TY - JOUR

T1 - Predicting maximally random jammed packing density of non-spherical hard particles

T2 - Via analytical continuation of fluid equation of state

AU - Tian, Jianxiang

AU - Jiao, Yang

N1 - Funding Information:
J. X. Tian thanks the support from the Youth Innovations and Talents Project of Shandong Provincial Colleges and Universities (Grant No. 201909118), the National Natural Science Foundation of China under Grant No. 11274200, the Natural Science Foundation of Shandong Province under Grant No. ZR2011AM017 and the foundations of QFNU and DUT. Y. J. thanks Arizona State University for the kind support and Peking University for hospitality during his sabbatical leave. The authors thank the anonymous reviewers for their valuable comments and suggestions.
Publisher Copyright:
© the Owner Societies.

PY - 2020/10/21

Y1 - 2020/10/21

N2 - Dense packings of hard particles are useful models for condensed matters including crystalline and glassy state of solids, simple liquids, granular materials and composites. It is very challenging to devise predictive theories of random packings, due to the intrinsic non-equilibrium and non-local nature of the system. Here, we develop a formalism for accurately predicting the density (i.e., fraction of space covered by the particles) ηMRJ of the maximally random jammed (MRJ) packing state of a wide spectrum of congruent non-spherical hard particles in three-dimensional Euclidean space 3, via analytical continuation of the corresponding fluid equation of state (EOS). This formalism is based on the assumption that the fluid branch of the EOS can be analytically extended into the meta-stable region, which leads to a diverging pressure at the jamming point (i.e., the MRJ state). This allows us to estimate ηMRJ as the pole in the EOS, which can be expressed in terms of the virial coefficients encoding intrinsic local n-body packing information of the particles, and depending alone on particle shape. The accuracy of our formalism is verified using the hard sphere system and is subsequently applied to a wide spectrum of non-spherical shapes. The predictions are compared to numerical results whenever possible, and excellent agreements are found.

AB - Dense packings of hard particles are useful models for condensed matters including crystalline and glassy state of solids, simple liquids, granular materials and composites. It is very challenging to devise predictive theories of random packings, due to the intrinsic non-equilibrium and non-local nature of the system. Here, we develop a formalism for accurately predicting the density (i.e., fraction of space covered by the particles) ηMRJ of the maximally random jammed (MRJ) packing state of a wide spectrum of congruent non-spherical hard particles in three-dimensional Euclidean space 3, via analytical continuation of the corresponding fluid equation of state (EOS). This formalism is based on the assumption that the fluid branch of the EOS can be analytically extended into the meta-stable region, which leads to a diverging pressure at the jamming point (i.e., the MRJ state). This allows us to estimate ηMRJ as the pole in the EOS, which can be expressed in terms of the virial coefficients encoding intrinsic local n-body packing information of the particles, and depending alone on particle shape. The accuracy of our formalism is verified using the hard sphere system and is subsequently applied to a wide spectrum of non-spherical shapes. The predictions are compared to numerical results whenever possible, and excellent agreements are found.

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U2 - 10.1039/d0cp03799k

DO - 10.1039/d0cp03799k

M3 - Article

C2 - 33015690

AN - SCOPUS:85093539361

SN - 1463-9076

VL - 22

SP - 22635

EP - 22644

JO - Physical Chemistry Chemical Physics

JF - Physical Chemistry Chemical Physics

IS - 39

ER -