We study in this work a competitive reaction model between monomers on a catalytic surface. The surface is represented by a square lattice and we consider the following reactions: A+A(B)→A2(AB), where A and B are two monomers that arrive at the surface with probabilities yA and yB, respectively. The model is studied in the adsorption controlled limit, and every time a monomer A or B lands on the surface it occupies a single empty site of the lattice. When a A monomer sits on the surface, it stays there unless it finds another A or B monomer. In this case the reaction occurs instantaneously leaving two new vacant sites on the lattice. The reactions between two A monomers and between A and B monomers are assumed to happen with the same probability. The model is studied in the site and pair mean-field approximations as well as through Monte Carlo simulations. We show that the model exhibits a continuous phase transition between an active and a B-absorbing state, when the parameter yA is varied through a critical value. Monte Carlo simulations and finite-size scaling analysis at the critical point are used to determine the critical exponents β, ν⊥, and ν∥. Our results seem to confirm that this reaction model is in the same universality class of the directed percolation in (2+1) dimensions.
We studied in this work a competitive reaction model between monomers on a catalyst. The catalyst is represented by hypercubic lattices in d = 1, 2 and 3 dimensions. The model is described by the following reactions: A + A → A2 and A + B → AB, where A and B are two monomers that arrive at the surface with probabilities y A and y B , respectively. The model is studied in the adsorption controlled limit where the reaction rate is infinitely larger than the adsorption rate. We employ site and pair mean-field approximations as well as static and dynamical Monte Carlo simulations. We show that, for all d, the model exhibits a continuous phase transition between an active steady state and a B-absorbing state, when the parameter y A is varied through a critical value. Monte Carlo simulations and finite-size scaling analysis near the critical point are used to determine the static critical exponents β, ν ⊥ and the dynamical critical exponents ν || , δ, η and z. The results found for this competitive reaction model are in accordance with the conjecture of Grassberger, which states that any system undergoing a continuous phase transition from an active steady state to a single absorbing state, exhibits the same critical behavior of the directed percolation universality class. I IntroductionIn the course of the last decade the statistical mechanics community has made great progress in the study of nonequilibrium phenomena. Until now, we do not have a complete theory accounting for the nonequilibrium systems. The fundamental concept of a Gibbsian distribution of states in equilibrium has no counterpart in the nonequilibrium situation. This happens because many of these systems do not present even an hamiltonian function and, if it is possible to define an hamiltonian, the detailed balance would be violated.Examples of recent problems on nonequilibrium processes include markets [1, 2], rain precipitation [3], sandpiles [4] and conserved contact process [5]. There is also a great interest in modeling interface growth [6,7], traffic flow [8], temperature dependent catalytic reactions [9], etc. Nonequilibrium magnetic systems, with a well defined hamiltonian, have been also studied in the context of nonequilibrium processes [10,11] as well.For the equilibrium systems we can induce phase transitions by changing some external parameters. Usually, the temperature is the selected control parameter to study phase transitions between equilibrium states. In the case of continuous phase transitions, at the critical point, long range correlations are established inside the system and a set of critical exponents can be defined to describe the critical behavior of some thermodynamic properties. The renormalization group theory [12] is a well known theory that allows the calculation of these critical exponents.We can also consider external constraints for the nonequilibrium systems that can drive the dynamical behavior of the system. The nature of the external parameter depends on the nature of the system. For instance, in an epidemic mode...
We studied the dynamical critical behavior of a recently proposed competitive reaction model between monomers on a catalytic surface [E. C. da Costa and W. Figueiredo, J. Chem. Phys. 117, 331 (2002)]. The surface is represented by a square lattice and we consider the following reactions: A+A(B)→A2(AB) where A and B are two monomers that arrive at surface with probabilities yA and yB=1−yA, respectively. The model is studied in the adsorption controlled limit by an epidemic analysis, where the initial condition is close to the absorbing state. We have determined the dynamic critical exponents of the model, which are related to the asymptotic behavior of the survival probability, number of empty sites (the order parameter) and mean square displacement from origin. These exponents agree with that of the directed percolation.
Enthalpy data were measured for mixtures of benzene and 1-propanol containing 0.250 and 0.480 mole fraction benzene. Data covered the range from 40 to 440 p.s.i.a. and 250°to 429c F. and included the critical region.In ORDER TO TEST and develop methods for predicting thermodynamic properties of polar systems experimental data are needed for both pure components and mixtures. A flow calorimeter developed earlier has been used to measure enthalpies of alcohols, ethers, and ketones (/) and binary mixtures of benzene with methanol (3), and with ethanol ( ), In continuation of this work, the present paper presents p-H data for the benzene-1propanol system. EXPERIMENTAL Range of Measurements. Measurements were carried out
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