“Modified” phase equilibria

Summary The Authors examine first and second order phase equilibria for classical bodies in the sense of Toupin and Truesdell[9], by assuming a partial equality between the intensive thermal substates of the two phases.In the case of first order equilibria, a system of partial differential equations for the equilibrium manifold is proposed. This system, which reduces to the generalized Clapeyron equations on the assumption of complete equality of the intensive variables[13], is shown to be always integrable.In the case of second order equilibria, a similar modification of the generalized Ehrenfest equations[14] is proved. A straight-forward derivation of the integrability conditions for the system of partial differential equations is given.

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Sommario Gli Autori esaminano gli equilibri di fase del primo e del secondo ordine per corpi classici nel senso di Toupin and Truesdell[9], nella ipotesi di eguaglianza parziale dei sottostati termici intensivi delle due fasi.Nel caso di equilibri del primo ordine gli Autori deducono un sistema di equazioni alle derivate parziali per la varietà di equilibrio, estendendo le equazioni di Clapeyron generalizzate relative agli equilibri di fase con completa eguaglianza delle variabili intensive[13]. Vengono ricavate e discusse le condizioni di integrabilità del sistema.Per gli equilibri del secondo ordine, gli Autori pervengono ad un sistema di equazioni che estende le equazioni di Ehrenfest generalizzate, perchè rimuovono l'ipotesi di totale eguaglianza delle variabili intensive[14]. Anche di questo sistema vengono ricavate le condizioni di integrabilità.

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Work supported by the Gruppo Nazionale per la Fisica Matematica, C.N.R.     

Parahydrogen studies of H2 addition to Ir(I) complexes containing chiral phosphine-thioether ligands: implications for catalysis

Ir(CO)[CpFe{eta5-C5H3(PPh2)CH2SR}]Cl [R = Ph and (t)Bu], containing a kappa2:P,S ligand, undergoes H2 addition across the S-Ir-CO axis under kinetic control to form two distinct diastereoisomeric products, which then rearrange via S dissociation in a process that can be hijacked for useful catalysis, but ultimately form a single diastereoisomer of the thermodynamic product where the hydride ligands are trans to chloride and phosphine.     

Sonic Hyperbolic Phase Transitions and Chapman-Jouguet Detonations

We prove that the Cauchy problem for an n×n system of strictly hyperbolic conservation laws in one space dimension admits a weak global solution also in presence of sonic phase boundaries. Applications to Chapman-Jouguet detonations, liquid-vapor transitions and elastodynamics are considered.     

The asymmetric contact process on a finite set

The contact process onZ has one phase transition; let _c be the critical value at which the transition occurs. Let _N be the extinction time of the contact process on {0,...,N}. Durrett and Liu (1988), Durrett and Schonmann (1988), and Durrett, Schonmann, and Tanaka (1989) have respectively proved that the subcritical, supercritical, and critical phases can be characterized using a large finite system (instead ofZ) in the following way. There are constants ₁() and ₂() such that if < _c , lim _{N N} /logN = 1/₁(); if > _c , lim _N log _N /N = ₂(); if = _c , lim _{N N} /N= and lim _{N N} /N ⁴=0 in probability. In this paper we consider the asymmetric contact process onZ when it has two distinct critical values _c1< _c2. The arguments of Durrett and Liu and of Durrett and Schonmann hold for < _c1 and > _c2. We show that for [ _c1< _c2), lim _{N N} /N=-1/, (where _i is an edge speed) and for = _c2, lim _N log _N /logN=2 in probability.     

An Experimental and Mechanistic Investigation of the Complexities Arising During Inhibition of the Briggs?Rauscher Reaction by Antioxidants

A method to determine the relative antioxidant capacity of radical scavengers based on the inhibition of the oscillations of the Briggs? Rauscher (BR) oscillating reaction was previously reported. A semiquantitative mechanistic interpretation of the inhibitory effects required two steps to obtain simulated inhibition times in very good agreement with the experimental ones. The first step is inhibitory, involving H‐atom transfer from antioxidant to the HOO^. radical; the second step is a first‐order degradation of the antioxidant to unspecified products. Since the degradation may be due to oxidation and/or iodination of the antioxidant, we studied the kinetics of the subsystems IO (H⁺)+antioxidant and I₂(H⁺)+antioxidant. We used 2,5‐ and 2,6‐dihydroxybenzoic acids, caffeic acid (=3‐(3,4‐dihydroxyphenyl)prop‐2‐enoic acid), ferulic acid (=3‐(4‐hydroxy‐3‐methoxyphenyl)prop‐2‐enoic acid), pyrocatechol (=benzene‐1,2‐diol), and hydroquinone (=benzene‐1,4‐diol) as antioxidants. Spectra in the wavelength range 500–250 nm were repeated at given time intervals to follow the peaks of the iodine and oxidation products, which were mainly quinones. For the iodination of the above diphenols (=benzenediol derivatives) the substitution and/or addition reactions with I₂ or HOI were found to be relatively slow compared to oxidation by IO . Approximate rate constants for oxidation were obtained on the basis of a reasonable kinetic model by using a suitable numerical integration program. Although these complexities can arise also in the completely inhibited BR oscillator, we believe that the inhibitory effects are due to the HOO^. scavenging action by diphenols or by quinones since HOO^. radicals are also potential reducing agents. We propose two steps that could maintain a small reservoir of diphenol, while both quinone and diphenol deplete HOO^. radicals. In short, the complexities do not affect the method for monitoring the relative activity of antioxidants based on the BR oscillating reaction. The effects of temperature on the inverse of the oscillatory time in the BR‐uninhibited system, on the inverse of inhibition times, and on the time length of the resumed oscillations for four antioxidants were also investigated. Apparent average activation energies were obtained.     

The radical trap in atom transfer radical polymerization need not be thermodynamically stable. A study of the MoX(3)(PMe(3))(3) catalysts

The molybdenum(III) coordination complexes MoX(3)(PMe(3))(3) (X = Cl, Br, and I) are capable of controlling styrene polymerization under typical atom transfer radical polymerization (ATRP) conditions, in conjunction with 2-bromoethylbenzene (BEB) as an initiator. The process is accelerated by the presence of Al(OPr(i))(3) as a cocatalyst. Electrochemical and synthetic studies aimed at identifying the nature of the spin trap have been carried out. The cyclic voltammogram of MoX(3)(PMe(3))(3) (X = Cl, Br, I) shows partial reversibility (increasing in the order Cl < Br < I) for the one-electron oxidation wave. Addition of X(-) changes the voltammogram, indicating the formation of MoX(4)(PMe(3))(3) for X = Cl and Br. On the other hand, I(-) is more easily oxidized than the MoI(3)(PMe(3))(3) complex; thus, the putative MoI(4)(PMe(3))(3) complex is redox unstable. Electrochemical studies of MoI(3)(PMe(3))(3) in the presence of X(-) (X = Cl or Br) reveal the occurrence of facile halide-exchange processes, leading to the conclusion that the MoI(3)X(PMe(3))(3) products are also redox unstable. The oxidation of MoX(3)(PMe(3))(3) with (1)/(2)Br(2) yields MoX(3)Br(PMe(3))(3) (X = Cl, Br), whose molecular nature is confirmed by single-crystal X-ray analyses. On the other hand, the oxidation of MoI(3)(PMe(3))(3) by I(2) slowly yields a tetraiodomolybdate(III) salt of iodotrimethylphosphonium, [Me(3)PI][MoI(4)(PMe(3))(3)], as confirmed by an X-ray study. This product has no controlling ability in radical polymerization. The redox instability of MoI(3)X(PMe(3))(3) can be reconciled with its involvement as a radical trapping species in the MoI(3)(PMe(3))(3)-catalyzed ATRP, given the second-order nature of its decomposition rate.     

Controlled radical polymerization of alkyl acrylates and styrene using a half-sandwich molybdenum(III) complex containing diazadiene ligands

The half-sandwich molybdenum(III) complex CpMoCl₂(ⁱPr₂-dad) (ⁱPr₂-dad=ⁱPr-NCH-CHN-ⁱPr) proved to be an effective metal catalyst for the controlled radical polymerization of methyl acrylate, butyl acrylate, and styrene. In conjunction with an alkyl iodide [R-I: CH₃CH(COOEt)I] as an initiator and in the presence or absence of Al(O-i-Pr)₃ as a co-catalyst, the molybdenum-based system gave polymers with narrow molecular weight distributions. The in situ addition of styrene to a macroinitiator of poly(methylacrylate) afforded an AB-type block copolymer.