Self-consistent Field Theory Study Research Articles

Dihydropyrene/Cyclophanediene Photoswitching Mechanism Revisited with Spin-Flip Time-Dependent Density Functional Theory: Nature of the Photoisomerization Funnel at Stake!

The complex photoisomerization mechanism of the dihydropyrene (DHP) photochromic system is revisited using spin-flip time-dependent density functional theory (SF-TD-DFT). The photoinduced ring-opening reaction of DHP into its cyclophanediene isomer involves multiple coupled electronic states of different character. A balanced treatment of both static and dynamic electron correlations is required to determine both the photophysical and photochemical paths in this system. The present results provide a refinement of the mechanistic picture provided in a previous complete active space self-consistent field plus second-order perturbation theory (CASPT2//CASSCF) study based on geometry optimizations at the CASSCF level. In particular, the nature of the conical intersection playing the central role of the photochemical funnel is different. While at the CASSCF level, the crossing with the ground state involves a covalent doubly excited state leading to a three-electron/three-center bond conical intersection, SF-TD-DFT predicts a crossing between the ground state and a zwitterionic state. These results are supported by multi-state CASPT2 calculations. This study illustrates the importance of optimizing conical intersections at a sufficiently correlated level of theory to describe a photochemical path involving crossings between covalent and ionic states.

Rectangular Cylinders Formed by Compositionally Bidisperse ABC Triblock Terpolymer Blends: A Self-Consistent Field Theory Study.

Compared with traditional cylinders that have circular cross-sections, cylinders with rectangular cross-sections can endow nanomaterials with various novel optical properties and functions. In this work, the formation of the rectangular cylinders self-assembled by compositionally bidisperse ABC triblock terpolymer blends has been investigated via numerical simulations based on self-consistent field theory. The specially designed blending systems are composed of two types of linear ABC triblock terpolymers that have the same total chain lengths and the middle B block chain lengths, but different chain lengths of the side A/C blocks. By tuning the chain length fractions and the interactions between different blocks, rectangular cylinders with a fourfold symmetry pattern were successfully obtained in our simulations. Each rectangular phase domain is self-assembled together by the short and long side blocks of the same species. The simulation results indicate that the selective aggregation of the short side blocks determines the formation of the rectangular cylindrical phase, i.e., the short side blocks prefer to aggregate at the four corners within a rectangular cylindrical phase domain. This simulation result reveals a formation mechanism that is different from the mechanism proposed in previous experiments [Asai ACS Macro Lett., 2014, 3, 166-169]. Moreover, under different middle B block chain length fractions, phase diagrams as a function of the interaction parameter between different blocks and the short side block chain length fraction have been constructed. The phase diagrams show that the parameter window of the rectangular cylinders is considerably expanded by increasing the chain length fraction of the middle B blocks. Our simulation works can provide a theoretical basis for molecular design to regulate and fabricate nanomaterials with nontraditional phase domains in future experiments.

Self-consistent field theory study of polymer-mediated colloidal interactions in solution: Depletion effects and induced forces.

Polymer-mediated colloidal interactions control the stability and phase properties of colloid-polymer mixtures that are critical for a wide range of important applications. In this work, we develop a versatile self-consistent field theory (SCFT) approach to study this type of interaction based on a continuum confined polymer solution model with explicit solvent and confining walls. The model is formulated in the grand canonical ensemble, and the potential of mean force for the polymer-mediated interaction is computed from grand potentials. We focus on the case of non-adsorbing linear polymers and present a systematic investigation on depletion effects using SCFT. The properties of confined polymer solutions are probed, and mean-field profiles of induced interactions are shown across different physical regimes. We expose a detailed parametric dependence of the interaction, concerning both attractive and repulsive parts, on polymer concentration, chain length, and solvent quality and explore the effect of wall surface roughness, demonstrating the versatility of the proposed approach. Our findings show good agreement with previous numerical studies and experiments, yet extend prior work to new regimes. Moreover, the mechanisms of depletion attraction and repulsion, along with the influence of individual control factors, are further discussed. We anticipate that this study will provide useful insights into depletion forces and can be readily extended to examine more complex colloid-polymer mixtures.

Selective Adsorption of Confined Polymers: Self-Consistent Field Theory Studies

Selective adsorption of flexible polymers, where only a fraction of the “sticker” monomers can be adsorbed, confined to a cylindrical pore, is studied within the self-consistent field theory (SCFT). The selective adsorption, modeled with di-block, alternating, and random distributions of the sticker monomers along the chain, shows different adsorption–desorption transition behaviors: when the polymer chain possesses a high fraction of stickers, the di-block sequence adsorbs better than the alternating and the random sequence. On the other hand, when the polymer chain possesses a low fraction of stickers, the alternating sequence is the most adsorbed chain. Our theory indicates that the correlation between stickers and nonadsorbing monomers (neutrals) enhances the adsorption of polymers at a low fraction of sticker monomers, while it hinders the adsorption of polymers at a high fraction of sticker monomers, revealing the mechanism of adsorption efficiency determined by the sequence of sticker monomers in a polymer chain.

Quantifying Mg2+ Binding to ssDNA Oligomers: A Self-Consistent Field Theory Study at Varying Ionic Strengths and Grafting Densities.

The performance of aptamer-based biosensors is crucially impacted by their interactions with physiological metal ions, which can alter their structures and chemical properties. Therefore, elucidating the nature of these interactions carries the utmost importance in the robust design of highly efficient biosensors. We investigated Mg binding to varying sequences of polymers to capture the effects of ionic strength and grafting density on ion binding and molecular reorganization of the polymer layer. The polymers are modeled as ssDNA aptamers using a self-consistent field theory, which accounts for non-covalent ion binding by integrating experimentally-derived binding constants. Our model captures the typical polyelectrolyte behavior of chain collapse with increased ionic strength for the ssDNA chains at low grafting density and exhibits the well-known re-entrant phenomena of stretched chains with increased ionic strength at high grafting density. The binding results suggest that electrostatic attraction between the monomers and Mg plays the dominant role in defining the ion cloud around the ssDNA chains and generates a nearly-uniform ion distribution along the chains containing varying monomer sequences. These findings are in qualitative agreement with recent experimental results for Mg binding to surface-bound ssDNA.

Self-assembly Behavior of Symmetrical Linear ABCA Tetrablock Copolymer: A Self-consistent Field Theory Study

ABCA tetrablock copolymers offer new opportunities for design of materials with novel structures. Using real-space self-consistent field theory and simulation, we systematically examined the self-assembly behavior of linear ABCA tetrablock copolymers in a 2D space. The simulation was carried out under conditions of symmetrical compositions and interactions. We focus on the influence of chain length ratio of block A and interactions between block A and other blocks B and C on the self-assembly behavior of the copolymer system. The simulation results show that most of the structures self-assembled by the ABCA tetrablock copolymers are centrosymmetric, such as diblock-like lamella phase, two kinds of lamellae with beads at interface, two kinds of hierarchical lamella phase, hexagonal honeycomb-like phase, lamella phase with mixed BC and hexagonal spheres with mixed BC. Furthermore, we find that a novel noncentrosymmetric Janus spheres can be obtained when the interaction between blocks B and C is strong, whereas a noncentrosymmetric lamella phase was obtained at weak interaction between blocks B and C. Phase diagrams for the ABCA tetrablock copolymers with different interaction strength between blocks B and C are constructed by comparing free energies of candidate ordered structures. In addition, studies on the metastable behavior of the system reveal that enthalpy plays an important role in the metastable behavior of the ABCA tetrablock copolymer system. Our work can provide useful guide for structure control of such kind of tetrablock copolymers in experiments.

Self-consistent mean field theory studies of the thermodynamics and quantum spin dynamics of magnetic Skyrmions

A self-consistent mean field theory is introduced and used to investigate the thermodynamics and spin dynamics of an S = 1 quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. In addition, the spin dynamics of a magnetic Skyrmion is described by solving the time dependent Schrödinger equation with additional damping term. The Skyrmion annihilation process driven by an electric field is used to compare the trajectories of the quantum mechanical simulation with a semi-classical description for the spin expectation values using a differential equation similar to the classical Landau–Lifshitz–Gilbert equation.

Response of bi-disperse polyelectrolyte brushes to external electric fields — A numerical self-consistent field theory study

The self-consistent field theory has been employed to numerically study the response of bi-disperse flexible polyelectrolyte (PE) brushes grafted on an electrode to electric fields generated by opposite surface charges on the PE-grafted electrode and a second parallel electrode. The numerical study reveals that, under a positive external electric field, the shorter and negatively charged PE chains are more responsive than the longer PE chains in terms of the relative changes in their respective brush heights. Whereas under a negative external electric field, the opposite was observed. The total electric force on the grafted PE chains was calculated and it was found that, under a positive external electric field, the magnitude of the total electric force acting on one shorter PE chain is larger than that on one longer PE chain, or vice versa. The underlying mechanism was unraveled through analyzing the total electric field across the two oppositely charged electrodes.

Coarse-grained molecular dynamics modeling of the kinetics of lamellar block copolymer defect annealing

State-of-the-art block copolymer (BCP)—directed self-assembly (DSA) methods still yield defect densities orders of magnitude higher than is necessary in semiconductor fabrication despite free-energy calculations that suggest equilibrium defect densities are much lower than is necessary for economic fabrication. This disparity suggests that the main problem may lie in the kinetics of defect removal. This work uses a coarse-grained model to study the rates, pathways, and dependencies of healing a common defect to give insight into the fundamental processes that control defect healing and give guidance on optimal process conditions for BCP-DSA. It is found that bulk simulations yield an exponential drop in defect heal rate above χN∼30. Thin films show no change in rate associated with the energy barrier below χN∼50, significantly higher than the χN values found previously for self-consistent field theory studies that neglect fluctuations. Above χN∼50, the simulations show an increase in energy barrier scaling with 1/2 to 1/3 of the bulk systems. This is because thin films always begin healing at the free interface or the BCP-underlayer interface, where the increased A−B contact area associated with the transition state is minimized, while the infinitely thick films cannot begin healing at an interface.

Phase diagrams of diblock copolymers in electric fields: a self-consistent field theory study.

We investigated the phase diagrams of diblock copolymers in external electrostatic fields by using real-space self-consistent field theory. The lamella, cylinder, sphere, and ellipsoid structures were observed and analyzed by their segment distributions, which were arranged to two types of phase diagrams to examine the phase behavior in weak and strong electric fields. One type was constructed on the basis of Flory-Huggins interaction parameter and volume fraction. We identified an ellipsoid structure with a body-centered cuboid arrangement as a stable phase and discussed the shift of phase boundaries in the electric fields. The other type of phase diagrams was established on the basis of the dielectric constants of two blocks in the electric fields. We then determined the regions of ellipsoid phase in the phase diagrams to examine the influence of dielectric constants on the phase transition between ellipsoidal and hexagonally packed cylinder phases. A general agreement was obtained by comparing our results with those described in previous experimental and theoretical studies.

Numerical self-consistent field theory study of the response of strong polyelectrolyte brushes to external electric fields.

The response of strong polyelectrolyte (PE) brushes grafted on an electrode to electric fields generated by opposite surface charges on the PE-grafted electrode and a second parallel electrode has been numerically investigated by self-consistent field theory. The influences of grafting density, average charge fraction, salt concentration, and mobile ion size on the variation of the brush height against an applied voltage bias were investigated. In agreement with molecular dynamics simulation results, a higher grafting density requires a larger magnitude of voltage bias to achieve the same amount of relative change in the brush height. In the experimentally relevant parameter regime of the applied voltage, the brush height becomes insensitive to the voltage bias when the grafting density is high. Including the contribution of surface charges on the grafting electrode, overall charge neutrality inside the PE brushes is generally maintained, especially for PE brushes with high grafting density and high average charge fraction. Our numerical study further reveals that the electric field across the two electrodes is highly non-uniform because of the complex interplay between the surface charges on the electrodes, the charges on the grafted PE chains, and counterions.

A Complete Active Space Self-Consistent Field and Density Functional Theory Study of S0, T1, S1 States of Five Phenol ortho-Derivatives

A Complete Active Space Self-Consistent Field and Density Functional Theory Study of S0, T1, S1 States of Five Phenol ortho-Derivatives

SCFT Study of Microphase Separation in Mixed Polymer Brushes Grafted on Cylindrical Surface

We report on microphase separation behaviors of mixed polymer brushes grafted onto an infinitely long cylindri- cal rod by performing polymer self-consistent field theory (SCFT) calculation with "masking" technique. The "masking" technique is especially suitable to deal with systems of confined polymers grafted onto curved surfaces. We have developed a method to solve the morphology of block copolymers confined into complicated topographic surfaces with SCFT. In this paper, this unique technique is extended to solve the SCFT for nanorod grafted by mixed polymer brushes. Furthermore, the use of simple Cartesian grids in a cubic computational cell with periodic boundary conditions makes it possible to solve dif- fusion equations in SCFT by utilizing an efficient and highly accurate pseudo-spectral method involving fast Fourier trans- form. Both parallel rippled phase and ring-shaped phase are predicted. We have investigated the influences of the cylinder radius, grafting density and interaction between the two incompatible grafting polymers on the stability of the two typical phases. Our results show that the system prefers the ring-shaped phase with the increase of the cylinder radius, grafting den- sity and interaction between the two grafting polymers. Phase diagrams involving these parameters are constructed, and we explain the reason of the transition between the parallel rippled phase and ring-shaped phase in terms of the degree of phase segregation. Again, the degree of phase segregation is higher with larger cylinder radius, grafting density and interaction between the two grafting polymers. By comparing the degree of phase segregation and free energy of the parallel rippled and ring-shaped phases at the same condition, we found that the ring-shaped phase favors the entropic part of the free energy while the parallel rippled phase significantly reduces the enthalpy. Therefore, when the degree of phase segregation is low, the free energy of the system is dominated by the enthalpy, leading to the parallel rippled phase; when the degree of phase segregation is high, the free energy of the system is dominated by the entropic part and the ring-shaped phase is stable. We also found that the domain numbers of parallel rippled phase and the period of alternating ring-shaped phase vary with the radius of cylinder. These predictions are expected to be helpful in rational design and fabrication of such novel polymer brushes.

Binary mixed homopolymer brushes grafted on nanorod particles: A self-consistent field theory study

We employ the self-consistent field theory to study phase structures of brush-rod systems composed of two chemically distinct linear homopolymers. The polymer chains are uniformly grafted on the surface of a nanorod particle of finite length and comparable radius to the polymer radius of gyration. A "masking" technique treating the cylindrical boundary is introduced to solve the modified diffusion equations with an efficient and high-order accurate pseudospectral method involving fast Fourier transform on an orthorhombic cell. A rich variety of structures for the phase separated brushes is predicted. Phase diagrams involving a series of system parameters, such as the aspect ratio of the nanorod, the grafting density, and the chain length are constructed. The results indicate that the phase structure of the mixed brush-rod system can be tailored by varying the grafted chain length and/or the aspect ratio of the rod to benefit the fabrication of polymeric nanocomposites.

Phase behavior of polymer blends with reversible crosslinks—A self-consistent field theory study

Abstract

Interfacial Behavior in Polyelectrolyte Blends: Hybrid Liquid-State Integral Equation and Self-Consistent Field Theory Study

Polyelectrolytes and electrolyte solutions are known to demonstrate a rich array of phase behaviors due to the effects of long-ranged interactions inherent in Coulombic attractions and repulsions. While there is a wealth of literature examining these materials to provide some physical insight into their thermodynamics, all of these methods make strong approximations with regards to the nature of the ionic component. In this investigation we develop a hybrid liquid-state integral equation and self-consistent field theory numerical theory, and systematically demonstrate the ramifications on local ion structure on the overall thermodynamics of segregated polymer blends. We show effects on phase separation such as suppression due to hard sphere interactions and enhancement due to ion cohesion that are not described using traditional Poisson-Boltzmann mean-field theory.

Self-consistent field theory study of the solvation effect in polyelectrolyte solutions: beyond the Poisson–Boltzmann model

We developed a self-consistent field theory to study the solvation effect in polyelectrolyte solutions by taking into account the dipolar feature of polar solvents. A Langevin Poisson–Boltzmann equation describing the electrostatic interactions was derived at the mean-field level and numerically solved by an ad-hoc direct spectral algorithm. This method enables the SCFT to be implemented in real space. The developed self-consistent field model was applied to salt-free concentrated solutions of diblock polyampholytes and charged–neutral diblock copolymers. It was found that an increase in the magnitude of dipole moments can lead to an increase in the effective dielectric constant and thereby the change of the phase behaviors. As the magnitude of the dipole moment increases, the segregation between dissimilar blocks becomes strong, and the lamellar spacing undergoes a non-monotonic variation where the spacing first decreases and then increases to reach a plateau. The proposed calculation method can be extended to the solutions of polyelectrolytes with different architectures and polar solutions containing added salts.

Spectral collocation methods for polymer brushes

We provide an in-depth study of pseudo-spectral numerical methods associated with modeling the self-assembly of molten mixed polymer brushes in the framework of self-consistent field theory (SCFT). SCFT of molten polymer brushes has proved numerically challenging in the past because of sharp features that arise in the self-consistent pressure field at the grafting surface due to the chain end tethering constraint. We show that this pressure anomaly can be reduced by smearing the grafting points over a narrow zone normal to the surface in an incompressible model, and/or by switching to a compressible model for the molten brush. In both cases, we use results obtained from a source (delta function) distribution of grafting points as a reference. At the grafting surface, we consider both Neumann and Dirichlet conditions, where the latter is paired with a masking method to mimic a confining surface. When only the density profiles and relative free energies of two comparison phases are of interest, either source or smeared distributions of grafting points can be used, but a smeared distribution of grafting points exhibits faster convergence with respect to the number of chain contour steps. Absolute free energies converge only within the smeared model. In addition, when a sine basis is used with the masking method and a smeared distribution, fewer iterations are necessary to converge the SCFT fields for the compressible model. The numerical methods described here and investigated in one-dimension will provide an enabling platform for computationally more demanding three-dimensional SCFT studies of a broad range of mixed polymer brush systems.

Sterically stabilized lock and key colloids: A self-consistent field theory study

A self-consistent field theory study of lock and key type interactions between sterically stabilized colloids in polymer solution is performed. Both the key particle and the lock cavity are assumed to have cylindrical shape and their surfaces are uniformly grafted with polymer chains. The lock-key potential of mean force is computed for various model parameters, such as length of free and grafted chains, lock and key size matching, free chain volume fraction, grafting density, and various enthalpic interactions present in the system. The lock-key interaction is found to be highly tunable, which is important in the rapidly developing field of particle self-assembly.

Bilayers Connected by Threadlike Micelles in Amphiphilic Mixtures: A Self-Consistent Field Theory Study

Binary mixtures of amphiphiles in solution can self-assemble into a wide range of structures when the two species individually form aggregates of different curvatures. A specific example of this is seen in solutions of lipid mixtures where the two species form lamellar structures and spherical micelles, respectively. Here, vesicles connected by threadlike micelles can form in a narrow concentration range of the sphere-forming lipid. We present a study of these structures based on self-consistent field theory (SCFT), a coarse-grained model of amphiphiles. First, we show that the addition of sphere-forming lipid to a solution of lamella-former can lower the free energy of cylindrical, threadlike micelles and hence encourage their formation. Next, we demonstrate the coupling between composition and curvature; specifically, that increasing the concentration of sphere-former in a system of two bilayers connected by a thread leads to a transfer of amphiphile to the thread. We further show that the two species are segregated within the structure, with the concentration of sphere-former being significantly higher in the thread. Finally, the addition of larger amounts of sphere-former is found to destabilize the junctions linking the bilayers to the cylindrical micelle, leading to a breakdown of the connected structures. The degree of segregation of the amphiphiles and the amount of sphere-former required to destabilize the junctions is shown to be sensitive to the length of the hydrophilic block of the sphere-forming amphiphiles.