The microcanonical thermodynamics of finite systems: the microscopic origin of condensation and phase separations, and the conditions for heat flow from lower to higher temperatures

Microcanonical thermodynamics [D. H. E. Gross, Microcanonical Thermodynamics, Phase Transitions in "Small" Systems (World Scientific, Singapore, 2001)] allows the application of statistical mechanics both to finite and even small systems and also to the largest, self-gravitating ones. However, one must reconsider the fundamental principles of statistical mechanics especially its key quantity, entropy. Whereas in conventional thermostatistics, the homogeneity and extensivity of the system and the concavity of its entropy are central conditions, these fail for the systems considered here. For example, at phase separation, the entropy S(E) is necessarily convex to make e(S(E)-E/T) bimodal in E. Particularly, as inhomogeneities and surface effects cannot be scaled away, one must be careful with the standard arguments of splitting a system into two subsystems, or bringing two systems into thermal contact with energy or particle exchange. Not only the volume part of the entropy must be considered; the addition of any other external constraint [A. Wehrl, Rev. Mod. Phys. 50, 221 (1978)], such as a dividing surface, or the enforcement of gradients of the energy or particle profile, reduce the entropy. As will be shown here, when removing such constraints in regions of a negative heat capacity, the system may even relax under a flow of heat (energy) against a temperature slope. Thus the Clausius formulation of the second law: "Heat always flows from hot to cold," can be violated. Temperature is not a necessary or fundamental control parameter of thermostatistics. However, the second law is still satisfied and the total Boltzmann entropy increases. In the final sections of this paper, the general microscopic mechanism leading to condensation and to the convexity of the microcanonical entropy at phase separation is sketched. Also the microscopic conditions for the existence (or nonexistence) of a critical end point of the phase separation are discussed. This is explained for the liquid-gas and the solid-liquid transition.     

Methodology for the preparation of 2-argininylbenzothiazole

An efficient process to produce kilogram quantities of a key argininylbenzo[d]thiazole intermediate was developed for the preparation of the tryptase inhibitor RWJ-56423. A variety of activated arginine esters and benzo[d]thiazole nucleophiles were evaluated as coupling partners. Our work led to the selection and optimization of an argininyl imidazolide ester and benzothiazol-2-yl MgCl nucleophile. This paper focuses on the preparation, use, and stability of the benzothiazol-2-yl Grignard reagents.     

Irradiation-induced enhancement of Pc 4 fluorescence and changes in light scattering are potential dosimeters for Pc 4-PDT

Phthalocyanine 4 (Pc 4) is a promising photosensitizer currently in clinical trials. Photobiological responses to Pc 4 photodynamic therapy (Pc 4-PDT) have been characterized extensively, but relatively little has been done to evaluate dose metrics for this sensitizer. We describe an irradiation-induced increase in fluorescence in tumor cell monolayers. This increase is due solely to enhanced fluorescence from Pc 4, as confirmed by confocal spectroscopy. In EMT6 cells incubated with 250 nM Pc 4 for 24 h, the maximum increase in fluorescence is approximately 3.7-fold above baseline levels. This increase occurs over a range of fluences, 0.05-0.6 J cm(-2), where clonogenic survival decreases by 3 orders of magnitude. Light scattering measurements performed on similarly treated EMT6 cells in suspension suggested a Pc 4-PDT-mediated mitochondrial swelling of approximately 13% at 0.6 J cm(-2), where fluorescence enhancement saturates under these treatment conditions. Fluorescence imaging and light scattering experiments performed at a five-fold lower Pc 4 incubation concentration revealed a reduced fluorescence enhancement at a five-fold higher fluence, which produced comparable mitochondrial swelling. Taken together, these data suggest that Pc 4 is initially aggregated at high local concentration in mitochondria and that irradiation relaxes the quenching of Pc 4 fluorescence through a mechanism that may involve mitochondrial swelling.     

Near-infrared-emitting phthalocyanines. A combined experimental and density functional theory study of the structural, optical, and photophysical properties of Pd(II) and Pt(II) α-butoxyphthalocyanines

The structural, optical, and photophysical properties of 1,4,8,11,15,18,22,25-octabutoxyphthalocyaninato-palladium(II), PdPc(OBu)(8), and the newly synthesized platinum analogue PtPc(OBu)(8) are investigated combining X-ray crystallography, static and transient absorption spectroscopy, and relativistic zeroth-order regular approximation (ZORA) Density Functional Theory (DFT)/Time Dependent DFT (TDDFT) calculations where spin-orbit coupling (SOC) effects are explicitly considered. The results are compared to those previously reported for NiPc(OBu)(8) (J. Phys. Chem. A 2005, 109, 2078) in an effort to highlight the effect of the central metal on the structural and photophysical properties of the group 10 transition metal octabutoxyphthalocyanines. Different from the nickel analogue, PdPc(OBu)(8) and PtPc(OBu)(8) show a modest and irregular saddling distortion of the macrocycle, but share with the first member of the group similar UV-vis spectra, with the deep red and intense Q-band absorption experiencing a blue shift down the group, as observed in virtually all tetrapyrrolic complexes of this triad. The blue shift of the Q-band along the MPc(OBu)(8) (M = Ni, Pd, Pt) series is interpreted on the basis of the metal-induced electronic structure changes. Besides the intense deep red absorption, the title complexes exhibit a distinct near-infrared (NIR) absorption due to a transition to the double-group 1E (π,π*) state, which is dominated by the lowest single-group (3)E (π,π*) state. Unlike NiPc(OBu)(8), which is nonluminescent, PdPc(OBu)(8) and PtPc(OBu)(8) show both deep red fluorescence emission and NIR phosphorescence emission. Transient absorption experiments and relativistic spin-orbit TDDFT calculations consistently indicate that fluorescence and phosphorescence emissions occur from the S(1)(π,π*) and T(1)(π,π*) states, respectively, the latter being directly populated from the former, and the triplet state decays directly to the S(0) surface (the triplet lifetime in deaerated benzene solution was 3.04 μs for Pd and 0.55 μs for Pt). Owing to their triplet properties, PdPc(OBu)(8) and PtPc(OBu)(8) have potential for use in photodynamic therapy (PDT) and are potential candidates for NIR light emitting diodes or NIR emitting probes.     

Conducting Polymers: Partially Oxidized Bridge-Stacked Metallophthalocyanines

The synthesis and characterization of a novel class of polymeric phthalocyanines (Pc), (PcMX)_n (M-Al, Ga, Cr; X?F and M-Si, Ge, Sn; X?0) of exceptional thermal stability are summarized. These materials possess a linear MX backbone surrounded by a sheath of cofacial M-centered Pc rings.

(PcAlF)_n and (PcGaF)_n are sublimable (10^?3mmHg,540°C and 430°C, respectively) allowing for thin film formation. Iodine-doping leading to compositions (PcMXI_y)_n with y ranging from 0.06 to 5.5 is reported. Thermogravimetric analysis has proven useful for iodine analyses and has revealed that the order of thermal stability with regard to loss of iodine is (PcCrFI_y)_n < (PcGaFI_y)_n< (PcAlFI_y)_n

< (PcSioI_y)_n. Raman spectra point to I₃-and I₅-as the principle polyiodide species, though their relative proportions vary depending on M and doping level. Increases in the electrical conductivity by as much as 10⁹ with maximum conductivities in the range of 0.01–1 ohm^?1cm^?1 result from iodine doping. Conduction appears to be thermally activated (77–300K) with an apparent activation energy of 0.04eV. It is likely that electron transport is primarily ligand based and is metal-like in character.     

Time‐Resolved High and Low Temperature Phase Transitions of the Nanocrystalline Cubic Phase in the Y2O3‐ZrO2 and Fe2O3‐ZrO2 System

The nanocrystalline cubic Phase of zirconia was found to be thermally stabilized by the addition of 2.56 to 17.65 mol % Y₂O₃ (5.0 to 30.0 mol % Y, 95.0 to 70.0 mol % Zr cation content). The cubic phase of yttria stabilized zirconia was prepared by thermal decomposition of the hydroxides at 400°C for 1 hr. 2.56 mol % Y₂O₃‐ZrO₂ was stable up to 800°C in an argon atmosphere. The samples with 4.17 to 17.65 mol % Y₂O₃ were stable to 1200°C and higher. All samples at temperatures between 1450°C to 1700°C were cubic except the sample with 2.56 mol % Y₂O₃ which was tetragonal. The crystallite sizes observed for the cubic phase ranged from 50 to 150 Å at temperatures below 900°C and varied from 600 to 800 nm between 1450°C and 1700°C. Control of furnace atmosphere is the main factor for obtaining the cubic phase of Y‐SZ at higher temperature. Nanocrystalline cubic Fe‐SZ (Iron Stabilized Zirconia) with crystallite sizes from 70 to 137 Å was also prepared at 400°C. It transformed isothermally at temperatures above 800°C to the tetragonal Fe‐SZ and ultimately to the monoclinic phase at 900°C. The addition of up to 30 mol % Fe(III) thermally stabilized the cubic phase above 800°C in argon. Higher mol % resulted in a separation of Fe₂O₃. The nanocrystalline cubic Fe‐SZ containing a minimum 20 mol % Fe (III) was found to have the greatest thermal stability. The particle size was a primary factor in determining cubic or tetragonal formation. The oxidation state of Fe in zirconia remained Fe³⁺. Fe‐SZ lattice parameters and rate of particle growth were observed to decrease with higher iron content. The thermal stability of Fe‐SZ is comparable with that of Ca‐SZ, Mg‐SZ and Mn‐SZ prepared by this method.     

Effect of Soft Segment Molecular Weight and 3-Methyl Side Group on Microstructural Separation in Polyurethane Elastomers

Abstract

The object of this study was to assess the effect of the chain length and of the pendant 3-methyl side group in the soft segment of polyurethane (PU) elastomers. In addition, the effect of annealing-quenching on the degree of microstructural segregation between the hard and soft segments was also investigated. The study employed electron spin resonance (ESR), differential scanning calorimetry (DSC), and dynamic mechanical analysis (DMA). Samples for ESR measurements were spin-labeled with the nitroxide probe, 4-hydroxy-2,2′,6,6′-piperidine-1-oxyl (TEMPOL), by reaction of an isocyanate group with the hydroxyl group of TEMPOL. The nitroxide label is therefore located at a chain end. The PU's were based on 4,4′-diphenylmethane diisocyanate (MDI), poly(oxytetramethylene) glycols (PTMO), and hydroxyl-terminated random copolymers of tetrahydrofuran and 3-methyl-tetrahydrofuran (THF/Me-THF). Purified 1,4-butanediol (BD) was used as a chain extender. The elastomers made from higher molecular weight (MW) soft segments have better phase segregation than their lower MW counterparts. The 3-methyl side groups on the PTMO backbone have some effect on the arrangements of the two domains. ESR analysis indicated that the increase in the MW of THF/Me-THF decreased the degree of mixing between the hard and soft segments. In PU elastomers made from high MW soft segments, the presence of crystallinity was observed from the DSC measurements. The crystallinity of the soft segments was disrupted by the existence of the 3-methyl side groups.