Total molecular cohesion

The internal pressure is a differential quantity that measures some of the forces of interaction between solvent molecules. A related quantity, the cohesive energy density (ced), defined by Eq. (8-35), is an integral quantity that measures the total molecular cohesion per unit volume. - p... 

The cohesive pressure c is a measure of the total molecular cohesion per unit volume, given by eqn. 3.11... 

An important measure of the total molecular cohesion per unit volume of liquid is the cohesive pressure c (also called cohesive energy density), which characterizes the energy associated with all the intermolecular solvent/solvent interactions in a mole of the solvent. The cohesive pressure is defined as the molar energy of vapourization to a gas at zero pressure, Af/y, per molar volume of the solvent, V, according to Eqs. (3-5) and (5-76) in Sections 3.2 and 5.4.2, respectively [93, 94]. The cohesive pressure c is related to the internal pressure n cf. Eq. (3-6) and Table 3-2 in Section 3.2. 

However, solvation is not the only mode of action taken by the solvent on chemical reactivity. Since chemical reactions typically are accompanied by changes in volume, even reactions with no alteration of charge distribution are sensitive to the solvent. The solvent dependence of a reaction where both reactants and products are neutral species ( neutral pathway) is often treated in terms of either of two solvent properties. The one is the cohesive energy density or cohesive pressure measuring the total molecular cohesion per unit volume,... 

The quantum mechanical approach cannot be used for the calculation of complete lattice energies of organic crystals, because of intrinsic limitations in the treatment of correlation energies. The classical approach is widely applicable, but is entirely parametric and does not adequately represent the implied physics. An intermediate approach, which allows a breakdown of the total intermolecular cohesion energy into recognizable coulombic, polarization, dispersion and repulsion contributions, and is based on numerical integrations over molecular electron densities, is called semi-dassical density sums (SCDS) or more briefly Pixel method. [12-14]... 

The molecular cohesive energy Ecoh is defined as the energy reduction upon forming a crystal from isolated molecules, i.e., Ecoh = Emoi - Ehlln /2. where Ebuik and Emoi denote the total energies of the bulk and the isolated molecule, respectively. The factor 2 takes into account the number of molecules in the unit cell. By this definition the cohesive energy is positive for any stable crystal. 

The results of cdculations of an electronic spectrum show that the HOMO is the fivefold degenerated hu state completely occupied by 10 electrons. The LUMO orbital is the three times degenerated tiu state separated from the HOMO orbitals by a g of about 2 eV [8]. The cohesive energy of a fullerene molecule, defined as the difference of the total molecular energy and the sum of the energies of the isolated atoms, is 7.0 eV/atom (for comparison, the cohesive energy of a diamond is 7.4 eV/atom). 

The most important quantity for understanding the trends in the formation of fullerene-like molecules is the cohesive energy, defined as the difference of the total molecular energy and the sum of the energies of the isolated atoms. As expected, the cohesive energy decreases considerably from Cso to Pbeo- The maximum HF (B3LYP) value of -15.160 a.u. (-18.503 a.u) corresponds to Ceo, and the minimum value -3.677 a.u. (-5.950 a.u.) corresponds to Pbeo- The other values lie in between and are relatively close to each other. 

The philosophical transition from the atomic prejudice to a view of intermolecular interaction in terms of diffuse electron density has its proper computational counterpart in full quantum mechanical calculations, which, however, cannot at present provide complete intermolecular energies because of limitations in the treatment of electron correlation, a major ingredient of the intermolecular interaction recipe. In a different perspective, the classical atom-atom force-field approach is widely applicable but entirely parametric and of scarce adherence to physical principles. The need is felt for an extension to represent in a more realistic manner the effects of diffuse electron clouds. This is done in the so-called semi-classical density sums (SCDS) or briefly. Pixel approach [9], which will now be described. The Pixel method is based on numerical integrations over molecular electron densities, and allows a separation of the total intermolecular cohesion energy into coulombic, polarization, dispersion, and repulsion contributions. 

Expression (9.15) gives the total electrostatic energy and not the cohesive energy of a molecular crystal. It ignores the quantum-mechanical nature of the charge distribution an electron cannot interact with itself, but just such a self-energy is included in the expression. 

These two fundamental characteristics, CS and MMD, determine all the properties of the polymer. In a direct way they determine the cohesive forces, the packing density (and potential crystallinity) and the molecular mobility (with phase transitions). In a more indirect way they control the morphology and the relaxation phenomena, i.e. the total behaviour of the polymer. 

Solvophobic theory provides a theoretical framework to evaluate hydrophobic effects. To place a polypeptide or protein into a solvent, a cavity of the same molecular dimensions must first be created. The amount of energy or work required to create this cavity is related to the cohesive energy density or the surface tension of the solvent. The fusion of cavities reduces the total surface area in the combined cavity, and thus the free energy of the... 

Further analysis of the above results may be obtained by studying the solubility parameters of the polymers and plasticizers. Solubility parameters provide a measure of the extent of Interaction possible between chemical species. To determine the solubility parameters, the structure of the smallest repeat unit was considered and the contribution of each atomic group to the total energy of vaporization and molar volume was summed over the molecular structure. The ratio Is calculated as the cohesive energy. The calculated solubility parameters of the polymers and plasticizers are shown In Table II. 

The solubility parameter or cohesive force of an individual solvent is believed to result from its inner molecular forces of attraction. Individual molecular forces characterize and dominate certain molecular regions of the structure. For instance dispersion (or London) forces result from the association between the electron systems of two adjacent molecules and the arrangement of the electrons. These forces are not affected by temperature, they operate within a short distance, they are accumulative, and they are general They reside in all molecules and represent the total attractive force known in saturated aliphatic hydrocarbons. 

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