Self-consistent Field Theory Model Research Articles

Implementation of solvent polarization in three-dimensional reference interaction-site model self-consistent field theory

The three-dimensional reference interaction-site model self-consistent field (3D-RISM-SCF) theory is an electronic structure theory of solvated molecules, which can handle the electronic polarization of the solute molecule induced by the interaction with the solvent, whereas the electronic polarization of solvent molecules is ignored. Here, the solvent-polarizable model is implemented to take into account the electronic polarization of solvent molecules. It is applied to the water molecule in an aqueous solution and the p-nitroaniline molecule in an aqueous solution, and the effects of the solvent polarization on the properties of these solutes are demonstrated.

A finite element method of the self-consistent field theory on general curved surfaces

Block copolymers provide a wonderful platform in the study of soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory (SCFT) has been proven to be a powerful tool for studying the equilibrium ordered structures. Many numerical methods have been developed to solve the SCFT model. However, most of these focus on the bulk systems, and little work on the confined systems, especially on general curved surfaces. In this work, we developed a linear surface finite element method, which has a rigorous mathematical theory to guarantee numerical precision, to study the self-assembled phases of block copolymers on general curved surfaces based on the SCFT. Furthermore, to capture the consistent surface for a given self-assembled pattern, an adaptive approach to optimize the size of the general curved surface has been proposed. To demonstrate the power of this approach, we investigate the self-assembled patterns of diblock copolymers on several distinct curved surfaces, including five closed surfaces and an unclosed surface. Numerical results illustrate the efficiency of the proposed method. The obtained ordered structures are consistent with the previous results on standard surfaces, such as sphere and torus. More significantly, the proposed numerical framework can be applied to study the phase behaviors of block copolymers on general surfaces accurately.

Optimizing self-consistent field theory block copolymer models with X-ray metrology.

A block copolymer self-consistent field theory (SCFT) model is used for direct analysis of experimental X-ray scattering data obtained from thin films of polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) made from directed self-assembly. In a departure from traditional approaches, which reconstruct the real space structure using simple geometric shapes, we build on recent work that has relied on physics-based models to determine shape profiles and extract thermodynamic processing information from the scattering data. More specifically, an SCFT model, coupled to a covariance matrix adaptation evolutionary strategy (CMAES), is used to find the set of simulation parameters for the model that best reproduces the scattering data. The SCFT model is detailed enough to capture the essential physics of the copolymer self-assembly, but sufficiently simple to rapidly produce structure profiles needed for interpreting the scattering data. The ability of the model to produce a matching scattering profile is assessed, and several improvements are proposed in order to more accurately recreate the experimental observations. The predicted parameters are compared to those extracted from model fits via additional experimental methods and with predicted parameters from direct particle-based simulations of the same model, which incorporate the effects of fluctuations. The Flory-Huggins interaction parameter for PS-b-PMMA is found to be in agreement with reported ranges for this material. These results serve to strengthen the case for relying on physics-based models for direct analysis of scattering and light signal based experiments.

A computational scheme of pKa values based on the three-dimensional reference interaction site model self-consistent field theory coupled with the linear fitting correction scheme.

A scheme for quantitatively computing the acid dissociation constant, pKa, of hydrated molecules is proposed. It is based on the three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) theory coupled with the linear fitting correction (LFC) scheme. In LFC/3D-RISM-SCF, pKa values of target molecules are evaluated using the Gibbs energy difference between the protonated and unprotonated states calculated by 3D-RISM-SCF and the parameters fitted by the LFC scheme to the experimental values of training set systems. The pKa values computed by LFC/3D-RISM-SCF show quantitative agreement with the experimental data.

Theoretical analysis of complex formation of p-carboxybenzeneboronic acid with a monosaccharide

Changes in the acid dissociation constant, pKa, of p-carboxybenzeneboronic acid (PCBA) upon complex formation with monosaccharide are considered by using the three-dimensional reference interaction site model self-consistent field theory. The pKa of PCBA is lowered through complex formation, which is consistent with experimental observations. Free energy component analysis of the dissociation reaction was performed to investigate the details of the contribution to the pKa shift. The magnitudes of the changes in both the electronic energy and the solvation free energy were smaller for the PCBA-complex than for PCBA. These smaller changes can be attributed to the delocalization of the excess charge and to a reduction of the solvent-accessible area near the boric acid group because of the steric bulk of the monosaccharide.

Theoretical analysis of co-solvent effect on the proton transfer reaction of glycine in a water-acetonitrile mixture.

The co-solvent effect on the proton transfer reaction of glycine in a water-acetonitrile mixture was examined using the reference interaction-site model self-consistent field theory. The free energy profiles of the proton transfer reaction of glycine between the carboxyl oxygen and amino nitrogen were computed in a water-acetonitrile mixture solvent at various molar fractions. Two types of reactions, the intramolecular proton transfer and water-mediated proton transfer, were considered. In both types of the reactions, a similar tendency was observed. In the pure water solvent, the zwitterionic form, where the carboxyl oxygen is deprotonated while the amino nitrogen is protonated, is more stable than the neutral form. The reaction free energy is -10.6 kcal mol(-1). On the other hand, in the pure acetonitrile solvent, glycine takes only the neutral form. The reaction free energy from the neutral to zwitterionic form gradually increases with increasing acetonitrile concentration, and in an equally mixed solvent, the zwitterionic and neutral forms are almost isoenergetic, with a difference of only 0.3 kcal mol(-1). The free energy component analysis based on the thermodynamic cycle of the reaction also revealed that the free energy change of the neutral form is insensitive to the change of solvent environment but the zwitterionic form shows drastic changes. In particular, the excess chemical potential, one of the components of the solvation free energy, is dominant and contributes to the stabilization of the zwitterionic form.

Effects of sodium dodecyl sulfate on structures of poly(N-isopropylacrylamide) at the particle surface.

The effect of sodium dodecyl sulfate (SDS) on the poly(N-isopropylacrylamide) (PNIPAM) tethered to nanoparticles was experimentally investigated using dynamic light scattering below the lower critical solution temperature. A mean-field analytical model was used to calculate the parameters of interfacial PNIPAM-SDS complexes. Particularly, the magnitude of SDS adsorption energy obtained decreases with decreasing excluded volume parameter, implying that the partially collapsed PNIPAM brush virtually favors the adsorption of SDS onto the PNIPAM chains. A self-consistent field theory (SCFT) model was used to get a detailed quantitative description of monomer density distribution. By lowering the solvent quality, a number of phenomena related to the noncontinuity of monomer density are revealed. These phenomena are either referred to as the vertical phase separation or as its precursor, which can be delayed and eventually eliminated as the SDS coverage is increased. The distribution of free chain ends was calculated using the SCFT model. Increasing the SDS coverage gives rise to a broader and more asymmetric distribution of free chain ends, accompanied by a considerable expansion of the dead zone (below which the free chain ends do not exist), but lowering the solvent quality has opposite influences. The relative thickness of the dead zone can be scaled to a master curve, regardless of SDS coverage.

Theoretical analysis of salt effect on intramolecular proton transfer reaction of glycine in aqueous NaCl solution

The salt effect on the intramolecular proton transfer reaction of glycine in aqueous NaCl solution was considered using the reference interaction-site model self-consistent field theory. The free energy profiles were computed for various salt concentrations. The set of profiles clearly showed that the free energy gap between the zwitterionic form (ZW) and the neutral form (NF) became larger as the NaCl concentration increased. The transition-state structure of the solute glycine approaches the NF structure, and the reaction barrier height is reduced. From the energy decomposition analysis of the free energy of solvation, we found that the changes in the solvation free energy are determined by the balance between the electronic distortion energy, the electrostatic interaction, the solvent reorganization, and the entropic effects caused by the NaCl addition. The salt effect of NaCl makes all the species associated with the reaction unstable; however, the destabilization of NFs caused by NaCl addition is stronger than that of ZWs. In the ZW, the penalty coming from the solvent reorganization and the entropic effects are compensated by the strong solute–solvent electrostatic interaction.

Boundary effects in confined copolymer system and compressible SCFT model

The conventionally used Modified Self-consistent Field Theory (MSCFT) for confined system is known to have two major difficulties: numerical instability and dependence on artificial constraints. Here we use Compressible Model based Self-consistent Field Theory (CMSCFT), which has no artificial constraints, and furthermore overcomes numerical instability problems. CMSCFT asymptotically converges to the conventional Self-consistent Field Theory (SCFT) as the compressibility tends to zero. Satisfactory simulations on some hard-surface confinements, focusing on one-dimensional situation, are also given. We suggest that CMSCFT will be a promising tool for copolymer systems with hard surface confinements.

Mean-Field Modeling of the Encapsulation of Weakly Acidic Molecules in Polyelectrolyte Dendrimers

The unique architecture of dendrimers has attracted interest in a wide variety of biomedical applications such as drug delivery. In order to gain insight into the solubilization of drugs inside dendrimer architectures, we have developed and numerically implemented a self-consistent field theory model for the equilibrium characteristics of charged dendrimer molecules in the presence of weakly acidic drug molecules. Using such a model, we examine the relative influence of excluded volume, electrostatic, and local enthalpic interactions upon the solubilization of drugs in dendrimers. When only excluded volume interactions are accounted, there is no driving force for drug solubilization inside the dendrimer, and hence depletion of the drug from the dendrimer molecule (relative to the bulk drug concentration) is observed. The inclusion of electrostatic interactions within the model results in solubilization of drugs within the dendrimer. The solubilization of the drugs is shown to increase with increasing drug charge density and increasing dendrimer generation number. We probe the effect of enthalpic interactions and demonstrate that the number of drug molecules encapsulated through enthalpic interaction is dependent upon the number of dendrimer monomers, the enthalpic interaction parameters between the dendrimer and drug (χPD), and the drug and solvent (χDS). We also analyze the combined effects of the preceding interactions to identify the synergism in their influence and delineate the relative importance of different parameters such as pOH, size of the drugs, and the Bjerrum length of the solution in influencing the encapsulation of drugs by dendrimer molecules.

Correlations between Morphologies and Photovoltaic Properties of Rod−Coil Block Copolymers

We present results obtained using a drift-diffusion model for the structure−property correlations in photovoltaic devices based on self-assembly of rod−coil block copolymers. We use a self-consistent field theory model to generate the self-assembly morphologies of rod−coil block copolymers in confined situations. The density and orientational order parameter profiles so-obtained are then used as input to a recently proposed drift-diffusion model which predicts the photovoltaic device characteristics. The latter model allows for prescription of arbitrary morphologies of donor and acceptor phases while simultaneously incorporating the role of anisotropic charge transport of holes and excitons that arise in the ordered phases of rod−coil block copolymers. We present results elucidating the role of morphology of self-assembly, orientation of lamellar phases, domain widths, and the degree of phase separation and orientational ordering, upon the photovoltaic device characteristics.

Thermodynamics of Polymer−Clay Nanocomposites Revisited: Compressible Self-Consistent Field Theory Modeling of Melt-Intercalated Organoclays

We formulate a “compressible” version of lattice self-consistent field theory (SCFT) to describe thermodynamic behavior of organically modified clays in polymer melt. The melt consists of the homopolymer matrix and a fraction of end-functionalized “active” chains, each chain having a single “sticker” end-group with strong affinity to the clay surface. We calculate the phase map for this system as a function of the melt composition and the strength of the “sticker” adhesion to the clay. It is shown that within the compressible SCFT model intercalated morphologies are favored in a significantly broader parameter range than was expected based on the incompressible SCFT analysis. We provide a qualitative analysis of this result and discuss implications for the physics of nanocomposites in general.

Theoretical Study of Temperature and Solvent Dependence of the Free-Energy Surface of the Intramolecular Electron-Transfer Based on the RISM-SCF Theory: Application to the 1,3-Dinitrobenzene Radical Anion in Acetonitrile and Methanol

The free-energy surfaces along the intramolecular electron-transfer reaction path of the 1,3-dinitrobenzene radical anion in acetonitrile and methanol are investigated with the reference interaction site model self-consistent field theory. Although acetonitrile and methanol have similar values of the dielectric constant, the free-energy profiles are quite different. In the methanol solution, the charge is strongly localized on one of the nitrile substituents due to a strong hydrogen bond between 1,3-dinitrobenzene and the solvent, while the polarization is not so large in the case of acetonitrile. The temperature dependence of the reorganization energy, the coupling strength, and the activation barrier is evaluated in both acetonitrile and methanol. The reorganization energy and the activation barrier decrease with increasing temperature for both cases. The electronic coupling strength also shows a similar tendency in the temperature dependence; it increases with increasing temperature in both solvents but with different rates. The behavior is explained in terms of the strong polarization induced by the hydrogen bond between the solute and solvent in the methanol solution.

Self-assembly of rod-coil block copolymers.

We present a self-consistent field theory model for the self-assembly behavior of rod-coil block copolymers. The orientational interactions between the rods were modeled through a Maier-Saupe interaction, while the enthalpic interactions between rods and coils were modeled through a standard Flory-Huggins approach. We outline a "real-space" numerical approach to solve the self-consistent field equations for such rod-coil block copolymers. A major focus of our work is upon the nonlamellar phases observed in the experiments on such polymers. To develop a physical understanding of these phases and their regimes of occurrence, we compute the two-dimensional phase diagram for our model. The latter shows significant departures from the one-dimensional phase diagram, but matches qualitatively with the existing experimental results. We also present scaling arguments that rationalize the numerical results for the self-assembly behavior.

Dirac fermions on graphite cones

The electronic structure of graphitic cones is investigated within the self-consistent field-theory model. The local and total density of states near the apex are found for cones of different opening angles. For extended electronic states, the total density of states is found to vanish at the Fermi level at any opening angles more than 60° In turn, for power-law localized states, normalized zero-energy modes are shown to emerge.