Self-consistent Field Analysis Research Articles

First-principles investigation of lanthanides diffusion in HCP zirconium via vacancy-mediated transport

The diffusion of lanthanide fission products plays an important role in the growth of the fuel-cladding chemical interaction (FCCI) region in metallic fuels. The use of a Zr interdiffusion barrier may mitigate the transport of lanthanides from the fuel to the cladding, but the efficacy of such a liner is not yet known. In this paper, the stability and vacancy-mediated diffusion of La, Ce, Pr, and Nd in hexagonal close-packed (HCP) Zr is investigated via density functional theory (DFT) calculations and self-consistent mean field (SCMF) analysis. DFT is used to calculate the formation, binding, and migration energies of vacancies and vacancy-solute pairs. The DFT energetics are used in the KineCluE code to calculate the Onsager transport coefficients. La is found to be the fastest diffusing species in HCP Zr and experiences an almost isotropic diffusion behavior. The other three species (Ce, Pr, and Nd) demonstrate anisotropic diffusion where the diffusion in the basal planes is significantly faster than that along the c-axis. The calculated lanthanide diffusivities in HCP Zr are fitted to an Arrhenius relation and the activation energies and prefactors are reported for the first time. Furthermore, the vacancy drag and the segregation tendencies were analyzed using the calculated off-diagonal transport coefficients. According to our vacancy-mediated diffusion model, lanthanides are expected to be enriched at vacancy sinks at low temperatures, while at high temperatures, lanthanides are depleted at sinks and will preferably diffuse into the bulk. The enrichment/depletion transition temperature depends on the diffusion direction (basal or axial) and hence will be controlled by the grain texture and orientation.

Development of a deep-learning model for phase-separation structure of diblock copolymer based on self-consistent field analysis

Self-consistent field (SCF) analysis is an indispensable tool for predicting the microphase separation structures of polymer alloys. However, the computation of the phase-separated structures in the equilibrium state is computationally intensive, leading to high costs. To address this challenge, we propose a novel deep learning approach that leverages a generative adversarial network (GAN), a powerful deep generative model, to accelerate SCF analysis. Specifically, we trained the GAN using comprehensive data obtained from SCF analysis, enabling us to generate various images of feasible structures that are similar to the SCF analysis results. Our results demonstrate that the latent variables in the GAN are linked to the physical parameters and features of the phase-separation structures.

Inverse design of polymer alloys using deep learning based on self-consistent field analysis and finite element analysis

In this study, a framework that deals with the inverse design of material structures based on macroscopic properties using deep learning models is proposed. For the framework, “polymer alloy’s phase separation structures” as material structures and “stresses” as macroscopic properties are considered. The results of self-consistent field analysis are used as structure data, in particular, the analysis result of two-dimensional phase separation structures of a diblock copolymer melt in the equilibrium state. For the stress data, the results of finite element analysis are used, in particular, the analysis results of average stresses over the system under the small-enforced-displacement condition. This framework consists of two deep learning models—one aimed at generating phase separation structures, and the other at predicting properties from structures. For the second model, we incorporate a convolutional neural network. By implementing a random search toward a model that combines these two deep learning models, we constructed the framework for the inverse design of phase separation structures that possess desired macroscopic properties. This framework is demonstrated to be able to suggest phase separation structures that realize desired stresses that are input to the framework through examples. The innovation of the method is the development of framework to propose the optimal structure of polymer alloys by using machine learning. The main novelties of this method are the construction of generative adversarial network that reproduces the phase-separation structure of polymer alloy specified by label information, realization of inverse analysis based on mechanical properties, and the simultaneous optimization of multiple mechanical properties.

Interplay of Hückel and Möbius Aromaticity in Metal-Metal Quintuple Bonded Complexes of Cr, Mo, and W with Amidinate Ligand: Ab initio DFT and Multireference Analysis*.

The aromaticity of metal-metal quintuple bonded complexes of the type M2 L2 (M=Cr, Mo, and W; L=amidinate) are studied employing gauge including magnetically induced ring current (GIMIC) analysis and electron density of delocalized bonds (EDDB). It is found that the complexes possess two types of aromaticity: i) Hückel aromaticity through delocalization of ligand π electrons with metal-metal δ-bond-forming 6 conjugated electrons (4π and 2δ) ring; ii) Craig-Möbius aromaticity through delocalization of π electrons of both the ligands with metal d-orbitals in Craig type orientation forming 10π electrons ring with a double twist. Extended transition state natural orbital chemical valence (ETS-NOCV) and canonical molecular orbital natural chemical shielding (CMO-NCS) analysis confirm the Craig-Möbius type arrangement of the orbitals. Furthermore, the unprecedented Hückel and Möbius type aromaticity is confirmed from the plot of the current pathways using 3D line integral convolution (3D-LIC) plots. The metal-metal bond order also increases down the group as justified from the complete active space self-consistent field (CASSCF) analysis. Due to an increase in the π and δ electron conjugation, both the Hückel and Möbius aromaticity increase down the group.

Self-Consistent Field Analysis of Molecular Bottle-Brushes with Primary and Secondary Side Chains: Induced Persistence Length and Lateral Thickness

Macromolecules may feature liquid crystalline behavior when the chain aspect ratio, that is the ratio between the chain persistence length and the cross-sectional thickness of its segments, is large. Scaling theory suggests that for molecular bottle-brushes under good solvent condition the induced persistence length does not depend on the chain architecture but only on the amount of segments in the side chains per unit length of the backbone. Numerical self-consistent field results are presented for macromolecular bottle-brushes with side chains of variable architecture attached at regular intervals along the backbone chain. We consider side chains (flexible “flagstaffs”), which feature one branch-point onto which secondary side chains (the “flag”) emanate. We varied the distance of this branch-point from the main chain as our tuning parameter, resembling the “raising of the flag.” For a given height of the flags, that is when the mass-distribution along a side chain is architecturally fixed, the induced persistence length is a function of the branching parameter (ratio between the length of the longest path and the total number of segments in the graft). We found that the induced persistence length and hence the chain aspect ratio, vary non-monotonically with the height of the flags. The lowest aspect ratio is found when the flag is raised to about a quarter of the full height of the flagstaff. The induced persistence length is independent of this height when upon bending the translocation of the side chains from compressed to expanded regions is artificially suppressed, which leads us to speculate that the non-monotonic behavior of aspect ratio is related to the efficiency of side chains to partly translocate themselves upon bending.

Electrostatic stiffening and induced persistence length for coassembled molecular bottlebrushes.

A self-consistent field analysis for tunable contributions to the persistence length of isolated semiflexible polymer chains including electrostatically driven coassembled deoxyribonucleic acid (DNA) bottlebrushes is presented. When a chain is charged, i.e., for polyelectrolytes, there is, in addition to an intrinsic rigidity, an electrostatic stiffening effect, because the electric double layer resists bending. For molecular bottlebrushes, there is an induced contribution due to the grafts. We explore cases beyond the classical phantom main-chain approximation and elaborate molecularly more realistic models where the backbone has a finite volume, which is necessary for treating coassembled bottlebrushes. We find that the way in which the linear charge density or the grafting density is regulated is important. Typically, the stiffening effect is reduced when there is freedom for these quantities to adapt to the curvature stresses. Electrostatically driven coassembled bottlebrushes, however, are relatively stiff because the chains have a low tendency to escape from the compressed regions and the electrostatic binding force is largest in the convex part. For coassembled bottlebrushes, the induced persistence length is a nonmonotonic function of the polymer concentration: For low polymer concentrations, the stiffening grows quadratically with coverage; for semidilute polymer concentrations, the brush chains retract and regain their Gaussian size. When doing so, they lose their induced persistence length contribution. Our results correlate well with observed physical characteristics of electrostatically driven coassembled DNA-bioengineered protein-polymer bottlebrushes.

Self-Consistent Field Analysis of Molecular Bottle-Brushes with Primary and Secondary Side Chains: Induced Persistence Length and Lateral Thickness

Self-Consistent Field Analysis of Molecular Bottle-Brushes with Primary and Secondary Side Chains: Induced Persistence Length and Lateral Thickness

Complex coacervates formed across liquid interfaces: A self-consistent field analysis

The Scheutjens–Fleer self-consistent field (SF-SCF) theory is used to study complexation between two oppositely charged polyelectrolytes across an interface formed by two solvents, here called oil and water. The focus is on the composition and the lateral stability of such interfacial coacervate. One polyelectrolyte is chosen to be oil soluble and the other one prefers water, whereas the counter and salt ions are taken to distribute ideally over all phases. There exists an electrostatic associative driving force for the formation of the coacervate phase which increases with decreasing ionic strength and may be assisted by some specific affinity between the associating units and an effective poor solvency for the coacervate. As with respect to the lateral stability an unusual wetting scenario, called pseudo-partial wetting, presents itself, which results from interactions on two different length scales. On the segmental length the screening of oil–water contacts promotes the wetting by the coacervate: a pre-wetting jump-like transition takes place off-coexistence from a microscopically thin to a mesoscopically thin film. Usually this implies complete wetting. However, the mesoscopically thin film is exposed to long-ranged attractive electrostatic interactions and therefore cannot grow to macroscopic dimensions upon approach towards coexistence. Hence the system remains partial wet. The bulk correlation length controls the thickness of the mesoscopically thin film and as a result the wetting transition occurs extremely close to the bulk critical point. We therefore expect that a thick coacervate film typically is laterally inhomogeneous: there are drops on top of a mesoscopically thin coacervate film. This conclusion qualitatively explains the experimental observation that such a coacervate film scatters visible light.

A Polymer-Brush-Based Nanovalve Controlled by Nanoparticle Additives: Design Principles.

Polymer-grafted surfaces and channels are increasingly used for the design of responsive materials and sensors due to robust performance and ease of use. Various strategies for the control of the nanoscale morphologies of such materials and devices are being tested. Entropic repulsion between the polymer chains in a grafted brush of sufficient density causes the chains to extend in the direction perpendicular to the grafting surface in comparison to the position of unattached polymers. When nanoparticles having attractive interactions with the polymers are introduced into the solvent, these nanoparticles tend to infiltrate into the brush and reduce its extension. Under certain conditions, a sharp reduction in brush height extension can occur over a narrow range of nanoparticle concentrations in solution. We describe a way of controlling transport through polymer-functionalized nanochannels with nanoparticle additives, relying on the physics of nanoparticles and polymer brushes under confinement, and we suggest a blueprint for the creation of a tunable nanovalve. The nanovalve is modeled as a cylinder with a polymer brush grafted on its inside surface. Brush properties such as the chain length and the grafting density are chosen so that the brush chains extend into the center of the cylinder in the absence of nanoparticles, occluding the flux of analyte molecules through the pore. When nanoparticles that are attracted to the polymers are introduced into solution, they infiltrate into the brush and partially collapse it against the cylindrical grafting surface, opening space in the center of the cylinder through which analyte molecules can flow. The operation of such a nanovalve is analyzed via self-consistent field theory calculations in the strong-stretching approximation. Self-consistent field analysis is supported by Langevin dynamics simulations of the underlying coarse-grained model of the polymer-nanoparticle system.

Three-dimensional reference interaction site model self-consistent field analysis of solvent and substituent effects on the absorption spectra of Brooker's merocyanine.

Solvent and substituent effects on the absorption spectra of Brooker's merocyanine (BM) are investigated using the three-dimensional reference interaction site model self-consistent field method and time-dependent density functional theory. The π-π* excitation energies are computed for BM and its derivative 2,6-di-tert-butyl (di-t-Bu) BM. The behaviors of the computed excitation energies with increasing solvent polarity are in good agreement with those of the corresponding experimental measurements. In addition, analysis of the solute-solvent interaction energies and spatial distribution functions reveals that the effects of the solvent on the absorption spectra are reduced by the steric hindrance of the t-Bu groups. Furthermore, from the difference in the solute-solvent interaction energies of BM and di-t-Bu BM, it is shown that the effect of the t-Bu substituents on the absorption spectrum is greater in high-polarity solvents.

Self-Assembly of Lamellar Microphases in Linear Gradient Copolymer Melts

We investigate lamellar microphases in linear gradient copolymer melts by a combination of techniques, including numerical solutions of self-consistent field equations, scaling theory, and analysis of the strong-segregation limit. In particular, we construct a Flory theory to predict the scaling of the equilibrium lamellar width Leq as a function of comonomer incompatibility measured by χN. The Flory theory balances chain stretching with increased monomer repulsive interactions resulting from conformational fluctuations about a state of uniformly stretched chains, that obtains in the strong-segregation limit. We find Leq/Rg ∼ (χN)1/6, which agrees well with numerical results. Remarkably, this is the same result as for symmetric diblock copolymers, although for quite different physical reasons.

Modeling of the 3RS tau protein with self-consistent field method and Monte Carlo simulation

Using a model with amino acid resolution of the 196 aa N-terminus of the 3RS tau protein, we performed both a Monte Carlo study and a complementary self-consistent field (SCF) analysis to obtain detailed information on conformational properties of these moieties near a charged plane (mimicking the microtubule surface). The SCF model implements a second level of coarse graining wherein amino acids are grouped according to charge and solvency properties. In the low ionic strength regime, both approaches give very similar predictions for the concentration dependence, namely that the tau fragment has a compact fence-like structure near the surface and an extended tail pointing away from the surface. The correspondence between the two approaches is remarkable considering the vast difference in computational effort. The MC method samples self-avoiding conformations in a continuum space and predicts both lateral as well as normal distributions, whereas the SCF analysis uses a freely-jointed chain model on a lattice in combination with mean-field approximations and focuses merely on the concentration profile normal to the interface. Motivated by the good correspondence, we use the SCF approach to explore various consequences of the choices made in the MC analysis.

New ends to the tale of tails: adsorption of comb polymers and the effect on colloidal stability

In this paper we consider the classical problem of homopolymer adsorption at the solid–liquid interface and discuss its implications for colloidal stability. More specifically, our focus is on comb-like homopolymers in the strong adsorption limit. A self-consistent field analysis shows that for relatively long side chains but still much longer backbones, the adsorbed layer is dominated by the side chains near the surface, whereas at larger distances the layer has features that belong to the backbone. As a rule, homopolymer adsorption promotes flocculation of colloids. This is attributed to the long polymer chains that form bridges between the colloidal particles. However, the free ends of the chains do not participate in the bridging and thus contribute with a small repulsive term to the mainly attractive pair interaction. For comb polymers, the free ends of the side chains amplify the repulsion dramatically. As a result, in contrast to linear adsorbed homopolymers, comb polymers typically prevent flocculation.

A Self-Consistent Field Analysis of the Neurofilament Brush with Amino-Acid Resolution

Using the numerical model of Scheutjens and Fleer we investigated, on a self-consistent field level, the equilibrium structure of the neurofilament brush formed by the projection domains of NF-H, NF-M, and NF-L proteins. Although the actual amino-acid sequences in the projection domains are coarse-grained, the different (realistic) solubilities of amino-acid residues and the specific distribution of its intrinsic charges inside the arms of the NF proteins are taken explicitly into account. We collect strong evidence that the electrostatic interactions are a dominant force that controls the NF brush structure. There exists a remarkable spatial separation of the H, M, and L tails. In a dephosphorylated NF we found confined and flowerlike conformations for the H and M projection domains, respectively. We demonstrate that the ionization of KSP repeats in NF proteins triggers a conformational transition in the H tail that leads to the expulsion of its terminal (KEP) domain to the periphery of the NF brush. We argue that the phosphorylation of the NF proteins in axons can both increase the interfilament distance and stabilize cross bridges between neurofilaments.

On the Mechanism of Uptake of Globular Proteins by Polyelectrolyte Brushes: A Two-Gradient Self-Consistent Field Analysis

We present model calculations for the interaction of a protein-like inhomogeneously charged nanoscale object with a layer of densely grafted polyelectrolytes ("polyelectrolyte brush"). The motivation of this work is the recent experimental observation that proteins that carry an overall negative charge are absorbed into negatively charged polyelectrolyte brushes. Two-gradient self-consistent field (2G-SCF) calculations have been performed to unravel the physical mechanism of the uptake of protein thus effected. Our results prove that an overall neutral, protein-like object can electrostatically be attracted and therefore spontaneously driven into a polyelectrolyte brush when the object has two faces (patches, domains), one with a permanent positive charge and the other with a permanent negative charge. Using a 2G-SCF analysis, we evaluate the free energy of insertion, such that the electric dipole of the inclusion is oriented parallel to the brush surface. An electroneutral protein-like object is attracted into the brush because the polyelectrolyte brush interacts asymmetrically with the charged patches of opposite sign. At high ionic strength and low charge density on the patches, the attraction cannot compete with the repulsive excluded-volume interaction. However, for low ionic strengths and sufficiently high charge density on the patches, a gain on the order of k(B)T per charge becomes possible. Hence, the asymmetry of interaction for patches of different charges may result in a total attractive force between the protein and the brush. All results obtained herein are in excellent agreement with recent experimental data.

Why Surfaces Modified by Flexible Polymers Often Have a Finite Contact Angle for Good Solvents

Polymers adsorbing from a dilute solution onto the solvent-vapor interface generate a nonzero surface pressure. When the same polymers are end-grafted onto a surface such that a so-called polymer brush is formed, one will find that the solvent wets this compound interface partially. The partial wetting and the finite surface pressure are intimately linked properties of the polymer-solvent-vapor combination. It is shown that the spreading parameter in the wetting problem is proportional to the surface pressure in the adsorption case. Complete wetting is only possible when this surface pressure is nonpositive. The wetting characteristics are hardly influenced by the grafting density and chain length characterizing the brush. We argue that the grafted polymer chains can bridge to the solvent-vapor interface, thereby preventing the wetting film to become macroscopically thick. We present experimental data underpinning our self-consistent field analysis. Indeed, finite contact angles should be expected in various systems in which bridging attraction contributes to the disjoining pressure in wetting films.

Surface forces in a confined polymer melt: Self-consistent field analysis of full and restricted equilibrium cases

In full equilibrium the self-consistent field theory for a homopolymer melt confined between two surfaces predicts pronounced oscillatory interaction forces on the monomer length scale. However, when not all the polymer molecules can reversibly equilibrate with the bulk, the trapped molecules may be squeezed, adding a repulsive contribution to the interaction energy. The classical constrained or restricted equilibrium approach by Scheutjens and Fleer two decades ago to deal with this for polymers adsorbed from dilute solutions, breaks down in semidilute and concentrated polymer solutions. We present a generalized restricted equilibrium ansatz applicable also for concentrated polymer solutions. The key idea is that only the adsorbed polymer molecules, i.e., molecules that touch the surface at least once, are forced to remain inside the gap, whereas the nonadsorbing chains are free to move out of the gap when the surfaces approach each other. As in dilute solutions, the forces found in confined melt with trapped adsorbed chains become repulsive. We analyse the dependence of the interaction forces both in full as well as in restricted equilibrium cases as a function of the chain length and the interactions with the surface for a compressible polymer melt.

Coexistence of Spheres and Rods in Micellar Solution of Dodecyldimethylamine Oxide

Micelles of dimethyldodecylamine oxide (DMDAO) are known to exhibit sphere-to-rod transitions as a function of pH and ionic strength. Long micelles are stabilized at pH corresponding to half-protonation, because hydrogen bonding between nonionic and protonated monomers yields an effectively double-tailed monomer whose geometry favors cylindrical growth. Dynamic light scattering (DLS) was used to follow particle size distribution as a function of pH, ionic strength (I), and surfactant concentration. The key finding was the coexistence of spherical micelles with rodlike ones at 4 < pH < 6 and I > 0.2 M. These observations have been verified by varying the algorithm used for the Laplace transformation of the autocorrelation function and also with different DLS systems. The effect of surfactant concentration was used to confirm the absence of any influence of micelle−micelle interaction on the dynamics of diffusion. A molecular level self-consistent field analysis of finite size rodlike micelles confirms the idea that the endcaps are swollen with respect to the cylindrical part. The theoretical results support the coexistence of rods and spherical micelles, i.e., the existence of gaps in the size distribution of wormlike micelles. The cause of coexistence has been explained in terms of the instability of dumbbell-like micelles with domains of negative curvature (neck). The endcap energy is shown to be given (in first order) by the grand potential of spherical micelles that coexist with the wormlike micelles.

Self-Consistent Field Analysis of Ionic Surfactant Adsorption Regulation in the Aqueous Film between Two Neutral Solids

Self-consistent field theory for adsorption and association is utilized to calculate the adsorption of the ionic surfactant (C16P3+) on two neutral, slightly hydrophobic solids separated by a thin aqueous film and immersed in an infinite reservoir of aqueous 1:1 electrolyte. The change in surfactant adsorption as a function of the separation between the solids is discussed in relation to the forces between the solids as well as the shape of the adsorption vs concentration curve for an isolated surface. Surfactants desorb from the surface as the electrostatic potential in the gap between the surfaces is increased due to the overlap of electric potential profiles. Changes in adsorption are most sensitive to solid−solid separation when the surfactant concentration is near the step in the adsorption isotherm. Adsorbed surfactant layers also become thinner as the surfaces approach, and the adsorbed amount can change in more complex ways when the adsorbed layers come into contact.

Multiscale modelling of titanium aluminides

In this work a three-scale model of the mechanical behaviour of titanium aluminides is presented. The first scale transition between the macroscopic length scale and the scale of an individual α 2, γ or lamellar α 2 + γ grain is made using elastically self-consistent transformation field analysis (TFA) with anisotropic elasticity. The constitutive equations of the α 2 and γ-phases are obtained through the framework of crystal plasticity. The effective behaviour of the lamellar α 2–γ phase, however, necessitates a second scale transition. This transition, derived from a system of linear equations for a multilayer, is obtained and shown to be equivalent to the formalism of transformation field analysis. Some simple simulations are presented to show the viability of the method.