Earthquakes of the Nepal Himalaya : towards a physical model of the seismic cycle

Home to hundreds of millions of souls and land of excessiveness, the Himalaya is also the locus of a unique seismicity whose scope and peculiarities still remain to this day somewhat mysterious. Having claimed the lives of kings, or turned ancient timeworn cities into heaps of rubbles and ruins, earthquakes eerily inhabit Nepalese folk tales with the fatalistic message that nothing lasts forever. From a scientific point of view as much as from a human perspective, solving the mysteries of Himalayan seismicity thus represents a challenge of prime importance. Documenting geodetic strain across the Nepal Himalaya with various GPS and leveling data, we show that unlike other subduction zones that exhibit a heterogeneous and patchy coupling pattern along strike, the last hundred kilometers of the Main Himalayan Thrust fault, or MHT, appear to be uniformly locked, devoid of any of the “creeping barriers” that traditionally ward off the propagation of large events. The approximately 20 mm/yr of reckoned convergence across the Himalaya matching previously established estimates of the secular deformation at the front of the arc, the slip accumulated at depth has to somehow elastically propagate all the way to the surface at some point. And yet, neither large events from the past nor currently recorded microseismicity nearly compensate for the massive moment deficit that quietly builds up under the giant mountains. Along with this large unbalanced moment deficit, the uncommonly homogeneous coupling pattern on the MHT raises the question of whether or not the locked portion of the MHT can rupture all at once in a giant earthquake. Univocally answering this question appears contingent on the still elusive estimate of the magnitude of the largest possible earthquake in the Himalaya, and requires tight constraints on local fault properties. What makes the Himalaya enigmatic also makes it the potential source of an incredible wealth of information, and we exploit some of the oddities of Himalayan seismicity in an effort to improve the understanding of earthquake physics and cipher out the properties of the MHT. Thanks to the Himalaya, the Indo-Gangetic plain is deluged each year under a tremendous amount of water during the annual summer monsoon that collects and bears down on the Indian plate enough to pull it away from the Eurasian plate slightly, temporarily relieving a small portion of the stress mounting on the MHT. As the rainwater evaporates in the dry winter season, the plate rebounds and tension is increased back on the fault. Interestingly, the mild waggle of stress induced by the monsoon rains is about the same size as that from solid-Earth tides which gently tug at the planets solid layers, but whereas changes in earthquake frequency correspond with the annually occurring monsoon, there is no such correlation with Earth tides, which oscillate back-and-forth twice a day. We therefore investigate the general response of the creeping and seismogenic parts of MHT to periodic stresses in order to link these observations to physical parameters. First, the response of the creeping part of the MHT is analyzed with a simple spring-and-slider system bearing rate-strengthening rheology, and we show that at the transition with the locked zone, where the friction becomes near velocity neutral, the response of the slip rate may be amplified at some periods, which values are analytically related to the physical parameters of the problem. Such predictions therefore hold the potential of constraining fault properties on the MHT, but still await observational counterparts to be applied, as nothing indicates that the variations of seismicity rate on the locked part of the MHT are the direct expressions of variations of the slip rate on its creeping part, and no variations of the slip rate have been singled out from the GPS measurements to this day. When shifting to the locked seismogenic part of the MHT, spring-and-slider models with rate-weakening rheology are insufficient to explain the contrasted responses of the seismicity to the periodic loads that tides and monsoon both place on the MHT. Instead, we resort to numerical simulations using the Boundary Integral CYCLes of Earthquakes algorithm and examine the response of a 2D finite fault embedded with a rate-weakening patch to harmonic stress perturbations of various periods. We show that such simulations are able to reproduce results consistent with a gradual amplification of sensitivity as the perturbing period get larger, up to a critical period corresponding to the characteristic time of evolution of the seismicity in response to a step-like perturbation of stress. This increase of sensitivity was not reproduced by simple 1D-spring-slider systems, probably because of the complexity of the nucleation process, reproduced only by 2D-fault models. When the nucleation zone is close to its critical unstable size, its growth becomes highly sensitive to any external perturbations and the timings of produced events may therefore find themselves highly affected. A fully analytical framework has yet to be developed and further work is needed to fully describe the behavior of the fault in terms of physical parameters, which will likely provide the keys to deduce constitutive properties of the MHT from seismological observations.

Zirconocenes as models for homogeneous Ziegler-Natta olefin polymerization catalysts

Using density functional theory, we studied the fundamental steps of olefin polymerization for zwitterionic and cationic Group IV ansa-zirconocenes and a neutral ansa- yttrocene. Complexes [H₂E(C₅H₄)₂ZrMe]ⁿ (n = 0: E = BH₂ (1), BF₂ (2), AlH₂(3); n = +: E = CH₂(4), SiH₂(5)) and H₂Si(C₅H₄)₂YMe were used as computational models. The largest differences among these three classes of compounds were the strength of olefin binding and the stability of the β-agostic alkyl intermediate towards β-hydrogen elimination. We investigated the effect of solvent on the reaction energetics for land 5. We found that in benzene the energetics became very similar except that a higher olefin insertion barrier was calculated for 1. The calculated anion affinity of [CH₃BF₃]^- was weaker towards 1 than 5. The calculated olefin binding depended primarily on the charge of the ansa linker, and the olefin insertion barrier was found to decrease steadily in the following order: [H₂C(C₅H₄)₂ZrMe]⁺ > [F₂B(C₅H₄)₂ZrMe] ≈ [H₂B(C₅H₄)₂ZrMe] > [H₂Si(C₅H₄)₂ZrMe]⁺ > [H₂Al(C₅H₄)₂ZrMe].

We prepared ansa-zirconocene dicarbonyl complexes Me₂ECp₂Zr(CO)₂ (E = Si, C), and t-butyl substituted complexes (t-BuCp)₂Zr(CO)₂, Me₂E(t-BuCp)₂Zr(CO)₂ (E = Si, C), (Me₂Si)₂(t-BuCp)₂Zr(CO)₂ as well as analogous zirconocene complexes. Both the reduction potentials and carbonyl stretching frequencies follow the same order: Me₂SiCp₂ZrCl₂> Me₂CCp₂ZrCl₂> Cp₂ZrCl₂> (Me₂Si)₂Cp₂ZrCl₂. This ordering is a result of both the donating abilities of the cyclopentadienyl substituents and the orientation of the cyclopentadiene rings. Additionally, we prepared a series of analogous cationic zirconocene complexes [LZrOCMe₃][MeB(C₆F₅)₃] (L = CP₂, Me₂SiCp₂, Me₂CCP₂, (Me₂Si)₂Cp₂) and studied the kinetics of anion dissociation. We found that the enthalpy of anion dissociation increased from 10.3 kcal•mol^-1 to 17.6 kcal•mol^-1 as exposure of the zirconium center increased.

We also prepared series of zirconocene complexes bearing 2,2-dimethyl-2-sila-4-pentenyl substituents (and methyl-substituted olefin variants). Methide abstraction with B(C₆F₅) results in reversible coordination of the tethered olefin to the cationic zirconium center. The kinetics of olefin dissociation have been examined using NMR methods, and the effects of ligand variation for unlinked, singly [SiMe₂]-linked and doubly [SiMe₂]-linked bis(cyclopentadienyl) arrangements has been compared (ΔG‡ for olefin dissociation varies from 12.8 to 15.6 kcal•mol^-1). Methide abstraction from 1,2-(SiMe₂)₂(η⁵-C₅H₃)₂Zr(CH₃)-(CH₂CMe₂CH₂CH = CH₂) results in rapid β-allyl elimination with loss of isobutene yielding the allyl cation [{1,2-(SiMe₂)₂(η⁵-C₅H₃)₂Zr(η³-CH₂CH=CH₂)]⁺.

Ancillary ligand effects : from zirconium(IV)-catalyzed homogeneous propylene polymerization to platinum(II)-mediated C-H bond activation

A series of C_s- and C₁-symmetric doubly-linked ansa-metallocenes of the general formula {1,1'-SiMe₂-2,2'-E-('ƞ⁵-C₅H₂-4-R¹)-(ƞ⁵-C₅H-3',5'-(CHMe₂)₂)}ZrC₂ (E = SiMe₂ (1), SiPh₂ (2), SiMe₂ -SiMe₂ (3); R¹ = H, CHMe₂, C₅H₉, C₆H₁₁, C₆H₅) has been prepared. When activated by methylaluminoxane, these are active propylene polymerization catalysts. 1 and 2 produce syndiotactic polypropylenes, and 3 produces isotactic polypropylenes. Site epimerization is the major pathway for stereoerror formation for 1 and 2. In addition, the polymer chain has slightly stronger steric interaction with the diphenylsilylene linker than with the dimethylsilylene linker. This results in more frequent site epimerization and reduced syndiospecificity for 2 compared to 1.

C₁-Symmetric ansa-zirconocenes [1,1 '-SiMe₂-(C₅H₄)-(3-R-C₅H₃)]ZrCl₂ (4), [1,1 '-SiMe₂-(C₅H₄)-(2,4-R₂-C₅H₂)]ZrCl₂ (5) and [1,1 '-SiMe₂-2,2 '-(SiMe₂-SiMe₂)-(C₅H₃)-( 4-R-C₅H₂)]ZrCl₂ (6) have been prepared to probe the origin of isospecificity in 3. While 4 and 3 produce polymers with similar isospecificity, 5 and 6 give mostly hemi-isotactic-like polymers. It is proposed that the facile site epimerization via an associative pathway allows rapid equilibration of the polymer chain between the isospecific and aspecific insertion sites. This results in more frequent insertion from the isospecific site, which has a lower kinetic barrier for chain propagation. On the other hand, site epimerization for 5 and 6 is slow. This leads to mostly alternating insertion from the isospecific and aspecific sites, and consequently, a hemi-isotactic-like polymers. In comparison, site epimerization is even slower for 3, but enchainment from the aspecific site has an extremely high kinetic barrier for monomer coordination. Therefore, enchainment occurs preferentially from the isospecific site to produce isotactic polymers.

A series of cationic complexes [(ArN=CR-CR=NAr)PtMe(L)]⁺[BF₄]⁺ (Ar = aryl; R = H, CH₃; L = water, trifluoroethanol) has been prepared. They react smoothly with benzene at approximately room temperature in trifluoroethanol solvent to yield methane and the corresponding phenyl Pt(II) cations, via Pt(IV)-methyl-phenyl-hydride intermediates. The reaction products of methyl-substituted benzenes suggest an inherent reactivity preference for aromatic over benzylic C-H bond activation, which can however be overridden by steric effects. For the reaction of benzene with cationic Pt(II) complexes, in which the diimine ligands bear 3,5-disubstituted aryl groups at the nitrogen atoms, the rate-determining step is C-H bond activation. For the more sterically crowded analogs with 2,6-dimethyl-substituted aryl groups, benzene coordination becomes rate-determining. The more electron-rich the ligand, as reflected by the CO stretching frequency in the IR spectrum of the corresponding cationic carbonyl complex, the faster the rate of C-H bond activation. This finding, however, does not reflect the actual C-H bond activation process, but rather reflects only the relative ease of solvent molecules displacing water molecules to initiate the reaction. That is, the change in rates is mostly due to a ground state effect. Several lines of evidence suggest that associative substitution pathways operate to get the hydrocarbon substrate into, and out of, the coordination sphere; i.e., that benzene substitution proceeds by a solvent- (TFE-) assisted associative pathway.