Analysis of exponent values in Gaussian‐type functions for development of protonic and deuteronic basis functions

We analyzed the exponent (α) values in Gaussian‐type functions (GTF) for protons and deuterons in BH₃, CH₄, NH₃, H₂O, HF, and their deuterated molecules for the development of nuclear basis functions, which are used for molecular orbital (MO) calculations that directly include nuclear quantum effects. The optimized α (α_opt) value in the single s‐type ([1s]) GTF for protons is changed due to the difference in flexibility of the electronic basis sets. The difference between the energy obtained by using the α_opt value for each molecule and that obtained by using the average α (α_ave) value for these exponents with the 6‐31G(d,p) electronic basis function is only 2 × 10^?5 a.u. The α_ave values of protonic and deuteronic [1s] GTFs by the present calculation are 24.1825 and 35.6214, respectively. We found that the α_ave values enable the evaluation of the total energy and the geometrical changes in hydrogen bonding, such as O…H? O, O…H? N, and O…H? C, while the α_opt value became small by forming a hydrogen bond. The result using only the [1s] GTF for the protonic and deuteronic basis functions is sufficient to explain the differences of energy and geometry induced by the H/D isotope effect, although the total energy of ～5 × 10^?4 a.u. was improved by using the s‐, p‐, and d‐type ([1s1p1d]) GTFs for protons and deuterons. We clearly demonstrate that the protonic and deuteronic basis functions based on the α_ave value enable us to apply the method to other sample molecules (glycine, malonaldehyde, and formic acid dimer). The protonic and deuteronic basis functions we developed treat the quantum effects of protons and deuterons effectively and extend the application range of the MO calculation to include nuclear quantum effects. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Raman spectra,Pippard relations and critical exponents for NH4Cl

The Pippard relations have been extended to correlate the vibrational frequency shifts with the relevant thermodynamic quantities in the vicinity of the λ-point in NH₄Cl. It has been shown that they describe the NH₄Cl system adequately below its λ-transition temperature. (T_λ = 242.8 K). This has been examined using our temperature-dependent frequency data for the ν₅ (174 cm^?1) Raman mode of NH₄Cl at zero pressure by means of the equations developed. The slope of the λ-transition line. (dP/dT)_λ that has been calculated from these equations, is in good agreement with those obtained by previous workers. We have deduced the critical exponents a′ and c′ for the thermal expansion and the isothermal compressibility of NH₄Cl from our temperature and pressure-dependent frequency data for the ν₅ mode. We have identified our exponent value for the thermal expasion with the specific heat exponent, a′, (Pippard relation) to demonstrate the scaling law a′+2b+c′=2, using our value of the critical exponent b for the order parameter from our previous work on NH₄Cl.     

Critical behavior of the bend elastic constant of a liquid crystalline comblike polymer near the nematic–smectic A phase transition

The temperature dependence of the bending elastic constant of a combined comblike side- and main-chain liquid crystalline polymer near the nematic–smectic A phase transition was investigated. The bending constant K₃ diverges at the transition, but the critical exponent ν = 1.4 does not agree with the theoretical prediction. The large value of the exponent ν may be explained by the polydispersity of the polymer investigated.     

On the Calculation of Liquid–Vapor Interfacial Thickness Using Experimental Surface Tension Data

In this paper we investigate the vapor–liquid interfacial thickness of several pure fluids using a new method. In this method, the surface thickness is obtained using experimental surface tension data, and its dependence on the temperature is evaluated. The interfacial width is found to increase with increasing temperature and goes to infinity when the temperature approaches its critical value. Also, we find that a plot of ln δ versus ln {(1−T _r)⁻¹} is linear, in which δ and T _r are the interfacial thickness and reduced temperature, respectively. In this method, the equation of state obtained from the Statistical Associating Fluid Theory (SAFT EOS), which is molecular based, is accepted.     

Influences of nonsolvent and temperature on critical viscoelastic behaviors of ternary polyacrylonitrile solutions around the sol-gel threshold

Viscoelastic experiments were performed to study the influence of nonsolvent and temperature on critical viscoelastic behaviors of ternary polyacrylonitrile (PAN) solutions around the sol-gel threshold. The dynamic critical parameters around the sol-gel threshold were determined using dynamic rheometer. The sol-gel transition takes place at a critical gel temperature at which the scaling law of G′(ω) ∼ G″(ω) ∝ ωⁿ holds, allowing an accurate determination of the critical gel temperature by means of the frequency independence of the loss tangent. Although the gel points of PAN solutions increase with increasing H₂O content, the results show that the scaling exponent n at the gel point is found to be universal for all ternary PAN solutions, which is independent of temperature and H₂O content, indicating the similarity of the fractal structure in the critical PAN gels. The gelation of ternary PAN solutions induced by adding a nonsolvent and by decreasing the temperature is demonstrated to be a thermoreversible process, which implies that the PAN gels are physical gels. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2637–2643, 2008     

Eight-arm star polystyrene in methylcyclohexane: Cloud-point curves,critical lines,and coexisting densities and viscosities

We measured the cloud-point curves of eight-arm star polystyrene (sPS) in methylcyclohexane (MCH) for polymer samples of three total molecular masses [weight-average molecular weight (M_w) × 10⁻³ = 77, 215, or 268]. We found a downward shift of 5–15 K in the critical temperature (T_c) of the star polymer solutions with respect to linear polystyrene (PS) solutions of the same M_w. The shift in T_c became smaller as M_w increased. The critical volume fraction for eight-arm sPS in MCH was equal within experimental uncertainty (10–40%) to that of linear PS in MCH. For sPS of M_w = 77,000 in MCH, we studied the mass density (ρ) as a function of temperature (T). As for linear polymers in solution, the difference in ρ between coexisting phases (Δρ) could be described over t = (T_c − T)/T_c for 1.1 × 10⁻⁴ < t < 4.7 × 10⁻³ with the Ising value of the exponent β in the expression Δρ = B t^β. Both ρ(T) above T_c and the average value of ρ below T_c were linear functions of temperature; no singular corrections were observed. The measurements of the shear viscosity (η) near T_c for sPS (M_w = 74,000) in MCH indicated a strong critical anomaly in η, but the data were not precise enough for a quantitative analysis. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 129–145, 2004     

Critical behaviour of optical birefringence in the vicinity of nematic–isotropic and smectic A–isotropic phase transitions of the eight members of alkyloxy-cyanobiphenyls

We report the measurements of birefringence (Δn) as a function of the temperature of a homologous series of alkyloxy-cyanobiphenyls (nOCB) liquid crystalline compounds by means of high-resolution optical transmission method. The temperature dependence of the birefringence has been determined from the transmitted intensity data for two different wavelengths. The order parameter critical exponent β, obtained by using a four-parameter fitting procedure consistent with the mean-field theory for a weakly first order transition, is found to be in good agreement with the theoretically predicted tricritical value. A weak birefringence has been found to develop on approaching the clearing temperature, which is tentatively attributed to the formation of a small mesophase domain within the isotropic phase. This striking behaviour leads to a further quantification of the critical fluctuation close to the transition. Finally, the order character of the nematic–isotropic (N–I) and smectic A–isotropic (SmA–I) phase transitions have been assessed by using the birefringence data. The critical exponent α (usually assigned to the heat capacity) extracted from Δn data describes the critical nature of N–I and SmA–I transitions and strongly supports the tricritical nature of the same.     

Absolute quantum yield of O(1D2) in the photolysis of ozone in the hartley band

The absolute quantum yield of O(¹D₂) in the photolysis of ozone in the Hartley band, between about 230 and 280 nm, has been determined using the isotopic exchange reaction between C¹⁶O₂ and ¹⁸O(¹D₂). A value of 1.00 ± 0.05 has been obtained within a 95% confidence limit. A value of unity may therefore be accepted as the average quantum yield of O(¹D₂) atoms in the 230–280-nm region within an uncertainty of only several percent.     

New Method for Determining H-Bond Energy: Fluorescence from Neutral Red in Water Compared to Fluorescence from Neutral Red in Benzene

A new method is presented for determining the H-bond energy between a fluorescent solute and water. In the current example the hydrogen-bond energy between neutral red (NR) and water was measured. The H-bond energy was obtained from the temperature dependence of the ratio of the 625 nm fluorescence intensity from NR in water, which increases with increasing temperature, to that of the 530 nm intensity from NR in benzene, which decreases with increasing temperature. The H-bond energy so determined is (10050 ± 60) J-mol⁻¹, which compares favorably with an H-bond E_HB value for pure water of 10170 J-mol⁻¹. Intermolecular hydrogen-bonding between water and NR increases the nonradiative deactivation process of the excited molecule due to fast energy dissipation through the vibrations associated with the hydrogen bonds. Some of the hydrogen bonds are broken with an increase in temperature, resulting in an increase in the number of free NR molecules, thus increasing the fluorescence quantum yield.     

Analysis of exponent values of Gaussian‐type functions on quantum protons and deuterons in charged or polarized systems

The optimal exponent α values (α_opt) in s‐type Gaussian‐type functions (GTFs) for quantum protons and deuterons, which are used for multicomponent molecular orbital calculations including nuclear quantum nature of protons and deuterons, are analyzed for several charged or polarized systems and their deuterated species. Ishimoto and coworkers (Ishimoto, Int. J. Quantum Chem. 2006 , 106, 1465) have already proposed the average exponent values for five neutral molecules (α_ave), and demonstrated that their α_ave enables us to evaluate the H/D isotope effect on energies and geometries of various neutral species. The differences between total energies of several charged or polarized systems with previous α_ave and our α_opt correspond to only less than 0.004% of the total energy (0.47 kcal·mol^?1) except for HeH⁺ and HeD⁺ molecules, while the difference between interaction energies of H₂OH^+…OH₂ and H₂OD^+…OH₂ systems with previous α_ave is 19% (0.22 kcal·mol^?1) smaller than that with our α_opt. Meanwhile, the difference between O? H bond lengths in H₂OH^+…OH₂ system with α_ave and α_opt values is 0.027 Å. We also found that the interaction energies with α_opt value at the geometry optimized with previous α_ave value (α_sp) well reproduce those at the geometry optimized with α_opt value. We have demonstrated that the nuclear basis functions based on s‐type GTFs with previous α_ave values enable us to evaluate the H/D isotope effect on energies and geometries of charged or polarized systems. © 2016 Wiley Periodicals, Inc.     

An experimental trial for the determination of the critical coagulation concentration using the sedimentation method

A method for determining the critical coagulation concentration (C _c) from the change in the transmittance of the sol with stand time after adding a coagulating agent is discussed. Potassium nitrate was used as the coagulating agent because the specific adsorption of electrolyte ions on the particle and the hydrolysis of electrolyte ions are negligible. Apparent critical coagulation concentrations,C _c ^a, of iron (III) hydroxide and silver iodide sols were obtained from the transmittance vs. potassium nitrate concentration curves for various stand times. The values ofC _c ^a decreased with increasing stand time. TheC _c ^a value obtained for the shortest stand time was closer toC _c obtained from the initial turbidity change of the sol by applying Rayleigh's law. The Hamaker constant for the particle in water was calculated from theC _c ^a value obtained at the shortest time and the experimentally determined outer Helmholtz plane potential. The calculated Hamaker constants were comparable to the theoretical values for iron (III) hydroxide and silver iodide.     

Power law relationship between yield stress and shear modulus for glassy polymers

The published data on the yielding of glassy polymers under a variety of testing conditions reveal that the yield stress increases with the elastic modulus. However, fundamental understanding of the interrelation has not yet been established. In this paper, a power law relation between the shear yield stress τ_y and the shear modulus G is presented: T₀τ_y/Tτ_y0 = (T₀G/TG₀)ⁿ, where T is the absolute temperature, T₀. is reference temperature, and τ_y0 and G₀ are, respectively, the shear yield stress and the shear modules at T₀. The exponent n takes a value 1.63 for amorphous polymers without exception, whereas it is about 0.8–0.9 for crystalline polymers. The exponent 1.63 for amorphous polymers is in good agreement with the value derived from the approximation of the Bowden–Raha dislocation analog. This law may enable us to investigate a model for the yielding of glassy polymers.     

On the Constant Pressure Specific Heat CP of a Simple Fluid

Abstract

Calculation of C_P from a model soft-core equation of state reveals a line in the phase diagram on which C_P is equal to its zero pressure value C _{P 0} . This line commences on the temperature axis where the second virial coefficient has a point of inflexion. At higher temperatures (and pressures) C_P falls below C _{P 0} . The detailed behaviour of C_P is presented via contour maps, illustrating the effects of changing the exponent N(= 3/n, where n is the repulsive potential exponent) which parameterizes the model. For soft-core fluids at high temperatures C_P deviates only slightly from the ideal gas value over a wide range of temperature and density, in marked contrast to the behaviour of hard-core models.     

Electron correlation effects in ionic hydrogen clusters

We employ density functional, post‐Hartree–Fock, and quantum Monte Carlo methods to study the electronic structure, geometries, and behavior of positively charged H_m⁺ clusters with m=3,5,…,17. Their structure consists of a tightly bound H₃⁺ core ion surrounded by successive solvation shells of H₂ molecules. For the largest clusters, we propose new geometries. We find that correlated methods yield the stepwise decrease of enthalpies for dissociation of H₂ from the clusters observed in experiments. Our best results are obtained by the diffusion Monte Carlo method, and by including finite temperature entropic effects, we are able to reproduce the experimental dissociation enthalpies with an unprecedented accuracy of less than 0.5 kcal/mol. These benchmark results contrast with erroneous predictions discovered in the density functional approaches. Finally, our analysis of the cluster energy surfaces indicates that under quantum and thermal fluctuations, the outer solvation shells will exhibit pronounced fluctional behavior. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 86–95, 2001     

DENSITY, EQUILIBRIUM HEAT OF FUSION AND EQUILIBRIUM MELTING TEMPERATURE OF NYLON 1010

The density, equilibrium heat of fusion and equilibrium melting temperature of Nylon 1010 were determined by means of infrared spectrum, differential scanning calorimetry, wide angle X-ray diffraction and density measurement techniques. According to Starkweatber' s method crystalline density ρ_c and amorphous density ρ_a were estimated to be 1.098 and 1.003 g/cm~3 respectively by extrapolating the straight lines of the IR absorbanee against density to zero intensity. Owing to the less intense in absorbance and less sensitive to the change in crystallinity of the amorphors band the thus obtained ρ_c was too low in value. Thereby the value of the ratio ρ_c /ρ_a is far less than generally accepted mean value for most crystalline polymers. Accordingly, traditional X-ray diffraction method was used through determining thc crystalline dimension(a=4.9, b=5.4, c=27.8, α=49°β=77.0°, γ=63.5°), and a rather correct value of ρ_c or the crystal density 1.13 g/cm~3 was obtained. The equilibrium heat of fusion △H_m~0 was estimated to be 244.0 J/g piotting △H_m 's of specimens with different crystallinity against their corre sponding specific volumes _(sp), and extrapolating to completely crystalline condition (_(sp)~c= 1/ρ_c) As to the equilibrium melting temperature T_m~0, because of the easiness of recrystallization of melt crystallized Nylon 1010 specimen, the well-known Hoffman's T_m-T_c method failed in determining this value and an usually rarely used Kamide double extrapolation method was adopted. The so obtained value of T_m~0 487 seems to be fairly reasonable.     

Influence of Excitation of the Lanthanide 4 fShell on Complexation with Organic Substrates in Solutions: 2. Isotope Effects in Complexation of Tris(heptafluorodimethyloctanedionato)europium(III) with Dimethyl Sulfoxide in Benzene Solutions

The effect of deuteration of dimethyl sulfoxide on the fluorescence quantum yield, temperature quenching of fluorescence, and its complexation with tris(heptafluorodimethyloctanedionato)europium(III) (Eu(fod)₃) in the ground and excited states was studied. It was found that excitation of f–ftransitions in Eu(III) increases the stability of Eu(fod)₃complexes with sulfoxides but has a very insignificantly influence on isotope effects. The deuterium effect is displayed to a small extent in altering the quantum yield and is accompanied by a decrease in the efficiency of temperature quenching of Eu(fod)^* ₃fluorescence.     

Tetrasulphur Tetranitride: Phase Transition and Crystal Structure at Elevated Temperature

Rietveld X‐ray crystal structure investigations on S₄N₄ give evidence for a new orthorhombic high‐temperature phase (Pbcn, a = 883.9(1) pm, b = 875.5(1) pm, c = 725.81(9) pm) very close to the explosion temperature of the solid‐state material. The phase transition can be described using Landau's theory, yielding a critical temperature of 397 K and a critical exponent of 0.50.     

QUANTUM YIELD RATIO OF THE FORWARD and BACK LIGHT REACTIONS OF BACTERIORHODOPSIN T LOW TEMPERATURE and PHOTOSTEADY-STATE CONCENTRATION OF THE BATHOPRODUCT K*

The maximum photosteady state fraction of K, x_K^max, and the ratio of the quantum yields of the forward and back light reactions, trans-bacteriorhodopsin (bR) hArr; K, φ_bR/φ_K, were obtained by measuring the absorption changes produced by illumination of frozen water-glycerol (1:2) suspensions of light-adapted purple membrane at different wavelengths at -165°C. An independent method based on the second derivative of the absorption spectrum in the region of the β-bands was also used. It was found that The quantum yield ratio (0.66 ± 0.06) was found to be independent of excitation wavelength within experimental error in the range510–610 nm. The calculated absorption spectrum of K has its maximum at603–606 nm and an extinction 0.85 ± 0.03 that of bR. At shorter wavelengths there are P-bands at 410, 354 and 336 rim. Using the data of Hurley et al. (Nature 270,540–542, 1977) on relative rates of rhodopsin bleaching and K formation, the quantum yield of K formation was determined to be 0.66 ± 0.04 at low temperature. The quantum efficiency of the back reaction was estimated to be 0.93 ± 0.07. These values of quantum efficiencies of the forward and back light reactions of bR at - 165°C coincide with those recently obtained at room temperature. This indicates that the quantum efficiencies of both forward and back light reactions of bacteriorhodopsin are temperature independent down to -165°C.     

用非等温DSC基于Harcourt-Esson方程估算含能材料热爆炸临界温度的一种简单方法

用合理假设,由Semenov热爆炸理论和基于Harcourt-Esson速率表达式非等温动力学方程 ,推导了估算含能材料热爆炸临界温度的一种简单方法。该计算式为 ,比较简单。从非等温DSC曲线上onset温度（ ）通过表达式 可得到 ,由方程 可求得 值,随后算出 。该方法计算结果与Zhang-Hu-Xie-Li方法结果相一致。     

Errors involved in the activation energy calculated by integral methods when the frequency factor depends on the temperature ( A = A 0 T m)

The dependence of the frequency factor on the temperature (A=A ₀ T ^m) has been examined and the errors involved in the activation energy calculated from some integral methods without considering such dependence have been estimated. Investigated integral methods are the Coats-Redfern method, the Gorbachev-Lee-Beck method, the Wanjun-Yuwen method and the Junmeng-Fusheng method. The results have shown that the error in the determination of the activation energy calculated ignoring the dependence of the frequency factor on the temperature can be rather large and it is dependent on x=E/RT and the exponent m.