The Ising free-energy functional

We show that the Ising free-energy functional f(T, X) yields a second-order phase transition. The value of X, a generalized order parameter, which minimizes the functional is the real-order parameter, Ω = tanh[Ω(T_C/T)] where T_c = J/(2k) and J is the Ising coupling constant. The Ising theory is applicable to the second-order phase transitions in ferromagnets, ferroelectrics, and superconductors. The constant temperature slices of f(T, X) yields the Ising functional which is valid over the entire range of T and which is identical to the Landau functional for T/T_C close to unity. © 1996 John Wiley & Sons, Inc.     

A model for the helix–coil transition of DNA

The helix–coil phase transition of DNA is studied through a model equivalent to the one used in the theory of superconductivity. A distribution function for the excitations analogous to the usual Fermi function is obtained which depends on the parameter T₀, the maximum temperature at which all pairs of bases are bonded. The expression for the number of unbonded pairs of bases depends only on the two parameters, T₀ and T_c (critical temperature).     

Calculation of the specific heat close to the multicritical and second order phase regions in ND<Subscript>4</Subscript>Cl

We calculated the specific heat C _V of ND₄Cl under the prediction of an Ising model presented here. Our calculated C _V agrees with the experimental C _P data for the multicritical (P = 0.1 MPa) and second order (P = 150 MPa) phase regions in this crystalline system. This agreement is particularly good above T _C 250 K) for the multicritical regime and below T _C 261 K) for the second order phase transition in ND₄Cl. This shows that the observed behaviour of ND₄Cl can be well described by an Ising model close to the phase transitions considered in this crystalline system.     

A Thermally Populated,Perpendicularly Twisted Alkene Triplet Diradical

Variable‐temperature NMR and ESR spectroscopic studies reveal that bis(dibenzo[a,i]fluorenylidene) 1 possesses a singlet ground state, 1 (S₀), while the 90° twisted triplet 1 (T₁) is populated to a small extent already at room temperature. Analysis of the increasing amount of paramagnetic 1 (T₁) at temperatures between 300 and 500 K yields the exchange interaction J_ex/h c=3351 cm^?1 and a singlet–triplet energy splitting of 9.6 kcal mol^?1, which is in excellent agreement with calculations (9.3 kcal mol^?1 at the UKS BP86/B3LYP/revPBE level of theory). In contrast, the zero‐field splitting parameter D is very small (calculated value ?0.018 cm^?1) and unmeasurable.     

A Thermally Populated,Perpendicularly Twisted Alkene Triplet Diradical

Variable‐temperature NMR and ESR spectroscopic studies reveal that bis(dibenzo[a,i]fluorenylidene) 1 possesses a singlet ground state, 1 (S₀), while the 90° twisted triplet 1 (T₁) is populated to a small extent already at room temperature. Analysis of the increasing amount of paramagnetic 1 (T₁) at temperatures between 300 and 500 K yields the exchange interaction J_ex/h c=3351 cm⁻¹ and a singlet–triplet energy splitting of 9.6 kcal mol⁻¹, which is in excellent agreement with calculations (9.3 kcal mol⁻¹ at the UKS BP86/B3LYP/revPBE level of theory). In contrast, the zero‐field splitting parameter D is very small (calculated value −0.018 cm⁻¹) and unmeasurable.     

Effect of core substituents on the intramolecular exchange interaction in N,N′‐dioxy‐2,6‐diazaadamantane biradical: DFT studies

Density‐functional theory calculations of a series of organic biradicals on the basis of the N,N′‐dioxy‐2,6‐diazaadamantane core with different substituents at carbon atoms adjacent to the nitroxyl groups have been performed by the UB3LYP/6‐311++G(2d,2p) method. Using the breaking symmetry approach, the values of the exchange interaction parameter, J, between the radical centers are calculated. It is shown that the intramolecular exchange interaction for the most part is ferromagnetic in nature, but the J parameter gradually decreases, changing its sign to antiferromagnetic interaction for the last substituent in the following sequence: CF₃(CH₃)COH > CH₂F(H)COH > CH₂OH > H > CBr₃ > CH₂F > CCl₃ > CF₃ > CH₂Br > CH₂Cl > CH₃ > C₂H₅ > C₃H₇ > i‐C₄H₉ > F > Br > OCH₃ > Cl > CH₂C₆H₅. The calculations at the UHSEH1PBE/6‐311++G(2d,2p) level with the most of substituents show nearly the same variation sequence for the J parameter. It is concluded that spin polarization effects in the diazaadamantane cage and a direct through‐space antiferromagnetic exchange interaction between the nitroxyl groups are the main mechanisms contributing to the exchange interaction parameter value in the studied series of compounds. The exchange coupling constant, J, depends on the electronic effects and geometry of the substituents, as well as on their specific interactions with the nitroxyl radical groups.     

Internal conrotation and disrotation in H2BCH2BH2 and diborylmethane 1,3 H exchange

The paths of correlated internal disrotation (barrier less than 0.4 kcal/mol) and conrotation (barrier around 1.9 kcal/mol) of the two BH₂ groups in H₂BCH₂BH₂ have been computed employing ab initio [MP2(full)/6–31G**] and density functional theory (Becke3LYP/6–311+G**) methods. Two B(SINGLE BOND)C(DOTTED BOND)B(p) hyperconjugative interactions stabilize the C_s symmetric H₂BCH₂BH₂ isomer ( 1 ). The B(SINGLE BOND)C(DOTTED BOND)B(p) hyperconjugative stabilization, evaluated by homodesmotic reactions and using the orbital deletion procedure (which “deactivates” the “vacant” born p orbital), is less than 6 kcal/mol in diborylmethane. The B(SINGLE BOND)C(DOTTED BOND)B(p) stabilization is shown to be remarkably large in C₄B₆H₁₀ (Td). At MP2(fu)/6–31G**, disproportionation into 1 and methane is only 5.6 kcal/mol exothermic. The 1,3 H exchange in diborylmethane is an asynchronous process and proceeds via a doubly bridged cyclic intermediate with 9.3 kcal/mol barrier. Structures with “planar tetracoordinate” carbon are stabilized considerably by BH₂ substituents, but they are still high in energy. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1792–1803, 1997     

Analysis of the specific heat of p-azoxyanisole (PAA) near the phase transitions

The analysis of the experimental data for the specific heat C_p at various temperatures is given here near the nematic-isotropic liquid (T_NI = 133.9°C) and the solid-nematic (T_SN = 117.6°C) transitions in p-azoxyanisole (PAA). The analysis of the specific heat C_p is performed according to a simple power-law formula and a renormalisation-group expression. The values of the critical exponent α are extracted above and below the transition temperatures of T_NI and T_SN for this liquid crystalline material. Our exponent values are compared with the predictions of a three-dimensional Ising model and XY model for liquid crystals. Using the specific heat C_p , the temperature dependence of the enthalpy H and the entropy S is calculated in the nematic phase (T > T_SN ) of p-azoxyanisole.     

A study of C–35Cl coupling constants and 35Cl relaxation times through 13C relaxation in the rotating frame

Values of one-bond J(C³⁵ Cl) and T₁(³⁵Cl) were determined for small chlorine-containing molecules through ¹³C scalar relaxation in the rotating frame. A method is suggested for evaluating the contribution of scalar relaxation which eliminates experimental imperfections. The magnitude of J(C³⁵Cl) seems to be influenced by the same factors as J(CF) values. The differences in ³⁵Cl relaxation times are rationalized in terms of the molecular reorientation time.     

Correlated and gauge origin independent calculations of magnetic properties

Summary We have applied a gauge origin invariant method for calculations of nuclear magnetic shielding constants to the singly bonded molecules BF, F₂, BH₃, CH₄, NH₃, H₂O, and HF as well as to the¹H shielding constants of HCN and C₂H₂. The calculations were performed at the RPA and second order polarization propagator (SOPPA) level of theory. For most molecules the correlation contribution in SOPPA is less diamagnetic than in the comparable MP2 calculations. For F₂, SOPPA gives a large paramagnetic correlation correction whereas the MP2 method gives a very small correlation contribution. For all molecules agreement with experimental results is generally improved at the SOPPA level compared to RPA. We have also demonstrated that second order gauge origin invariant, common and local origin (SOLO) methods do not necessarily give the same shielding even in the limit of a converged basis set.     

Structure and properties of nonclassical polymers. III. Magnetic characteristics at finite temperatures

Within the Ising model, the two-dimensional alternant nonclassical polymers display magnetic order at finite temperatures and are characterized by a nonzero critical point T_c. It is shown that magnetic ordering at finite temperatures occurs when interchain interactions in a quasi- dimensional nonclassical altemant polymer are taken into account.     

Self diffusion and viscoelasticity of elongated micelles from cetyltrimethyl-ammonium bromide in aqueous sodium salicylate solution. II. Temperature effect

Forced Rayleigh scattering and dynamic viscoelastic experiments are performed to study slow global motions of networks formed by elongated micelles from cetyltrimethylammonium bromide (CTAB) in aqueous sodium salicylate (NaSal) solutions at six temperatureT from 25° to 60°C. The CTAB concentrationC _D of the solutions is fixed atC _D=0.01 M and a ratio of salt concentrationC _s toC _D is varied from 1 to 41. The self-diffusion coefficientD of the dye-labeled cetyldimethylamine incorporated in the micelles shows a complicatedC _s/C _D dependence with a maximum that is followed by a minimum at lower temperatures, but these two extremes gradually disappear with increasingT. TheC _s/C _D dependencies of both the steady-state viscosity and the terminal relaxation time are found consistent with the diffusion behaviour. TheD of all solutions tested monotonically increases withT, but shows different functional dependence onT asC _s/C _D varies. The applicability of the theory of Brownian motion of a rigid rod in the semidilute regime is examined usingD and values.     

The physical properties of bisphenol-a-based epoxy resins during and after curing. II. Creep behavior above and below the glass transition temperature

The creep behavior of a series of fully cured epoxy resins with different crosslink densities was determined from the glassy compliance level to the equilibrium compliance J_e at temperatures above T_g and at the glassy level below T_g during spontaneous densification at four aging temperatures, 4,4-diamino diphenyl sulfone DDS was used to crosslink the epoxy resins. The shear creep compliance curves J(t) obtained with materials at equilibrium densities near and above T_g were compared at their respective T_gs. T_gs from 101 to 205°C were observed for the epoxies which were based on the diglycidyl ether of bisphenol A. Creep rates were found to be the same at short times, and equilibrium compliances J_e were close to the predictions of the kinetic theory of rubberlike elasticity. Time scale shift factors determined during physical aging were reduced to T_g. At compliances below 2 × 10^?10 cm²/dyn, Andrade creep, where J(t) is a linear function of the cube root of creep time, was observed. The time to reach an equilibrium volume at T_g was found to be longer for the epoxy resin with lower crosslink densities. The increase of density during curing is illustrated for the epoxy resin with the highest crosslink density.     

Depolarized light scattering studies on single-phase mixtures of dissimilar polymers: Evidence for local ordering

Depolarized light scattering measurements on single-phase mixtures of dissimilar polymers, poly(methyl methacrylate) (PMMA)/poly (acrylonitrile-co-styrene) (SAN, AN content = 15 wt %) and PMMA/poly (vinylidene fluoride) (PVDF) were carried out. The effective mean-square optical anisotropy γ² of the mixtures was found to be much higher than that estimated by the simple additivity of γ² of component polymers. From the deviation, the order parameter (1 + J₁₂) was estimated to be in a range of 2–13, depending on the blend composition. This suggests local ordering in the single-phase mixtures, i.e., nematic alignment of the locally stretched dissimilar chains. In contrast, the deviation was slight in the polymer/solvent systems, SAN/MMA (monomer) and PVDF/butanone. The degree of ordering decreased with increasing temperature. T. The Specific interaction evidenced by FTIR spectroscopy exhibited a similar temperature dependence. Thus, local ordering seems to be induced by specific interactions and chain connectivity. The temperature dependence of J₁₂ was successfully described by the Landau-de Gennes theory; J ∞ (T + T₀)/ T, T₀ being the isotropic-nematic transition temperature, as in the case of liquid crystals.     

Energy transfer as a function of collision energy. I Collision partners: Hydrogen halides + inert gases,hydrogen halides,H2S and propane

Infrared emission has been recorded from a heated seeded supersonic primary beam of HCl or HF (1) prior to collision with a target beam, and (2) subsequent to that collision. Mean collision energy and collision partner were varied systematically. After correction for elastic scattering, the net population change due to inelastic scattering in a translation—rotation (T ? R) energy-transfer encounter was obtained for specific J states ranging from J = 0–16 of vibrational level υ = 1 of the primary-beam molecule. The broad picture is that a net transfer into low-J states out of higher-J states takes place at low collision energies, and the converse at high collision energies. These observations are interpreted in terms of the “exponential model” for the relative cross sections of T ? R inelastic collisions, S^R (J_i → J_f), proposed earlier [J.C. Polanyi and K.B. Woodall, J. Chem. Phys. 56 (1972) 1563], modified here to satisfy microscopic reversibility. The constant C in the model, which governs the exponential decrease in S^R with increasing energy difference ΔE_J between J_f and J_i, can be derived, as a function of collision energy T, from the present experimental data; C decreases as T increases, i.e. larger ΔJ become more probable. In order to check the validity of the model, it was compared with 3D trajectory results; according to this criterion it was found to give a very good representation of S^R(J_i → J_f) with a single value for C, within a limited range of J_i. The collision partners HCl + HF exhibit anomalously efficient rotational deactivation; evidence is presented which indicates that at low collision energies this is due to resonant R → R transfer. Very efficient deactivation of HCl by HCl, at low collision energy, is likely to be due to V — V transfer.     

Calculation of j and jm symbols for arbitrary compact groups. III. Application to SO3 ⊃ T ⊃ C3 ⊃ C1

The methodology developed in earlier papers is used to compute the 6j symbols and 3jm factors that arise in the group chain SO₃ ? T ? C₁. The relevant character theory is given and the 2j and 3j symbols calculated. Selection rules are used to predict which j symbols or jm factors are necessarily zero, and then a set of 6j fundamentals computed for T. The complete set of primitive 6j symbols are then computed by application of the orthogonality and Racah backcoupling relations. Primitive 3jm factors are calculated for SO₃ ? T and T ? C₃ and, from these, all the 3jm factors for T ? C₃ and some of those for SO₃ ? T computed. A complete table of non-equivalent 6j symbols for T and 3jm factors for T ? C₃ is given, together with a table for SO₃ ? T of all 3jm factors with j ≤ 2.     

Héterocycles contenant du phosphore—XVII: Etude par Résonance Magnétique Nucléaire et analyse conformationnelle de quelques oxazaphosphorinanes-1,3,2

The PMR spectra of some new 1,3,2-oxazaphosphorinanes are analysed. In one case, after elimination of the P? H spin coupling, the spectra give rise to a particular ABKLXY pattern in which certain coupling constants between vicinal protons are zero. The ABKLXY system where J_AK = J_AL = J_BK = J_BL is studied and most of the parameters of the related compound are calculated. The ring conformation is discussed and the free energy is given; for one oxazaphosphorinane, the calculation of the torsional angle of the C₄? C₅ and C₅? C₆ fragments is described.     

E.S.R. and D.S.C. investigations of phase transitions in polymorphic 4-n-alkoxybenzylidene-4′-n-alkylanilines

Abstract

It is shown that the McMillan parameter M = T _SAN/T _N1 (where T _SAN and T _NI are respectively the temperatures of the smectic A to nematic (SAN) and the nematic to isotropic (NI) phase transitions) is useful in analysing the crossover between second and first order behaviour of the S_NN transition in the nO.m homologous liquid crystal series (the 4-n-alkoxybenzylidene-4′-n-alkylanilines). Using a phase diagram of orientational ordering versus M for this series, as obtained in this work (from E.S.R. and D.S.C), a symmetric tricritical point with mean field exponent β₂ = 1 is demonstrated. In a preliminary study of E.S.R. linewidth parameters B and C of nitroxide spin probes dissolved in members of the nO.m series exhibiting a first order S_AN transition, critical-type divergences are observed near this transition. In the case where M is closer to 0.959 (the value at the tricritical point), these divergences appear similar to those previously observed in related nO.m members with a second order S_AN transition; however, they are considerably enhanced for an M value closer to unity (i.e. more removed from the tricritical point). This indicates the importance of coupling between orientational and positional order parameters in the observed critical-type divergences.     

Interaction and superconducting transition in alkali-doped C_(60)

The intermolecular interactions in alkali-doped C60 solids, A3-x-yA'xA"yC60(A, A', A" =alkali; x y ≤3), have been calculated, and their correlations with the structures and the superconducting transition temperaturesTc have also been investigated. It is found that the variations of the lattice constants a0 of A3-x-yA'x A"yC60 solids and the superconducting transition temperatures Tc can be satisfactorily explained from the viewpoint of interaction. It is shown that the relationship of Tc with interaction is much closer than that of Tc with lattice constant a0. Therefore, we can say it is the physical factors such as interaction, other than the geometrical structure factors such as a0, that should be reasonably taken as the primitive cause of the sudden change of superconductivity from pristine C60 to its alkali-doped compounds and of the variation of Tc among superconductors of A3-x-yA'xA'yC60.     

Favorable performance of the DFT methods in predicting the minimum‐energy structure of the lowest triplet state of WF4

The tetrahedral structure of the lowest triplet state of the WF₄ complex was examined using different variants of the density functional theory (DFT) and conventional ab initio methods. The low‐level, conventional, ab initio methods, such as SCF, MP2, MP3, and CISD, predict the tetrahedral structure to be a minimum, whereas the DFT schemes predict an imaginary frequency for the e vibrational mode. Only after recovering electron correlation effects at the MP4 and higher levels, the conventional electronic structure methods also predict the T_d structure to be a second‐order stationary point. This is not the correlation but the exchange part of the DFT functionals which is responsible for the discrepancy between the DFT and low‐level, conventional, ab initio predictions. The lowering of symmetry to C_2v leads to a minimum on the lowest triplet potential energy surface and the electronic energy difference between the T_d and C_2v stationary points amounts to 0.85 and 0.96 kcal/mol at the B3LYP and CCSD(T) levels, respectively. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 369–375, 1999