Remarks on Negative Heat Capacities of Clusters

Berry, R. Stephen

doi:10.1560/vc0e-9ad7-0duk-nx66

Cited by 12 publications

(10 citation statements)

References 28 publications

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“…37 The one, well-known, exception occurs in the vicinity of phase transitions, a phenomenon we shall encounter when we apply these ideas to liquids. 38 The other kind of problem we want to touch on briefly is that of a fluid of hardspheres.…”

Section: The Statistical Thermodynamics Of the Potential Energy Lmentioning

confidence: 99%

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Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble

Wang

Stratt

2007

The Journal of Chemical Physics

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In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move -an observation that suggests that the essentials of the dynamics ought to be determined by the geometry of those landscapes. But what are the principal geometric features that control the long-time dynamics? We suggest that the key lies not in the local minima and saddles of the landscape, but in a more global property of the surface: its accessible pathways. In order to make this notion more precise we introduce two ideas: (1) a switch to a new ensemble that removes the concept of potential barriers from the problem, and (2) a way of finding optimum pathways within this new ensemble. The potential energy landscape ensemble, which we describe in the current paper, regards the maximum accessible potential energy, rather than the temperature, as a control variable.We show here that while this approach is thermodynamically equivalent to the canonical ensemble, it not only sidesteps the idea of barriers, it allows us to be quantitative about the connectivity of a landscape. We illustrate these ideas with calculations on a simple atomic liquid and on the Kob-Andersen model of a glass-forming liquid, showing, in the process, that the landscape of the Kob-Anderson model appears to have a connectivity transition at the landscape energy associated with its mode-coupling transition. We turn to the problem of finding the most efficient pathways through potential energy landscapes in our companion paper.3

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Section: The Statistical Thermodynamics Of the Potential Energy Lmentioning

confidence: 99%

“…For finite systems quite generally, one can find other, still different, routes to obtaining energy/temperature relationships, but they all tend to give identical results in the thermodynamic limit. 37 The one, well-known, exception occurs in the vicinity of phase transitions, a phenomenon we shall encounter when we apply these ideas to liquids.…”

Section: 13)mentioning

confidence: 99%

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble

Wang

Stratt

2007

The Journal of Chemical Physics

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“…With these particular clusters, the density of states in the liquid region increases rapidly, in fact so much more rapidly with energy than the density of states in the solid region, that a small increase in total energy puts many more clusters in the region of the cold liquid. The result is that the mean kinetic energy and corresponding effective temperature drop when the total energy increases [85]. How can two (or more) phases be observable over a range of temperatures and pressures, as the simulations of clusters clearly show?…”

Section: Coexistence Caloric Curves and Heat Capacitiesmentioning

confidence: 99%

Insights into phase transitions from phase changes of clusters

Proykova¹,

Berry²

2006

J. Phys. B: At. Mol. Opt. Phys.

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The phases and phase transitions of bulk matter differ in several important ways from the phases or phase-like forms of small systems, notably atomic and molecular clusters. However, understanding those differences gives insights into the nature of bulk transitions, as well as into understanding the behaviour of the small systems. Small systems exhibit dynamic phase equilibria, large fluctuations and size-dependent behaviour in ways one cannot see with macroscopic systems. The Gibbs phase rule loses its applicability, the distinction between first-order and second-order transitions reveals a size dependence, and one can see phases in equilibrium (as minority populations) that are never the most stable thermodynamically. Introduction: phases of clusters and of macroscopic systemsThis review addresses the relations between phases and phase changes exhibited by bulk, macroscopic systems and their counterparts in small systems, atomic and molecular clusters and nanoscale particles. The differences between the phase behaviour of bulk matter and of clusters can, for the most part, be attributed to two factors. The more important is the enormous free energy differences between phases of bulk matter, which make only the most favoured phase observable, compared with the small free energy differences for clusters, which make less favoured phases nearly as observable as more favoured or most favoured phases [1]. The other is the relative contribution of the surface in a macroscopic and a small system. In a d-dimensional system containing N atoms, approximately N (d−1)/d of atoms will be on the surface; for large N the relative fraction N −1/d is very small and the surface effects on the bulk properties of the system are commonly neglected. In contrast, a high proportion of atoms or molecules are in surface layers of clusters which makes the surface as important for many cluster properties as the interior part is. In the spherical approximation used above to estimate the surface contribution one finds that about one half of the particles are on the surface of a cluster containing 500 particles. Because the ratio of surface area to bulk is large for small

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“…The key to theoretically reconcile these results with the thermodynamics was addressed by Thirring and coworkers: A system may display negative heat capacity, even in the thermodynamics limit, provided that it is not ergodic [9][10][11]. The ambiguity of negative heat capacity concept has been extensively examined by the work of RS Berry and coworkers [24][25][26][27][28][29] . In this letter we investigate whether this phenomenon could also be observed in the quantum domain, in particular, for small systems.…”

mentioning

confidence: 99%

Quantum confinement and negative heat capacity

Serra

Carignano

Alharbi

et al. 2013

EPL

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Thermodynamics dictates that the specific heat of a system is strictly non-negative. However, in finite classical systems there are well known theoretical and experimental cases where this rule is violated, in particular finite atomic clusters. Here, we show for the first time that negative heat capacity can also occur in finite quantum systems. The physical scenario on which this effect might be experimentally observed is discussed. Observing such an effect might lead to the design of new light harvesting nano devices, in particular a solar nano refrigerator.Thermodynamics dictates that the specific heat of a system is strictly non-negative, implying that the addition (subtraction) of energy cannot result in a decrease (increase) of the system's temperature [1]. Nevertheless there are well known cases where this rule is apparently violated [2,3]. For example, this phenomenom occurs at the nanoscale and it was eloquently showed by Schmidt et al. who, in an elegant series of experiments, determined a negative heat capacity of a Na cluster with 147 atoms for temperatures neighboring the melting temperature of the cluster [4][5][6]. Also at the astronomical scale negative heat capacities have been known for years [7], where it is observed that stars and star clusters increase their temperature as they age while loosing energy by radiation [8]. Therefore, invoking the thermodynamic limit is not sufficient to guarantee the equivalence of Canonical and Microcanonical ensembles. The key to theoretically reconcile these results with the thermodynamics was addressed by Thirring and coworkers: A system may display negative heat capacity, even in the thermodynamics limit, provided that it is not ergodic [9][10][11]. The ambiguity of negative heat capacity concept has been extensively examined by the work of RS Berry and coworkers [24][25][26][27][28][29] . In this letter we investigate whether this phenomenon could also be observed in the quantum domain, in particular, for small systems. An important motivation for the understanding and control of this phenomenon would be the implementation of refrigeration strategies at the nano scale, for example for light harvesting nano devices that would benefit from an inverted thermal response.Following previous ideas [12, 13] on a minimal model having negative specific heat for classical systems we study the effect of the delocalization of the wave function on the average kinetic energy of the system, and also on several definitions of temperature corresponding to the Canonical and Microcanonical statistics. Let us consider a 1d potential well trapped between impenetrable walls:This potential represents a simple example that suffices to show how a negative heat capacity emerges. The solution of the Schrödinger equation for one particle in V (x) given by Eq. (1) can be * kais@purdue.edu

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Remarks on Negative Heat Capacities of Clusters

Cited by 12 publications

References 28 publications

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble

Insights into phase transitions from phase changes of clusters

Quantum confinement and negative heat capacity

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