PhysicoChemical Correlations

The principle of the stability of a chemical substance is a set of qualititaive regularities according to which the relatively low chemical (ch) thermodynamic stability of a compound in a state of ideal gas or solution () causes relatively high supramolecular (intermolecular, im) thermodynamic stability of condensed phases formed by that compound (). Conversely, the higher the chemical thermodynamic stability of a substance, the lower its supramolecular thermodynaic stability in a condensed state. This regularity can be expressed through values of DH_{comb} , DH_{form }and other functions.
The principle was applied by the author to various hierarchies as part of the theory of the evolution of life. It is in agreement with the principle of structural stabilization.
The principle of the stability of a chemical substance can be applied with a number of qualifications to multicomponent systems ( Figures 4 and 7) and reflects the tendency of atoms of different elements to condense around other atoms through chemical and nonchemical (intermolecular, im) ties. The above regularities can be identified for isoatomic substances, several homologous series, lyophilic, lyophobic and biophilic chemical compounds by building the folowing dependencies:
,
,
where ,  coeffcients and the subscript j relates to the substance.
The available data demonstrate that the above relationships cover most simple substances soluble in water.
Precise mathematical formulation of the principle may be impeded, because the measurement of the absolute values of thermodynaic functions is not possible.
Principle of structure stabilisation  the principle stating that in hierarchic systems each higherlevel partial evolution or, in other words, higher ith partial process, which is a component of the general evolution  the process of hierarchic structure formation  stabilises, due to the aggregation, the products of the lower partial evolution, or (i1)th partial process. For instance, in a nonstationary open system where various chemical reactions and other processes take place, structure stabilization “chooses” supramolecular structures that are most stable thermodynamically.
The principle of stability of supramolecular structures of biological mass
The biological systems that I have been discussing are apparently governed by the principle of stabilization of chemical substance. The gist of that principle can be generally stated as follows: during the formation of the more stable structures of a higher hierarchical level (j) i.e., supramolecular structure, nature spontaneously predominantly uses the least stable structures of a lower hierarchical level, i.e., molecular (j1).
The schema illustrates that principle. 
Molecular and Supramolecular Thermal Stability (Molecules of Life)
Gases and Water  H_{2}, N_{2 }, O_{2},CO_{2}, H_{2}O
T_{mol.decay}

3000–1000 K

High molecular stability

T_{melting}

20–273 K

Low supramolecular stability

Tissues  Fats (Lipids), Proteins, Proteids, Sugars, RNA, DNA
T_{mol.decay}

320 – 380 K

Low molecular stability

T_{melting}

273 – 383 K

High supramolecular stability

For instance, the molecularly (chemically) stable substances such as H_{2 }, N_{2 }, O_{2 }, CO_{2 }, H_{2}O have relatively low melting and boiling points that indicates the low thermodynamic stability of their condensed phases. On the other hand, such energyintensive substances (with low molecular thermodynamic stability) as sugars, peptides, nucleic acids melt at relatively high temperatures and decompose during melting and “boiling”. The aggregated phases of these substances are highly stable!
The principle defined here is in agreement with the experimental data and calculations done for the Gibbs  Helmholtz equation:
(4)
where is an averaged measure of the stability of supramolecular structure,  specific enthalpy (variation of specific enthalpy) of melting  denaturation
(), T_{o } standard temperature, i.e., 25 ^{0}С,  melting point of ith substance, and  variation of specific heat during melting.
It is very important to bear in mind that the principle of the stability of chemical substance is a thermodynamic principle. According to it the tendency of biological system during evolution (ontogenesis and phylogenesis) to generate relatively highly stable structures of higher hierarchies lead to the selection of relatively less stable structures of lower hierarchies. That evolutionary tendency of the biological system “rejuvenates” the lower hierarchical structures and causes unbounded evolution of the biological world.
Thermodynamic stability of supramolecular structures and melting points.
(From the Book: "Thermodynamic Theory of the Evolution of Living Beings")
For closed systems, the dependence of the Gibbs function variation on temperature T is determined by the GibbsHelmholtz equation:
, (6)
where is the enthalpy variation during the process, T and p are temperature and pressure.
An equation analogous to the GibbsHelmholtz equation can be also written for systems whose composition is not identical. (Note that T and p are constant.) This assumption is precise only for substances (i) that have the same values of thermodynamic parameters. Nevertheless, it proved reasonable for a certain range of the variation of thermodynamic characteristics. Indeed, the experimental data revealed the correlation (predicted in [9]) between  the specific Gibbs function of the structure formation  and D T=T_{m}298, 298 being the standard temperature, K. The correlation has been obtained for nonequilibrium phase transitions “overcooled liquid  solid” for a wide range of organic compounds with varying within a broad temperature interval. (The index relates to the melting point of the ith substance.)
Several results of calculation by means of Eq. 7 relating to fatty acids are shown in Fig.10. One can see that natural substances with high (i.e., with high ), which have been studied by us, indeed have a tendency to form thermodynamically stable phases  solid structures (with more negative values of , see Eq. 7, since condensation (crystallisation) processes of pure substances can be considered as enthalpycontrolled processes, from the viewpoint of the summarised effect. If more precise calculations are necessary, corrections for the specific heat variation of the substances at their melting, , are to be made, and so on. Note that the chemical energy capacity of a series of similar natural compounds () grows as their increases ([27, 28], see also Table 1).

Fig.10. The specific Gibbs function of nonequilibrium phase transition “supercooled liquid ѕ solid” as a function of (=  298.2K) at 298K for a series of fatty acids; and are the specific Gibbs function of crystallization (condensation) and the melting temperature of the ith compound, respectively. The value of is calculated per unit mass. The correlation does not vanish when is calculated per unit volume. Empty circles ()relate to the saturated fatty acids, filled circles () to the unsaturated fatty acid. 
This verifies the predicted behaviour of in the course of ontogenesis and evolution in general (Fig.7).
In the case of entropycontrolled processes, such as aggregation of cells during the selfassembly of cellular structures, denaturation of some proteins, etc., the rise in the thermal stability of the structures is accompanied by a drop of . However, apparently, the relative share of such entropycontrolled processes is rather small during the structure formation in some biotissues, and also some organells.
Thus, the data of Fig.10 are in agreement with the conclusion that it is thermodynamically beneficial for living organisms to accumulate substances with high chemical energy capacity, which oust water from the biotissue.
Let us make some comments. In fact, the author has studied the correlation between the values of (25° C) calculated for individual closed systems (substances), and . The existence of such correlations enables one to estimate the differences between the values of the Gibbs function of the structure formation () of various systems (for instance, supramolecular ones). These differences are characterised by the values calculated for constant temperature (T_{0}). The values of are determined by the differences in the chemical (supramolecular) composition of the systems under study (= ). The GibbsHelmholtz equation is given by the relation for a closed system. As to the correlation equations suggested by the author, they are given by relations of the type or , and so on. The GibbsHelmholtz equation is a general strict thermodynamic equation, whereas the correlation equations written by the author describe particular cases. They are well satisfied only within a limited temperature interval for uniform systems (substances) of variable (different) composition. Thus, despite the limited scope of the correlations considered by the author, they can be used for predicting the thermodynamical tendency of the open systems evolution. The equation of the type , suggested by the author, where is the specific enthalpy variation due to crystallisation, are variables and is a constant, is an analogue of the GibbsHelmholtz equation [9, 1416]. The same equation considered for constant , and variable is the approximate GibbsHelmholtz equation.

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Institute of PhysicoChemical Problems of Evolution
Commmerce and Law Institute
