Crystals rupture

To enable an atomic interpretation of the AFM experiments, we have developed a molecular dynamics technique to simulate these experiments [49], Prom such force simulations rupture models at atomic resolution were derived and checked by comparisons of the computed rupture forces with the experimental ones. In order to facilitate such checks, the simulations have been set up to resemble the AFM experiment in as many details as possible (Fig. 4, bottom) the protein-ligand complex was simulated in atomic detail starting from the crystal structure, water solvent was included within the simulation system to account for solvation effects, the protein was held in place by keeping its center of mass fixed (so that internal motions were not hindered), the cantilever was simulated by use of a harmonic spring potential and, finally, the simulated cantilever was connected to the particular atom of the ligand, to which in the AFM experiment the linker molecule was connected. 

The most developed and widely used approach to electroporation and membrane rupture views pore formation as a result of large nonlinear fluctuations, rather than loss of stability for small (linear) fluctuations. This theory of electroporation has been intensively reviewed [68-70], and we will discuss it only briefly. The approach is similar to the theory of crystal defect formation or to the phenomenology of nucleation in first-order phase transitions. The idea of applying this approach to pore formation in bimolecular free films can be traced back to the work of Deryagin and Gutop [71]. 

AHs may be either positive or negative. That principally depends on the relative magnitudes of the terms that figure on the right-hand side of the equation. In some cases heat is evolved on the dissolution of a salt in water. It is mainly due to the fact that heat evolved when the gaseous ions are hydrated (AHX) is more than the heat absorbed in rupturing the crystal lattice. In the majority of cases, however, there is an absorption ofheat when a salt dissolves in water. 

It is supposed that this displacement can occur only in the direction normal to the rupture surface, not parallel to the latter. When all the above distances are systematically varied until the minimum of the total interaction energy is reached, then the most probable position of all 6 centers of force is found. It appears that the distance between the Li nuclei in the outermost and the H nuclei in the second layer is smaller (by 0.00032 angstrom) than in the bulk of the crystal, and the distance between the H nuclei in the external and the Li nuclei in the penultimate layer is... 

The energy excess possessed by a broken, as compared with an unbroken, crystal exists because the atoms (or ions, or molecules) at the rupture surface are attracted by the solid stronger than by the vacuum. This field of force causes re-arrangement of the particles but produces no surface tension. 

Ultimate properties of toughness (energy to rupture), tensile strength, and maximum extensibility are all affected by strain-induced crystallization. In general, the higher the temperature the lower the extent of crystallization and consequently the lower these stress/strain related properties. There is also a parallel result brought about by the presence of increased amounts of diluent since this also discourages stress-related crystallization. 

Example 12.4 Influence of the Environment on D i. Nitromethane is interesting to some people because it explodes. The reason is, of course, in the cleavage of the carbon-nitrogen bond. The monomer, compared to its trimer (taken as a model for the crystal), reveals that the C and N net charges change by A c — 8.7 and A n—1-1 me. respectively, on crystallization. Our bond energy formula and the appropriate parameters thus indicate that the crystalline environment reinforces the CN bond by 4.7 kcal/mol, which is significant at the local point of rupture, responsible for the reaction [251]. 

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