Static properties of end-tethered polymers in good solution: a comparison between different models

We present a comparison between results, obtained from different simulation models, for the static properties of end-tethered polymer layers in good solvent. Our analysis includes data from two previous studies--the bond fluctuation model of Wittmer et al. [J. Chem. Phys. 101, 4379 (1994)] and the off-lattice bead-spring model of Grest and Murat [Macromolecules 26, 3108 (1993)]. Additionally, we explore the properties of a similar off-lattice model simulated close to the Theta temperature. We show that the data for the bond fluctuation and the Grest-Murat model can be analyzed in terms of scaling theory because chains are swollen inside the Pincus blob. In the vicinity of the Theta point the structure of the chains is essentially Gaussian in the Pincus blob. Therefore, the data for the second off-lattice model can be compared quantitatively to the self-consistent field theory. Different ways to determine the parameters of the self-consistent field theory are discussed.     

Applications of self-consistent field theory in polymer systems

1Introduction Owing to the specificity of the long chain,polymers present complexity and versatility.These molecules in the system can be various in their topological struc-tures,such as linear,star,comb or circle structures;meanwhile they can be polymeri…     

Self-consistent field equations in the distribution function theory of polymeric liquids

In the distribution function approach to the conformational and thermodynamic properties of polymeric liquids site-site (pair) distribution functions are essential components of the theory. These site-site pair distribution functions are basically mean fields obeying integral equations. In our recent works, a set of self-consistent field equations has been proposed for site-site pair correlation functions which allow us to study conformational and thermodynamic properties of polymeric liquids. In this article, we present a short review of the theory and its applications to a number of aspects of polymeric liquids we have made until now. We also present a self-consistent version of the polymer reference interaction site model where the integral equations for the intramolecular site-site correlation functions are obtained from the Kirkwood hierarchy on the basis of the present theory. The present theory is shown to predict correctly the scaling properties associated with swollen and collapsed polymers in good and poor solvents, respectively. At finite densities, self-consistent solutions of the intra- and intermolecular equations yield the structures and thermodynamics of polymer melts which are favorably compared with Monte Carlo simulation results. Self-consistent theory results are found to be more accurate than the non-self-consistent approaches that use an ideal Gaussian chain conformation distribution function. © 1995 John Wiley & Sons, Inc.     

Voids, generic van der Waals equation of state, and transport coefficients of liquids

In this Perspective, we discuss the role of voids in transport processes in liquids and the manner in which the concept of voids enters the generic van der Waals equation of state and the modified free volume theory. The density fluctuation theory is then discussed and we show how the density fluctuation theory can be made a molecular theory with the help of the modified free volume theory and the generic van der Waals equation of state. The confluence of the aforementioned three theories makes it possible to calculate the transport coefficients of liquids by using the information on the equilibrium pair correlation function, which can be calculated either by an integral equation theory or Monte Carlo simulations. A number of relations between transport coefficients are also presented, which are derived on the basis of the density fluctuation theory. Since they can be used to obtain one transport coefficient from another they can be very useful in handling experimental and theoretical data. An application of the modified free volume theory to polymer melts is discussed as an example for a theory of transport properties of complex liquids.     

SCF perturbation theory and intermolecular interactions

A self-consistent perturbation theory is derived in the framework of Roothaan's MOLCAO procedure for closed shell systems. Contrary to previous investigations which have considered only one particle perturbations, two particle perturbation operators are considered. Expressions for the first-order density matrix and first- and second-order energy corrections are obtained. A diagram formulation of the complete perturbation expansion is presented. The results are applied to the treatment of the intermolecular interaction problem. The interaction energy is represented as a sum of several contributions: Coulomb, exchange, resonance, polarization and exchange repulsion. A semi-empirical version of the theory is suggested which explicitly involves all the physically significant energy terms and may be useful for the investigation of complex systems.     

Some remarks on the SCRF theory of solvent effects and the calculation of proton potentials

Some aspects concerning the self-consistent reaction field theory of solvent effects are discussed. In particular, the variational solution to the non-linear Schrödinger equation is considered; a necessary and sufficient constraint to be added to the standard variational procedure is discussed. The exact solution of the non-linear equation is presented within the molecular orbital approach; correlation defaults to the Hartree-Fock like solutions are stated. Some thermodynamical correspondences are established with the magnitudes calculated with the self-consistent reaction field theory. Finally, we have commented upon the proton potentials calculated within this theory. An INDO calculation of a water trimer has been used as an example to discuss different types of proton translocation potentials.     

Two- and three-body interactions among nanoparticles in a polymer melt

We perform direct three-dimensional density functional theory (DFT) calculations of two- and three-body interactions in polymer nanocomposites. The nanoparticles are modeled as hard spheres, immersed in a hard-sphere homopolymer melt of freely jointed chains. The two-particle potential of mean force obtained from the DFT is in near quantitative agreement with the potential of mean force obtained from self-consistent polymer reference interaction site model theory. Three-body interactions among three nanoparticles are found to be significant, such that it is not possible to describe these systems with a polymer-mediated two-body interaction calculated from the potential of mean force.     

Time-dependent self-consistent field approximation for semiclassical dynamics using gaussian wavepackets in phase space

Gaussian wavepackets in phase space, which are constructed to have the exact first and second moments with respect to the coordinates and momenta, are used to develop self-consistent equations of motion for the semiclassical time evolution of interacting anharmonic systems. The equations apply to pure as well as to mixed states and may, therefore, be particularly useful for molecular dynamics in condensed phases.     

Energy decomposition analysis based on a block-localized wavefunction and multistate density functional theory

An interaction energy decomposition analysis method based on the block-localized wavefunction (BLW-ED) approach is described. The first main feature of the BLW-ED method is that it combines concepts of valence bond and molecular orbital theories such that the intermediate and physically intuitive electron-localized states are variationally optimized by self-consistent field calculations. Furthermore, the block-localization scheme can be used both in wave function theory and in density functional theory, providing a useful tool to gain insights on intermolecular interactions that would otherwise be difficult to obtain using the delocalized Kohn-Sham DFT. These features allow broad applications of the BLW method to energy decomposition (BLW-ED) analysis for intermolecular interactions. In this perspective, we outline theoretical aspects of the BLW-ED method, and illustrate its applications in hydrogen-bonding and π-cation intermolecular interactions as well as metal-carbonyl complexes. Future prospects on the development of a multistate density functional theory (MSDFT) are presented, making use of block-localized electronic states as the basis configurations.     

Incompatibility of polymer solutions. II. Concentration and angle dependence of the light scattering in the system polystyrene + polyisobutylene + toluene

Light scattering experiments are described on the system polystyrene (PS) + polyisobutylene (PIB) + toluene at constant temperature. At a fixed concentration of the nearly “invisible” PIB the light scattering at various angles was measured as a function of varying PS concentration up to the region of incompatibility. For interpretation of the results use is made of an extension of the classical fluctuation theory for multicomponent systems to finite scattering angles. The experimental data can be described qualitatively with this theory. Addition of a second polymer has little influence on the size of the other polymer. The variation of the light scattering with the wavelength can be explained in terms of the (negative) adsorption of one polymer by the other.     

Choice of Spin–Orbit Correction Terms in Gaussian Model Chemistries

Spin–orbit correction terms for use in Gaussian‐2 theory and other model chemistries for third‐row atoms and molecules are calculated by several methods with the objective of finding a reliable method that can be applied in a routine and economical manner in the spirit of Gaussian model chemistries. The results are evaluated for the test set of molecules and ions used in the original extension of Gaussian‐2 theory to third‐row atoms. Further results are presented for systems where Gaussian‐2 results are reported in the literature without spin–orbit correction terms and for some larger molecules. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1552–1556, 2001     

Theory of nematic ordering in supramolecular systems: Self-assembly of mesogenic groups and self-organization of the system

The behaviors of two systems are considered: a low-molecular system (a binary mixture of low-molecular components) and a polymer system (mixture of a macromolecules and a low-molecular dopant) whose components reversibly bind to form dimers capable of liquid-crystal ordering. The general theory of binary-mixture structuring, where two processes occur—self-assembly of mesogenic dimers of the mixture components and their self-organization—is presented. The theory demonstrates general laws of the behavior of low-molecular and polymer systems as well as differences related to the features of polymer thermodynamics.     

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.     

Monte Carlo simulation of polymeric materials: Recent progress

Monte Carlo simulations are presented, dealing with phase diagrams of block copolymer melts and polymer blends, including the unmixing kinetics of the latter systems. The theoretical background is briefly reviewed: Ginzburg-type criteria reveal that in mixtures of long flexible polymers a “crossover” occurs from mean-field behavior (as described by Flory-Huggins theory) to nonclassical Ising-type behavior, and spinodal curves can be unusually sharp. This crossover is demonstrated by large scale simulations of the bond fluctuation model, and it is also shown that for symmetric mixtures the critical temperature scales with chain length as T_c α N. The prefactor in this relation is distinctly smaller than predicted by Flory-Huggins, but the Curro-Schweizer integral equation theory prediction T_c α √N is clearly ruled out. Tests of the Cahn theory on the initial stages of spinodal decomposition of polymer blends will also be reported. To conclude, the mesophase formation in block copolymers is discussed, and it is shown that the simulations agree very well with experiment. The pronounced chain stretching that already occurs in the disordered phase is compelling evidence against the validity of simple random phase approximation concepts for these systems. This shows how Monte Carlo simulations can assist in better understanding large classes of polymeric materials.     

Synthesis,characterization and recent developments of liquid crystalline polymers

Recent developments of polymer liquid crystals (PLCs) are reviewed. The virial expansion method of Onsager and the lattice model used by Flory to appreciate the most relevant parameters in establishing mesomorphic behavior in polymeric systems are presented. These and other theoretical predictions are confirmed by numerous experiments. Both lyotropic (polymer solutions) and thermotropic (polymer melts) types of PLCs are considered with emphasis placed on the latter. The general properties of mesophases formed by such polymers are surveyed and some chemical structures capable of producing mesophases are classified in relation to their ability to form lyotropic and thermotropic systems. The synthetic routes, the effects of polymer structure on physical properties, and applications of two major classes of lyotropic systems (polypeptides, polyamides) and of a range of potentially important thermotropic polymers are discussed.     

Self-consistent mode-coupling theory for the viscosity of rodlike polyelectrolyte solutions

A self-consistent mode-coupling theory is presented for the viscosity of solutions of charged rodlike polymers. The static structure factor used in the theory is obtained from polymer integral equation theory; the Debye-Huckel approximation is inadequate even at low concentrations. The theory predicts a nonmonotonic dependence of the reduced excess viscosity eta(R) on concentration from the behavior of the static structure factor in polyelectrolyte solutions. The theory predicts that the peak in eta(R) occurs at concentrations slightly lower than the overlap threshold concentration, c*. The peak height increases dramatically with increasing molecular weight and decreases with increased concentrations of added salt. The position of the peak, as a function of concentration divided by c*, is independent of salt concentration or molecular weight. The predictions can be tested experimentally.     

Polymer microfluidic chips for electrochemical and biochemical analyses

Our recent developments concerning the fabrication of polymer microchips and their applications for biochemical analyses are reviewed. We first describe two methods of fabrication of polymer microfluidic chips, namely UV-laser photoablation and plasma etching that are well suited for the prototyping and mass fabrication of microchannel networks with integrated microelectrodes. These microanalytical systems can be coupled with various detection means including mass spectrometry, and their applications in capillary electrophoresis are presented here. We also present how UV laser photoablation can be used for the patterning of biomolecules on polymer surfaces for generating two-dimensional arrays of microspots to carry out affinity assays. Finally, the use of the microchips for the development of fast affinity and immunological assays with electrochemical detection is presented, demonstrating the potential of these polymer microchips for medical diagnostics and drug discovery.     

Quantum chemical methods for the investigation of photoinitiated processes in biological systems: theory and applications.

With the advent of modern computers and advances in the development of efficient quantum chemical computer codes, the meaningful computation of large molecular systems at a quantum mechanical level became feasible. Recent experimental effort to understand photoinitiated processes in biological systems, for instance photosynthesis or vision, at a molecular level also triggered theoretical investigations in this field. In this Minireview, standard quantum chemical methods are presented that are applicable and recently used for the calculation of excited states of photoinitiated processes in biological molecular systems. These methods comprise configuration interaction singles, the complete active space self-consistent field method, and time-dependent density functional theory and its variants. Semiempirical approaches are also covered. Their basic theoretical concepts and mathematical equations are briefly outlined, and their properties and limitations are discussed. Recent successful applications of the methods to photoinitiated processes in biological systems are described and theoretical tools for the analysis of excited states are presented.