Determination of thermodynamic stability of CdMoO4 by knudsen effusion vapor pressure measurement method

Thermodynamic stability of CdMoO₄ was determined by measuring the vapor pressures of Cd and MoO₃ bearing gaseous species. Th vaporization reaction could be described as CdMoO₄(s)+MoO₂(s) =Cd(g)+2/n(MoO₃)_n (n=3, 4 and 5). The vapor pressures of the cadmium (p _Cd) and trimer (p _(MoO3)3) measured in the temperature range 987≤T/K≤1111 could be expressed, respectively, as ln (p _Cd/Pa) = –32643.9/T+29.46±0.08 and ln(p _(MoO3)3/Pa) = –32289.6/T+29.28±0.08. The standard molar Gibbs free energy of formation of CdMoO₄(s), derived from the vaporization results could be expressed by the equations: °_f G _{CdMoO4 (s)} ⁰= –1002.0+0.267T±14.5 kJ mol^–1 (987≤T/K≤1033) and °_f G _{CdMoO4 (s)} ⁰ = –1101.9+0.363T±14.4 kJ mol^–1 (1044≤T/K≤1111). The standard enthalpy of formation of CdMoO₄(s) was found to be –1015.4±14.5 kJ mol^–1 .     

Rate constant for the reaction of bromine atoms with ethane: Kinetic and thermochemical implications

Relative-rate kinetic experiments were carried-out at T = 310 ± 3 K to determine rate constant ratios for the reactions of Br atoms with C₂H₆(1), CH₂ClBr(2) and neo-C₅H₁₂(3). Br atoms were produced by stationary photolysis of Br₂ and the consumption of the reactants was determined by gas-chromatography. k ₂/k ₁ = 1.174 ± 0.053 and k ₃/k ₁ = 0.458 ± 0.027 were determined (with 1σ precision given). The rate constant ratios were resolved to absolute k ₁ values, and k ₁(310 K) = (2.27 ± 0.30) × 10⁵ cm³ mol⁻¹ s⁻¹ was recommended. The recommended k ₁ was applied in a third law analysis providing Δ_f H ^o ₂₉₈(C₂H₅) = (122.0 ± 1.9) kJ mol⁻¹.     

Rate constants for the elementary reactions between CN radicals and CH4, C2H6, C2H4, C3H6, and C2H2 in the range: 295 ⩽ T/K ⩽ 700

Pulsed laser photolysis, time-resolved laser-induced fluorescence experiments have been carried out on the reactions of CN radicals with CH₄, C₂H₆, C₂H₄, C₃H₆, and C₂H₂. They have yielded rate constants for these five reactions at temperatures between 295 and 700 K. The data for the reactions with methane and ethane have been combined with other recent results and fitted to modified Arrhenius expressions, k(T) = A′(298) (T/298)ⁿ exp(?θ/T), yielding: for CH₄, A′(298) = 7.0 × 10^?13 cm³ molecule^?1 s^?1, n = 2.3, and θ = ?16 K; and for C₂H₆, A′(298) = 5.6 × 10^?12 cm³ molecule^?1 s^?1, n = 1.8, and θ = ?500 K. The rate constants for the reactions with C₂H₄, C₃H₆, and C₂H₂ all decrease monotonically with temperature and have been fitted to expressions of the form, k(T) = k(298) (T/298)ⁿ with k(298) = 2.5 × 10^?10 cm³ molecule^?1 s^?1, n = ?0.24 for CN + C₂H₄; k(298) = 3.4 × 10^?10 cm³ molecule^?1 s^?1, n = ?0.19 for CN + C₃H₆; and k(298) = 2.9 × 10^?10 cm³ molecule^?1 s^?1, n = ?0.53 for CN + C₂H₂. These reactions almost certainly proceed via addition-elimination yielding an unsaturated cyanide and an H-atom. Our kinetic results for reactions of CN are compared with those for reactions of the same hydrocarbons with other simple free radical species. © John Wiley & Sons, Inc.     

Low-temperature heat capacity and standard entropy of PdO(cr.)

The temperature dependence of the heat capacity C _p ^o = f(T) of palladium oxide PdO(cr.) was studied for the first time in an adiabatic vacuum calorimeter in the range of 6.48–328.86 K. Standard thermodynamic functions C _p ^o(T), H ^o(T) — H ^o(0), S ^o(T), and G ^o(T) — H ^o(0) in the range of T → 0 to 330 K (key quantities in different thermodynamic calculations with the participation of palladium compounds) were calculated on the basis of the experimental data. Based on an analysis of studies on determining the thermodynamic properties of PdO(cr.), the following values of absolute entropy, standard enthalpy, and Gibbs function of the formation of palladium oxide are recommended: S ^o(298.15) = 39.58 ± 0.15 J/(K mol), Δ_f H ^o(298.15) = −112.69 ± 0.32 kJ/mol, Δ_f G ^o(298.15) = −82.68 ± 0.35 kJ/mol. The stability of Pd(OH)₂ (amorph.) with respect to PdO(cr.) was estimated.     

Very-low-pressure pyrolysis of nitroso- and pentafluoronitrosobenzene C?NO bond dissociation energies

The high-pressure absolute rate constants for the decomposition of nitrosobenzene and pentafluoronitrosobenzene were determined using the very-low-pressure pyrolysis (VLPP) technique. Bond dissociation energies of DH⁰(C₆H₅? NO) = 51.5 ± 1 kcal/mole and DH⁰ (C₆F₅? NO) = 50.5 ± 1 kcal/mole could be deduced if the radical combination rate constant is set at log k_r(M^?1·sec^?1) = 10.0 ± 0.5 for both systems and the activation energy for combination is taken as 0 kcal/mole at 298°K. δH_f⁰(C₆H₅NO), δH_f⁰(C₆F₅NO), and δH_f⁰(C₆F₅) could be estimated from our kinetic data and group additivity. The values are 48.1 ± 1, –160 ± 2, and – 130.9 ± 2 kcal/mole, respectively. C–X bond dissociation energies of several perfluorinated phenyl compounds, DH⁰(C₆F₅–X), were obtained from the reported values of δH_f⁰(C₆F₅X) and our estimated δH_f⁰(C₆F₅) [X = H, CH₃, NO, Cl, F, CF₃, I, and OH].     

Twinkling fractal theory of the glass transition: Rate dependence and time–temperature superposition

The twinkling fractal theory (TFT) of the glass transition temperature T_g provides a new method of analyzing rate effects and time–temperature superposition in amorphous materials. The rate dependence of T_g was examined in the light of new experimental and theoretical evidence for the nature of the dynamic heterogeneity near T_g. As T_g is approached from above, dynamic solid fractal clusters begin to form and eventually percolate rigidity at T_g. The percolation cluster is a solid fractal and to the observer, appears to “twinkle” as solid and liquid clusters interchange in dynamic equilibrium with a vibrational density of states g(ω) ∼ ω. The solid-to-liquid twinkling frequencies ω_TF are controlled by the Boltzmann population of intermolecular oscillators in excited energy levels of their anharmonic potential energy functions U(x) such that ω_TF = ω exp −B(T*² − T²)/kT in which T* ≈ 1.2T_g. An oscillator changes from a solid to a liquid when a thermal fluctuation causes it to expand beyond its inflection point in the anharmonic potential. This leads to a continuous solid fraction P_s near T_g given by P_S ≈ 1−[(1 − p_c) T/T_g] where p_c ≈ 1/2 is the rigidity percolation threshold. Since g(ω) is continuous from very low to very high frequencies, the complex twinkling dynamics existing near T_g produces a continuous relaxation spectrum with many different length scales and times associated with the fractal clusters. The twinkling frequencies control the kinetics of T_g such that for a given observation time t when the rate γ > 1/t, only those parts of the twinkling spectrum with ω > γ can contribute to relaxation or percolation upto time t. The most important results in this article are as follows: The TFT describes the rate dependence of T_g, both for DSC thermal heating/cooling rates and DMA frequencies as the classic T_g − lnγ law as T_g(γ) = T_go + (k/2B) ln γ/γ_o in which the constant B = 0.3 cal/mol K². The constant B appears quite universal for the 17 thermoset polymers investigated in this study and 18 linear polymers investigated by others. Many other amorphous metal and ceramic glass materials exhibited the same rate law but required a new B value approximately half that for polymers. The same B = 0.3 value was also used to successfully describe the TTS shift factors using the twinkling fractal frequencies ω_TF = ωexp −B(T*² − T²)/kT, as ln a_T(TFT) = exp B(T_R² − T²)/kT, which gave comparable results with the classical WLF equation, log a_T = [−C₁(T − T_R)]/[C₂ + (T − T_R)]. The advantage of the TFT over the WLF is that C₁ and C₂ are not universal constants and must be determined for every material, whereas the TFT uses one known constant B which appears to be the same for all polymers. The TFT has also been found to describe the strong and fragile nature of the viscosity behavior of liquids and the rate and temperature dependence of the yield stress in polymers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2578–2590, 2009     

Twinkling fractal theory of the glass transition

In this paper we propose a solution to an unsolved problem in solid state physics, namely, the nature and structure of the glass transition in amorphous materials. The development of dynamic percolating fractal structures near T_g is the main element of the Twinkling Fractal Theory (TFT) presented herein and the percolating fractal twinkles with a frequency spectrum F(ω) ∼ ω^df–1 exp −|ΔE|/kT as solid and liquid clusters interchange with frequency ω. The Orbach vibrational density of states for a fractal is g(ω) ∼ ω^df–1, where d_f = 4/3 and the temperature dependent activation energy behaves as ΔE ∼ (T² − T). The key concept of the TFT derives from the Boltzmann population of excited states in the anharmonic intermolecular potential between atoms, coupled with percolating solid fractal structures near T_g. The twinkling fractal spectrum F(ω) at T_g predicts the correct dynamic heterogeneity behavior via the spatio-temporal thermal fluctuation autocorrelation relaxation function C(t). This function behaves as C(t) ∼ t^−1/3 (short times), C(t) ∼ t^−4/3 (long times) and C(t) ∼ t⁻² (ω < ω_c), which were found to be in excellent agreement with published nanoscale AFM dielectric force fluctuation experiments on a glassy polymer near T_g. Using the Morse potential, the TFT predicts that T_g = 2D_o/9k, where D_o is the interatomic bonding energy ∼ 2–5 kcal/mol and is comparable to the heat of fusion ΔH_f. Because anharmonicity controls both the thermal expansion coefficient α_L and T_g, the TFT uniquely predicts that α_L×T_g ≈ 0.03, which is found to be universal for a broad range of glassy materials from Pyrex to polymers to glycerol. Below T_g, the glassy structure attains a frustrated nonequilibrium state by getting constrained on the fractal structure and the thermal expansion in the glass is reduced by the percolation threshold p_c as α_g ≈ p_cα_L. The change in heat capacity ΔC_p = C_pL–C_pg at T_g was found to be related to the change in dimensionality from D_f to 3 in the Debye approximation as the ratio C_pL/C_pg = 3/D_f, where D_f is the fractal dimension of the glass. For polymers, the TFT describes the molecular weight dependence of T_g, the role of crosslinks on T_g, the Flory-Fox rule of mixtures and the WLF relation for the time-temperature shift factor a_T, which are traditionally viewed in terms of Free-Volume theory. The TFT offers new insight into the behavior of nano-confined glassy materials and the dynamics of physical aging. It also predicts the relation between the melting point T_m and T_g as T_m/T_g = 1/[1−p_c] ≈ 2. The TFT is universal to all glass forming liquids. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2765–2778, 2008     

The thermodynamic functions of fullerene derivative (<Emphasis Type="Italic">t</Emphasis>-Bu)<Subscript>12</Subscript>C<Subscript>60</Subscript> over the temperature range from <Emphasis Type="Italic">T</Emphasis> → 0 to 420 K

The temperature dependence of heat capacity C _p ^o = f(T) of fullerene derivative (t-Bu)₁₂C₆₀ has been measured by a adiabatic vacuum calorimeter over the temperature range T = 6–350 K and by a differential scanning calorimeter over the temperature range T = 330–420 K for the first time. The low-temperature (T ≤ 50 K) dependence of the heat capacity was analyzed based on Debye’s the heat capacity theory of solids and its fractal variant. As a consequence, the conclusion about structure heterodynamicity is given. The experimental results have been used to calculate the standard thermodynamic functions C _p ^o (T), H ^o(T)−H ^o(0), S ^o(T) and G ^o(T) − H ^o(0) over the range from T → 0 to 420 K. The standard entropy of formation at 298.15 K of fullerene derivative under study was calculated. The temperature of decomposition onset of derivative was determined by differential scanning calorimetery and thermogravimetric analysis. The standard thermodynamic characteristics of (t-Bu)₁₂C₆₀ and C₆₀ fullerite were compared.     

Kristallstruktur,Schwingungsspektren und Normalkoordinatenanalyse von K2[IrCl5(NH3)]

Crystal Structure, Vibrational Spectra, and Normal Coordinate Analysis of K₂[IrCl₅(NH₃)] The X-ray structure determination of K₂[IrCl₅(NH₃)] (orthorhombic, space group Pnma, a = 13.426(4), b = 10.015(2), c = 6.8717(7) Å, Z = 4) revealed the C_s point symmetry of the complex anion [IrCl₅(NH₃)]^2? (Ir? Cl = 2.337–2.365, Ir? N = 2.067(10); N? H = 0.73–0.79 Å). Using the molecular parameters the IR and Raman spectra are assigned by normal coordinate analysis. The valence force constants are f_d(NH) = 5.88, f_d(IrN) = 2.66, f_d(IrCl) = 1.68 mdyn/Å.     

Thermodynamic properties of crystalline polymeric C60 phases in the temperature region from O → 0 to 340 E

The temperature dependences of the heat capacity C _p° = f(T) were studied in an adiabatic vacuum calorimeter for the orthorhombic, tetragonal, and rhombohedral polymeric C₆₀ phases in the 7—340 K temperature interval with an error of 0.2%. Comparative analysis of C _p° of these phases formed by stacking of one-dimensional and two types of two-dimensional polyfullerenes C₆₀, was performed, and their fractal dimensionalities D were determined for temperatures below 50 K. The thermodynamic functions of the crystalline polymeric C₆₀ phases were calculated in the temperature region from O 0 to 340 K: C _p°(T), H°(T) — H°(0), S°(T) — S°(0), and G°(T) — H°(0). Assuming that S°(0) = 0, the standard entropies of formation _f S° of these phases from graphite at T = 298.15 K and standard pressure were calculated. In addition, the entropies of transformation of the initial face-centered cubic phase of fullerite C₆₀ in the crystalline polymeric C₆₀ phases and entropies of their interconversions under the same conditions were estimated. The thermodynamic characteristics of the polymeric C₆₀ phases were reviewed.     

Thermodynamics of C70 fullerence in the 0–390 K temperature range

The temperature dependence of heat capacity of C₇₀ fullerene was studied by calorimetry in the range between 6 and 390 K. Phase transitions were established and their thermodynamic characteristics were determined. From the experimental data obtained, the thermodynamic functionsH ^o (T)-H ^o(0),S ^o(T),G ^o(T)-H ^o(0) for temperatures between 0 and 390 K were calculated. The results were used to calculate the standard values of Δ_f S ^o, Δ_f G ^o, and logK _f ^o for the formation of C₇₀ from graphite. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 647–650, April, 1998.     

Darstellung,Schwingungsspektren und Normalkoordinatenanalyse von Hexachlororhenat(V) sowie Kristallstruktur von [P(C6H5)4][ReCl6]

Preparation, Vibrational Spectra, and Normal Coordinate Analysis of Hexachlororhenate(V) and Crystal Structure of [P(C₆H₅)₄][ReCl₆] By oxidation of A₂[ReCl₆], A = [(n-C₄H₉)₄N]⁺, [P(C₆H₅)₄]⁺, with Cl₂ in dichloromethane/trifluoracetic acid A[ReCl₆] is formed. [P(C₆H₅)₄][ReCl₆] crystallizes with tetragonal symmetry, space group P4/n-C, a = 12.967(4), c = 7.6992(8) Å, Z = 2. The octahedral complexion [ReCl₆]^? is compressed (C_4v) with the bond lengths, axial Re? Cl1 = 2.28 and Re? Cl3 = 2.24 Å, equatorial Re? Cl2 = 2.31 Å. The infrared active antisymmetric Re? Cl stretching vibration is split into v′₃ = 346 an v″₃ = 326 cm^?1. The assignment of all IR and Raman modes is confirmed by a normal coordinate analysis. The different valence force constants, f_d(ReCl1) = 2.09, f_d(ReCl3) = 2.10, f_d(ReCl2) = 1.88 mdyn/ Å result from the distortion of the octahedron. On excitation with the Ar laser line 514.5 nm a resonance Raman spectrum is observed, showing 8 overtones of v′(A₁) = 382 cm^?1, from which the harmonic frequency ω₁ = 382.1 cm^?1, the anharmonicity constant X₁₁ = ?0.76 cm^?1, and the maximum bond dissociation energy of the [ReCl₆]^? ion to be 138 kcal/mol, are calculated. The vibrational fine structure of the intraconfigurational transitions in the near infrared has been resolved by measuring the absorption spectrum of [(n-C₄H₉)₄N][ReCl₆] at low temperature (10 K), resulting in the assignment of the following electronic origins: Γ₃(³T_1g) → Γ₄(³T_1g): 7 512, Γ₃(³T_1g) → Γ₁(³T_1g): 7 624 and Γ₃(³T_1g) → Γ₅(¹T_2g), Γ₃(¹E_g): 8 368 cm^?1.     

The thermodynamic properties of 2-ethylhexyl acrylate over the temperature range from <Emphasis Type="Italic">T</Emphasis> → 0 to 350 K

The temperature dependence of the heat capacity C _p ^o= f(T) 2 of 2-ethylhexyl acrylate was studied in an adiabatic vacuum calorimeter over the temperature range 6–350 K. Measurement errors were mainly of 0.2%. Glass formation and vitreous state parameters were determined. An isothermic shell calorimeter with a static bomb was used to measure the energy of combustion of 2-ethylhexyl acrylate. The experimental data were used to calculate the standard thermodynamic functions C _p ^o(T), H ^o(T)-H ^o(0), S ^o(T)-S ^o(0), and G ^o(T)-H ^o(0) of the compound in the vitreous and liquid states over the temperature range from T → 0 to 350 K, the standard enthalpies of combustion Δ_c H ^o, and the thermodynamic characteristics of formation Δ_f H ^o, Δ_f S ^o, and Δ_f G ^o at 298.15 K and p = 0.1 MPa.     

Kinetics of the reactions of C2H5, n‐C3H7, and n‐C4H9 radicals with Cl2 at the temperature range 190–360 K

The kinetics of the C₂H₅ + Cl₂, n‐C₃H₇ + Cl₂, and n‐C₄H₉ + Cl₂ reactions has been studied at temperatures between 190 and 360 K using laser photolysis/photoionization mass spectrometry. Decays of radical concentrations have been monitored in time‐resolved measurements to obtain reaction rate coefficients under pseudo‐first‐order conditions. The bimolecular rate coefficients of all three reactions are independent of the helium bath gas pressure within the experimental range (0.5–5 Torr) and are found to depend on the temperature as follows (ranges are given in parenthesis): k(C₂H₅ + Cl₂) = (1.45 ± 0.04) × 10^?11 (T/300 K)^{?1.73 ± 0.09} cm³ molecule^?1 s^?1 (190–359 K), k(n‐C₃H₇ + Cl₂) = (1.88 ± 0.06) × 10^?11 (T/300 K)^{?1.57 ± 0.14} cm³ molecule^?1 s^?1 (204–363 K), and k(n‐C₄H₉ + Cl₂) = (2.21 ± 0.07) × 10^?11 (T/300 K)^{?2.38 ± 0.14} cm³ molecule^?1 s^?1 (202–359 K), with the uncertainties given as one‐standard deviations. Estimated overall uncertainties in the measured bimolecular reaction rate coefficients are ±20%. Current results are generally in good agreement with previous experiments. However, one former measurement for the bimolecular rate coefficient of C₂H₅ + Cl₂ reaction, derived at 298 K using the very low pressure reactor method, is significantly lower than obtained in this work and in previous determinations. © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 614–619, 2007     

Thermodynamic characteristics of triphenylantimony bis(acetophenoneoximate)

The temperature dependence of heat capacity C _p ^° = f(T) of triphenylantimony bis(acetophenoneoximate) Ph₃Sb(ONCPhMe)₂ was measured for the first time in an adiabatic vacuum calorimeter in the range of 6.5–370 K and a differential scanning calorimeter in the range of 350–463 K. The temperature, enthalpy, and entropy of fusion were determined. Treatment of low-temperature (20 K ≤ T ≤ 50 K) heat capacity was performed on the basis of Debye’s theory of the heat capacity of solids and its multifractal model and, as a consequence, a conclusion was drawn on the type of structure topology. Standard thermodynamic functions C _p ^°(T), H°(T) — H°(0), S°(T), and G°(T) — H°(0) were calculated according to the experimental data obtained for the compound mentioned in the crystalline and liquid states for the range of T → 0–460 K. The standard entropy of the formation of crystalline Ph₃Sb(ONCPhMe)₂ was determined at T = 298.15 K.     

Kinetics of phenyl radical reactions with propane,n‐butane,n‐hexane,and n‐octane: Reactivity of C6H5 toward the secondary C?H bond of alkanes

The kinetics of C₆H₅ reactions with n‐C_nH_2n+2 (n = 3, 4, 6, 8) have been studied by the pulsed laser photolysis/mass spectrometric method using C₆H₅COCH₃ as the phenyl precursor at temperatures between 494 and 1051 K. The rate constants were determined by kinetic modeling of the absolute yields of C₆H₆ at each temperature. Another major product C₆H₅CH₃ formed by the recombination of C₆H₅ and CH₃ could also be quantitatively modeled using the known rate constant for the reaction. A weighted least‐squares analysis of the four sets of data gave k (C₃H₈) = (1.96 ± 0.15) × 10¹¹ exp[?(1938 ± 56)/T], and k (n‐C₄H₁₀) = (2.65 ± 0.23) × 10¹¹ exp[?(1950 ± 55)/T] k (n‐C₆H₁₄) = (4.56 ± 0.21) × 10¹¹ exp[?(1735 ± 55)/T], and k (n?C₈H₁₈) = (4.31 ± 0.39) × 10¹¹ exp[?(1415 ± 65)T] cm³ mol^?1 s^?1 for the temperature range studied. For the butane and hexane reactions, we have also applied the CRDS technique to extend our temperature range down to 297 K; the results obtained by the decay of C₆H₅ with CRDS agree fully with those determined by absolute product yield measurements with PLP/MS. Weighted least‐squares analyses of these two sets of data gave rise to k (n?C₄H₁₀) = (2.70 ± 0.15) × 10¹¹ exp[?(1880 ± 127)/T] and k (n?C₆H₁₄) = (4.81 ± 0.30) × 10¹¹ exp[?(1780 ± 133)/T] cm³ mol^?1 s^?1 for the temperature range 297‐‐1046 K. From the absolute rate constants for the two larger molecular reactions (C₆H₅ + n‐C₆H₁₄ and n‐C₈H₁₈), we derived the rate constant for H‐abstraction from a secondary C? H bond, k_s?CH = (4.19 ± 0.24) × 10¹⁰ exp[?(1770 ± 48)/T] cm³ mol^?1 s^?1. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 49–56, 2004     

Translational and rotational invariance requisites for density functional derivatives

Translational and rotational invariance of functionals lead to hierarchies of equations between successive derivatives. These hierarchies allow alternating series expansions of some density functionals in terms of functional derivatives and charge density. Translational and rotational invariance also give rise to integrodifferential equations that link derivatives of all orders. From the minimal properties of the kinetic energy functional T_s[ρ] and the functional F[ρ] = min_Ψ→ρ <Ψ|T + V_ee|Ψ>, it follows that $int dˆ3 r dˆ3 rˆprimef({bold r}) {delˆ2 T―s[rho]}over{delrho({bold r})delrho({bold rˆprime})}f({bold rˆprime}) geq 0hspace{1cm}hbox{and}hspace{1cm}int dˆ3 r dˆ3 rˆprimef({bold r}) {delˆ2 F[rho]}over{delrho({bold r})delrho({bold rˆprime})}f({bold rˆprime}) geq 0$ for all ∫ d³ r d³ f′ f(r) = 0. This property combined with constraints on functionals due to translational invariance lead to inequalities satisfied by first derivatives of selected density functionals. © 1997 John Wiley & Sons, Inc.     

Folded chain crystals as micro-phases

Summary A thermodynamic treatment of homo-polymer systems out of linear chains with folded chain crystals is developed outgoing from appropriate models for single component systems. An expansion of thermodynamics to multi-micro-phase systems the structure of which is partially or totaly frozen is indispensable. General properties of melt crystallized homopolymers with folded chain crystals can be recognized indeed when the thermodynamic formalisms developed are applied.

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Zusammenfassung Das Schmelzen in polymeren Einteilchensystemen mit Faltungskristallen einheitlicher Dicke kann thermodynamisch als Umwandlung 1. Ordnung in einer Richtung behandelt werden, wenn die Faltungslänge bis zur Umwandlungstemperatur konstant bleibt (Faltungslänge als innerer Zusatzparameter). Eine wesentliche begriffliche Erweiterung ist für eine phänomenologische Beschreibung mit den Mitteln der Thermodynamik unumgänglich, wenn eine Faltungskristallit-Dickenverteilung existiert, weil dann prinzipiell nur noch partielle Koexistenz bestimmter Fraktionen metastabiler autonomer Mikrophasen mit der Schmelze möglich ist. Partielles Aufschmelzen und Rektistallisation können so dann auch in Betracht genommen werden. Die entwickelten Konzeptionen bewähren sich in der Anwendung auf bekannte Experimente.

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Notation g ^c (y);g ^m (Y) molar Gibbs-free energy of a chain of a lengthy within an extended chain crystal and the melt rsp - g _o ^c ;g _o ^m molar free enthalpy of the unit in the crystal lattice and the melt rsp - g(y,y, f) molar Gibbs-function of an ideally folded chain crystal with the fold heighty _f - gco(y, y _ef,y _f) molar free enthalpy of the crystal corey _co - g ₀ ^ex ((y_ef) excess free enthalpy of the longitudinal layers of folded chain crystals - g ^f(y_ef,g _o ^ex ) molar free enthalpy of the longitudinal layers of the folded chain crystals - g ^tot molar free enthalpy of a chain of the lengthy within a folded chain crystal with longitudinal layers - h _o ^1c ,h _o ^m molar enthalpy of the chain unit within the crystal lattice and the melt rsp - h =h _o ^m -h _o ^c molar heat of fusion of the unit - C _p=C _p ^m -C _p ^c difference of the molar specific heat of a unit within the melt and within the chain crystal - h ^D molar defect enthalpy of local defects within the crystal lattice - h ^D molar defect enthalpy of the unit - s _o ^c ,s _o ^m molar entropy of the chain unit within the crystal lattice and the melt rsp - s _c ^m conformational entropy of a chain in the melt - s _gk conformational entropy of a chain of lengthy within a super-lattice as indicated in figure 5, - s molar entropy of fusion of the melt - s _n ^c nematic configurational entropy - T absolute temperature - T _M melting temperature of extended chain crystals of infinite size - T _M(y) melting temperature of extended chain crystals containing only chains of the lengthy - T _M (y, y _f) melting temperatureof folded chain crystals of the thicknessy _f composed of chains of the lengthy - T _M(y _f) melting temperature of folded chain crystals of the thicknessy _fy - _eh excess free enthalpy of the chain ends occupying crystallographic places - _ef excess free enthalpy of a single fold loop - z coordination number of the lattice - 7 Euler's constant - R Boltzmann's constant - y number of chain units - y _f height of lamelliform folded chain crystals - f=(y/y _f - 1) number of fold loops of a chain of a lengthy when being built into a folded chain crystal of the thicknessy _f - y _co thickness of the crystal core of the simplified twophase model - y _et average thickness of the surface layers of folded chain crystals - N _c number of crystallized units of a chain of the lengthy - x _c molar number of crystallized units of a chain of the lengthy - x _nc molar number of noncrystallized units - excess free enthalpy parameter - (y _f) thickness distribution of the fold heightsy _f With 15 figures and 2 tables     

Triplet Lifetime Determination of Molecules in the Gas Phase by T-T Energy Transfer

It has been demonstrated that the triplet lifetime of nonemitting molecules in the dilute vapor phase - even for complex triplet decays - can be accurately determined by means of time-resolved triplet-triplet (T-T) energy transfer to a strong emitter molecule. Besides the test molecules 1-butyne-3-one and benzaldehyde the lifetime of the vibrationally relaxed nonemitting T₁(nπ*) state of cycloheptanone, τ=63 ± 5 µs at ～?0.5 Torr, together with its energy transfer rate constant to biacetyl, k_ET=(1.80±0.08) x 10⁶ s^?1 Torr^?1, have been measured.