FLUCTUATION DYNAMICS OF A SINGLE MAGNETIC CHAIN

''Tunable'' fluids such as magnetorheological (MR) and electrorheologi cal (ER) fluids are comprised of paramagnetic or dielectric particles suspended in a low-viscosity liquid. Upon the application of a magneti c or electric field, these fluids display a dramatic, reversible, and rapid increase of the viscosity. This change in viscosity can, in fact , be tuned by varying the applied field, hence the name ''tunable flui ds.'' This effect is due to longitudinal aggregation of the particles into chains in the direction of the applied field and the subsequent l ateral aggregation into larger semisolid domains. A recent theoretical model by Halsey and Toor (HT) explains chain aggregation in dipolar f luids by a fluctuation-mediated long-range interaction between chains and predicts that this interaction will be equally efficient at all ap plied fields. This paper describes videomicroscopy observations of lon g, isolated magnetic chains that test HT theory. The measurements show that, in contrast to the HT theory, chain aggregation occurs more eff iciently at higher magnetic field strength (He) and that this efficien cy scales as H-0(1/2). Our experiments also yield the steady-state and time-dependent fluctuation spectra C(x,x')=[[h(x)-h(x')](2)](1/2) and C(x,x',t,t')=[[h(x,t)-h(x',t')](2)](1/2) for the instantaneous deviat ion h(x,t) from an axis parallel to the field direction to a point x o n the chain. Results show that the steady-state fluctuation growth is similar to a biased random walk with respect to the interspacing \x-x' \ along the chain, C(x,x')approximate to\x-x'\(alpha), with a roughnes s exponent alpha=0.53+/-0.02. This result is partially confirmed by Mo nte Carlo simulations. Time-dependent results also show that chain rel axation is slowed down with respect to classical Brownian diffusion du e to the magnetic chain connectivity, C(x,x',t,t')approximate to\t-t'\ (beta), with a growth exponent beta=0.35+/-0.05<1/2. All data can be c ollapsed onto a single curve according to C(x,x,t,t')approximate to\x- x'\(alpha)psi(\t-t'\/\x-x'\(z)), with a dynamic exponent z=alpha/beta congruent to 1.42.