Deryagin-Landau-Ferwey-Overbeck Theory of Coagulation. Deryagin-Landau-Verwey-Overbeck Theory of Coagulation The Effect of Electrolytes on the Electrokinetic Potential

Concerning the technology of many dosage forms.

Rule wording:

Rule explanation

The particles of the medicinal substance have cracks (Griffiths gaps) into which the liquid penetrates. The liquid exerts a disjoining pressure on the particle, which exceeds the contracting forces, which contributes to the grinding. If the substance to be ground is swelling, then it is thoroughly ground in dry form and only then the liquid is added. After grinding the medicinal substance, agitation is used to fractionate the particles. Resuspension consists in the fact that when a solid is mixed with a liquid, 10-20 times its mass in volume, small particles are in suspension, and large ones settle to the bottom. This effect is explained by different sedimentation rates of particles of different sizes (Stokes' law). The suspension of the most crushed particles is drained, and the sediment is again crushed and stirred up with a new portion of the liquid until the entire sediment passes into a fine suspension.

Application in technology

Bismuthi subnitratis ana 3.0
Aquae destillatae 200 ml
M.D.S. Wipe the skin of the face

Recipe value: 200 ml of purified water is measured into a stand. 3 g of starch and 3 g of basic bismuth nitrate are crushed in a mortar with 3 ml of water (according to the Deryagin rule), then 60-90 ml of water are added, the mixture is stirred and left for several minutes. Carefully drain the fine suspension from the sediment into the vial. The wet sediment is additionally triturated with a pestle, mixed with a new portion of water, and drained. Grinding and stirring are repeated until all large particles turn into a fine suspension.

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Notes

An excerpt characterizing the Deryagin Rule

She led him into a dark living room and Pierre was glad that no one there saw his face. Anna Mikhaylovna left him, and when she returned, he put his hand under his head and slept soundly.
The next morning Anna Mikhailovna said to Pierre:
- Oui, mon cher, c "est une grande perte pour nous tous. Je ne parle pas de vous. Mais Dieu vous soutndra, vous etes jeune et vous voila a la tete d" une immense fortune, je l "espere. Le testament n "a pas ete encore ouvert. Je vous connais assez pour savoir que cela ne vous tourienera pas la tete, mais cela vous impose des devoirs, et il faut etre homme. [Yes, my friend, this is a great loss for all of us, not to mention you. But God will support you, you are young, and now you are, I hope, the owner of great wealth. The will has not yet been opened. I know you well enough and I'm sure it won't turn your head; but it imposes obligations on you; and you have to be a man.]
Pierre was silent.
- Peut etre plus tard je vous dirai, mon cher, que si je n "avais pas ete la, Dieu sait ce qui serait arrive. Vous savez, mon oncle avant hier encore me promettait de ne pas oublier Boris. Mais il n" a pas eu le temps. J "espere, mon cher ami, que vous remplirez le desir de votre pere. [Afterwards, I may tell you that if I had not been there, God knows what would have happened. You know that uncle of the third day promised me not to forget Boris, but I didn’t have time. I hope, my friend, you will fulfill your father’s wish.]
Pierre, not understanding anything and silently, blushing shyly, looked at Princess Anna Mikhailovna. After talking with Pierre, Anna Mikhailovna went to the Rostovs and went to bed. Waking up in the morning, she told the Rostovs and everyone she knew the details of the death of Count Bezukhy. She said that the count died the way she would have wished to die, that his end was not only touching, but also instructive; the last meeting between father and son was so touching that she could not remember it without tears, and that she did not know who behaved better in these terrible moments: whether the father, who remembered everything and everyone in such a way in the last minutes and such he said touching words to his son, or Pierre, whom it was a pity to look at how he was killed and how, despite this, he tried to hide his sadness so as not to upset his dying father. "C" est penible, mais cela fait du bien; ca eleve l "ame de voir des hommes, comme le vieux comte et son digne fils", [It's hard, but it's saving; the soul rises when one sees such people as the old earl and his worthy son,] she said. She also spoke about the actions of the princess and Prince Vasily, not approving them, but under great secrecy and whispering.

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

A quantitative refinement and theoretical substantiation 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 the electrolyte is characterized by the threshold of coagulation, i.e., the minimum concentration of electrolyte D in a colloidal solution, which causes its coagulation. The coagulation threshold depends on the valency of the coagulating ion. This dependence is expressed by the significance rule (Schulze-Hurdy rule). A more rigorous, theoretically substantiated quantitative relationship between the rapid coagulation threshold y and the ion valency is expressed by the Deryagin-Landau rule

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

The main regularities of coagulation under the action of electrolytes. The change in the stability of sols with a change 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. Borshchov). Later, thanks to the work of G. Schulz, W. Hardy, G. Picton, O. Linder, G. Freindlich, W. Pauli, G. Kroyt, N. P. Peskov, A. V. Dumansky and others, extensive experimental material was accumulated and made the main theoretical generalizations. 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. The experimentally established regularities in coagulation with electrolytes are known as coagulation rules.

Build graphs of the dependence of the optical density O on the concentration of the electrolyte Set (Fig. III.5). From the point of intersection of the continuation of both rectilinear sections of the curve, a perpendicular is lowered to the abscissa axis and the rapid coagulation threshold is found for each electrolyte. By dividing the obtained values of the coagulation thresholds by the smallest of them, a rule of significance 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 even earlier by V. V. Karasev and B. V. Deryagin when measuring the dependence of the viscosity of some organic liquids on the distance to a 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 a phase. The difference with ordinary phases lies in the fact that the thickness of the boundary phase is a value quite definite for a given temperature.

The theory of Deryagin - Verwey - Overbeck establishes that Sk is inversely proportional to the sixth degree of valency of the coagulating ion. The same dependence reflects 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 valency of coagulating ions in powers of 5 to 9, often to powers 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 (r) of counterions. Nevertheless, it is sometimes identified with the theoretically derived law 2 of Deryagin-Landau.

The influence of the valency 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 power or the lower the coagulation threshold. The theoretical substantiation of 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 the 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, coalin, sodium bicarbonate, iron glycerophosphate), it is most advisable to use the stirring method, which is a kind of dispersion method. The essence of the technique lies in the fact that the substance is dispersed first in a dry form, then - taking into account the Deryagin rule. The resulting thin pulp is diluted approximately 10 times with water (solution), triturated and the top layer of the suspension is poured into a dispensing bottle. The stirring operation is repeated until all the substance is dispersed and obtained in the form of a fine slurry.

The influence of a lubricant on friction parameters under boundary lubrication conditions is usually estimated by the adsorption value of the oil (medium) and by its chemical activity. The adsorption capacity is taken into account mainly for the case of using a chemically inactive lubricating medium. So, B. V. Deryagin proposed to evaluate the effectiveness of the oil film by the criterion of lubricity, which is the ratio of the roughness of the lubricated and non-lubricated surfaces. Another criterion of lubricity is characterized by the ratio of the difference in the work of the friction forces of unlubricated and lubricated surfaces during the time required to abrade a film of thickness /r to the thickness of this film. The lubricity criteria are mainly determined by the residence time of the 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 Cc, in accordance with the Deryagin-Landau rule (justification of the empirical Schulze-Hardy rule), is inversely proportional to the charge of 2 counteriono13 to the sixth power, i.e.

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

Recently, however, 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. Experimentally, significant deviations from this pattern are often observed, namely, in some cases, the coagulating effect of electrolytes is proportional to the valence of counterions to a degree less than six. According to I. F. Efremov and O. G. Usyarov, this is a deviation from

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

However, even in the considered first approximation, the theory gives good agreement with experimental data (for example, the data of Schenkel and Kitchener 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. 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 Umax = 0 and domax/ek = 0, where C/max is the maximum energy (Fig. XIII. 7). These conditions express the reduction of the barrier height to zero.

In the simplest case, u = onst. Coef. T. rest, as a rule, more coefficient. kinematic T., so that the starting force (starting torque) is greater than the resistance to uniform movement. More precisely, physical processes with dry T. are reflected in the so-called. two-term by Deryagin's law of friction ts = F / (N + PgS), where / - complements, to N the pressure caused by the forces of the intermol. interaction rubbing bodies, and S-pov-et actually. contact of rubbing bodies due to the waviness and roughness of surfaces T. contact of bodies is not complete.

In the works of 1937 and 1940. Deryagin, using the 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 particle radius is much less than the thickness of ionic atmospheres, or, in other words, the characteristic Debye length, and when the particle radius is much greater than the thickness of ionic atmospheres . In the second case, the criterion generalizes and quantitatively refines the empirical rule of Eilers-Korf, which is in agreement with a number of experimental facts. At the same time, the existence of a far minimum on the curve expressing the dependence of the interaction (repulsion) force on the distance was shown.

A well-known difficulty for the theory was that the rule of the inverse sixth degree (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 shown by Glazman et al. , if the product of the potential and the charge of the counterion changes little when the latter changes. A quantitative explanation for this on the basis of the independence of the adsorption of counterions from the charge was given by Usyarov.

The most developed theory of the stability of ionostabilized colloidal solutions has led to a number of fundamental results. The theory of strongly charged sols, considering only concentration coagulation, made it possible to substantiate the Schulze-Hardy rule in the form of the Deryagin-Laidau law 2. At moderate potentials of colloidal particles, the coagulation thresholds change with the valency of counterions according to the law 2, where 2 a 6, which is also in accordance. with the Schulze-Hurdy rule. The theory made it possible to substantiate the various regularities of the coagulating action of electrolyte mixtures and the effect of synergism that could not be explained before. It should also be noted that, on the basis of the theory, the illegality of the widespread

Having obtained the values of the exact coagulation threshold for all electrolytes, a significance rule is derived, for which the found threshold values are divided by the smallest coagulation threshold (for AI I3). The experimental ratio of coagulation thresholds is compared with the theoretical ratio 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 registered in a laboratory journal.

See pages where the term is mentioned Deryagin's rule: Synthetic polymers in printing (1961) - [ c.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 values of the coagulation threshold calculated according to this rule do not always coincide with the experimental values due to the fact that the coagulating effect of ions depends not only on valence, but also on specific adsorption, which is not taken into account by the above equation.

A brilliant confirmation of the DLVO theory was the calculation by B. V. Deryagin and L. D. Landau (1941) of the ratio of the thresholds for coagulation by electrolytes containing ions of different charge values. It turned out that the coagulation threshold is inversely proportional to the sixth degree of the charge of the coagulating horse. 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 disperse systems by Deryagin, Landau, Verwey, and Overbeck (the DLVO theory).

The coagulation of emulsions has been poorly studied experimentally, since until recently there were no reliable methods for studying this process. On the other hand, the theory of coagulation of disperse 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 the conditions for spontaneous coagulation and determine the stability threshold in terms of concentration and represent a generalization of the stability theory of Deryagin and Landau.

Theoretical ideas about the causes that determine 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 them from approaching. The action increases rapidly with thinning of the film and decreases to a large extent from the presence of electrolytes. From this point of view, the coagulation of the particles is prevented by the wedging action 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 particles, and thus to a violation of the stability of the sol. The harmoniously developed mathematical theory of stability and coagulation by Deryagin and Landau leads to a rigorous physical substantiation of the Schulze-Hardy valence rule and, at the same time, provides a physical basis for the empirical regularities discovered by Ostwald.

Along with the qualitative relationships between coagulation interaction and coagulation effects, there is also a quantitative relationship between them. For sols and suspensions, the coagulation threshold is always higher than the minimum electrolyte concentration causing the 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 Smoluchovsky, an approximate presentation of the theory of stability and coagulation by Deryagin-Landau-Verwey-Overbeck electrolytes. 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), but their further approach is prevented by the so-called disjoining pressure that occurs in thin layers of water located between two surfaces. Disjoining pressure is an excess (compared to hydrostatic) pressure acting from the side of a thin layer on the bounding surfaces. In sols, it is mainly due to the mutual repulsion of the counterions of the diffuse layer of approaching particles and, in addition, 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 theory of coagulation, the value of R0 10 m corresponds to the fixation of particles at a distance of near coagulation (strong coagulation contacts) m determines the position of particles at a distance

For the first time, a qualitative approach to the study of the stability of sols was outlined by Kalman and Wilstetter 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 the study of the stability of colloidal systems was further developed in the works of the Dutch researchers Ferwey and Overbeck. By the initial letters of the main authors of the emerging physical theory of coagulation, this theory is now often called the DLVO theory.

For the first time, an explanation of the aggregative stability of disperse systems and their coagulation with a quantitative account of the total energy of particle interaction 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 DLVO 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 and the beginning of the present. They are of historical interest only. At present, the Deryagin-Landau-Verwey-Overbeck physical theory of coagulation of lyophobic sols is generally accepted, in which the degree of system stability 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 various nature, made it possible to explain a number of colloid-chemical phenomena.

The development of a quantitative theory of the stability and coagulation of colloidal systems, in particular, the theory of DLVO (the theory of Deryagin - Landau - Verwey - Overbeck) led, starting from 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 a modern theory of coagulation. In the field of the general theory of solutions, the works of N. A. Izmailov, devoted to the differentiating action of solvents, are of great importance for analytical chemistry. In them, he used the already long-known effect of a solvent on the strength of acids and bases, established that there are solvents in which this effect is manifested especially, specifically in relation to acids of different classes, that is, it is differentiating, and on 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 the stabilization of colloidal systems, from which the coagulation of colloids is already derived.

The coagulation process in emulsions is described by the DLVO theory (Deryagin-Landau-Werwey-Overbeck). Its essence boils down to the fact that in the presence of hydrophilic areas on the globules of the dispersed phase and the approach of particles to the distance of action of dispersed forces, they aggregate into conglomerates of particles of a progressively increasing size. This process occurs with a decrease in free energy and proceeds spontaneously. The presence of a structural-mechanical barrier around the globules of the dispersed phase does not protect them from adhesion by the outer layers, although it depends on the viscosity of the external medium. The rate of coagulation in a concentrated system can be estimated from the growth kinetics of 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 St. is provided by stabilization. For highly dispersed systems with a liquid dispersion medium, the introduction of in-in - stabilizers (electrolytes, surfactants, polymers) is used. In the stability theory of Deryagin-Landau-Verwey-Overbeck (DLVO theory) main. the role is assigned to ion-electrostatic. stabilization factor. Stabilization is provided by electrostatic. repulsion of the diffuse parts of the double electric. layer, to-ry is formed by the adsorption of electrolyte ions on the surface of the particles. At a certain distance between the particles, the repulsion of the diffuse layers causes the presence of a minimum of the ua potential. curve (far, or secondary, minimum, see Fig.). Although this minimum is relatively shallow, it can prevent further approach of the particles attracted by the forces of intermolecular interaction. The near, or primary, minimum corresponds to a strong cohesion of particles, with Krom the energy of thermal motion is not enough to separate them. Approaching at a distance corresponding to this minimum, the particles are combined 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 energetic. 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 introduced by him. 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 interlayers and the interaction of colloidal particles, which allowed him to create a theory of coagulation and heterocoagulation of colloidal and dispersed systems. Together with the Soviet physicist L. D. Landau, he created (1928) the theory of stability of lyophobic colloids, now known as the DLVO theory (the theory of stability of dispersed systems of Deryagin - Landau - Verwey - Overbeck). He discovered the special properties of the boundary layers of liquids, determined by their specific (anisotropic) structure. He developed the theory of thermoosmosis and capillary osmosis in liquids, thermophoresis and diffusiophoresis of aerosol particles. Author of the two-term law of external friction. Under his leadership, whiskers 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 theory of Deryagin - Landau - Verwey - Overbeck to describe 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. value as regulators P. I. they affect wetting, dispersion, adhesion, etc. The role of surfactants is especially great in colloidal systems, which have a large excess of surface energy. Thermodynamic instability of such systems. manifests itself in coagulation and coalescence / gnatia when the particles approach each other, Krom can be prevented by the disjoining pressure arising from the overlapping of the surface layers of the approaching particles. On this basis, a physical theory of stability of colloids Deryagin - Landau - Verwey - Overbeck.

The most developed theory of the stability of ionostabilized colloidal solutions has led to a number of fundamental results. The theory of strongly charged sols, considering only concentration coagulation, made it possible to substantiate the Schulze-Hardy rule in the form of the Deryagin-Landau law 2. At moderate potentials of colloidal particles, the coagulation thresholds change with the valency of counterions according to the law 2 , where 2 a See pages where the term is mentioned Deryagin Landau's theory of coagulation: Fluid Adhesion and Wetting (1974) - [ c.196 ]

Landau-Deryagin rule

History of the development of colloid chemistry

Getting to know each other better

coagulation rules

1. All strong electrolytes added to the sol in sufficient quantities cause it to coagulate.

The minimum electrolyte concentration 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 the ion whose charge coincides in sign with the charge of the counterions of the micelles 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 coagulating ability of an ion - coagulant is the greater, the greater the charge of the ion. Quantitatively, this regularity is described by the empirical Schulze-Hurdy rule, and the 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 ( significance rule) :

Therefore, the coagulating ability of a three-charged ion is 729 times higher than the coagulating ability of a single-charged ion.

At present, deviations from the Schulze - Hardy - Deryagin - Landau rule (significance rule) have been established. In addition to the charge, the coagulation threshold is influenced by the radius of the coagulating ion, the ability to adsorb and hydrate, as well as the nature of the ion accompanying the coagulating one.

When multiply charged ions, such an effect as particle recharge, i.e. change in the sign of the charge and potential of the colloidal particle. The added ions can exchange with counterions, replacing them both in the diffuse and in the adsorption layers. In this case, if a multiply charged ion is small enough (for example, Al 3+ , Th 4+ , etc.), it replaces on the particle surface (in the adsorption layer) non-equivalent in charge the 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 larger in absolute value than the charge of potential-determining ions. This means a change in the sign of the charge and potential. Now such ions become potential-determining (instead of the former ones) and other counterions are oriented around the particle.

4. The coagulating ability of an ion with the same charge is greater than larger than 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 adding a certain amount of any electrolyte that does not chemically react with the dispersed phase of the system. G. Schulze's observations established that one of the electrolyte ions causes coagulation. This ion is called the coagulator ion. Moreover, the coagulating ability of an ion increases exponentially with an increase in the ion charge at a ratio of 1:100:1000 (the rule of significance or the Schulze rule). Landau, Deryagin found that the coagulating ability changes in accordance with the 6th degree of ion charge: 1 6:2 6:3 6 = 1:64:729.

The patterns found by Schulze and Hardy are combined into one rule (the Schulze-Hardy rule): that electrolyte ion has a coagulating effect, 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: on the moment of fixation after the addition of 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 by titrating the colloidal solution with an electrolyte until overt coagulation begins.

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

The coagulating ability depends on the 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 solvate shell becomes thinner. Therefore, large ions more easily penetrate 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 +, indifferent electrolytes are KNO 3, NaNO 3, Ca (NO 3) 2, Al (NO 3) 3, Th (NO 3) 4, and 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; stronger coagulative effect. The hydration shell increases the size of the ion and prevents the penetration of the ion into the adsorption layer. The coagulating ability of organic compounds increases in accordance with the Traube rule.

Later, M. Hardy revealed 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 action of anions of the added electrolyte.

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

, mol/l.

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

Theories of coagulation by electrolytes

Existing theories of coagulation attempted to answer 3 questions:

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

– why does the concentration of the ion, which is opposite to the charge of the granule, play the main role in this case?

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

Freindlich's adsorption theory. According to this theory, coagulating ions are adsorbed on the particle surface 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 various ions. Due to neutralization, the number of charges of potential-determining ions decreases, which leads to a decrease in 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 various ions are different, 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 DEL, 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 z-potential, which reduces the stability of the sol.

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

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.

DLVO theory developed by Deryagin, Landau, Verwey and Overbeck (1941). In accordance with the first letters of the names of the authors, it is called DLFO. It takes into account the potential energy of particles and the balance 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 repulsion force is greater, then the system is stable. The predominance of the energy of attraction causes coagulation. The attraction energy is due to the van der Waals forces and varies inversely with the square of the distance between the 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 the particles approach at the proper distance. Such convergence occurs during the thermal motion of particles and therefore influences that increase the speed of particle movement and the number of collisions (see factors causing coagulation) promote coagulation.

Fig.1. Overlapping ionic atmospheres of colloidal particles

As the distance between the particles decreases, the forces of electrostatic repulsion increase. The solvate shell also prevents the particles from coming into contact. Usually, 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 built). 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 the energy of attraction, i.e. in them U pr >> U ott.

There is a maximum in the region of average distances. If it is located above the abscissa axis, then repulsive forces act between the particles, i.e. the system is aggregate stable. In this case, U otm >> U pr. The higher the maximum, the more stable the system.

To start coagulation, preliminary partial neutralization of the particle charge to a certain value and the destruction of the solvate shell are sufficient. This is achieved by introducing an electrolyte or removing a stabilizing electrolyte. The minimum particle charge at which coagulation begins is called the critical charge. 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 otm) and sticking of particles into aggregates.

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

At concentration coagulation the added indifferent ions do not change the value of the -potential. Coagulation occurs due to the 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 the -potential. This type of coagulation is caused by electrolytes, whose ions can (are able) to be adsorbed on the surface of particles and have an opposite charge to the granule. They penetrate into the adsorption layer, neutralize the 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 the sol x K +, the addition of KI causes coagulation due to the adsorption of iodide ions. In this case, at first - and -potentials increase. After saturation of the centers, adsorption stops. A further increase in the KI concentration 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 the diffuse layer is compressed.

When AgNO 3 is added, 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 AgI compound. As a result of this, 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 by the adsorption mechanism. Further addition of AgNO 3 leads to recharging and an increase in 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 AgNO3, the sol coagulates according to the concentration mechanism under the action of nitrate ions.

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

Rule wording:

To obtain a finely ground medicinal substance during its dispersion, it is recommended to add a solvent in half the amount of the mass of the crushed medicinal substance.

Rule explanation

Application in technology

Bismuthi subnitratis ana 3.0
Aquae destillatae 200 ml
M.D.S. Wipe the skin of the face

purpose of work: Synthesis of iron hydroxide hydrosol by condensation method; determining the threshold of electrolyte coagulation of the sol and studying its dependence on the charge of the coagulating ion; determination of the protective number of the stabilizer (high molecular weight compound). (The work is calculated for 3 hours)

Brief theoretical introduction

Iron hydroxide hydrosol is synthesized by the condensation method by carrying out the hydrolysis reaction of iron chloride at 100ºС:

The FeCl 3 hydrolysis reaction proceeds intensively with the formation of highly dispersed water-insoluble particles of Fe(OH) 3 .

The aggregative stability of iron hydroxide sol is provided, first of all, by the presence of double electrical layers on the surface of dispersed particles. The elementary particle of such a sol is called a micelle. A micelle is based on an aggregate insoluble in a given dispersion medium, consisting of many molecules (atoms): n, where n is the number of molecules (atoms) included in the aggregate.

The aggregate surface can be charged due to the selective adsorption of ions from the dispersion medium or the dissociation of molecules in the surface layer of the aggregate. In accordance with the Peskov-Fajans rule, ions that are part of the aggregate or specifically interact with it are adsorbed predominantly. Ions that impart a surface charge to an aggregate are called potential-determining ions. The charged aggregate forms the core of a micelle.

With this method of obtaining an iron hydroxide sol, the core n m Fe 3+ has a positive surface charge due to the adsorption of Fe 3+ ions from the medium (m is the number of adsorbed ions). The charge of the nucleus is compensated by the equivalent charge of oppositely charged ions - counterions located in the volume of the medium.

Counterions located directly at the surface of the nucleus (at distances close to the diameters of the ions), in addition to electrostatic forces, experience forces of adsorption attraction of the surface. Therefore, they are especially strongly bound to the micelle core and are called adsorption layer counterions (their number is m - x). The rest of the counterions make up the diffusely constructed ionic shell and are called counterions of the diffuse layer (their number corresponds to x).

The micelle of a hydrophobic sol is electrically neutral. The micelle formula of an ionostabilized iron hydroxide sol can be written as follows:

aggregate potential-counterions diffuse ions

defining dense layer

layer ions

_______________________

micelle core

_________________________________________

colloidal particle

______________________________________________________

In the micelle formula, the boundaries of a colloidal particle are indicated by curly brackets. Adsorption layer thickness δ small (< 1 нм) и постоянна. Толщина диффузного слоя λ is much larger (may be > 10 nm) and strongly depends on the concentration of electrolytes in the system.

According to the Gouy-Chapman theory, the counterions of the diffuse part of the DEL are distributed in the surface potential field in accordance with the Boltzmann law. The theory shows that the potential in the diffuse part of the layer decreases exponentially with distance. For a small value of the potential, this dependence is expressed by the equation

φ \u003d φ δ e - χ x(1)

where φ δ is the potential of the diffuse layer; X is the distance from the beginning of the diffuse part of the DEL; χ is the reciprocal of the thickness of the diffuse part of the layer.

The thickness of the diffuse part of the layer is taken to be the distance at which the potential of the diffuse part of the layer φ δ decreases by a factor of e.

According to the same theory, the thickness of the diffuse part of the layer is:

where ε 0 - electrical constant; ε - relative permittivity of the medium; F is the Faraday constant; I is the ionic strength of the solution; c 0 i is the ion concentration in the solution; z i is the charge of the electrolyte ion.

It follows from the equation that λ decreases with an increase in the concentration of the electrolyte and the charge of its ions and with a decrease in temperature.

When one phase moves relative to the other on the slip plane, the DEL breaks (usually in the diffuse part) and the electrokinetic ("zeta") ζ – potential (see Fig. 1).

In the process of coagulation of a highly dispersed layer of iron hydroxide, relatively small-sized sedimentation-resistant aggregates are formed.

ghats. Therefore, it is most convenient to study the coagulation of Fe(OH) 3 particles using the turbidimetric method. The applicability of this method is based on the strong dependence of the light scattering intensity on the particle size. When the particles coagulate, it increases, and the optical density of the sol increases accordingly. Since, when a light flux passes through colored sols, part of the light is scattered and part is absorbed, when studying coagulation in such systems by turbidimetry, it is necessary to exclude light absorption. For the Fe(OH)3 sol, this can be achieved by carrying out measurements with a red light filter, i.e. at the wavelength of the incident light λ = 620 - 625 nm.

The threshold of rapid coagulation is found by the threshold volume of electrolyte V to(ml), at which the optical density of the sol reaches its maximum value, and does not change with further addition of electrolyte. The value from to is calculated by the formula:

where from to is the concentration of the introduced electrolyte, mol/l; V is the volume of the sol, ml.

To prevent particle aggregation and protect hydrosols from the coagulating action of electrolytes, high-molecular compounds and colloidal surfactants that are soluble in water, such as proteins, soaps, starch, and dextrin, are used. Their stabilizing effect is based on the formation of adsorption gel-like films on the surface of particles of the dispersed phase and is associated both with a decrease in interfacial tension and with structural and mechanical properties of surface layers.

The protective ability of polymers or surfactants relative to the selected sol is characterized by a protective number S is the amount of substance required to stabilize a unit volume of the sol. Guard number S, as well as the coagulation threshold from to, determined by turbidimetry. Guard number S(g/l sol) is calculated by the equation:

where with st is the concentration of the stabilizer solution, g/l; V def is the volume of the stabilizer solution required to prevent coagulation of the sol, ml.

In the case of coagulation by electrolytes according to the concentration mechanism (for strongly charged particles), the coagulation threshold c to is inversely proportional to the charge z coagulating ion to the sixth power, i.e.

Fig 2. Dependence of optical density D sols on the volume of electrolyte - coagulator V el.

Fig 3. Dependence of optical density D sol on the volume of the stabilizer solution V st.

Meaning V def corresponds to the volume of stabilizer in the ash containing the threshold volume V to electrolyte, at which on the dependence curve D= f(V st) a lower horizontal section appears (Fig. 3).

Instruments and measurement methods

Photoelectrocolorimeter type FEK - 56M

electric hob

250 ml conical flask

20 ml tubes

25 ml burettes and graduated pipettes

2% (wt.) sodium sulfate solution

0.5 M sodium acetate solution

0.01% (mass.) gelatin solution

To obtain hydrosol Fe (OH) 3, 10 ml of iron chloride solution is poured into a flask with 250 ml of boiling distilled water. The resulting sol, red-brown in color, is cooled to room temperature.

10 ml of sol, water and electrolyte (Na 2 SO 4 or CH 3 COOHa solution) are poured into 10 test tubes in the following volumes:

Tube number … 1 2 3 4 5 6 7 8 9 10

Volume of water, ml ...... 10.0 9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.5 5.0

Electrolyte volume

V el, ml ……………. 0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

The electrolyte is introduced into each sample of the Sol for 2-4 minutes immediately before measuring its optical density.

Measure the optical density of the sol in each flask using a photoelectric colorimeter using a light filter No. 8 or No. 9.

Work sequence

The data obtained is recorded in table 1.

Table 1 . Results of the study of iron hydroxide sol coagulation by the optical method.

Concerning the technology of many dosage forms.

Rule wording:

Rule explanation

Application in technology

Bismuthi subnitratis ana 3.0

Aquae destillatae 200 ml

M.D.S. Wipe the skin of the face

Notes

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