Repulsion between curves

The repulsion between two double layers is important in determining the stability of colloidal particles against coagulation and in setting the thickness of a soap film (see Section VI-5B). The situation for two planar surfaces, separated by a distance 2d, is illustrated in Fig. V-4, where two versus x curves are shown along with the actual potential. 

An important point of the electrocapillary curve is its maximum. Such maximum value of y, obtained when q = 0, corresponds to the potential of zero charge (E ). The surface tension is a maximum because on the uncharged surface there is no repulsion between like charges. The charge on the electrode changes its sign after the... 

Values of the calibration curves for the various column sets are given in Table IV. The corves themselves are shown in Figure 5. The slope of the calibration curves decrease with increasing ionic strength. This is the result of reduced electrostatic repulsion between particles and substrate which permits greater penetration of the porous matrix. 

The force-distance profiles Al, A2 appear to show the relaxed, or quasi-equilibrium limit for the interaction between the mica plates bearing the PEO in the good solvent conditions of the present study. The adsorbed layer thicknesses 6 are then about half the value of D at which onset of repulsion (A curves) is first noted. 6 thus corresponds to some 3Rg for both polymers in the present investigation, a value comparable to that obtained for hydrodynamic layer thickness of PEO absorbed on latex particles in water, for similar molecular weights, from light scattering studies. 

The steric repulsions between off-axis lone pairs at Req are stronger in F2 than in Cl2, and the difference increases rapidly at smaller R. This is shown in the plot below, which compares the full potential curves (solid lines) with the pairwise sum of steric repulsions between off-axis lone pairs (dashed lines) for F2 (circles) and Cl2 (squares), both shifted to a common origin at Req (1.4083 and 2.0528 A, respectively) ... 

Voltammetry curves for all three low-index surfaces are given in Fig. 1. Hydrogen adsorption at Pt(lll), the process at -0.25 < E < -0.05 V in Fig. 1, is not affected by the nature of the anion (such as SO 2-, CIO.- or F-) (12). The lack of a well defined peak, in the drawn-out curve of Fig. 1 clearly indicates a strong lateral repulsion between adsorbed hydrogen adatoms. This is probably a consequence of a partially charge on the adsorbed hydrogen adatoms which, in turn, does not allow the... 

Schematic forms of the curves of interaction energies (electrostatic repulsion Vr, van der Waals attraction Va, and total (net) interaction Vj) as a function of the distance of surface separation. Summing up repulsive (conventionally considered positive) and attractive energies (considered negative) gives the total energy of interaction. Electrolyte concentration cs is smaller than cj. At very small distances a repulsion between the electronic clouds (Born repulsion) becomes effective. Thus, at the distance of closest approach, a deep potential energy minimum reflecting particle aggregation occurs. A shallow so-called secondary minimum may cause a kind of aggregation that is easily counteracted by stirring.

SDS. This is expected because of the shielding of electrostatic repulsion between the SDS molecules in the micelle ( 7). The solid curve in Figure 1 is calculated from Equation 24, i.e. under the assumption that the two surfactants mix ideally in the micelle (X 2 ... 

The n vs A curves obtained are shown in Figure 7. It is seen that the condensed state is realized in a very small mole fraction range. This might be attributed to the electrostatic repulsion between dodecylammonium ions. The curves in Figure 7 are more appropriate than those in Figures 6(a) and 6(b) for the purpose of thermodynamic considerations at the interface. 

The bulge in the centre of the bond flux-bond length correlation in Fig. 7.1 is, however, unexpected and is quite unlike the behaviour shown by any other cation (cf. Fig. 3.1). As pointed out below, the reason for this bulge is the repulsion between the donor and acceptor 0 ions. The bulge is an artefact of anion-anion repulsion and is not intrinsic to the H-O bond itself. The thin line in Fig. 7.1 represents a reasonable interpolation between the two ends of the bond flux-bond length curve and indicates the correlation that might be expected if there were no anion-anion repulsion. 

Consider a molecule above a surface with the distance from the surface being normal to the surface. There are two competitive types of influence occuring (a) repulsion between the cloud of electrons in the atoms that form the surface and those of the molecule and (b) van der Waals nuclear attraction force. The nuclear attraction has a much shorter radius of influence and as a result of the balance of these two forces, there is a well in the potential energy curve at a short distance from the surface, as shown in Figure 2.1. Molecules or atoms that reach this well are trapped or adsorbed by this potential energy well and cannot escape, unless they obtain enough kinetic energy to be desorbed. 

In curve 2 we switch on the A-A interaction (EAA = 1 and EAb = 0), which corresponds to a repulsion between the A particles. Due to the repulsion the phase transition at t/2 nearly disappears and we obtain a very... 

In Fig. 9.24 the particle densities and the production rate are shown as functions of Yco- The phase transition at y disappears due to the effect of B desorption (which is equivalent to the effect of A-desorption at yf). The repulsive interaction of A particles (curve 2) smoothes the phase transition at 2/2- Eab = 1 (curve 3) shifts y2 to lower values of Yco- This comes from the fact that the A particles can easily adsorb on the free sites created by B-desorption. The increased number of A particles on the lattice leads to an increased B-desorption due to the repulsive A-B interaction (see Fig. 10 and 11). In curve 4 the repulsion between the A particles leads to to shift of 2/2 to larger values of kco- Smoothing of the phase transition (compare curve 2) can be observed only at the beginning of the phase transition. At larger values of Yco, CA increases abruptly. This can be explained by the... 

Why do these calculations yield results so far from the ub initio curve There are two reasons. First, atomic orbitals are used that are appropriate for isolated atoms, but are hardly expected to be the best orbitals for the electrons when two or more atoms are in close proximity. It is convenient to use atomic orbitals in simple calculations because they are mathematically simple, but more complicated orbitals are known to give better results. Second, neither treatment properly takes into account electron-electron repulsions. For two electrons, a term of the form e2lr2n (in which e is the electronic charge and r12 is the distance between the electrons) is required to describe the repulsion between electrons. The exact calculations avoid both difficulties but are so complex mathematically as to be devoid of any capability for providing qualitative understanding. 

The slow peak was associated with the dissociation channel that produces an H atom and an X(2) fragment, while the fast peak was identified with the channel that produces the I( 3/2) fragment. From the polarization measurements they could obtain the anisotropy parameter 3, and this along with the TOF spectra could be used to derive the branching ratio between the two channels as a function of wavelength. Combining this information with the measured extinction coefficients, they were able to derive the partial extinction coefficients to the upper states that correlate with each of the channels. A modified 6 approximation was then combined with all of this information to calculate the upper repulsive potential curves that lead to dissociation into these products. Four upper states are involved in the dissociation in this region. The symmetries of these four states are 3nx, fjl, 3no, and The first two states produce... 

Takahashi et al.67) prepared ionene-tetrahydrofuran-ionene (ITI) triblock copolymers and investigated their surface activities. Surface tension-concentration curves for salt-free aqueous solutions of ITI showed that the critical micelle concentration (CMC) decreased with increasing mole fraction of tetrahydrofuran units in the copolymer. This behavior is due to an increase in hydrophobicity. The adsorbance and the thickness of the adsorbed layer for various ITI at the air-water interface were measured by ellipsometry. The adsorbance was also estimated from the Gibbs adsorption equation extended to aqueous polyelectrolyte solutions. The measured and calculated adsorbances were of the same order of magnitude. The thickness of the adsorbed layer was almost equal to the contour length of the ionene blocks. The intramolecular electrostatic repulsion between charged groups in the ionene blocks is probably responsible for the full extension of the... 

Scheme 32. -Repulsion between the Pseudo-JT-orbitals of the Abridged Bicycle of 30 and K2. (a) Pseudo-rr-orbitals. (b) n—a Interplay between the Displaced rr-Curve and the <7-Curve Causes a Significant Bond Alternation Indicated by the Arrow on the AR Coordinate (consult Eq 13)...

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