The size distribution for theA g RB f−g Model of polymerization

This paper gives the equilibrium distribution of polymer sizes for Flory'sA _g RB _f–g model of polymerization. In this model, the polymers are composed of structural units withg functional groups of the typeA and (f-g) functional groups of the typeB. Reaction is subject to three conditions: (1) Functional groups of the typeA react only with those of typeB, and vice versa. (2) Intramolecular reactions do not occur [and therefore only branched-chain (noncyclic) polymers and formed]. (3) Subject to conditions (1) and (2), all functional groups are equally reactive. The derivation employs Stockmayer's statistical mechanical method (first used on Flory'sRA _f model), coupled with a recursion giving the number of distinct polymers which may be assembled fromk units of theA _g RB _f–g type. We also give distributions for a limiting case of theA _g RB _f–g model, the so-calledA _g RB model. This paper completes the solution of the Smoluchowski coagulation equation (monodisperse case) for the kernelsa _ij =A + B(i +j)+ Cij. The proof will be given in another publication.     

Kinetics of reversible polymerization

This paper extends the kinetic theory of irreversible polymerization (Smoluchowski's equation) by including fragmentation effects in such a way, that the most probable (equilibrium) size distribution from the classical polymerization theories is contained in our theory as the stationary distribution. The time-dependent cluster size distributionc _k (a(t)) in Flory's polymerization modelsRA _f andA _f RB _g , expressed in terms of the extent of reaction, has the same canonical form as in equilibrium, and the time dependence of(t) is determined from a macroscopic rate equation. We show that a gelation transition may or may not occur, depending on the value of the fragmentation strength, and, in case a phase transition takes place, we give Flory- and Stockmayer-type postgel distributions.Inspec numbers: 0550, 6460, 8235, 6475.     

Polymers and random graphs: Asymptotic equivalence to branching processes

In 1974, Falk and Thomas did a computer simulation of Flory's Equireactive RA _f Polymer model, rings forbidden and rings allowed. Asymptotically, the Rings Forbidden model tended to Stockmayer's RA _f distribution (in which the sol distribution sticks after gelation), while the Rings Allowed model tended to the Flory version of the RA _f distribution. In 1965, Whittle introduced the Tree and Pseudomultigraph models. We show that these random graphs generalize the Falk and Thomas models by incorporating first-shell substitution effects. Moreover, asymptotically the Tree model displays postgelation sticking. Hence this phenomenon results from the absence of rings and occurs independently of equireactivity. We also show that the Pseudomultigraph model is asymptotically identical to the Branching Process model introduced by Gordon in 1962. This provides a possible basis for the Branching Process model in standard statistical mechanics.     

LARGE-SCALE PATHOLOGY OF UNIVERSES WITH VII0×VIII ISOMETRIES

The goal of this paper is to show somewhat unexpected globally pathologic properties in universes described by a class of static planary symmetric exact solutions with G ₆-group of motion. In order to achieve this aim, the Killing vectors, the null geodesics and the Penrose diagrams corresponding to different expressions of g ₄₄=–e ^2f(z), with f(z) solutions of Einstein's equations, have been employed. Finally, woking in a particular gauge, we focus on the behaviour of the radiating electromagnetic modes and derive the observable components of E and B and the expressions of the essential component of the Umov-Poynting vector.     

Efficient heteronuclear dipolar decoupling in solid-state NMR using frequency-swept SPINAL sequences

Aiming to improve heteronuclear spin decoupling efficiency in NMR spectroscopy of solids and liquid crystals, we have modified the original Small Phase Incremental ALteration (SPINAL) sequence by incorporating a frequency sweep into it. For the resulting sequence, termed SW_f-SPINAL, the decoupling performance of a large number of sweep variants was explored by both numerical simulations and NMR experiments. It is found that introducing a frequency sweep generally increases both the ‘on-resonance’ decoupling performance and the robustness towards parameter offsets compared to the original SPINAL sequence. This validates the concept of extending the range of efficient decoupling by introducing frequency sweeps, which was recently suggested in the context of the frequency-swept SW_f-TPPM method. The sequence found to be best performing among the SW_f-SPINAL variants consists of fully swept 16 pulse pairs and is designated (32)-SPINAL-32. Its good decoupling performance for rigid spin systems is confirmed by numerical simulations and also experimentally, by evaluating the CH₂ resonance of a powder sample of l-tyrosine under MAS. For moderate MAS frequencies, the new sequence matches the decoupling achieved with SW_f-TPPM, and outperforms all other tested sequences, including TPPM and SPINAL-64. (32)-SPINAL-32 also shows excellent decoupling characteristics for liquid crystalline systems, as exemplified by experiments on the 5CB liquid crystal.     

NOR gate response in a double quantum ring: An exact result

NOR gate response in a double quantum ring, where each ring is threaded by a magnetic flux , is investigated. The double quantum ring is sandwiched symmetrically between two semi-infinite one-dimensional metallic electrodes, and two gate voltages, namely, V_a and V_b, are applied, respectively, in lower arms of the two rings those are treated as the two inputs of the NOR gate. A simple tight-binding model is used to describe the system, and all the calculations are done through the Green’s function formalism. Here we calculate exactly the conductance–energy and current–voltage characteristics as functions of the ring-to-electrode coupling strengths, magnetic flux and gate voltages. Our numerical study predicts that, for a typical value of the magnetic flux =₀/2 (₀=ch/e, the elementary flux-quantum), a high output current (1) (in the logical sense) appears if both the inputs to the gate are low (0), while if one or both are high (1), a low output current (0) results. It clearly demonstrates the NOR gate behavior, and this aspect may be utilized in designing an electronic logic gate.     

Unusual Pathways of Triplet State Dynamic Relaxation in Meso-Aryl-Substituted Porphyrins and Their Chemical Dimers at 295 K

It was found that mono- and di-meso-phenyl substitution in octaethylporphyrins (OEP)and their chemical dimers with the phenyl ring as a spacer manifests itself in the dramatical shortening of T₁ state lifetimes at 295 K (from 1.5 ms down to 2–5 s in degassed toluene solutions). On the other hand, this substitution does not influence spectral-kinetic parameters of S₀ and S₁ states. The enhancement of the T₁ state non-radiative deactivation is explained by torsional librations of the phenyl ring around a single C-C bond in sterically encumbered OEP molecules leading to non-planar dynamic distorted conformations in the excited T₁ states. For these compounds with electron-accepting NO₂-groups in the meso-phenyl ring the strong non-radiative deactivation of S₁ and T₁ states (by 2–3 orders of magnitude) is observed upon the displacement of NO₂-group from para-to ortho-position of the phenyl ring. The S₁ state quenching is caused by the direct intramolecular electron transfer to low-lying CT state of the radical ion pair (the normal region, non-adiabatic case presumably, V = 130–190 cm^–1 in dimethylformamide). The additional deactivation of the T₁ state is connected with thermally activated transitions to upper-lying CT states as well as the strengthening of intersystem crossing probabilities.     

Studies of the spin-Hamiltonian parameters, d–d transitions and defect structures for two tetragonal Cu centers in Ba2ZnF6:Cu crystal

Two theoretical methods, the perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM), are applied to calculate the spin-Hamiltonian parameters (g-factors g, g and hyperfine structure constants A, A, obtained from electron paramagnetic resonance (EPR) spectra) and d–d transitions (obtained from optical spectra) for two tetragonal Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ crystals. The Cu²⁺(I) ion replaces the Zn²⁺ ion at tetragonally compressed octahedral coordination and has the ground state ²A₁(|d_z²), whereas the Cu²⁺(II) ion is at an interstitial site with a square-planar F⁻coordination and has the ground state ²B₂(|d_x²-y²). The calculated spin-Hamiltonian parameters and d–d transitions from the PTM and CDM coincide and are in reasonable agreement with the experimental values. This suggests that both methods are effective for the theoretical studies of EPR and optical spectral data for 3d⁹ ions in tetragonal symmetry with different ground states. The defect structures of the two Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ are also estimated.     

Microwave dielectric properties of (1 − x)(Mg0.95Co0.05)TiO3–x(Na0.5La0.5)TiO3 ceramic system

The microstructures and the microwave dielectric properties of the (1 − x)(Mg_0.95Co_0.05)TiO₃–x(Na_0.5La_0.5)TiO₃ ceramic system were investigated. Two-phase system was confirmed by the XRD patterns and the EDX analysis. A co-existed second phase (Mg_0.95Co_0.05)Ti₂O₅ was also detected. The microwave dielectric properties are strongly related to the density and the matrix of the specimen. A new microwave dielectric material 0.88(Mg_0.95Co_0.05)TiO₃–0.12(Na_0.5La_0.5)TiO₃, possessing an excellent combination of dielectric properties: ε_r  22.36, Q × f  110,000 GHz (at 9 GHz), τ_f  2.9 ppm/°C), is proposed as a candidate dielectric for GPS patch antennas.     

Mutual Action of Optical Activity and Electro-Optic Effect and Its Influence on the Electro-Optic Q-switch

In this paper, we have studied the mutual action of the optical activity and the electro-optic effect, and its influence on the electro-optic Q-switch. The birefringence (g₃₃/n₀)(/n₀)² resulting from the mutual action is calculated. In the polarization light interferometric experiment setup, the outgoing light intensity expression is given by I = A²₀ cos² (/)(g₃₃/n₀)l – ] + (/)[(–2) + (g₃₃/n₀)(/n₀)²]l, for the optically active crystal on which the voltage is applied.We discuss the influence on the turn-off and turn-on states of the Q-switch caused by the mutual action term (g₃₃/n₀) /n₀)², and the advantage and disadvantage of the two work-manners of the Q-switch (i.e., step-up manner and step-down manner). The synthetic properties of La₃Ga₅SiQ₁₄ electro-optic Q-switch are described in comparison to KD₂PO₄ and LiNbO₃ Q-switches.     

Nuclear Spin Orientation Created in Heavy Ion Collisions and the Sign of the Q Moment of 13B

The momentum dependences of the nuclear spin polarization P and alignment A of ¹³B(, T _1/2 = 17.36 ms) produced in the 100A MeV ¹⁵N + Be collisions have been measured by detecting β-ray asymmetry. Because both the P and A were significantly smaller than the prediction from a simple kinematical model, some relaxation mechanisms must be take into account. Comparing the signs of the observed alignment of ¹²B, the sign of the quadrupole coupling constant eqQ of ¹³B in TiO₂ was determined to be positive.     

Nature of Thermally Induced Ion-Radicals in γ-Irradiated Barium Dithionate

The physicochemical properties of -irradiated barium dithionate in the temperature range 40-80°C were investigated by EPR and IR spectroscopy methods. It has been revealed that on decomposition of the substance, thermally induced ion-radicals of two types are formed, which are interpreted as SO₃ ^– (g = 2.0049, g = 2.0034) and SO₂ ^– (g ₁ = 2.0107, g ₂ = 2.0066, g ₃ = 2.0034). The conditions of their formation and limits of their stability have been determined. The heterogeneous phase BaSO₃/BaSO₄ is considered as the stabilizing one. The upper limit of applicability of barium dithionate as a dosimeter is 40°C.     

Electronic absorption and emission spectral data and fluorescence quantum yields of bridgedp-oligophenylenes,bi- to deciphenyls,and related furans and carbazoles

Absorption and fluorescence emission spectral data, as well as fluorescence quantum yields (_f), were determined for 41p-oligophenylene compounds containing 2–6, 8, and 10 benzene rings. Of 29 compounds containing carbon-bridged rings (fluorenes), 28 were dialkylated on each bridge for improved solubility and photostability. Absorption maxima for oligophenylenes were observed at wavelengths as long as 366 nm, emission maxima to 437 nm, and molar extinction coefficients () as large as 153,000 L/mol-cm; all three exceeded predicted maximum values for the corresponding unbridged oligophenylenes. The substitution of furan for benzene or carbazole for a fluorene (two examples each) bathochromically shifted absorption and emission maxima. Dialkylated carbon bridges bathochromically shifted absorption and emission maxima, and lowered _f in biphenyl and in one terphenyl analogue, but appeared to cause no diminution of _f in higher oligophenylenes. Bis(2-methoxyethyl) substitution on the bridges, incorporated to provide solubility in polar solvents, lowered _f in all examples. Tertiary alkyl substituents on terminal rings bathochromically shifted the absorption and emission maxima and generally increased _f. The loose bolt effect, which lowers _f in mononuclear substituted benzenes, may operate in 9,9-dialkylfluorenes, but not in 2,7-di-t-butylfluorene or in higher oligophenylenes. Cyclic ether and methoxy substituents as auxofluors on terminal rings generally bathochromically shifted absorption and emission maxima and increased and _f. Cyano substituents bathochromically shifted absorption and emission maxima, and increased , but lowered _f slightly.     

Design and Analysis of InGaN-GaN Modulation Doped Field-Effect Transistors (MODFETs) for Over 60 GHz Operation

A Modulation-Doped Field-Effect Transistor (MODFET) structure realized in InGaN-GaN material system is presented for the first time. An analytical model predicting the transport characteristics of the proposed MODFET structure is given in detail. Electron energy levels inside and outside the quantum well channel of the MODFET are evaluated. The two-dimensional electron gas (2DEG) density in the channel is calculated by self-consistently solving Schrödinger and Poisson's equations simultaneously. Analytical results of the current-voltage and transconductance characteristics are presented. The unity-current gain cutoff frequency (f _T) of the proposed device is computed as a function of the gate voltage V _G . The results are compared well with experimental f _T value of a GaN/AlGaN HFET device. By scaling the gate length down to 0.25 m the proposed InGaN-GaN MODFET can be operated up to about 80GHz. It is shown in this paper that InGaN-GaN system has small degradation in f _T as the operating temperature is increased from 300°K to 400°K.     

Theoretical studies of the spin-Hamiltonian parameters for the orthorhombic Pr4+ centers in Sr2CeO4 crystals

Theoretical studies of spin-Hamiltonian (SH) parameters associated with Pr⁴⁺ in Sr₂CeO₄ single crystals have been made by using the complete diagonalizing energy matrix method (CDM) for the 4f ¹ electronic configuration. The calculated results are in excellent agreement with the experimental data. The negative signs of the anisotropic g _i -factors and hyperfine structure constants A _i (where i = ∥ or ⊥) for the orthorhombic Pr⁴⁺ ion in Sr₂CeO₄ are suggested from the calculations. By comparing the results obtained by the CDM with the experimental data, one finds it is valid to interpret the SH parameters for 4f ¹ ions in crystals. The results are discussed.      

The Dynamics of Intramolecular Excited State Relaxation of <Emphasis Type="Italic">N</Emphasis>-Anthryl Substituted Pyridinium Cations

N-(1-Anthryl)-2,4,6-trimethyl-pyridinium (I), N-(2-anthryl)-2,4,6-trimethyl-pyridinium (II) and 10-(1-anthryl)-1,2,3,4,5,6,7,8-octahydro-acridinium cations (III) with anomalously high fluorescence Stokes shift have been investigated. Fluorescence kinetics analysis at various temperatures showed that in the range 293–77 K, the radiative deactivation rate constants (k_f) increase by 5.5 to 30 times. The low-temperature time-resolved emission spectra of I–III were found to be consistent with the model: A A^* B^* where A^* is the local excited twisted form and B^* is the relaxed more planar, bent conformer of the molecule. The rate constants of the excited relaxed state formation (k₁) and back reaction (k_–1) of compounds studied were estimated.