Theoretical estimates of equilibrium chain lengths in magnetic colloids

Jordan's theory of chaining in a magnetic colloid has been carried through for a range of grain densities and coupling constants, /gl = /gm²k_BTd³). The theory assumes all grains are of the same size. The nonlinear equations involving infinite sums have been rearranged to improve convergence, and the average number of grains per agglomerate has been calculated. The range of validity of the approximate expression for (n) is established. The results of this theory are compared to five different experimental observations of agglomeration. There is agreement in some cases, but estimates of grain sizes are critical. The distribution of sizes of grains is essential to making reasonable estimates of λ. Very large agglomerates are needle-like with a width much greater than a grain diameter indicating that simple chains are inadequate.