Variational approximations for renormalization group transformations

Approximate recursion relations which give upper and lower bounds on the free energy are described. Optimal calculations of the free energy can then be obtained by treating parameters within the renormalization equations variationally. As an example, a particularly simple lower bound approximation which preserves the symmetry of the Hamiltonian (the one-hypercube approximation) is described. The approximation is applied to both the Ising model and the Wilson-Fisher model. At the fixed point a parameter is set variationally and critical indices are calculated. For the Ising model the agreement with the exact results atd = 2 is surprisingly good, 0.1%, and is good atd=3 and evend=4. For the Wilson-Fisher model the recursion relation is reduced to a one-dimensional integral equation which can be solved numerically givingv=0.652 atd=3, or by expansion in agreement with the results of Wilson and Fisher to leading order in . The method is also used to calculate thermodynamic functions for thed = 2 Ising model; excellent agreement with the Onsager solution is found.Supported in part by the National Science Foundation under Grants Nos. MPS73-04886A01 and GH-41512 and by the Brown University Materials Research Laboratory supported by the National Science Foundation. M.C.Y. was supported by a grant from the Scientific and Technical Research Council of Turkey.     

A New Entropy Function to Analyze Isentropic Processes of Ideal Gases with Variable Specific Heats

A new entropy function s⁺ is defined in terms of the existing entropy function s° and temperature as s⁺ = s° − R lnT to facilitate the analysis of isentropic processes of ideal gases with variable specific heats. The function s⁺ also makes it possible to calculate the entropy changes of ideal gases during processes when volume information is available instead of pressure information and the variation of specific heats with temperature is to be accounted for. The introduction of the function s⁺ eliminates the need to use the dimensionless isentropic functions relative pressure P_r and relative specific volume v_r of ideal gases and to tabulate their values. The P_r and v_r data are often confused with pressure and specific volume, with an adverse effect on the study of the second law of thermodynamics. The new s⁺ function nicely complements the existing s° function in entropy change calculations: the former is conveniently used when volume information is given while the latter is used when pressure information is available. Therefore, the introduction of the new entropy function s⁺ is expected to make a significant contribution to the thermodynamics education and research by streamlining entropy analysis of ideal gases.     

Effect of reactive and nonreactive surface modifications and compatibilizer use on mechanical and flame-retardant properties of linear low-density polyethylene filled with huntite and hydromagnesite mineral

Journal of Thermal Analysis and Calorimetry - In the current study, huntite and hydromagnesite (HH) was used as flame-retardant additive in linear low-density polyethylene (LLDPE). The effect of HH...     

Design and construction of an quasi-adiabatic dissolution calorimeter with a novel dosing apparatus and a low heat capacity

A quasi-adiabatic calorimeter for determining the molar solution enthalpies (Δ_sol H) of non-volatile solids was constructed. The design of the instrument was adjusted to allow the determination of solution enthalpies of small amounts of solids. For that purpose, the novel apparatus for sample dosage with virtually negligible “blank heat” was built. The rather low heat capacity of the calorimeter was achieved by reducing the volume of the reaction cell (20 mL), the dosing unit, and electric elements (the thermistor and the heater). Good thermal isolation of the reaction cell from the surroundings was accomplished by placing the cell into an evacuated polypropylene vessel. A computer program for processing the calorimetric data according to modified Regnault–Pfaundler method was written. The performance of the calorimeter was tested by determining the heats of the reactions serving as thermochemical standards at 25 °C (the dissolution of KCl and NaCl in water and the dissolution of tris(hydroxymethyl)-aminomethane in 0.1 mol dm^?3 HCl(aq)). The obtained data were in very good agreement with the literature values.     

Transfer hydrogenation of aryl ketones with homogeneous ruthenium catalysts containing diazafluorene ligands

Novel cationic ruthenium(II) complexes bearing a 4,5‐diazafluorene unit and p‐cymene as ligands have been synthesised. The complexes were characterised based on elemental analysis and Fourier transform infrared and nuclear magnetic resonance spectroscopies. The synthesised Ru(II) complexes were employed as pre‐catalysts for the transfer hydrogenation of aromatic ketones using 2‐propanol as both hydrogen source and solvent in the presence of NaOH. All complexes showed high catalytic activity as catalysts in the reduction of substituted acetophenones to corresponding secondary alcohols. The products of catalysis were obtained with conversion rates of between 80 and 99%. Among the seven new complexes investigated, the most efficient catalyst showed turnover frequencies in the range 255–291 h^?1 corresponding to 85 to 97% conversion, respectively. Copyright © 2016 John Wiley & Sons, Ltd.     

New functional chiral P-based ligands and application in ruthenium-catalyzed enantioselective transfer hydrogenation of ketones

Metal-catalyzed asymmetric transfer hydrogenation is a powerful and practical method for the reduction of ketones to produce the corresponding secondary alcohols, which are valuable building blocks in the pharmaceutical, perfume, and agrochemical industries. Hence, a series of novel chiral β-amino alcohols were synthesized by chiral amines with regioselective ring opening of (S)-propylene oxide or reaction with (S)-(+)-2-hydroxypropyl p-toluenesulfonate by a straightforward method. The chiral ruthenium catalytic systems generated from [Ru(arene)(μ-Cl)Cl]₂ complexes and chiral phosphinite ligands based on amino alcohol derivatives were employed in asymmetric transfer hydrogenation of ketones to give the corresponding optically active alcohols; (2S)-1-{[(2S)-2-[(diphenylphosphanyl)oxy]propyl][(1R)-1-phenylethyl]amino}propan-2-yldiphenylphosphinitobis[dichol-oro(η⁶-benzene)ruthenium(II)] acts an excellent catalyst in the reduction of α-naphthyl methyl ketone, giving the corresponding alcohol with up to 99% ee. The substituents on the backbone of the ligands were found to have a remarkable effect on both the conversion and enantioselectivity of the catalysts. Furthermore, this transfer hydrogenation is characterized by low reversibility under these conditions.     

Aliphatic Polyester/polyhedral Oligomeric Silsesquioxanes Hybrid Networks via Copper‐free 1,3‐dipolar Cycloaddition Click Reaction

In this study, we describe the preparation and characterization of a new class of thermoset hybrid networks containing aliphatic polyester and polyhedral oligomeric silsesquioxanes (POSS). The copper‐free 1,3‐dipolar cycloaddition click reaction of internal alkyne functionalized aliphatic polyester and multifunctional azido POSS with different concentrations led to highly crosslinked thermoset networks. The click reactions performed under ambient conditions (i.e., in tetrahydrofuran at room temperature for 1 day) in the absence of any catalyst. The chemical composition of hybrid networks and homogenous distribution of POSS molecules were confirmed by Fourier transform infrared spectroscopy and scanning electron microscopy with energy dispersive spectroscopy. The swelling ratios of hybrid networks were commonly decreased by increasing POSS‐N₃ content and by changing polar solvents to apolar solvents. Thermogravimetric analysis results demonstrated that the thermal stability of hybrid networks increased with higher POSS feeding ratio. Tensile tests were applied to evaluate the mechanical properties of hybrid networks. Compared to neat aliphatic polyester, the mechanical properties of hybrid networks significantly improved. For instance, the tensile strength were enhanced from 5 MPa to 19 MPa by increasing the concentration of azido functionalized POSS from 10 to 40. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2222–2227     

Microencapsulated oleic–capric acid/hexadecane mixture as phase change material for thermal energy storage

Journal of Thermal Analysis and Calorimetry - Thermal energy storage systems provide efficiency in order to have better utilization of energy sources while protecting the environment. Thermal...