Kinetics and mechanism of base hydrolysis of Reinecke's salt revisited – specific salt effects

The kinetics of base hydrolysis of the trans-[Cr(NH₃)₂(NCS)₄]^– anion follows the rate law: -d[complex]/dt = k ₀ + k ₁[OH^–] (50–70 °C, [OH^–] = 0.1–1.9 M and = 2.0 M). The specific salt effect has been investigated for eight aqueous media: NaCl, NaBr, NaI, NaClO₄, KCl, KBr, CsCl and CsBr. The alkali-independent path (k ₀) does not show any specific effect of inert electrolyte ions, the activation parameters: H = 113.5 ± 0.4 kJ mol^–1 and S = 24.1 ± 1.3 J mol^–1 K^–1 are interpreted in the frame of a dissociative interchange mechanism (I _d). For the alkali-dependent path (k ₁) the specific salt effect is observed for cations of the inert electrolyte, showing an important role for ion-pair formation between the cations and reagent complex anion in the activation process. A linear correlation between lnk ₁ and lnK ₀ (K ₀ – ion-pair formation constant) has been found for the cations studied. The dissociative, via conjugate base, mechanism (D _CB) has been proposed for the alkali-dependent path.     

Kinetics and mechanism of one dipicolinato ligand substitution in the chromium(III)–bis(dipicolinato) complex: an unusual rate dependence on acid concentration

The Na[Cr(PDA)₂] · 2H₂O complex (PDA¹ = dipicolinic acid anion) and its aquation product, [Cr(PDA)(H₂O)₃]⁺, were prepared and characterized. The electronic spectra demonstrate that the bis(dipicolinato) complex undergoes very fast partial dechelation during dissolution. In acidic media, pH controlled, rapid protolytic and ring opening processes lead to coexistence of complexes with one tridentate (PDA) and the other bi- or mono-dentate (PDA). The kinetics of PDA ligand liberation were followed spectrophotometrically within the 0.1–2.0 M HClO₄ range at I = 2.0 M. The observed first-order rate constant depends on [H⁺] according to the equation: k _obs = A[H⁺]/(1 + B[H⁺] + C[H⁺]²). A reaction course via the uncharged [Cr(PDA)(HPDA)(H₂O)₂]⁰ complex is proposed. The observed rate increase, followed by rate retardation with [H⁺] increase, is attributed to the unreactive [Cr(PDA)(H₂PDA)(H₂O)₂]⁺ complex. In terms of the proposed mechanism, A, B, C parameters have been defined as: A = k ₁ Q ₁, B = Q ₁, C = Q ₁ Q ₂ where k ₁ is the rate constant of the Cr^III-carboxylato oxygen bond-breaking in the monodentate HPDA ligand, Q ₁ is a composite value describing protolytic and dechelation processes and Q ₂ is the protonation constant of the uncharged [Cr(PDA)(HPDA)(H₂O)₂]⁰ complex.     

Integration of Langevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions

Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic part, the latter being performed by sampling exactly the solution of the associated Fokker-Planck equation. We demonstrate the computational power of this method by applying it to the most absorbing phase transitions for which Langevin equations have been proposed. This provides precise estimates of the associated scaling exponents, clarifying the classification of these nonequilibrium problems, and confirms or refutes some existing theories.     

Nonperturbative fixed point in a nonequilibrium phase transition

We apply the nonperturbative renormalization group method to a class of out-of-equilibrium phase transitions (usually called "parity-conserving" or, more properly, "generalized voter" class) which is out of the reach of perturbative approaches. We show the existence of a genuinely nonperturbative fixed point, i.e., a critical point that does not seem to be Gaussian in any dimension.     

Absorbing phase transitions of branching-annihilating random walks

The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA-->(m+k)A, nA-->(n-l)A are studied systematically in one space dimension within a new family of models. Four universality classes of nontrivial critical behavior are found. This provides, in particular, the first evidence of universal scaling laws for pair and triplet processes.     

On Potentially Graphical Sequences of G-E(H)

A loopless graph on n vertices in which vertices are connected at least by a and at most by b edges is called a(a,b,n)-graph. A(b,b,n)-graph is called(b,n)-graph and is denoted by K_n~b(it is a complete graph), its complement by K_n~b. A non increasing sequence π =(d_1,…,d_n) of nonnegative integers is said to be(a,b,n) graphic if it is realizable by an(a,b,n)-graph. We say a simple graphic sequence π=(d_1,…,d_n) is potentially K_4-K_2∪K_2-graphic if it has a a realization containing an K_4-K_2∪K_2 as a subgraph where K_4 is a complete graph on four vertices and K_2∪K_2 is a set of independent edges. In this paper, we find the smallest degree sum such that every n-term graphical sequence contains K_4-K_2∪K_2 as subgraph.     

Renormalization Group for Strongly Coupled Maps

Systems of strongly coupled chaotic maps generically exhibit collective behavior emerging out of extensive chaos. We show how the well-known renormalization group (RG) of unimodal maps can be extended to the coupled systems, and in particular to coupled map lattices (CMLs) with local diffusive coupling. The RG relation derived for CMLs is nonperturbative, i.e., not restricted to a particular class of configurations nor to some vanishingly small region of parameter space. After defining the strong-coupling limit in which the RG applies to almost all asymptotic solutions, we first present the simple case of coupled tent maps. We then turn to the general case of unimodal maps coupled by diffusive coupling operators satisfying basic properties, extending the formal approach developed by Collet and Eckmann for single maps. We finally discuss and illustrate the general consequences of the RG: CMLs are shown to share universal properties in the space-continuous limit which emerges naturally as the group is iterated. We prove that the scaling properly ties of the local map carry to the coupled systems, with an additional scaling factor of length scales implied by the synchronous updating of these dynamical systems. This explains various scaling laws and self-similar features previously observed numerically.