Microscopic Mean-Field Theory of the Jamming Transition

Jacquin, Hugo; Berthier, Ludovic; Zamponi, Francesco

doi:10.1103/physrevlett.106.135702

Cited by 58 publications

(79 citation statements)

References 29 publications

(85 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Both colloidal experiments and simulations have also shown that inside the glass regime, at fixed temperature, there exists a crossover pressure p j at which the first peak of the pair distribution function reaches the maximum height g max 1 [7,8,[13][14][15], reminiscing the structural signature of the T = 0 jamming transition [16]. At such a crossover, the pressure dependence of the temperature…”

mentioning

confidence: 99%

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

et al. 2015

View full text Add to dashboard Cite

We probe the Ioffe-Regel limits of glasses with repulsions near the zero-temperature jamming transition by measuring the dynamical structure factors. At zero temperature, the transverse IoffeRegel frequency vanishes at the jamming transition with a diverging length, but the longitudinal one does not, which excludes the existence of a diverging length associated with the longitudinal excitations. At low temperatures, the transverse and longitudinal Ioffe-Regel frequencies approach zero at the jamming-like transition and glass transition, respectively. As a consequence, glasses between the glass transition and jamming-like transition, which are hard sphere glasses in the low temperature limit, can only carry well-defined longitudinal phonons and have an opposite pressure dependence of the ratio of the shear modulus to the bulk modulus from glasses beyond the jamminglike transition.PACS numbers: 63.50. Lm,64.70.pv,61.43.Bn Upon compression, colloidal systems undergo the glass transition when the relaxation time (or the viscosity) exceeds the measurable value [1][2][3]. In the absence of the thermal energy, the compression leads to the jamming transition of packings of repulsive particles with the sudden formation of rigidity and static force networks [4,5]. Although the initial jamming phase diagram [4] proposes that the glass transition of purely repulsive systems collapses with the jamming transition in the zero temperature (T = 0) limit, or equivalently in the hard sphere limit [6], recent studies have evidenced that the T = 0 or hard sphere glass transition happens at a packing fraction φ g0 lower than the critical value φ j0 of the T = 0 jamming transition at the so-called point J [7][8][9][10][11][12].The departure of φ g0 from φ j0 leaves φ ∈ (φ g0 , φ j0 ) a special region. At T = 0, the systems in this region are unjammed and unable to sustain the shear or compression. However, they are by definition glasses when being thermally excited, because particles are unable to diffuse freely. While glasses are believed to be mechanically rigid solids, it seems perplexing that the systems in (φ g0 , φ j0 ) are rigid in the glass perspective but not in the T = 0 jamming perspective, which makes T = 0 singular.For soft and repulsive spheres, recent simulations have indicated that the glass transition temperature T g is proportional to the pressure p and vanishes at φ g0 [6][7][8][9]. Both colloidal experiments and simulations have also shown that inside the glass regime, at fixed temperature, there exists a crossover pressure p j at which the first peak of the pair distribution function reaches the maximum height g max 1 [7,8,[13][14][15], reminiscing the structural signature of the T = 0 jamming transition [16]. At such a crossover, the pressure dependence of the temperatureand vanishes at φ j0 [7,8]. In other words, when compressed at a fixed low temperature, the system undergoes the glass transition first and then the emergence of g max 1 .The whole picture is reproduced here as well in Fig. 3.A recent study ha...

show abstract

mentioning

confidence: 99%

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

et al. 2015

View full text Add to dashboard Cite

show abstract

“…Hence, describing thermal soft spheres in the vicinity of point J requires first to handle the complexity of the glass state, a notoriously difficult task. Within some approximations, this has been achieved only recently for both soft spheres [6,7] and hard spheres [14,20,21]. This description recovers all the observed scalings in temperature and packing fraction but the square root singularity of the pair correlation function when T = 0 + and ϕ = ϕ + J .…”

Section: Introductionmentioning

confidence: 76%

“…However, as already stated, the present granular system unlike thermal systems is in an out-of-equilibrium and mechanically driven state; and one must remain cautious when comparing with packings of thermal soft spheres. Recent numerical simulations [7,19,49,50] suggest that the similarities with thermal systems are much stronger than one may have expected at first sight. For instance, the structural crossover reported here might be related to the finite temperature first-peak paircorrelation maxima near the Jamming point reported in [7,28,49].…”

Section: Dynamical and Structural Crossover In The Vicinity Of The Jamentioning

confidence: 99%

“…One prominent signature of jamming is the singular behavior of the average number of contacts per particle z − z J ∝ (ϕ − ϕ J ) α , where z J is equal to 2 times d, the space dimension, ϕ J is the packing fraction at point J, and α ≃ 0.5 [4,12]. The distribution of the gaps between particles displays a delta at zero and a square root decay for increasing gaps, which is the key to the singular behavior of the average contact number [7,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

“…From a theoretical point of view, the simplest case of athermal and frictionless soft spheres packings has been extensively studied [4,5,6,7] and now serves as a reference situation for which Jamming has a precise meaning: the transition occurs when the system can not be compressed further without allowing overlaps between particles. From that point of view, it is essentially a matter of satisfying geometric constraints, and indeed, a formal identification with algorithmic has been established [8,9].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The glass and jamming transitions in dense granular matter

Coulais¹,

Dauchot²

2013

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. Everyday life tells us that matter acquires rigidity either when it cools down, like lava flows which turn into solid rocks, or when it is compacted, like tablets simply formed by powder compression. As suggested by these examples, solidification is not the sole privilege of crystals but also happens for disordered media such as glass formers, granular media, foams, emulsions and colloidal suspensions. Fifteen years ago the "Jamming paradigm" emerged to encompass in a unique framework the glass transition and the emergence of yield stress, two challenging issues in modern condensed matter physics. One must realize how bold this proposal was, given that the glass transition is a finite temperature transition governing the dynamical properties of supercooled liquids, while Jamming is essentially a zero temperature, zero external stress and purely geometric transition which occurs when a given packing of particles reaches the maximum compression state above which particles start to overlap. More recently, the observation of remarkable scaling properties on the approach to jamming led to the conjecture that this zero temperature "critical point" could determine the properties of dense particle systems within a region of the parameter space to be determined, which in principle could include thermal and stressed systems. Fifteen years of intense theoretical and experimental work later, what have we learned about Jamming and glassy dynamics ? In this paper, we discuss these issues in the light of the experiments we have been conducting with vibrated grains.

show abstract

Complex Fluids, Soft Matter and the Jamming Transition Problem

Diaz

Trujillo

2014

Computational and Experimental Fluid Mechanics With Applications to Physics, Engineering and the Environment

View full text Add to dashboard Cite

Microscopic Mean-Field Theory of the Jamming Transition

Cited by 58 publications

References 29 publications

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

Disordered Solids without Well-Defined Transverse Phonons: The Nature of Hard-Sphere Glasses

The glass and jamming transitions in dense granular matter

Complex Fluids, Soft Matter and the Jamming Transition Problem

Contact Info

Product

Resources

About