Continuum formulation of the Scheutjens-Fleer lattice statistical theory for homopolymer adsorption from solution

Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n(1,e) and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction phi; both n(1,e) and phi enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field. The equilibrium distribution of chain ends and, consequently, of chain conformational probabilities is found by minimizing the system free energy. This results in a set of model equations that constitute the exact continuum-space analog of the Scheutjens-Fleer (SF) lattice statistical theory for the adsorption of interacting chains. Since for distances too close to the surface the continuum formulation breaks down, the continuum model is here employed to describe the probability of chain configurations only for distances z greater than 2l, where l denotes the segment length, from the surface; instead, for distances z < or = 2l, the SF lattice model is utilized. Through this novel formulation, the lattice solution at z = 2l provides the boundary condition for the continuum model. The resulting hybrid (lattice for distances z < or = 2l, continuum for distances z > 2l) model is solved numerically through an efficient implementation of the pseudospectral collocation method. Representative results obtained with the new model and a direct application of the SF lattice model are extensively compared with each other and, in all cases studied, are found to be practically identical.     

Thermodynamically guided nonequilibrium Monte Carlo method for generating realistic shear flows in polymeric systems

A thermodynamically guided atomistic Monte Carlo methodology is presented for simulating systems beyond equilibrium by expanding the statistical ensemble to include a tensorial variable accounting for the overall structure of the system subjected to flow. For a given shear rate, the corresponding tensorial conjugate field is determined iteratively through independent nonequilibrium molecular dynamics simulations. Test simulations for the effect of flow on the conformation of a C50H102 polyethylene liquid show that the two methods (expanded Monte Carlo and nonequilibrium molecular dynamics) provide identical results.     

Pseudospectral calculations of stress-induced concentration changes in viscometric flows of polymer solutions

We investigate the flow of dilute polymer solutions in viscometric devices where the polymer concentration is allowed to vary due to the existence of nonzero stress gradients. A spectral collocation method is used in order to solve for the axisymmetric steady-state solution of the full set of the governing equations. Two alternative continuum formulations are considered based on a single- and two-fluid concept, respectively. For the parallel-plate flow problem and for the two-fluid model, the analytical solution obtained by Brunn (1984) is recovered. This solution describes a polymer migration toward the centerline that depends solely on the Weissenberg number. The results obtained for the single-fluid model are qualitatively similar; however, they also depend on additional molecular parameters. Variations in the geometry which initiate even a small secondary recirculation are found to result in a significant decrease in the concentration gradients, as shown in the analysis of the cone-and-plate flow for a small angular inclination and a large centerline gap thickness. When the centerline gap thickness decreases, the results are dominated by the ideal, purely azimuthal cone-and-plate flow behavior, according to which substantial variations in the radial concentration are observed mainly close to the centerline. This is in agreement with the predictions of Aubert et al. (1980) and Brunn (1984).The authors would like to acknowledge the financial support of NSF, Grant No. CTS-9114508 (to V.G.M. and A.N.B.), and the Center of Composite Materials for a Center-Industry fellowship (to A.S.). The computational support provided by the Pittsburgh Supercomputing Center is also gratefully acknowledged.     

Shape resonances in slow electron scattering by aromatic molecules. I. Anthraquinone derivatives

A series of anthraquinone (C(14)O(2)H(8)) derivatives has been studied by means of electron capture negative ion mass spectrometry (ECNI-MS), photoelectron spectroscopy (PES), and AM1 quantum chemical calculations. Mean lifetimes of molecular negative ions M(-.) (MNI) have been measured. The mechanism of long-lived MNI formation in the epithermal energy region of incident electrons has been investigated. A simple model of a molecule (a spherical potential well with the repulsive centrifugal term) has been applied for the analysis of the energy dependence of cross sections at the first stage of the electron capture process. It has been shown that a temporary resonance of MNI at the energy approximately 0.5 eV corresponds to a shape resonance with lifetime 1-2.10(-13) s in the f-partial wave (l = 3) of the incident electron. The next resonant state of MNI at the energy approximately 1.7 eV has been associated with the electron excited Feshbach resonance (whose parent state is a triplet npi* transition). In all cases the initial electron state of the MNI relaxes into the ground state by means of a radiationless transition, and the final state of the MNI is a nuclear excited resonance with a lifetime measurable on the mass spectrometry timescale. Copyright 1999 John Wiley & Sons, Ltd.     

Analysis of a shielded TE011 mode composite dielectric resonator for stable frequency reference

Analysis of a TE₀₁₁ mode composite sapphire-rutile dielectric resonator has been carried out to study the temperature variation of resonance frequency, close to the Cs atomic clock hyperfine frequency of 9.192 GHz. The complementary behavior of dielectric permittivity with temperature of the composite has been exploited to obtain the desired turning point in the resonant frequency. The frequency of the composite structure is found to be independent of the shield diameter beyond four times the puck diameter.     

Electrospray ionization multiple-stage tandem mass spectrometric analysis of diglycosyldiacylglycerol glycolipids from the bacteria Bacillus pumilus

Electrospray ionization (ESI) combined with multiple-stage tandem mass spectrometry (MS(n)) was used to directly analyze the glycolipid mixture from bacteria Bacillus pumilus without preliminary separation. Full scan ESI-MS revealed the composition of picomole quantities of glycerolglycolipid species containing C(14)-C(19) fatty acids, some of which were monounsaturated. Two main components were identified from their molecular masses and fragmentation pathways. The fragmentation pathway of the known compound compared with the investigated compound verified the proposed structure as 1(3)-acyl-2-pentadecanoyl-3(1)-O-[beta-D-glucopyranosyl-(1-->6)-O-beta-D-glucopyranosyl]-sn-glycerols. A comparison of the multiple tandem mass spectra of the different alkali-metal cation adducts indicates that the intensity of fragments and the dissociation pathways are dependent on the alkali-metal type. The basic structures of glycerolglycolipids were reflected clearly from the fragmentation patterns of the sodium cations. The intense fragments of the sugar residue from the precursor ions were obtained from the lithiated adduct ions. ESI-MS(n) spectra of [M + K](+) ions did not provide as much fragmentation as [M + Na](+) and [M + Li](+) adducts, but their spectra allow the position of glycerol acylation to be determined. On the basis of MS(2) spectra of [M + K](+) ions, it was established that all components have a C(15:0) fatty acid at the sn-2 position of the glycerol backbone and C(14)-C(19) acids at the sn-1 position of the glycerol backbone. Copyright 1999 John Wiley & Sons, Ltd.     

An efficient Monte Carlo algorithm for the fast equilibration and atomistic simulation of alkanethiol self-assembled monolayers on a Au(111) substrate

A new Monte Carlo algorithm is presented for the simulation of atomistically detailed alkanethiol self-assembled monolayers (R-SH) on a Au(111) surface. Built on a set of simpler but also more complex (sometimes nonphysical) moves, the new algorithm is capable of efficiently driving all alkanethiol molecules to the Au(111) surface, thereby leading to full surface coverage, irrespective of the initial setup of the system. This circumvents a significant limitation of previous methods in which the simulations typically started from optimally packed structures on the substrate close to thermal equilibrium. Further, by considering an extended ensemble of configurations each one of which corresponds to a different value of the sulfur-sulfur repulsive core potential, sigmass, and by allowing for configurations to swap between systems characterized by different sigmass values, the new algorithm can adequately simulate model R-SH/Au(111) systems for values of sigmass ranging from 4.25 A corresponding to the Hautman-Klein molecular model (J. Chem. Phys. 1989, 91, 4994; 1990, 93, 7483) to 4.97 A corresponding to the Siepmann-McDonald model (Langmuir 1993, 9, 2351), and practically any chain length. Detailed results are presented quantifying the efficiency and robustness of the new method. Representative simulation data for the dependence of the structural and conformational properties of the formed monolayer on the details of the employed molecular model are reported and discussed; an investigation of the variation of molecular organization and ordering on the Au(111) substrate for three CH3-(CH2)n-SH/Au(111) systems with n=9, 15, and 21 is also included.     

The effect of data scaling on dual prices and sensitivity analysis in linear programs

In many practical situations scaling the data is necessary to solve linear programs. This note explores the relationships in translating the sensitivity analysis between the original and the scaled problems.     

Temperature and Pressure Effects on Local Structure and Chain Packing in cis‐1,4‐Polybutadiene from Detailed Molecular Dynamics Simulations

Summary: We present results for the temperature and pressure dependence of local structure and chain packing in cis‐1,4‐polybutadiene (cis‐1,4‐PB) from detailed molecular dynamics (MD) simulations with a united‐atom model. The simulations have been executed in the NPT statistical ensemble with a parallel, multiple time step MD algorithm, which allowed us to access simulation times up to 1 µs. Because of this, a 32 chain C₁₂₈ cis‐1,4‐PB system was successfully simulated over a wide range of temperature (from 430 to 195 K) and pressure (from 1 atm to 3 kbar) conditions. Simulation predictions are reported for the temperature and pressure dependence of the: (a) density; (b) chain characteristic ratio, C_n; (c) intermolecular pair distribution function, g(r), static structure factor, S(q), and first peak position, Q_max, in the S(q) pattern; (d) free volume around each monomer unit along a chain for the simulated polymer system. These were thoroughly compared against available experimental data. One of the most important findings of this work is that the component of the S(q) vs. q plot representing intramolecular contributions in a fully deuterated cis‐1,4‐PB sample exhibits a monotonic decrease with q which remains completely unaffected by the pressure. In contrast, the intermolecular contribution exhibits a distinct peak (at around 1.4 Å⁻¹) whose position shifts towards higher q values as the pressure is raised, accompanied by a decrease in its intensity.

3D view of the simulation box containing 32 chains of C₁₂₈ cis‐1,4‐polybutadiene at density ρ = 0.849 g · cm⁻³ and the conformation of a single C₁₂₈ cis‐1,4‐PB chain fully unwrapped in space.     

Variable-temperature x-ray structural investigation of [Fe[HC(3,5-Me2pz)3]2](BF4)2 (pz= pyrazolyl ring): observation of a thermally induced spin state change from all high spin to an equal high spin-low spin mixture, concomitant with the onset of nonmerohedral twinning

The complex [Fe[HC(3,5-Me(2)pz)(3)](2)](BF(4))(2) (pz = pyrazolyl ring) undergoes a phase transition that occurs concomitantly with a thermally induced spin conversion between the high-spin (HS, S = 2) and low-spin (LS, S = 0) states. Above 204 K the compound is completely HS with the structure in the C2/c space group with Z = 4. A crystal structure determination of this phase was performed at 220 K yielding the cell constants a = 20.338(2) A, b = 10.332(1) A, c = 19.644(2) A, beta = 111.097(2) degrees, and V = 3851.5(6) A(3). There is one unique iron(II) site at this temperature. Below 206 K the compound converts to a 50:50 mixture of HS and LS. The radical change in the coordination sphere for half of the iron(II) sites, most notably a shortening of the Fe-N bond distances by ca. 0.2 A, that accompanies this magnetic transition causes a phase transition. The crystal system changes from C-centered monoclinic to primitive triclinic with Z = 2 with two half-molecules on independent inversion centers. A crystal structure determination was performed at 173 K in space group P1 with a = 10.287(2) A, b = 11.355(3) A, c = 18.949(4) A, alpha = 90.852(4) degrees, beta = 105.245(4) degrees, gamma = 116.304(4) degrees, and V = 1892.3(8) A(3). All specimens investigated below the phase transition temperature were determined to be nonmerohedral twins. Temperature cycling between these two forms does not appear to degrade crystal quality. Previous magnetic susceptibility measurements indicate a second, irreversible increase in the magnetic moment the first time the crystals are cooled below 85 K. A crystal structure determination at 220 K of a specimen precooled to 78 K was not significantly different from those not cooled below 220 K.