Self-consistent Field Model Research Articles

Self-consistent field study of copolymer adsorption at planar chemically ‘rough’ surfaces: an interplay between the substrate chemical pattern and copolymer sequence distribution

We extend the one-dimensional self-consistent field (SCF) scheme of Scheutjens-Fleer to three dimensions (3D) and use this three-dimensional SCF model to investigate the adsorption of A–B copolymers from A homopolymer matrices onto planar substrates composed of two chemically distinct sites (C and D), one of which has a preferential affinity for the B segments of the copolymer. To address the role of the substrate chemical heterogeneity on copolymer adsorption, we keep the fraction of the C and D sites constant (50% of each site) and vary their spatial distribution on the substrate. The interplay between the surface chemical heterogeneity and the chain microstructure is examined for A–B diblock, A–B–A, B–A–B triblock, and A–alt–B alternating copolymers. Our results indicate that regardless of the type of the surface chemical heterogeneity, the A–B diblock and triblock copolymers adopt ‘brush’-like and ‘bridge’-like structures, respectively, with the B block being anchored to the substrate. In contrast, the A–alt–B macromolecule is found to be ‘zipped’ to the substrate. For a fixed chemical potential of the copolymer in the A–B/A mixture and the surface adsorption energy of B, the amount of the adsorbed copolymer depends on: (1) the number of the B segments; (2) the copolymer microstructure; and (3) the distribution of the C and D regions on the substrate. Three-dimensional maps of the spatial density of copolymer segments provide insight into copolymer conformation at the mixture/substrate interface and also the ability of the copolymer to recognize and mimic the substrate pattern. In addition, we discuss the circumstances under which the substrate pattern is transferred deep inside the A–B/A mixture and those, which lead to strong damping of the substrate motif as one moves away from the substrate/mixture interface.

Interfacial properties of elastomer blends as studied by neutron reflectivity

The interfacial properties of a homopolymer (polybutadiene (PB)) and a terpolymer (brominated poly(isobutylene-co-p-methylstyrene) (BIMS)) are reported. Neutron reflectivity was used to study the interfacial structure. The results were complemented by scanning transmission X-ray microscopy and atomic force microscopy, which were used to probe the morphology of these binary blends. Our results show that the interfacial behavior of these elastomeric blends is a direct function of the BIMS chemical composition. The interfacial width decreased with increasing bromide functionality. At levels below 8mol%, the para-methylstyrene concentration had a less pronounced effect on the compatibility and interfacial characteristics. We also studied the effect of styrene butadiene random copolymers on the miscibility of the PB/BIMS blends. The results showed that styrene-butadiene rubber (SBR) was not fully miscible with BIMS and PB on an individual basis, but addition of relatively small amount of SBR enhances the compatibilization of the PB/BIMS interface. Self-consistent field (SCF) modeling was used to determine the optimum copolymer composition. The calculations are consistent with the experimental results.

Partitioning of a heterotelechelic polystyrene to separate interfaces of thin films

Heterotelechelic deuteropolystyrenes have been synthesised with a tertiary amine functionality at one end and a fluorocarbon group at the other end of the polymer chain. A layer of this polymer, circa 120 A thick, has been attached to the surface of a silicon substrate and subsequently covered with a much thicker layer of hydrogenous polystyrene. The combination has then been annealed at 413 K under vacuum for defined times and the subsequent distribution of the deutero heterotelechelic polymer determined using nuclear reaction analysis and neutron reflectometry. The influences of annealing time, molecular weight and thickness of the hydrogenous polymer have been examined. Nuclear reaction analysis showed that an excess of the heterotelechelic polymer formed at both interfaces with a larger excess remaining at the substrate-polymer interface. When the molecular weight of the hydrogenous polymer is lower than that of the deuteropolymer, the deutero layer is initially swollen by the hydrogenous polymer but the thickness then decreases as deutero polymer becomes detached from the silicon substrate and an additional excess layer is eventually formed at the vacuum-polymer surface. When the molecular weight of the hydrogenous polymer is higher, there is an initial shrinkage of the deuteropolymer layer, but the original thickness (∼ radius of gyration of the deuteropolymer) is regained on prolonged annealing. There is no evidence for bridging between the two interfaces by the heterotelechelic polymer. After five days annealing the volume fraction distribution of the deuteropolymer at the silicon substrate was well described by a self-consistent field model where the only adjustable parameter was the sticking energy of the tertiary amine group to the silicon substrate for which a value of 8kBT was obtained. Comparison of the dependence of the equilibrium layer thickness of the deuteropolymer on the equilibrium grafting density at the silicon surface with the predictions of scaling theory for brush-like polymer layers suggested that the grafted molecules were in the ideal, unperturbed brush region.

Theoretical study of solvent modulation of the first hyperpolarizability of PNA, DNBT and DCH

The solvent modulated first hyperpolarizabilities (βμ) of p-nitroaniline (PNA), 5-dimethyl amino-5′-nitro-2,2′-bithiophene (DNBT) and 1,1-dicyano-6-amino-hexatriene (DCH) are studied by semiempirical finite field SCF method under the scaled self-consistent reaction field (SSCRF) model of solvation recently proposed by us. Simultaneously, the two-state optical model is invoked to calculate the static solvent modified β (=β0), using SSCRF energies. βμ is directly comparable with the EFISH results in solution while β0 values refer more closely to what is obtained in hyper Rayleigh scattering (HRS) measurements. Appreciable changes in both βμ and β0 are predicted to occur as function of solvent polarity.

Nonlinear optics. A semiempirical study of organic chromophores

Many donor–acceptor substituted organic compounds show internal charge separation upon excitation. Within this class, the following compounds are studied as suitable candidates for molecules with high second-order nonlinear optical (NLO) response: 4- N, N-dimethylamino-benzonitrile (DMABN), 6-propanoyl-2-(dimethylamino)-naphthalene (PRODAN), and various 4-(4- N, N-dimethylamino-phenyl)-1,3-diphenyl-pyrazolo[3,4-b]quinolines (DMA-DPPQ). The configuration interaction method with single and double excitations (CISD) is used in combination with the sum over states (SOS) approach within the semiempirical AM1 parametrization to calculate the vector component of the hyperpolarizability along the dipole axis β μ . The influence of changing molecular geometry on the second-order nonlinear properties is calculated for various intramolecular relaxation coordinates. Solvent effects are explicitly studied for DMABN by a self-consistent reaction field (SCRF) model revealing an increasing NLO-effect with increasing solvent polarity. The hyperpolarizability is discussed in relationship to the charge transfer properties of the excited state. The calculated values are in good agreement with experimental data for both DMABN and PRODAN. DMA-DPPQ is found to be a good NLO chromophore only when increasing either the donor or acceptor strength. Its nonlinear response can be drastically increased by an additional strong electron acceptor group, e.g. a NO 2-group, at the primary acceptor moiety.

Protection of Colloidal Suspensions with Random Poly(vinyl acetate) Copolymers

We present experimental and self-consistent field (SCF) modeling results on partially hydrolyzed poly(vinyl acetate) (PVA) chains adsorbed on poly(vinyl chloride) (PVC) latex particles to determine the relationship between the structure of PVA and the steric force between the colloidal particles with adsorbed PVA. By measuring the surface pressure−area isotherms for a PVA-coated PVC latex monolayer at the air/water interface with the Langmuir−Blodgett surface balance, we found that both an increase in chain length and a decrease in degree of hydrolysis increase the repulsive energy between colloidal particles. Surface pressure−area isotherms also reveal that temperatures ranging from 20 to 50 °C have little effect on the repulsive energy between the colloidal particles. We also used this method to analyze the effect of PVA mixtures on colloidal stability. SCF modeling was used to analyze our experimental results. Our results showed excellent agreement between the SCF modeling results and the experimental ...

Energetically most likely substrate and active-site protonation sites and pathways in the catalytic mechanism of dihydrofolate reductase.

Despite much experimental and computational study, key aspects of the mechanism of reduction of dihydrofolate (DHF) by dihydrofolate reductase (DHFR) remain unresolved, while the secondary DHFR-catalyzed reduction of folate has been little studied. Major differences between proposed DHF mechanisms are whether the carboxylate group of the conserved active-site Asp or Glu residue is protonated or ionized during the reaction, and whether there is direct protonation of N5 or a proton shuttle from an initially protonated carboxylate group via O4. We have addressed these questions for both reduction steps with a comprehensive set of ab initio quantum chemical calculations on active-site fragment complexes, including the carboxyl side chain and, progressively, all other polar active-site residue groups including conserved water molecules. Addition of two protons in two steps was considered. The polarization effects of the remainder of the enzyme system were approximated by a dielectric continuum self-consistent reaction field (SCRF) model using an effective dielectric constant (epsilon) of 2. Optimized geometries were calculated using the density functional (B3LYP) method and Onsager SCRF model with the 6-31G basis. Single-point energy calculations were then carried out at the B3LYP/6-311+G level with either the Onsager or dielectric polarizable continuum model. Additional checking calculations at MP2 and HF levels, or with other basis sets or values of epsilon, were also done. From the results, the conserved water molecule, corresponding to W206 in the E. coli DHFR complexes, that is H-bonded to both the OD2 oxygen atom of the carboxyl (Asp) side chain and O4 of the pterin/dihydropterin ring, appears critically important and may determine the protonation site for the enzyme-bound substrates. In the absence of W206, the most stable monoprotonated species are the neutral-pair 4-enol forms of substrates with the carboxyl group OD2 oxygen protonated and H-bonded to N3. If W206 is included, then the most stable forms are still the neutral-pair complexes but now for the N3-H keto forms with the protonated OD2 atom H-bonding with W206. A second proton addition to these complexes gives protonations at N8 (folate) or N5 (DHF). Calculated H-bond distances correlate well with those for the conserved W206 observed in many X-ray structures. For all structures with occluded M20 loop conformations (closed active site), OD2-N3 distances are less than OD2-NA2 distances, which is consistent with those calculated for protonated OD2 complexes. Thus, the results (B3LYP; epsilon = 2 calculations) support a mechanism for both folate and DHF reduction in which the OD2 carboxyl oxygen is first protonated, followed by a direct protonation at N8 (folate) and N5 (DHF) to obtain the active cation complexes, i.e., doubly protonated. The results do not support a proposed protonated carboxyl with DHF in the enol form for the Michaelis complex, nor an ionized carboxyl with protonated enol-DHF as a catalytic intermediate. However, as additional calculations for the monoprotonated complete complexes show a reduction in the energy differences between the neutral-pair keto and ion-pair keto (N8- or N5-protonated) forms, we are extending the treatment using combined quantum mechanics and molecular mechanics (QM/MM) and molecular dynamics simulation methods to refine the description of the protein/solvent environment and prediction of the relative stabilization free energies of the various (OD2, O4, N5, and N8) protonation sites.

Self-consistent field modelling of poly(lactic acid)–poly(ethylene glycol) particles

Self-consistent field (SCF) modelling studies on a series of varying molecular weight poly(lactic acid):poly(ethylene glycol) (PLA:PEG) particles (2:5–15:5 kDa) that form micelles in aqueous solutions have been performed using the formalism of Scheutjens and Fleer. The parameters were chosen to represent a central core made from collapsed hydrophobic PLA blocks, and PEG blocks, which form a corona layer extended into the solvent. These different phases have been confirmed in 1H and 13C NMR experiments. From the analysis of the relevant thermodynamic data of the series, particle radii and aggregation numbers varying from 12.6 to 24.9 nm and from 17 to 280, respectively, have been predicted, which agree well with those obtained experimentally. The actual thickness of the PEG corona is fairly constant at approximately 11 nm for the whole particle series indicating that the size of the PLA core has little effect on the thickness of the PEG corona layer. Another important consideration of these particles is the PEG density at the surface, which is related to the in vivo properties of these particles. The surface area available to each PEG block at the central PLA core has been obtained in order to compare the members of the particle series. It has been shown that the surface area available to each PEG block decreases and then increases throughout the PLA:PEG series.

Copolymer-assisted generation of three-dimensional patterns by replicating two-dimensional substrate motifs.

We use a three-dimensional self-consistent field model to study copolymer adsorption from polymer melts onto chemically heterogeneous substrates. We show that in situations where the copolymer sequence distribution is commensurate with the spatial distribution of the substrate chemical impurities, the two-dimensional substrate pattern gets transcribed into three dimensions and propagates into the polymer mixture. This transference scheme can assist in designing nanostructures that find use in various areas of science and technology.

SCRF study of the conformational equilibrium of chorismate in water

The conformational equilibrium between the diequatorial and diaxial forms of chorismate molecule in water has been studied with a self-consistent reaction field (SCRF) model. Conformational energies in the gas phase have been calculated at the MP2/6-31 + G*//HF/6-31G* level, and solvation energies have been obtained with PCM/6-31G* and PCM/6-31 + G* calculations. The cavity definition of the united atom model for Hartree–Fock (UAHF) was used in the polarizable continuum model (PCM) calculations. The conformational energy surface as a function of the two main degrees of freedom of the principal side-chain has been constructed for the chorismate molecule in the gas phase and in water solution. These surfaces allow a more exhaustive search for conformational minima and the calculation of the entropic contribution to the conformational equilibrium. Five diaxial minima, three of them not described before, two diequatorial minima and a planar ring minimum have been detected. One of the new diaxial minima is essential to correctly reproduce the experimental diaxial–diequatorial proportions in water.

Solvent effect on static vibrational and electronic contribution of first-order hyperpolarizability of π-conjugated push–pull molecules: quantum-chemical calculations

Results of ab initio quantum-chemical calculations of the first-order static electronic ( β e) and vibrational ( β v) hyperpolarizabilities for the prototype push–pull conjugated molecules 4-nitro-aniline, 4-nitro-4 ′-aminostilbene, 4-amino-4 ′-nitrobiphenyl, and 4-amino-4 ′-nitrodiphenylacetylene in the gas phase and in chloroform and aqueous solvents are presented. The coupled perturbed Hartree–Fock method and the sum-over-modes formalism was used to calculate individual components of β e and β v tensors. The solvent effect has been included via the continuum self-consistent reaction field model. The calculations demonstrate the existence of larger solvent effect on the β v compared with β e for molecules investigated in this paper.

Mixed supercrystalline structures in mixtures of ABC triblock and ab(bc) diblock copolymers, 2. Lamellar structures in tricomponent mixtures

The theory of lamellar superstructures in ternary mixtures of ab and bc diblock and linear ABC triblock copolymers under the condition of strong segregation between chemically different blocks is developed. This system is considered using Alexander-de Gennes (box) and self-consistent field (SCF) models. The theory predicts the possibility of phase segregation in the microphase-segregated superstructures. It is shown that the ABC triblock copolymer has unlimited capacity with respect to ab and bc diblock copolymers which include cooperatively into mixed lamella.

Theoretical Phase Diagrams of Polymer/Clay Composites: The Role of Grafted Organic Modifiers

We combine a density functional theory (DFT) with a self-consistent field model (SCF) to calculate the phase behavior of thin, oblate colloidal particles that are coated with surfactants and dispersed in a polymer melt. These coated particles represent organically modified clay sheets. By integrating the two methods, we can investigate the effect of the surfactants' characteristics (grafting density ρgr and length Ngr) and the polymer−surfactant interaction energy on the polymer−clay phase diagram. Depending on the values of these critical parameters and the clay volume fraction, φ, the system can be in an isotropic or nematic phase (which corresponds to an exfoliated composite). The system can also form a smectic, crystal, columnar, or “house-of-cards” plastic solid, as well as a two-phase (immiscible) mixture. Using this model, we isolate conditions that lead to the stabilization of the homogeneous, exfoliated phases (the isotropic and nematic regions) and to the narrowing of the immiscible two-phase re...

Molecular-continuum model for the cyanide ion adsorption from aqueous solutions on copper metals

Quantum-chemical calculations of the cyanide ion adsorption from aqueous solutions on copper metals are performed for the first time in a combined molecular–continuum model of polar solvent. The calculations use the cluster model of the surface and are carried out by the density functional in the B3LYP version. The effect of the adsorption system's polar dielectric environment is considered in a self-consistent reactive field model, namely, the SCIPCM model. The dielectric cavity is built in SCIPCM self-consistently with the particle's electron density distribution in solution. Calculations show that the CN– adsorption energy decreases in the sequence Au > Cu > Ag. The calculated energy agrees best with the experimental data when the molecular–continuum model is used, rather than the simpler molecular and continuum models.

DFT studies on the mechanism of the cycloaddition reaction between methyleneketene and 5-methylene-1,3-dioxan-4,6-dione: regioselectivity and solvent effect

Three different reaction schemes for the cycloaddition reaction between methyleneketene and 5-methylene-1,3-dioxan-4,6-dione were studied by means of the B3LYP/6-31G* methods both in the gas phase and in a solvent of dichloromethane. All the geometries of the stationary points on the reaction paths were optimized by energy gradient technique, and all transition states optimized by the Berny technique. Transition states were ascertained by frequency analysis. The results can be summed up as follows: there are three possible sites of cycloaddition in methyleneketene, i.e., 2,3-CC, 1,2-CC and CO. In the gas phase, the cycloadditions of different double bonds of methyleneketene with 5-methylene-1,3-dioxan-4,6-dione are all concerted but asynchronous, taking place through twisted transition states. The activation barriers for reactions (1), (2) and (3) are calculated to be 2.96, 0.25, and 21.81 kcal/mol at the B3LYP/6-31G* level, respectively. The computational results show that the energy barrier for the reaction leading to 1,2-adduct is the lowest one, which is in consistence with the regioselectivity of the reactions observed by experiments. For comparison, the solvent effect was also studied in the solvent of dichloromethane using self-consistent reaction field model.

A theoretical investigation of tautomeric equilibria and proton transfer in isolated and monohydrated cytosine and isocytosine molecules

The results of an ab initio post Hartree–Fock (HF) comparable study of the relative stabilities and mechanisms of intramolecular proton transfer in isolated and monohydrated cytosine and isocytosine molecules are reported. The geometries of local minima and transition states were optimized without symmetry restrictions by the gradient procedure at the HF and MP2 levels of theory and were verified by energy second derivative calculations. The standard 6-31G(d) basis set was used. The single point calculations have been performed at the MP4(SDQ)/6-31G(d,p)//MP2/6-31G(d) and MP2/6-311++G(d,p)//MP2/6-31G(d) approximations. The post HF ab initio theory predicts different distributions of the tautomers for cytosine and isocytosine both in the gas phase and in polar media (Onsager's self-consistent reaction field model). The interactions with one water molecule change the order of relative stability of cytosine and isocytosine tautomers to those corresponding to the experimentally measured relative stabilities in polar solutions. Ab initio calculations predict the heights of the proton transfer barriers for monohydrated nucleic bases to be approximately three times lower compared with non-water-assisted processes.

Low-Frequency Dielectric Responses, Static Conductivities, and Streaming Potentials of Polymer-Coated Latex Dispersions and Porous Plugs

The low-frequency permittivity and conductivity increments and the static conductivity of well-characterized latex dispersions and plugs have been measured over a wide range of ionic strengths. We have investigated the effects of adsorption of the neutral polymer polyethylene oxide on these electrodynamic phenomena. It is shown that the counterion mobility in the double layer is significantly reduced by the adsorbed polymer. A model is developed to describe the retarded motion of ions in the gel-like polymer layer, which is considered a Brinkman fluid. The required ionic and polymer distribution functions are obtained from a self-consistent field model. Furthermore, ζ-potentials were inferred from streaming potentials of close-packed latex plugs. Since a significant part of the conduction is due to ions behind the shear plane, it was necessary to make use of the plug conductivity data in obtaining the correct ζ-potentials, especially at low ionic strengths. The ζ-potentials of the polymer-coated surface a...

Basic conformers in β‐peptides

The conformation of oligomers of β-amino acids of the general type Ac-[β-Xaa]n-NHMe (β-Xaa = β-Ala, β-Aib, and β-Abu; n = 1–4) was systematically examined at different levels of ab initio molecular orbital theory (HF/6-31G*, HF/3-21G). The solvent influence was considered employing two quantum-mechanical self-consistent reaction field models. The results show a wide variety of possibilities for the formation of characteristic elements of secondary structure in β-peptides. Most of them can be derived from the monomer units of blocked β-peptides with n = 1. The stability and geometries of the β-peptide structures are considerably influenced by the side-chain positions, by the configurations at the Cα- and Cβ-atoms of the β-amino acid constituents, and especially by environmental effects. Structure peculiarities of β-peptides, in particular those of various helix alternatives, are discussed in relation to typical elements of secondary structure in α-peptides. © 1999 John Wiley & Sons, Inc. Biopoly 50: 167–184, 1999

Basic conformers in beta-peptides.

The conformation of oligomers of beta-amino acids of the general type Ac-[beta-Xaa]n-NHMe (beta-Xaa = beta-Ala, beta-Aib, and beta-Abu; n = 1-4) was systematically examined at different levels of ab initio molecular orbital theory (HF/6-31G*, HF/3-21G). The solvent influence was considered employing two quantum-mechanical self-consistent reaction field models. The results show a wide variety of possibilities for the formation of characteristic elements of secondary structure in beta-peptides. Most of them can be derived from the monomer units of blocked beta-peptides with n = 1. The stability and geometries of the beta-peptide structures are considerably influenced by the side-chain positions, by the configurations at the C alpha- and C beta-atoms of the beta-amino acid constituents, and especially by environmental effects. Structure peculiarities of beta-peptides, in particular those of various helix alternatives, are discussed in relation to typical elements of secondary structure in alpha-peptides.

Molecular Mechanism of the Renneting Process of Casein Micelles in Skim Milk, Examined by Viscosity and Light-Scattering Experiments and Simulated by Model SCF Calculations

The properties of the outer hairy layer of casein micelles have been studied using several methods. Viscosity and light-scattering measurements have been performed on rennet-destabilized skim milk at different concentrations of calcium. We have reproduced the known result that calcium promotes destabilization at relatively high κ-casein surface coverages (even at only 50% of the κ-casein molecules cut off). This suggests that calcium bridges contribute to the casein micelle attraction. The effect may be direct by calcium-mediated bridging of β-casein or αs1-casein (phosphate/carboxylate) or κ-casein (carboxylate) or indirect by altering the interplay between several types of caseins in the micelle. In the analysis of the experiments, we make use of an adhesive hard sphere approximation. The casein hairy layer has further been modeled by a self-consistent field (SCF) theory in which coarse-grained molecular details were included. In these calculations the effect of calcium bridges cannot directly be accounted for. It is shown that a κ-casein layer induces repulsive interactions of mainly steric origin. Cutting the N-terminus part results in reduced (shorter-ranged) repulsive pair potentials, which still dominate over the van der Waals attraction. As a result of the altered interplay between the several types of casein molecules during the renneting process, the αs1-casein concentration in the outer hairy layer may increase. Again using the SCF model, but now using a less-detailed description of the system, we examine a possible result of this. We confirm that diblock copolymers (simple model for κ-casein) and diblock copolymer with shorter soluble block (simple model for para-κ-casein) give repulsion and triblock copolymers (simple model for αs1-casein) give attraction by means of bridging (adsorption). The renneting process is simulated by increasing the ratio of model para-κ-casein to κ-casein at a fixed αs1-casein concentration. As a result, the potential shifts from repulsive to attractive. We show that by reducing the range of repulsive interactions of the diblock copolymers, we can make room available to express the attractive contributions of the model αs1-casein. This comprises a novel molecular-based mechanism for the renneting process.