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教师简介
Avik Chatterjee

橙色横尺

Avik Chatterjee

副教授

化学系
220约翰实验室

achatter@sxjiuxin.com
315-470-4747

研究及奖学金

Ph.D., 1996, Cornell University; Postdoctoral Associate, 1996-1998, University of Illinois at Urbana-Champaign; Postdoctoral Associate, 1998-1999, Institute of 理论物理ical Science and Technology, 马里兰大学帕克分校.

纳米颗粒渗透:

Dr. Chatterjee’s efforts focus on understanding the formation of networks of connected particles (“percolation”). These particles can have different shapes ranging from elongated rods to flattened disks (representing, 例如, carbon nanotubes or graphene or clay platelets, 分别). The concentration at which there emerges a physically connected network capable of transmitting electrical current or bearing mechanical stress is referred to as the percolation threshold. This key concentration varies greatly as a function of the shapes and sizes of the particles, how they are distributed in the embedding medium, and also with the criterion used for deciding when a pair of objects are said to be “connected”. These dependences are examined within an analogy to discrete lattice-based models that assign a central role to the average number of contacts that a representative particle experiences with its neighbors.

例如, the figure below compares percolation thresholds for random, isotropic spherocylinders as a function of the aspect ratio calculated from (i) our theory (solid line: “Connectedness percolation in isotropic systems of monodisperse spherocylinders”, A.P. Chatterjee, J. 理论物理.:凝聚态物质, 27, 375302, (2015)), with: (ii) results from Monte Carlo simulations (filled triangles: “Percolation in suspensions of hard nanoparticles: From spheres to needles”, T. 先令,M.A. 米勒和P. 范德斯库特， Europhys. 列托语., 111, 56004, (2015)).

A graph showing how the percolation threshold varies with aspect ratio for rodlike particles. Results from simulations are indicated by triangles, while theoretical results are shown by a solid line. Close agreement is found for all but the smallest aspect ratios.

分形聚集体渗流:

More recently this approach has been generalized to examine percolation by fractal aggregates comprised of numerous smaller spherical “primary particles”. 分形维数表示为 dF) of an aggregate can vary from 3 (three) for a dense three-dimensional object (such as a sphere), to 1 (unity) for a linear rod-like assembly, and structures of varying internal porosity or compactness in between:

A pair of interpenetrating fractal aggregates with some contacts formed between subunits from each object that are close to each other.

Our work suggests that the volume fraction at the percolation threshold may show a minimum as a function of the fractal dimension if other variables (such as the overall sizes of individual aggregates) are held fixed: “Percolation Thresholds for Spherically Symmetric Fractal Aggregates”, A.P. Chatterjee, J. 统计. 理论物理.,卷. 190, 113, 150, (2023):

The percolation threshold is shown as a function of the fractal dimension for different choices of the connectedness range between pairs of subunits. A minimum is observed in the dependence of the percolation threshold upon fractal dimension. This minimum moves towards smaller values of the fractal dimension and eventually disappears as the connectedness range is enlarged.

The various curves in the above figure represent different choices for the distance over which pairs of subunits are considered “connected”. The percolation threshold shows a minimum at intermediate values of dF that moves towards smaller value of the fractal dimension and eventually disappears as the connectedness range is increased.

这个最小浓度(at dF ˜ 1.5 - 2) arises because: (i) dense and compact aggregates form contacts as soon as they touch each other tangentially, but: (ii) more tenuous objects must interpenetrate more deeply before contacts appear between their subunits. We model these effects by treating the subunits that comprise each object as a smeared-out “cloud” of points and estimating how many contacts might result depending on the degree of interpenetration:

A schematic image of a pair of interpenetrating fractal aggregates of identical radii. For one aggregate the subunits are shown as a cloud of density while for the other the center of each subunit is represented by a point. 联系 numbers are estimated from the overlaps between these points and the cloud of density.

The schematic image shows a pair of interpenetrating fractal aggregates, each of radius R,在那里 γδ denotes the separation within which a pair of subunits are defined as being “connected”. For one aggregate the subunits are shown as a cloud of density while for the other the center of each subunit is represented by a point. 联系 numbers are estimated from the overlaps between these points and the cloud of density.

选定的出版物

选择出版物:

“Percolation Thresholds for Spherically Symmetric Fractal Aggregates”, A.P. Chatterjee, J. 统计. 理论物理.,卷. 190, 113, (2023).

“Geometric Percolation of Spherically Symmetric Fractal Aggregates”, A.P. 查特吉和C. 格里马尔迪, J. 统计. 理论物理.,卷. 188, 29, (2022).

“Bethe lattice model with site and bond correlations for continuum percolation by isotropic 单分散棒系统”, A.P. Chatterjee, 理论物理. 牧师. E, 96, 022142, (2017).

“Tunneling conductivity in anisotropic nanofiber composites: a percolation-based model”, A.P. 查特吉和C. 格里马尔迪, J. 理论物理.:凝聚态物质, 27, 145302, (2015).

“Quasiuniversal connectedness percolation of polydisperse rod systems”, B. Nigro C. 格里马尔迪P. 《突袭,.P. 查特吉和P. 范德斯库特， 理论物理. 牧师. 信, 110, 015701, (2013).

教学

课程:

FCH 360:物理化学1

FCH 361:物理化学II

fch650:统计物理学 & 大分子化学