Surface tension. The concept of surface energy and surface tension What is the energy of the surface layer of a liquid

Rice. 9.3. The action of intermolecular forces in the volume and on the surface

The resultant of all these forces is equal to 0. A molecule located on the surface is attracted only by internal molecules (the gas interacts weakly due to its rarefaction), the resultant of these forces is directed inside the body, i.e. the tendency to retract surface molecules into the body is clearly expressed, the surface of the body is, as it were, in a tense state and tends to contract. Since the action of forces on surface molecules is not compensated, such molecules have a free surface energy. Let's give a definition.

Free surface energy is the excess energy of the molecules of the surface layer compared to the molecules located inside DE = E* – E cf.

This energy depends on the nature of the substance of the contacting phases, on the temperature and on the area of ​​the interface between the phases.

S is the phase separation area, m 2;

s - coefficient of proportionality, called the coefficient of surface tension (or simply surface tension), J / m 2.

As you know, any system tends to a minimum of energy. To reduce the free surface energy (F s = sS), the system has two ways: to reduce the surface tension s or

area of ​​the phase interface S .

A decrease in s occurs during the adsorption of substances on solid and liquid surfaces (this is driving force adsorption), when one liquid spreads over another.

The desire to reduce the surface area S leads to the merging of the particles of the dispersed phase, to their enlargement (in this case, the specific surface decreases), i.e. this is the reason for the thermodynamic instability of dispersed systems.

The desire of the liquid to reduce the surface leads to the fact that it tends to take the form of a ball. Mathematical calculations show that the sphere has the smallest area at constant volume, so the particles of the liquid take on a spherical shape, unless these drops are flattened by gravity. Drops of mercury on the surface take the form of balls. The spherical shape of the planets is also attributed to the action of surface forces.

Surface tension

physical meaning surface tension coefficient (s) can be interpreted from different points of view.

1. Free surface energy (specific surface energy)

From expression 9.3. should

[J/m2], (9.4)

where F s – free surface energy, J;

Hence the physical meaning s is the free surface energy of the molecules of the surface layer on an area of ​​1 m 2 (or on another unit area), i.e. specific surface energy.

The greater the coefficient s, the greater the magnitude of the surface energy (see Table 9.1.).

2. Work on creating a new surface

Since energy is a measure of performance, then, replacing F s with W, we get:

[J / m 2 ], (9.5)

where W is the work to create a new interface, J;

S is the area of ​​the interface, m 2 .

From expression 9.5 it follows that s is the work that must be done in order to increase by unit area of ​​the phase interface under isothermal conditions with a constant volume of liquid(i.e. transfer the appropriate number of liquid molecules from the volume to the surface layer).

For example, when a liquid is sprayed, work is done that goes into free surface energy (when spraying, the phase separation surface increases many times). The same work is expended in the crushing of solids.

Since surface tension is related to the work expended on breaking intermolecular bonds during the transfer of molecules from the volume to the surface layer, it is obvious that surface tension is a measure of the forces of intermolecular interaction inside a liquid. The more polar the liquid, the stronger the interaction between molecules, the stronger the surface molecules are drawn inward, the higher the value of s.

From liquids highest value s near water (see Table 9.1.). This is no coincidence, since sufficiently strong hydrogen bonds are formed between water molecules. In non-polar hydrocarbons, only weak dispersion interactions exist between molecules, so their surface tension is low. The value of s is even greater for liquid mercury. This indicates a significant interatomic interaction (and a large value of the free surface energy).

Solids are characterized by a high value of s.

surface force

There is also a force interpretation of surface tension. Based on the dimension of the surface tension coefficient J / m 2, we can write

In this way, surface tension is a surface force applied to a unit length of the contour that bounds the surface and is aimed at reducing the interface.

The existence of this force is vividly illustrated by Dupre's experience. A movable jumper is fixed on a rigid wire frame (Fig. 9.2). A soap film is stretched in the frame (position 1). To stretch this film to position 2, a force F 1 must be applied, which is counteracted by the surface tension force F 2 . This force is directed along the surface (tangentially), perpendicular to the contour that bounds the surface. For the film in Fig. 9.2 the role of part of the circuit is played by a movable jumper.

Rice. 9.3. The action of surface tension forces

Thus, surface tension forces have the following properties:

1) evenly distributed along the phase line;

Surface tension occurs at all interfaces. In accordance with the state of aggregation of these phases, the following designations are introduced:

s L-G (at the liquid-gas boundary)

s L1-L2 (on the border of two immiscible liquids)

s T-G (at the boundary of a solid body - gas)

s T-L (on the border of a solid body - liquid)

The values ​​of the surface tension coefficients of some substances at the boundary with air and at some interfluid boundaries are given in Table. 9.3.

Directly experimentally, it is possible to determine the surface tension at the liquid-gas and liquid-liquid interfaces. Methods for determining surface tension at the interface with a solid body are based on indirect measurements.

Methods for determining surface tension are divided into three groups: static, semi-static and dynamic.

Static methods determine the surface tension of practically immobile surfaces formed long before the start of measurements and therefore in equilibrium with the volume of the liquid. These methods include the capillary rise method and the sessile or hanging drop (bubble) method.

Dynamic methods are based on the fact that some types of mechanical actions on a liquid are accompanied by periodic stretching and compression of its surface, which are affected by surface tension. These methods determine the nonequilibrium value of s. Dynamic methods include methods of capillary waves and an oscillating jet.

semi-static called methods for determining the surface tension of the phase boundary that arises and is periodically updated in the measurement process (the method of maximum bubble pressure and the stalagmometric method), as well as methods for tearing off the ring and retracting the plate. These methods make it possible to determine the equilibrium value of surface tension if the measurements are carried out under such conditions that the time during which the formation of the interface occurs is much longer than the time for equilibrium in the system to be established.

Table 9.3

Surface tension (specific surface energy)

some substances at the border with air (298 K)

Substance	s, mJ/m2		Substance	s, mJ/m2
Liquid		Solids
Hexane	18,4		Ice (270 K)
Octane	21,8		Quartz
ethanol	22,0		MgO
Petrol	25,0		Aluminum
Benzene	28,2		Iron
Acetic acid	27,8		Tungsten
Formic acid	36,6		Diamond
Aniline	43,2		Polymers
Water	71,95		Polytetrafluoroethylene	18,5
Mercury	473,5		Polyethylene	31,0
liquid - liquid		Polystyrene	33,0
benzene - water	34,4		PVC	40,0
aniline - water	4,8		Plexiglass	38,0
Chloroform - water	33,8		Enamel K-2	31,7

capillary rise method

The rise of a liquid in a capillary (if the liquid wets the walls of the capillary well) is caused by surface tension. Between the surface tension and the height of the rise of the liquid in the capillary (Fig. 9.4) there is the following relationship

, (9.7)

where s is the surface tension; h is the height of the liquid column; r 2 and r 1 are the densities of liquid and saturated vapor; g is the free fall acceleration; q is the contact angle of wetting; r is the capillary radius.

For the experiment, you need: a capillary with a diameter of 0.2-0.3 mm; a vessel into which the test liquid is poured; a cathetometer for measuring the height of liquid rise (accuracy ± 1 µm) and a device for highlighting the meniscus.

The greatest difficulties are caused by the measurement of the wetting angle q. Therefore, this method is most convenient to apply to liquids, in which q = 0 0 .

Rice. 9.4. Elevation of fluid in a capillary

This condition is observed for water and many organic liquids. Since cos 0 0 = 1, expression (9.7) is simplified and can be used to calculate s. The capillary rise method is one of the most accurate methods for determining surface tension.

The most characteristic property of a liquid, which distinguishes it from a gas, is that at the boundary with a gas, the liquid forms a free surface, the presence of which leads to the appearance of a special kind of phenomena called surface. They owe their appearance to the special physical conditions in which the molecules are located near the free surface.

Attractive forces act on each liquid molecule from the molecules surrounding it, located at a distance of about 10 -9 m from it (radius of molecular action). per molecule M 1 located inside the liquid (Fig. 1), forces from the same molecules act, and the resultant of these forces is close to zero.

For molecules M 2 resultant forces are nonzero and are directed inside the liquid, perpendicular to its surface. Thus, all liquid molecules in the surface layer are drawn into the liquid. But the space inside the liquid is occupied by other molecules, so the surface layer creates pressure on the liquid (molecular pressure).

To move a molecule M 3 located directly under the surface layer, on the surface, it is necessary to perform work against the forces of molecular pressure. Therefore, the molecules of the surface layer of the liquid have additional potential energy compared to the molecules inside the liquid. This energy is called surface energy.

Obviously, the larger the free surface area, the greater the surface energy.

Let the free surface area change by Δ S, while the surface energy changed to \(~\Delta W_p = \alpha \Delta S\), where α - coefficient of surface tension.

Since for this change it is necessary to do work

\(~A = \Delta W_p ,\) then \(~A = \alpha \cdot \Delta S .\)

Hence \(~\alpha = \frac(A)(\Delta S)\) .

The SI unit for surface tension is the joule per square meter (J/m2).

Surface tension coefficient- a value numerically equal to the work done by molecular forces when the area of ​​the free surface of the liquid changes per unit during an isothermal process.

Since any system, left to itself, tends to take a position in which its potential energy is the smallest, the liquid exhibits a tendency to reduce the free surface.

The surface layer of the liquid behaves like a stretched rubber film, i.e. all the time strives to reduce its surface area to the minimum dimensions possible for a given volume.

Example: a drop of liquid in a state of weightlessness has a spherical shape.

Literature

Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsia i vykhavanne, 2004. - C. 178-179.

1

The issue of forecasting and formation of the friction coefficient in movable detachable joints is considered. As a tool for controlling the value of the required friction coefficient, the energy "pumped" into the surface layer of the mating surfaces is proposed. The saturation of the surface layer with energy occurs during the implementation of the technological process of manufacturing a specific part at all stages of production, from the creation of a workpiece to the finishing operation. It is assumed that in order to the smallest value the value of the friction coefficient of the mating surfaces requires a minimum difference between their energies of the surface layer. Friction control by methods of technological influence will make it possible to approach the solution of the problem of smooth movement of contacting surfaces and positioning accuracy. The proposed approach will improve modern product designs and avoid significant economic costs.

surface layer energy

coefficient of friction

technological impact

1. Kragalsky I.V., Mikhin N.M. Friction units of machines: a Handbook. - M .: Mashinostroenie, 1984. - 280 p., ill.

2. Musokhranov M.V., Antonyuk F.I., Kalmykov V.V. Surface energy and the process of setting contact surfaces // Science and education: Electronic scientific and technical edition. 2014. - No. 11. URL: http://technomag.bmstu.ru/doc/737377.html (date of access: 12.01.2015).

3. Musokhranov M.V., Antonyuk F.I., Kalmykov V.V. Determining the value of surface energy through the electron work function // Contemporary Issues science and education: Electronic scientific journal. 2014. - No. 6. URL: http://www.science-education.ru/120-16036 (date of access: 15.01.2015).

4. Musokhranov M.V. Technological assurance of the quality of the surface layer of mechanical engineering guide elements: diss. cand. tech. Sciences - M. 2006. - S. 65.

5. Suslov A.G. The quality of the surface layer of machine parts. – M.: Mashinostroenie, 2000. – 320 p.

6. Suslov A.G., Dalsky A.M. Scientific foundations of engineering technology. – M.: Mashinostroenie, 2002. – 684 p.

The presence in the reference literature of normalized data for various cases of the layout of mating parts, it would seem, completely solves the problem of their operation. At the same time, it becomes obvious that in this case, when designing the surfaces of machine parts, both rubbing and constituting fixed pairs of mating parts, are characterized very approximately. The effect of the consequences of technological impact, as well as many natural properties kinematic pairs are not taken into account at all. Energy of the surface layers in best case only stated, but not used in practice. As a result, there may be cases of design errors and, as a result, certain economic costs. The determination of such costs requires special calculations in relation to individual pairs of parts and machines as a whole.

Influence of the energy of the surface layer on the coefficient of friction

In the vast majority of cases, for the functioning of friction pairs, they try to create structures with a relatively small coefficient of friction. This, as a rule, leads to some improvement in designs. In other cases, a relatively high coefficient of friction is needed, which can be called a friction coefficient with a value of more than one, and then the guiding element plays a special role in determining the position of the part in space. Thus, the design becomes more perfect.

The situation with the use of the friction coefficient in the most general form is conventionally presented in Fig. 1. The coefficient f1, taken from the reference literature, is most often used. At the same time, the actual coefficient of friction may turn out to be equal to f1', since the influence of the microgeometry and the energy of the surface layer will certainly manifest itself. In another case, for the same reasons, the coefficient of friction may be equal to f1″. But the constructor is sure that in his case the factor f1 works.

Determining the actual values ​​of friction coefficients, as well as ensuring their value by technological methods up to the required ones, is a priority task. modern technology machine and instrument making.

Rice. 1. Conditional representation of the use of friction coefficients. A typical case is when the coefficients fluctuate in the interval Δ: Δ= f1″ - f1′

For kinematic pairs of machines, the constant reduction of friction coefficients in practice is relevant. The need for this is determined by the following circumstances:

Reducing the coefficients invariably leads to economic benefits, having a beneficial effect in turn on the values ​​of the efficiency of products;

Numerical definition of economic benefits does not cause difficulties. This was especially clearly noted in the period of the creation of the bearing industry, when sliding friction was replaced by rolling friction;

The problem of smooth movement of contacting parts. The very nature of the profile of rubbing surfaces already predetermines the presence of so-called intermittent oscillations of elements in their relative movement. Any movement is always uneven, spasmodic. Reducing the values ​​of friction coefficients will invariably increase the uniformity of movement;

Requirements for positioning accuracy. In particular, this applies to the whole direction in electrovacuum engineering. At the same time, studies devoted to the coefficients of friction both in the ordinary atmosphere and in vacuum are of great interest. Positioning accuracy is one of the most important indicators of the quality of CNC machines used not only in mechanical engineering.

A synergistic approach to the impact of two microprotrusions of contacting surfaces requires special consideration. However, even here, considering one's own collision as a bifurcation, one can use the coefficient of friction as a kind of tool for the formation of a post-bifurcation self-organizing space. Such a process can be extended to the entire surface of the contacting parts.

Traditionally, contact is considered as a result of engagement and deformation of mutually intercalating roughness (microroughness) of two mating surfaces. According to this hypothesis, the friction coefficient will be the smaller, the smaller the roughness, i.e., the more carefully the rubbing surfaces are processed.

This point of view fits very well in the minds of designers and technologists. However, in the light of considering the issue of contacting parts, it is necessary to focus on the diagram in Fig. 2. With the relative movement of parts Dg and the presence of force Q, elastic-plastic states arise at the points of microcontacts of roughness. Deformation of microsurfaces occurs almost always, despite the fact that the angles β (according to the scheme of Fig. 2.) are small and do not exceed practically 35 ... 40 °, depending on the processing method. One pair of mating microprotrusions is shown in a deformed form in a very conventional way.

Rice. 2. Scheme of interaction of microroughnesses of contacting parts

The manifestation of the energy field is shown conditionally by arrows so that each mating part transfers the corresponding portion of energy to the other part. In turn, another part, which also has an energy potential, transfers the energy of the first part. Mutual energy transfer is shown schematically by solid and dotted arrows. Obviously, both the deformation of the microprotrusions and the transfer of energy always occur, even when there is a small gap between the contacting surfaces. Experience shows that with very smooth, "purely" polished surfaces, the friction forces not only do not decrease, but increase significantly. An example is the sticking effect when connecting gage blocks.

The expected dependence of the energy state and the friction coefficient can be shown by an example when the moment of seizing of two rubbing surfaces of the same roughness Ra = 0.08 μm was studied, the value of which was obtained by different technological operations. On fig. 3. The first column of the diagram illustrates that when grinding two contacting surfaces with the periphery of the circle along the intended movement, the force Q at which the jamming moment occurs is 1.8 MPa. The second column of the diagram illustrates the moment of seizing at the contact between the ground surface and the scraped surface. The third - two scraped surfaces. Fourth - polished surface and surface treated with lapping. Fifth - two ground surfaces. Sixth - lapped and scraped. V is the direction of the movement speed. It can be seen from the diagram that Q changes by more than 3 times. Its change is due to different values ​​of the friction coefficient. Since the roughness of all surfaces is identical, they apparently have a different level of energy that they received from the technological impact.

Rice. 3. Influence of the processing method on the moment of jamming

Thus, based on the foregoing, the contact must be considered not only as a result of the engagement of microprotrusions, but also taking into account the energy interaction forces that manifest themselves during the interaction of two surfaces. For very small gaps and distances between the parts, several molecules of the surface of the mating parts exchange the accumulated energy more intensively, thereby changing the nature of the interaction - the coefficient of friction. This hypothesis can probably more fully explain the nature and cause of the friction that occurs as a result of the interaction of carefully processed surface layers of machine-building parts.

The appearance of various mathematical dependences has a positive meaning, which makes it possible to link together the parameters of solid state physics, contrary to both design and technology. At the same time, it is obvious that the use of the scientific data presented directly in practice is difficult due to the lack of numerical values at the disposal of enterprises. It is necessary to continue the work begun, as well as to create a methodology for determining the energy components of friction coefficients, primarily for precision engineering.

Of great scientific interest is the process of energy transfer, which depends on the gap between microprotrusions and plastic deformation, leading to an intense energy exchange in the contact zones of mating parts. To the greatest extent, this usually occurs on surfaces whose roughness parameters are 0.1< Ra < 2,5 мкм, а радиусы кривизны микронеровностей 30-670 мкм, толщина деформированного слоя 17-58 мкм. И вероятно, обмен энергией идет по принципу перетекания ее из «объемов» с large quantity- in smaller ones.

Conclusion

Therefore, to create the lowest coefficient of friction, it is necessary, as follows from what was said above, that the difference in the values ​​of the energies of the rubbing pair be minimal. The best option is when the energies of the parts are the same, and the difference is zero.

Reviewers:

Astakhov M.V., Doctor of Technical Sciences, Professor, Head of the Department of Applied Mechanics, Kaluga branch of FSBEI HPE "Moscow State Technical University them. N.E. Bauman, Kaluga;

Shatalov V.K., Doctor of Technical Sciences, Professor, Head of the Department "Technologies of Materials Processing", Kaluga branch of FSBEI HPE "Moscow State Technical University named after I.I. N.E. Bauman, Kaluga.

The work was received by the editors on February 12, 2015.

Bibliographic link

Musokhranov M.V., Kalmykov V.V., Malyshev E.N., Zenkin N.V. ENERGY OF THE SURFACE LAYER OF METALS AS A TOOL OF INFLUENCE ON THE VALUE OF THE FRICTION COEFFICIENT // Basic Research. - 2015. - No. 2-2. – S. 251-254;
URL: http://fundamental-research.ru/ru/article/view?id=36797 (date of access: 07/14/2019). We bring to your attention the journals published by the publishing house "Academy of Natural History"

(molecular physics and thermodynamics)

Coefficient measurement

surface tension of the liquid.

Equipment : dynamometer, movable water cup, loop.

Brief theory.

Liquid particles (atoms, molecules, ions), like gas molecules, perform continuous chaotic oscillations around the equilibrium position, and the average kinetic energy of these oscillations determines the temperature of the body. The "freedom" of these movements is limited by the forces of interaction between particles, however, they can occasionally move, jump from one place to another. Therefore, the liquid has the property of fluidity. The same jumps explain the process of diffusion in a liquid. When heated, liquids expand, but their temperature coefficient of volumetric expansion is much lower than that of gases at constant pressure. Due to the small distances between the particles, liquids are not very compressible. The most characteristic feature of a liquid, which distinguishes it from gases, is that the liquid forms a free surface at the interface with a gas or vapor. That is why, for example, water in a vessel occupies only a part of the volume determined by its mass and density, while gases occupy the entire volume provided to them.

Consider the properties of the liquid surface. Molecules located in the surface layer of a liquid are in different conditions compared to molecules inside the liquid. Each molecule of a liquid, surrounded on all sides by other molecules, is subject to attractive forces that rapidly decrease with distance (Fig. 1); therefore, starting from a certain minimum distance, the forces of attraction between molecules can be neglected. This distance (of the order of 10 -9 m) is called the radius of molecular action r , and the sphere of radius r - sphere of molecular action.

Molecules on the surface of a liquid and in its depth are in different conditions. Consider a molecule located in the bulk of a liquid - a molecule BUT(Fig. 1). This molecule will be affected only by those neighbors that are within the sphere of molecular action of radius r. The forces with which these molecules act on the molecule BUT, are directed in different directions and are compensated on average, so the resulting force acting on a molecule inside the liquid from other molecules is equal to zero.

The situation is quite different if the molecule AT located at a distance from the surface r. AT this case the sphere of molecular action is only partially located inside the liquid. There is vapor above the surface of the liquid, the density of which is many times less than the density of the liquid (at temperatures below the critical temperature), so the interaction of vapor molecules with liquid molecules can be neglected. That is why the resultant of forces F, applied to each molecule of the surface layer, is not equal to zero and is directed inside the liquid. In this way, the resulting forces of all molecules of the surface layer exert pressure on the liquid, called molecular pressure.

The total energy of liquid particles is the sum of the energy of their chaotic (thermal) motion and the potential energy due to the forces of intermolecular interaction. To move a molecule from the depth of the liquid to the surface layer, work must be expended. This work is done at the expense of the kinetic energy of the molecules and goes to increase their potential energy. Therefore, the molecules of the surface layer of the liquid have a greater potential energy than the molecules inside the liquid. The larger the surface of the liquid, the more molecules that have excess potential energy. This extra energy possessed by molecules in the surface layer of a liquid is called surface energy, is proportional to the area of ​​the layer

, (1)

where σ is surface tension coefficient, which is the specific surface energy of the layer.

Surface energy is one of the types of internal energy that is absent in gases, but available in liquids and solids.

Molecules that are on the surface of the liquid will tend to "draw" into the liquid. Due to thermal motion, a small part of the molecules again comes to the surface. Molecules are drawn inward at a faster rate than the movement of molecules towards the surface. However, all molecules cannot go inside, so the number of molecules remains on the surface, at which the surface area is minimal for a given volume of liquid. The surface of the liquid will shrink until dynamic equilibrium is reached, i.e. until the number of molecules leaving the surface layer and returning to it in the same time is the same. Since the equilibrium state is characterized by a minimum of potential energy, the liquid, in the absence of external forces, will take such a shape that, for a given volume, it has a minimum surface, i.e. ball shape.

R consider a part of the liquid surface bounded by a closed contour abcd(Fig. 2).

The desire of this section to reduce leads to the fact that it acts on the adjacent sections with forces distributed over the entire contour. These forces called surface tension forces: a force that acts along the surface of a liquid perpendicular to the line that bounds this surface, and tends to reduce it to a minimum.

If an external force acts on the circuit F 1 , seeking to increase the area of ​​the contour by moving the section ab at a distance dx to a new position a" b" , then the following work will be done:

, (2)

it is taken into account here that
according to Newton's III law, where F- the force of the surface tension of the liquid, tending to keep the state of the liquid in equilibrium.

According to the law of conservation of energy
- work is equal to the change in the energy of the liquid surface, i.e. change in surface energy. In this way,

. (3)

Let us equate the right parts of equations (2) and (3), taking into account that
, where ℓ - contour length:

, Consequently,

. (4)

Formula (4) is the formula for calculating the surface tension force.

The value σ - is called the coefficient of surface tension. Its physical meaning can be determined using formulas (3) and (4):

Units of measurement of the coefficient of surface tension:

.

The surface tension coefficient depends on the type of liquid, on its temperature, on the degree of purity of the substance. For example, surfactants reduce the surface tension coefficient.

Solids and liquids have interfaces with neighboring phases. The state of substance molecules in the volume of the phase and in the surface layer is not the same. The main difference is that the surface layer of molecules of a solid or liquid has an excess of Gibbs energy in comparison with molecules of the bulk phase. The presence of the surface Gibbs energy is due to the incomplete compensation of the intermolecular attractive forces of the molecules of the surface layer due to their weak interaction with the adjacent phase.

Consider the action of molecular forces on a molecule in depth and on the surface of a liquid using the example of a two-phase liquid-air system (Fig. 1)

forces of different values, since the total attractive forces of a unit volume of liquid are much greater than a unit volume of air.

The resultant P of the forces of the molecule B is directed downward perpendicular to the surface of the liquid. Under the influence of such uncompensated forces are all molecules of the surface layer of the liquid.

Therefore, the potential energy of molecules at the interface is higher than that of molecules inside the phase. These differences in the energy state of all molecules of the surface layer are characterized by the free surface energy G s .

free surface energy is called the thermodynamic function that characterizes the energy of intermolecular interaction of particles on the phase interface with the particles of each of the contacting phases. The free surface energy depends on the number of particles on the interface, and therefore is directly proportional to the phase separation area and the specific energy of interfacial interaction:

where σ is the surface tension or specific free surface energy, which characterizes the energy of interfacial interaction per unit area of ​​the phase separation surface; S is the area of ​​the interface.

Equation (1) implies:

Surface tension σ is an important characteristic of any liquid. The physical meaning of surface tension can have an energy and force expression.

According to the energy expression, surface tension is the surface Gibbs energy per unit surface. In this case, σ is equal to the work spent on the formation of a unit surface. The energy unit of σ is .

The force definition of surface tension is formulated as follows: σ is the force acting on the surface tangentially to it and tending to reduce the free surface of the body to the smallest possible limits for a given volume. In this case, the unit of σ is .

In heterogeneous systems, the interface per unit mass is very small. Therefore, the Gibbs surface energy G s can be neglected.

According to the second law of thermodynamics, the Gibbs energy of a system spontaneously tends to a minimum. In individual liquids, the decrease in the surface Gibbs energy is carried out mainly due to the reduction of the surface (merger of small droplets into larger, spherical shape of liquid droplets in suspension). In solutions, a decrease in the surface Gibbs energy can also occur due to a change in the concentration of components in the surface layer.

Surface energy and surface tension depend on temperature, the nature of the adjacent media, the nature and concentration of dissolved substances.

Adsorption, its basic concepts and types

Adsorption called the concentration (thickening) of substances on the interface. A substance that adsorbs another substance is called an adsorbent (Fig. 2). The name of the adsorbed substance depends on its position in relation to the adsorbent. If a substance is in volume and can be adsorbed (its chemical potential is μ V, and its concentration is c), then it is called adsorbent. The same substance in the adsorbed state (its chemical potential already becomes equal to μ B, and the concentration to c B) will be called adsorbate. In other words, to designate the position of the adsorbed substance, the terms adsorbent(before adsorption) and adsorbate(after adsorption).

liquid or gas (see fig. 2). Some of the molecules from the surface can go back into the bulk. The reverse process of adsorption is called desorption.

Depending on the state of aggregation of the adsorbent and adsorbent, adsorption is distinguished at the boundary of a solid body and a gas (S-G), a liquid and a gas (L-G) and a solid body and a liquid (T-L).

Let us consider some adsorption processes as an example.

Activated carbon has a significant porosity and increased adsorption capacity, adsorbs volatile substances well. The fats and proteins that make up milk are adsorbed at the water-air interface and reduce the surface tension of water from 73 to 45-60 mJ/m 2 . Purification of vegetable oils from dyes, the so-called bleaching process, is carried out using bentonite clays, which act as an adsorbent. On the basis of adsorption, the liquid is purified and clarified.

The adsorption of gases on coal occurs at T-G border, fats and proteins - on Y-G border, and coloring substances on bentonite - along the border of two condensed tel T-F. Moreover, in the first case, gas or vapor molecules are adsorbed on a solid surface, and in the second and third cases, the substance dissolved in the liquid acts as an adsorbate. In the course of all these processes, substances are concentrated at the interface.

The excess of the adsorbate in the surface layer compared to its surface amount in this layer characterizes excess, or the so-called Gibbs adsorption(G). It shows how much the adsorbate concentration increased as a result of adsorption:

where N is the amount of adsorbate in the adsorption layer when its concentration on the surface corresponds to the concentration in the bulk phase.

When the concentration of the adsorbate on the surface of the adsorbent significantly exceeds its concentration in the volume, i.e. c B >> c, then the value of N can be neglected and we can assume that

In the case of adsorption at the liquid-gas interface and adsorption on solid smooth surfaces, the quantities Г and А are determined relative to the unit area of ​​the phase interface, i.e. the dimension of G and A will be mol / m 2.

For a solid and especially porous powdered adsorbent having a significant phase boundary, adsorption is expressed in relation to a unit mass of the adsorbent, i.e. in this case, the quantities Г and А have the dimension mol/kg.

Thus, the adsorption value for the ith component

where n i is the excess number of moles of the adsorbate of the i-th component on the surface compared to its content in the volume; B is the surface area of ​​the phase separation, m 2; m is the mass of the porous powdered adsorbent, kg.

In the case of adsorption of one component, the equations are simplified:

(6)

Adsorption at the liquid-gas, liquid-liquid interface.
Gibbs adsorption equation

When dissolved in water, surfactants accumulate in the surface layer; surface-inactive substances (SIS), on the contrary, are concentrated in the volume of the solution. In both cases, the distribution of the substance between the surface layer and the internal volume obeys the principle of minimum Gibbs energy: on the surface is the substance that provides the lowest surface tension possible under given conditions. In the first case, these are surfactant molecules, in the second, solvent (water) molecules. adsorption takes place.

The difference in concentrations in the surface layer and the volume of the solution leads to the emergence of osmotic pressure forces and the diffusion process, which tends to equalize the concentrations throughout the volume.

When the decrease in surface energy associated with the depletion or enrichment of the surface layer in solute will be balanced by the opposing forces of osmotic pressure (or when the chemical potentials of the solute and solvent in the surface layer will be equal to their chemical potentials in the volume of the solution). A mobile equilibrium will come in the system, which is characterized by a certain concentration difference between the surface layer and the volume of the solution.

The excess or deficiency of solute in the surface layer, per unit area. Denoted through G, called Gibbs adsorption and expressed in mol / m 2, kg / m 2, etc.

In those cases when the concentration of the adsorbent in the surface layer is greater than in the volume of the solution, Г>0 - adsorption is positive. This is typical for surfactant solutions. With a lack of substance in the surface layer G<0 – адсорбция отрицательна, что имеет место для растворов ПИВ.

Thus, positive adsorption is called adsorption, accompanied by the accumulation of dissolved substances in the surface layer. Adsorption is called negative, accompanied by the displacement of the dissolved substance from the surface layer into the medium.

Only positive adsorption is of practical importance; therefore, the term “adsorption” means precisely this case.

Adsorption isotherm for liquid interfaces, i.e. for liquid-gas and liquid-liquid systems, as a rule, it has the form shown in Figure 3.

Fig 3 Adsorption isotherm

The greatest and constant value of adsorption G or A, at which saturation of the adsorption layer is achieved and adsorption is no longer dependent on concentration, is called the limiting adsorption G PR (A PR).

The limit of positive adsorption is the complete saturation of the surface layer with solute molecules. The process of saturation of the monolayer is retarded by thermal motion, which entrains some of the molecules of the adsorbed substance from the surface layer into the solution. As the temperature decreases, the thermal motion weakens and the surface excess at the same concentration c of the solution increases.

The limit to which negative adsorption tends is the complete displacement of the solute by solvent molecules from the surface layer.

There are no simple and accessible methods for direct determination of the excess of a dissolved substance in an adsorption layer at moving interfaces. However, at liquid-gas and liquid-liquid interfaces, surface tension can be accurately measured, so the Gibbs adsorption isotherm equation is especially important to determine adsorption:

(7)

where c is the equilibrium concentration of the adsorption layer and the gaseous or dissolved substance in the medium from which adsorption occurs;

dσ is an infinitesimal change in surface tension; R is the universal gas constant; T is temperature; dc is an infinitesimal change in the concentration of the solution; Г - surface excess of the adsorbed substance.

The Gibbs equation makes it possible to determine the value of the surface excess from the decrease in the value of σ caused by a change in the concentration of the solution. Г is the difference between the concentrations of the adsorbent in the surface layer and in the volume of the solution. The final result of calculating r does not depend on how the concentration c is expressed. The sign of adsorption is determined by the sign of the derivative.

If adsorption is positive, then according to equation (7)<0, Г>0. At negative adsorption >0, Г<0. Зависимость знака адсорбции от знака называют правилом Гиббса.

From the point of view of thermodynamics, the Gibbs adsorption isotherm equation is universal and applicable to the interfaces of any phases. However, the field of practical use of the equation for determining the adsorption value is limited to systems in which experimental measurement of surface tension is available, i.e. liquid-gas and liquid-liquid systems. The values ​​of Γ calculated from this equation coincide most closely with the values ​​found by other methods in the region of dilute solutions.