Short distance interactions

It is generally recognized that the average dimensions of a macromolecule are dependent on two factors one related to short distance interactions, those to which conformational analysis is applied, and one concerned with long distance interactions that are often considered in terms of excluded volume effects or covolume effects. One may, therefore, put ... 

In the following, we will review several imaging techniques, either based on beam/matter interactions (like electron microscopy either TEM or SEM) or techniques that probe the short distance interactions (like AFM), as they are well suited for the observation of nano-objects and have been extensively used to study nanotubes alone. The principles and the main results on polymer/nanotube composites provided by these imaging techniques (AFM, TEM and SEM) will be presented. 

In other words, the medium-specific contribution is not easily measured or quantified for probe molecules in interaction with solid surfaces. Moreover, in the case of microporous solids, the short-distance interactions known as "confinement effects" are even more difficult to evaluate. In all comparisons of experimental data one should be aware that the reactivity of probe base molecules is largely influenced by the size of adsorbates and micropore dimensions. As a result, the acidity scales based on the free energy of proton transfer to a specific base are expected to depend on the choice of reference base. This fact has been confirmed experimentally, as calorimetric heats of adsorption of various bases on, e.g., zeolites, depend on the base chosen. For example, a ZH zeolite may be a stronger acid... 

If our container now contains a hquid mixture of alcohol and water, we would choose to describe the system by a double collection of water molecules and alcohol molecules. This description would not only cancel out the interactions between particles but would reduce these to three types over a short distance interactions between two water molecules, between molecules of alcohol and between one molecule of water and one molecule of alcohol. 

Van der Waals forces are short distances interaction forces of the order of 4 kj/mole, to be compared with hydrophobic interactions (around 8 kj/mole) and hydrogen bonds (20-40 kj/ mole, depending of chemical groups involved). 

Themiodynamic stability requires a repulsive core m the interatomic potential of atoms and molecules, which is a manifestation of the Pauli exclusion principle operating at short distances. This means that the Coulomb and dipole interaction potentials between charged and uncharged real atoms or molecules must be supplemented by a hard core or other repulsive interactions. Examples are as follows. 

At very short distances, less than about 2.5 A, a reasonable description of the interaction will be strongly repulsive, to prevent excessive interpenetration a Lemrard-Jones fiinction will be adequate ... 

The biasing function is applied to spread the range of configurations sampled such that the trajectory contains configurations appropriate to both the initial and final states. For the creation or deletion of atoms a softcore interaction function may be used. The standard Lennard-Jones (LJ) function used to model van der Waals interactions between atoms is strongly repulsive at short distances and contains a singularity at r = 0. This precludes two atoms from occupying the same position. A so-called softcore potential in contrast approaches a finite value at short distances. This removes the sin-... 

Interfacial Forces. Neighboring bubbles in a foam interact through a variety of forces which depend on the composition and thickness of Hquid between them, and on the physical chemistry of their Hquid—vapor interfaces. For a foam to be relatively stable, the net interaction must be sufficiently repulsive at short distances to maintain a significant layer of Hquid in between neighboring bubbles. Otherwise two bubbles could approach so closely as to expel all the Hquid and fuse into one larger bubble. Repulsive interactions typically become important only for bubble separations smaller than a few hundredths of a micrometer, a length small in comparison with typical bubble sizes. Thus attention can be restricted to the vapor—Hquid—vapor film stmcture formed between neighboring bubbles, and this stmcture can be considered essentially flat. 

The classical kinetic theoty of gases treats a system of non-interacting particles, but in real gases there is a short-range interaction which has an effect on the physical properties of gases. The most simple description of this interaction uses the Lennard-Jones potential which postulates a central force between molecules, giving an energy of interaction as a function of the inter-nuclear distance, r. 

The main difference between the three functions is in the repulsive part at short distances the Lennard-Jones potential is much too hard, and the Exp.-6 also tends to overestimate the repulsion. It furthermore has the problem of inverting at short distances. For chemical purposes these problems are irrelevant, energies in excess of lOOkcal/mol are sufficient to break most bonds, and will never be sampled in actual calculations. The behaviour in the attractive part of the potential, which is essential for intermolecular interactions, is very similar for the three functions, as shown in... 

Gas density has a significant effect on the interactions among molecules of a gas. As molecules move about, they collide regularly with one another and with the walls of their container. Figure 5-13 shows that the frequency of collisions depends on the density of the gas. At low density, a molecule may move all the way across a container before it encounters another molecule. At high density, a molecule travels only a short distance before it collides with another molecule. As our Tools for Discovery Box describes, many scientific experiments require gas densities low enough to provide collision-free environments. 

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