Mutual penetration

The stacking model (Fig. 8.42c) does not carry this inconsistency [128,229], It cannot be discriminated from the lattice models if the polydispersity is strong. For small polydispersity even the lattice models make physical sense, because then the mutual penetration is negligible. Computation and fitting of stacking and lattice models are described in Sects. 8.7.3.4 and 8.133. 

Several issues remain to be addressed. The effect of the mutual penetration of the electron distributions should be analyzed, while the use of theoretical densities on isolated molecules does not take into account the induced polarization of the molecular charge distribution in a crystal. In the calculations by Coombes et al. (1996), the effect of electron correlation on the isolated molecule density is approximately accounted for by a scaling of the electrostatic contributions by a factor of 0.9. Some of these effects are in opposite directions and may roughly cancel. As pointed out by Price and coworkers, lattice energy calculations based on the average static structure ignore the dynamical aspects of the molecular crystal. However, the necessity to include electrostatic interactions in lattice energy calculations of molecular crystals is evident and has been established unequivocally. 

We note, finally, that with the help of equations (12) with a concrete form of the function F [e.g., (26)], it is also possible to solve the very interesting problem of the diffusion jump of fuel across the flame zone as is shown in Fig. 3, the concentration of the mutually penetrating substances in the transition across the reaction zone falls sharply, but does not become zero. Since the temperature and reaction rate also fall on both sides of the reaction zone, the concentration of fuel which has already reached a certain distance from the flame in the oxidation zone no longer changes. 

Such investigations of elementary reactions lead to fundamental questions on the inner mobility of polymer molecules, their mutual penetration, and on general diffusion problems not yet solved. 

Considering the calculation of coil density, this is not surprising. A concentration of 1% in a solution seems small, but when the coil is more than 100 times diluted, considerable mutual penetrations of the coils can be expected, and, therefore, strong deviations from the behaviour of single, separate coils. 

The stability and stoichiometry of the complex between polymers containing nucleic add bases are affected by the compatibility of the different base-base distances in the polymers, and also by the mutual penetration ability between the main chains. In the polyMAOA-polyMAOT system, for example, intramolecular base-base distances in each polymer are compatible and these polymers are able to penetrate each other38, Poly-L-lysine derivatives and vinyl polymers are apparently incompatible. This situation alone would lead to unstable complex formation where the overall stoichiometry would not be simple and thus could not reflect the stoichiometry on the binding site. 

It can thus be concluded that both the mutual penetration ability and the compatibility of base-base distances of the polymers are substantial for the formation of the stable polymer complexes by specific base pairing. 

Unlike the polarization of the base atom in a regular hydrogen bond interaction, the dipolar polarization of a noble gas atom is towards the hydrogen. In the relatively weak complex of HF with N2, the change in the polarization of the base N away from H is very small. This interaction is transitional between the two patterns of atomic polarizations that result from the mutual penetration of closed-shell systems with little or no accompanying charge transfer, the features common to van der Waals and hydrogen-bonded interactions. 

In paper [4] the first case is considered. The fact that the compositions of the solution and hydroxide remain the same from the beginning to the end is its distinction. This is caused by coincidence of the pH values of the initial and complete precipitation of components that is accompanied by implantation of one hydroxide into the network of the other to produce a mixed structure. Properties of the final product depend on the size of hydroxide particles and their capability of isomorphic substitution.The character of these substitutions and the type of their mutual penetration change substantially with alterations in composition of the components. 

In case of large overlapping or mutually penetrating cores a core-core repulsion correction (CCRC) to the point charge repulsion model in Eq. 27 is needed. A similar core-nucleus repulsion correction (CNRC) has to be applied for the interaction between nuclei of atoms treated without ECP and centers with large-core ECPs. A Bom-Mayer type ansatz proved to be quite successful to model the pairwise repulsive correction [206,207]... 

A composite concentration gradient, formed from two zones Ca and C% by mutual penetration (Fig. 2.26, top), can be exploited for analytical purposes when a range of mixing ratios of the two components A and B yield useful information. This is because the dispersion coefficients Da and Db for each zone will have a given value for any given delay time r, and, therefore, the ratio of the Da/Db values for these sample zones will remain constant for any given value of tjc. This property of the dispersion... 

Figure 2.26. Zone penetration as used for interference studies (or for standard addition). Top separately injected zones C and C% mutually penetrate each other forming a composite zone (CaCs), and (below) separate (A, B) and composite (A + B) response curves. The Ha+b value measured at delay time Im on the composite curve as compared to the Ha value of point M reflects the influence of B on the measurement of A (see text for details).

Figure 2.27. Standard addition by zone penetration. Separately injected zones of a sample Ca and a standard C% solution disperse into Ca and Cb, which mutually penetrate into each other forming a composite zone Al A + B/ B, yielding a composite peak A + B. Readouts at Ia and Ia+b yield values for pure A and its mixture with B due to standard addition of B. (See text for details.)...

C48H42N303- C21H10N2O4 poly(cyanurate)- poly(bis-maleinimide) mutually penetrating net 336... 

Because of donor-acceptor interactions through hydrogen bonding between pyridine derivatives and coordination to Pt or Ni, a square-planar cavity structure was obtained that showed decomposition above 300°C (Fig. 3b).Mutual penetration of individual networks can give rise to an increase in thermal stability, even though empty cavities still exist. 

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