Force close-spaced

The need to integrate the fast forces analytically can be avoided by approximating it by a sequence of suitably weighted impulses but more closely spaced in time than the slow force impulses ... 

In 1948 the Dutch physicist H.B.G. Casimir predicted a remarkable effect (Casimir, 1948) two parallel, very closely spaced, flat, uncharged, metallic plates of separation L attract each other in vacuum with a force per area A... 

If e = 2, this amounts to 174 kj/mol for single charges at a distance of 0.40 nm 69 kj/mol at 1 nm and only 6.9 kj/mol at 10 nm, the distance across a cell membrane. We see that very large forces exist between closely spaced charges. 

Tn the Rohr model of the hydrogen atom, the proton is a massive positive point charge about which the electron moves. By placing quantum mechanical conditions upon an otherwise classical planetary motion of the electron, Bohr explained the lines observed in optical spectra as transitions between discrete quantum mechanical energy states. Except for hvperfine splitting, which is a minute decomposition of spectrum lines into a group of closely spaced lines, the proton plays a passive role in the mechanics of the hydrogen atom, It simply provides the attractive central force field for the electron,... 

Table I summarizes some of the results of the dynamical calculations for adsorbed butane. The calculated surface vibratory mode frequencies are in reasonable agreement with the observed spectrum, lying in the range 50-125 cm"1 with the rocking mode about the chain axis having the highest frequency followed by the closely spaced bouncing and orthogonal rocking modes. Although there is some variation depending on the force-constant model used, the calculated frequencies are within 30 cm of the experimental values.

When an outgassed solid (the adsorbent) is confined to a closed space and exposed to a gas or vapor (the adsorptive) at a given pressure and temperature, an adsorption process takes place. The adsorptive molecules are transferred to, and accumulate in, the interfacial layer, as a consequence of an attractive force between the surface of the solid and the adsorptive (the adsorptive actually adsorbed by the adsorbent is named adsorbate). After some time, the pressure becomes constant and the thermodynamic equilibrium of adsorption is achieved. 

The physical mechanism of thermal-energy conduction in liquids is qualitatively the same as in gases however, the situation is considerably more complex because the molecules are more closely spaced and molecular force fields exert a strong influence on the energy exchange in the collision process. Thermal conductivities of some typical liquids are shown in Fig. 1-5. 

Chains also contribute to the robustness of natural electron transfer protein design because the close spacing between successive redox centers means that the driving force of the reaction can usually vary widely with relatively little effect on the overall electron transfer rate through the protein. Indeed, many naturally occurring chains have uphill electron transfer steps of hundreds of meV. 

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