Surface energy of a liquid. Surface tension

Molecules in a liquid have kinetic energy thermal motion and potential energy of intermolecular interaction. To move a molecule from the depth of a liquid to the surface, work must be done to overcome the force of molecular pressure. This work is done by the molecule due to the stock of kinetic energy and is used to increase its potential energy. Therefore, the molecules of the surface layer have additional potential energy compared to the molecules inside the liquid. This additional potential energy possessed by the molecules of the surface layer is called surface energy.

If the surface of the liquid is stretched, then more and more new molecules will come to the surface, and the potential energy of the surface layer will increase. Therefore, the surface energy is proportional to the area of ​​the liquid surface itself (Fig. 4).

Where A is the work of the surface tension force; F is the force of surface tension; D x– stretching of the film; D S– change in the surface area of ​​the film.

From this expression, one more definition of the surface tension coefficient can be given.

The surface tension coefficient is equal to the free surface energy per unit surface area. In this case, the unit of measurement is [a]=[J/m 2 ].

Impurities in the liquid have a great influence on the surface tension. For example, soap dissolved in water reduces the surface tension to 0.045 N/m, while sugar or salt increases it. Substances that change surface tension are called superficially active. These include oil, soap, alcohol. This phenomenon is explained by intermolecular interactions between molecules. If the interaction between the molecules of the liquid itself is greater than between the molecules of the liquid and the impurity, then the impurity molecules are pushed to the surface and the impurity concentration on the surface is greater; than in volume, which leads to a decrease in surface tension.

Surfactants are widely used in cutting metals, drilling rocks, etc., since the destruction of rocks in their presence is easier, being adsorbed on the surface of a solid body, they penetrate inside microcracks and contribute to the further development of these cracks in depth.

(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 various conditions. Consider a molecule located in the bulk of a liquid - a molecule A(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 A, 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 IN located at a distance from the surface r. In this case, the sphere of molecular action is only partially located inside the liquid. Above the surface of the liquid there is vapor, 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. Thus, 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. Thus,

. (3)

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

, hence,

. (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.

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 experiences attraction only of 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 when substances are adsorbed on solid and liquid surfaces (this is the driving force of 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. More more value s y 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

Thus, 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 notation:

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 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. This additional energy possessed by the molecules in the surface layer of the liquid, called the surface energy, is proportional to the area of ​​the layer D S:

Where s- surface tension.

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., the shape of a ball. Observing the smallest droplets suspended in the air, we can see that they really have the shape of balls, but somewhat distorted due to the action of the forces of gravity.

So, the condition for stable equilibrium of a liquid is a minimum of surface energy. This means that a liquid for a given volume should have the smallest surface area, i.e., the liquid tends to reduce the free surface area. In this case, the surface layer of the liquid can be likened to a stretched elastic film in which tension forces act.

Under the action of surface tension forces (directed tangentially to the liquid surface and perpendicular to the section of the contour on which they act), the liquid surface contracted and the considered contour moved to the position marked in light gray. The forces acting from the selected area to the adjacent areas do work

Where f is the surface tension force acting per unit length of the liquid surface contour.

From fig. 97 shows that D lDx=D S, i.e.

This work is done by reducing the surface energy, i.e.

Comparison of expressions (66.1) - (66.3) shows that

i.e. surface tension s is equal to the force of surface tension per unit length of the contour that bounds the surface. Unit of surface tension - newton per meter(N/m) or joule per square meter(J / m 2) (see (66.4) and (bb.1)). Most liquids at a temperature of 300 K have a surface tension of the order of 10 -2 -10 -1 N/m. Surface tension decreases with increasing temperature, as the average distances between liquid molecules increase.

Surface tension essentially depends on the impurities present in liquids. Substances that reduce the surface tension of a liquid are called surface active. The best known surfactant for x water is soap. It greatly reduces its surface tension (approximately from 7.5 10 -2 to 4.5 10 -2 N/m). Surfactants that lower the surface tension of water are also alcohols, ethers, oil, etc.

There are substances (sugar, salt) that increase the surface tension of a liquid due to the fact that their molecules interact with the molecules of the liquid more strongly than the molecules of the liquid interact with each other. For example, if you salt a soap solution, then more soap molecules are pushed into the surface layer of the liquid than in fresh water.

Lecture 11. Characteristics of the liquid state of matter. The surface layer of the liquid. The energy of the surface layer. Phenomena at the boundary of a liquid with a solid body. capillary phenomena.

CHARACTERISTICS OF THE LIQUID STATE OF A SUBSTANCE

Liquid is an aggregate state of matter, intermediate between gaseous and solid.

A substance in a liquid state retains its volume, but takes the shape of the vessel in which it is located. The conservation of volume in a liquid proves that attractive forces act between its molecules.

If a sphere of molecular action is described around a liquid molecule, then inside this sphere there will be centers of many other molecules that will interact with our molecule. These interaction forces keep the liquid molecule near its temporary equilibrium position for approximately 10 -12 -10 -10 s, after which it jumps to a new temporary equilibrium position approximately the distance of its diameter. Between jumps, liquid molecules oscillate around a temporary equilibrium position.

The time between two jumps of a molecule from one position to another is called the time of settled life.

This time depends on the type of liquid and temperature. When a liquid is heated, the average time of the settled life of molecules decreases.

So, in a small volume of liquid, an ordered arrangement of its molecules is observed, and in a large volume it turns out to be chaotic. In this sense, it is said that in a liquid there is a short-range order in the arrangement of molecules and there is no long-range order. This structure of the liquid is called quasi-crystalline (crystal-like).

LIQUID PROPERTIES

1. If the time of action of the force on the liquid is short, then the liquid exhibits elastic properties. For example, when a stick is struck sharply against the surface of the water, the stick may fly out of the hand or break; A stone can be thrown in such a way that when it hits the surface of the water, it bounces off it, and only after making a few jumps does it sink in the water.

2. If the time of exposure to the liquid is long, then instead of elasticity, the fluidity of the liquid appears. For example, the hand easily penetrates into the water.

3. With a short-term action of a force on a liquid jet, the latter exhibits brittleness. The strength of a liquid and rupture, although less than that of solids, are not much inferior to them in magnitude. For water, it is 2.5-10 7 N/m 2 .

4. The compressibility of a liquid is also very small, although it is greater than that of the same substances in the solid state. For example, with an increase in pressure by 1 atm, the volume of water decreases by 50 ppm.

Breaks inside a liquid, in which there are no foreign substances, such as air, can only be obtained with an intense impact on the liquid, for example, when propellers rotate in water, when ultrasonic waves propagate in the liquid. Such voids inside the liquid cannot exist for a long time and abruptly collapse, i.e., disappear. This phenomenon is called cavitation (from the Greek "cavitas" - a cavity). It causes rapid wear of propellers.

SURFACE LIQUID

The average value of the resultant of the molecular forces of attraction applied to a molecule located inside a liquid (Fig. 2) is close to zero. Random fluctuations of this resultant force the molecule to perform only chaotic motion inside the liquid. The situation is somewhat different with molecules located in the surface layer of a liquid.

Let us describe spheres of molecular action around the molecules with a radius R (of the order of 10 -8 m). Then for the upper molecule in the lower hemisphere there will be many molecules, and in the upper hemisphere - much less, since the bottom is liquid, and the top is vapor and air. Therefore, for the upper molecule, the resultant of the molecular forces of attraction in the lower hemisphere is much greater than the resultant of the molecular forces in the upper hemisphere.

Thus, all liquid molecules located in the surface layer with a thickness equal to the radius of molecular action 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, which is called molecular pressure.

Forces acting in the horizontal plane pull the surface of the liquid together. They're called surface tension forces

Surface tension- physical quantity equal to the ratio of the surface tension force F applied to the boundary of the surface layer of the liquid and directed tangentially to the surface, to the length l of this boundary:

The unit of surface tension is newton per meter (N/m).

Surface tension is different for different liquids and depends on temperature.

Typically, surface tension decreases with increasing temperature, and at the critical temperature, when the density of the liquid and vapor are the same, the surface tension of the liquid is zero.

Substances that reduce surface tension are called surface-active (alcohol, soap, washing powder)

To increase the surface area of ​​a liquid, work must be done against surface tension.

There is another definition of the surface tension coefficient - energy. It proceeds from the fact that if the surface area of ​​a liquid increases, then a certain number of molecules from its volume rise to the surface layer. To this end external forces do work against the molecular cohesive forces of molecules. The value of this work will be proportional to the change in the surface area of ​​the liquid:

The coefficient of proportionality σ is called the surface tension of the liquid.

Let's derive the unit of surface tension a in SI: o \u003d 1 J / 1 m 2 \u003d 1 J / m 2.