The physical foundation of FN = kh(3/2) for conical/pyramidal indentation loading curves.

A physical deduction of the FN = kh(3/2) relation (where FN is normal force, k penetration resistance, and h penetration depth) for conical/pyramidal indentation loading curves has been achieved on the basis of elementary mathematics. The indentation process couples the productions of volume and pressure to the displaced material that often partly plasticizes due to such pressure. As the pressure/plasticizing depends on the indenter volume, it follows that FN = FNp(1/3) · FNV(2/3), where the index p stands for pressure/plasticizing and V for indentation volume. FNp does not contribute to the penetration, only FNV. The exponent 2/3 on FNV shows that while FN is experimentally applied; only FN(2/3) is responsible for the penetration depth h. Thus, FN = kh(3/2) is deduced and the physical reason is the loss of FN(1/3) for the depth. Unfortunately, this has not been considered in teaching, textbooks, and the previous deduction of numerous common mechanical parameters, when the Love/Sneddon deductions of an exponent 2 on h were accepted and applied. The various unexpected experimental verifications and applications of the correct exponent 3/2 are mentioned and cited. Undue mechanical parameters require correction not only for safety reasons.

The exponent 3/2 at pyramidal nanoindentations.

The analysis of published loading curves reveals the exponent 3/2 to the depth for nanoindentations with sharp pyramidal or conical tips. This has geometric reasons, as it occurs independent on the bonding states and indentation mechanisms. Nevertheless, most mathematical deductions and finite element simulations of nanomechanical parameters in the literature continue using the experimentally not supported Hertzian exponent 2. Therefore, numerous published loading curves of various authors are plotted using the experimental exponent 3/2 to present unbiased proof for its generality with metals, oxides, semiconductors, biomaterials, polymers, and organics. Linearity is independent of equipment and valid for load controlled, or depth controlled, or continuous stiffness, or AFM force measurements. The linearity with exponent 3/2 often extends from the nano- into the microindentation ranges. The tip rounding and taper influence of the "geometrical similar" indenters are discussed. When kinks occur in such linear plots through the origin, these indicate change of the materials' mechanical properties under pressure by phase transition. These events are discussed for nanoindentations with respect to the known hydrostatic transformation pressures that are, of course, always higher than the necessary indentation mean pressure. Numerous Raman, as well as X-ray and electron diffraction results from the literature support the phase transitions that are now easily detected. Nanoporous materials first fill the pores upon indentation. Published loading curves exhibit more information than hitherto assumed.

Waste-free solid-state syntheses with quantitative yield.

Unexpected organic solid-state reactions in the gas-solid and stoichiometric solid-solid versions are highly promising new tools for solvent-free sustainable synthesis and production if they occur with 100% yield. Costly workup is obsolete, no wastes are formed and resources and energy saved. More than 500 published 100%-yield, solid-state reactions in 25 reaction types cover virtually all fields of synthetic organic chemistry. Atomic force microscopy (AFM) reveals that solid-state reactions require long-range molecular movements and are strictly and sensibly guided by the crystal packing. Three steps govern the issue: phase rebuilding, phase transformation, and crystal disintegration (detachment). If one of these fails, or if liquid phases are not avoided, the reaction will usually not run to completion. Repeated creation of fresh contacts of crystallites is essential in solid-solid reactions. New, otherwise inaccessible and highly reactive products are most easily obtained. Cooling below eutectic temperatures, but also thermal activation above room temperature, may be necessary. Liquids may be solidified by cooling or inclusion complexation. Typical single-step, multi-step and cascade reactions have been performed with 100% yield using commonly available starting materials in various fields. Upscaling to the kilogram scale has been achieved under various conditions. Further upscaling to technical size productions seems possible.

The solid-state E/Z-photoisomerization of 1,2-dibenzoylethene .

The E/Z-photoisomerization of trans-1,2-dibenzoylethene (DBE) in the confinement of its crystal lattice proceeds readily, but not as a single crystal to single crystal process which was claimed previously by others. This model for the Z-->E isomerization at the 11-12 double bond of the retinal moiety in the crystal-like confinement of rhodopsin was investigated in view of the fact that the precise geometric features are crucial for a better understanding of the postulated twist mechanism. Atomic force microscopy (AFM) monitored long-range anisotropic molecular movements if trans-DBE was photoisomerized, but cis-DBE was unreactive even at the extreme sensitivity of AFM. The crystal lattices of both isomers cannot accommodate a rotational mechanism but at best the twist mechanism with the large groups not leaving their planes. The unidirectional solid-state photochemistry derives from the crystal packing of cis-DBE which exhibits severe 3D-interlocking. Thus, trans-DBE molecules are not formed in the cis-lattice, because their moving away would be prohibited. Conversely, photochemically formed cis-DBE molecules escape the foreign trans-DBE lattice easily along its glide planes, as is experimentally observed by AFM. These findings are reminiscent of the escape of 11-trans-retinal from the rhodopsin array in the vision cascade.

Cascade Reactions in Quantitative Solid-State Syntheses.

100 % yield in the absence of the liquid phase: A one-pot synthesis of highly substituted pyrroles, which proceeds in solution with moderate yields, functions quantitatively in the solid-solid variant, and that at much lower temperatures, although at least four reaction steps are required. The reaction execution in the absence of liquid phases avoids product workup because of the 100 % yield and is thus resource-saving and environmentally friendly.