Fluid Density Functional Theory Research Articles

Determination of Interfacial Mixing in Tapered Block Polymer Thin Films: Experimental and Theoretical Investigations

Tapered block polymers are an emerging class of macromolecules with unique and diverse self-assembly behavior and properties. Herein, we directly examine the manipulation of self-assembled interfaces in poly(isoprene-b-styrene) (I-S)-based block polymers (BPs) by synthesizing non-tapered (I-S), normal tapered (I-IS-S), and inverse tapered (I-SI-S) BPs with controlled monomer segment distributions. We provide the first direct measurements of interfacial mixing for these tapered polymers through X-ray reflectivity (XRR). The density profiles from XRR are compared to results from fluids density functional theory (fDFT) with good agreement. We find that our normal tapered BPs (30 vol % tapering) have similar interfacial mixing to diblock polymers, while our inverse tapered BPs (30 vol % tapering) have much wider interfaces. Additionally, differential scanning calorimetry (DSC) studies elucidate the influence of tapering on the glass transition temperature (Tg) and change of heat capacity (ΔCP) for each BP phase, and quantitative analysis from ΔCP also indicates enhanced mixing in the inverse tapered I-SI-S BPs. Finally, we investigate the free surface morphologies of these tapered polymers in thin film geometries. The inverse tapered BP form larger island/hole structures likely due to decreased surface elasticity from mixing as a result of the modified interblock interfacial characteristics. These results demonstrate that BPs with similar molecular weights and compositions can exhibit different thermodynamic properties and free surface morphologies in thin film geometries, as influenced by monomer sequence.

A reference-modified density functional theory: An application to solvation free-energy calculations for a Lennard-Jones solution.

In the conventional classical density functional theory (DFT) for simple fluids, an ideal gas is usually chosen as the reference system because there is a one-to-one correspondence between the external field and the density distribution function, and the exact intrinsic free-energy functional is available for the ideal gas. In this case, the second-order density functional Taylor series expansion of the excess intrinsic free-energy functional provides the hypernetted-chain (HNC) approximation. Recently, it has been shown that the HNC approximation significantly overestimates the solvation free energy (SFE) for an infinitely dilute Lennard-Jones (LJ) solution, especially when the solute particles are several times larger than the solvent particles [T. Miyata and J. Thapa, Chem. Phys. Lett. 604, 122 (2014)]. In the present study, we propose a reference-modified density functional theory as a systematic approach to improve the SFE functional as well as the pair distribution functions. The second-order density functional Taylor series expansion for the excess part of the intrinsic free-energy functional in which a hard-sphere fluid is introduced as the reference system instead of an ideal gas is applied to the LJ pure and infinitely dilute solution systems and is proved to remarkably improve the drawbacks of the HNC approximation. Furthermore, the third-order density functional expansion approximation in which a factorization approximation is applied to the triplet direct correlation function is examined for the LJ systems. We also show that the third-order contribution can yield further refinements for both the pair distribution function and the excess chemical potential for the pure LJ liquids.

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.

Fluids density functional theory and initializing molecular dynamics simulations of block copolymers.

Classical, fluids density functional theory (fDFT), which can predict the equilibrium density profiles of polymeric systems, and coarse-grained molecular dynamics (MD) simulations, which are often used to show both structure and dynamics of soft materials, can be implemented using very similar bead-based polymer models. We aim to use fDFT and MD in tandem to examine the same system from these two points of view and take advantage of the different features of each methodology. Additionally, the density profiles resulting from fDFT calculations can be used to initialize the MD simulations in a close to equilibrated structure, speeding up the simulations. Here, we show how this method can be applied to study microphase separated states of both typical diblock and tapered diblock copolymers in which there is a region with a gradient in composition placed between the pure blocks. Both methods, applied at constant pressure, predict a decrease in total density as segregation strength or the length of the tapered region is increased. The predictions for the density profiles from fDFT and MD are similar across materials with a wide range of interfacial widths.

Atomistic and Molecular Effects in Electric Double Layers at High Surface Charges.

The Poisson-Boltzmann theory for electrolytes near a charged surface is known to be invalid due to unaccounted physics associated with high ion concentration regimes. To investigate this regime, fluids density functional theory (f-DFT) and molecular dynamics (MD) simulations were used to determine electric surface potential as a function of surface charge. Based on these detailed computations, for electrolytes with nonpolar solvent, the surface potential is shown to depend quadratically on the surface charge in the high charge limit. We demonstrate that modified Poisson-Boltzmann theories can model this limit if they are augmented with atomic packing densities provided by MD. However, when the solvent is a highly polar molecule, water in this case, an intermediate regime is identified in which a constant capacitance is realized. Simulation results demonstrate the mechanism underlying this regime, and for the salt water system studied here, it persists throughout the range of physically realistic surface charge densities so the potential's quadratic surface charge dependence is not obtained.

A solvation-free-energy functional: a reference-modified density functional formulation.

The three-dimensional reference interaction site model (3D-RISM) theory, which is one of the most applicable integral equation theories for molecular liquids, overestimates the absolute values of solvation-free-energy (SFE) for large solute molecules in water. To improve the free-energy density functional for the SFE of solute molecules, we propose a reference-modified density functional theory (RMDFT) that is a general theoretical approach to construct the free-energy density functional systematically. In the RMDFT formulation, hard-sphere (HS) fluids are introduced as the reference system instead of an ideal polyatomic molecular gas, which has been regarded as the appropriate reference system of the interaction-site-model density functional theory for polyatomic molecular fluids. We show that using RMDFT with a reference HS system can significantly improve the absolute values of the SFE for a set of neutral amino acid side-chain analogues as well as for 504 small organic molecules.

Restoring the consistency with the contact density theorem of a classical density functional theory of ions at a planar electrical double layer.

Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991)PLRAAN1050-294710.1103/PhysRevA.44.5025] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993)JCPSA60021-960610.1063/1.464569], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied.

Species separation of binary colloidal mixtures in the multi-Gauss potential: Effect of depletion

For the asymmetrical colloidal mixture subject to a confining potential and an external multi-Gauss potential, the separation of species is studied based on the classical density functional theory of simple fluids. The multi-Gauss potential consists of several Gauss barriers, which are distributed along the axial direction with uniform distance. The barrier width, barrier distance, and barrier height are individually adjusted to investigate their effects on the species separation. From the numerical results, it is concluded that in each condition, the competition between the external potential and the depletion potential determines the phase equilibrium and the separation. Species separation appears only in the region where the depletion is dominant. On the contrary, both species are absent in the regions where the external potential takes the absolute advantage.

Reactivity dynamics of a confined molecule in presence of an external magnetic field

Reactivity dynamics and stability of a confined hydrogen molecule in presence of an external magnetic field has been studied using quantum fluid density functional theory. Dynamic profiles of various reactivity parameters such as hardness, electrophilicity, magnetizability, phase volume, entropy, etc. have been studied within a confined environment. Responses in the reactivity parameters as well as the associated electronic structure principles validate the stability of the confined H2 molecule in ground and excited states in presence of an external magnetic field. Confinement to the system has been imposed by the Dirichlet type boundary condition. Confinement and excitation act in opposite directions. Ground state type dynamics is obtained on simultaneous electronic excitation and confinement. © 2014 Wiley Periodicals, Inc.

Physical adsorption characterization of nanoporous materials: progress and challenges

Within the last two decades major progress has been achieved in understanding the adsorption and phase behavior of fluids in ordered nanoporous materials and in the development of advanced approaches based on statistical mechanics such as molecular simulation and density functional theory (DFT) of inhomogeneous fluids. This progress, coupled with the availability of high resolution experimental procedures for the adsorption of various subcritical fluids, has led to advances in the structural characterization by physical adsorption. It was demonstrated that the application of DFT based methods on high resolution experimental adsorption isotherms provides a much more accurate and comprehensive pore size analysis compared to classical, macroscopic methods. This article discusses important aspects of major underlying mechanisms associated with adsorption, pore condensation and hysteresis behavior in nanoporous solids. We discuss selected examples of state-of-the-art pore size characterization and also reflect briefly on the existing challenges in physical adsorption characterization.

Comparison of Molecular and Primitive Solvent Models for Electrical Double Layers in Nanochannels.

In a recent article (Lee et al. J. Comput. Theor. Chem., 2012, 8, 2012-2022.), it was shown that an electrolyte solution can be modeled in molecular dynamics (MD) simulations using a uniform dielectric constant in place of a polar solvent to validate Fluid Density Functional Theory (f-DFT) simulations. This technique can be viewed as a coarse-grained approximation of the polar solvent and reduces computational cost by an order of magnitude. However, the consequences of replacing the polar solvent with an effective permittivity are not well characterized, despite its common usage in f-DFT, Monte Carlo simulation, and Poisson-Boltzmann theory. In this paper, we have examined two solvent models of different fidelities with MD simulation of nanochannels. We find that the models produce qualitatively similar ion density profiles, but physical quantities such as electric field, electric potential, and capacitance differ by over an order of magnitude. In all cases, the bulk is explicitly modeled so that surface properties can be evaluated relative to a reference state. Moreover, quantities that define the reference state, such as bulk ion density, bulk solvent density, applied electric field, and temperature, are measurable, so cases with the same thermodynamic state can be compared. Insights into the solvent arrangement, most of which can not be determined from the coarse-grained model, are drawn from the model with an explicitly described polar solvent.

Triplet correlations and bridge functions in classical density functional theory for liquid water

Density functional theory for molecular fluids developed by Donley et al. (J. Chem. Phys. 101 (1994) 3205) is extended to include the effects of orientation-dependent bridge functions associated with the inter-particle, triplet correlations. Resultant integral equations for the pair and direct correlation functions are solved for water, where the three-body direct correlation functions are approximated in terms of two-body functions. A test calculation employing a simple Gaussian form for the two-body function between the oxygen sites then provides a promising result to improve the description of the oxygen–oxygen correlations in liquid water at room temperature.

Density dynamics in some quantum systems

The quantum domain behavior of classical nonintegrable systems is well-understood by the implementation of quantum fluid dynamics and quantum theory of motion. These approaches properly explain the quantum analogs of the classical Kolmogorov–Arnold–Moser type transitions from regular to chaotic domain in different anharmonic oscillators. Field-induced tunneling and chaotic ionization in Rydberg atoms are also analyzed with the help of these theories. Quantum fluid density functional theory may be used to understand different time-dependent processes like ion-atom/molecule collisions, atom-field interactions, and so forth. Regioselectivity as well as confined atomic/molecular systems and their reactivity dynamics have also been explained. © 2013 Wiley Periodicals, Inc.

Ion Correlations in Nanofluidic Channels: Effects of Ion Size, Valence, and Concentration on Voltage- and Pressure-Driven Currents

The effects of ion-ion and ion-wall correlations in nanochannels are explored, specifically how they influence voltage- and pressure-driven currents and pressure-to-voltage energy conversion. Cations of different diameters (0.15, 0.3, and 0.9 nm) and different valences (+1, +2, and +3) at concentrations ranging from 10(-6) M to 1 M are considered in 50-nm- and 100-nm-wide nanoslits with wall surface charges ranging from 0 C/m(2) to -0.3 C/m(2). These parameters are typical of nanofluidic devices. Ion correlations have significant effects on device properties over large parts of this parameter space. These effects are the result of ion layering (oscillatory concentration profiles) for large monovalent cations and charge inversion (more cations in the first layer near the wall than necessary to neutralize the surface charge) for the multivalent cations. The ions were modeled as charged, hard spheres using density functional theory of fluids, and current was computed with the Navier-Stokes equations with two different no-slip conditions.

Molecular reactivity dynamics in a confined environment

Time evolution of various reactivity parameters viz. hardness, electrophilicity, chemical potential, polarizability, etc. in a confined environment has been studied through quantum fluid density functional theory formalism during time dependent processes such as proton-molecule collisions and molecule-field interaction. A Dirichlet type boundary condition has been incorporated to confine the systems. Responses in the reactivity parameters of the diatomic molecules, in the dynamical context, in ground state as well as in excited state, have been reported. Harmonic spectra are generated in the cases of the external laser field interacting with H2 and N2 molecules.

Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic interactions: derivation and numerical experiments

Starting from the Kramers equation for the phase-space dynamics of the N-body probability distribution, we derive a dynamical density functional theory (DDFT) for colloidal fluids including the effects of inertia and hydrodynamic interactions (HI). We compare the resulting theory to extensive Langevin dynamics simulations for both hard rod systems and three-dimensional hard sphere systems with radially symmetric external potentials. As well as demonstrating the accuracy of the new DDFT, by comparing with previous DDFTs which neglect inertia, HI, or both, we also scrutinize the significance of including these effects. Close to local equilibrium we derive a continuum equation from the microscopic dynamics which is a generalized Navier–Stokes-like equation with additional non-local terms governing the effects of HI. For the overdamped limit we recover analogues of existing configuration-space DDFTs but with a novel diffusion tensor.

Density functional theory for inhomogeneous ring polymeric fluids

The modeling of ring polymers remains a challenge in classical density functional theory (DFT) due to the difficulty in solving the direct bond connectivity of the ring architecture without free ends. By considering the feature that all of the segments in a ring are equivalent, we give an algorithm to solve the integral of direct bond connectivity for ideal ring polymers, and therefore propose a DFT for inhomogeneous ring polymers, where the excess free energy functional is extended from an equation of state (EOS). This EOS exhibits better agreement than other EOSs for the compressibility factors, compared to Monte Carlo data. Importantly, the DFT satisfactorily reproduces the data of the configurational-bias Monte Carlo (CBMC) simulations for ring polymers. The local density profiles from the DFT show that the bead density of inhomogeneous ring fluids is independent of ring size, which is also confirmed by the CBMC simulations. Interestingly, the behavior of solvation force for ring polymers is quite similar to that of the polymers with infinite chain length.

Fourier space approach to the classical density functional theory for multi-Yukawa and square-well fluids

We present a Fourier space density functional approach for hard particles with attractive interactions, which is based on a previously developed two-dimensional approach [S. Hlushak, W. Rżysko, and S. Sokołowski, J. Chem. Phys. 131, 094904 (2009)] for hard-sphere chains. The interactions are incorporated by means of a three-dimensional Fourier image of the direct correlation function that is obtained from the first-order mean-spherical approximation. In order to improve the computational efficiency, we make extensive use of fast Fourier transforms for calculating density convolution integrals. A two-dimensional implementation of the new density functional approach, based on the expansion of the functional around the bulk fluid density, is used to study structure and adsorption of two model fluids in narrow cylindrical pores. We also investigate two methods that improve the accuracy of the theory as compared to the conventional DFT approach, which expands the free energy functional around the bulk fluid density: One a variant of the reference fluid density functional theory used by Gillespie et al. [Phys. Rev. E 68, 031503 (2003)], and the second a weighted density approach with energy route thermodynamics. Results from these two methods are compared to the conventional approach and also to the results of Monte Carlo simulations. We find that the method of Gillespie et al. and the weighted density approach with energy route thermodynamics yield significant improvement over the conventional approach.

Scalar fundamental measure theory for hard spheres in three dimensions: Application to hydrophobic solvation

Hard-sphere mixtures provide one a solvable reference system that can be used to improve the density functional theory of realistic molecular fluids. We show how the Kierlik-Rosinberg's scalar version of the fundamental measure density functional theory of hard spheres [E. Kierlik and M. L. Rosinberg, Phys. Rev. A 42, 3382 (1990)], which presents computational advantages with respect to the original Rosenfeld's vectorial formulation or its extensions, can be implemented and minimized in three dimensions to describe fluid mixtures in complex environments. This implementation is used as a basis for defining a molecular density functional theory of water around molecular hydrophobic solutes of arbitrary shape.