Interaction number

Numbers not in parentheses refer to the heat of adsorption or interaction, in kilocalories per mole or kilocalories per atom depending on the stoichiometry of the proposed interaction numbers in parentheses refer to the corresponding surface coverages in cubic centimeters per gram. 

Saccharide residue Polar interactions Number of non-polar interactions"... 

From (10) we can obtain values for fN assuming different interaction numbers. The parameter A is difficult to determine, particularly for a polymeric system. Nevertheless, we can make calculations assuming values for A, notably A l, A = 1, A 1. Each of these cases has significance in terms of the physical processes. For A 1 the formation of the excimer is a relatively slow process and the excimer fluorescence is dependent on the number of neighbors it has. Equation 17 reduces to... 

Figure 15b illustrates the dependence of fluorescence intensity ratios on the f0 function prescribed by (21), with different assumed values for the interaction number. 

For A 1, the theoretical curve (Fig. 15 a) is the same irrespective of the assumed interaction number. Clearly, the observations cannot be fitted to a straight line, as is required by (18). Thus A 1 is not an appropriate parameter for the pyrenylpolyethylenimine adducts. 

As Fig. 15b illustrates, the graphical relation appears to be linear for an interaction number of 3 to 4, if A 1. Alternatively, for A = 1, linearity is evident (Fig. 15c) when the interaction number is 5 to 6. Thus a large value of A is compatible with the smallest interaction number. Excimer formation occurs within the fluorescence lifetime, about 8 nsec. Within that time the pyrene-labeled amine side chains must approach within about 4 A of each other. For the 5.3% pyrenylpolyethylenimine derivative in ethanol, where no ground-state association occurs, the effective local concentration of pyrene on the polymer matrix is about 10-2 M, as calculated from excimer fluorescence. In aqueous solution, where clusters form within the polymer matrix, the effective local concentration of pyrene adduct must be even greater. The quantitative assessment of fluorescence intensities (Fig. 15) points to a minimum interaction number of 3 to 4 pyrenyl-labeled amine side chains, within the 8 nsec lifetime. Since A 1, it appears from (12) that kDM(A) kMD + kD. Thus excimer formation must be very rapid in the polymer environment. We can conclude, therefore, that the primary-amine side chains of poly-ethylenimine are very flexible and mobile. 

The excessive pair number for the thin target, normalized to the proton interaction number for thick target, is n1 = 47 55. 

As a conclusion, the parameters of the protonation/deprotonation of edge sites, namely, the number of edge sites and intrinsic stability constants, can be estimated if the parameters of the cation-layer charge interactions (number of layer charge [cation-exchange capacity] and the specific surface area) are known from independent experimental data and they can be included in the equation describing the system as constant values. 

Molecule Heat of formation kcals Number of H H interactions Number of ionic structures... 

Degree of interaction Number of carbon atoms in macrolide ring ... 

The elements in the RCA can be numbers that vary from very large negative values to very large positive values. If the RGA is close to 1, there should be little effect on the control loop by closing the other loops in the multivariable system. Therefore, there should be less interaction, so the proponents of the RGA claim that variables should be paired so that they have RGA elements near 1. Numbers around 0.5 indicate interaction. Numbers that are very large indicate interaction. Numbers that are negative indicate that the sign of the controller may have to be different when other loops are on automatic. 

Reynolds number = (DppV /)j,) or Interaction number = 18 l/KmppDv Diffusional separation number Electrostatic-attraction separation number Electrostatic-induction separation number Flow-line separation number Gravitational separation number Inertial separation number Thermal separation number Number of transfer units = In [1/(1 fl)]... 

The empirical AN and DN indexes obtained by our approach also lend themselves easily for calculations of pair interaction numbers. Tliere is no formal theoretical guideline on how best to combine individual AN and DN numbers. Arithmetic, geometric and harmonic mean averaging may be used, with a decision as to preferred approach left to an empirical examination of results. One pair interaction number, I p, which has proven to be useful, is defined as follows ... 

Figure 5 Correlating plateau adsorption of polymer PI on pigment surfaces with relevant pair interaction numbers, I p.

Powder interaction time 1 hour. Abbreviations CS, completely soluble SS, slightly soluble NR, no interaction. Numbers indicate solubility in wt.% compared to initial mass of sample. 

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