General Non-Existence Theorem for Phase Transitions in One-Dimensional Systems with Short Range Interactions, and Physical Examples of Such Transitions

Cuesta, José A.; Sánchez, Ángel

doi:10.1023/b:joss.0000022373.63640.4e

Cited by 105 publications

(108 citation statements)

References 39 publications

(70 reference statements)

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“…Our system is one-dimensional, all particle interactions are short-ranged and there are no external fields. For such systems, the existence of a phase transition can be ruled out [39,40,61,62]. This fact is accurately captured by our MC-simulations that display a and otherwise with the same parameters as in Fig.…”

Section: A Non-magnetic Systemsupporting

confidence: 59%

“…Second, we have a pinning potential suppressing large amplitude fluctuations of the particles around their pinning positions. Together, both contributions counteract the Landau-Peierls instability and can facilitate periodic structures also in one spatial dimension [39,40,61,62,67]. In this way, the role of thermal fluctuations is substantially reduced, and our mean-field DFT performs much better when compared to the MC-simulations.…”

Section: B Resultsmentioning

confidence: 89%

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A density functional approach to ferrogels

Cremer¹,

Heinen²,

Menzel³

et al. 2017

J. Phys.: Condens. Matter

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Ferrogels consist of magnetic colloidal particles embedded in an elastic polymer matrix. As a consequence, their structural and rheological properties are governed by a competition between magnetic particle-particle interactions and mechanical matrix elasticity. Typically, the particles are permanently fixed within the matrix, which makes them distinguishable by their positions. Over time, particle neighbors do not change due to the fixation by the matrix. Here we present a classical density functional approach for such ferrogels. We map the elastic matrix-induced interactions between neighboring colloidal particles distinguishable by their positions onto effective pairwise interactions between indistinguishable particles similar to a "pairwise pseudopotential". Using Monte-Carlo computer simulations, we demonstrate for one-dimensional dipole-spring models of ferrogels that this mapping is justified. We then use the pseudopotential as an input into classical density functional theory of inhomogeneous fluids and predict the bulk elastic modulus of the ferrogel under various conditions. In addition, we propose the use of an "external pseudopotential" when one switches from the viewpoint of a one-dimensional dipole-spring object to a one-dimensional chain embedded in an infinitely extended bulk matrix. Our mapping approach paves the way to describe various inhomogeneous situations of ferrogels using classical density functional concepts of inhomogeneous fluids.

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Section: A Non-magnetic Systemsupporting

confidence: 59%

Section: B Resultsmentioning

confidence: 89%

A density functional approach to ferrogels

Cremer¹,

Heinen²,

Menzel³

et al. 2017

J. Phys.: Condens. Matter

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“…There are standard arguments against there being any genuine phase transition in one dimension [7] which we expect will apply to our narrow channel problem, and will rule out any genuine phase transition at finite pressure. The ideal glass transition of hard spheres in three dimensions is estimated to occur at a φ K of around 0.62 [6]; the analogue of the dynamical transition at φ d is around 0.58.…”

Section: Introductionmentioning

confidence: 92%

Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel

Godfrey

Moore

2015

Phys. Rev. E

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We use an exact transfer-matrix approach to compute the equilibrium properties of a system of hard disks of diameter σ confined to a two-dimensional channel of width 1.95 σ at constant longitudinal applied force. At this channel width, which is sufficient for next-nearest-neighbor disks to interact, the system is known to have a great many jammed states. Our calculations show that the longitudinal force (pressure) extrapolates to infinity at a well-defined packing fraction φK that is less than the maximum possible φmax, the latter corresponding to a buckled crystal. In this quasi-onedimensional problem there is no question of there being any real divergence of the pressure at φK . We give arguments that this avoided phase transition is a structural feature -the remnant in our narrow channel system of the hexatic to crystal transition -but that it has the phenomenology of the (avoided) ideal glass transition. We identify a length scaleξ3 as our equivalent of the penetration length for amorphous order: In the channel system, it reaches a maximum value of around 15 σ at φK , which is larger than the penetration lengths that have been reported for three dimensional systems. It is argued that the α-relaxation time would appear on extrapolation to diverge in a Vogel-Fulcher manner as the packing fraction approaches φK .

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“…It is based on either conclusions derived from exactly solvable models (10), Landau's phenomenological argument (9), or van Hove's theorem (30). However, it is established with counterexamples (31)(32)(33)(34)(35)(36) that van Hove's theorem is valid for a limited class of 1D systems (30,37), and the model system we studied here is not included in the class. Rather, ours belongs to "almost 1D" systems, which may well have phase transitions (38): It has an external field due to the cylindrical wall, intermolecular interactions in a transverse dimension in addition to those along the tube axis, and an infinite number of states for each molecule at given position z.…”

Section: Significancementioning

confidence: 99%

Solid−liquid critical behavior of water in nanopores

Mochizuki

Koga

2015

Proc. Natl. Acad. Sci. U.S.A.

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Nanoconfined liquid water can transform into low-dimensional ices whose crystalline structures are dissimilar to any bulk ices and whose melting point may significantly rise with reducing the pore size, as revealed by computer simulation and confirmed by experiment. One of the intriguing, and as yet unresolved, questions concerns the observation that the liquid water may transform into a low-dimensional ice either via a first-order phase change or without any discontinuity in thermodynamic and dynamic properties, which suggests the existence of solid−liquid critical points in this class of nanoconfined systems. Here we explore the phase behavior of a model of water in carbon nanotubes in the temperature−pressure− diameter space by molecular dynamics simulation and provide unambiguous evidence to support solid−liquid critical phenomena of nanoconfined water. Solid−liquid first-order phase boundaries are determined by tracing spontaneous phase separation at various temperatures. All of the boundaries eventually cease to exist at the critical points and there appear loci of response function maxima, or the Widom lines, extending to the supercritical region. The finite-size scaling analysis of the density distribution supports the presence of both first-order and continuous phase changes between solid and liquid. At around the Widom line, there are microscopic domains of two phases, and continuous solid−liquid phase changes occur in such a way that the domains of one phase grow and those of the other evanesce as the thermodynamic state departs from the Widom line.T he possibility of the solid-liquid critical point has been reported by computer simulation studies of various systems in quasi-one, quasi-two, and three dimensions that exhibit both continuous and discontinuous changes in thermodynamic functions and other order parameters (1-7). However, the idea that a solid-liquid phase boundary never terminates at the critical point is still commonly accepted as a law of nature, largely because of the famous symmetry argument (8, 9) together with the lack of experimental observations. Furthermore, critical phenomena in quasi-1D systems are often considered impossible from a different point of view; that is, to begin with, there is no first-order phase transition in 1D systems as proved for solvable models (10) or shown by the phenomenological argument (9). Therefore, a thorough investigation is much needed to support or reject the possibility of the solid-liquid critical point. We examine the phase behavior of a model system of water confined in a quasi-1D nanopore (1,(11)(12)(13)(14)(15) and provide evidence to support the existence of first-order phase transitions and solid-liquid critical points. Results and DiscussionsFirst, we explore possible solid-liquid critical points of the confined water by calculating isotherms in the "pressure-volume" plane, where the pressure is actually P zz , a component of pressure tensor along the tube axis, or simply the axial pressure, and the volume is ℓ z , the length of simulatio...

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General Non-Existence Theorem for Phase Transitions in One-Dimensional Systems with Short Range Interactions, and Physical Examples of Such Transitions

Cited by 105 publications

References 39 publications

A density functional approach to ferrogels

A density functional approach to ferrogels

Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel

Solid−liquid critical behavior of water in nanopores

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