Σe Values Research Articles

Surface Tension of the 4-Methyl-2-Pentanone/Ethyl Benzoate Binary System in the Temperature Range from 278.15 to 308.15K

Surface tensions (σ) and densities (ρ) of 4-methyl-2-pentanone/ethyl benzoate binary mixtures have been measured over the entire composition range at 278.15, 288.15, 298.15, and 308.15 K. Values of the excess surface tensions (σE) and excess molar volumes (VE) have been calculated. The σE and VE values were fitted by to the Redlich–Kister polynomial equation and the Ak coefficients have been derived. The standard deviations between the calculated and the experimental excess properties have also been derived. The surface tension values have been further used to calculate the surface entropies (SS) and surface enthalpies (HS) per unit surface area. The lyophobicity (β) and the surface mole fractions (x1S) of the surfactant 4-methyl-2-pentanone have been derived using the extended Langmuir model. The obtained results are discussed from the viewpoint of the existence of specific interactions between unlike molecules in the bulk region and the surface.

Cocrystallization mechanism of poly(3-alkyl thiophenes) with different alkyl chain length

The crystallization rates of poly(3-alkyl thiophene) (P3AT) cocrystals having different alkyl chain length (e.g. hexyl and octyl) of the components are measured using differential scanning calorimetry (DSC) technique. Two pairs of cocrystals with varying compositions of the components viz. poly(3-octyl thiophene) (P3OT(R), regioregularity 89mol%) and poly(3-hexyl thiophene) [P3HT(R), regioregularity 92mol% and P3HT-2 regioregularity 82mol%] are used. In both the systems the isothermal temperature range (TR) in the same time scale of crystallization is found to decrease with increasing alkyl chain length in the blends. The crystallization rate at the same Tc decreases with increasing alkyl chain length P3AT concentration and the Avrami exponent values of cocrystals are same with those of the component values. The low Avrami exponent values (0.23–1.16) in all the samples suggest the presence of rigid amorphous portion which can not diffuse out quickly from the crystal growth front (soft impingement). Analysis of crystallization rate using Laurintzen–Hoffman (L–H) growth rate theory indicates that there is regime-I to regime-II transition in all the samples. The product of lateral (σ) and end surface energy (σe) values are found to decrease with increasing the concentration of longer alkyl chain P3AT in the blend. Analysis of σ values according to a theory of Hoffman et al. [Hoffman JD, Miller RL, Marand H, Rotiman DR. Macromolecules 1992;25:2221. [14]] indicates that there is chain extension of the components in the melt of the blends, however, the entropy of cocrystallization has different sign to the two systems. Cocrystallization in P3HT(R)/P3OT(R) system is an entropy driven process but that in P3HT(2)/P3OT(R) system is entropy forbidden process. A possible explanation of cocrystallization in the later system has been attributed from small interaction between the components.

Crystallization regime characteristics of exfoliated polyethylene/vermiculite nanocomposites

AbstractPolyethylene (PE)–vermiculite (VMT) nanocomposites containing 0.5, 2, 4, 6, and 8 wt % clay loadings were fabricated via direct melt compounding in a twin‐screw extruder. Crystallization kinetics was investigated by means of polarized optical microscopy and differential scanning calorimetry. Moreover, the kinetics of the spherulitic growth of PE–VMT nanocomposites was evaluated with the Lauritzen–Hoffman (LH) secondary nucleation theory. The results showed that the PE–VMT nanocomposite exhibits crystallization regime characteristics. The nucleation constants for regimes I and II were determined from the slope of the LH plots. The fold surface energies (σe) of the PE–VMT nanocomposites were estimated from these slopes. The σe values were found to decrease with an increasing VMT content, up to 2%, in regime I. Further increasing the VMT content resulted in a slight increase of the σe values. In regime II, the σe values of the nanocomposites were generally lower than that of pure PE. These results demonstrated that the exfoliated silicate layers acted as effective nucleation sites for the secondary nucleus of the nanocomposites. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 253–263, 2005

Crystallization and Melting Behaviors of PPC‐BS/PVA Blends

AbstractThe isothermal crystallization and melting behaviors of poly(propylene carbonate) end‐capped with benzenesulfonyl/poly(vinyl alcohol) (PPC‐BS/PVA) blends over rich PVA composition range were first investigated by differential scanning calorimetry (DSC). PPC‐BS/PVA interaction parameter, χ12, calculated from equilibrium melting temperature depression was −0.44, revealing miscibility of PPC‐BS with PVA in the melt and favorable interactions. The temperature dependence of crystallization rate constant at initial crystallization stage was analyzed using the modified Lauritzen‐Hoffman expression. The chain width, a0, the thickness of a monomolecular layer, b0, the fold and lateral surface free energies, σe and σ, and the work of chain folding, q, for neat PVA were first reckoned to be 4.50 Å, 4.78 Å, 76.0 erg · cm−2, 8.81 erg · cm−2, and 4.70 kcal · mol−1, respectively. The values of σe and q for PVA in PPC‐BS/PVA blends exhibited a maximum in the neighborhood of 10/90 PPC‐BS/PVA, respectively.Kinetic analysis of the temperature dependence of crystallization rate constant at initial crystallization stage for neat PVA and PPC‐BS/PVA blends.magnified imageKinetic analysis of the temperature dependence of crystallization rate constant at initial crystallization stage for neat PVA and PPC‐BS/PVA blends.

Experimental determination of the thermo-optic coefficient (dn /dT ) and the effective stimulated emission cross-section (σ e ) of an a -axis cut 1.-at. % doped Nd:GdVO4 crystal at 1.06 μm wavelength

In this paper, we report the experimental determination of the thermo-optical coefficient (dn/dT) and the effective stimulated emission cross-section (σe) at 1064 nm for an a-axis cut 1.3-at.% doped Nd:GdVO4 crystal in a monolithic laser configuration. The pump-power-induced thermal lensing effect in the monolithic laser was used to determine these parameters. While measuring the dn/dT parameter, we also took into consideration the effect of pump-power-induced thermal expansion of the crystal. The dn/dT values obtained were 2.64-6 and 4.87×10-6 K-1, respectively, for directions parallel and perpendicular to the c-axis of the crystal. We show that the neglect of pump-power-induced thermal expansion of the crystal can overestimate the value of dn/dT by 30–50%. With the measured variation of the focal length of the thermal lens as a function of the absorbed pump power, we also computed the overlap integrals at the threshold pump power. These overlap integral values were used to estimate the product of the effective stimulated emission cross-section (σe) and the excited state lifetime (τ) of the Nd:GdVO4 crystal, which was found to be 1.476×10-22 cm2 s. With the reported values of τ for a 1.3-at.% doped Nd:GdVO4 crystal, we estimated the value of σe to be in the range 14.76×10-19 to 16.4×10-19 cm2. The value of the effective stimulated emission cross-section measured in this way was found to be around two times higher in magnitude than earlier reported values measured by spectroscopic methods.

Structure, Dynamics, and Magnetic Shieldings of Permanganate Ion in Aqueous Solution. A Density Functional Study

Car−Parrinello molecular dynamics simulations have been performed for MnO4- in the gas phase and in aqueous solution. Dynamic averaging at ca. 300 K affords only minor changes for the mean Mn−O bond length with respect to the optimized value re = 1.622 A (BP86 value). Magnetic shieldings, evaluated at the GIAO-B3LYP level for snapshots along the trajectories, decrease upon going from the equilibrium values to the dynamic averages in water. For 55Mn and 17O, the resulting σ300K − σe values amount to −36 and +31 ppm, respectively. The structure of the solvation shell around permanganate ion in water is characterized by the mean number of hydrogen-bonded solvent molecules (approximately 4) and by the gMnO pair correlation function.

Quiescent crystallization kinetics and morphology of isotactic polypropylene resins for injection molding. I. Isothermal crystallization

The quiescent isothermal crystallization kinetics of polypropylene was studied as a function of molecular weight (Mw), amount of ethene, and amount of maleic anhydride and acrylic acid grafting. Differential scanning calorimetry and polarized light optical microscopy were used to follow this kinetics. It was observed that the linear growth rate, G, decreased with the increase of Mw, but increased with the amount of ethene. In the grafted polymers, as the amount of grafting increased, G decreased. The fold surface free energy, σe, was found to increase with the increase in Mw. The heterophasic and grafted polymers had σe values higher than the homopolymers. All samples showed spherulitic morphology, except the acrylic acid-grafted polypropylene that showed axialitic morphology. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 68: 1159–1176, 1998

How to make a random graph irregular

AbstractAn irregular edge labeling of a graph G = (V, E) is a weight assignment f: E→ N such that the sums f + (v):= Σv∈e∈E f(e) are pairwise distinct. If such labelings exist in G, then the value of minf Σe∈E (f(e) ‐ 1) measures the minimum number of edges needed to make G irregular. We prove that this minimum for the random graph G(n, p) with n vertices and edge probability p = p(n) is equal to n2/4 + o(n2) as n→∞, whenever p(n)‐n2/3→∞. This asymptotic result is deduced from a general estimate (valid for every graph) involving vertex degrees and the size of largest triangle packings. © 1995 John Wiley & Sons, Inc.

Criteria for determining the long-term strength under conditions of complex loading

It has been pointed out that the problem of determining the long-term strength under complex conditions of loading consists in the simultaneous choice of an equivalent stress σe and the nature of the dependency of the failure time t* on the value of σe. This is best described by a series of experimental data taken at constant temperature. The problem can be solved by introducing a parameter D which characterizes the total discrepancy between the experimental and theoretical values of t*, and through the use of a technique for determining the material constants which will lead to a minimum value of D. As an example of this approach, a quantitative treatment of the experimental data given by I.I. Trunin and A. A. Lebedev is presented.

Special melting behaviour of highly oriented polyethylene

The DSC method has been applied for the study of melting behaviour of polyethylene [PE] films in dependence on the number of repeated stretching λ. Some samples have been subjected to annealing and etching by nitric acid. The melting process characteristics have been correlated with structural parameters. It was found that the longitudinal dimension of a crystallite l, calculated from the value of long period and degree of crystallinity, had increased slightly with increasing λ. A rise in the melting point temperature Tm with increasing λ has not been caused so much by the value of l but has been related to the decrease of σe values—the specific free surface energy of the edges of crystallites. The values of σe, calculated according to the Thomson formula, have significantly decreased with increasing λ and have increased after annealing of the samples. The etching process has been accompanied by increase of σe. The structural changes, occuring during stretching, annealing and etching of PE samples, have had their significance presumably in amorphous zones and the end facets of crystallites, affecting also σe and, consequently, Tm values.

Determination of Transport Properties of Alumina Oxide Scale

By measuring the potential difference between the two interfaces of an alumina scale developed on a FeCrAl alloy, or by applying an electric field during its growth, values of ti, σi, and σe along with their temperature dependence were determined. A residual potential, V0, which was measured between the two oxide interfaces, is related to the oxygen chemical potential gradient on the scale. Alumina growth is controlled by oxygenion diffusion (by either V″ or O″i), and the transport properties are modified by the amount and distribution of impurities.

Profiles of optical Extinction Coefficients Calculated from Droplet Spectra Observed in Marine Stratus Cloud Layers

Airborne measurements of droplet spectra n(r) where r is droplet radius were made in stratus cloud layers over the ocean 130 km southwest of San Diego. Optical extinction coefficients σe were calculated at selected wavelengths (λ= 0.53, 3.75 and 10.59 μm) from these n(r) and were used to construct average vertical profiles of σe between 200 m above cloud base to 250 m below cloud base. An approximation to σe a power function of the liquid water content w was found to be superior compared with approximations involving linear functions of w or the cross-section area. The horizontal variability of σe in the clouds was examined. The average horizontal scale size of σe was estimated to be 3 km and the horizontal measuring distance required to obtain values of σe with a relative accuracy of 10% was found to be in excess of 30 km.

Crystallization kinetics of syndiotactic polypropylene

AbstractMelting‐point and spherulite growth rate measurements for a sample of syndiotactic polypropylene (S = 0.716 and η = 0.356) were analyzed for the parameters characterizing crystal formation and growth: Tm = 159 ± 2°C, σe = 47 erg cm −2, σ = 4.4 erg cm−2, and q = 5.6 kcal per mole of folds. The q and σe values place syndiotactic polypropylene in the group of “unhindered” polymers. Failure of the isotactic‐polypropylene spherulite growth rate data to follow current theories of crystal growth precluded a comparison of crystal parameters of the two stereoisomers. At comparable degrees of supercooling, the absolute growth rates for the two forms are of the same order of magnitude and exhibit one or more crossover(s) in relative position.

On the Reliability of the Parameterization of Microphysics in Fog Models

Abstract The relationships between the mean terminal speed of fog droplets (vE) and the liquid water content (W), and between the integral volume droplet absorption coefficient (σE) and W, have been examined on the basis of 107 experimental fog droplet size spectra selected from the literature, in order to investigate the reliability of parameterizing the microphysics, in fog models, through W. The results show that a weak correlation exists between vE and W, the values of the linear correlation coefficients (R) being 0.12, 0.30, −0.19 and 0.67, for valley, advection, radiation and artificial fog, respectively. Thus parameterizations of vE through W only are generally unreliable, and other parameterizations, in terms of more than one parameter, should be developed. On the other hand, a good correlation between σE and W has been found, with R = 0.98, 0.87, 0.91 and 0.99 for the fog types indicated above. Comparisons between the values of σE and those obtained by the best-fit lines and by the parameterizati...

An improved procedure for the description of substituent effects on equilibrium and rate constants, based on factor analysis of the whole body of appropriate data

By comparing the two most widely used descriptions of substituent effects by Hammett type substituent constants, viz., the Taft equation and the Yukawa–Tsuno relation, it is shown that a general descriptive equation should be of the type: log (KX/KH)= [graphic omitted]ρiσi. In this equation, the left hand side is the substituent effect, ρ is a reaction constant, and σ is a substituent constant. With the aim of finding optimal values of ρ and σ which can be used in this general equation, a large number (570) of log (KX/KH) values for chemical reactions and equilibria was selected from the literature. These data were taken for 76 reactions or equilibria, and 17 substituents. A special statistical procedure, which included factor analysis, was designed and applied to extract optimal ρ and σ values from the data. The results of the procedure show that only three substituent constants, σI, σR, and σE, are required to describe log (KX/KH) values for all reaction types mentioned by Ehrenson, Brownlee, and Taft, viz.σI, σR0, σR(BA), σR+, and σR– reaction types. So, the general regression equation is log (KX/KH)=ρIσI+ρRσR+ρEσE. The constants σI and σR are comparable to Taft's σI and σR0. The magnitude of the ρEσE term is indicative of the reaction type : ρE is zero for σR0 reactions, negative for para-substituted σR– reactions, and positive for σR+ reactions (the substituent effects were defined in such a way that ρI and ρR are positive for all reactions). Optimal values of σI, σR, and σE are given for the 17 substituents. As an illustration of their applicability, regression analysis of phase equilibrium data on σI, σR, and σE is performed, and the results are compared with those of regression analysis on the Taft σ parameters.

Emission cross section and fluorescence quenching of Nd3+ lanthanum pentaphosphate

The stimulated emission cross section σ for the transitions 4F3/2→4I9/2,11/2 in NdP5O14 and La0.75Nd0.25P5O14 has been measured at 300 °K. For the strongest emission line at 1.0510 μm the value of σE∥b is 18×10−20 cm2, which is to be compared to the value of 46×10−20 cm2 for Nd : YAG. The fluorescence lifetimes of the 4F3/2 state in La1−xNdxP5O14 have been measured at 300 and 77 °K and were found to be independent of temperature. Based on the measured spectroscopic parameters the performance of LED−pumped La0.75Nd0.25P5O14, NdP5O14, and Nd : YAG have been compared both in the end−pumped and side−pumped configurations. In the end−pumped configuration the pentaphosphate has no advantage over Nd:YAG. In the side−pumped case the threshold for La0.75Nd0.25P5O14 is predicted to be lower than that for Nd:YAG.

Crystallization of polyethylene at high pressure: A kinetic view

AbstractA model for the crystallization kinetics of polymers is outlined and is used to interpret observations of the crystallization of polyethylene at high pressures. This model introduces a distinction between σe the lamellar surface energy which controls the lamellar thickness, and σe′, the surface nucleus surface energy which controls the growth rate. Differential scanning calorimetry and electron microscopy data for several polyethylenes crystallized at pressures of up to 8 kb are presented. From the dependence of lamellar thickness on the crystallization undercooling at 5 kb, it is found that σe increases markedly with pressure leading to the formation of very thick crystals at high pressures. The magnitude of the increase in σe is in agreement with σe values calculated from the dependence of melting temperatures on pressure. The nucleus surface energy σe′ is not expected to vary significantly with pressure, and estimates of growth rates of 5 kb which indicate that the growth rate does not vary significantly with pressure at constant under‐cooling confirm this. Fractionation effects and the differences in behavior between different polyethylenes are also discussed.