We investigate the effect of the magnetic fields of M dwarf (dM) stars on potentially habitable Earth-like planets. These fields can reduce the size of planetary magnetospheres to such an extent that a significant fraction of the planet's atmosphere may be exposed to erosion by the stellar wind. We used a sample of 15 active dM stars, for which surface magnetic-field maps were reconstructed, to determine the magnetic pressure at the planet orbit and hence the largest size of its magnetosphere, which would only be decreased by considering the stellar wind. Our method provides a fast means to assess which planets are most affected by the stellar magnetic field, which can be used as a first study to be followed by more sophisticated models. We show that hypothetical Earth-like planets with similar terrestrial magnetisation (∼1 G) orbiting at the inner (outer) edge of the habitable zone of these stars would present magnetospheres that extend at most up to 6 (11.7) planetary radii. To be able to sustain an Earth-sized magnetosphere, with the exception of only a few cases, the terrestrial planet would either (1) need to orbit significantly farther out than the traditional limits of the habitable zone; or else, (2) if it were orbiting within the habitable zone, it would require at least a magnetic field ranging from a few G to up to a few thousand G. By assuming a magnetospheric size that is more appropriate for the young-Earth (3.4 Gyr ago), the required planetary magnetic fields are one order of magnitude weaker. However, in this case, the polar-cap area of the planet, which is unprotected from transport of particles to/from interplanetary space, is twice as large. At present, we do not know how small the smallest area of the planetary surface is that could be exposed and would still not affect the potential for formation and development of life in a planet. As the star becomes older and, therefore, its rotation rate and magnetic field reduce, the interplanetary magnetic pressure decreases and the magnetosphere of planets probably expands. Using an empirically derived rotation-activity/magnetism relation, we provide an analytical expression for estimating the shortest stellar rotation period for which an Earth-analogue in the habitable zone could sustain an Earth-sized magnetosphere. We find that the required rotation rate of the early-and mid-dM stars (with periods 37-202 days) is slower than the solar one, and even slower for the late-dM stars ( 63-263 days). Planets orbiting in the habitable zone of dM stars that rotate faster than this have smaller magnetospheric sizes than that of the Earth magnetosphere. Because many late-dM stars are fast rotators, conditions for terrestrial planets to harbour Earth-sized magnetospheres are more easily achieved for planets orbiting slowly rotating early-and mid-dM stars.

The reduction from three‐ to two‐dimensional analysis of the permeability of a fractured rock mass introduces errors in both the magnitude and direction of principal permeabilities. This error is numerically quantified for porous rock by comparing the equivalent permeability of three‐dimensional fracture networks with the values computed on arbitrarily extracted planar trace maps. A method to compute the full permeability tensor of three‐dimensional discrete fracture and matrix models is described. The method is based on the element‐wise averaging of pressure and flux, obtained from a finite element solution to the Laplace problem, and is validated against analytical expressions for periodic anisotropic porous media. For isotropic networks of power law size‐distributed fractures with length‐correlated aperture, two‐dimensional cut planes are shown to underestimate the magnitude of permeability by up to 3 orders of magnitude near the percolation threshold, approaching an average factor of deviation of 3 with increasing fracture density. At low‐fracture densities, percolation may occur in three dimensions but not in any of the two‐dimensional cut planes. Anisotropy of the equivalent permeability tensor varies accordingly and is more pronounced in two‐dimensional extractions. These results confirm that two‐dimensional analysis cannot be directly used as an approximation of three‐dimensional equivalent permeability. However, an alternative expression of the excluded area relates trace map fracture density to an equivalent three‐dimensional fracture density, yielding comparable minimum and maximum permeability. This formulation can be used to approximate three‐dimensional flow properties in cases where only two‐dimensional analysis is available.

An electrohydraulic discharge (EHD) process for the treatment of hazardous chemical wastes in water has been developed. The liquid waste in a 4-L EHD reactor is directly exposed to high-energy pulsed electrical discharges between two submerged electrodes. The high-temperature (>14 000 K) plasma channel created by an EHD emits ultraviolet radiation and produces an intense shockwave as it expands against the surrounding water. The oxidative degradation of 4-chlorophenol (4-CP), 3,4-dichloroaniline (3,4-DCA), and 2,4,6-trinitrotoluene (TNT) in an EHD reactor was explored. The initial rates of degradation for the three substrates are described by dC/dN = −k 1 C i − k 0, where dC/dN is the change in concentration per discharge; C i is the initial substrate concentration; k 0 is the zero-order term that accounts for direct photolysis; and k 1 is the first-order term that accounts for oxidation in the plasma channel region. For 4-CP in the 4-L reactor, the values of these two rate constants are k 0 = 0.73 ± 0.08 μM discharge-1 and k 1 = (9.4 ± 1.4) × 10-4 discharge-1. For a 200 μM 4-CP solution, this corresponds to an overall intrinsic zero-order rate constant of 0.022 M s-1 and a G value of 4.45 × 10-3. Ozone increases the rate and extent of degradation of the substrates in the EHD reactor. Combined EHD/ozone treatment of a 160 μM TNT solution resulted in the complete degradation of TNT and a 34% reduction of the total organic carbon (TOC). The intrinsic initial rate constant of TNT degradation was 0.024 M s-1. The results of these experiments demonstrate the potential application of the EHD process for the treatment of hazardous wastes.

Mechanistic studies on dinuclear complexes that can activate CO 2 are rare. Based on the investigations done for the mononuclear compound (bpy)Re(CO) 3 Cl (bpy-Re, with bpy = 2,2′-bipyridine), many reports favor a mononuclear catalytic cycle, while the possibility of a dinuclear catalytic species is discussed in the literature in only a few cases. Here, we report the synthesis and characterization of a homobimetallic rhenium(I) compound, in which two (bipyridine)Re(CO) 3 Cl fragments are brought into close vicinity by attaching them to a xanthene backbone. First, photocatalytic investigations show a significant increase of the catalytic performance compared to the mononuclear parent compound. Second, spectroelectrochemical experiments demonstrate the remarkable fast formation of an intermediate with a Re−Re bond that forms upon reduction of the starting compound, but which is not able to activate CO 2 . Third, spectroscopic investigations under (photo)catalytic conditions were performed to shed light on the crucial intermediates emerging in the reaction cycle. The assignment of these intermediates is assisted by extensive density functional theory calculations. As a result, the enhanced photocatalytic activity is reasoned by inhibition of deactivation channels and a cooperative reaction mechanism, in which one metal center functions as a photosensitizer to assist the second, catalytically active, metal.

The photocatalytic generation of hydrogen (H2) from protons by two cyclometalated ruthenium-platinum polypyridyl complexes, [Ru(bpy)2(2,5-bpp)PtIS](2+) (1) and [Ru(dceb)2(2,5-bpp)PtIS](2+) (2) [where bpy = 2,2'-bipyridine, 2,5-bpp = 2,2',5',2″-terpyridine, dceb = 4,4'-di(carboxyethyl)bipyridine, and S = solvent], is reported. Turnover numbers (TONs) for H2 generation were increased by nearly an order of magnitude by the introduction of carboxyethyl ester units, i.e., from 80 for 1P to 650 for 2P after 6 h of irradiation, with an early turnover frequency (TOF) increasing from 15 to 200 h(-1). The TON and TOF values for 2P are among the highest reported to date for supramolecular photocatalysts. The increase correlates with stabilization of the excited states localized on the peripheral ligands of the light-harvesting Ru(II) center.