Effect of composition changes on the structural relaxation of a binary mixture

Götze, W.; Voigtmann, Thomas

doi:10.1103/physreve.67.021502

Cited by 127 publications

(212 citation statements)

References 43 publications

Supporting

Mentioning

186

Contrasting

Order By: Relevance

“…The prediction of our theory are qualitatively similar to previous ones [12,13], but the quantitative agreement is much better. Interestingly, a similar qualitative behavior for the glass transition density has been predicted in [36,37]; although there is no a priori reason why the jamming and glass transition density should be related [23], it is reasonable to expect that they show similar trends [37].…”

mentioning

confidence: 67%

See 1 more Smart Citation

Theory of Amorphous Packings of Binary Mixtures of Hard Spheres

et al. 2009

View full text Add to dashboard Cite

We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical protocols can be identified with the infinite pressure limit of long lived metastable glassy states. We test this assumption against numerical and experimental data and show that the theory correctly reproduces the variation with mixture composition of structural observables, such as the total packing fraction and the partial coordination numbers.Amorphous packings of hard spheres are ubiquitous in physics: they have been used as models for liquids, glasses, colloidal systems, granular systems, and powders. They are also related to important problems in mathematics and information theory, such as digitalization of signals, error correcting codes, and optimization problems. Moreover, the structure and density (or porosity) of amorphous multicomponent packings is important in many branches of science and technology, ranging from oil extraction to storage of grains in silos.Despite being empirically studied since at least sixty years, amorphous packings still lack a precise mathematical definition, due to the intrinsic difficulty of quantifying "randomness" [1]. Indeed, even if a sphere packing is a purely geometrical object, in practice dense amorphous packings always result from rather complicated dynamical protocols: for instance, spheres can be thrown at random in a box that is subsequently shaken to achieve compactification [2], or they can be deposited onto a random seed cluster [3]. In numerical simulations, one starts from a random distribution of small spheres and inflates them until a jammed state is reached [4,5]; alternatively, one starts from large overlapping spheres and reduces the diameter in order to eliminate the overlaps [6][7][8][9]. In principle, each of these dynamical prescriptions produces an ensemble of final packings that depends on the details of the procedure used. Still, very remarkably, if the presence of crystalline regions is avoided, the structural properties of amorphous packings turn out to be very similar. This observation led to the proposal that "typical" amorphous packings should have common structure and density; the latter has been denoted Random Close Packing (RCP) density. The definition of RCP has been intensively debated in the last few years, in connection with the progresses of numerical simulations [1,10].Nevertheless, the empirical evidence, that amorphous packings produced according to very different protocols have common structural properties, is striking and call for an explanation. This is all the more true for binary or multicomponent mixtures, where in addition to the usual structural observables, such as the structure factor, one can investigate other quantities such as the coordination between spheres of different type, and study their variation with the composition of the mixture.In earlier attempts to build statistical models of ...

show abstract

mentioning

confidence: 67%

“…Comparison of theory and numerical/experimental data -During the four stages of compression, the pressure initially follows the liquid equation of state up to some density close to the glass transition density [20,36,37]. Above this density, pressure increases faster and diverges on approaching jamming at ϕ j .…”

mentioning

confidence: 99%

Theory of Amorphous Packings of Binary Mixtures of Hard Spheres

et al. 2009

View full text Add to dashboard Cite

show abstract

“…These are normally modeled by modecoupling theory [31] and are associated with a genuine dynamical transition, within that approximation. Our system is effectively one dimensional and is unlikely to have a genuine phase transition.…”

Section: Discussionmentioning

confidence: 99%

Glasslike behavior of a hard-disk fluid confined to a narrow channel

2016

View full text Add to dashboard Cite

Disks moving in a narrow channel have many features in common with the glassy behavior of hard spheres in three dimensions. In this paper we study the caging behavior of the disks which sets in at characteristic packing fraction φ d . Four-point overlap functions similar to those studied when investigating dynamical heterogeneities have been determined from event driven molecular dynamics simulations and the time dependent dynamical length scale has been extracted from them. The dynamical length scale increases with time and, on the equilibration time scale, it is proportional to the static length scale associated with the zigzag ordering in the system, which grows rapidly above φ d . The structural features responsible for the onset of caging and the glassy behavior are easy to identify as they show up in the structure factor, which we have determined exactly from the transfer matrix approach.

show abstract

“…[3,10,11] This value is generally taken to be independent of the particle diameter, σ . [12] The size-independence underscores the geometrical nature of the glass transition in hard spheres. It also implies that, to the extent that both colloidal and molecular systems resemble hard spheres, generic features of the glass transition may be consistent as the particle size continuously transitions from molecular to colloidal length scales.…”

Section: Introductionmentioning

confidence: 99%

Effect of particle size on the glass transition

Larsen

Zukoski

2011

Phys. Rev. E

View full text Add to dashboard Cite

The glass transition temperature of a broad class of molecules is shown to depend on molecular size. This dependency results from the size dependence of the pair potential. A generalized equation of state is used to estimate how the volume fraction at the glass transition depends on the size of the molecule, for rigid molecule glass-formers. The model shows that at a given pressure and temperature there is a size-induced glass transition: for molecules larger than a critical size, the volume fraction required to support the effective pressure due to particle attractions is above that which characterizes the glassy state. This observation establishes the boundary between nanoparticles, which exist in liquid form only as a dispersion in low molecular weight solvents, and large molecules which form liquids that have viscosities below those characterized by the glassy state.

show abstract

Effect of composition changes on the structural relaxation of a binary mixture

Cited by 127 publications

References 43 publications

Theory of Amorphous Packings of Binary Mixtures of Hard Spheres

Theory of Amorphous Packings of Binary Mixtures of Hard Spheres

Glasslike behavior of a hard-disk fluid confined to a narrow channel

Effect of particle size on the glass transition

Contact Info

Product

Resources

About