Atomic electron-pair distances and subshell radii in position and momentum space

For the 53 neutral atoms from He to Xe in their ground states, the average distances < u> _{n l , n ′ l ′} in position space and < v> _{n l , n ′ l ′} in momentum space between an electron in a subshell nl and another electron in a subshell n ^′ l ^′ are studied, where n and l are the principal and azimuthal quantum numbers of an atomic subshell, respectively. Analysis of 1700 subshell pairs shows that the electron-pair distances < u> _{n l , n ′ l ′} in position space have an empirical but very accurate linear correlation with a one-electron quantity U _{n l , n ′ l ′}≡L _r +S _r ²/(3L _r ), where L _r and S _r are the larger and smaller of subshell radii < r> _{n l} and < r> _{n ′ l ′}, respectively. The correlation coefficients are never smaller than 0.999 for the 66 different combinations of two subshells appearing in the 53 atoms. The same is also true in momentum space, and the electron-pair momentum distances < > _{n l , n ′ l ′} have an accurate linear correlation with a one-electron momentum quantity V _{n l , n ′ l ′}≡L _p +S _p ²/(3L _p ), where L _p and S _p are the larger and smaller of average subshell momenta < p> _{n l} and < p> _{n ′ l ′}, respectively. Trends in the proportionality constants between < u> _{n l , n ′ l ′} and U _{n l , n ′ l ′} and between < > _{n l , n ′ l ′} and V _{n l , n ′ l ′} are discussed based on a hydrogenic model for the subshell radial functions. Received: 8 April 1998 / Accepted: 6 July 1998 / Published online: 18 September 1998     

ORGANOSTANNOXANE MOTIFS IN CAGES AND SUPRAMOLECULAR ARCHITECTURES

The reactions of n-butyl stannonic acid with(PhO) ₂ P(O)H leads to the formation of a hexameric tin cage [{(n-BuSn) ₃ (PhO) ₃ O} ₂ {HPO ₃ } ₄ ].This reaction involves an in situ P─O bond cleavage and the generation of a [HPO ₃ ] ^2? ion. A direct reaction of six equivalents of n-BuSnO(OH) acid with six equivalents of C ₆ H ₅ OH and four equivalents of H ₃ PO ₃ also leads to the formation of same cage structure. A tetranuclear organooxotin cage[(PhCH ₂ ) ₂ Sn ₂ O(O ₂ P(OH)-t-Bu) ₄ ] ₂ has been assembled by debenzylation involving the reaction of (PhCH ₂ ) ₂ SnCl ₂ ,(PhCH ₂ ) ₂ SnO·H ₂ O or (PhCH ₂ ) ₃ SnCl with two equivalents of t-BuP(O)OH ₂ . A half-cage intermediate [(PhCH ₂ ) ₂ Sn ₂ O(O ₂ P(OH)-t-Bu) ₄ ] has been detected. New organotin cations of the type [n-Bu ₂ Sn(H ₂ O) ₄ ] ²⁺[2,5-Me ₂ -C ₆ H ₃ SO ₃ ]^? ₂ and {[n-Bu ₂ Sn(H ₂ O) ₃ LSn(H ₂ O) ₃ (n-Bu) ₂ ] ²⁺[1,5-(SO ₃ ) ₂ -C ₁₀ H ₆ ] ^2?} have been obtained in the reactions of n-Bu ₂ SnO or (n-Bu ₃ Sn) ₃ O with 2,5-dimethyl sulfonic acid and 1,5-naphthalene disulfonic acid respectively. These organotin cations form interesting supramolecular structures in the solid state as a result of O─H─···O hydrogen bonding.     

New Organic Derivatives of O,O′-(o-, m-, and p-Ditolyl)/Dibenzyldithiophosphates: Synthesis and Characterization

Reactions of (m- and p-ClC ₆ H ₄ NH ₂ ), (p-BrC ₆ H ₄ NO ₂ ), and (p-ClCOC ₆ H ₄ NO ₂ ) with sodium O,O′-ditolyl/dibenzylphosphorodithionates, (ArO) ₂ PS ₂ Na, (Ar = o?, m?, and p?CH ₃ C ₆ H ₄ or –C ₆ H ₅ CH ₂ ) in 1:1 molar ratio in refluxing toluene under anhydrous conditions resulted in the formation of the compounds (ArO) ₂ PS ₂ C ₆ H ₄ L and (ArO) ₂ PS ₂ COC ₆ H ₄ L (L = NH ₂ or NO ₂ ) in 87–94% yield. These viscous compounds were characterized by elemental analyses, molecular weight determination, and IR and NMR ( ¹ H, ¹³ C, and ³¹ P) spectroscopic studies, which revealed a monodentate mode of bonding of the dithiophosphate moiety with the carbon of the phenyl ring of the organic moiety leading to a P–S–C linkage.     

Relationships on the effect of water on glass transition temperature and young's modulus of nylon 6

The glass transition temperature T_g of nylon 6 decreases monotonically toward a finite value T_gl upon increase of the moisture content. The mechanism of this decrease entails the reversible replacement of intercaternary hydrogen bonds in the accessible regions of the polyamide. The limiting glass transition temperature T_gl is approached when the moisture content approaches W_l, which corresponds to the amount of water required for complete interaction with all accessible amide groups. Denoting with T_g0 the glass transition temperature of the dry polymer, the effect of water on T_g is represented by the equation, T_g = (ΔT_g)₀ exp{?[ln(ΔT_g)₀]W/_τW_l} + T_gl, where (ΔT_g)₀ = T_g0 ?T_gl, and τ = W(T_gl+1)/W_l. This equation appears to be generally applicable to hydrophilic polymers, since correspondingly calculated data are also in very good agreement with experimental data for polymers such as nylon 66, poly(vinyl alcohol), and polyN-vinylpyrrolidone. The effect of water of Young's modulus E of nylon 6 is represented by an analogous relationship, and the quantity In[(E?E_l)/(T_g?T_gl)] is a linear function of the moisture content.     

The hard-sphere model for linear and regular star polybutadienes

The dilute solution properties of linear, 18-arm, and 270-arm star polybutadienes have been studied in a theta solvent and in a good solvent. Values of the radius of gyration R_G, the second virial coefficient A₂, the intrinsic viscosity [η], and the diffusion coefficient D₀ have been measured for each polymer. The ratios R_T/R_G, R_V/R_G, and R_H/R_G for each type of polymer are used to compare the four dilute solution properties. R_T is termed the “thermodynamic radius.” It is the radius of the hard sphere with the same excluded volume as the polymer coil. R_T is calculated from A₂ by R_T = (3A₂M₂/16ηN_A)^1/3. R_V and R_H are equivalent hard spheres defined for the intrinsic viscosity and translational diffusion coefficient, respectively. R_T/R_G, R_V/R_G, and R_H/R_G increase from about 0.7 for linear polymer coils as the number of arms in the star increases. Values of the ratios for the 18-arm stars are less than the value for the hard-sphere, but the values of the ratios of the 270-arm stars are equal to the hard-sphere limit within experimental error.     

Molecular weight-dependence of free volume in polystyrene studied by positron annihilation measurements

Positron annihilation lifetime measurements are reported for four monodisperse polystyrenes with molar mass M = 4,000, 9,200, 25,000, and 400,000. The temperature dependences of orthopositronium (o-Ps) lifetime (τ₃) and intensity (I₃) were measured from 5°C to T_g + 30°C for each sample. From these data, the free volume hole size, 〈v_f(τ₃)〉, and fractional free volume h_ps=CI₃〈v_f(τ₃)〉 were calculated. The temperature dependences of τ₃, 〈v_f(τ₃)〉 and h_ps show a discrete change in slope at an effective glass transition temperature, T_g,ps, which is measurably below the conventional bulk T_g. This suggests that τ₃ is sensitive to large holes which retain their liquid-like mobility in the glassy state. Good agreement was found for T > h_g,ps between h_ps and the theoretical free volume fraction h_th deduced from experimental P-V-T data for polystyrene using the statistical mechanical theory of Simha and Somcynsky. Below T_g,ps, deviations between h_ps and h_th are observed, h_ps falling increasingly below h_th as temperature decreases. Whereas h_ps and h_th depend strongly on M in the melt, each essentially independent of M in the glass. A free volume quantity, computed from the bulk volume, which is in good numerical agreement with the Simha-Somcynsky h-function in the melt, gives improved agreement with h_ps in the glassy state. © 1994 John Wiley & Sons, Inc.     

A variation principle for energy differences between states of two different Hamiltonians

A modification of a variation principle due to Delves, is derived which permits the direct calculation of energy differences between states of two different Hamiltonians: [Δ ??] = 〈X₀| ??_x – W_x|X₁〉 – 〈Y₀|??_y – W_y|y₁〉 + 〈X₀| Δ ??|Y₀〉 · 〈X₀| Y₀〉^?1. Δ ?? = ??_y – ??_x, |X₀〉 and |Y₀〉 are the wave functions for the X and Y states and |X₁〉 and |Y₁〉 are functions defined in the text. The principle is applied to a few simple examples.     

STEREOELECTRONIC PROPERTIES OF PHOTOSYNTHETIC AND RELATED SYSTEMS — V. AB INITIO CONFIGURATION INTERACTION CALCULATIONS ON THE GROUND AND LOWER EXCITED SINGLET AND TRIPLET STATES OF ETHYL CHLOROPHYLLIDE a AND ETHYL PHEOPHORBIDE a

Abstract— Ab initio configuration interaction wavefunctions and energies are reported for the ground state and many low-lying excited singlet and triplet states of ethyl pheophorbide a (Et-Pheo a) and ethyl chlorophyllide a (Et-Chl a), and are employed in an analysis of the electronic absorption spectra of these systems. In both molecules the visible spectrum is found to consist of transitions to the two lowest-lying ¹(π, π*) states, S₁ and S₂. The configurational compositions of S₁ and S₂ in both molecules are similar, and are described qualitatively in terms of a four-orbital model. The S₁← S₀ transition in each case is predicted to be intense, and is largely in-plane y-polarized, while the S₂← S₀ transition is predicted to be extremely weak and in-plane polarized. The orientation of the S₂← S₀ transition dipole is not conclusively established in the present calculations. The Soret band in both molecules is composed of transitions to no less than ten states (S_3-S₁₂ in Et-Chl a and S₃-S₇S₉-S₁₂. and S₁₄ in Et-Pheo a), which exhibit primarily (π, π*) character. The configurational compositions of these states are generally a complex mixture of excitations from both occupied macrocyclic π molecular orbitals and occupied orbitals with electron density in the cyclopen-tanone ring and the carbomethoxy chain. No clear correspondences are evident between respective Soret states of the two systems. Transitions to these states are generally intense and display a variety of in-plane polarizations. Two additional Soret states of Et-Pheo a, S₈ and S₁₃, exhibit primarily (n. π*) character. S₈ is characterized by excitations from u and non-bonding regions of the carbomethoxy chain, while S₁₃ is described by n →π* excitations involving the nitrogen atom of ring II. No corresponding (n, π*) states were found for Et-Chl a. In both molecules the lowest two triplet states, T₁ and T₂, are found to lie lower in energy than S₁. while T, and S₁ are approximately degenerate. The configurational compositions of T₁-T₄ of both molecules are nearly identical, and may be described by a four-orbital model. However, the compositions of T₁-T₄ differ sharply from those of S₁ and S₂. A number of higher-lying ³(π, π*) states of both molecules (T₅-T₁₃ in Et-Chi a and T₈-T₉, T₁₁-T₁₃ in Et-Pheo a) are found to have energies similar to the singlet Soret states, relative to S₀. They are characterized by a complex mixture of configurations which do not include significant contributions involving the four-orbital model. In addition, two ³(n, π*) states of Et-Pheo a, T₁₀ and T₁₄, are found, which are somewhat analogous to S₈ and S₁₃. Additional data presented include the charge distributions and molecular dipole moments of the S₀. S₁, and T₁ states of both molecules, as well as energies and oscillator strengths of computed S_n←S₁ and T_n←₁ transitions.     

An optimized orbital transformation able to reproduce partially prefixed overlaps

Given a function space spanned by a basis {?_i}, we are interested in finding another basis {g_i} for which the overlaps (g_i | g_i) assume arbitrarily prefixed values in a subset ?? of the full set of the pairs of indices (i, j). The other overlaps are let free. We show how it is possible to perform this linear transformation ?_i → g_i minimizing the “distortion” J = Σ_i(g_i – ?_i | g_i – ?_i).     

Oxidation and Reduction Processes During NO x Removal with Corona-Induced Nonthermal Plasma

In this paper, the NO-to-NO ₂ conversion in various gaseous mixtures is experimentally investigated. Streamer coronas are produced with a dc-superimposed high-frequency ac power supply (10–60 kHz). According to NO _x removal experiments in N ₂ +NO _x and N ₂ +O ₂ +NO _x gaseous mixtures, it is supposed that the reverse reaction NO ₂ +ONO+O ₂ may not only limit NO ₂ production in N ₂ +NO _x mixtures, but also increase the energy cost for NO removal. Oxygen could significantly suppress reduction reactions and enhance oxidation processes. The reduction reactions, such as N+NON ₂ +O, induce negligible NO removal provided the O ₂ concentration is larger than 3.6%. With adding H ₂ O into the reactor, the produced NO ₂ per unit removed NO can be significantly reduced due to NO ₂ oxidation. NH ₃ injection could also significantly decrease the produced NO ₂ via NH and NH ₂ - related reduction reactions. Almost 100% of NO ₂ can be removed in gaseous mixtures of N ₂ +O ₂ +H ₂ O+NO ₂ with negligible NO production.     

Variationen modulo 4–4+, 4+3–3+4–, 4–5+, 5–4+4–5+4–4+ bei Seltenerdcarbidhalogeniden

The new compounds Pr₈(C₂)₄Cl₅ (1), Pr₁₄(C₂)₇Cl₉ (2), Pr₂₂(C₂)₁₁Cl₁₄ (3), Ce₂(C₂)Cl (4), La₂(C₂)Br (5), Ce₂(C₂)Br (6), Pr₂(C₂)Br (7), Ce₁₈(C₂)₉Cl₁₁ (8), and Ce₂₆(C₂)₁₃Cl₁₆ (9) were prepared by heating mixtures of LnX₃, Ln and carbon or in an alternatively way LnX₃, and “Ln₂C_3–x” in appropriate amounts for several days between 750 and 1200 °C. The crystal structures were investigated by X‐ray powder analysis (5–7) and/or single crystal diffraction (1–4, 8, 9). Pr₈(C₂)₄Cl₅ crystallizes in space group P2₁/c with the lattice parameters a = 7.6169(12), b = 16.689(2), c = 6.7688(2) Å, β = 103.94(1) °, Pr₁₄(C₂)₇Cl₉ in Pc with a = 7.6134(15), b = 29.432(6), c = 6.7705(14) Å, β = 104.00(3) °, Pr₂₂(C₂)₁₁Cl₁₄ in P2₁/c with a = 7.612(2), b = 46.127(9), c = 6.761(1) Å, β = 103.92(3) °, Ce₂(C₂)₂Cl in C2/c with a = 14.573(3), b = 4.129(1), c = 6.696(1) Å, β = 101.37(3) °, La₂(C₂)₂Br in C2/c with a = 15.313(5), b = 4.193(2), c = 6.842(2) Å, β = 100.53(3) °, Ce₂(C₂)₂Br in C2/c with a = 15.120(3), b = 4.179(1), c = 6.743(2) Å, β = 101.09(3) °, Pr₂(C₂)₂Br in C2/c with a = 15.054(5), b = 4.139(1), c = 6.713(3) Å, β = 101.08(3) °, Ce₁₈(C₂)₉Cl₁₁ in P$\bar{1}$ with a = 6.7705(14), b = 7.6573(15), c = 18.980(4) Å,α = 88.90(3) °, β = 80.32(3) °, γ = 76.09(3) °, and Ce₂₆(C₂)₁₃Cl₁₆ in P2₁/c with a = 7.6644(15), b = 54.249(11), c = 6.7956(14) Å, β = 103.98(3) ° The crystal structures are composed of Ln octahedra centered by C₂ dumbbells. Such Ln₆(C₂)‐octahedra are condensed into chains which are joined into undulated sheets. In compounds 1–4 three and four up and down inclined ribbons alternate (4₊4_–, 4₊3_–3₊4_–, 4₊4_–3₊4_–4₊3_–), in compounds 8 and 9 four and five (4₊5_–, 5₊4_–4₊5_–4₊4_–), and in compounds 4–7 one, one ribbons (1₊1_–) are present. The Ln‐(C₂)‐Ln layers are separated by monolayers of X atoms.     

Farbe und Konstitution bei anorganischen Feststoffen, 14. Mitt.: Die Lichtabsorption des zweiwertigen Kupfers in oxidischen Wirtsgittern

Zusammenfassung Um die Beziehungen zwischen der Lichtabsorption des zweiwertigen Kupfers nach isomorphem Einbau in ein oxidisches Wirtsgitter und dessen Konstitution aufzufinden, wurde Cu²⁺ in oktaedrischer (Cu _x Mg _1–x TiO₃, Cu _x Cd _1–x TiO₃, Cu _x Mg _1–x CaSiO₄, Cu _x Mg _1–x CaGeO₄, Cu _x Mg _2–x SiO₄, Cu _x Mg _2–x GeO₄) und tetraedrischer Koordination (Cu _x Zn_2–x SiO₄, Cu _x Mg _1–x Cr₂O₄) spektralphotometrisch untersucht. Die Farbkurven besitzen mindestens 2 Absorptionsbanden (Kristallfeldbanden) im längerwelligen und eine oft gut ausgeprägte Elektronenübergangsbande (charge transfer) im kürzerwelligen Spektralbereich. In einigen Fällen ist noch eine zweite Elektronenübergangsbande als Schulter zu erkennen. Es wurden auch Cu-haltige 2,3- und 2,4-Spinelle spektralphotometrisch untersucht (Cu _x Mg _1–x Al₂O₄, Cu _x Mg _1–x Ga₂O₄, Cu _x Cd _y Zn _1–x–y Al₂O₄, Cu _x Mg _2–x SnO₄, Cu _x Mg _2–x TiO₄, Cu _x Zn _1–x MgTiO₄, Cu _x Mg _1–x Cd _y TiO₄). Es zeigte sich, daß Cu²⁺ immer auf Tetraeder- und Oktaederlücken verteilt ist. Eine Aufweitung des Wirtsgitters durch isomorphen Einbau größerer Kationen bewirkt nicht immer eine IR-Verschiebung der Banden, sondern in einigen Fällen (Spinellphasen) auch eine UV-Verschiebung. Eine Sonderstellung nimmt das ägyptisch-Blau CuCaSi₄O₁₀ ein, da hier das Cu²⁺ von 4 O_2– in planarer Anordnung umgeben ist. Die Farbkurve weist 3 Maxima auf im Einklang mit der Kristallfeldtheorie.

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In order to find out relations between the lightabsorption of bivalent copper isomorphously incorporated into an oxidic host lattice and the constitution of this lattice, the spectrum of Cu²⁺ has been investigated in octahedral (Cu _x Mg_1–x TiO₃, Cu _x Cd _1–x TiO₃, Cu _x Mg _1–x CaSiO₄, Cu _x Mg _1–x CaGeO₄, Cu _x Mg _2–x SiO₄, Cu _x Mg _2–x GeO₄) and tetrahedral coordination (Cu _x Zn _2–x SiO₄, Cu _x Mg _1–x Cr₂O₄). The colour curves show at least 2 absorption bands within the region of longer wave length and a charge transfer band often well developed in the range of shorter wavelength. In some cases also a second charge transfer band becomes conspicuous as a shoulder. Copper containing 2,3- and 2,4-spinels have been also investigated (Cu _x Mg _1–x Al₂O₄, Cu _x Mg _1–x Ga₂O₄, Cu _x Cd _y Zn _1–x–y Al₂O₄, Cu _x Mg _2–x SnO₄, Cu _x Mg _2–x TiO₄, Cu _x Zn _1–x MgTiO₄, Cu _x Mg _1–x Cd _y Zn _1–y TiO₄). From the colour curve one can infer that Cu²⁺ occupies in the spinels always tetrahedral as well as octahedral interstices. A widening of the lattice does not effect always a shifting of the absorption bands towards IR but in some cases (spinel phases) also the inverse shifting will occur. An exceptional case represents the egyptian blue CuCaSi₄O₁₀ since in this lattice the Cu₂₊ are surrounded by four O^2– in a coplanar arrangement. The colour curve shows three absorption bands in agreement with the crystal field theory.

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Mit 20 Abbildungen     

Study on the reactions of the dinitrogen complexestrans-[M(N2)2(Ph 2PCH2CH2PPh 2)2] (M=Mo or W) with ethyldiazoacetate: Formation of an Azo compound and of a phosphazene species

Complextrans-[Mo(N₂)₂(dppe)₂] (dppe=Ph ₂PCH₂CH₂PPh ₂) reacts with NN=CHCOOEt in benzene solution to afford benzene-azomethane,Ph-N=N-CH₃, as the main organic product. However, the phosphazene speciesPh ₂P(N₂CHCOOEt)(CH₂CH₂)P(N₂CHCOOEt)Ph ₂ is formed by irradiating aTHF solution oftrans-[W(N₂)₂(dppe)₂] in the presence of ethyldiazoacetate; in moist solution, the phosphazene bonds undergo a partial hydrolysis, and the phosphonium species [Ph ₂P(NHNCHCOOEt)(CH₂CH₂)P(NHNCHCOOEt)Ph ₂]²⁺ appears to be formed.

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Untersuchungen zu den Reaktionen der Distickstoff-Komplexetrans-[M(N₂)₂(Ph ₂PCH₂CH₂PPh ₂)₂] (M=Mo oder W) mit Ethyldiazoacetat: Die Bildung einer Azoverbindung und eines Phosphazens

Zusammenfassung Die Komplexetrans-[Mo(N₂)₂(dppe)₂] (dppe=Ph ₂PCH₂CH₂PPh ₂) reagieren mit NN=CHCOOEt in benzolischer Lösung zuPh-N=N-CH₃ als organischem Hauptprodukt. Andererseits wird bei der Bestrahlung vontrans-[W(N₂)₂(dppe)₂] inTHF-Lösung in der Gegenwart von Ethyldiazoacetat das PhosphazenPh ₂P(N₂CHCOOEt)(CH₂CH₂)P(N₂CHCOOEt)Ph ₂ gebildet; in feuchter Lösung erleidet die Phosphazen-Bindung eine teilweise Hydrolyse und die Phosphonium-Spezies [Ph ₂P(NHNCHCOOEt)(CH₂CH₂)P(NHNCHCOOEt)Ph ₂]²⁺ scheint gebildet zu werden.

     

Polyfluorophenylamino Germanes and Their Titanium (IV) Chloride Adducts

Disproportionation reactions between (CF ₃ CH ₂ O) ₃ GeNHC ₆ H _{5 ? n} F _n and TiCl ₄ in petroleum ether (40?60°C) at 0° to ?10°C give (CF ₃ CH ₂ O) ₂ Ge(NHC ₆ H _{5 ? n} F _n ) ₂ ^.2TiCl ₄ and (CF ₃ CH ₂ O)Ge(NHC ₆ H _{5 ? n} F _n ) ₃ ^. 2TiCl ₄ adducts. However, complete disproportionation of (CF ₃ CH ₂ O) ₃ Ge(NHC ₆ H _{5 ? n} F _n ) (n = 1,2) occurs at ?55 to ?60°C to give Ge(NHC ₆ H _{5 ? n} F _n ) ₄ ^.3TiCl ₄ . These complexes give double adducts on reactions with CH ₃ NO ₂ and CH ₃ CN. All the products are characterized by elemental analyses and IR, ¹ H, and ¹⁹ F NMR spectroscopy. A comparative disproportionation of the germanamines and analogous silanamines is discussed.     

Platinum Indolylphosphine Fluorido and Polyfluorido Complexes: An Interplay between Cyclometallation,Fluoride Migration,and Hydrogen Bonding

The reaction of [PtCl₂(COD)] (COD=1,5-cyclooctadiene) with diisopropyl-2-(3-methyl)indolylphosphine (iPr₂P(C₉H₈N)) led to the formation of the platinum(ii ) chlorido complexes, cis-[PtCl₂{iPr₂P(C₉H₈N)}₂] ( 1 ) and trans-[PtCl₂{iPr₂P(C₉H₈N)}₂] ( 2 ). The cis-complex 1 reacted with NEt₃ yielding the complex cis-[PtCl{κ²-(P,N)-iPr₂P(C₉H₇N)}{iPr₂P(C₉H₈N)}] ( 3 ) bearing a cyclometalated κ²-(P,N)-phosphine ligand, while the isomer 2 with a trans-configuration did not show any reactivity towards NEt₃. Treatment of 1 or 3 with (CH₃)₄NF (TMAF) resulted in the formation of the twofold cyclometalated complex cis-[Pt{κ²-(P,N)-iPr₂P(C₉H₇N)}₂] ( 4 ). The molecular structures of the complexes 1–4 were determined by single-crystal X-ray diffraction. The fluorido complex cis-[PtF{κ²-(P,N)-iPr₂P(C₉H₇N)}{iPr₂P(C₉H₈N)}] ⋅ (HF)₄ ( 5 ⋅ (HF)₄) was formed when complex 4 was treated with different hydrogen fluoride sources. The Pt(ii ) fluorido complex 5 ⋅ (HF)₄ exhibits intramolecular hydrogen bonding in its outer coordination sphere between the fluorido ligand and the NH group of the 3-methylindolyl moiety. In contrast to its chlorido analogue 3 , complex 5 ⋅ (HF)₄ reacted with CO or the ynamide 1-(2-phenylethynyl)-2-pyrrolidinone to yield the complexes trans-[Pt(CO){κ²-(P,C)-iPr₂P(C₉H₇NCO)}{iPr₂P(C₉H₈N)}][F(HF)₄] ( 7 ) and a complex, which we suggest to be cis-[Pt{C=C(Ph)OCN(C₃H₆)}{κ²-(P,N)-iPr₂P(C₉H₇N)}{iPr₂P(C₉H₈N)}][F(HF)₄] ( 9 ), respectively. The structure of 9 was assigned on the basis of DFT calculations as well as NMR and IR data. Hydrogen bonding of HF and NH to fluoride was proven to be crucial for the existence of 7 and 9 .     

Estimation of the lattice heat capacity of rare-earth compounds

On the basis of the experimental data reported in literature, the contributions of cation mass (m) and molar volume (V) to lattice heat capacity (C) were analyzed. The volumetric-mass formula, C_x=(l —f)·C₁+f·C₂+C_m·(m_x — m_x′), was presented for estimating the heat capacities of rare-earth compounds. In the formula C₁ and C₂ represent the lattice heat capacities of two reference substances respectively, f = V_x—V₁/V₂—V₁ and C_m represents the lattice heat capacity variation with the variation 1 g of cation mass. The equation relating the C_m with temperatures was derived as follows: C_m = 0.084 e ?0.0074T ?0.27 e ?0.045T, and m_x and m_x′ (= (1 - f) m₁₊f m₂) represent the practical and “assumed” cation masses of the substance in question respectively.     

Free‐volume variation in polyethylenes of different crystallinities: Positron lifetime,density, and X‐ray studies

High‐quality positron lifetime measurements (70 million total counts) are reported for polyethylenes (PEs) of different crystallinities (X_c = 3–82%). The specific volumes of the crystalline and amorphous phases (V_c and V_a, respectively) were estimated from density and wide‐angle X‐ray scattering (WAXS) experiments. Some samples (those with low values of X_c) were branched PEs, and those with high values of X_c were linear PEs for which X_c was varied with changes in the crystallization temperature. Both V_c and V_a increase with decreasing X_c in the range 0% ≤ X_c ≤ 56% (the branched PEs) but are constant for X_c ≥ 56% (the linear PEs). The lifetime spectra were analyzed with the MELT and LIFSPECFIT routines. Artifacts that can appear in the spectrum analysis were checked via an analysis of computer‐generated spectra. Four lifetime components appeared in all of the PEs; the two long‐lived ones are attributed to pick‐off annihilation of ortho‐positronium (o‐Ps) in crystalline regions (τ₃) and in holes of the amorphous phase (τ₄). With increasing X_c, τ₃ decreases from about 1.2 to 1 ns, τ₄ decreases from 3.0 to 2.5 ns, and the intensity I₄ decreases from 29 to 0%. An increase in I₃ from 6 to 12% was observed. A comparison with simulations shows that the true I₃ value approaches 0 for X_c → 0%. The decrease in I₄ is weaker than the increase in X_c; this leads to the conclusion that the apparent specific o‐Ps yield in the amorphous phase I₄^Xc increases with X_c. Possible reasons for this surprising results are discussed. The fractional free hole volume [h = (V_a ? V_occ)/V_a, where V_occ is the crystalline occupied volume] was estimated from density and WAXS results. Between X_c = 0 and 56%, h decreases from 0.151 to 0.090, but it does not change further above X_c = 56%. The mean size (v) of the local free volumes (holes) estimated from τ₄ decreases from 200 to 150 ų. The number density of holes (N_h) calculated from these values (N_h = h/v) also decreases from 0.8 to 0.6 nm^?3 in the range 0% ≤ X_c ≤ 56%. The values of V_a, V_c, h, and N_h increase with an increasing degree of branching but do not vary for linear PEs. The possible influence of a crystalline–amorphous interfacial phase (three‐phase model) on the observed lifetime parameters is also discussed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 65–81, 2002     

Relationship between kinetic chain length and radical polymerization rate

In the copolymerization of monomers M₁ and M₂ which form polymer radicals of chain length n of N¹_n with electron on a M₁ type and N²_n with one on a M₂ type, it is assumed that the specific rates of termination between N¹_n and N¹_n and N¹_s, N¹_n and N²_s, and N²_n and N²_s are k_α(ns)^?a, k_β(ns)^?a, and k_γ(ns)^?a, respectively, where k_α, k_β, and k_γ are the rate constants of reaction between segment radicals in the respective termination, and a is constant. The relation between kinetic chain length n? and polymerization rate R_p is derived as: 1/n? = 1/n?₀ + const. (R_p)^A(a), where n?₀ is the kinetic chain length of the polymer formed by transfer and A (a) is unity (predominance of transfer) and 1/(1–2a) (no transfer). In the copolymerization between methyl methacrylate (M₁) and styrene (M₂) at 60°C, when R_p → 0, k_r12/k₁₂ + k_r21/k₂₁ = 5.9× 10^?5 is obtained, where k_r12 and k_r21 are the rate constants of transfer of N¹ to M₂ and N² to M₁, and k₁₂ and k₂₁ are the rate constants of propagation of N¹ to M₂ and N² to M₁. In the absence of transfer, the a value is found to be 0.065 ± 0.008, from the relation between n? and R_p, regardless of the monomer composition. Such a value is also estimated by setting b = 0.72 in a = 0.153 (2b–1), where b is the constant in the Mark-Houwink equation. Further, the value of k_β is found to be 1.18 × 10⁹l./mole-sec, which is comparable with the diffusion-controlled rate of reaction between small molecules. The rate of reaction between segment radicals is fivefold larger than the polymer-polymer termination when transfer predominates.     

Mechanical properties of natural rubber vulcanizates in finite deformation

Mechanical properties of four kinds of natural rubber vulcanizates differing in vulcanization conditions, and consequently in degree of crosslinking (having values of the Mooney-Rivlin constant C₁ ranging from 0.68 to 1.98) were observed under orthogonal biaxial stretching in a range of strain invariants I_i from 3.4 to 9.0 (extension ratios λ_i from 0.7 to 3.0). The results obtained were analyzed by two methods. One method employed the Valanis-Landel postulate that the strain-energy function W(λ₁, λ₂, λ₃) is a separable symmetric function of the principal extension ratios, i.e., W(λ₁,λ₂,λ₃) = w(λ₁) + w(λ₂) + w(λ₃); the other utilized the contour plots of ?W(I₁, I₂)/?I₁ and ?W(I₁, I₂)/?I₂ surface within the (I₁, I₂) domain. The postulate for W was examined in detail with good agreement with experimental results. The dependences of ?W(I₁, I₂)/?I₁ and ?W(I₁, I₂)/?I₂ surfaces on the degree of crosslinking and temperature were further investigated, with the following conclusions. The surfaces have fairly steep slopes for the region of relatively small deformation (i.e., I₁ < 5) and become flat with increasing I_i for all the test specimens. The slope becomes less steep with decreasing degree of crosslinking. The values of ?W/?I₁ increase linearly and the ?W(I₁,I₂)/?I₂ surface becomes flat, both with increasing temperature: i.e., the temperature dependence of ?W/?I₁ further depends on I_i. The ?W(I₁,I₂)/?I₂ surface has a maximum near 40°C.