Kinetic theory for a simple modeling of phase transition: Dynamics out of local equilibrium

This is a continuation of the previous work (Takata & Noguchi, J. Stat. Phys., 2018) that introduces the presumably simplest model of kinetic theory for phase transition. Here, main concern is to clarify the stability of uniform equilibrium states in the kinetic regime, rather than that in the continuum limit. It is found by the linear stability analysis that the linear neutral curve is invariant with respect to the Knudsen number, though the transition process is dependent on the Knudsen number. In addition, numerical computations of the (nonlinear) kinetic model are performed to investigate the transition processes in detail. Numerical results show that (unexpected) incomplete transitions may happen as well as clear phase transitions.Comment: 21 pages, 7 figure

Bis(2,2′-bipyridine){ethyl 4′-[N-(4-carbamoylphen­yl)carbamo­yl]-2,2′-bi­pyridine-4-carboxyl­ate}ruthenium(II) bis­[hexa­fluorido­phosphate(V)]

In the title compound, [Ru(C10H8N2)2(C21H18N4O4)](PF6)2, the RuII complex cation reveals a slightly distorted octa­hedral coordination. The coordination bonds of the 4,4′-substituted bipyridyl donors [Ru—N = 2.038 (3) and 2.051 (3) Å] are shorter than those of the 2,2′-bipyridyl donors [Ru—N1 = 2.065 (3)–2.077 (3) Å], due to the electron-withdrawing effects of the substituents at the 4,4′-positions. The angles between the pyridyl planes of the three bipyridyl ligands are 1.5 (2), 6.3 (3) and 8.7 (2)°, respectively. The cations are connected by anions via N—H⋯F inter­actions

Fabrication of Three-Layer-Component Organoclay Hybrid Films with Reverse Deposition Orders by a Modified Langmuir–Schaefer Technique and Their Pyroelectric Currents Measured by a Noncontact Method

In an aqueous clay mineral (montmorillonite) dispersion at a low concentration, isolated clay nanosheets with negative charges were suspended. When a solution of amphiphilic octadecylammonium chloride (ODAH⁺Cl^–) was spread on an air-dispersion interface, the clay nanosheets were adsorbed on the ODAH⁺ cations at the interface to form a stable ultrathin floating film. The floating film was transferred onto a substrate by the Schaefer method, and then the film was immersed in a [Ru­(dpp)₃]­Cl₂ (dpp = 4,7-diphenyl-1,10-phenanthroline) solution. The Ru­(II) complex cations were adsorbed on the film surface because the film surface possessed a cation-exchange ability. The layers of ODAH⁺, clay nanosheets, and [Ru­(dpp)₃]²⁺ were deposited in this order. By repeating these procedures, three-layer-component films were fabricated (OCR films). In a similar way, three-layer-component films in which the layers of [Ru­(dpp)₃]²⁺, clay nanosheets, and ODAH⁺ were deposited in the reverse order (RCO films) were prepared by spreading a [Ru­(dpp)₃]­(ClO₄)₂ solution and immersing the films in an ODAH⁺Cl^– solution. Both OCR and RCO films were characterized by surface pressure–molecular area (π–<i>A</i>) curve measurements, IR and visible spectroscopy, and the XRD method. The OCR and RCO film systems possessed nearly the same properties in the densities of ODAH⁺ and [Ru­(dpp)₃]²⁺ and the tilt angle of the Ru­(II) complex cation, although the layer distance for the RCO film was a little longer than that for the OCR film and the layered structure for the RCO film was less ordered than that for the OCR film. Pyroelectric currents for the films were measured by a noncontact method using an ²⁴¹Am radioactive electrode. When the films were heated, the pyroelectric currents were observed and the current directions for the OCR and RCO films were different. This was clear evidence that the layer order in the OCR film was reverse of that in the RCO film

New Series of Dinuclear Ruthenium(II) Complexes Synthesized Using Photoisomerization for Efficient Water Oxidation Catalysis

A new series of <i>proximal,proximal</i>-[Ru₂(tpy)₂(L)­XY]^<i>n</i>+ (<i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>XY</b>, tpy = 2,2′:6′,2″-terpyridine, L = 5-phenyl-2,8-di­(2-pyridyl)-1,9,10-anthyridine, X and Y = other coordination sites) were synthesized using photoisomerization of a mononuclear complex. The <i>p</i>,<i>p</i><b>-Ru</b>_<b>2</b><b>XY</b> complexes undergo unusual reversible bridge-exchange reactions to generate <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(μ-Cl)</b>, <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(μ-OH)</b>, and <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b> with μ-Cl, μ-OH, as well as hydroxo and aquo ligands at X and Y sites of <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>XY</b>, respectively. The geometric and electronic structures of these complexes were characterized based on UV–vis and ¹H NMR spectra, X-ray crystallography, and density functional theory (DFT) calculations. ¹H NMR data showed <i>C</i>₂ symmetry of <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b>) with the distorted L chelate and nonequivalence of two tpy ligands, in contrast to the <i>C</i>_2<i>v</i> symmetry of <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(μ-Cl)</b> and <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(μ-OH)</b>. However, irrespective of the lower symmetry, <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b> is predominantly formed in neutral and weakly basic conditions due to the specially stabilized core structure by multiple hydrogen-bond interactions among aquo, hydroxo, and backbone L ligands. The electrochemical data suggested that <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b> (Ru^II–OH:Ru^II–OH₂) is oxidized to the Ru^III–OH:Ru^III–OH state at 0.64 V vs saturated calomel electrode (SCE) and further to Ru^IVO:Ru^IVOH at 0.79 V by successive 1-proton-coupled 2-electron processes at pH 7.0. The cyclic voltammogram data exhibited that the <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b> complex works more efficiently for electrocatalytic water oxidation, compared with a similar mononuclear complex <i>distal-</i>[Ru­(tpy)­(L)­OH₂]²⁺ (<i>d-</i><b>RuOH</b>_<b>2</b>) and <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(μ-Cl)</b> and <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(μ-OH)</b>, showing that the <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b> core structure with aquo and hydroxo ligands is important for efficient electrocatalytic water oxidation. Bulk electrolysis of the <i>p</i>,<i>p</i>-<b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b> solution corroborated the electrocatalytic cycle involving the Ru^III–OH:Ru^III–OH state species as a resting state. The mechanistic insight into O–O bond formation for O₂ production was provided by the isotope effect on electrocatalytic water oxidation by <i>p,p</i>-<b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b> and <i>d-</i><b>RuOH</b>_<b>2</b> in H₂O and D₂O media

Binding of Stimuli-Responsive Ruthenium Aqua Complexes with 9‑Ethylguanine

Stimuli-responsive ruthenium complexes proximal- and distal-[Ru(C10tpy)(C10pyqu) OH2]2+ (proximal-1 and distal-1; C10tpy = 4′-decyloxy-2,2′:6′,2″-terpyridine and C10pyqu = 2-[2′-(6′-decyloxy)-pyridyl]quinoline) were experimentally studied for adduct formation with a model DNA base. At 303 K, proximal-1 exhibited 1:1 adduct formation with 9-ethylguanine (9-EtG) to yield proximal-[Ru(C10tpy)(C10pyqu)(9-EtG)]2+ (proximal-RuEtG). Rotation of the guanine ligand on the ruthenium center was sterically hindered by the presence of an adjacent quinoline moiety at 303 K. Results from 1H NMR measurements indicated that photoirradiation of a proximal-RuEtG solution caused photoisomerization to distal-RuEtG, whereas heating of proximal-RuEtG caused ligand substitution to proximal-1. The distal isomer of the aqua complex, distal-1, was observed to slowly revert to proximal-1 at 303 K. In the presence of 9-EtG, distal-1 underwent thermal back-isomerization to proximal-1 and adduct formation to distal-RuEtG. Kinetic analysis of 1H NMR measurements showed that adduct formation between proximal-1 and 9-EtG was 8-fold faster than that between distal-1 and 9-EtG. This difference may be attributed to intramolecular hydrogen bonding and steric repulsion between the aqua ligand and the pendant moiety of the bidentate ligand.

Mechanisms of Photoisomerization and Water-Oxidation Catalysis of Mononuclear Ruthenium(II) Monoaquo Complexes

A ligation of Ru­(tpy)­Cl₃ (tpy = 2,2′:6′,2″-terpyridine) with 2-(2-pyridyl)-1,8-naphthyridine) (pynp) in the presence of LiCl gave <i>distal</i>-[Ru­(tpy)­(pynp)­Cl]⁺ (<i>d</i>-<b>1Cl</b>) selectively, whereas the ligation gave <i>proximal</i>-[Ru­(tpy)­(pynp)­OH₂]²⁺ (<i>p</i>-<b>1H</b>_<b>2</b><b>O</b>) selectively in the absence of halide ions. (The proximal/distal isomers were defined by the structural configuration between the 1,8-naphthyridine moiety and the aquo or chloro ligand.) An aquation reaction of <i>d</i>-<b>1Cl</b> quantitatively afforded <i>distal</i>-[Ru­(tpy)­(pynp)­OH₂]²⁺ (<i>d</i>-<b>1H</b>_<b>2</b><b>O</b>) in water, and <i>d</i>-<b>1H</b>_<b>2</b><b>O</b> is quantitatively photoisomerized to <i>p</i>-<b>1H</b>_<b>2</b><b>O</b>. The mechanism of the photoisomerization was investigated by transient absorption spectroscopy and quantum chemical calculations. The temperature dependence of the transient absorption spectral change suggests existence of the thermally activated process from the ³MLCT state with the activation energy (Δ<i>E</i> = 49 kJ mol^–1), which is close to that (41.7 kJ mol^–1) of the overall photoisomerization reaction. However, quantum chemical calculations suggest another activation process involving the conformational change of the pentacoordinated distal structure to the proximal structure. Quantum chemical calculations provide redox potentials and p<i>K</i>_a values for proton-coupled electron transfer reactions from Ru^II–OH₂ to Ru^IVO in good agreement with experiments and provide an explanation for mechanistic differences between <i>d</i>-<b>1H</b>_<b>2</b><b>O</b> and <i>p</i>-<b>1H</b>_<b>2</b><b>O</b> with respect to water oxidation. The calculations show that water nucleophilic attack (WNA) on <i>d</i>-<b>[Ru</b>^<b>V</b><b>–O]</b>^<b>3+</b> (the ruthenyl oxo species derived from <i>d</i>-<b>1H</b>_<b>2</b><b>O</b>, calculated Δ<i>G</i>^⧧ of 87.9 kJ/mol) is favored over <i>p</i>-<b>[Ru</b>^<b>V</b><b>–O]</b>^<b>3+</b> (calculated Δ<i>G</i>^⧧ of 104.6 kJ/mol) for O–O bond formation. Examination of the lowest unoccupied molecular orbitals in <i>d</i>- and <i>p</i>-<b>[Ru</b>^<b>V</b><b>–O]</b>^<b>3+</b> indicates that more orbital amplitude is concentrated on the [Ru–O] unit in the case of <i>d</i>-<b>[Ru</b>^<b>V</b><b>–O]</b>^<b>3+</b> than in the case of <i>p</i>-<b>[Ru</b>^<b>V</b><b>–O]</b>^<b>3+</b>, where some of the amplitude is instead delocalized over the pynp ligand, making this isomer less electrophilic

Mechanistic Insight into Reversible Core Structural Changes of Dinuclear μ‑Hydroxoruthenium(II) Complexes with a 2,8-Di-2-pyridyl-1,9,10-anthyridine Backbone Prior to Water Oxidation Catalysis

<i>proximal,proximal</i>-(<i>p</i>,<i>p</i>)-[Ru^II₂(tpy)₂LXY]^<i>n</i>+ (tpy = 2,2′;6′,2″-terpyridine, L = 5-phenyl-2,8-di-2-pyridyl-1,9,10-anthyridine, and X and Y = other coordination sites) yields the structurally and functionally unusual Ru^II(μ-OH)­Ru^II core, which is capable of catalyzing water oxidation with key water insertion to the core (<i>Inorg. Chem.</i> <b>2015</b>, <i>54</i>, 7627). Herein, we studied a sequence of bridging-ligand substitution among <i>p</i>,<i>p</i>-[Ru₂(tpy)₂L­(μ-Cl)]³⁺ (<b>Ru</b>_<b>2</b><b>(μ-Cl)</b>), <i>p</i>,<i>p</i>-[Ru₂(tpy)₂L­(μ-OH)]³⁺ (<b>Ru</b>_<b>2</b><b>(μ-OH)</b>), <i>p</i>,<i>p</i>-[Ru₂(tpy)₂L­(OH)­(OH₂)]³⁺ (<b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b>), and <i>p</i>,<i>p</i>-[Ru₂(tpy)₂L­(OH)₂]²⁺ (<b>Ru</b>_<b>2</b><b>(OH)</b>_<b>2</b>) in aqueous solution. <b>Ru</b>_<b>2</b><b>(μ-Cl)</b> converted slowly (10^–4 s^–1) to <b>Ru</b>_<b>2</b><b>(μ-OH)</b>, and further <b>Ru</b>_<b>2</b><b>(μ-OH)</b> converted very slowly (10^–6 s^–1) to <b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b> by the insertion of water to reach equilibrium at pH 8.5–12.3. On the basis of density functional theory (DFT) calculations, <b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b> was predicted to be thermodynamically stable by 13.3 kJ mol^–1 in water compared to <b>Ru</b>_<b>2</b><b>(μ-OH)</b> because of the specially stabilized core structure by multiple hydrogen-bonding interactions involving aquo, hydroxo, and L backbone ligands. The observed rate from <b>Ru</b>_<b>2</b><b>(μ-OH)</b> to <b>Ru</b>_<b>2</b><b>(OH)</b>_<b>2</b> by the insertion of an OH^– ion increased linearly with an increase in the OH^– concentration from 10 to 100 mM. The water insertion to the core is very slow (∼10^–6 s^–1) in aqueous solution at pH 8.5–12.3, whereas the insertion of OH^– ions is accelerated (10^–5–10^–4 s^–1) above pH 13.4 by 2 orders of magnitude. The kinetic data including activation parameters suggest that the associative mechanism for the insertion of water to the Ru^II(μ-OH)­Ru^II core of <b>Ru</b>_<b>2</b><b>(μ-OH)</b> at pH 8.5–12.3 alters the interchange mechanism for the insertion of an OH^– ion to the core above pH 13.4 because of relatively stronger nucleophilic attack of OH^– ions. The hypothesized <i>p</i>,<i>p</i>-[Ru₂(tpy)₂L­(μ-OH₂)]⁴⁺ and <i>p</i>,<i>p</i>-[Ru₂(tpy)₂L­(OH₂)₂]⁴⁺ formed by protonation from <b>Ru</b>_<b>2</b><b>(μ-OH)</b> and <b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b> were predicted to be unstable by 71.3 and 112.4 kJ mol^–1 compared to <b>Ru</b>_<b>2</b><b>(μ-OH)</b> and <b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b>, respectively. The reverse reactions of <b>Ru</b>_<b>2</b><b>(μ-OH)</b>, <b>Ru</b>_<b>2</b><b>(OH)­(OH</b>_<b>2</b><b>)</b>, and <b>Ru</b>_<b>2</b><b>(OH)</b>_<b>2</b> to <b>Ru</b>_<b>2</b><b>(μ-Cl)</b> below pH 5 could be caused by lowering the core charge by protonation of the μ-OH^– or OH^– ligand