We report a novel surface-tension driven instability observed for droplets spreading on a compliant substrate. When a droplet is released on the surface of an agar gel, it forms arms/cracks when the ratio of surface tension gradient to gel strength is sufficiently large. We explore a range of gel strengths and droplet surface tensions and find that the onset of the instability and the number of arms depend on the ratio of surface tension to gel strength. However, the arm length grows with an apparently universal law L ∝ t 3/4 .PACS numbers: 47.55.nd, 62.20.Mk, 47.20.Dr, 47.20.Gv The surface-tension driven spreading of liquids is industrially and biologically important, and has been studied in detail on both solid and liquid substrates [1,2,3]. Less is known about how droplet spreading is modified in the presence of a compliant substrate, a situation especially relevant to biological applications [4,5]. We perform droplet-spreading experiments on gel agar, a viscoelastic material, to explore the influence of substrate on the spreading dynamics of the droplet. We find a novel branching instability with an onset that is controlled by the ratio of surface tension difference to the shear strength of the gel. The existence of a spreading morphology in which a spreading droplet becomes spatially localized has important implications for the industrial and medical application of surfactants.Droplets spread differently on liquids, which are mobile, than on solids, which are essentially rigid [3,6,7]. The present experiments on spreading on a viscoelastic substrate (gel agar) are intended as a way to span these two limits: by increasing the agar concentration, one can tune the substrate from liquid-like to solid-like behavior. The difference in surface tension between the droplet (PDMS, a silicone oil; or Triton X-305, a surfactant solution) and the substrate drives the spreading process.Previous work on the spreading of droplets on gel substrates [8,9] showed circular spreading with rates intermediate between those observed on solid and liquid substrates, contrary to what we find. In addition, prior studies of viscoelastic substrates have focused on substrate breakup or fracture when subjected to stresses [10,11,12,13]. Here, we observe a failure of the gel driven by surface tension. After the initial failure, there are two morphologically different manifestations of the instability, influenced by both the substrate elasticity and the surface tensions, which we call starbursts and wispy drops. For weak gels (shear modulus G 30 Pa), the drop breaks into distinct crack-like spreading arms in a starburst formation, as shown in Fig. 1a. Morphologically, this is similar to cracking patterns observed in [10,12]. We observe that the arms have steep sides ex- tending into the gel and are filled with material from the spreading droplet. Above the onset of the starburst instability, the rate of spreading is found to be controlled only by the width of the arms, with collapse in the data across substrate modulus, surface tension, ...

The detailed syntheses of complexes of the form [Re(O)(X)(RNCH(2)CH(2))(2)N(Me)] (X = Me, Cl, I, R = mesityl, C(6)F(5)), 1-3, incorporating diamidoamine ancillary ligands are described. X-ray crystal structures for the complexes [Re(O)(Me)((C(6)F(5))NCH(2)CH(2))(2)N(Me)], 1a, [Re(O)(I)((C(6)F(5))N CH(2)CH(2))(2)N(Me)], 3a, and [Re(O)(I)((Mes)NCH(2))(2)N(Me)], 3b, are reported. The geometry about the metal center in 1a is best described as a severely distorted square pyramid with the oxo ligand in the apical position. In contrast, the geometry about the metal center in 3a is best described as a severely distorted trigonal bipyramid, with the iodo ligand occupying the apical position and the diamido nitrogens and the oxo ligand occupying the equatorial plane. The catalytic activities of these complexes for oxygen atom transfer, OAT, from pyridine-N-oxides, PyO, to PPh(3) were also examined. The reactions exhibited a clear dependence on the diamido ligand substituent and the X ligand (Me, I, Cl) attached to the metal, with the combined effect that electron-withdrawing substituents on the diamido ligand and poor sigma donors directly attached to the metal center increases the rate of catalytic activity. The kinetics of OAT from pyridine-N-oxides to Re were also investigated. The reactions displayed clean first order kinetics in Re and saturation kinetics for the dependence on PyO. Changing the PyO substrate had no effect on the saturation value, k(sat), suggesting that the OAT reaction in these five-coordinate complexes appears to be governed by isomerization of the starting complex. Attempts to isolate a postulated Re(VII) intermediate were not successful because of hydrolytic degradation. The product of hydrolytic degradation [((C(6)F(5))N(H)CH(2)CH(2)))(2)NH(Me)][X], (X = ReO(4)(-), or I(-)), 4 can be isolated, and its X-ray crystal structure is reported. Although the Re(VII) intermediate could not be isolated, its activity in OAT reactions was probed by competition experiments with PPh(3) and four para-substituted triarylphosphines (p-X-Ph)(3)P (X = OMe, Me, Cl, CF(3)). These experiments led to a Hammett that yielded a reaction constant of rho = -0.30 +/- 0.01. This data suggests a positive charge buildup on phosphorus for the OAT reaction and is consistent with the nucleophilic attack of phosphorus on an electrophilic metal oxo.