Fisher's Droplet Research Articles

Global asymmetry of fluids and local singularity in the diameter of the coexistence curve

By combining a measurable vapor-liquid coexistence curve and the extended van der Waals-type of equation of state (EOS) with the additional temperature-dependent coefficient, the phenomenological model of global fluid asymmetry has been developed separately for both coexisting bulk phases in the entire range of subcritical states. It is shown, in particular, that the adequate description of a liquid branch and its near-critical vicinity in terms of appropriate critical exponents and amplitudes connected by the two-scale-factor universal interrelations can be achieved. The asymmetric influence of heterophase fluctuations on the criticality of gaseous states is demonstrated. It is inherently similar to the well-known Fisher's droplet model, which corresponds to the scaling EOS too. The principle of corresponding isotherms has been formulated without any adjustable parameters. An attempt to avoid the use of a locally singular coexistence-curve diameter is proposed in the framework of two alternative models. The accurate vapor-liquid data for two fluid metals, Rb and Cs, as well as two molecular fluids, C(2)H(6) and CO(2), are reanalyzed by the above models to confirm the presumed opportunity.

Determination of the coexistence curve, critical temperature, density, and pressure of bulk nuclear matter from fragment emission data

An analysis of six different sets of experimental data indicates that infinite, neutron-proton symmetric, neutral nuclear matter has a critical temperature of ${T}_{c}=17.9\ifmmode\pm\else\textpm\fi{}0.4$ MeV, a critical density of ${\ensuremath{\rho}}_{c}=0.06\ifmmode\pm\else\textpm\fi{}0.01$ nucleons/fm${}^{3}$, and a critical pressure of ${p}_{c}=0.31\ifmmode\pm\else\textpm\fi{}0.07$ MeV/fm${}^{3}$. These values have been obtained by analyzing data from six different reactions studied in three experiments: two ``compound nuclear'' reactions, ${}^{58}\mathrm{Ni}{+}^{12}\mathrm{C}{\ensuremath{\rightarrow}}^{70}$Se and ${}^{64}\mathrm{Ni}{+}^{12}\mathrm{C}{\ensuremath{\rightarrow}}^{76}$Se (both performed at the LBNL 88-in. cyclotron); and four ``multifragmentation'' reactions, 1 GeV/$c$ $\ensuremath{\pi}{+}^{197}$Au (performed by the Indiana Silicon Sphere Collaboration), 1 GeV/nucleon ${}^{197}\mathrm{Au}{+}^{12}$C, 1 GeV/nucleon ${}^{139}\mathrm{La}{+}^{12}$C, and 1 GeV/nucleon ${}^{84}\mathrm{Kr}{+}^{12}$C (all performed by the Equation of State Collaboration). The charge yields of all reactions as a function of the excitation energy were fit with a version of Fisher's droplet model modified to account for the dual components of the fluid (i.e., protons and neutrons), Coulomb effects, finite-size effects, and angular momentum arising from the nuclear collisions.

Nuclear matter phase diagram from compound nucleus decay

The finite size of nuclei and the Coulomb interaction make it di ffi cult to de- scribe systems interacting through the strong force into thermodynamic terms. Our task is to extract the phase diagram of the theoretical infinite symmetrical uncharged nuclear mat- ter from experiments of nuclear collisions where the systems are neither infinite, symmet- rical, nor uncharged. Decay yields from such experiments are translated into coexistence densities and pressures by use of Fisher's droplet model. This method is tested on model systems such as the Ising model and a system of particles interacting via the Lennard- Jones potential. The specific problems inherent to nuclear reactions are considered. These include finite size e ffects, Coulomb repulsion, and the lack of a physical vapor in contact with a decaying system. Experimental data of compound nucleus experiments are studied within this framework, which is also shown to extend to higher energy reactions. Finally, the phase diagram of nuclear matter is extracted.

Finite size scalings and the nuclear liquid-gas phase transition

Finite size effects on cluster distributions are investigated within Ising and Fisher's Droplet Model. Fixed magnetization calculations suggest that the introduction of a complement correction of the emitting system is a promising approach for finite size scalings.

Finite size scalings and the nuclear liquid-gas phase transition

Finite size effects on cluster distributions are investigated within Ising and Fisher's Droplet Model. Fixed magnetization calculations suggest that the introduction of a complement correction of the emitting system is a promising approach for finite size scalings.

Constructing the phase diagram of finite neutral nuclear matter

The fragment yields from the multifragmentation of gold, lanthanum and krypton nuclei obtained by the EOS Collaboration are examined in terms of Fisher's droplet formalism modifed to account for Coulomb energy. The critical exponents sigma and tau and the surface energy coefficient c0 are obtained. Estimates are made of the pressure-temperature and temperature-density coexistence curves of finite neutral nuclear matter as well as the location of the critical point.

Vapor Phase Homogeneous Nucleation of Higher Alkanes: Dodecane, Hexadecane, and Octadecane. 2. Corresponding States and Scaling Law Analysis

The results from corresponding states and scaled nucleation models indicate that the nucleation behavior of the normal alkanes follows a predictable trend. Systematic deviations from ideal fluid behavior can be correlated to physical properties, such as the increase in the entropy of vaporization and the increase in the excess surface entropy of the nucleating clusters. Hale's scaled nucleation model allows for the accurate prediction of nucleation threshold behavior for the alkanes. Experimental agreement with the model is maintained throughout the temperature range studied. The scaled model for the nucleation rate provides a better description of the experimental rates than the classical nucleation theory. The addition of extra terms to the classical expression of the free energy of cluster formation and the inclusion of the Fisher's droplet model term significantly compensate for the strong temperature dependence present in the flux prefactor of the classical rate equation. For accurate predictions of ...

Critical exponents of the statistical multifragmentation model

For the statistical multifragmentation model the critical indices $\alpha^\prime, \beta, \gamma^\prime, \delta$ are calculated as functions of the Fisher parameter $\tau$. It is found that these indices have different values than in Fisher's droplet model. Some peculiarities of the scaling relations are discussed. The basic model predicts for the index $\tau$ a narrow range of values, $1.799< \tau < 1.846$, which is consistent with two experiments on nuclear multifragmentation.

Quantum molecular dynamics simulation of expanding nuclear matter and nuclear multifragmentation

Multifragmentation resulting from an expanding nuclear matter is investigated on the basis of quantum molecular dynamics. In particular, the dependence of the fragment mass distribution on the initial temperature ${(T}_{\mathrm{init}})$ and the radial flow velocity $(h)$ is studied. When $h$ is large, the distribution shows exponential shape, whereas for small $h,$ it obeys the power law. Although the power law is what Fisher's droplet model predicts, the fragmentation mechanism in an expanding system is found to be different from the one in a thermally equilibrated system.

QMD simulation of expanding nuclear matter

We study the properties of dynamically expanding nuclear matter. For this purpose, we apply quantum molecular dynamics (QMD) model to homogeneously expanding three-dimensional system with periodic boundary condition. Simulation is performed for given initial temperatures and expanding velocities. The calculated fragment mass distribution for slow expansion obeys the power law predicted by Fisher's droplet model, while that for rapid expansion exhibits the exponential shape.

Signatures of critical phenomena in rare atom clusters

We study the occurrence of a critical behaviour related to a liquid-gas phase transition in an atomic cluster. In particular, we analyse some experimental possibilities to investigate the role of finite size effects on the phase behaviour. In mass distributions, conditional moments, as well as scaled factorial moments of fragment mass distributions we find evidence for the presence of critical behaviour. It can be connected, by the use of Fisher's droplet model and Campi analysis, to a liquid-gas phase transition.

Second order phase transitions: from infinite to finite systems

We investigate the Equation of State (EOS) of classical systems having 300 and 512 particles confined in a box with periodic boundary conditions. We show that such a system, independently on the number of particles investigated, has a critical density of about 1/3 the ground state density and a critical temperature of about $2.5~ MeV$. The mass distribution at the critical point exhibits a power law with $\tau = 2.23$. Making use of the grand partition function of Fisher's droplet model, we obtain an analytical EOS around the critical point in good agreement with the one extracted from the numerical simulations.

On Homogeneous Nucleation Theories from the Vapor Phase

Homogeneous nucleation theories from the vapor phase are revisited and recent semi-phenomenological models [1,2] based on Fisher's droplet model [3] for the Gibbs free energy of formation of a cluster are discussed. These models allow for the variation of surface tension with cluster size in addition to the contribution from translational, rotational, vibrational and configurational degrees of freedom of clusters. The resulting steady-state nucleation rate equations are derived and compared with expansion and diffusion cloud chamber experiments for a variety of substances (water, methanol, n-nonane, etc...). An overall good agreement is achieved for the range of temperatures investigated in contrast to comprasion with the classical Becker-D\"oring-Z'eldovich-Frenkel theory.

Critical evolution of a finite system.

In this work, we investigate the possibility of occurrence of a critical behavior related to a liquid-gas phase transition in a finite classical system. The equation of state of such a classical system resembles that of nuclear matter. Through a study of mass distributions, scaled factorial moments, anomalous fractal dimensions, and moments of cluster mass distributions, we find evidence for the presence of a critical behavior of our finite system. Such a critical behavior is connected, by the use of Fisher's droplet model and Campi analysis, to a liquid-gas phase transition.

Intermittency in the Fisher's droplet model

Intermittent behaviour of fragment multiplicity distributions in the nuclear liquid-gas phase transition is studied in terms of the droplet model of Fisher. The anomalous fractal dimensions are compared with data on heavy ion reactions and classical molecular dynamics simulations. A signature of the transition in the anomalous fractal dimensions is shown.

Influence of allowance for cluster interaction on scaling in Fisher's droplet model of phase transitions. The cluster fluctuation model

Influence of allowance for cluster interaction on scaling in Fisher's droplet model of phase transitions. The cluster fluctuation model

Sputtered cluster mass distributions, thermodynamic equilibrium and critical phenomena

The mass distribution of clusters, sputtered by keV atom or ion bombardment of a target surface, is investigated under the assumption that local thermodynamic equilibrium is established in part of the irradiated volume. When cooling down, that region may pass the liquid-gas coexistence curve and undergo a (non-equilibrium) phase transition. The resulting cluster mass distribution is described using Fisher's droplet model: The distribution decays exponentially with cluster mass, if chemical equilibrium between the liquid and the gas phase is not established; otherwise its decay is determined by the cluster surface free energy. Around the critical temperature T c , the mass distribution follows a power law with a power of − 7 3 . Experimentally measured mass distributions of clusters sputtered from condensed gas targets follow the power law valid at T c . Metal and alkali halide cluster mass distributions may be described, if the surface free energy is used as a fit parameter. Its value is small, indicating that the relevant temperature is slightly below T c . The relationship of the present approach to existing models is discussed.

Modified droplet model with mean droplet interaction for gases below Tc

Abstract Fisher's droplet model for gases below T c is modified to account for the mean field interaction between the droplets. The equations of state and the internal energies of Ar, H 2 O and O 2 are tested. Agreement with experiment for the equation of state is 99% and for the internal energy is above 95%.

Extension of fisher's droplet model for a gas above Tc and the metastable phase

Extension of fisher's droplet model for a gas above Tc and the metastable phase

A droplet model for ferromagnetic spin waves aboveTC

Fisher's droplet model is used to calculate the neutron-scattering cross section for spin waves in a ferromagnet above ${T}_{C}$. Predictions are made for the wave-vector dependence of cross section, and a neutron-scattering experiment is proposed to test these predictions.