title: Divergence of the long-wavelength collective diffusion coefficient in quasi-one- and quasi-two-dimensional colloidal suspensions.
abstract: We report the results of experimental studies of the short-time-long-wavelength behavior of collective particle displacements in quasi-one-dimensional (q1D) and quasi-two-dimensional (q2D) colloid suspensions. Our results are reported via the q → 0 behavior of the hydrodynamic function H(q) that relates the effective collective diffusion coefficient D(e)(q), with the static structure factor S(q) and the self-diffusion coefficient of isolated particles D(0): H(q) ≡ D(e)(q)S(q)/D(0). We find an apparent divergence of H(q) as q → 0 with the form H(q) ∝ q(-γ) (1.7 < γ < 1.9) for both q1D and q2D colloid suspensions. Given that S(q) does not diverge as q → 0 we infer that D(e)(q) does. This behavior is qualitatively different from that of the three-dimensional H(q) and D(e)(q) as q → 0, and the divergence is of a different functional form from that predicted for the diffusion coefficient in one-component one-dimensional and two-dimensional fluids not subject to boundary conditions that define the dimensionality of the system. We provide support for the contention that the boundary conditions that define a confined system play a very important role in determining the long-wavelength behavior of the collective diffusion coefficient from two sources: (i) the results of simulations of H(q) and D(e)(q) in quasi-1D and quasi-2D systems and (ii) verification, using data from the work of Lin, Rice and Weitz [Phys. Rev. E 51, 423 (1995)], of the prediction by Bleibel et al., arXiv:1305.3715, that D(e)(q) for a monolayer of colloid particles constrained to lie in the interface between two fluids diverges as q(-1) as q → 0.
authors.affiliation: The James Franck Institute and Center for Advanced Radiation Sources, The University of Chicago, Chicago, Illinois 60637, USA.
authors.forename: Binhua
authors.initials: B
authors.lastname: Lin
authors.affiliation: Department of Chemistry, Stanford University, Stanford, California 94305, USA.
authors.forename: Bianxiao
authors.initials: B
authors.lastname: Cui
authors.affiliation: Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Xinliang
authors.initials: X
authors.lastname: Xu
authors.affiliation: Department of Organic Chemistry I, University of the Basque Country, San Sebastian, Spain and IKERBASQUE, Basque Foundation for Science, Bilbao, Spain.
authors.forename: Ronen
authors.initials: R
authors.lastname: Zangi
authors.affiliation: Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv, Israel.
authors.forename: Haim
authors.initials: H
authors.lastname: Diamant
authors.affiliation: The James Franck Institute and Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA.
authors.forename: Stuart A
authors.initials: SA
authors.lastname: Rice