Metallacryptate single-molecule magnets: effect of lower molecular symmetry on blocking temperature

The structural characterization of complexes [Mn(II)4Mn(III)22(pdol)12(OCH3)12(O)16(N3)6] (1) and [Mn(II)4Mn(III)22(pdol)12(OCH3)12(O)16(OH)2(H3O)(OCH3)3].ClO4.5CH3OH (2), where pdol(2-) is di-2-pyridyl methanediol, reveals that each has a metallacryptand shell that encapsulates a manganese oxide core. Variable-temperature direct current magnetic susceptibility measurements on 2 indicate a paramagnetic ground state that results from an overall antiferromagnetic interaction in the cluster, with chiT values decreasing from 300 K (51.2 cm3 K mol(-1)) to 2 K (19.8 cm3 K mol(-1)). Variable-temperature alternating current magnetic susceptibility measurements imply that both 1 and 2 behave as single-molecule magnets. Fitting the frequency-dependent out-of-phase magnetic susceptibility to the Arrhenius equation yields an effective energy barrier, Ueff, to magnetization relaxation of 16.5 +/- 0.7 K (11.5 +/- 0.5 cm(-1)) for 1 and 36.2 +/- 2.0 K (25.1 +/- 1.4 cm(-1)) for 2. The larger value for 2 is in agreement with the lower molecular symmetry, larger magnetoanisotropy, and higher ground spin state of 2 compared to those of 1. This observation suggests a new strategy for increasing the blocking temperatures in high-nuclearity manganese clusters.     

Effect of strain on the thermodynamic melting temperature of polymers

X-ray diffraction, sonic velocity, and birefringence measurements were used to study the variation of the apparent melting point of strained natural rubber and polychloroprene vulcanizates with elongation ratio and crystallization temperature. The procedure of Hoffman and Weeks was employed to obtain the thermodynamic melting point, t_m, for each elongation ratio α. The parameter β relating to the distribution of fold lengths is unusually large for low elongation ratios and decreases into the usual range only at higher elongations. The observed variations of t_m with α for these two polymers are compared with the theoretical predictions of Flory and Roe and Krigbaum. Although the predictions of the Flory theory depend somewhat upon the value assigned for the number of repeating units per statistical link, and this parameter is not well known for polychloroprene, we nevertheless conclude that his treatment offers a better representation of the melting point elevation for high elongations. Due to the approximations introduced, the treatment of Flory is not valid for lower elongations. Any attempt to improve this treatment must begin by specifying the free energy of the semicrystalline system, which implies a knowledge of the distribution of crystallite orientations and how this distribution varies with strain and with the crystallization conditions.     

Effect of temperature on the solubility of carnallite type double salts

A method based on Pitzer's model has been used for calculation of the solubilities of carnallite type double salts crystallizing in the systems MeX–MgX₂–H₂O (Me=Li, NH₄, K, Rb, Cs; X=Cl, Br). The solubility of congruently soluble double salts was also determined experimentally at 25–75°C. The results from studies of the solubility diagrams of ternary carnallite type water-salt systems over a wide temperature range are summarized. It is found that the width of the crystallization region for each of the salts can be explained by the relative differences in the solubilities of the ternary solution components (MeX, MgX₂·6H₂O and MeX·MgX₂·6H₂O) and by a change of temperature, and by the effect of temperature on the solubility. A method is proposed for calculating Pitzer's ternary parameters of interionic interaction (_MN and _MNX) on the basis of experimental data for the solubility in water of the double salts crystallizing in the corresponding ternary water-salt systems.     

Influence of molecular characteristics on overall isothermal melt-crystallization behavior and equilibrium melting temperature of syndiotactic polypropylene

Overall isothermal melt-crystallization and subsequent melting behavior of metallocene-catalyzed syndiotactic polypropylene resins of various molecular weights were investigated using differential scanning calorimetry (DSC) technique. Two sets of molecular weight range were synthesized with two different metallocene catalyst systems. The kinetics of the overall isothermal melt-crystallization process was analyzed based on various macrokinetic models, i.e. the Avrami, Malkin and Urbanovici-Segal models. The effective activation energy describing the overall isothermal crystallization process over the crystallization temperature range studied was estimated based on an Arrhenius approximation of the obtained Avrami crystallization rate constants. The equilibrium melting temperature for each of these resins was estimated based on the linear and non-linear Hoffman-Weeks extrapolative methods.     

Effect of molecular association on solubility,diffusion, and permeability in polymeric membranes

The filling‐type membrane is composed of grafted polymer and solvent‐resistant substrate; the calculation of solubility, diffusivity and swelling‐suppression effect by the substrate permits the prediction of solvent permeability. As noted in our previous article, the use of this approach, called membrane design, resulted in accurate prediction of the permeability of aromatic compounds. In this study, the influence of hydrogen bonding on solubility and diffusivity is investigated both theoretically and experimentally. The solubility of chloroform and dichloromethane in poly(acrylate)s increases, and their diffusivity decreases, compared with that estimated without considering the hydrogen‐bonding effect. Solubilities predicted by the lattice‐fluid hydrogen‐bonding (LFHB) model show good agreement with the results of vapor sorption. Comparison of diffusion coefficients measured by vapor permeation with those predicted from free volume theory reveals that the decrease of solvent diffusion coefficient is approximately proportional to the fraction of associated molecules. Fluxes of chloroform and dichloromethane were measured by vapor permeation experiments through filling‐type acrylate membranes, and predictions agree well with experiments. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 171–181, 2000     

Extended molecular symmetry groups

The group theoretical analysis of Longuet-Higgins molecular symmetry groupsG(m, n) andGB(m) and their torsional extensionsG ^q (m, n) andGB ²(m) of molecules consisting of two coaxially rotated parts is presented. The structure of the groups is described in terms of direct and semi-direct products. The groupsG ^q (m, n) andGB ²(m) are shown to be group extensions of the groupsG(m,n) andGB(m), respectively. All irreducible representations of the groupsG(m,n),GB(m), andGB ²(m) are derived using standard techniques of the extension or induction. A restriction method is proposed for derivation of irreducible representations of the groupG ^q (m,n). The class structure of the groups is determined and the character tables are given in the most general case.     

Effect of temperature on the molecular mobility in polylactide

The effects of temperature on the molecular mobility in the amorphous phase and on the structural parameters of the crystalline phase of three brands of polylactide have been studied. It was found that annealing increases the melting temperature by 2–3°C and increases the degree of crystallinity by 2–6%. X-Ray analysis showed the possibility of formation of crystal structures of the α and β modifications in polylactide. The change in correlation time of radical rotation in amorphous regions of polylactide as a function of the history of thermal pretreatment of the samples was shown via the electron paramagnetic resonance method.     

Effect of temperature and molecular weight on enthalpy relaxation in polystyrene

Isothermal enthalpy relaxation in polystyrene was measured as a function of temperature and molecular weight on a differential scanning calorimeter. Relaxation spectra were derived from the data and expressed as a distribution of relaxation times. For a given molecular weight the relaxation spectra at different temperatures could not be superimposed by a shift in time. The relaxation curves of samples of different molecular weights could be superimposed only when the difference between the temperature at which the relaxation was monitored (T_a) and their respective T_g was the same. The relaxation spectrum at any temperature for a given molecular weight was also expressed as a distribution of energies. The average energy represented by this distribution was associated with an activation energy required for the motion of a chemical repeat unit. The activation energy extracted from the temperature shift in the relaxation spectra corresponded to the motion of a statistical unit (Kuhn's segment) in polystyrene.     

Local symmetry and chirality of molecular faces

The concept of local symmetry has been applied to faces of planar sites such as carbon–carbon double bonds and aromatic rings with the principal results being as follows. The two faces of a planar site must have the same local symmetry group. This local symmetry group is limited to the polar point groups. For cyclic compounds, directed cycles must have chirotopic faces although the reverse is not necessarily true: chirotopic faces are possible for both directed and undirected cycles. A number of examples are provided to illustrate these results. Received: 30 June 1999 / Accepted: 4 October 1999 / Published online: 19 April 2000     

Permutation representations in molecular symmetry

The reducible representations of the point groups are generally studied because of their relevance to molecular orbital and vibration theory. Triple correlations within the polyhedra are described by group-theoretical invariants that are related to the permutation representations and termed polyhedral isoscalar factors. These invariants are applied in theorems on matrix elements referring to the symmetry-adapted bases at different centres. Further invariants or geometrical weight factors inter-relate different types of reduced matrix elements of irreducible tensors (generalization of the Wigner-Eckart theorem to the polycentric case). As a demonstration a complete tabulation is given for the point group C ₄.     

The molecular and ionic solubility of nickel dimethylglyoximate

Values are reported for the solubility product constant and the ionization constant of nickel(II) dimethylglyoximate in aqueous solution. The solubility of nickel dimethylglyoximate in the investigated pH range from 2 to 9 is accounted for by the species Ni⁺² and Ni(HDx)₂; there is no evidence for the existence of a significant amount of NiHDx⁺.The extraction constant

has been calculated from the ionization constants of Ni(HDx)₂ and H₂Dx and the molecular solubilities of the former in water and chloroform.     

The symmetry of molecular polarization tensors

Polarization tensors are discussed in terms of their intrinsic symmetry group which is a direct product of the point group and the subgroup of the permutation group relevant to the experiment. The study of these latter groups is simplified by use of the isomorphism with certain point groups and permutations of suffixes can be visualized by rotations and reflections of the vertices of various objects in space. The approach unites the previous treatments and provides a means of constructing the bases for the irreducible tensor components. The difficulties introduced by Laplace's equation are explained and the information obtainable from induced birefringence experiments (Kerr and Cotton–Mouton effects) discussed for various systems.     

The effect of molecular weight on the crystallization kinetics and equilibrium melting temperature of poly(tetramethylene ether glycol)

Isothermal crystallization of poly(tetramethylene ether glycol) (PTMEG) with relatively low molecular weight (M_n = 991, 2004 and 2864, respectively) was investigated by differential scanning calorimetry, and the equilibrium melting temperature (T) determined using the Hoffman–Weeks analysis. The crystallization kinetics of PTMEG were characterized using an Avrami analysis. Mechanistic n values ranged from 2.2 to 2.9 for the primary crystallization process for three molecular weight grades, indicating heterogeneous nucleation of spherulites. Polarized light microscopy confirmed that PTMEG crystallized by the growth of spherulites from heterogeneous nuclei. The half–life for crystallization (t_1/2) and the composite rate constant were found to be dependent on the degree of supercooling (ΔT) and the molecular weight. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of molecular weight on the growth rates of low melting spherulites of trans-1,4-polyisoprene

Growth rates of G of low-melting spherulites in fractions of trans-1,4-polyisoprene have been measured. The data were analyzed by use of an equation, ln G = ln G₀ ? ΔF^*/RT_c, valid at temperatures close to the equilibrium melting point. Plots of ln G against a function of the critical free energy of nucleation ΔF^* result in a family of straight lines having a common intercept, ln G₀, which is independent of molecular weight. The slope of these lines is a measure of the interfacial free energy of the crystallites and increases with the molecular weight, reflecting increasing irregularity in the structure of the semicrystalline mass. Comparison of growth rates of low-melting and high-melting trans-1,4-polyisoprene indicates that G₀ does not, to a first approximation, depend on the nature of the crystals growing from the melt. The temperature at which spherulites of the two crystalline forms grow at equal rates has been calculated.     

Substrate effect on the melting temperature of gold nanoparticles

Previous experimental, molecular dynamics, and thermodynamic researches on the melting temperature of Au nanoparticles on tungsten substrate provide entirely different results. To account for the substrate effect upon the melting point of nanoparticles, three different substrates were tested by using a thermodynamic model: tungsten, amorphous carbon, and graphite. The results reveal that the melting point suppression of a substrate-supported Au nanoparticle is principally ruled by the free surface-to-volume ratio of the particle or the contact angle between the particle and the substrate. When the contact angle θ is less than 90°, a stronger size-dependent melting point depression compared with those for free nanoparticles is predicted; when the contact angle θ is greater than 90°, the melting temperature of the supported Au nanoparticles are somewhat higher than those for free nanoparticles.     

Maximum overlap symmetry molecular orbital model

This paper provides a brief and systematic presentation of the basic principle and method of the maximum overlap symmetry molecular orbital (MOSMO ) model and its application to simplification of molecular orbital calculation and to calculation of molecular structures and properties, together with some new results about the MOSMO calculation and new insights concerning the further extension of the principle and method. It has been shown that the theoretical method of the MOSMO model is very simple, reliable, and useful and can be employed to study the structure–property relation in even very large molecular systems. The numerical results obtained from the MOSMO calculation on various semiempirical molecular orbital approximation levels show that when the same parametrization, such as one of those employed in EHMO , CNDO /2, and HMO methods, is adopted, the MOSMOS are very close to the canonical molecular orbitals obtained from the customary LCAO method and the MOSMO calculation requires less computing time than does the LCAO method. The MOSMO calculation can be used for rapidly obtaining reasonably good molecular geometries, vibrational frequencies, and other properties of molecules by employing a simple improved semiempirical parametrization. Equilibrium geometries, vibrational frequencies, and other results are in good agreement with the experimental data and the results obtained from ab initio molecular orbital calculation. The basic calculational procedure of the MOSMO model can be extended further and has been employed to give some new results, to propose some new theoretical schemes and principles, and to introduce some new interesting theoretical problems that deserve to be studied further.     

Combined effects of salinity and temperature on the solubility of organic compounds

This study deals with the solubility limits of organic liquids liable to be spilled at sea during ship-wrecking or other incidents at sea. The effects under consideration are induced by both salinity and temperature. The former is described through use of the Setchenov relationship, and the latter by using the Van’t Hoff equation. A coupling of both relationships led to an equation applicable to scarcely soluble liquids and expressed in a simplified form usable in decision-support systems as a result of the choice of the reference state when writing the thermodynamic relationships. The mathematical relation we found was tested on experimental data about four compounds, i.e. dimethyldisulfide (DMDS), methyl methacrylate (MMA), 1-butanol (1-But), and methyl ethyl ketone (MEK), chosen because of their wide use in the industry and frequent transport by sea. All of them were studied at four salinity values and five temperatures, and the mathematical relation under test proved to be quite satisfactory.     

Use of molecular symmetry in SCF calculations

A method is described whereby molecular symmetry properties may be used to reduce the numbers of one- and two-electron integrals that need to be calculated and stored in the course of a molecular SCF calculation. The method is a generalization of a previously reported procedure, extending the earlier work to cover those molecules belonging to point groups which have complex representations. The practical application of the method is discussed and an illustrative example given. The quite extensive tables of molecular symmetry properties which the method uses may be computer generated in a straightforward manner. A procedure for doing this using a minimum amount of input data is presented.