More on the size of molecules

This contribution examines the size and shape of aromatic organic molecules against a background of existing concepts of molecular size and shape, and against a background of data for aliphatics. It is therefore partly a review and partly an analysis of new computational results. It is stressed that the notion of shape can be-and has been-detached from the notion of size, that the notion of size can be-and has been-detached from the notion of shape, but also that the two can be and have been wedded to advantage. A substantial amount of new material is presented, discussion concentrating on molecular volumes, surface areas, cross-sectional areas, average free volumes in the bulk, and packing densities. A distinction is made between the bare and the expanded molecular bodies. It is concluded that attributes of the first type of body work better in correlations, while attributes of the second are closer to experimental measures of size.     

The critical size of clusters of water molecules on a carbon surface

The experimental adsorption isotherms of water and nitrogen vapors on graphitized carbonaceous adsorbents with large pore size prepared from ultradispersive technical carbon black have been compared with those on the surface of non-porous graphitized carbon black. The saturation value of water vapor adsorption has been shown to be proportional to the concentration of primary adsorption centers. At low concentrations of these centers the saturation value corresponds to the formation of fractions of a dense monolayer on the surface. The maximum size of clusters of water molecules on a carbonaceous adsorbent surface has been estimated.Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 54–56, January, 1993.     

Dependence of the cyclization behavior of multifunctional network molecules on molecular size

The tendency for cyclization of nonlinear network molecules is quantitatively expressed by the cyclization probability, defined as the ratio of cyclization to total reaction rate. In contrast to branching, the rate of cyclization depends on the configurational statistical mechanics of segments joining functional groups. Direct integration of the joint configurational probability density in the subspace of encounters yields the distribution of the number of configurationally formed intramolecular functional group encounters (nearest neighbors). Statistically independent network segments are assumed to obey the Gaussian statistics. A recursive relationship for the distribution of chain lengths is developed, and it is shown that for large molecular sizes this relationship tends to a limiting distribution. Corresponding average and standard deviation follow power law dependence on degree of polymerization (DP). With these results, cyclization probabilities are explicitly expressed as functions of DP. When segmental diffusion is the rate controlling factor, cyclization is similar to short range (or primary) cyclization. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 861–870, 2005     

Molecular size and shape properties of diamondoid molecules occurring in crude oil

The molecular size and shape for 27 diamondoids molecules (adamantanes and alkyladamantanes, diamantine and alkyldiamantanes) were calculated by computational quantum mechanical modeling method of dispersion correction B3LYP-D3/6-311+G**, in which the family of adamantanes presents molecular sizes in terms of width of 6.8–7.9 Å, and for the family of diamantanes 6.8–7.4 Å, in terms of length the size for adamantanes are 7.6–9.5 Å and for diamantanes 9.3–10.0 Å and in terms of height are rounded from 7.4 to 9.6 Å for adamantanes and 7.4 to 8.5 Å for diamantanes. This size depends on the alkyl substitution either in CH₂ or CH bridgehead positions. A measure of spherical shape deviation in terms of ovality, (O = 1 for sphere shape) was calculated, in which for adamantane, methyladamantanes, dimethyladamantanes, and multi-substituted adamantanes, is 1.17, 1.21, 1.24, and 1.26–1.31, respectively and ovality value for diamantane is 1.20 and 1.22–1.27 for methyl substituted diamantanes. Ovality (shape) and molecular size differences between adamantane, methyladamantanes, dimethyladamantanes, multi-substituted adamantanes, and the corresponding diamantanes allow suggesting a dynamic model for separation from the linear alkanes in a mixture into a slit pore shape typical for microporous carbons.     

The shape of molecules

The two most important molecular shape models are the Valence-Shell-Electron-Pair-Repulsion scheme and the Walsh-Mulliken Diagrams. These models, with illustrative examples, are described and a rigorous quantum mechanical definition of each is stated. A physical-mathematical proof ot their equivalence and of their origin is given along with an analysis of the failures to be expected. The theoretical prediction of bond angles is contrasted with the corresponding prediction of bond lengths, and the low information content inherent to the specification of bond angles shows their determination to be considerably easier than bond lengths.

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Zusammenfassung Die beiden wichtigsten Modelle zur Molekülgeometrie sind das Modell der Valenzelektronen-Paar-Abstoßung und das Walsh-Mulliken-Diagramm. Beide Modelle werden anhand illustrativer Beispiele vorgestellt, eine quantenchemische Definition beider wird gegeben. Ihre physikalische Äquivalenz wird bewiesen; diese Analyse zeigt auch die Grenzen der Modelle. Die theoretische Voraussage von Winkeln wird der von Bindungslängen gegenübergestellt. Da der Informationsgehalt der Winkelspezifikation niedriger ist, ist diese Angabe wesentlich leichter als die der Bindungslängen.

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Résumé Les deux modèles de forme moléculaire les plus importants sont le schéma de répulsion électronique des paires d'électrons des couches de valence et les diagrammes de Walsh-Mulliken. Ces modèles sont décrits, avec des examples illustratifs, et l'on donne une définition quantique rigoureuse de chacun d'entre eux. Une preuve physicomathématique de leur équivalence et de leur origine est fournie avec une analyse des échecs à attendre. La prédiction théorique des angles de valence est opposée aux prédictions théoriques des longueurs de liaison; le faible contenu informationnel inhérent à la spécification des angles de liaison montre que leur détermination est considérablement plus aisée que celle des longueurs de liaison.

     

Molecular thermodynamics of fluid mixtures containing molecules differing in size and potential energy

Recent computer-simulation work by Shing and Gubbins (1983) for binary mixtures has shown that common semiempirical models (van der Waals n-fluid models) are in error when the molecules of the two components differ appreciably in size; the error is most severe in the dilute region. While perturbation theories are much better, they (like computer simulations) are not as yet useful for engineering work because of prohibitive computer requirements.This work proposes an algebraic expression for the Helmholtz energy of a mixture which gives results in very good agreement with those reported by Shing and Gubbins. This expression, using the local-composition concept, is based on a simplified but realistic picture of a fluid mixture: short-range order and long-range disorder. The proposed expression uses the Mansoori-Carnahan-Starling-Leland equation for the contribution of repulsive forces. For the contribution of attractive forces, it uses a new expression based on not one but several radii for the first-neighbor shell, one radius for each component.With reasonable simplifications, the resulting equation for the Helmholtz energy indicates that the van der Waals “constant” a is a strict quadratic function of mole fraction only at very low densities; at advanced densities, there are small deviations from the quadratic mixing rule. For practical calculations, the computer requirements are nearly the same as those for conventional engineering models.     

Theory of the thermodynamic properties of binary mixtures of organic molecules with size mismatch

The Flory expression for the Gibbs free energy of mixing of a binary mixture is improved by introducing a hard-sphere form for the entropy of mixing. The resulting expression is used to describe the characteristic features of organic mixtures of globular molecules with size mismatch. In particular, we show that the above model, with an interchange energy depending on temperature, accounts for the thermodynamic properties and concentration fluctuations of a number of octamethylcyclotetrasiloxane-based mixtures.     

Free energy and chemical potentials of regular multicomponent solution with molecules of different size

Equations are proposed for the free energy and chemical potentials of regular multicomponent solutions containing molecules of different sizes. The use of the equations for calculations on the three-component system, methyl ethyl ketone—heptane—toluene, gives results which agree well with experiment.     

The knot theory of molecules

Macromolecules (such as polymethelyene and DNA) are large and flexible, and can present themselves in 3-space in topologically interesting ways. The branch of topology known asknot theory is the mathematical study of flexible graphs in 3-space. Knot theory can be used to quantify and compare the various configurations of large molecules, and to study the various spatial isomers of molecules which have complicated molecular graphs.     

Viscoelastic properties of single polysaccharide molecules determined by analysis of thermally driven oscillations of an atomic force microscope cantilever

We report on single molecule measurements of the viscoelastic properties of the polysaccharide dextran using a new approach which involves acquiring the power spectral density of the thermal noise of an atomic force microscope cantilever while holding the single molecule of interest under force-clamp conditions. The attractiveness of this approach when compared with techniques which use forced oscillations under constant loading rate conditions is that it is a near-equilibrium measure of mechanical response which provides a more relevant probe of thermally driven biomolecular dynamics. Using a simple harmonic oscillator model of the cantilever-molecule system and by subtracting the response of the free cantilever taking into account hydrodynamic effects, the effective damping zetamol and elastic constant kmol of a single molecule are obtained. The molecular elasticity measured by this new technique shows a dependence on applied force that reflects the chair-boat conformational transition of the pyranose rings of the dextran molecule which is in good agreement with values obtained directly from the gradient of a conventional constant loading rate force-extension curve. The molecular damping is also seen to follow a nontrivial dependence on loading which we suggest indicates that it is internal friction and not work done on the solvent that is the dominant dissipative process.     

玉米芯碱提水溶性多糖及其硫酸酯抗病毒活性的研究

从玉米芯中,用2%NaOH提取,HCl中和,经乙醇醇析,制备碱提水溶性多糖.用氯磺酸吡啶法修饰制备多糖硫酸酯.离子色谱法测其硫酸根含量为11.23%.玉米芯多糖经硫酸化修饰后对柯萨奇病毒(Coxsackie B3Virus)有一定的抑制作用,但对人全血凝血时间无显著影响.     

Instantaneous inclusion of a polynucleotide and hydrophobic guest molecules into a helical core of cationic beta-1,3-glucan polysaccharide

We succeeded in the quantitative and selective introduction of an ammonium cationic group into the C6 position of Curdlan (CUR) by "Click Chemistry", and the obtained cationic Curdlan (CUR-N+) showed good solubility in water. ORD studies suggested that CUR-N+ adopts a single-stranded structure, different from a right-handed, triple-stranded helical structure of beta-1,3-glucan polysaccharides in water. It has been revealed that the polymeric complexes of CUR-N+ with polymeric guest molecules, such as polycytidylic acid (poly(C)), permethyldecasilane (PMDS), and single-walled carbon nanotubes (SWNTs), can be easily obtained by just mixing them in water with sonication. The characterization of the resultant CUR-N+-poly(C) complexes by UV-vis, CD spectroscopic measurements, and AFM and TEM observations revealed that they have stoichiometric, nanosized fibrous structures. From these experimental results as well as our precedent studies (e.g., refs 6 and 23), we propose that the complexation would be driven by the cooperative action of (1) the hydrogen-bonding interaction between the OH group at the C2 position and hydrogen-bonding sites of the cytosine ring (ref 6d), (2) the electrostatic interaction between the ammonium cation and the phosphate anion (ref 23), as well as (3) the background hydrophobic interaction. In addition, the complexed polynucleotide chain showed a strong resistance against enzymatic hydrolysis. Likewise, the dispersion of PMDS and SWNTs in water by CUR-N+ and the fibrous structures of the complexes were confirmed by spectroscopic measurements as well as microscopic observations. These binding properties of CUR-N+, which can proceed spontaneously in water, clearly differ from those of schizophyllan (SPG), which inevitably require a denature-renature process corresponding to a conversion of a triple strand to single strands induced by DMSO or base for inclusion of polymeric guest molecules.     

The influence of the size and position of the alkyl groups in alkylimidazole molecules on their acid‐base properties

Dissociation constants of HL⁺ acids, where L stands for 1‐alkylimidazole, 1‐alkyl‐2‐methylimidazole, 1‐alkyl‐2‐ethylimidazole, 1‐alkyl‐2‐propylimidazole, 1‐alkyl‐4‐methylimidazole and 1‐alkyl‐2‐ethyl‐4‐methylimidazole, were determined potentiometrically. For each of the homologous series of these bases, a relationship has been derived between the pK_a value and the number of carbon atoms in the hydrocarbon group for (CH₂)_n ≤ 13. The basicity of the alkylimidazoles has been found to increase linearly with increasing carbon chain length. The slopes of straight plots of pK_a = f(n_CH2) have been found to increase with increasing basicity of homologous series of the alkylimidazoles.     

The pyrolytic identification of organic molecules: I. The pyrolytic behavior of organic molecules

Results of a study on the pyrolysis of about 70 organic compounds of varied composition are presented and discussed. Identification of the volatile products formed was accomplished by mass spectrometry. It is shown how the pyrolytic patterns may be employed to distinguish one molecule from another. Some attention has been given to isomeric compounds and to aromatic structures containing one or more functional groups.     

Selective photocatalytic transformations on microporous titanosilicate ETS-10 driven by size and polarity of molecules

Photocatalytic activity of microporous titanosilicate ETS-10 has been studied in water. The photoactivated ETS-10 shows catalytic activity driven by size and polarity of substrates. ETS-10 efficiently catalyzes a conversion of substrates with a size larger than the pore diameter of ETS-10. In contrast, the reactivity of small substrates depends strongly on substrate polarity; less polar substrates show higher reactivity on ETS-10. Electron spin resonance analysis reveals that large substrates or less polar substrates scarcely diffuse inside the highly polarized micropores of ETS-10 and, hence, react efficiently with hydroxyl radicals (*OH) formed on titanol (Ti-OH) groups exposed on the external surface of ETS-10. In contrast, small polar substrates diffuse easily inside the micropores of ETS-10 and scarcely react with *OH, resulting in low reactivity. The photocatalytic activity of ETS-10 is successfully applicable to selective transformations of large reactants or less polar reactants to small polar products, enabling highly selective dehalogenation and hydroxylation of aromatics.