Experimental Data Analysis

Investigation of various solutions.
The subject of the study was solutions of different alkali: KCl, NaCl, KNO3, NaNO3 in deionised distilled water at different concentrations. For each concentration 30-40 measurements were carried out (except for KCl). Investigating various concentrations of solutions from normal to 16000th dilution, which correspond to the range from 101,1 to 0,00357 (gram*mole), the data analysis disclosed the following regularities.

At the level of second dilution (approximately 0.5 (gram*ecv)/litre) fractality coefficient decreases relatively to its normal value, and then, at the level of the fourth (0.27 (gram*ecv)/litre), goes up. Further, having some small differences which statistics is shown in Tables 3.5-3.16, it falls to the level of 256th dilution (0,004 (gram*ecv)/litre). At the level of 512th dilution (0,00197 (gram*ecv)/litre) it grows again, and starting from the level of 1024th dilution (0,00987 (gram*mole)/litre) goes down stable till the 16384th dilution (0,0000617 (gram*mole)/litre), at which level the statistically significant differences between solutions and water disappear (Tables 3.5-3.16 and Fig. 3.5-3.8).

It is remarkable that no other method was sensitive to the indicated "anomalies" at the level of the second and 512th dilution. The explanation should apparently consist in peculiar interstructuring of solutions in the given dilutions. At present the physico-chemical interpretation of this phenomenon is well underway.

In spite of a certain conformity of general behavior of electrolytes and some statistically indistinguishable points, on the whole, the difference of each concentration line from all the others is statistically significant. The general picture of the sensitivity (planned at about 60%) shows that the sensitivity is lower than it was planned, which fact results from a small difference of the average values and from the quantity of samples not more than 40. This problem could be solved by a further optimisation of experiment, for example, using two or more experimental setups simultaneously, which would enable to decide the issue of quantity of samples received under the same conditions.

Now let us pass over to the analysis of dependence of such parameters as illumination area, entropy, and autocorrelation angle, upon concentration degree using the example of NaNO 3. The corresponding data and diagrams are given in Tables 3.7, 3.10-3.12 and Fig. 3.5-3.8. Data for KNO3 are given in tables 3.6, 3.14, 3.15; for NaCl in Tables 3.9, 3.13, 3.14; for KCl in Table 3.8. Comparison of averaged data for all the solutions are given in Table 3.5. and at fig.3.8. From these data it is clearly seen statistical difference between different alkali solutions, but as demonstrate fig.3.8, this difference is not monotonous for all concentrations.

Data on the respective parameters of distilled water is presented in Table 3.16, which makes it obvious the statistical difference between water and alkali solutions and prove the fact that analysing the type of fractal parameter distribution for water and solutions we deal with normal distribution for the stated above reasons.

Fig. 3.8 demonstrate that a "curvature" remains at the second dilution and a "curvature" appears at 256th dilution (approximately 0,395 (gram*mole)/litre), preceding the "curvature" mentioned before at 512th dilution (approximately 0,197 (gram*mole)/litre), fractal coefficient depending upon the concentration degree. Same curvatures may be seen at the other parameters (Fig.3.5-3.7). This proves that these curvatures correlate with some properties of the solutions and should be treated from the basic positions.

The given number of measurements is necessary to provide above 60% sensitivity of the experiment.
The given solutions were different in ion radiuses (Table 3.14) and electroconductivity (equivalent electroconductivity for various concentrations is represented in Table 33.14 and Fig.3.5, 3.6), but were similar, being strong electrolytes and being able to dissociate completely into ions by the solvent.

During the given research the following parameters were considered: Fractality coefficient, Entropy, Area and Autocorrelation angle.

Fractality coefficient is peculiar due to the following empiric assumptions. Fractality of GDV-grams of solutions must probably reflect flexibility and activity of ions in the given solution. With the lower concentration of solutions ions move apart so that their interaction decreases and reflection of the processes in solutions on GDV-grams under the influence of electromagnetic field is getting more systematic. This dependency on the properties and concentration of ions is similar to the dependency of equivalent electroconductivity of solutions, which is of great physical-mathematical and diagnostic value. Thus, the task to reveal the relation between Fractality coefficient and equivalent electroconductivity is actual.

Entropy is the measure of deviation from the balance: it decreases with reaching the balance. From this point, its dynamics during dilution is interesting.

Autocorrelation function characterizes regularity of the process. If autocorrelation from some distance r equals zero, there are no correlations at the distance r. The study of biological objects of different nature demonstrates that this parameter has a great practical meaning. Autocorrelation dynamics during dilution is also interesting.

The glow area of drops of the same size is the function of photon emission from their surface. Consequently, activity and flexibility of ions as well as ionization and dissociation degree will contribute to the value of the given parameter. This suggestions allows assumption on the connection between glow area and equivalent electroconductivity.

Lets consider all the studied parameters.
Despite some similarity in the general behavior of electrolytes and some statistically significant points, each line of concentration, in general, statistically differs from the others. This can be observed in the dispersion analysis represented in the table 3.22. However, dispersion analysis allows to check out only the hypothesis on the equality of all the average values. But, if the hypothesis is not confirmed, there is no possibility to find out which group is different from the others. This can be done, applying the methods of comparison based on the Student's criteria, such as Bonferrony's remark, Newman-Kales criteria and etc. Comparing two points of different concentrations of one solution or two points with similar concentration of different solutions one can apply Student's t-criteria. The examples of this comparisons are represented in Table 3.19 - 3.21.

Basing on the described data the graphs of dependency of Fractality coefficient on the equivalent electroconductivity were built (Fig. 3.25 - 3.28). The analysis demonstrated that the given dependency can be approximated applying the method of the smallest squares of polynomial curve of the third range. Equations, describing this approximate values and coefficients of multiple correlation (CMC) are marked on the graphs. The given CMC values indicate high reliability of such approximation. X indicates the normalized according to the equivalent electroconductivity which equals 1cm2/ (Ohm g-eqv). Coefficients in polynomials are probably connected with the size of ions of corresponding anions and cations. Diminution of values of the given coefficients corresponds to the decrease of values of ion radiuses. Physical-chemical interpretation and mathematical model of the given dependency in the nearest future will be activity developed.

Lets analyze the dependency of Entropy on the concentration of solutions. Corresponding data and graphs are represented in the Table 3.23 - 3.26 and Fig. 3.29 - 3.30. The data on the corresponding distilled water parameters are represented in the Table 3.8.

Fig. 3.29 - 3.30 demonstrates, that the "gap" in the second dilution is preserved and reveals a "gap" on the level 0.00195 (g-eqv)\L depending on Fractality coefficient and concentration degree. This can be interpreted according to the definition, characterizing entropy as the increase of deflection from the balance unstable in dynamics of entropy diminution with the lower concentration of solutions.

According to the data obtained and figures, it is obvious that there is no statistically significant differences between points, corresponding to entropies of diverse solutions in consequence of entropy, which, in the given case, corresponds not to the differences in sizes of ions and electroconductivity, but to the degree of dissociation which is lower among the investigated electrolytes.

The data of the analysis of Autocorrelation function is given in Table 3.27 - 3.30 and Figure 3.31 - 3.32. Autocorrelation function as a measure of the process regularity is revealed, as expected, according to the chemical properties of solutions of strong electrolytes, analogous for all the solutions. Concentration of 0,125 (g-eqv)\L for KC1 is the exception. The difference for this concentration in comparison to the other points is statistically important. The explanation of the given phenomena should be found in the solubility of the given electrolyte.

The analysis of dependencies of Autocorrelation function and Entropy on the equivalent conductivity, corresponding to various concentrations of solutions (fig. 3.38 - 3.45) revealed no adequate and highly reliable approximate values with the similar degree of polynomial, like in the case with Fractality coefficient, having, obviously, the same model of approximation for all concentrations of the investigated strong electrolytes.

The results of the analysis of area, represented in Table 3.31 - 3.33 and Fig. 3.33 - 3.34 demonstrate similar behavior in dynamics of curves of solutions and, at the same time, statistically significant differences in the majority of concentrations.
According to the data described, the graphs of the area dependency from equivalent electroconductivity were built (Fig. 3.35 - 3.37). The analysis demonstrated that the given dependency can be approximated by the polynomial curve of the fifth range. Equations relating to these approximations are given in the graphs. Just as in the case with Fractality coefficient the coefficients values of multiple correlation reveal high reliability of such approximation.

According to the data, it is evident that on the level of dilution 0.000061 (g-eqv)\L the solution still has statistically significant differences from water, revealed in three parameters - Area, Entropy and Autocorrelation angle.

Thus, the data obtained demonstrate that these three parameters are more sensitive than Fractality coefficient when comparing solutions with water,. According to sensitivity they are ranged as follows: Area, Entropy, Autocorrelation angle. However, Fractality coefficient is significant due to the high sensitivity when revealing such differences in solutions as ion radiuses and elctroconductivity.

However, experimental data show that the 16000th dilution (about 0,00357 (gram*mole)/litre) still has statistically significant differences from water by all the parameters - illumination area, entropy, fractal parameter and autocorrelation angle. Thus, the data received indicates that all these parameters are sensitive for comparison solutions and water. Nevertheless, all the parameters are valuable for the fact that their comparison gives an opportunity to observe different details of solutions behaviour, that is important for analysing of the interstructuring of solutions (512th dilution). All data received contribute for the fact that GDV Technique is much more sensitive than the other well-known methods of revealing differences according to various parameters, which, as a rule, become insignificant at the level of 2000th dilution already.

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