[show abstract][hide abstract] ABSTRACT: We present a brief survey of methods that utilize computer simulations and quantum and statistical mechanics in the analysis of electrochemical systems. The methods, Molecular Dynamics and Monte Carlo simulations and quantum-mechanical density-functional theory, are illustrated with examples from simulations of lithium-battery charging and electrochemical adsorption of bromine on single-crystal silver electrodes. Comment: 12 pages, 5 figures, Invited Book Chapter
[show abstract][hide abstract] ABSTRACT: The dynamics near first- and second-order phase transitions in a two-dimensional lattice-gas model are compared using the
first-order reversal curve (FORC) method. The FORC diagram of a first-order transition is characterized by a negative region
separating two positive regions, reflecting a competition between the time-varying electrochemical potential and the tendency
of the system to phase order.
[show abstract][hide abstract] ABSTRACT: The two-dimensional kinetic Ising model, when exposed to an oscillating applied magnetic field, has been shown to exhibit a nonequilibrium, second-order dynamic phase transition (DPT), whose order parameter Q is the period-averaged magnetization. It has been established that this DPT falls in the same universality class as the equilibrium phase transition in the two-dimensional Ising model in zero applied field. Here we study the scaling of the dynamic order parameter with respect to a nonzero, period-averaged, magnetic "bias" field, H(b) for a DPT produced by a square-wave applied field. We find evidence that the scaling exponent, delta(d), of H(b) at the critical period of the DPT is equal to the exponent for the critical isotherm, delta(e), in the equilibrium Ising model. This implies that H(b) is a significant component of the field conjugate to Q. A finite-size scaling analysis of the dynamic order parameter above the critical period provides further support for this result. We also demonstrate numerically that, for a range of periods and values of H(b) in the critical region, a fluctuation-dissipation relation (FDR), with an effective temperature T(eff)(T,P,H0) depending on the period, and possibly the temperature and field amplitude, holds for the variables Q and H(b). This FDR justifies the use of the scaled variance of Q as a proxy for the nonequilibrium susceptibility, partial differential Q/partial differential H(b), in the critical region.
[show abstract][hide abstract] ABSTRACT: A dynamic phase transition (DPT) with respect to the period P of an applied alternating magnetic field has been observed previously in numerical simulations of magnetic systems. However, experimental evidence for this DPT has thus far been limited to qualitative observations of hysteresis loop collapse in studies of hysteresis loop area scaling. Here, we present significantly stronger evidence for the experimental observation of this DPT, in a [Co(4 A)/Pt(7 A)]_3-multilayer system with strong perpendicular anisotropy. We applied an out-of-plane, time-varying (sawtooth) field to the [Co/Pt]_3 multilayer, in the presence of a small additional constant field, H_b. We then measured the resulting out-of-plane magnetization time series to produce nonequilibrium phase diagrams (NEPDs) of the cycle-averaged magnetization, Q, and its variance, Var(Q), as functions of P and H_b. The experimental NEPDs are found to strongly resemble those calculated from simulations of a kinetic Ising model under analagous conditions. The similarity of the experimental and simulated NEPDs, in particular the presence of a localized peak in the variance Var(Q) in the experimental results, constitutes strong evidence for the presence of this DPT in our magnetic multilayer samples. Technical challenges related to the hysteretic nature and response time of the electromagnet used to generate the time-varying applied field precluded us from extracting meaningful critical scaling exponents from the current data. However, based on our results, we propose refinements to the experimental procedure which could potentially enable the determination of critical exponents in the future. Comment: substantial revision; 26 pages, 9 figures; to appear in Phys. Rev. B
[show abstract][hide abstract] ABSTRACT: We propose a new, cyclic-voltammetry based experimental technique that can not only differentiate between discontinuous and continuous phase transitions in an adsorbate layer, but also quite accurately recover equilibrium behavior from dynamic analysis of systems with a continuous phase transition. The Electrochemical first-order reversal curve (EC-FORC) diagram for a discontinuous phase transition (nucleation and growth), such as occurs in underpotential deposition, is characterized by a negative region, while such a region does not exist for a continuous phase transition, such as occurs in the electrosorption of Br on Ag(100). Moreover, for systems with a continuous phase transition, the minima of the individual EC-FORCs trace the equilibrium curve, even at very high scan rates. Since obtaining experimental data for the EC-FORC method would require only a simple reprogramming of the potentiostat used in conventional cyclic-voltammetry experiments, we believe that this method has significant potential for easy, rapid, in-situ analysis of systems undergoing electrochemical deposition.
[show abstract][hide abstract] ABSTRACT: The first-order reversal curve (FORC) method for analysis of systems undergoing hysteresis is applied to dynamical models of electrochemical adsorption. In this setting, the method can not only differentiate between discontinuous and continuous phase transitions, but can also quite accurately recover equilibrium behavior from dynamic analysis for systems with a continuous phase transition. Discontinuous and continuous phase transitions in a two-dimensional lattice-gas model are compared using the FORC method. The FORC diagram for a discontinuous phase transition is characterized by a negative (unstable) region separating two positive (stable) regions, while such a negative region does not exist for continuous phase transitions. Experimental data for FORC analysis could easily be obtained by simple reprogramming of a potentiostat designed for cyclic-voltammetry experiments.
[show abstract][hide abstract] ABSTRACT: We propose a new experimental technique for cyclic voltammetry, based on the first-order reversal curve (FORC) method for analysis of systems undergoing hysteresis. The advantages of this electrochemical FORC (EC-FORC) technique are demonstrated by applying it to dynamical models of electrochemical adsorption. The method can not only differentiate between discontinuous and continuous phase transitions, but can also quite accurately recover equilibrium behavior from dynamic analysis of systems with a continuous phase transition. Experimental data for EC-FORC analysis could easily be obtained by simple reprogramming of a potentiostat designed for conventional cyclic-voltammetry experiments.
[show abstract][hide abstract] ABSTRACT: We present the first convincing evidence for an experimental observation of a Dynamic Phase Transition (DPT) in a magnetic system: an ultra-thin [Co(0.4nm)/Pt(0.7nm)]3 multilayer, which is well modeled by a two-dimensional kinetic Ising system. This DPT, as a function of the period P of an applied alternating magnetic field, has been observed previously in simulations of magnetic systems . For several values of P and bias field Hb, the magnetization was measured for 50 cycles of the field . The order parameter, which was identified in simulations as the magnetization averaged over the ith cycle, Qi, was obtained from the experimental data as a time series. Kinetic Monte Carlo simulations produced close agreement with the experimental data for the order parameter averaged over the final 30 cycles, , as a function of P and Hb. The experimental fluctuations in the order parameter are also consistent with a DPT.  S.W. Sides, P.A. Rikvold, and M.A. Novotny, Phys. Rev. Lett. 59, 2710 (1999).  D.T. Robb, Y.H. Xu, O. Hellwig, A. Berger, M.A. Novotny, and P.A. Rikvold, submitted to PRL.
[show abstract][hide abstract] ABSTRACT: The dynamic phase transition (DPT), observed in numerical simulations of magnetic systems [1,2], manifests itself by the spontaneous occurrence of a non-vanishing period-averaged magnetization (the order parameter Q) when the frequency f of an applied alternating magnetic field exceeds a critical value fc. Near fc, the DPT shows all common characteristics of a second-order phase transition. Our experimental studies of ultrathin Co/Pt-multilayers provide the first strong experimental evidence of a DPT. The multilayer structure results in perpendicular anisotropy and negligible demagnetizing effects . We measure out-of-plane magnetization time series by the polar-Kerr effect as a function of f and an applied bias field Hb, observing a sharp increase in Q as f is increased above fc. In addition, we see sharp switching of Q as Hb is changed from positive to negative values. The data sets allow the assembly of an experimental phase diagram. Detailed comparison with simulations of a kinetic Ising model provides strong evidence that our data represent the first unequivocal experimental observation of the DPT.  S.W. Sides et al., Phys. Rev. Lett. 81, 834 (1998)  B. Chakrabarti and M. Acharyya, Rev. Mod. Phys. 71, 847 (1999)  Y.Yafet and E.M. Gyorgy, Phys. Rev. B 38, 9145 (1988).
[show abstract][hide abstract] ABSTRACT: We examine different models and methods for studying finite-temperature magnetic hysteresis in nanoparticles and ultrathin films. This includes micromagnetic results for the hysteresis of a single magnetic nanoparticle which is misaligned with respect to the magnetic field. We present results from both a representation of the particle as a one-dimensional array of magnetic rotors, and from full micromagnetic simulations. The results are compared with the Stoner-Wohlfarth model. Results of kinetic Monte Carlo simulations of ultrathin films are also presented. In addition, we discuss other topics of current interest in the modeling of magnetic hysteresis in nanostructures, including kinetic Monte Carlo simulations of dynamic phase transitions and First-Order Reversal Curves.