The spread of unicyclic graphs with given size of maximum matchings

The spread s(G) of a graph G is defined as s(G) = max _i,j |λ _i − λ _j |, where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U ^*(n,k) the set of triangle-free graphs in U(n,k). In this paper, we determine the graphs with the largest and second largest spectral radius in U ^*(n,k), and the graph with the largest spread in U(n,k).      

Bestimmung der Stabilit?tskonstanten von mehrkernigen Komplexen mit Hilfe einer spektrophotometrischen Methode

Zusammenfassung Es wurde eine allgemeine Gleichung für die Berechnung der Stabilitätskonstante von Komplexen L _mH_iM_nZ_j (Z=OH^–, usw.) abgeleitet und für Maximumbedingungen der Jobschen Kurve die Schwarzenbachsche graphische Methode so modifiziert, daß sie die allgemeine Bestimmung der Zusammensetzung und Stabilität von Komplexen L _mH_iM_nZ_j ermöglicht.

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Summary A general equation has been derived for the calculation of stability constants of complexes L _mH_iM_nZ_j (Z=OH^–, etc.). The graphic method of Schwarzenbach has been modified for maximum conditions of Job's curve in order to make possible the general determination of the composition and stability of complexes L _mH_iM_nZ_j.

     

Phase Behavior and Structural Properties of the Triton X − 100/n − C n H2n + 1OH/H2O System

ABSTRACT

In the Triton X ? 100/n-C_nH_2n + 1OH/H₂O system, the lamellar liquid crystalline region increases and the regions of O/W, W/O and bicontinuous microemulsion domains shrink, simultaneously, with the length of the chain in the unbranched aliphatic alcohol. In the O/W region, the Gibbs free energy for alcohol transfer from the water continuous phase to Triton X ? 100 micellar phase increases linearly with the chain length of alcohol. In the W/O region of the Triton X ? 100/n ? C_nH_2n + 1OH/n ? C₇ H₁₆/H₂O system, as the solubilized water content increases, the effective radius (R _e ), the inner water radius (R _W ), the thickness of the interfacial layer (L) and the average aggregation number ([nbar]) of the reverse micelles increase, whereas the total number (N _d ), the total interfacial area (A _d ) and the change of the standard free energy (Δ _c ? i G ⁰) for alcohol transfer from the oil continuous phase to the interfacial layer of the reverse micelles decrease; and with the longer chain alcohols, the values of R _e , R _W , L, and [nbar] all increase, while the Δ _c-i G⁰ value decreases drastically with increasing chain length. In the lamellar liquid crystalline region, increasing the alcohol chain length can increase the stability of the lamellar liquid crystalline domain. All the results show that the alcohols, n ? C _n H_2n + 1OH, can be used as cosurfactants in the nonionic surfactant system and function similarly as in ionic surfactant systems.     

Microemulsion polymerization of styrene stabilized by sodium dodecyl sulfate and diethylene glycol monoalkyl ether

The effects of the cosurfactants diethylene glycol monoalkyl ether [C _i H_{2 i +1}O(CH₂CH₂O) _j OH (C _i E _j ; i=4, 6 and j=1, 2)] on the formation of an oil-in-water styrene (ST) microemulsion and the subsequent free radical polymerization were studied. For comparison, the data for the C _i H_{2 i +1}OH (C _i OH; i=4, 6) systems obtained from the literature were also included in this work. Sodium dodecyl sulfate was used as the surfactant. The pseudo three-component phase diagram (macroemulsion, microemulsion and lamellar gel phases) was constructed for each cosurfactant. The primary parameters selected for the polymerization study are the concentrations of cosurfactant and styrene. The number of latex particles nucleated is much smaller than that of the microemulsion droplets initially present in the reaction system. Limited flocculation of the latex particles occurs to some extent during polymerization. Among the cosurfactants investigated, the C₄OH-containing polymerization system is the least stable. By contrast, the diethylene glycol monoalkyl ether group of C _i E _j tends to enhance the latex stability. C _i E _j is more effective in stabilizing the ST microemulsion and the subsequent polymerization in comparison with the C _i OH counterpart. Received: 24 December 1999 Accepted: 9 February 2000     

Kirchhoff index of linear pentagonal chains

The resistance distance r_ij between two vertices v_i and v_j of a connected graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices. In this article, following the method of Yang and Zhang in the proof of the Kirchhoff index of liner hexagonal chain, we obtain the closed‐form formulae of the Kirchhoff index of liner pentagonal chain P_n in terms of its Laplacian spectrum. Finally, we show that the Kirchhoff index of P_n is approximately one half of its Wiener index. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Kirchhoff index of linear hexagonal chains

The resistance distance r_ij between vertices i and j of a connected (molecular) graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices. In this work, according to the decomposition theorem of Laplacian polynomial, we obtain that the Laplacian spectrum of linear hexagonal chain L_n consists of the Laplacian spectrum of path P_2n+1 and eigenvalues of a symmetric tridiagonal matrix of order 2n + 1. By applying the relationship between roots and coefficients of the characteristic polynomial of the above matrix, explicit closed‐form formula for Kirchhoff index of L_n is derived in terms of Laplacian spectrum. To our surprise, the Krichhoff index of L_n is approximately to one half of its Wiener index. Finally, we show that holds for all graphs G in a class of graphs including L_n. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Micellar parameters of diblock copolymers and their interactions with ionic surfactants

The interactions of non-ionic amphiphilic diblock copolymer poly（oxyethylene/oxybutylene）(E₃₉B₁₈) with anionic surfactant sodium dodecyl sulphate（SDS） and cationic surfactant hexadecyltrimethylammonium bromide（CTAB） were studied by using various techniques such as surface tension,conductivity,steady-state fluorescence and dynamic light scattering.Surface tension measurements were used to determine the critical micelle concentration（CMC） and thereby the free energy of micellization(△G_mic),free energy of adsorption(△G_ads),surface excess concentration（Γ） and minimum area per molecule（A）.Conductivity measurements were used to determine the critical micelle concentration（CMC）,critical aggregation concentration（CAC）,polymer saturation point（PSP）,degree of ionization（α） and counter ion binding（β）. Dynamic light scattering experiments were performed to check the changes in physiochemical properties of the block copolymer micelles taken place due to the interactions of diblock copolymers with ionic surfactants.The ratio of the first and third vibronic peaks（I₁/I₃） indicated the polarity of the pyrene micro environment and was used for the detection of micelle as well as polymer-surfactant interactions.Aggregation number（N）,number of binding sites（n） and free energy of binding （△G_b） for pure surfactants as well as for polymer-surfactant mixed micellar systems were determined by the fluorescence quenching method.     

Hydration of the carboxylate group: Anab initio molecular orbital study of acetate-water complexes

The hydration of the carboxylate group in the acetate anion has been investigated by performingab initio molecular orbital calculations on selected conformers of complexes with the form CH₃CO₂ ^– ·nH₂O·mH₂O, wheren andm denote the number of water molecules in the first and second hydration spheres around the carboxylate group, andn + m 7. The results of RHF/6–31G^* optimizations for all the complexes and MP2/6–31+G^** optimizations for several one-water complexes are reported. The primary consequence of hydration on the structure of the acetate anion is a decrease in the length of the C-C bond. Enthalpy and free energy changes calculated at the MP2/6–31+G^** and MP2/6–311+ +G^** levels are reported for the reactions CH₃CO₂ ^– + [H₂O] _P CH₃CO₂ ^– ·nH₂O ·mH₂O where [H₂O] _P is a water cluster containingp water molecules andp=n+m 7. The calculations show that conformers with the lowest enthalpy change on complex formation are often not those with the lowest free energy change, due to a greater entropic loss in complexes with tighter and more favorable enthalpic interactions. Hydrogen bonding of six water molecules directly to the carboxylate group in CH₃CO₂ ^– is found to account for approximately 40% of the enthalpy change and 37% of the free energy change associated with bulk solvation.     

Cubic equations of state for adsorption layer: alkylthiopolyoxyethylene glycols

The van der Waals, Redlich-Kwong, Peng-Robinson and an equation of state derived by Smith were applied to approximate the run of surface pressure () — area () curves of the adsorption layer ofn-pentyl ton-octyl thioethers of tri- and tetraoxyethylene glycols. The equation parameters: excluded molar area (_oi) and an interaction energy term (a _i) were determined by simplex method for values in the range of 2–23.5 mN/m. The equations parameters were found to be related to the structure of the amphiphile. The _oi decreased with the length of hydrocarbon thioether chain and was nearly uniform for equations of state in question except for Smith equation. The value ofa _i was dependent on the amphiphile structure. It was used to obtain the interaction energy _i between amphiphiles in the adsorption layer. The values of _i determined as an increment per methylene group was in the range of ca. 0.2–0.32R*T, depending on the equation of state used.     

Dealkylation ofpara-nitrophenyldimethyl thiophosphate in micellar and liquid-crystalline media of then-decylammonium chloride-n-decylamine-water system

The kinetics of decomposition of p-nitrophenyldimethyl thiophosphate (1) were investigated spectrophotometrically in the n-decylammonium chloride-n-decylamine-water system (DAC-DA-H₂O), in which micellar or lamellar liquid-crystalline phases are formed as a function of the concentration of components. It was shown that1 is dealkylated in both phases. An increase in the surface charge density of associates decreases the rate of dealkylation. The activation energy in the lamellar phase is significantly higher than in the micellar phase.A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan' Scientific Center, Russian Academy of Sciences, 420083 Kazan'. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 5, pp. 1042–1048, May, 1992.     

Prediction of adsorption of organic component and water vapour mixture onto activated carbon

A simple isotherm equation is derived for the adsorption of an organic component onto activated carbon in presence of water vapour. The theoretical results are compared with experimental data for toluene-water vapour-activated carbon, which were published byRipperger andGermerdonk [10].

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Vorhersage der Adsorption einer organischen Komponente und Wasserdampf an Aktivkohle

Zusammenfassung Es wird eine einfache Adsorptionsisotherme abgeleitet, welche die gleichzeitige Adsorption eines organischen Stoffes und Wasser an Aktivkohle beschreibt. Die theoretischen Ergebnisse werden mit experimentellen Resultaten vonRipperger undGermerdonk [10] für Toluol-Wasser-Aktivkohle verglichen.

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Symbols a _i adsorbate concentration in adsorbent, kg/kg of carbon - a _0i monolayer capacity, kg/kg of carbon - b _i kinetic parameter of theLangmuir equation - E _j adsorption energy in thej-th layer - i i-th component (1 — water vapour, 2 — organic compound) - j j-th layer - m number of layers - n number of adsorbed components - p partial pressure, Pa - p* saturation partial pressure, Pa - p _C water vapour partial pressure at begining of capillary condensation, Pa - surface coverage     

Equation of State for Adsorption of Gases and Their Mixtures in Porous Materials

Desorption functions (G, H, S) are useful for adsorbent characterization, phase equilibria, and enthalpy and entropy balances. Adsorption isotherms, enthalpy, and entropy are temperature and pressure derivatives of the free energy, so that G(T, P) is an adsorption equation-of-state which contains complete thermodynamic information about the system. The free energy of desorption is the minimum isothermal work necessary to regenerate the adsorbent. The free energy of desorption also determines the selectivity of an adsorbent for different gases. The ideal enthalpy of desorption for a mixture (H = _i n _i h° _i ) is a simple function of the enthalpies of desorption for the individual components. Sample calculations of the free energy, enthalpy, and entropy desorption functions are provided for pure components and mixtures.     

Construction of orthogonal subspaces

An orthogonalization procedure is presented that allows construction of at least (n?m) vectors orthogonal to {X_j}, j equals; 1, m, by linear combinations solely among {η_i}, i equals; 1, n, n>m, and 〈X_j/η_i〉≠0. An important application of the procedure is in effective core potential methods for which valence orbitals can be constructed that are orthogonal to the core orbitals and yet involve no component of the core. Thus, a separate calculation for only the valence electrons can be performed without any explicit reference to the core electrons (orbitals).     

Some upper bounds for the energy of graphs

Let G = (V,E) be a graph with n vertices and e edges. Denote V(G) = {v ₁,v ₂,...,v _n }. The 2-degree of v _i , denoted by t _i , is the sum of degrees of the vertices adjacent to . Let σ _i be the sum of the 2-degree of vertices adjacent to v _i . In this paper, we present two sharp upper bounds for the energy of G in terms of n, e, t _i , and σ _i , from which we can get some known results. Also we give a sharp bound for the energy of a forest, from which we can improve some known results for trees.     

Thermochemical data for n-alkylmonoamine intercalation into crystalline lamellar zirconium phenylphosphonate

Layered crystalline zirconium phenylphosphonate, Zr(O₃PC₆H₅)₂, changed its interlamellar distance of 1481 pm after intercalation of n-alkylmonoamines, CH₃---(CH₂)_n---NH₂ (n=0–6). The infrared spectra of the precursor host and the corresponding intercalated compounds presented vibrations associated with PO₃ groups in the 1163–1039 cm⁻¹ range and additional bands related to C---H stretching bands in the 2950–2850 cm⁻¹ interval were observed after amine insertion. The thermogravimetric curves showed a mass loss assigned to the phenyl group; however, the amine intercalated fraction was not quantitatively determined. A peak in the ³¹P NMR spectrum centered at −6 ppm for the host was observed. The surface area was 42.0±0.2 m² g⁻¹ and the scanning electron micrograph gave images consistent with lamellar structural features. The layered compound was calorimetrically titrated with amine in ethanol, requiring three independent operations: (i) titration of matrix with amine, (ii) matrix salvation, and (iii) dilution of the amine solution. From those thermal effects the variation in enthalpy was calculated as: −41±1.00,−33.28±0.50,−34.40±0.80,−10.40±0.40,−12.40±0.42,−16.10±0.08 and −7.0±0.04 kJ mol⁻¹, for n=0–6, respectively. The exothermic enthalpic values reflected a favorable energetic process of amine–host intercalation in ethanol. The negative Gibbs free energy results supported the spontaneity of all these intercalation reactions. The positive favorable entropic values, as carbon chain size increased, are in agreement with the free solvent molecules in the medium, as the amines are progressively bonded to the crystalline lamellar inorganic matrix at the solid/liquid interface.     

NMR study on solubility of benzyl alcohol and its transfer free energy from D_2O to cationic micelle

A new kind of surfactant, [CnH_(2n+1)OCH2CH(OH)CH2N(CH3)3]Cl (n=12, 14, 16) was synthesized. The solubility of benzyl alcohol in micellar solutions was determined by 1H NMR method. The results indicate that the length of alkyl chains of surfactant affects the solubility of ben-zyl alcohol in 2.5 × l0~(-2) mol/L micellar solutions. The solubility of benzyl alcohol per liter of micellar solution is 0.095 mole for n=12, 0.115 mole for n=14, 0.165 mole for n=16. The transfer free energy of benzyl alcohol from aqueous phase to micellar phase is -24.29 kJ/mol for n=12, -24.37 kJ/mol for n=14, -24.49 kJ/mol for n=16.     

Micellization behavior of [C16-12-C16], 2Br gemini surfactant in binary aqueous-solvent mixtures

The micellization behavior of bis cationic gemini surfactant, N,N′-dihexadecyl-N,N,N′,N′-tetramethyl-1,12-dodecanediammonium dibromide [C₁₆H₃₃N⁺(CH₃)₂-(CH₂)₁₂-N⁺(CH₃)₂C₁₆H₃₃, 2Br⁻] has been studied in binary aqueous mixtures of dimethyl sulfoxide, methanol, 1,4-dioxane, glycerol and ethylene glycol by conductivity and surface tension measurements at 300 K. The critical micellar concentration, degree of micelle ionization (α), surface excess concentration (Г_max), minimum surface area per molecule of surfactant (A_min), Gibbs free energy of micellization (ΔG_m°), the surface pressure at cmc (π_cmc), and the Gibbs energy of adsorption (ΔG_ad°) of the gemini surfactant have also been determined. The cmc, α, A_min increases where as (ΔG_m°), Г_max, and π_cmc decreases with increasing volume percentage of the solvents in the solvent–water binary mixture. The interfacial properties of the gemini surfactant, solute–solute, solvent–solute interactions and the effectiveness of a surface-active molecule in binary solvent systems have been discussed.     

Isentropic Compressibility Changes of Mixing for 1,3-Dioxolane or 1,4-Dioxane + Water + Propanol Ternary Mixtures

Speed of sound data, u_ijk, of 1,3-dioxolane or 1,4-dioxane(i) + water(j) + propan-1-ol or propan-2-ol(k) ternary mixtures and their sub-binary mixtures, u_ij, of 1,3-dioxolane or 1,4-dioxane(i) + water or propan-1-ol or propan-2-ol(j) and water(i) + propan-1-ol or propan-2-ol(j) mixtures have been measured over the entire composition range at 308.15 K. Isentropic compressibility changes of mixing, (κ_s^E)_ij and (κ_s^E) _ijk, for the binary and ternary mixtures have been determined by employing the observed speeds of sound data and densities (calculated from their molar excess volumes data). The (κ_s^E) _ij and (κ_s^E) _ijk values have also been predicated by the graph theoretical approach and the Flory theory. It has been observed that (κ_s^E) _ij and (κ_s^E) _ijk predicted by the graph theoretical approach compare well with their corresponding experimental values.     

The Effect of Anomeric Head Groups, Surfactant Hydrophilicity, and Electrolytes onn-Alkyl Monoglucoside Microemulsions

The effects of the variables of head group structure and salt concentration on microemulsions formed in mixtures of water, alkyl ethylene glycol ethers (C_kOC₂OC_k), andn-alkyl β- -glucopyranosides (C_mβG₁) are explored. Phase behavior of mixtures containing an anomer of the surfactant (n-alkyl α- -glucopyranoside, C_mαG₁), or surfactants with long head groups (n-alkyl maltopyranosides, C_mG₂), or NaCl or NaClO₄as electrolyte are systematically reported as a function of temperature and composition. The substitution ofn-alkyl α- -glucopyranosides forn-alkyl β- -glucopyranosides causes precipitation under some conditions in all mixtures studied. These solubility boundaries begin in the water–surfactant binary mixture at the Krafft boundary, then extend to high concentrations of both surfactant and oil. Increasing the effective length of the surfactant head group by adding C_mG₂to water–C_kOC₂OC_k–C_mβG₁mixtures moves the phase behavior dramatically up in temperature when even small amounts of C_mG₂are used. Adding a lyotropic electrolyte, NaCl, to water–C_kOC₂OC_k–C_mβG₁mixtures moves the phase behavior down in temperature, while the hydrotropic electrolyte NaClO₄moves the phase behavior up in temperature.     

Many protic ionic liquids mediate hydrocarbon-solvent interactions and promote amphiphile self-assembly

A large number of protic ionic liquids (PILs) have been found to mediate solvent-hydrocarbon interactions and promote amphiphile self-assembly. Hexagonal, cubic, and lamellar lyotropic liquid crystalline phases were observed in PIL-hexadecyltrimethylammonium bromide systems. The driving force for the formation of the self-assembled aggregate structures has been attributed to an entropic contribution to the free energy of association, analogous to the hydrophobic effect in water. The specific aggregate structures formed depend upon the cationic and anionic components of the PIL and their interactions with the amphiphiles.