Deryagin's rule formulation. Deryagin-Landau-fairway-overback theory of coagulation

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99. Antagonism and synergism in the action of electrolytes on the coagulation process

Mutual coagulation occurs when two colloids with different charge signs are mixed. Each colloid can be considered as an electrolyte, in which one ion is normal and the other has a huge mass. It follows that a colloid with positively charged particles will play the role of a coagulating electrolyte for a sol with negative particles, and vice versa. Naturally, the most complete coagulation occurs at a certain optimal ratio of colloidal solutions, corresponding to the mutual neutralization of particles. If there is an excess of one of the colloids, partial coagulation will occur, or the system will remain stable with the sign of the charge of the excess colloid (recharge). The results of coagulation of colloidal solutions with mixtures of electrolytes are different. There are three cases here:

1) the phenomenon of additivity;

2) ion antagonism;

3) ion synergism.

In the works Yu. M. Glazman, E. Matievich and other authors studied a more complex, but very important case for practice - coagulation with a mixture of electrolytes.

Additive The effect is that the coagulation capacity in the mixture is added arithmetically according to the mixing rule. In the case of additive action, if one electrolyte is added from 1/2 to 1 sol, then to achieve coagulation you need to add 2/2. An additive effect is often observed, especially during coagulation with mixtures of electrolytes with dominant ions of the same valence.

It has long been known that, along with the additive coagulating effect of two counterions, cases of antagonism and synergism in their action are observed, which are very important not only for many technological processes, but also for understanding the patterns of the effect of ions on the organs and tissues of a living organism, in which biologically active ions often appear as antagonists or synergists.

The coagulating action of one electrolyte begins in the presence of another, which is a phenomenon that is observed in mixtures of ions of different valences (for example, Al 3+ and R +), as well as during coagulation of a negative sol. The reasons for deviation from additivity may be an electrostatic decrease in the activity of the ion in a mixture of electrolytes and complex formation.

When coagulating with mixtures of electrolytes, in some cases, synergism of ions is observed (the opposite effect of the phenomenon of antagonism, that is, when the coagulating effect of one electrolyte increases in the presence of another). At low concentrations of electrolytes, colloidal solutions undergo coagulation. By additionally creating adsorption layers on the surface of colloidal particles with enhanced structural and mechanical properties, the stability of solutions against electromagnetic coagulation can be significantly increased. These layers can prevent coagulation by electrolytes. Such stabilization of the sol with respect to electrons by adding a small amount of a solution of high-molecular compounds (gelatin, agar-agar, egg albumin, etc.) is called protection.

Protective sols are very resistant to electrolytes. For example, colloidal solutions of silver, which are protected by protein substances and used as medicines (protargal, collargal), become insensitive to electrolytes and can be evaporated to dryness. After treatment with water, the dry residue is again converted into a sol. However, the protective effects of different substances are not the same. An amount of a substance sufficient to prevent coagulation of a particular sol, under certain standard conditions, serves as a measure of protective action. For example, the “Golden Number” of gelatin is 0.01, which means that 0.01 mg of it protects 10 ml. Gold sol from coagulation 1 ml of 10% NaCl solution “Golden number” of egg albumin – 2.5, starch – 20. In a similar way, you can evaluate the “Silver number”, “Sulfur number”, etc.

100. Coagulation of strongly and weakly charged sols

In the process of development of colloidal chemistry, many theories arose that attempted to connect the stability of hydrophobic sols (in particular, the coagulating effect of electrolytes) with certain parameters of the system and phenomena that arise during the interaction of the dispersed phase with the dispersion medium. The most successful was the modern theory of stability, which bears the name of Soviet scientists and is designated as the DLFO theory (B.V. Deryagina, L. D. Landau, E. Fairway, J. Overbeck). According to the DLPO theory, an increase in the electrolyte concentration in a dispersion medium causes a decrease in the thickness of the diffuse layer. The thickness of the diffuse layer decreases to a size at which the forces of molecular attraction begin to act. As a result of this, a loss of aggregative and then kinetic stability occurs. The DLFO physical theory of coagulation represents the first quantitative theory. It can be used to calculate the coagulation threshold. As a consequence, the Schulze-Hardy rule follows from this theory.

Deryagin’s “sixth degree law” Z 6 Z 6 establishes the dependence of the coagulation threshold or coagulating ability ( V k = 1/Sk) on the charges of the ion. Quantities V k for one-, two- and three charged counterions correlate with each other as 1:64:729 in accordance with the Schulze-Hardy rule.

If coagulation occurs as a result of short-range interaction of particles, then such systems are unstable, and coagulation is irreversible in most cases, since the depth of the first minimum is usually greater than kT. The decrease in barrier height may be caused by specific adsorption. Therefore, we can talk about two types of coagulation: concentration and adsorption.

It should be noted that a comparison of the considered simple theory with experiment for z > 2 is not possible, since this version of the theory does not take into account ψ 1 (c) for multiply charged counterions, relating to both the magnitude and sign of ψ 1 .

With further development of the DLFO theory for mutual fixation of particles in the second minimum, one can arrive at an exponent value of 3.5–2.5. This is confirmed by imaginary experimental data on further interaction.

All joint work is based on the DLVO theory, which establishes a connection between the properties of the electrical layer and the stability of dispersed systems. In these works, more complex cases are considered (for example, taking into account the adsorption of ions), and, consequently, changes in ψ 1, leading to the phenomenon of coagulation zones.

The idea of the electrical nature or repulsion becomes more legitimate when a connection is established between coagulation zones and the nature of changes in ψ 1 in solutions of electrolytes with multiply charged counterions. With the same charge of particles of the dispersion phase of the same composition, it seems obvious that they should repel each other electrostatically.

Consequently, within the framework of a qualitative consideration, repulsive forces arise when the diffuse layer is deformed, and in order to approach the particles, they need to overcome a barrier that is higher, the higher ψ 1, and the further lagging from the surface, the greater the thickness of the diffuse layer.

For multivalent counterions, the values of ψ 1 decrease with increasing concentration much faster, which explains the Schulze-Hardy rule.

101. Flocculation, heterocoagulation (definitions, examples)

Flocculation- a type of coagulation that leads to the formation of loose, flaky coagulates - floccules.

In many cases, the dependence of stability, expressed through any quantitative characteristic, for example c, on the amount of added “protective” colloid (PMC), passes through a clearly defined minimum. In other words, resistance decreases when IUD is added in an amount insufficient to provide a protective effect. This phenomenon, especially characteristic of linear macromolecules bearing polar groups at both ends of the chain (for example, polyvinyl alcohols), is currently explained by the fact that a long polymer molecule is attached at two ends to two different particles of the dispersed phase, holding them together with a hydrocarbon “bridge.”

Quantitative interpretation of the flocculation phenomenon carried out in theory La Mera based on views I. Langmuir , showed that the probability of adsorption by the other end on the second particle for molecules already adsorbed on the first particle will be greater, the greater the number of these molecules and the greater the fraction of free surface. Consequently, the minimum stability corresponds to half the filling of the surface layer with macromolecules.

This phenomenon (flocculation), due to the comparative cheapness of flocculants, is widely used for the sedimentation of suspensions, sols, and especially for the purification of natural and waste waters.

Heterocoagulation– interaction between particles of different composition or size. The concept of heterocoagulation is general; it includes, as a special case, the interaction of two identical bodies in the considered case.

An example of heterocoagulation is mutual coagulation oppositely charged particles. In this case, the electrostatic forces change sign and become attractive forces. The absence of an energy barrier leads to rapid coagulation at any value With.

This process is quite widely used for the practical destruction of dispersed systems, which is especially important in connection with the problem of purifying natural and industrial waters. Thus, at water supply stations, before water enters sand filters, Al 2 (SO 4) 3 or FeCl 3 is added to it; positively charged sols of Fe or Al oxide hydrates, formed as a result of hydrolysis, cause rapid coagulation of suspended negatively charged soil particles. The phenomenon of mutual coagulation of sols is of great importance in a number of natural and technological processes. Mutual coagulation is common in nature (for example, when mixing sea and river water). Coagulation of river water colloids occurs as follows. Ions of seawater salts are adsorbed on charged colloidal particles of river water. As a result of adsorption, the particles are discharged, combine into large aggregates and settle. That is why a lot of silt gradually accumulates at the bottom, and later islands and shoals are formed. This is how the deltas of many of our rivers were formed.

Application of DLFO theory to heterocoagulation processes shows that in some cases the sign of not only U ter, but also U a changes. The nature of London forces in these cases does not change; they are always forces of attraction. A significant role in the process of fixation of adsorbed colloids is played by their coagulation, caused by the opposite charges of the adsorbed particles and the surface of the adsorbent.

L. A. Kulsky established that it is not the colloidal impurities of water that undergo coagulation, but the hydroxides formed during the hydrolysis of the coagulant. Water purification itself does not occur as a result of coagulation, but due to the adsorption of colloidal impurities on the surface of hydroxides. Coagulation of aluminum hydroxide particles and their associated precipitation from water occur under the influence of electrolytes dissolved in water.

102. The influence of electrolytes on the electrokinetic potential. Coagulation zone

Magnitude ζ -potential is determined by the total content of electrolytes in the solution. An increase in concentration entails a reduction in the thickness of the diffuse layer and, therefore, is accompanied by a decrease in the electrokinetic potential. It depends not only on the concentration of ions, but also on their valence, and counterions, i.e., ions whose charge is opposite to the charge of the particles, play a particularly important role. Particularly strong influence on ζ -potential is exerted by monovalent complex organic ions (dyes, alkaloids, etc.), the influence of which is commensurate with the influence on the potential of divalent inorganic ions.

Experience shows that hydrogen and hydroxyl ions, high valence ions (AI 3+, Fe 3+, PO 3-, citrate ions, etc.), as well as complex organic ions of alkaloids and dyes are not only capable of greatly reducing ζ -potential, but also at a certain concentration cause a change in its sign.

During coagulation, the particles must approach each other to a distance at which the energy of mutual attraction would be greater than the energy of thermal (Brownian) motion, which moves the particles away from each other. The necessary approach is prevented by electrostatic repulsion that occurs when the ionic shells of the diffuse layer come into contact. When an electrolyte is introduced into a colloidal solution, two independent processes occur.

First– exchange adsorption of ions in the outer diffuse shell, i.e. exchange of ions of the diffuse layer for the dominant ions of the introduced electrolyte; this explains their entrainment in the coagulum.

Second process– compression of this diffuse layer, as a result of which part of its ions passes into the internal (Helmholtz) part of the double electrical layer. Due to the reduction in the thickness of the diffuse layer, colloidal particles acquire the possibility of closer approach without repulsive forces arising between them; at some sufficiently small distance, the forces of mutual attraction are able to cause adhesion and coagulation of particles.

The compression of the electrical double layer can be judged by the drop ζ -potential, which is usually observed as the electrolyte is added. Its fall is not in itself the cause of coagulation, but serves as an indicator of changes occurring in the structure of the electrical double layer. Connection ζ - potential with coagulation is clearly manifested in the occurrence of irregular rows or zones of coagulation and can be considered with an example. Ions of tri- and tetravalent metals, as well as large organic cations, when added to a negative sol in increasing quantities, behave in a completely special way. Initially, upon reaching the coagulation threshold, they, like other coagulating ions, cause coagulation of the sol (the first coagulation zone). Then, in a new portion of the sol at a higher electrolyte concentration, coagulation does not occur (stability zone). Further, at an even higher electrolyte concentration, coagulation occurs again (second coagulation zone). In the second stability zone, as can be easily established by electrophoresis, colloidal particles no longer have a negative charge, but a positive one. Obviously, highly adsorbed highly charged cations and large organic cations can enter the Helmholtz part of the double layer in super-equivalent quantities. Due to this, the anions accompanying them enter the diffuse part of the double layer, which changes the sign ζ -potential.

This phenomenon is called coagulation zones, which consists in the appearance of a second stability zone after the coagulation zone with increasing electrolyte concentration. In this second zone, the particle charge turns out to be opposite in sign to the charge in the initial stability zone. With further growth With at some new critical value s"k the second zone of coagulation begins.

103. Kinetics of rapid coagulation. Smoluchowski's theory

In a narrow concentration range there is a rapid increase v to a certain value that does not change with further increase With. In accordance with this, three clearly demarcated zones can be distinguished: stability, slow coagulation (with a threshold sk m) and fast coagulation (with a threshold sk b).

Because with growth With the height of the energy barrier U decreases, we can explain the observed pattern by the fact that at c = sk m there appears a certain probability of the “hottest” particles passing through the barrier (T ≥ U) particles; further this probability increases and at c > sk b reaches the limiting value - one. In other words, in this region the barrier is reduced so much that all particles overcome it and the number of effective collisions leading to the connection of particles no longer changes. This number depends only on the particle concentration v and their speed.

The rapid coagulation region is defined as the region in which all impacts are effective.

Calculating v for this region is significantly simplified, since it comes down to counting the number of collisions. However, many difficulties arise here, since it is necessary to take into account the collisions of not only primary particles, but also more complex ones formed during the coagulation process. This task was brilliantly solved M. Smoluchowski (1916), who proposed a quantitative interpretation of the kinetics of fast coagulation based on the consideration of Brownian motion (diffusion) of particles.

Process speed v is a function of concentration v and the intensity of Brownian motion, characterized by the diffusion coefficient D.

The kinetics of coagulation was developed by M. Smoluchowski in relation to the simplest case of homogeneous spherical particles. When a known electrolyte concentration corresponding to the stability limit is reached, the initial single particles collide and form double particles; they, in turn, colliding with each other or with primary particles, form increasingly complex (quintuple, six, etc.) aggregates. If we denote by p 1, p 2, p 3, ... the concentration of particles consisting of one, two, three initial ones, then the total number of all particles after the start of coagulation is Σp = p 1 + p 2 + p 3 + ...

Since each time two particles combine, one is formed (a halving occurs), the coagulation process formally proceeds as a bimolecular reaction, i.e., the total number of particles decreases over time according to the second-order reaction kinetics equation:

Where k– coagulation rate constant, depending on the particle diffusion rate constant and on the radius of the sphere of attraction.

Smoluchowski's theory has been repeatedly subjected to experimental testing. Values v(process speed) and ξ , (coagulation period) is determined experimentally: either directly - by counting the number of particles per unit volume using the ultramicroscopic method at various points in time, with the construction of curves v – t, or by the light scattering method using the Rayleigh formula. Values v found by the tangent of the angle of inclination of the tangent to the curve, the values ξ – by the tangent of the angle of inclination of the straight line in coordinates. It should be noted that for an approximate estimate v And from to The time elapsed from the onset of exposure to the coagulating agent to the onset of noticeable turbidity of the solution is often used, as well as the ratio of the optical density (or light scattering) of the sol at a given standard point in time (for example, 1 or 24 hours from the beginning) to the initial optical density. This method is usually called turbidimetric or nephelometric. Experimental confirmation of the theory of rapid coagulation is an excellent proof of the correctness of the basic concepts of the theory of diffusion and Brownian motion.

104. Kinetics of coagulation. Reversibility of the coagulation process. Peptization

Theory developed by the Soviet physicist and chemist N. A. Fuks initially for coagulation of aerosols, takes into account the interaction of particles by introducing the value of the energy barrier into the kinetic equations.

Where W– coagulation slowdown coefficient or randomness factor, showing how many times the speed of the process decreases compared to fast coagulation.

It is clear from the equation that coagulation sharply slows down with increasing height of the energy barrier U, expressed in units kT, as well as with an increase in the thickness of the diffuse layer (braking at “distant” approaches) and with a decrease in the radius of the particle.

Theory shows a linear relationship W from With, confirmed experimentally. The physical meaning of the result corresponds to the fact that the speed of coagulation in a force field turns out to be greater than during fast coagulation in the absence of a field. Consequently, the influence of energy parameters on the kinetics of the process is described by the theory of slow coagulation.

Slow coagulation can be explained by the incomplete efficiency of collisions due to the existence of an energy barrier.

Reversibility of the coagulation process– the ability of coagulated systems to peptize.

The precipitation that falls during coagulation has a different structure. Some of them are dense and compact, which indicates close contact of particles, and coagulation is irreversible. Other coagulates occupy a large volume and have a loose, openwork structure. The particles in them remain isolated, separated by thin layers of liquid and compressed electrical layers. It can be assumed that by increasing the degree of diffusion of the electrical double layer, it is possible to again transfer the coagulum to the sol state. Indeed, in some cases, by freeing oneself from the electrolyte-coagulator by washing the sediment, it is possible to induce the reverse process of coagulation - peptization (transition of the coagel into a sol).

Peptization– this is the disaggregation of particles, the disruption of the connection between them, their separation from each other. Peptization is the more likely the more lyophilized the original sol is and the less time has passed since coagulation, since over time, during close interaction, particles gradually coalesce with a decrease in dispersion and surface energy. In this case, coagulation becomes irreversible and peptization is excluded. Method for practical implementation of peptization depends on the reasons causing coagulation. Indeed, peptization will be possible if the coagulum is washed from the electrolyte with water (using decantation, filtration or dialysis). For example, by washing it is possible to peptize fresh, especially precipitates of silicon dioxide, tin dioxide, metal sulfides, and sulfur coagulated with singly charged ions. An example of peptization with a pure liquid is peptization of clay under the influence of water. When interacting with water, ion-solvate layers appear on the surface of clay particles, weakening the bond between clay particles; As a result, a fairly stable suspension of clay in water is formed. Peptization is easier when adding a small amount of peptization agent, which allows you to restore the structure of the electrical double layer. Peptizers are potential-forming electrolytes. Soils have water permeability, increased swelling, are structureless, in a word, peptized. The detergent effect of soap is also associated with the peptization process. Fatty acid ions are adsorbed on the surface of “dirt” particles, thereby tearing them away from the contaminated surface and converting them into a sol state - peptizing; The sol is removed from the object with a stream of water and bubbles of foam.

Deryagin's rule

Deryagin's rule- a rule developed by the chemist B.V. Deryagin concerning the technology of many dosage forms.

The rule itself sounds like this: “To obtain a finely ground medicinal substance when dispersing it, it is recommended to add a solvent in half the mass of the crushed medicinal substance.”

Explanation of the rule: The drug particles have cracks (Griffith's fissures) into which liquid penetrates. The liquid exerts disjoining pressure on the particle, which exceeds the contracting forces, which promotes grinding. If the substance being ground is swelling, then it is thoroughly ground in dry form and only then liquid is added. After grinding the medicinal substance, agitation is used to fractionate the particles. Rustening consists of the fact that when a solid substance is mixed with a liquid that is 10-20 times larger in volume than its mass, small particles are suspended, and large ones settle to the bottom. This effect is explained by different rates of sedimentation of particles of different sizes (Stokes' law). The suspension of the most crushed particles is drained, and the sediment is re-crushed and stirred with a new portion of liquid until the entire sediment turns into a thin suspension. ,

Application in technology

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Concerning the technology of many dosage forms.

Rule wording:

Explanation of the rule

The drug particles have cracks (Griffith's fissures) into which liquid penetrates. The liquid exerts disjoining pressure on the particle, which exceeds the contracting forces, which promotes grinding. If the substance being ground is swelling, then it is thoroughly ground in dry form and only then liquid is added. After grinding the medicinal substance, agitation is used to fractionate the particles. Rustening consists of the fact that when a solid substance is mixed with a liquid 10-20 times larger in volume than its mass, small particles are suspended, and large ones settle to the bottom. This effect is explained by different rates of sedimentation of particles of different sizes (Stokes' law). The suspension of the most crushed particles is drained, and the sediment is re-crushed and stirred with a new portion of liquid until the entire sediment turns into a thin suspension.

Application in technology

Bismuthi subnitratis ana 3.0

Aqua destillatae 200 ml

M.D.S. Wipe your face

Recipe meaning: 200 ml of purified water is measured into the stand. In a mortar, grind 3 g of starch and 3 g of basic bismuth nitrate with 3 ml of water (according to Deryagin’s rule), then add 60-90 ml of water, stir the mixture and leave for several minutes. Carefully pour the thin suspension from the sediment into a bottle. The wet sediment is additionally ground with a pestle, mixed with a new portion of water, and drained. Grinding and agitation are repeated until all large particles turn into a thin suspension.

Notes

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See what the “Deryagin Rule” is in other dictionaries:

Deryagin's rule is a rule developed by the chemist B.V. Deryagin concerning the technology of many dosage forms. The rule itself sounds like this: “To obtain a finely ground medicinal substance when dispersing it, it is recommended to add ... Wikipedia

Boris Vladimirovich Deryagin Date of birth: August 9, 1902 (1902 08 09) Place of birth: Moscow Date of death: May 16, 1994 (1994 05 16) (91 years old) ... Wikipedia

Article on the topic Hinduism History · Pantheon Directions ... Wikipedia

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The calculated ratio is compared with the ratio of rapid coagulation thresholds, which follows from the Deryagin-Landau rule (Schulze-Hardy rule).

A quantitative clarification and theoretical justification of the Schulze-Hardy rule were given by Deryagin and Landau. To calculate the coagulation threshold, the theory gives the following formula

The coagulating ability of an electrolyte is characterized by a coagulation threshold, i.e., the minimum concentration of electrolyte in a colloidal solution that causes its coagulation. The coagulation threshold depends on the valence of the coagulating ion. This dependence is expressed by the rule of significance (Schulze-Hardy rule). A more strict, theoretically substantiated quantitative relationship between the rapid coagulation threshold y and the valence of the ion is expressed by the Deryagin-Landau rule

This result, first obtained theoretically by Deryagin and Landau, refines the Schulze-Hardy rule.

Basic principles of coagulation under the influence of electrolytes. The change in the stability of sols with changes in the content of electrolytes in them was already known to the first researchers of colloidal systems (F. Selmi, T. Graham, M. Faraday, G. I. Borschov). Subsequently, thanks to the work of G. Schultz, W. Hardy, G. Picton, O. Linder, G. Freundlich, W. Pauli, G. Kreut, N. P. Peskov, A. V. Dumansky and others, extensive experimental material was accumulated and basic theoretical generalizations were made. A huge contribution to the development of the theory of electrolyte coagulation was made by Soviet scientists B.V. Deryagin et al., P.A. Rebinder and his school. Experimentally established patterns during coagulation with electrolytes are known as coagulation rules

Graph the dependence of the optical density of O on the concentration of the electrolyte Se (Fig. III.5). From the intersection point of the continuation of both straight sections of the curve, a perpendicular is lowered onto the abscissa axis and the rapid coagulation threshold is found for each electrolyte. By dividing the obtained values of coagulation thresholds by the smallest of them, a significance rule is derived and compared with the Deryagin-Landau rule.

The existence of a sharp jump in properties at a certain distance from the substrate was discovered earlier by V.V. Karasev and B.V. Deryagin when measuring the dependence of the viscosity of some organic liquids on the distance to the solid wall. All this gives the right to call such layers a special, boundary phase, since the presence of a sharp interface is the main definition of the phase. The difference with ordinary phases is that the thickness of the boundary phase is a completely definite value for a given temperature.

The Deryagin-Verwey-Overbeck theory establishes that C is inversely proportional to the sixth power of the valency of the coagulating ion. The same dependence is reflected by the experimentally found Schulze-Hardy rule. The obtained excellent agreement well confirms the correctness of the theory of coagulation of lyophobic sols.

Numerous objects have shown that the coagulation threshold is inversely proportional to the valence of the coagulating ions to the power of 5 to 9, often to the power of 6. Lower values of the exponent (2-3) have also been observed. Thus, the Schulze-Hardy rule assumes only a high degree of dependence of the coagulation threshold on the valence (g) of counterions. Nevertheless, it is sometimes identified with the theoretically derived Deryagin-Landau law 2.

The influence of the valence of coagulating ions on the coagulation threshold is determined by the Schulze-Hardy rule: the greater the valence of coagulating ions, the greater their coagulating force or the lower the coagulation threshold. The theoretical justification for this rule was given in 1945 by B.V. Deryagin and L.D. Landau. The relationship they found between the coagulation threshold and the valence of coagulating ions is expressed in the form

If we take into account that in the case of a barrier mechanism at r

To obtain thinner and more stable aqueous suspensions of hydrophilic swelling substances (basic bismuth nitrate, zinc oxide, magnesium oxide, calcium phosphate, carbonate and glycerophosphate, koalin, sodium bicarbonate, iron glycerophosphate), it is most advisable to use the stirring method, which is a type of dispersion method. The essence of the technique is that the substance is dispersed first in dry form, then taking into account Deryagin’s rule. The resulting thin pulp is diluted approximately 10 times with water (solution), ground and the top layer of suspension is poured into a bottle for dispensing. The agitation operation is repeated until all the substance is dispersed and obtained in the form of a fine suspension.

The influence of a lubricant on friction parameters under boundary lubrication conditions is assessed, as a rule, by the amount of oil (medium) adsorption and by its chemical activity. Adsorption capacity is taken into account mainly for the case of using a chemically inactive lubricant medium. Thus, B.V. Deryagin proposed to evaluate the effectiveness of the oil film according to the oiliness criterion, which is the ratio of the roughness of lubricated and unlubricated surfaces. Another lubricity criterion is characterized by the ratio of the difference in the work done by the friction forces of non-lubricated and lubricated surfaces during the time required to abrade a film of thickness /g to the thickness of this film. Oiliness criteria are mainly determined by the duration of residence of oil (lubricant) molecules on the friction surface and the activity of the lubricant.

In electrolyte coagulation according to the concentration mechanism (for highly charged particles), the coagulation threshold C in accordance with the Deryagin-Landau rule (the rationale for the empirical Schulze-Hardy rule) is inversely proportional to the charge of 2 counterion13 to the sixth power, i.e.

The theory of the electric double layer was developed in the works of Frumkin and Deryagin. According to their ideas, the inner layer of ions of the double electric layer, called potential-forming, is closely adjacent to a certain part of oppositely charged ions (Fig. 50, a), called opposite ions and. This part of the counterions moves with the particle and forms a 6″ thick layer called adsorption. In Fig. 50, and the boundary between such a particle and the medium is indicated by a dotted line. The remaining counterions are located in a dispersion medium, where they are distributed, as a rule, diffusely.

However, recently experimental data have been obtained that indicate the inapplicability in some cases of the Schulze-Hardy rule in the form of the Deryagin-Landau law. In experience, significant deviations from this pattern are often observed, namely, in a number of cases, the coagulating effect of electrolytes is proportional to the valence of counterions to a degree less six. According to I. F. Efremov and O. G. Usyarov, this is a deviation from

The applicability of Deryagin's theory and the Schulze-Hardy rule for the coagulation of high-molecular compounds was shown using the example of rubber latexes when they interact with electrolytes of different valences (Voyutsky, Neumann, Sandomirsky).

However, even in the first approximation considered, the theory gives good agreement with experimental data (for example, Schenkel and Kitchener data obtained on monodisperse latexes), but perhaps its most important achievement is the substantiation of the Schulze-Hardy rule, which is rightly considered the cornerstone for testing stability theories. Let's consider this explanation. An analysis of the conditions for the stability of dispersed systems shows that the boundary conditions for rapid coagulation in terms of Deryagin’s theory can be written as Utyakh = O and dOmax/ek = 0, where C/max is the maximum energy (Fig. XIII. 7). These conditions express a decrease in the barrier height to zero.

In the simplest case, q = onst. Coef. Resting temperature is, as a rule, greater than the coefficient. kinematic T., so that the starting force (starting torque) is greater than the resistance to uniform movement. More precisely physical. processes during dry T. are reflected by the so-called. according to Deryagin's two-part friction law q = F/(N + PgS), where / is added to N by the pressure caused by intermolecular forces. interaction rubbing bodies, and S-pov-et factual. contact of rubbing bodies due to the waviness and roughness of T surfaces. contact of bodies is not complete.

In works of 1937 and 1940. Deryagin, using Fuchs' formulas for the coagulation rate of interacting particles, derived a criterion for the aggregative stability of weakly charged colloidal particles for two limiting cases when the radius of the particles is much less than the thickness of the ionic atmospheres, or, in other words, the characteristic Debye length, and when the radius of the particles is much greater than the thickness of the ionic atmospheres . In the second case, the criterion generalizes and quantitatively refines the empirical Eulers-Korff rule, which is in agreement with a number of experimental facts. At the same time, the existence of a distant minimum was shown on the curve expressing the dependence of the force of interaction (repulsion) on distance.

A well-known difficulty for the theory is that the inverse sixth degree rule (the Hardy-Schulze rule refined by Deryagin and Landau) is also observed when the dimensionless potential of the surface is not only small, but less than unity. This is possible, as Glazman et al. showed. , if the product of the potential and the charge of the counterion changes little when the latter changes. A quantitative explanation for this based on the charge independence of counterion adsorption was given by Usyarov.

The most developed theory of the stability of ion-stabilized colloidal solutions has led to a number of fundamental results. The theory of highly charged sols, which considers only concentration coagulation, made it possible to substantiate the Schulze-Hardy rule in the form of Deryagin-Laidau law 2. At moderate potentials of colloidal particles, coagulation thresholds change with the valence of counterions according to the law 2, where 2 a 6, which is also in accordance. with the Schulze-Hardy rule. The theory made it possible to substantiate the various patterns of the coagulating action of mixtures of electrolytes and the effect of synergism, which could not find any explanation. It should also be noted that, based on the theory, the widespread illegality of

Having obtained the exact coagulation threshold values for all electrolytes, a significance rule is derived, for which the found threshold values are divided by the lowest coagulation threshold (for AI I3). The experimental ratio of coagulation thresholds is compared with the theoretical one, calculated according to the Deryagin-Landau rule, according to which Y a b Vai u 11 1. The results of the comparison are analyzed and the work is documented in a laboratory journal.

See pages where the term is mentioned Deryagin's rule: Synthetic polymers in printing (1961) - [p.130]

Chemistry and chemical technology

Deryagin Landau's theory of coagulation

The Deryagin-Landau rule, derived by the authors on the basis of the concepts of the physical theory of coagulation, makes it possible to determine the value of the rapid coagulation threshold, which corresponds to the disappearance of the energy barrier on the curve of the general interaction of colloidal particles depending on the distance between them. The coagulation threshold values calculated using this rule do not always coincide with the experimental values due to the fact that the coagulating effect of ions depends not only on the valence, but also on specific adsorption, which is not taken into account by the above equation.

A brilliant confirmation of the DLFO theory was the calculation by B.V. Deryagin and L.D. Landau (1941) of the relationship between the values of coagulation thresholds for electrolytes containing ions of different charge values. It turned out that the coagulation threshold is inversely proportional to the sixth degree of charge of the coagulating cone. Therefore, the values of the coagulation thresholds for one-, two-, three- and four-charged ions should be related as

This is the essence of the theory of electrical stabilization and coagulation of dispersed systems by Deryagin, Landau, Verwey and Overbeck (DLVO theory).

The coagulation of emulsions has been poorly studied experimentally, since until recently there were no reliable methods for studying this process. But the theory of coagulation of dispersed systems has been developed in detail. This is the so-called DLFO (Deryagin-Landau-Verwey-Overbeck) theory.

Let us show that in the case of a generally accepted understanding of the driving force of coagulation (aggregation), conditions (1.266) are conditions for spontaneous coagulation and determine the stability threshold in concentration and represent a generalization of the stability theory of Deryagin and Landau.

Theoretical ideas about the reasons determining the stability of lyophobic sols were further developed in the works of B.V. Deryagin and L.D. Landau. According to Deryagin’s theoretical views and experimental data, a liquid film enclosed between two solid bodies immersed in it exerts disjoining pressure on them and thereby prevents their approach. The action increases rapidly with thinning of the film and is greatly reduced by the presence of electrolytes. From this point of view, the coagulation of particles is prevented by the wedging effect of the films separating them. The introduction of electrolytes into the sol leads to a change in the electrical double layer, compression of its diffuse part and a change in the strength of the films separating the particles and, thereby, to a violation of the stability of the sol. The well-developed mathematical theory of stability and coagulation by Deryagin and Landau leads to a strict physical justification of the Schulze-Hardy valency rule and at the same time provides a physical basis for the empirical patterns discovered by Ostwald.

Along with the qualitative relationships between coagulation interaction and coagulation effects, there is also a quantitative connection between them. For sols and suspensions, the coagulation threshold is always higher than the minimum electrolyte concentration that causes a coagulation interaction detected by rheological methods. As is known, the Deryagin-Landau theory gives the following expression for the coagulation threshold

The description of the stability of lyophobic sols includes a detailed consideration of the theory of the kinetics of rapid coagulation according to Smoluchowski, an approximate presentation of the theory of stability and coagulation with electrolytes of Deryagin-Landau-Verwey-Overbeck. When describing the structure of foams, special attention is paid to the role of black films formed at certain, critical concentrations of surfactants. Here, Bulgarian scientists also play a leading role.

According to the theory of coagulation by B.V. Deryagin and L.D. Landau, during Brownian motion, colloidal particles freely approach each other at a distance of up to 10 cm (on average), however, their further approach is prevented by the so-called disjoining pressure that arises in thin layers of water located between two surfaces. Disjoining pressure is the excess (compared to hydrostatic) pressure acting from a thin layer on the bounding surfaces. In sols, it is caused mainly by the mutual repulsion of counterions of the diffuse layer of approaching particles and, in addition, by the forces of molecular interaction between the surfaces of these particles and water molecules. Under the influence of electrostatic fields,

As already noted, in accordance with the Deryagin-Landau coagulation theory, a value of R0 10 m corresponds to the fixation of particles at a distance of close coagulation (strong coagulation contacts) m determines the position of particles at a distance

For the first time, a qualitative approach to studying the stability of sols was outlined by Kalman and Willstetter in 1932. The first quantitative calculations were made by B.V. Deryagin in the late 30s and then completed in the work of B.V. Deryagin and L.D. Landau (1941 .). A similar approach to studying the stability of colloidal systems was later developed in the works of Dutch researchers Verwey and Overbeck. Based on the initial letters of the main authors of the emerging physical theory of coagulation, this theory is now often called the DLFO theory.

For the first time, an explanation of the aggregative stability of dispersed systems and their coagulation with quantitative consideration of the total energy of interaction of particles was given by Deryagin, and then in more detail by Deryagin and Landau. Somewhat later, the same approach to the problems of stability and coagulation was carried out by Verwey and Overbeck. Therefore, the theory of interaction and coagulation of dispersed particles is called the Deryagin-Landau-Verwey-Overbeck theory, or DLFO for short.

It is not our task to discuss the numerous theories of coagulation developed by various researchers at the end of the last century - the beginning of this one. They are of historical interest only. Currently, the generally accepted physical theory of coagulation of lyophobic sols is Deryagin - Landau - Verwey - Overbeck, in which the degree of stability of the system is determined from the balance of molecular and electrostatic forces (see Chapter I). Although the detailed development of this theory has not yet been completed, it, thanks to a fundamentally correct interpretation of the role of surface forces of different natures, has made it possible to explain a number of colloid-chemical phenomena.

The development of a quantitative theory of stability and coagulation of colloidal systems, in particular, the DLFO theory (Deryagin-Landau-Verwey-Overbeck theory), has led, since the Second World War, to an increase in the number of studies of various colloidal systems.

N.P. Peskov found out the reason for the stability of colloidal solutions, and B. Deryagin and L. Landau developed the modern theory of coagulation. In the field of general theory of solutions, the works of N. A. Izmailov, devoted to the differentiating effect of solvents, are of great importance for analytical chemistry. In them, he used the long-known influence of the solvent on the strength of acids and bases, established that there are solvents in which this influence is especially manifested, specific to acids of different classes, i.e. it is differentiating, and using a large experimental material showed how use this phenomenon in analytical chemistry.

Thus, the theory of Deryagin and Landau is broader than the theory of coagulation. It is a theory of stabilization of colloidal systems, from which the coagulation of colloids is also derived.

The coagulation process in emulsions is described by the DLVO (Deryagin-Landau-Verwey-Overbeck) theory. Its essence boils down to the fact that in the presence of hydrophilic areas on the globules of the dispersed phase and the particles approaching at a distance of action of dispersion forces, they aggregate into conglomerates of particles of progressively increasing size. This process occurs with a decrease in free energy and occurs spontaneously. The presence of a structural-mechanical barrier around the dispersed phase globules does not protect them from adhesion to the outer layers, although it depends on the viscosity of the external environment. The rate of coagulation in a concentrated system can be estimated from the kinetics of increase in its structural and mechanical properties, if the rate of coalescence of globules is small compared to the rate of their coagulation.

Aggregative stability and long-term existence of lyophobic D.s. with the preservation of their properties is ensured by stabilization. For highly dispersed systems with a liquid dispersion medium, the introduction of stabilizers (electrolytes, surfactants, polymers) is used. In the Deryagin-Landau-Verwey-Overbeck stability theory (DLFO theory) basic. the role is played by ion-electrostatic. stabilization factor. Stabilization is provided electrostatically. repulsion of diffuse parts of double electric. layer, which is formed by the adsorption of electrolyte ions on the surface of particles. At a certain distance between particles, the repulsion of diffuse layers determines the presence of a minimum potential. curve (far, or secondary, minimum, see figure). Although this minimum is relatively shallow, it can prevent further convergence of particles attracted by the forces of intermolecular interaction. The near, or primary, minimum corresponds to strong adhesion of particles, in which case the energy of thermal motion is not enough to separate them. When approaching a distance corresponding to this minimum, the particles combine into aggregates, the formation of which leads to the loss of aggregative stability by the system. In this case, the stability of the system to coagulation is determined by the height of the energy. barrier.

The main scientific works are devoted to the study of surface phenomena. He developed the thermodynamics of systems taking into account the concept of disjoining pressure of thin layers that he introduced. For the first time, he carried out direct measurements of the molecular attraction of solids as a function of distance and disjoining pressure of thin layers of liquids. He theoretically substantiated the influence of the overlap of ionic atmospheres on the disjoining pressure of liquid layers and the interaction of colloidal particles, which allowed him to create the theory of coagulation and heterocoagulation of colloidal and dispersed systems. Together with the Soviet physicist L.D. Landau created (1928) the theory of stability of lyophobic colloids, now known as the DLFO theory (theory of stability of dispersed systems of Deryagin - Landau - Verwey - Overbeck). He discovered special properties of boundary layers of liquids, determined by their specific (anisotropic) structure. He developed the theories of thermoosmosis and capillary osmosis in liquids, thermophoresis and diffusionophoresis of aerosol particles. Author of the two-term law of external friction. Under his leadership, whisker-like diamond crystals were synthesized for the first time at low pressures. He developed methods for growing diamond crystals and powders from gas at low pressures.

The applicability of the Deryagin-Landau-Verwey-Overbeck theory for describing the stability and coagulation of dispersions in non-polar media was substantiated by Parfit et al. , who carefully analyzed the factors that complicate the quantitative description of coagulation processes.

Important P. I. - surface activity, manifested in a decrease in surface tension during the adsorption of one of the components of the solution. Surfactants have a huge practical effect. significance as regulators of P. i. they affect wetting, dispersion, adhesion, etc. The role of surfactants is especially important in colloidal systems that have a large excess of surface energy. Thermodynamic instability of such systems. manifests itself in coagulation and coalescence/gnosis when particles approach each other, which can be hampered by disjoining pressure resulting from the overlap of the surface layers of approaching particles. On this basis, physical science arose. theory of stability of colloids Deryagin - Landau - Verwey - Overbeck.

The most developed theory of the stability of ion-stabilized colloidal solutions has led to a number of fundamental results. The theory of highly charged sols, which considers only concentration coagulation, made it possible to substantiate the Schulze-Hardy rule in the form of Deryagin-Landau law 2. At moderate potentials of colloidal particles, coagulation thresholds change with the valence of counterions according to the law 2, where 2 a See pages where the term is mentioned Deryagin Landau's theory of coagulation: Adhesion of liquid and wetting (1974) - [p.196]

Landau-Deryagin rule

History of the development of colloid chemistry

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Coagulation rules

1. All strong electrolytes added to the sol in sufficient quantities cause its coagulation.

The minimum concentration of electrolyte that causes coagulation of the sol in a certain short period of time is called coagulation threshold.

The coagulation threshold can be calculated by knowing the concentration of the coagulating electrolyte C, the volume of added electrolyte V, and the volume of sol V of the sol (usually 10 ml): The reciprocal of the coagulation threshold is called coagulating ability electrolyte. This means that the lower the coagulation threshold, the greater the coagulating ability of the electrolyte.

2. Not the entire electrolyte has a coagulating effect, but only that ion whose charge coincides in sign with the charge of the counterions of the micelle of the lyophobic sol (the charge of the coagulating ion is opposite to the charge of the colloidal particle). This ion is called ion - coagulant.

3. The greater the charge of the ion, the greater the coagulating ability of the coagulant ion. This pattern is quantitatively described by empirical Schulze–Hardy rule, and a theoretically substantiated relationship between the charge of the coagulating ion and the coagulation threshold is given by Deryagin–Landau theory.

The ratio of coagulation thresholds for one-, two- and trivalent ions is equal to ( value rule) :

Consequently, the coagulating ability of a triply charged ion is 729 times higher than the coagulating ability of a singly charged ion.

Currently, deviations from the Schulze–Hardy–Deryagin–Landau rule (rule of significance) have been established. In addition to the charge, the coagulation threshold is influenced by the radius of the coagulating ion, the ability for adsorption and hydration, as well as the nature of the ion accompanying the coagulating one.

When multi-charged ions, such an effect as particle recharging, i.e. change in the sign of charge and potential of a colloidal particle. Added ions can exchange with counterions, replacing them in both the diffuse and adsorption layers. Moreover, if the multiply charged ion is small enough (for example, Al 3+, Th 4+, etc.), it replaces on the surface of the particles (in the adsorption layer) non-equivalent in charge number of former ions ( superequivalent adsorption). For example, instead of one or two K + ions, there may be a Th 4+ ion. Therefore, at a sufficiently high concentration of such ions, the charge they create on the surface can become greater in absolute value than the charge of potential-determining ions. This means a change in the sign of charge and potential. Now such ions become potential-determining (instead of the previous ones) and other counterions are oriented around the particle.

4. The coagulating ability of an ion with the same charge is greater, the greater greater is its crystal radius.

For singly charged inorganic cations, the coagulating ability decreases in the following order:

Ag + > Cs + > Rb + > NH 4 + > K + > Na + > Li +

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Rules for coagulation with electrolytes

Coagulation is observed when a certain amount of any electrolyte is added that does not chemically react with the dispersed phase of the system. Observations by G. Schulze established that coagulation is caused by one of the electrolyte ions. This ion is called the coagulating ion. Moreover, the coagulating ability of the ion increases with increasing charge of the ion in geometric progression at a ratio of 1:100:1000 (rule of significance or Schulze’s rule). Landau, Deryagin established that the coagulating ability changes in accordance with the 6th degree of charge of the ions: 1 6:2 6:3 6 = 1:64:729.

The patterns found by Schulze and Hardy are combined into one rule (Schulze-Hardy rule): the coagulating effect is that of the electrolyte ion, the charge of which is opposite to the charge of the granule and the coagulating effect is stronger, the higher the charge of the coagulating ion.

, mol/l.

The coagulation threshold depends on a number of conditions: from the moment of fixation after adding the electrolyte; from the method of observation; on the concentration of the test solution and the added electrolyte. The coagulation threshold is determined by measuring light scattering or titrating a colloidal solution with an electrolyte until obvious coagulation begins.

The reciprocal of the coagulation threshold is called coagulating ability: . It expresses the volume of sol coagulated under the action of 1 mmol of a coagulating ion. The higher the coagulating ability, the less electrolyte is available to induce coagulation.

Coagulating ability depends on atomic mass and charge, i.e. ion charge density. As the atomic mass increases, the charge density decreases and the ions become less polarized. As a result, their solvation shell becomes thinner. Therefore, large ions penetrate more easily into the adsorption layer of the micelle and neutralize the charge of the particle, causing coagulation of the sol. For example, for a silver iodide sol of composition xK +, the indifferent electrolytes are KNO 3, NaNO 3, Ca(NO 3) 2, Al(NO 3) 3, Th(NO 3) 4, and the coagulating ions are K +, Na +, Ca 2+, Al 3+, Th 4+. The coagulating ability of ions increases in the series: Li + + + + + or Na + 2+ 3+ 4+. The lower the hydration (solvation) of the cation, the lower the coagulation threshold, i.e. stronger coagulating effect. The hydration shell increases the size of the ion and prevents the ion from penetrating into the adsorption layer. The coagulating ability of organic compounds increases in accordance with Traube's rule.

Later, M. Hardy discovered that the charge of the coagulating ion is always opposite to the charge of the micelle granule (Hardy's rule). Consequently, the negative granule coagulates under the influence of positively charged ions, and the positively charged granule coagulates under the influence of the anions of the added electrolyte.

To characterize and compare different electrolytes, the concept of “coagulation threshold” is used - this is the minimum concentration of the added electrolyte at which coagulation begins (is observed):

, mol/l.

The reciprocal of the coagulation threshold is called coagulating ability:
. It expresses the volume of sol coagulated under the action of 1 mmol of a coagulating ion. The higher the coagulating ability, the less electrolyte is available to induce coagulation.

Theories of coagulation by electrolytes

Existing theories of coagulation have tried to answer 3 questions:

- why does coagulation occur at a certain concentration of electrolyte-coagulator?

- why does the concentration of the ion opposite to the charge of the granule play the main role?

- why does the influence of the charge of the coagulator ion obey the Schulze-Hardy rule?

Freundlich adsorption theory. According to this theory, coagulating ions on the surface of particles are adsorbed in accordance with the adsorption isotherm:
. Moreover, coagulation occurs with a gradual, equal decrease in the zeta potential due to the adsorption of an equivalent amount of different ions. Due to neutralization, the number of charges of potential-determining ions decreases, which leads to a decrease z-potential to a critical value.

The limitation of the theory lies in the fact that in practice equivalent adsorption is not always observed, the adsorption isotherms of different ions are different, and sometimes coagulation affects only the diffuse layer.

Muller's electrostatic theory. According to this theory, the introduction of an electrolyte does not change the total charge in the DES, but only causes compression of the diffuse layer (displacement of counterions into the adsorption layer). A decrease in the thickness of the ionic atmosphere leads to a decrease in z-potential, which reduces the stability of the sol.

This theory does not take into account the adsorption of introduced ions and their entry into the EDL.

Both theories are valid, both take place during coagulation, but at different stages. Due to limitations, they cannot be used to explain other types of coagulation.

DLFO theory developed by Deryagin, Landau, Verwey and Overbeck (1941). In accordance with the first letters of the authors' surnames, it is called DLFO. It takes into account the potential energy of particles and the equilibrium of e/static forces acting between them. When particles approach each other, e/static forces of attraction and repulsion arise between them. The state of the system is determined by their ratio. If the repulsive force is greater, then the system is stable. The predominance of attractive energy causes coagulation. The attractive energy is due to van der Waals forces and varies inversely with the square of the distance between particles:
. These forces act only at very small distances (1.10 − 10 – 1.10 − 11 m, i.e. 1/10 of the size of colloidal particles). Therefore, coagulation is observed only when particles approach each other at the proper distance. This approach occurs during the thermal movement of particles and therefore influences that increase the speed of movement of particles and the number of collisions (see factors causing coagulation) promote coagulation.

Fig.1. Overlap of ionic atmospheres of colloidal particles

As the distance between particles decreases, the forces of electrostatic repulsion increase. The solvation shell also prevents the particles from coming into contact. Typically, electrostatic repulsion forces appear when diffuse layers (ionic spheres) of similarly charged particles overlap. The repulsion energy decreases with increasing distance between them.

Fig.2. Potential coagulation curve

To determine the state of the system, the total energy is calculated (a potential coagulation curve is constructed). It has several sections: a deep primary minimum (potential well 1) in the region of small distances, a shallow secondary minimum (potential well 2) in the region of large distances. They indicate a significant predominance of attractive energy, i.e. in them U pr >> U ott.

In the area of average distances there is a maximum. If it is located above the x-axis, then repulsive forces act between the particles, i.e. the system is aggregatively stable. In this case, U out >> U in. The higher the maximum, the more stable the system.

To begin coagulation, preliminary partial neutralization of the particle charge to a certain value and destruction of the solvation shell is sufficient. This is achieved by introducing an electrolyte or removing a stabilizing electrolyte. The minimum particle charge at which coagulation begins is called critical z-potential (

0.03 V). At a critical value of the zeta potential, the kinetic energy of particle motion is sufficient to overcome the forces of residual electrostatic repulsion (U pr

U ott) and the adhesion of particles into aggregates.

According to the DLFO theory, during rapid coagulation with electrolytes, two mechanisms are distinguished: concentration coagulation and adsorption (neutralization) coagulation.

At concentration coagulation added indifferent ions do not change the value of the -potential. Coagulation occurs due to compression of the diffuse layer, i.e. displacement of counterions into the adsorption layer or by increasing the ionic strength of the solution.

Adsorption coagulation occurs as a result of a decrease in -potential. This type of coagulation is caused by electrolytes, the ions of which can (are able to) be adsorbed on the surface of particles and have a charge opposite to that of the granule. Penetrating into the adsorption layer, they neutralize potential-determining ions and reduce the -potential.

If there are free centers on the surface of microcrystals, then the crystal lattice is completed. For example, in the case of x K + sol, the addition of KI causes coagulation due to the adsorption of iodide ions. In this case, first the - and -potentials increase. After the centers are saturated, adsorption stops. A further increase in the concentration of KI leads to a decrease in the -potential due to compression of the diffuse layer (displacement of potassium ions into the adsorption layer). When a certain concentration is reached, the sol begins to coagulate.

If there are no free centers on the surface, then adsorption is not observed and the -potential does not increase, but compression of the diffuse layer occurs.

When AgNO 3 is added, the silver ions Ag + are non-indifferent. Since the potential-determining ions are iodide ions, the addition of silver ions leads to the formation of a sparingly soluble compound AgI. As a result, the number of potential-determining ones gradually decreases, which leads to a decrease in - and -potentials. At a critical value of the -potential, the sol coagulates according to the adsorption mechanism. Further addition of AgNO 3 leads to recharging and increasing the positive charge of the granule due to the selective adsorption of silver ions with the formation of a new DES: x NO 3 ─. With further addition of AgNO 3, the sol coagulates according to the concentration mechanism under the influence of nitrate ions.