Resonance energy of very large benzenoid hydrocarbons

The resonance energy of conjugated benzenoid systems is expressed as contributions arising from independent conjugated circuits. The scheme has been applied to numerous very large conjugated systems. In many cases, it was possible to find regularities in the increments for the resonance energy within a family of benzenoid systems as the number of benzene rings is increased.     

Analytical expressions for topological properties of polycyclic benzenoid networks

Quantitative structure‐activity and structure‐property relationships of complex polycyclic benzenoid networks require expressions for the topological properties of these networks. Structure‐based topological indices of these networks enable prediction of chemical properties and the bioactivities of these compounds through quantitative structure‐activity and structure‐property relationships methods. We consider a number of infinite convex benzenoid networks that include polyacene, parallelogram, trapezium, triangular, bitrapezium, and circumcorone series benzenoid networks. For all such networks, we compute analytical expressions for both vertex‐degree and edge‐based topological indices such as edge‐Wiener, vertex‐edge Wiener, vertex‐Szeged, edge‐Szeged, edge‐vertex Szeged, total‐Szeged, Padmakar‐Ivan, Schultz, Gutman, Randić, generalized Randić, reciprocal Randić, reduced reciprocal Randić, first Zagreb, second Zagreb, reduced second Zagreb, hyper Zagreb, augmented Zagreb, atom‐bond connectivity, harmonic, sum‐connectivity, and geometric‐arithmetic indices. In addition we have obtained expressions for these topological indices for 3 types of parallelogram‐like polycyclic benzenoid networks.     

Counting of resonance structures for large benzenoid polynuclear hydrocarbons

A method is presented for counting the number of resonance structures for large benzenoid polynuclear hydrocarbons. Structure counts for even systems are made and compared with those of the odd systems resulting from the removal of one of the π centers from various points in the even structure. A computer program for performing the calculations is also given.     

Analytical expressions for the count of LM-conjugated circuits of benzenoid hydrocarbons

A recursive method for enumeration of linearly independent and minimal conjugated circuits of benzenoid hydrocarbons had previously been given which is valid for several classes of benzenoid hydrocarbons. In the present article, the properties and constructions of unique minimal conjugated circuits and pairs of minimal conjugated circuits of a ring s in a benzenoid hydrocarbon B are investigated. An analytical expression for the count of LM-conjugated circuits of B is given which is based on the counts of Kekulé structures of selected subgraphs of B. By using the method, the LMC expression of any benzenoid hydrocarbon can be obtained. © 1996 John Wiley & Sons, Inc.     

New approach to filled polymers

Mechanopolymerization of pentabromobenzyl (mono)acrylate (PBB-MA) on the surface of inorganic fillers Mg(OH)₂ and CaCO₃ was studied. The role of activated surface of fillers was investigated using DSC and FTIR. The influence of milling time and of the filler chemical content on polymerization starting temperature and polymerization enthalpy was studied using DSC. It was shown that an increase of the filler concentration leads to a higher maximum conversion degree. The correlation between conversion kinetics and polymerization enthalpy of the material notpolymerized during milling was shown. This paper was presented on the Second Conference of The Israel Group of Mechanochemistry.     

A modular approach to main-chain organometallic polymers

A highly efficient route to a new class of organometallic polymers containing difunctional N-heterocyclic carbenes has been developed. Bis(imidazolium) halides and divalent group X metals were copolymerized to afford organometallic polymers in up to quantitative yields and with molecular weights up to 10(6) Da, depending on the structure of the N-heterocyclic carbene and the incorporated transition metal. Enhanced solubilities were demonstrated through post-polymerization ligation with phosphines. Finally, selective end-group functionalization and excellent molecular weight control was achieved through the inclusion of monofunctional chain transfer agents during the polymerization.     

An approach to phase behaviour in polymers

Aspects of phase transition will be surveyed such as are direct consequences of straightforward thermodynamic considerations yet are not normally taken count of in traditional treatments of phase behaviour even if, as is here shown, they can assume special significance in polymers. The central theme will be the common experience that in most materials, but especially in polymers, the state of ultimate thermodynamic stability is hardly ever attained, consequently that we are dealing with metastable states, the issue of metastability thus becoming the main theme of the present treatise. This metastability can manifest itself either through the phase transformation, even in the thermodynamically stable phase, not reaching completion and/or that phases other than those of ultimate stability appear first often taking on a dominant role. The above two strands are being followed through first separately and finally, with the example of polymer crystallisation, in combination. In the course of it all a variety of phase transformations and numerous potentially intriguing consequences are being touched upon. These are encompassing aspects of liquid-liquid phase separation, liquid-crystal formation and crystallisation, the intervention of glass transition, the significance of supercooling, the effect on and influence of the morphology and the connection and interrelation between thermodynamic stability (including metastability) and the rates of the phase transformation, with passing comments on gels and also on some aspects of chain conformation in solution. In the case of the most extensively covered item of crystallisation attention is being drawn to the possibility of stability inversion with phase (here crystal) size. The latter, in terms of ‘Phase Stability Diagrams’, offers a new approach to crystal growth, which in the case of polymers, creates both new perspectives and opens up the possibility of treating so far largely disconnected aspects of the subject within a unifying framework. The survey ends with reference to recent work on amorphisation through pressure pointing to new aspects of material behaviour and to some new and possibly surprising variants of otherwise familiar phase diagrams.     

Ground-state properties of benzenoid hydrocarbons by simple bond orbital resonance theory approach

π-electron energies and bond orders of benzenoid hydrocarbons with up to five fused hexagons have been considered by the simple Bond Orbital Resonance Theory (BORT) approach. The corresponding ground states were determined according to four BORT models. In the first three models a diagonalisation of the Hückel-type Hamiltonian was performed in the bases of Kekulé, of Kekulé and mono-Claus and of Kekulé and Claus resonance structures, respectively. In the fourth model a simple BORT ansatz was used. According to this ansatz, the ground state is a linear combination of the positive Kekulé structures, all with equal coefficients. It was shown that π-electron energies and bond orders obtained by these models correlate much better with the PPP energies and bond orders than with the Hückel energies and bond orders. This indicates that a simple BORT approach is quite reliable in predicting the more sophisticated PPP results. Concerning the relative performance of the four BORT models, the best results were obtained with the BORT ansatz. The performance deteriorates with the expansion of the basis set. This is attributed to the fact that in these models the improvement of the basis set is not accompanied with the corresponding improvement of the Hamiltonian. Comparing the BORT-ansatz bond orders with the Pauling bond orders, it was shown that BORT-ansatz bond orders correlate much better with the PPP bond orders. This revised version was published online in July 2006 with corrections to the Cover Date.     

Flocculation by very high molecular weight polymers

Polymer-induced flocculation in which the size of polymer molecules is much greater than that of colloidal particles is investigated. A dynamic analysis is conducted which takes the transient behaviors of the adsorption of particles to a polymer molecule and the particle-particle interactions into account. We show that the number of particles adsorbed to a polymer molecule follows approximately a binomial distribution. An approximate expression for the degree of flocculation of the system under consideration is presented.     

An orthogonal approach to multifunctional molecularly imprinted polymers

[structure: see text] An "orthogonal" approach to molecularly imprinted polymers has been demonstrated using a crown ether derived monomer that does not exhibit cross-reactivity with other functional monomers. This strategy provides multiple functional groups in the binding site of molecularly imprinted polymers (MIPs) without unproductive interactions between functional monomers. The orthogonal functional group system was shown to act cooperatively in MIPs to bind a template with higher selectivity than any of the individual functional monomers alone.     

A synergistic approach to the polydispersity of polymers

A scheme for calculating polydispersity coefficients of polymers during chain propagation in living polymerization is proposed on the basis of the synergistic approach (the master equation) with allowance for fluctuations in the number of free radicals at the stage of initiation. The molecular-mass-distribution function of living chains is calculated. The form of this function is shown to be dependent on the ratio between the constants of the elementary stages of chain initiation and propagation.     

Analytical characterization of PEG polymers by MEKC

Characterization of PEGs with average molecular masses of up to 2000 has been achieved using MEKC with UV detection. A rapid derivatization procedure with phenyl isocyanate using microwave radiation, in order to introduce chromophore groups in PEGs, has been developed involving a reaction time of 60 s. Different optimized conditions in accordance with the molecular weight have been studied to obtain the oligomer separation. The weight‐average molecular mass the number‐average molecular mass and the degree of polydispersity (molecular mass distribution) were calculated for the different PEGs obtaining similar results with those certified for standards. A good precision was obtained for characterizing the different oligomers. Ethylene glycol was used as the internal standard for the analysis of low‐molecular‐weight PEGs. The developed method was satisfactorily applied to the characterization of these polymers in several real samples, such as lubricant eye drops, toothpaste, tap water and eye make‐up remover.     

Analytical techniques for polymers with complex architectures

Complex polymers are distributed in more than one direction of molecular heterogeneity. In addition to the molar mass distribution, they are frequently distributed with respect to chemical composition, functionality, and molecular architecture. For the characterization of the different types of molecular heterogeneity it is necessary to use a wide range of analytical techniques. Preferably, these techniques should be selective towards a specific type of heterogeneity. The combination of two selective analytical techniques is assumed to yield a two-dimensional information on the molecular heterogeneity. For the analysis of complex polymers different liquid chromatographic techniques have been developed, including size exclusion chromatography (SEC) separating with respect to hydrodynamic volume, and liquid adsorption chromatography (LAC) which is used to separate according to chemical composition. Liquid chromatography at the critical point of adsorption (LC-CC) has been shown to be a versatile method for the determination of the functionality type distribution of macromonomers, the molecular architecture of homopolymers and the chemical heterogeneity of block and graft copolymers. The present paper presents the principle ideas of combining different analytical techniques in multidimensional analysis schemes for the analysis of polymers with complex architectures. Branched block and graft copolymers can efficiently be analyzed with respect to chemical composition and molar mass by LC-CC and two-dimensional chromatography. The chemical heterogeneity as a function of molar mass can be determined by combining interaction chromatography and FTIR spectroscopy. For the analysis of star-like polymers LC-CC is shown to be a powerful technique when the molar mass of different segments (blocks, grafts) must be determined.     

A combinatorial approach to branched polymers’ statistics

At least ideally, a certain class of polymers presents itself as a collection (set) of connected components. Each of these components is a cycle of trees, that is branched polymers eventually rooted on a cycle. We derive (and study) an equilibrium statistical model that accounts for the main connectivity features of such structures, whose origin is to be found in combinatorial probability. Phase transition (gel–soltransition) is shown to occur when some internal control parameter crosses one (critical parameter). Various structural asymptotic results are shown to be available using singularity analysis. This revised version was published online in July 2006 with corrections to the Cover Date.     

Characterization of aromatic polymers (benzenoid and heterocyclic) by cross-polarization,magic-angle 13C-NMR spectroscopy

The cross-polarization, magic-angle ¹³C-NMR spectra of solid samples of poly(p-phenylene), its nitro derivative, polymerized biphenyl, poly(p-phenylene sulfide), poly(1-methyl-2,5-pyrrolylene), poly(1-phenyl-2,5-pyrrolylene), poly(2,5-thienylene), and poly(2,5-selenienylene) and the high-resolution ¹³C-NMR spectrum of poly(m-phenylene) in solution are presented and assigned. In all cases the chemical shifts are similar to those of model compounds in solution. In most instances the resonances of the nonprotonated carbon atoms in the solid polymers are more intense than those of the protonated carbons and appear to depend on the charge distribution in the molecular orbitals.     

Analytical time-dependent density functional derivative methods within the RI-J approximation, an approach to excited states of large molecules

Time-dependent density functional theory (TDDFT) is now well established as an efficient method for molecular excited state treatments. In this work, we introduce the resolution of the identity approximation for the Coulomb energy (RI-J) to excited state gradient calculations. In combination with nonhybrid functionals, the RI-J approximation leads to speed ups in total timings of an order of magnitude compared to the conventional method; this is demonstrated for oligothiophenes with up to 40 monomeric units and adamantane clusters. We assess the accuracy of the computed adiabatic excitation energies, excited state structures, and vibrational frequencies on a set of 36 excited states. The error introduced by the RI-J approximation is found to be negligible compared to deficiencies of standard basis sets and functionals. Auxiliary basis sets optimized for ground states are suitable for excited state calculations with small modifications. In conclusion, the RI-J approximation significantly extends the scope of applications of analytical TDDFT derivative methods in photophysics and photochemistry.     

Producing and detecting very large clusters

The cluster source we use, a low pressure, rare gas condensation cell, is capable of producing clusters containing more than 45 000 atoms or having masses exceeding 2 500 000 amu. Details of this source and the dependence of the cluster size distribution on adjustable working parameters (oven temperature, inert gas pressure, inert gas type) are discussed in this report. Measurements of the mass-dependent velocity distributions of the clusters emitted by the source are presented and compared to a simple model calculation. The clusters are mass-analyzed with a time-of-flight mass spectrometer and detected by a multi-channel plate. The dependence of the detectability of large clusters on the acceleration voltage is investigated.     

A molecular approach to chain entanglement in linear polymers

The phenomenon of chain entanglement in undiluted linear amorphous polymers is treated by calculating the probability of forming closed intramolecular loops. Adoption of the rotational isomeric state model of polymer chains permits an appropriate accounting of the detailed molecular structure to be made through the configurational characteristics of the polymer. The second (〈r〉₀) and fourth (〈r〉₀) moments of the vector r_hk connecting groups h and k in the isolated polymer chain and averaged over all chain conformations are calculated and used to evaluate the probability W_x(0) that r_hk is 0, or that an intramolecular loop of x = k ? h bonds is formed. Several linear polymers with widely differing molecular structures are treated. An attempt is made to correlate the degree of chain entanglement they manifest in the bulk with their ability to fold back upon themselves to form closed intramolecular loops.