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Molecular Forces and Valence in Physico-Chemical and Biological Processes
B. V. Ilyin.
At the present time there is no generally accepted model of molecular interactions.
Meanwhile, we encounter the force of molecular attraction in a whole series of questions of molecular physics and chemistry, and the elucidation of the questions belonging here, apart from its independent significance, is extraordinarily important for modern biology and physiology1, which seek to reduce complex vital processes to elementary physico-chemical phenomena. There is no doubt that the electronic theory of the structure of the atom, which, thanks to the recent work of Rutherford, has received brilliant confirmation, is closely connected with these questions.
1. The electric and magnetic field of the atom. Valence—the number of peripheral electrons. The double electric layer and its action.
The atom possesses electric and magnetic fields, the character of these fields being determined by the distribution of electrons in their orbits. Naturally, under such conditions the valence of the atom, determined by the number of electrons in the outer orbit (the number of the corresponding group in Mendeleev’s periodic system), must play a role in molecular attractions. Kossel2 succeeded in showing that chemical affinity is explained exclusively by these external electrons. The force fields created by the internal (non-valence) electrons apparently do not participate in intermolecular interactions. This is also what accounts for the periodicity of a whole series of properties of atoms.
Here too must be assigned those regularities which are observed at the boundary of two media, in particular, on the surface of a metal. On the surface separating two media there is a double electric layer3. If the surface is metallic, then the inner
the side of this layer is positive, the outer side negative. For this reason, in the thermionic and photoelectric effects, for the emission of an electron it is necessary to expend the energy \(V\cdot e\), where \(e\) is the charge of the electron, and \(V\) is the retarding internal potential.
If we assume that the electric double layer is due to peripheral (valence) electrons belonging to the boundary, surface atoms of the metal, then the retarding potential \(V\) is proportional to the number of valence electrons \(k\), i.e. proportional to the valence1. This assumption is confirmed by the fact that alkali metals (\(k=1\)) are the most photoelectric and electropositive.
Obviously, the magnetic field produced by the outer valence electrons depends on the valence \(k\) in the same way as the electric field. And therefore, in those cases where the force of molecular attraction \(F\) cannot be reduced solely to the action of the electric field, nevertheless \(F\) is proportional to \(k\). Under the assumption of those interactions between molecules of which Lebedev and Prince Golitsyn speak (ponderomotive forces between molecules-vibrators), valence must manifest itself in the same direction2.
2. Adsorption.
Valence and molecular attraction. Coagulation of colloids. Hofmeister’s series. Antagonism of ions in coagulation.
Molecular attractions manifest themselves in a whole series of processes connected with adsorption. In adsorption a gas or solution, under the influence of the force of molecular attraction \(F\) emanating from the molecules of the adsorbent, is distributed approximately in the same way as atmospheric air above the surface of the earth3. The law of distribution is like the well-known barometric formula of Laplace; moreover, the value of \(F\), and consequently also of the valence \(k\), will enter into the exponent. These are the theoretical grounds for the influence of valence on adsorption.
Closely connected with adsorption is a whole series of molecular processes4: the influence of dissolved gases and salts on surface tension, capillary phenomena, and coagulation processes.
The precipitation of colloidal solutions under the action of dissolved salts of equal valence was carefully studied as early as 1895 by Linder and Picton5.
This phenomenon must underlie the explanation of such frequently encountered processes in biology and physiology as coagulation, pro-
here irritation, fatigue, etc.,1 under which precipitation of the protein solution by the released ions takes place.
If the granules of a colloidal solution are considered to be negatively charged,2 then the addition of electrolytes introduces positively charged ions into the solution, which, owing to simple Coulomb attraction, are adsorbed by the colloid granules; large complexes are formed, no longer capable of being maintained in a suspended state by Brownian motion—and precipitation begins.
This point of view is the opposite of Hardy’s theory. There, as a result of neutralization, the granule acquires minimal surface area, loses the ability to float in the solvent like an aeroplane, begins to fall, and a precipitate is obtained (a complex of granules). Here, on the contrary: first coagulation, then falling. Against Hardy speaks the circumstance that a colloidal solution of gold coagulates excellently with electrolytes, and yet the granule does not change its hardness or its surface. If there is a solid granule, then it always has a spherical form, so that removal of its charge by an oppositely charged ion will not diminish its surface. Moreover, one must think that the charge of the granule is of a special kind: it is apparently caused by a double electric layer at the boundary of the two media, the substance of the granule and the solvent.3 The circumstance that the medium is not a perfect dielectric must also be taken into account.
If one takes monovalent salts (salts of \(Na, K\)), divalent \((Mg, Ca)\), trivalent \((Al)\), then the corresponding ions carry one, two, three charges, and naturally, if the same degree of dissociation is assumed, the same concentration of electrolytes of different valency must produce different effects: on \(Al\) there sit three charges, and therefore this ion coagulates more strongly than \(Na\), on which there sits only one charge.
It can be shown4 that if the force of adsorption attraction is proportional to the valency \(C\), then, all other conditions being equal, the quantity of adsorbed substance \(C_{\infty}\) (sorption capacity)
\[ C_{\infty}=\frac{c_{0}}{k}\left(e^{ak}-\beta\right) \]
where \(k\) is the valency, and \(c_{0}\), \(\alpha\), and \(\beta\) are constants. It is clear that, in order to obtain the same initial effect of coagulation (coagulation sensitivity) from 1-, 2-, and 3-valent ions, their concentrations must be taken not simply in the inverse ratio \(3:2:1\), but in a considerably larger one: \(100:20:1\) (Linder and Pickton). Such ratios should have—
would always result, if all other conditions besides valency were the same. But a priori it is already beyond doubt that the mass of the ion, its action on the solvent (the formation of a shell or coat of solvent molecules around the ion)¹, which alters the mobility of the ion, and, finally, the change in internal friction are different for different electrolytes. All this must distort the phenomenon beyond recognition.² And indeed, for monovalent cations $(+)$ the minimum precipitating concentration in Schulze ranges between 185.4 $(LiCl)$ and 8.4 $(Tl_2SO_4)$; in Linder and Pickton, 124.4 $(Li_2SO_4)$ and 1.6 $(Tl_2SO_4)$; in Freundlich, 240 and 0.1. For divalent cations: in Schulze, 3.2 $(MgSO_4)$ and 1.1 $(MgCl_2)$; in Linder and Pickton, 2.1 $(MgSO_4)$ and 0.2 $(PbCl_2)$; in Freundlich, 0.8 $(MgSO_4)$ and 0.6 $(SrCl_2)$. For trivalent cations: in Schulze, 0.3 $(CrCl_3)$ and 0.06 $(KFe(SO_4)_2)$; in Linder and Pickton, 0.2 $\left(\frac12 Fe_2(SO_4)_3\right)$ and 0.04 $(KAl(SO_4)_2)$.
We see from these figures that only the general tendency, prescribed by theoretical laws, is fulfilled.
If we return to the phenomena of classical adsorption, here too only the general tendency of the sorption capacity $C_\infty$ to follow valency is observed.³ As a result of the work of Rona and Michaelis⁴, in the sense of adsorption the cations are arranged in Hofmeister’s series:
\[ K, Na, NH_4 < Ca, Mg < Zn < Cu < Al < H. \]
In the processes of coagulation of colloidal solutions yet another peculiar phenomenon is observed, first noted by Loeb for biological processes. Namely, Loeb showed that by changing the concentration of a certain electrolyte one can produce irritation.⁵ If, however, two separately active electrolytes are made to act simultaneously, they behave antagonistically, as if counteracting one another, and at certain concentration ratios the effect of the action is equal to zero. Such salts Loeb called antagonists.
It turns out that the phenomenon of antagonism is also observed for the coagulation of colloidal solutions, for example, of gold.⁶
It is not now possible to give a fully detailed theory of antagonism, but, apparently, the essence of the matter here lies in competition between the attraction of the granules and precipitating ions and in the interaction of the antagonists with one another or with other elements of the solution.
3. Microscopic and macroscopic phenomena. Statistics. Mean values. General equation of the kinetics of sta-
¹ According to Jons, the shell may consist of 500 or more solvent molecules. Jons, Physikalische Chemie; Lewis, Zt. phys. Ch., 52 (1905), p. 224.
² Wo. Ostwald, Koll.-ZS., Januar, 1920, B. 26, p. 28.
³ Shilov and Lepin, Adsorption of electrolytes and molecular forces, Moscow, 1919.
⁴ Rona u. Michaelis, Biochem. ZS., 94 (1919), p. 240.
⁵ Loeb, Chemische Entwicklungsregung des tierischen Eies, 1919.
⁶ See the literature in Neuschlosz, Pflüger’s Archiv, 181 (1920), p. 20.
tistical processes. The negative temperature coefficient of sorption phenomena.
We have clarified the significance of valence for processes connected with adsorption. But if only the force of molecular attraction were acting, then all the gas would have to be adsorbed.
Meanwhile, a definite fraction is always lost. The whole matter lies in the perturbing influence of thermal motion, under whose action that distribution according to Laplace, of which we spoke earlier, is established. From this point of view adsorption represents the same phenomenon as diffusion. It is a statistical phenomenon. We observe macroscopic mean quantities, formed from the elementary microscopic quantities, whose values are distributed according to the laws of probability theory, of statistics.
If we have a gas or a solution, then the concentration (i.e. the number of particles in \(1\ \mathrm{cm}^3\)) is usually considered to be a constant value1. Strictly speaking, this is not so. If one mentally singles out some volume of gas, then, since the molecules are in continuous disordered motion, some of the molecules enter the volume so mentally isolated, while others leave it. The number of molecules in the given volume does not remain constant. As Smoluchowski showed,
\[ W = \frac{n'}{n} \]
where \(W\) is the frequency of recurrence for a given number of molecules \(n\), and \(n'\) is one of all the observed \(n\). And this was confirmed by the work of Svedberg and Il’in on analogous physical systems (colloidal solutions and emulsions)2.
If carbon is introduced into a gas, i.e. an adsorbing, absorbing body, then on each molecule there begin to act the forces of attraction from the adsorbing surface of the carbon \(F\), and the distribution according to the formula
\[ N = \frac{n_{0} e^{\frac{f}{RT}}}{n!} \]
must be disturbed. Under the influence of the forces \(F\), the motions of the molecules cease to be equiprobable. The direction toward the adsorbing surface will predominate over the others, the concentration at the surface of the adsorbent will begin to increase. If it were not for thermal motion, the molecules, owing to this phenomenon, would accumulate. If a molecule possesses its own velocity \(V\), then under the action of a certain force all molecules would arrive at the wall. But, owing to thermal motion, the molecules have velocities \(V\), distributed according to the law,
Maxwell in all possible directions, and therefore the motion of the molecule is composed of a velocity in the direction \(F\) and the Maxwellian velocity \(V\). If \(V\) is large and has the direction opposite to \(F\), then the molecule, notwithstanding its attraction by the adsorbent, will not adhere to the wall. Therefore, the macroscopically observed increase in the number of adsorbed molecules \(dc\) over the time \(dt\) is composed of the influx under the influence of attraction by the free molecular bonds \(N\) and of the outflux caused by thermal motion:
\[ dc=\alpha\cdot N\cdot dt-\beta c\,dt\ldots\ldots\ldots (I), \]
where \(\alpha\) and \(\beta\) are constants.
If this equation is integrated, we obtain a relation between the concentration in the adsorbent \(c\) and the time \(t\), showing how adsorption changes with time \(t\):
\[ c=C_{\infty}\left[1-e^{-(\alpha+\beta)t}\right]\ldots\ldots\ldots (II). \]
\(C_{\infty}\) is the sorption capacity (maximum absorption). The second term in formula (I), \(\beta\cdot c\,dt\), represents the reverse flow caused by thermal motion and proportional to the concentration \(c\) \(^{1}\).
It is interesting to note that equations I and II have a broader significance. One may apparently state a general theorem for the kinetics of statistical and quasi-static processes, consisting in the fact that equations I and II are always applicable to them in the first approximation \(^{2}\). For the dependence of \(C_{\infty}\) on temperature, relations may be derived proceeding from the already presented conception of the negative value of temperature for adsorption. The excellent agreement of the theoretical formulae with experiment speaks in favor of the correctness of the foundations of the given theory of absorption. The explanation of the experimentally observed negative temperature coefficient in absorption by animal and plant tissues speaks in favor of the sorption theory of these phenomena (Fischer) and against Büchli’s diffusion theory \(^{3}\).
In biology there are many processes whose negative coefficient can be explained from the same point of view. Eisenberg and Volk \(^{4}\) indicate that the absorption isotherm of typhoid agglutinin by typhoid bacteria has a clear adsorption course.
\(^{1}\) Ilyin, On the theory of sorption phenomena. Izv. Phys. Inst. Moscow Sci. Inst., vol. 1, issue V–VI, p. 219.
\(^{2}\) See, for example, Ilyin, On the kinetics of colloidal and emulsion processes, ibid., p. 218.
\(^{3}\) Ilyin, Dependence of the swelling of animal and plant tissues on temperature. Izv. Phys. Inst. Moscow Sci. Inst., Moscow, 1921, vol. 1, issue V–VI, p. 224.
\(^{4}\) Eisenberg and Volk, Zs. für Hygiene 40 (1902), p. 155.
The same, according to the work of Biltz and Madsen, may be said of the binding of toxins by antitoxins1.
The phenomena of coagulation are of interest for the complete theory of excitation developed by Nernst, Loeb, Lazarev2, since they are connected with the process of transition of an organ from the unexcited state into the excited one. It is precisely this transition that is accompanied by the association of the primary single protein granules into multifracted ones under the action of ion-coagulators. Lazarev3 believes that the equations for the kinetics of colloid coagulation give curves analogous to the excitation curve of a nerve and to the curve of muscle contraction under the action of a stimulus that brings its proteins into ions.
In favor of the considerations expressed concerning the significance of valency and the essence of adsorption interactions in the coagulation of colloids, there also speaks a whole series of works by Loeb and other authors (Neuschlosz, Michaelis) on the influence of ions on the physical and chemical properties of colloids (electrical conductivity, osmotic pressure, swelling, isoelectric number, etc.)4.
It should be noted the recent works of Loeb on the course of diffusion of electrolytes and nonelectrolytes (glucose) as a function of concentration5. If, for nonelectrolytes, diffusion follows Fick’s law, which is based on pure statistics, and increases with increasing concentration, then for electrolytes at low concentrations there is observed an undoubted effect of electrostatic attraction and repulsion of anions and cations, as a result of which we first have an abnormal increase in the rate of diffusion and then, conversely, a decrease. The curve of the dependence of the diffusion coefficient on concentration passes through a maximum. Analogous considerations have also been expressed by Shilov. They, undoubtedly, may also be used for constructing a rational theory of the distribution of a dissolved substance between different contacting solvents (Nernst)6. It is possible that electronic conceptions will also play a major role in the theory of definite and indefinite compounds (the daltonides and berthollides of Academician Kurnakov)7.
In any case, one cannot fail to point to the exceedingly interesting attempts by Kossel (Rutherford’s model1) and Langmuir2 (static, structural model) to provide, from this point of view, an explanation of chemical interactions.
Conclusion.
There is no doubt that the brilliant discoveries in the field of physics in recent times, which have placed the electronic theory of the structure of matter on a firm foundation, have made it possible to look more definitely and more boldly into the world of molecular interactions, to establish a number of quantitative laws of importance not only for physics and chemistry, but also for biology and physiology, enabling the latter as well to enter upon the path of strict quantitative accounting. Physics has enriched biology. But it would be unfair not to note the reverse action as well. In biology we see a far greater variety of phenomena and states, and acquaintance with them prompts physics toward new problems.
Without exaggeration one may say that the doctrine of the fourth (colloidal) state, in the form and in the broad direction in which it is now developing, would have been unthinkable without the stimulus from biological needs.
The boundaries between individual disciplines are being erased.
Cooperation is mutually enriching.
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Lazarev. Izv. Fiz. Instituta M. N. I-ta. 1919, vol. 1, issue 1. ↩↩↩↩
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Loeb. Zentralblatt f. Biochemie u. Biophysik B. 22 (1920), p. 195.
Neuschlosz, Pflüger’s Archiv 181 (1920), p. 20. ↩↩↩ -
Nernst, Theoret. Chemie u ZS. phys. Ch. 11 (1893), p. 345. ↩
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Acad. Kurnakov, Izv. Ross. Ak. Nauk. 1914, p. 321. ↩