of effective, environmentally friendly marine antifouling systems that minimize non-specific adsorption of extracellular polymeric substances (EPS). However, design and development of such systems are impeded by the poor knowledge of polymer-mediated interactions of biomacromolecules with the protected substrate. In this work, a polymer density functional theory (DFT) is used to predict the potential of mean force between spherical biomacromolecules and amphiphilic copolymer brushes within a coarse-grained model that captures essential non-specific interactions such as the molecular excluded volume effects and the hydrophobic energies. The relevance of theoretical results for practical control of the EPS adsorption is discussed in terms of the efficiency of different brush configurations to prevent biofouling. It is shown that the most effective antifouling surface may be accomplished by a good balance of the polymer chain length and the grafting density.

Mesoscopic structure prediction of nanoparticle assembly and coassembly: Theoretical foundation

In this work, we present a theoretical framework that unifies polymer field theory and density functional theory in order to efficiently predict ordered nanostructure formation of systems having considerable complexity in terms of molecular structures and interactions. We validate our approach by comparing its predictions with previous simulation results for model systems. We illustrate the flexibility of our approach by applying it to hybrid systems composed of block copolymers and ligand coated nanoparticles. We expect that our approach will enable the treatment of multicomponent self-assembly with a level of molecular complexity that approaches experimental systems.