An electric-field induced dynamical state in dispersions of highly charged colloidal rods: comparison of experiment and theory

Abstract

Concentrated dispersions of highly charged rod-like colloids (fd-virus particles) in isotropic-nematic coexistence exhibit a dynamical state when subjected to low-frequency electric fields [Soft Matter, 2010, 6, 273]. This dynamical state consists of nematic domains which persistently melt and form on time scales typically of the order of seconds. The origin of the dynamical state has been attributed to a field-induced, cyclic dissociation and association of condensed ions [Soft Matter, 2014, 10, 1987, Soft Matter, 2015, 11, 2893]. The ionic strength increases on dissociation of condensed ions, rendering the nematic domains unstable, while the subsequent decrease of the ionic strength due to association of condensed ions leads to a recurrent stabilization of the nematic state. The role of dissociation/association of condensed ions in the phase/state behaviour of charged colloids in electric fields has not been addressed before. The electric field strength that is necessary to dissociate sufficient condensed ions to render a nematic domain unstable, depends critically on the ambient ionic strength of the dispersion without the external field, as well as the rod-concentration. The aim of this paper is to compare experimental results for the location of transition lines and the dynamics of melting and forming of nematic domains at various ionic strengths and rod-concentrations with the ion-dissociation/association model. Phase/state diagrams in the field-amplitude versus frequency plane at two different ambient ionic strengths and various rod-concentrations are presented, and compared to the theory. The time scale on which melting and forming of the nematic domains occurs diverges on approach of the transition line where the dynamical state appears. The corresponding critical exponents have been measured by means of image time-correlation spectroscopy [Eur. Phys. J. E, 2009, 30, 333], and are compared to the theoretical values predicted by the ion-dissociation/association model.

Keywords: Colloids; Dynamical state; Electric fields; Fd-virus; Nematic.

Fig. 1

The phase/state diagram for a fd-concentration of 2.0 mg/ml and a TRIS/HCl-buffer concentration of 0.032 mM. The various phases are discussed in the main text

Fig. 2

A sketch of the microscopic origin of the dynamical state, where nematic domains melt and form. The different stages during a cycle of melting-and-forming of a domain are discussed in the main text

Fig. 3

A sketch of the bifurcation diagram for the isotropic-nematic phase transition, where the orientational order parameter λ is plotted against the effective concentration. The location of binodals, spinodals, and stability curves are given, which bound regions where the isotropic and nematic state are either unstable or meta-stable. The Onsager values of the effective concentration for the location of binodals and spinodals are given in the lower part of the figure. The red, closed curve is a sketch of the limit cycle, indicating cyclic melting and forming of nematic domains

Fig. 4

The lower a and upper b binodal and spinodal concentrations, as a function of the Debye length for several values of the number of effective charges N ₀−N _c,0. Dashed lines are spinodals and solid lines are binodals

Fig. 5

The phase/state diagrams for the buffer concentration of 0.16 mM for several fd-concentrations, as indicated in the figures. The red lines are the calculated N ^∗-to-D transition lines, the thin black lines are guides-to-the-eye, and the vertical red line in the second figure indicates the location of the critical point. The red and blue areas are outside the validity of the theory

Fig. 6

The same as in Fig. 5, but now for a buffer concentration of 0.032 mM

Fig. 7

The divergence of the characteristic time for melting and forming of nematic domains in the dynamical state. a A schematic of the experimentally found divergence of the characteristic time on approach of the N ^∗-to-D transition line: a power law divergence is found on approach of the critical point (with an exponent of 1.39±0.18 on lowering the amplitude, and 0.65±0.15 on increasing the frequency), while a logarithmic divergence is found for an off-critical approach. b The divergence as a function of the electric-field amplitude at the critical frequency ν _c, and c as a function of the frequency at the critical field amplitude E _c. d The divergence for the off-critical approach at a fixed frequency of 150 Hz, where E _trans is field strength at the transition line. The data points are taken from Ref. [11], for an fd-concentration of 2.0 mg/ml, with a buffer concentration of 0.16 mM. The dashed lines are the predictions by theory. The numbers in the figures are values for the critical exponents