Ab initio studies of the ground-state potential energy surface of formamide

Ab initio calculations employing a standard double-zeta basis set augmented with various polarization functions have been used to investigate the lowest energy region of the ground-state potential energy surface of the formamide molecule. Hartree-Fock calculations with only d polarization functions on the nonhydrogen atoms located two stable minima, that with geometry distorted from planarity having slightly lower energy; only one stable minimum with planar structure is found when p polarization functions on the hydrogens are included. In contrast optimizations, which account approximately for the correlation energy using second-order Møller-Plesset perturbation theory consistently favor a single slightly nonplanar minimum energy geometry.     

Bosonised DFT potential estimated from QMC calculations of the ground-state density for the inhomogeneous electron liquid in Be

To avoid the solution of numerous Kohn–Sham one-body potential equations for wave functions in density functional theory, various groups independently proposed the use of Pauli potential to bosonise the customary one-body potential theory. Here, we utilise our recent quantum Monte Carlo calculations of the ground-state electron density of the Be atom to estimate the bosonised one-body potential V_B(r) and hence extract the Pauli potential for this atom.     

Intermolecular potential energy surface for CS2 dimer

A new four‐dimensional intermolecular potential energy surface for CS₂ dimer is obtained by ab initio calculation of the interaction energies for a range of configurations and center‐of‐mass separation distances for the first time. The calculations were performed using the supermolecular approach at the Møller–Plesset second‐order perturbation (MP2) level of theory with the augmented correlation consistent basis sets (aug‐cc‐pVxZ, x = D, T) and corrected for the basis‐set superposition error using the full counterpoise correction method. A two‐point extrapolation method was used to extrapolate the calculated energy points to the complete basis set limit. The effect of using the higher levels of theory, quadratic configuration interaction containing single, double, and perturbative triple excitations QCISD(T) and coupled cluster singles, doubles and perturbative triples excitations CCSD(T), on the shape of potential energy surface was investigated. It is shown that the MP2 level of theory apparently performs extremely poorly for describing the intermolecular potential energy surface, overestimating the total energy by a factor of nearly 1.73 in comparison with the QCISD(T) and CCSD(T) values. The value of isotropic dipole–dipole dispersion coefficient (C₆) of CS₂ fluid was obtained from the extrapolated MP2 potential energy surface. The MP2 extrapolated energy points were fitted to well‐known analytical potential functions using two different methods to represent the potential energy surface analytically. The most stable configuration of the dimer was determined at R = 6.23 au, α = 90°, β = 90°, and γ = 90°, with a well depth of 3.980 kcal mol^?1 at the MP2 level of theory. Finally, the calculated second virial coefficients were compared with experimental values to test the quality of the presented potential energy surface. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011.     

Theoretical and experimental comparison of the colloid stability of two polystyrene latexes with different sign and value of the surface charge

 The purpose of this paper is to apply the classical DLVO theory to explain the colloid stability of two model colloids with similar size and different sign and value of the surface charge. For this comparison the hydrodynamic interaction and the presence of hydration forces (extended DLVO theory) have been taken into account. The experimental stability factor and the experimental doublet rate constant in diffusion conditions were compared with those evaluated theoretically. The mathematical treatment permits an easy evaluation and interpretation of the different adjustable parameters such as the Hamaker constant, diffuse layer potential and the hydration layer thickness. The theoretical and experimental comparison shows that the “extended DLVO theory” only permits to explain the stability curves Log[W]/Log[KBr] in a semiquantitative way by using, for the evaluation of the total interaction potential V _T, a value of the Hamaker constant (A) similar to the classical theoretical one for polystyrene particles dispersed in water. In the case of the anionic latex, it was necessary to admit the presence of a hydration layer of a thickness similar to the radius of the hydrated/dehydrated counterion. On the other hand, by using the experimental doublet rate constant in diffusion conditions, we obtain a lower value of the Hamaker constant (A), but within the range of the A values usually found in previous studies. Received: 8 September 1997 Accepted: 8 January 1998     

Surface diffusion and relaxation of partially adsorbed polymers

We studied by lattice simulation the surface diffusion and relaxation of isolated, self‐avoiding polymers partially adsorbed onto a flat surface. The key parameters describing the system are the number of segments in the chain, N, the adsorption energy of a segment, expressed as a dimensionless surface temperature T_s, and the segmental friction factor on the surface relative to that in the bulk, ζ_s/ζ_b. The simulation data indicate Rouse scaling of the surface diffusion coefficient, D_∥, and in‐plane relaxation time, τ, versus N for all values of T_s and ζ_s/ζ_b studied. A simple application of the Rouse model to a partially adsorbed chain, which ignores fluctuations in adsorbed trains, yields a formula for D_∥ with the correct N‐scaling. It can account for the effects of T_s when ζ_s/ζ_b is finite (≲10), but it fails when ζ_s/ζ_b diverges, predicting no surface diffusion at all, whereas simulations indicate finite surface mobilities facilitated by a caterpillar‐like motion. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1146–1154, 2000     

The glass transition in polymer melts

This paper presents some results of a Monte Carlo simulation for the glass transition in two- and three-dimensional polymer melts. The melt was simulated by the bond-fluctuation model on a d-dimensional cubic lattice which was combined with a two-level hamiltonian favouring long bonds in order to generate a competition between the energetic and topological constraints in the system. This competition prevents crystallization and makes the melt freeze in an amorphous structure as soon as the internal relaxation times match the observation time of the simulation set by the cooling rate. The freezing point of the melt, i.e the glass transition temperature T_g, thus depends upon the cooling rate and additionally upon the chain length of the polymers. The dependence of the glass transition temperature on the cooling rate was closely analysed in three and that on the chain length in both two and three dimensions, resulting in a non-linear relationship between T_g and the logarithm of the cooling rate and a linear relationship between T_g and the inverse chain length, respectively. In addition to this behaviour of the melt during the cooling process an example for the relaxational properties of the three-dimensional model is provided by a quantitative analysis of the incoherent intermediate scattering function in the framework of the idealized mode coupling theory.     

Functionalization of polyesters with multiple B vitamins

A method to covalently attach combinations of six different B vitamins provided an avenue to new functional thermosets without multi‐step coupling reactions. The melt polymerization strategy required no organic solvent and facilitated covalent attachment of OH (B₁, B₂, B₅, B₆) or COOH (B₇, B₉) groups on B vitamins via Fischer esterification. Characterization of model reactions with LC/MS, FTIR, and GPC confirmed covalent attachment. Based on control experiments, B vitamins demonstrated unexpected thermal stability and appreciable solubility in the melt polymerization. This approach was demonstrated with citric acid and diglycerol, but has wide‐ranging potential for other polar monomers with negative octanol–water partition coefficients (LogP). © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3308–3316     

Grafting of polymers with controlled molecular weight onto ultrafine silica surface

To graft polymers with controlled molecular weight and narrow molecular weight distribution, the grafting of polymers onto ultrafine silica surface by the termination of living polymer cation with amino groups introduced onto the surface was investigated. The introduction of amino or N-phenylamino groups onto the silica surface was achieved by the treatment of silica with γ-aminopropyltriethxysilane or N-phenyl-γ-aminopropyltrimethoxysilane. It was found that these amino groups on silica are readily reacted with living poly(isobutyl vinyl ether) (polyIBVE), which was generated with CF₃COOH/ZnCl₂ initiating system, and polyIBVE with controlled molecular weight and narrow molecular weight distribution is grafted onto the surface. By the termination of living poly(2-methyl-2-oxazoline), which was generated with methyl p-toluenesulfonate initiator, with amino groups on silica, polyMeOZO was also grafted onto the surface. The percentage of grafting of polymer onto the silica surface decreased with increasing molecular weight of the living polymer, because the steric hindrance of silica surface increases with increasing molecular weight of living polymer. Polymer-grafted silica gave a stable dispersion in a good solvent for grafted chains. © 1995 John Wiley & Sons, Inc.     

Electrophoresis of large colloidal particles with surface charge layers. Position of the slipping plane and surface layer thickness

A theory is proposed for the electrophoresis of a large colloidal particle with a surface charge layer. The slipping plane is assumed to be located within the surface layer but may not be located at the boundary between the surface layer and the particle core. In previous studies, the depth of the slipping plane is assumed to coincide with the surface layer thickness. The present theory makes it possible to examine the separate dependence of the electrophoretic mobility on the position of the slipping plane and on the surface layer thickness. It is shown that, at constant amount of particle-fixed charges in the surface layer, the mobility increases as the depth of the slipping plane (d _s ) increases, while it decreases as the surface layer thickness (d _c ) increases, causing a mobility maximum in some cases ifd _s =d _c . Several approximate analytic expressions for the mobility are presented.     

Exact electronic properties in the classically forbidden region of a metal surface

We derive exact properties of the inhomogeneous electron gas in the asymptotic classically forbidden region at a metal–vacuum interface within the framework of local effective potential energy theory. We derive a new expression for the asymptotic structure of the Kohn–Sham density functional theory (KS‐DFT) exchange‐correlation potential energy v_xc(r) in terms of the irreducible electron self‐energy. We also derive the exact asymptotic structure of the orbitals, density, the Dirac density matrix, the kinetic energy density, and KS exchange energy density. We further obtain the exact expression for the Fermi hole and demonstrate its structure in this asymptotic limit. The exchange‐correlation potential energy is derived to be v_xc(z → ∞) = ?α_KS,xc/z, and its exchange and correlation components to be v_x(z → ∞) = ?α_KS,x/z and v_c(z → ∞) = ?α_KS,c/z, respectively. The analytical expressions for the coefficients α_KS,xc and α_KS,x show them to be dependent on the bulk‐metal Wigner–Seitz radius and the barrier height at the surface. The coefficient α_KS,c = 1/4 is determined in the plasmon‐pole approximation and is independent of these metal parameters. Thus, the asymptotic structure of v_xc(z) in the vacuum region is image‐potential‐like but not the commonly accepted one of ?1/4z. Furthermore, this structure depends on the properties of the metal. Additionally, an analysis of these results via quantal density functional theory (Q‐DFT) shows that both the Pauli W_x(z → ∞) and lowest‐order correlation‐kinetic W(z → ∞) components of the exchange potential energy v_x(z → ∞), and the Coulomb W_c(z → ∞) and higher‐order correlation‐kinetic components of the correlation potential energy v_c(z → ∞), all contribute terms of O(1/z) to the structure. Hence correlations attributable to the Pauli exclusion principle, Coulomb repulsion, and correlation‐kinetic effects all contribute to the asymptotic structure of the effective potential energy at a metal surface. The relevance of the results derived to the theory of image states and to KS‐DFT is also discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Molecular dimensions and melt rheology of an all‐aromatic liquid crystalline polymer

The molecular dimensions and melt rheology of a thermotropic all‐aromatic liquid crystalline polyester (TLCP) composed of p‐hydroxy benzoic acid, hydroquinone, terephthalic acid, and 2,4‐naphthalenedicarboxylic acid is examined. The Mark–Houwink exponent (α) of 0.95 is estimated for the TLCP. The persistence length estimated from molecular weight (M) and intrinsic viscosity ([η]) data using the Bohdanecky–Bushin equation is about 95 Å, whereas that estimated from light scattering data is 117 Å. These persistence lengths and the observed α value, both higher than those for flexible polymers, suggest that the present TLCP is a semirigid polymer. The zero shear melt viscosity (η₀) varies with approximately M⁶ for molecular weight M > 3 × 10⁴ g/mol; below this molecular weight, η₀ varies almost linearly with M. Widely different entanglement molecular weights (M_e) are predicted, depending on the method used; the plateau modulus estimates M_e of about 8 × 10⁵ g/mol, whereas the ratio of mean square end‐to‐end distance and molecular weight (〈R²〉₀/M) predicts M_e's either too small (0.33 g/mol) or too large (2.5 × 10⁶ g/mol), depending on the theory used. Although the change in the molecular weight dependency of melt viscosity appears to be associated with the onset of entanglement coupling of the semirigid molecules, its origin needs further investigation. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2378–2389, 2001     

Monte Carlo simulations of the exchange kinetics of polymers adsorbed on a solid surface

The exchange kinetics of polymers adsorbing on a solid surface is extensively studied by dynamic Monte Carlo simulations. A model employed simulates a semidilute polymer solution placed in contact with a solid surface that attracts polymer segments by the adsorption interaction (χ_s). The exchange process of polymer chains, between the solution and the adsorbed polymer layer, is examined under various conditions. The exchange kinetics shows two characteristic regimes with increasing chain length. One is the diffusion‐controlled regime found with a small χ_s , and the other the detachment‐controlled regime with a large χ_s . These two regimes are well described by a kinetic theory. Various dynamic quantities show that the diffusion‐controlled regime is not due to sluggish dynamics near the surface, but rather to bulk diffusion of chains. The diffusion‐controlled regime found in this study is considered to appear at the high temperature limit.     

Influence of conformational asymmetry on the surface enrichment of polymer blends II

We reexamine the influence of statistical segment length asymmetry on the surface segregation of homopolymer blends in a mean field thread model of polymer melts. By developing numerical self-consistent field solutions of the Edwards-Helfand equations, we demonstrate that the component with the smaller value of the parameter β² = a²/(6ν) (a is the statistical segment length and ν is the segment volume) is enriched at a neutral, impenetrable surface. Qualitatively, this finding is in agreement with our earlier analytical work and with experiment. However, in contrast to our earlier work, we find that the absolute magnitude of the segregation is a sensitive function of the chain lengths of the two species and of the compressibility of the system. © 1995 John Wiley & Sons, Inc.     

Kinetics of wetting of a glass surface by molten polyethylene: An empirical approach

The spreading kinetics of molten polyethylene was studied on a flat type A glass surface. Empirical equations are known in the literature which fit the experimental data only at short times. We present a relationship between the surface free energy and the shape of the melt drop interpreted by the θ contact angle. Relating the experimental θ values obtained at different times with the surface free energy (F), we obtain curves F,t. Using isothermal data at 150°C, we could fit them with a linear relationship between In (F-F_∞)/(F₀-F_∞) and In t/t₀, where o and ∞ are related to initial and equilibrium conditions.     

Edge profiles at lamellar phase/melt interfaces

We study in the framework of the continuum theory of dislocations the structure of the interface between an AB diblock copolymer lamellar film deposited on a solid substrate and an A-homopolymer melt. The dislocation inside the lamellar phase induces steps at the interface. The shape of the profile at the edge of a step (edge profile) depends on the distance of the dislocation from the interface. The profile and the equilibrium location of the dislocations are both studied as a function of the film thickness, D. For large D, the dislocation is stabilized at a finite distance, h_eq, from the interface, due to the small surface tension and large surface bending elastic constant, K_s. For zero surface tension, h_eq ≈ K_s/(2K), where K is the bulk bending elastic constant. For small D, h_eq is mainly determined by the proximity of the solid substrate. The edge profile along the interface is a monotonic function of the distance along the interface for large D of the film and becomes nonmonotonic for small D. Also the dislocation energy strongly depends on D for small D. The theory is discussed in connection to recent experimental studies of diblock copolymer films deposited on a solid substrate.     

Transitions from static wetting to steady dewetting and deposition of liquid-film on partially wettable polymer surface

The transitions from static to steadily moving wetting perimeter and further to deposition of a liquid-film on partially wettable surface were studied with the same system under the same conditions. A polyethylene terephthalate (PET) tape was vertically withdrawn at constant velocity from glycerol–water mixture. Elevation L of the three-phase contact line above the liquid level was measured under static, steady, and dynamic wetting. The static receding Θ_R and the apparent dynamic angles Θ_app at different withdrawal velocities U were calculated from the static relationship Θ(L). It was found that the limiting static angle Θ_R,min, at which the wetting perimeter starts moving, depends on withdrawal velocity. Extrapolation of the Θ_R,min/U dependence to U = 0 yields the quasi-static value of this parameter , that coincides with the relaxation static angle Θ_R,rlx achieved after meniscus motion ceases. This conclusion holds also for the wetting mode, where the limiting static advancing angle = Θ_A,rlx. Both the limiting and relaxation angles could be used for calculation of the effective Young's contact angle on non-ideal surface following Adam's suggestion [N.K. Adam, Adv. Chem. Ser. 43 (1964) 53.].The critical velocity U_cr anfd apparent dynamic angle Θ_app,cr, at which transition between steady dewetting and dynamic wetting occurs, were determined. The value of Θ_app,cr = 0° ± 5° agrees with our previous results [R.V. Sedev, J.G. Petrov, Colloids and Surfaces, 53 (1991) 147] implying a quasi-static shape of the moving meniscus up to U_cr. At U > U_cr, the speed V of the contact line relative to the solid wall is independent of withdrawal velocity and thickness of the deposited film. The present data confirm the earlier findings [J.G. Petrov, R.V. Sedev, Colloids and Surfaces, 13 (1985) 317, T.D. Blake, K.J. Ruschak, Nature, 282 (1979) 489] that at U = U_cr, V reaches its maximum value V_max, which is most important parameter of dewetting kinetics.Weak linear decrease of Θ_app with U was found above Ca = 2.4 × 10⁻⁵ up to the critical capillary number Ca_cr = 4.1 × 10⁻⁴. Below Ca = 10⁻⁵ the apparent receding angle depends much stronger on withdrawal velocity. The hydrodynamic (HD), and the simple and more general versions of the molecular-kinetic (MK) and molecular-hydrodynamic (MHD) theories of the wetting dynamics were used for quantitative characterization of the system in the steady dewetting regime. The effective Young's angle was used in the MK and MHD treatment of the experimental data following our previous publication [J.G. Petrov, J. Ralston, M. Schneemilch, R. Hayes, J. Phys. Chem B, 107(7) (2003) 1637]. The HD theory only qualitatively satisfies our experimental data giving physically unreasonable value of the hydrodynamic cut-off (slip) length and too small static receding angle at U = 0. The MK theory gives acceptable values of the oscillation frequency K₀ of the molecules at the contact line. Its more general version, including the viscous dissipation in the contact line vicinity, yields higher oscillation frequency. Very large distance λ between adsorption centers on the solid substrate (about five times the diameter of a glycerol molecule) was obtained with both MK and MHD theories. The too small frequency K₀ obtained with the simple MHD theory is removed by the more general version, accounting for contact line and viscous friction in the inner and intermediate zone of the moving meniscus. All theories show discrepancies between theoretically expected and experimentally estimated values of some of the parameters of wetting dynamics.     

Reduction of the effective shear viscosity in polymer solutions due to crossflow migration in microchannels: Effective viscosity models based on DPD simulations

Molecular dynamics simulations (dissipative particle dynamics–DPD) were developed and used to quantify wall-normal migration of polymer chains in microchannel Poseuille flow. Crossflow migration due to viscous interaction with the walls results in lowered polymer concentration near the channel walls. A larger fraction of the total flow volume becomes depleted of polymer when the channel width h decreases into the submicron range, significantly reducing the effective viscosity. The effective viscosity was quantified in terms of channel width and Weissenberg number Wi, for 5% polymer volume fraction in water. Algebraic models for the depletion width δ(Wi, h) and effective viscosity μ_e(δ/h, Wi) were developed, based on the hydrodynamic theory of Ma and Graham and our simulation results. The depletion width model can be applied to longer polymer chains after a retuning of the polymer persistence length and the corresponding potential/thermal energy ratio.     

Numerical computation of surface areas of molecules

For a cubical tesselation of a finite region of space which contains an irregularly shaped surface, a fairly accurate estimate of the surface area is 2/3N a ², whereN is the total number of cubes cut by the surface and a is the length of the edges of the cubes. An estimate of slightly improved accuracy can be obtained by using different increments to the surface area, depending on the number of edges of the corresponding cube cut by the surface and the number of vertices on either side of the surface.     

A study of the pressure-volume-temperature relationships of four related amorphous polymers: Polycarbonate,polyarylate, phenoxy,and polysulfone

The pressure-volume-temperature (PVT) relationships of bisphenol-A polycarbonate, polyarylate, and phenoxy were studied at pressures to 1800 kg/cm² and in both the glassy and melt states. Earlier data on polysulfone are included in the analysis and discussion of the results. All four polymers contain the bisphenol-A residue in their repeat unit, together with a moiety of varying complexity, and are therefore somewhat related. At the glass transition, equations of the Ehrenfest type hold, provided the pressure dependence of the glass transition temperature is defined from the line obtained by intersecting the quasiequilibrium PVT relationship of the glass with the equilibrium PVT surface of the melt. The Prigogine-Defay ratio r = Δ_κΔC_p/T_gV_g(Δα)² at P = O is unity within experimental error for all four polymers. The melt data were fitted successfully to the Simha-Somcynsky theory. Molecular parameters deduced from the reducing parameters vary in a reasonable manner among these four related polymers, lending support to the foundations of the theory.     

A Strategy for the Regional Characterization of Potential Energy Surfaces

The problem of characterization of a region of an n-dimensional potential energy surface with maximization of the quality of representation for a given amount of computational effort is examined with the aid of well known theorems from numerical analysis. A choice of nonlinear grid and a representation of the potential expanded in Chebyshev polynomials is shown to be efficient. The strategy was applied to a two-dimensional analytical representation of a transition state and to the ground-state equilibrium geometry region of the Hartree-Fock potential energy surface obtained with split-valence basis sets for H₂O, H₂S, and H₂Se. Results are reported for the equilibrium geometries and force constants for these molecules. Results are comparable to those obtained by others for H₂O and H₂S. A full set of values is reported for H₂Se.