Self-consistent Field Model Research Articles

Analytical self-consistent field model of arm-grafted starlike polymers in nonlinear elasticity regime

We develop approximate analytical (AA) model to describe the structure of a brush made of starlike polymers (regularly branched dendrons of the first generation) grafted by one arm onto a planar surface. It is demonstrated that introduction of two sub-layers with distinct populations of strongly and weakly stretched dendrons allows for adequate semi-analytical description of these end-grafted macromolecules in nonlinear elasticity regime. We calculate brush thickness, fraction of strongly stretched dendrons and monotonously decreasing polymer density profiles as a function of polymer grafting density and number of branches in starlike macromolecule. The predictions of AA model are compared with the results of numerical self-consistent field model of Sheutjens and Fleer (SF-SCF). Good agreement between the two models is found at high grafting densities and/or at large number of branches of starlike polymers.

Hydrophobic-Radical Influence on the Structure and Vibrational Spectra of Zwitterionic Glycine and Alanine in the Condensed State

The structure and vibrational spectra of zwitterionic glycine and alanine in aqueous solution and the solid state were calculated in the B3LYP/6-311++G(d,p) approximation. The environment infl uence was taken into account by two methods, i.e., the self-consistent reaction fi eld (SCRF) model and a clear accounting for the effects of hydrogenbonds (complexes with water molecules). The geometric, energetic, and spectral characteristics required to establish that a hydrophobic radical affected the ability of glycine and alanine to form H-bonds were determined. It was found by comparison with experiment that zwitterionic glycine and alanine in the condensed states had to be surrounded with three water molecules, one of which was situated between the N+H3 and COO– ions, in order to calculate their vibrational (IR and Raman) spectra. The formation energies of the alanine complexes with water were 56.47 kcal/ mol and 12.55 kcal/mol greater than those of glycine for formation of a complex with one water molecule situated between the ionized groups and with three water molecules, respectively.

Particles Decorated by an Ionizable Thermoresponsive Polymer Brush in Water: Experiments and Self-Consistent Field Modeling

We have synthesized anionic multistimuli responsive core-shell polymer nanoparticles with low size dispersity composed of glassy poly(methyl methacrylate) (PMMA) cores of ca. 40 nm radius and poly(N-isopropylacrylamide) (PNIPAM) anionic brush-like shells with methacrylic acid comonomers. Using dynamic light scattering, we observed a volume phase transition upon an increase in temperature and this response was pH and ionic strength dependent. Already at room temperature we observed a pronounced polyelectrolyte effect, that is, a shift of the apparent pKa extracted from the degree of dissociation of the acids as a function of the pH. The multiresponsive behavior of the hydrophobic polyelectrolyte brush has been modeled using the Scheutjens-Fleer self-consistent field (SF-SCF) approach. Using a phenomenological relation between the Flory-Huggins χ parameter and the temperature, we confront the predicted change in the brush height with the observed change of the hydrodynamic radius and degree of dissociation and obtain estimates for the average chain lengths (number of Kuhn segments) of the corona chains, the grafting density and charge density distributions. The theory reveals a rich internal structure of the hydrophobic polyelectrolyte brush, especially near the collapse transition, where we find a microphase segregated structure. Considering this complexity, it is fair to state that the theoretical predictions follow the experimental data semiquantitatively, and it is attractive to attribute the observed disparity between theory and experiments to the unknown polydispersity of the chains, the unknown distribution of the charges, or other experimental complications. More likely, however, the deviations point to significant problems of the mean field theory, which focuses solely on the radial distributions and ignores the possibility of the formation of lateral (local) inhomogeneities in partially collapsed polyelectrolyte brushes. We argue that the PNIPAM brush at room temperature is already behaving nonideally.

Dendron brushes and dendronized polymers: a theoretical outlook

Dendron brushes are molecular structures built up of treelike macromolecules, with multiple generations of branches, grafted with a root segment to a surface (particle) or to a backbone chain (dendronized polymer) with a sufficiently high grafting density so that the dendrons interact laterally. Recent advances in the theory of dendron brushes are highlighted and complemented by insights from numerical self-consistent field modelling. Our focus is on controversial issues, which are still under debate, such as, the strain distribution in individual dendrons and the appearance of distinct populations with a different extent of stretching for dendrons in planar brushes. We anticipate that dendritic brushes (i) show a strong resistance against bending, which may manifest in a high apparent persistence length of dendronized polymers, and (ii) have an unusually large beneficial effect on the colloidal stability due to the sharp steric repulsive interaction observed when these surface layers are pushed towards the overlap.

Linking lipid architecture to bilayer structure and mechanics using self-consistent field modelling

To understand how lipid architecture determines the lipid bilayer structure and its mechanics, we implement a molecularly detailed model that uses the self-consistent field theory. This numerical model accurately predicts parameters such as Helfrichs mean and Gaussian bending modulus kc and k̄ and the preferred monolayer curvature J(0)(m), and also delivers structural membrane properties like the core thickness, and head group position and orientation. We studied how these mechanical parameters vary with system variations, such as lipid tail length, membrane composition, and those parameters that control the lipid tail and head group solvent quality. For the membrane composition, negatively charged phosphatidylglycerol (PG) or zwitterionic, phosphatidylcholine (PC), and -ethanolamine (PE) lipids were used. In line with experimental findings, we find that the values of kc and the area compression modulus kA are always positive. They respond similarly to parameters that affect the core thickness, but differently to parameters that affect the head group properties. We found that the trends for k̄ and J(0)(m) can be rationalised by the concept of Israelachivili's surfactant packing parameter, and that both k̄ and J(0)(m) change sign with relevant parameter changes. Although typically k̄ < 0, membranes can form stable cubic phases when the Gaussian bending modulus becomes positive, which occurs with membranes composed of PC lipids with long tails. Similarly, negative monolayer curvatures appear when a small head group such as PE is combined with long lipid tails, which hints towards the stability of inverse hexagonal phases at the cost of the bilayer topology. To prevent the destabilisation of bilayers, PG lipids can be mixed into these PC or PE lipid membranes. Progressive loading of bilayers with PG lipids lead to highly charged membranes, resulting in J(0)(m) >> 0, especially at low ionic strengths. We anticipate that these changes lead to unstable membranes as these become vulnerable to pore formation or disintegration into lipid disks.

Vibrational optical activity of chiral carbon nanoclusters treated by a generalized π-electron method.

Cross sections of inelastic light scattering accompanied by vibronic excitation in large conjugated carbon structures is assessed at the π-electron level. Intensities of Raman and vibrational Raman optical activity (VROA) spectra of fullerenes are computed, relying on a single electron per atom. When considering only first neighbor terms in the Hamiltonian (a tight-binding (TB) type or Hückel-model), Raman intensities are captured remarkably well, based on comparison with frequency-dependent linear response of the self-consistent field (SCF) method. Resorting to π-electron levels when computing spectral intensities brings a beneficial reduction in computational cost as compared to linear response SCF. At difference with total intensities, the first neighbor TB model is found inadequate for giving the left and right circularly polarized components of the scattered light, especially when the molecular surface is highly curved. To step beyond first neighbor approximation, an effective π-electron Hamiltonian, including interaction of all sites is derived from the all-electron Fockian, in the spirit of the Bloch-equation. Chiroptical cross-sections computed by this novel π-electron method improve upon first-neighbor TB considerably, with no increase in computational cost. Computed VROA spectra of chiral fullerenes, such as C76 and C28, are reported for the first time, both by conventional linear response SCF and effective π-electron models.

Theoretical Study of Different Solvent and Temperature Effects on Double-walled Carbon Nanotubes (DWNTs) and Calixarene with Amino Acid: A QM/MM Study

In this investigation, the interaction of Calixarene with amino acid (alanine) with double-walled carbon nanotubes (DWNTs) are examined, with OPLS, Amber and MM+ force field in molecular mechanic (MM) method. The calculations achieved by methods of Monte Carlo simulation in different temperatures. The calculations were carried out using HyperChem professional release 7.01 package of program. We investigate effects of gas phase (ϵ = 1) and in various solvent media with dielectric constants of water (ϵ = 78.39), DMSO (ϵ = 46.8), methanol (ϵ = 32.63), ethanol (ϵ = 24.55), CH2Cl2 (ϵ = 8.93) at seven temperatures on interaction of Calixarene with DWNTs, utilizing these force fields. The interaction of Calixarene with DWNTs in gas phase and five solvents such as water, DMSO, methanol, ethanol and dichloromethane has been processed applying the ab initio calculations. The calculations have been done with the GAUSSIAN 98 program according to Hartree-Fock (HF) theory at the HF/3-21G level. Thus, by utilizing a Hartree-Fock method, we studied the effects of different solvents on interaction of Calixarene with DWNTs within the Onsager self-consistent reaction field (SCRF) model, as well as the temperature effects on the stability of the interaction between Calixarene with DWNTs in various solvents.

Interaction of a Hydrophobic Weak Polyelectrolyte Star with an Apolar Surface

We consider star-like polymers with weak, that is, pH-dependent, hydrophobic polyelectrolyte arms. For low ionic strength conditions, a microphase-segregated quasimicellar structure is found, for which the star features a compact apolar core and a charged and swollen corona. This state is jump-like lost when the ionic strength is increased, i.e., at some intermediate ionic strength value. Using numerical self-consistent field modeling, we focus on the adsorption characteristics of these objects onto hydrophobic surfaces as a function of the ionic strength. In the quasimicellar state, the stars are attracted to the surface, albeit that, typically, an adsorption barrier is present. The strongest repulsion is found at intermediate ionic strength, where the star-like molecule is in a single-phase state and the barrier remains modest at both low and high ionic strength cases. Remarkably, it is possible that a star in a single swollen phase state is pushed into the quasimicellar state.

Quantum-Classical Path Integral with Self-Consistent Solvent-Driven Reference Propagators

Efficient procedures for evaluating the quantum-classical path integral (QCPI) [J. Chem. Phys. 2013, 137, 22A552] are described. The main idea is to identify a trajectory-specific reference Hamiltonian that captures the dominant effects of the classical "solvent" degrees of freedom on the dynamics of the quantum "system". This time-dependent reference is used to construct a system propagator that is valid for large time increments. Residual "quantum memory" interactions are included via the path integral representation of the density matrix, which converges with large time steps. Two physically motivated reference schemes are considered. The first involves the dynamics of the solvent unperturbed by the system, which forms the basis for the "classical path" approximation. The second is based on solvent trajectories determined self-consistently with the evolution of the system, according to the time-dependent self-consistent field or Ehrenfest model. Application to dissipative two-level systems indicates that both reference schemes allow a substantial increase of the path integral time step, leading to rapid convergence of the path sum. In addition, the time-dependent reference propagators automatically weigh state-to-state coupling against solvent reorganization in the determination of transition probabilities, further enhancing the convergence of the path integral.

Equivalence of chain conformations in the surface region of a polymer melt and a single Gaussian chain under critical conditions

In the melt polymer conformations are nearly ideal according to Flory's ideality hypothesis. Silberberg generalized this statement for chains in the interfacial region. We check the Silberberg argument by analyzing the conformations of a probe chain end-grafted at a solid surface in a sea of floating free chains of concentration φ by the self-consistent field (SCF) method. Apart from the grafting, probe chain and floating chains are identical. Most of the results were obtained for a standard SCF model with freely jointed chains on a six-choice lattice, where immediate step reversals are allowed. A few data were generated for a five-choice lattice, where such step reversals are forbidden. These coarse-grained models describe the equilibrium properties of flexible atactic polymer chains at the scale of the segment length. The concentration was varied over the whole range from φ = 0 (single grafted chain) to φ = 1 (probe chain in the melt). The number of contacts with the surface, average height of the free end and its dispersion, average loop and train length, tail size distribution, end-point and overall segment distributions were calculated for a grafted probe chain as a function of φ, for several chain lengths and substrate∕polymer interactions, which were varied from strong repulsion to strong adsorption. The computations show that the conformations of the probe chain in the melt do not depend on substrate∕polymer interactions and are very similar to the conformations of a single end-grafted chain under critical conditions, and can thus be described analytically. When the substrate∕polymer interaction is fixed at the value corresponding to critical conditions, all equilibrium properties of a probe chain are independent of φ, over the whole range from a dilute solution to the melt. We believe that the conformations of all flexible chains in the surface region of the melt are close to those of an appropriate single chain in critical conditions, provided that one end of the single chain is fixed at the same point as a chain in the melt.

Interfacial Tension and Wettability in Water–Carbon Dioxide Systems: Experiments and Self-consistent Field Modeling

This paper presents experimental and modeling results on water-CO2 interfacial tension (IFT) together with wettability studies of water on both hydrophilic and hydrophobic surfaces immersed in CO2. CO2-water interfacial tension (IFT) measurements showed that the IFT decreased with increasing pressure and the negative slopes of IFT-pressure isotherms decreased with increasing temperature. Water contact angle on a cellulose surface (hydrophilic) immersed in CO2 increased with pressure, whereas the water contact angle on a hydrophobic surface such as hexamethyl disilazane (HMDS) coated silicon surface was almost independent of pressure. These experimental findings were augmented by modeling using the self-consistent field theory. The theory applies the lattice discretization scheme of Scheutjens and Fleer, with a discretization length close to the size of the molecules. In line with this we have implemented a primitive molecular model, with just small variations in the molar volume. The theory makes use of the Bragg-Williams approximation and has binary Flory-Huggins interaction parameters (FH) between CO2, water, and free volume. Using this model, we generated the complete IFT-pressure isotherms at various temperatures, which coincided well with the trends reported in literature, that is, the water-CO2 interfacial tension decreased with increasing pressure for pressures ≤100 bar and became independent of pressure >100 bar. The transition point occurred at higher pressures with increasing temperature. At three-phase coexistence (water-CO2-free volume) and at the water-vapor interface (water-free volume), we always found the CO2 phase in between the water-rich and free volume-rich phases. This means that for the conditions studied, the water-vapor interface is always wet by CO2 and there are no signs of a nearby wetting transition. Calculation of the water contact angle on a solid surface was based on the computed adsorption isotherms of water from a vapor or from a pressurized CO2-rich phase and analysis of surface pressures at water-vapor or water-CO2 coexistence. The results matched reasonably well with the experimental contact angle data. Besides, we also computed the volume fraction profiles of the CO2, H2O, and the V phase, from which the preferential adsorption of CO2 near the hydrophilic surface was deduced.

Dendritic Spherical Polymer Brushes: Theory and Self-Consistent Field Modeling

Equilibrium structural properties of polymer brushes formed by dendrons grafted via the root segment onto spherical surfaces (dendritic spherical polymer brushes, DSPB) are studied by means of the Scheutjens–Fleer self-consistent field (SF-SCF) numerical approach and scaling analysis. In particular, we focus on the effects of the variable curvature of the surface on the polymer volume fraction distribution and extension of the individual dendrons in DSPB. A systematic comparison with spherical polymer brushes formed by linear polymer chains (LSPB) end-grafted to the surfaces of the same curvature radii is performed. We demonstrate that the difference in internal structural organization of DSPB and LSPB is most pronounced at small curvature radius of the grafting surface. In particular, the radial distribution of polymer volume fraction in DSPB is close to uniform, whereas in LSPB it decays in the radial direction following a power law. The quasi-plateau polymer volume fraction distribution in DSPB is ensu...

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.

Matrix Isolation Infrared and DFT Study of the Trimethyl Phosphite–Hydrogen Chloride Interaction: Hydrogen Bonding versus Nucleophilic Substitution

Trimethyl phosphite (TMPhite) and hydrogen chloride (HCl), when separately codeposited in a N(2) matrix, yielded a hydrogen bonded adduct, which was evidenced by shifts in the vibrational frequencies of the TMPhite and HCl submolecules. The structure and energy of the adducts were computed at the B3LYP level using 6-31++G** and aug-cc-pVDZ basis sets. While our computations indicated four minima for the TMPhite-HCl adducts, only one adduct was experimentally identified in the matrix at low temperatures, which interestingly was not the structure corresponding to the global minimum, but was the structure corresponding to the first higher energy local minimum. The Onsager self-consistent reaction field model was used to explain this observation. In an attempt to prepare the hydrogen bonded adduct in the gas phase and then trap it in the matrix, TMPhite and HCl were premixed prior to deposition. However, in these experiments, no hydrogen bonded adduct was observed; on the contrary, TMPhite reacted with HCl to yield CH(3)Cl, following a nucleophilic substitution, a reaction that is apparently frustrated in the matrix.

The Thomas-Fermi model in the theory of systems of charged particles above the surface of liquid dielectrics

A consistent theory of equilibrium states of same sign charges above the surface of liquid dielectric film located on solid substrate in the presence of external attracting constant electric field is proposed. The approach to the development of the theory is based on the Thomas-Fermi model generalized to the systems under consideration and on the variational principle. The using of self-consistent field model allows formulating a theory containing no adjustable constants. In the framework of the variational principle we obtain the self-consistency equations for the parameters describing the system: the distribution function of charges above the liquid dielectric surface, the electrostatic field potentials in all regions of the system and the surface profile of the liquid dielectric. The self-consistency equations are used to describe the phase transition associated with the formation of spatially periodic structures in the system of charges on liquid dielectric surface. Assuming the non-degeneracy of the gas of charges above the surface of liquid dielectric film the solutions of the self-consistency equations near the critical point are obtained. In the case of the symmetric phase we obtain the expressions for the potentials and electric fields in all regions of the studied system. The distribution of the charges above the surface of liquid dielectric film for the symmetric phase is derived. The system parameters of the phase transition to nonsymmetric phase – the states with a spatially periodic ordering are obtained. We derive the expression determining the period of two-dimensional lattice as a function of physical parameters of the problem – the temperature, the external attractive electric field, the number of electrons per unit of the flat surface area of the liquid dielectric, the density of the dielectric, its surface tension and permittivity, and the permittivity of the solid substrate. The possibility of generalizing the developed theory in the case of degenerate gas of like-charged particles above the liquid dielectric surface is discussed.

Mathematical simulation of acoustic wave scattering in fractured media

The simulation of acoustic waves in fractured media is considered. A self-consistent field model is proposed that describes the formation of a scattered field and the attenuation of the incident field. For the total field, a wave equation with a complex velocity is derived and the corresponding dispersion equation is studied. A frequency-dependent field damping law and an energy variation law are established. An initial and a boundary value problem for waves in a fractured medium is addressed. A finite-difference scheme for the initial value problem is constructed, and a condition for its stability is established. Numerical results are presented.

A Novel Approach for Deriving Force Field Torsion Angle Parameters Accounting for Conformation-Dependent Solvation Effects.

A procedure for deriving force field torsion parameters including certain previously neglected solvation effects is suggested. In contrast to the conventional in vacuo approaches, the dihedral parameters are obtained from the difference between the quantum-mechanical self-consistent reaction field and Poisson-Boltzmann continuum solvation models. An analysis of the solvation contributions shows that two major effects neglected when torsion parameters are derived in vacuo are (i) conformation-dependent solute polarization and (ii) solvation of conformation-dependent charge distribution. Using the glycosidic torsion as an example, we demonstrate that the corresponding correction for the torsion potential is substantial and important. Our approach avoids double counting of solvation effects and provides parameters that may be used in combination with any of the widely used nonpolarizable discrete solvent models, such as TIPnP or SPC/E, or with continuum solvent models. Differences between our model and the previously suggested solvation models are discussed. Improvements were demonstrated for the latest AMBER RNA χOL3 parameters derived with inclusion of solvent effects in a previous publication (Zgarbova et al. J. Chem. Theory Comput.2011, 7, 2886). The described procedure may help to provide consistently better force field parameters than the currently used parametrization approaches.

A three-state effective Hamiltonian for symmetric cationic diarylmethanes

We analyze the low-energy electronic structure of a series of symmetric cationic diarylmethanes, which are bridge-substituted derivatives of Michler's Hydrol Blue. We use a four-electron, three-orbital complete active space self-consistent field and multi-state multi-reference perturbation theory model to calculate a three-state diabatic effective Hamiltonian for each dye in the series. We exploit an isolobal analogy between the active spaces of the self-consistent field solutions for each dye to represent the electronic structure in a set of analogous diabatic states. The diabatic states can be identified with the bonding structures in classical resonance-theoretic models of cyanine dyes. We identify diabatic states with opposing charge and bond-order localization, analogous to the classical resonance structures, and a third state with charge on the bridge. While the left- and right-charged structures are similar for all dyes, the structure of the bridge-charged diabatic state, and the Hamiltonian matrix elements connected to it, change significantly across the series. The change is correlated with an inversion of the sign of the charge carrier on the bridge, which changes from an electron pair to a hole as the series is traversed.

Modeling of self consistent field due to volume charge using charge simulation method and method of characteristics line

This paper presents a numerical solution of electric field that is modified by the presence of volume charge within the region of interest. The effect of the presence of volume charge within the region of interest has been studied for both uniform and nonuniform fields. Charge simulation method coupled with the method of characteristics line is used to provide the numerical solution for the charge modified field. These two techniques are applied iteratively to converge to a self-consistent field model between the two surfaces in xerographic process. Detailed results are presented in the paper to show how the presence of toner as volume charges affects the field distribution when they are present within the field of interest.

Mechanisms and Kinetics for the Thermal Decomposition of 2-Azido-N,N-Dimethylethanamine (DMAZ)

To gain insight into the mechanisms and kinetics of 2-azido-N,N-dimethylethanamine's (DMAZ's) thermal decomposition postulated reaction paths were simulated with ab initio and density functional theory quantum chemistry models. Four reaction types were modeled: (i) spin-allowed and spin-forbidden paths involving N-N(2) bond fission and nitrene formation, (ii) HN(3) elimination with the formation of (dimethylamino)ethylene, (iii) N-N(2) bond fission with the formation of molecules with three- or four-membered heterocyclic rings, and (iv) simple scission of C-H, C-N, and C-C bonds. The geometries of stationary points of the reactions were obtained with a MPWB1K/6-31+G(d,p) model. To locate and model the geometries of minimum energy intersystem crossing points for triplet nitrene formation and isomerization, unrestricted broken spin symmetry calculations were performed. Employed to model an analogous path for methyl azide's decomposition, this approach was found to yield results similar to those obtained with a CASSCF(10,8)/aug-cc-pVDZ model. Of the four reaction types studied, N-N(2) bond fissions with singlet or triplet nitrene formation were found to have the lowest barriers. Barriers for paths to cyclic products were found to be 2-4 kcal/mol higher. Kinetic rate expressions for individual paths were derived from the quantum chemistry results, and spin-allowed nitrene formation was found to be dominant at all temperatures and pressures examined. The expression 2.69 × 10(9) (s(-1))T(1.405) exp(-39.0 (kcal/mol)/RT), which was derived from QCISD(T)/6-31++G(3df,2p)//MPWB1K/6-31+G(d,p) results, was found to be representative of this reaction's gas-phase rate. Adjusted on the basis of results from self-consistent reaction field models to account for solvation by n-dodecane, the expression became 1.11 × 10(9) (s(-1))T(1.480) exp(-37.6 (kcal/mol)/RT). Utilizing this result and others derived in the study, a model of the decomposition of n-dodecane-solvated DMAZ was constructed, and it generated simulations that well-reproduce previously published measured data for the process.