Molecular modeling of polymers, 14 quantitative structure-property relationship analyses of multicomponent systems containing polymers

One general class of polymer modeling applications involves materials which are large, in terms of molecular degrees of freedom, and poorly defined in terms of composition and morphology. Such materials are often multicomponent with respect to number of distinct polymers, fillers, additives, etc. Two obstacles limit the modeling of these materials. First, one normally does not have any idea about the key physicochemical molecular properties governing the system. Second, the functional dependence of the target properties of the material upon the key physicochemical molecular properties is usually totally unknown. Torsion angle unit (TAU) theory, a molecular decomposition technique, permits an arbitrarily large number of physicochemical properties to be computed in an open-ended fashion, and thus addresses the first problem. Genetic function approximation (GFA) analysis tackles the second problem by efficiently exploring any desired number of functional relationships between target properties and physicochemical molecular properties. Case studies of (TAU theory)-(GFA analysis) applications to estimate glass, Tg, and crystal-melt, Tm, transition temperatures will be described.     

Hydrogenation enthalpimetry--I: microcomputer-assisted calibration and data-acquisition

A calorimetric device is described which permits enthalpimetric determination of unsaturated hydrocarbons through the enthalpy change for their catalytic hydrogenation. Samples with weights from < 1 to about 20 mg can be analysed with a mean error of about 2%. The method makes extensive use of digital electronics and is well suited to routine automated determination of unsaturation. The principal drawback is lack of specificity.     

Two theorems on graceful trees

Let T be a tree on n vertices which are labelled by the integers in N = {1,2,…,n} such that each vertex of T is associated with a distinct number in N. The weight of an edge is defined to be the absolute value of the difference between the two numbers labelled at its end vertices. If the weights of all edges of T are distinct, we call T a graceful tree. In this note, two methods for constructing bigger graceful trees from a given one and a given pair of graceful trees are provided.     

Variational formulation for the equilibrium condition of a conducting fluid in an electric field

In this paper the variational formalism is used to derive a set of equations describing the equilibrium configuration of a conducting fluid in an applied electric field. The validity of the variational equations is confirmed by application to the well-defined problem of concentric spherical electrodes. It is further shown that a cone, including the so-called Taylor cone used to model the equilibrium configuration of liquid metal ion sources, is inconsistent with the general equations. An analysis of the Taylor derivation suggests that reasons for the disagreement are the omission of the pressure difference term in the Laplace formula and use of only an approximate solution to the electrostatic cone problem. Finally a quasi-empirical method is suggested for the self-consistent solution of the variational equations.     

The adsorption of C6H5Cl on Si(111)7 × 7 studied by STM

The adsorption of chlorobenzene on Si(111)7 × 7 at room temperature was studied by scanning tunneling microscopy (STM). Selective chemisorption was observed at different adatom sites. It was found that the center adatoms were more reactive than the corner adatoms, and the faulted half of the unit cell was more reactive than the unfaulted. The mechanism is discussed in terms of the electronic and atomic structures in Si(111)7 × 7. Both preferences indicate that chlorobenzene was present initially in a mobile precursor state.     

On a canonical nine-body problem. Integrable Ermakov decomposition via reciprocal transformations

Here, a recently introduced nine-body problem is shown to be decomposable via a novel class of reciprocal transformations into a set of integrable Ermakov systems. This Ermakov decomposition is exploited to construct more general integrable nine-body systems in which the canonical nine-body system is embedded.     

An electron spectroscopic investigation of the interaction of methanol with polycrystalline aluminum

X-ray and ultraviolet photoelectron spectroscopic results are reported for the interaction of CH₃OH with clean polycrystalline Al in the temperature range 110–500 K. Methanol is moleculary chemisorbed at low exposure and low temperature (110 K) followed by condensation at higher exposure. Bonding mechanisms and geometries in the condensed and chemisorbed layers are discussed. The multilayers desorb beginning near 170 K and the chemisorbed layer is converted into a surface methoxide. Room temperature adsorption also leads to formation of the methoxide species which is stable to ～500 K, at which point it decomposes evolving CH₄ and leaves the surface oxidized.     

Probability theory and polymer physics

This study applies the theory of stochastic processes to the equilibrium statistical physics of polymers in solution. The topics treated include random copolymers and randomly branching polymers, with self-consistent mean field effects. A new and more natural way of dealing with Boltzmann weighting is discussed, which makes it possible from the beginning of a calculation to consider only the physical polymer conformations. We also show that in general the random copolymer problem can be reduced to the ordinary polymer problem, and treat the self-consistent field problem for a general branching polymer.