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What determines the process of diffusion. NetAngels - professional hosting

13.02.2022

Diffusion rate

Diffusion is one of the simplest phenomena that are studied in the course of physics. This process can be represented at the household daily level.

Diffusion is a physical process of mutual penetration of atoms and molecules of one substance between the same structural elements of another substance. The result of this process is the leveling of the concentration level in the penetrating compounds. Diffusion or mixing can be seen every morning in your own kitchen when preparing tea, coffee or other drinks that include several basic components.

A similar process was first scientifically described by Adolf Fick in the middle of the 19th century. He gave it the original name, which is translated from Latin as interaction or distribution.

The rate of diffusion depends on several factors:

body temperature;
state of aggregation of the test substance.

In various gases, where there are very large distances between molecules, the diffusion rate will be the largest. In liquids, where the distance between molecules is noticeably smaller, the speed also decreases. The smallest diffusion rate is observed in solids, since a strict order is observed in molecular bonds. Atoms and molecules themselves make insignificant oscillatory movements in one place. The rate of diffusion increases with increasing ambient temperature.

Fick's law

Remark 1

Diffusion rate is usually measured by the amount of substance that is transferred per unit of time. All interactions must be through the cross-sectional area of the solution.

The basic formula for diffusion rate is:

$\frac(dm)(dt)=-DC\frac(dC)(dx)$ where:

$D$ is the proportionality factor,
$S$ is the surface area, and the "-" sign means that diffusion goes from an area of higher concentration to a lower one.

Fick presented such a formula in the form of a mathematical description.

According to it, the diffusion rate is directly proportional to the concentration gradient and the area through which the diffusion process is carried out. The proportionality factor determines the diffusion of a substance.

The famous physicist Albert Einstein derived equations for the diffusion coefficient:

$D=RT/NA \cdot 1/6\pi\etaŋr$, where:

$R$ is the universal gas constant,
$T$ - absolute temperature,
$r$ - radius of diffusing particles,
$D$ - diffusion coefficient,
$ŋ$ is the viscosity of the medium.

It follows from these equations that the diffusion rate will increase:

when the temperature rises;
with increasing concentration gradient.

Diffusion rate decreases:

with an increase in the viscosity of the solvent;
with an increase in the size of diffusing particles.

If the molar mass increases, then the diffusion coefficient decreases. In this case, the diffusion rate also decreases.

Diffusion acceleration

There are various conditions that contribute to the acceleration of diffusion. The rate of diffusion depends on the state of aggregation of the test substance. The high density of the material slows down the chemical reaction. The temperature regime affects the rate of interaction of molecules. The quantitative characteristic of the diffusion rate is the coefficient. In the SI measurement system, it is denoted as the Latin capital letter D. It is measured in square centimeters or meters per second of time.

Definition 1

The diffusion coefficient is equal to the amount of a substance that is distributed among another substance through a certain unit of surface. The interaction should be carried out for a unit of time. To effectively solve the problem, it is necessary to achieve the condition when the density difference on both surfaces is equal to unity.

Also, the rate of diffusion in solids, liquids in gases is affected by pressure and radiation. Radiation can be of different types, including induction, as well as high-frequency. Diffusion begins when exposed to a specific catalyst substance. They often act as a trigger for the emergence of a stable particle scattering process.

Using the Arrhenius equation, the dependence of the coefficient on temperature is described. It looks like this:

$D = D0exp(-E/TR)$ where:

$T$ - absolute temperature, which is measured in Kelvins,
$E$ is the minimum energy required for diffusion.

The formula allows you to understand more about the characteristics of the entire diffusion process and determines the reaction rate.

Special diffusion methods

Today it is practically impossible to apply conventional methods to determine the molecular weight of proteins. They are usually based on the measurement:

steam pressure;
increase in boiling point;
lowering the freezing point of solutions.

To effectively solve the problem, special methods are used that are developed for the study of substances with a high molecular structure. They involve determining the rate of diffusion or the viscosity of solutions.

The method for determining the orientation and shape of pores by diffusion rate is based on the study of dialysis rates. Free diffusion must occur in the membrane at this point.

Various radioisotopes can also be used to determine the sodium diffusion rate. This special method is used to solve problems in the field of mineralogy and geology.

The diffusion method is actively used, which is based on the determination of the diffusion of macromolecules in solution. It was developed for polymeric materials. According to the method, the diffusion coefficient is being determined, and then the weight average molecular weight is determined from these data.

Currently, there are no direct methods for determining the diffusion rate of hydrogen in a catalyst. For this, the so-called second activation pathway is used.

To determine the speed, it is customary to use special devices. They differ in appearance from the set practical and scientific tasks.

Physics is one of the most interesting, mysterious and at the same time logical sciences. She explains everything that can be explained, even how tea becomes sweet and soup becomes salty. A true physicist would say otherwise: this is how diffusion proceeds in liquids.

Diffusion

Diffusion is a magical process of penetration of the smallest particles of one substance into the intermolecular spaces of another. By the way, this penetration is mutual.

Do you know how this word is translated from Latin? Spreading, spreading.

How does diffusion occur in liquids?

Diffusion can be observed in the interaction of any substances: liquid, gaseous and solid.

To find out how diffusion proceeds in liquids, you can try throwing a few grains of paint, ground lead or, for example, potassium permanganate into a transparent vessel with clean water. It is better if this vessel is high. What will we see? First, the crystals will sink to the bottom under the action of gravity, but after a while a halo of colored water will appear around them, which will spread and spread. If we do not approach these vessels for at least a few weeks, we will find that the water is almost completely colored.

Another good example. In order for sugar or salt to dissolve faster, they must be stirred in water. But if this is not done, sugar or salt will dissolve on their own after a while: tea or compote will become sweet, and soup or brine will become salty.

How diffusion proceeds in liquids: experience

In order to determine how the diffusion rate depends on the temperature of a substance, a small but very revealing experiment can be carried out.

Take two glasses of the same volume: one with cold water, the other with hot. Pour an equal amount of instant powder (for example, coffee or cocoa) into both glasses. In one of the vessels, the powder will begin to dissolve more intensively. Do you know which one exactly? Guess? Where the water temperature is higher! After all, diffusion proceeds in the course of a random, chaotic movement of molecules, and at high temperatures this movement occurs much faster.

Diffusion can occur in any substance, only the time of the occurrence of this phenomenon differs. The highest speed is in gases. That is why you can not store butter in the refrigerator next to herring or lard, grated with finely chopped garlic. Liquids follow (from the lowest density to the highest). And the slowest is the diffusion of solids. Although at first glance there is no diffusion in solids.

Diffusion

An example of diffusion is the mixing of gases (for example, the spread of odors) or liquids (if you drop ink into water, the liquid will become uniformly colored after a while). Another example is connected with a solid body: the atoms of adjoining metals are mixed at the contact boundary. Particle diffusion plays an important role in plasma physics.

Usually, diffusion is understood as processes accompanied by the transfer of matter, however, sometimes other transfer processes are also called diffusion: thermal conductivity, viscous friction, etc.

The diffusion rate depends on many factors. So, in the case of a metal rod, thermal diffusion takes place very quickly. If the rod is made of synthetic material, thermal diffusion proceeds slowly. Diffusion of molecules in the general case proceeds even more slowly. For example, if a piece of sugar is lowered to the bottom of a glass of water and the water is not stirred, it will take several weeks before the solution becomes homogeneous. Even slower is the diffusion of one solid into another. For example, if copper is coated with gold, then diffusion of gold into copper will occur, but under normal conditions (room temperature and atmospheric pressure), the gold-bearing layer will reach a thickness of several microns only after several thousand years.

A quantitative description of diffusion processes was given by the German physiologist A. Fick ( English) in 1855

general description

All types of diffusion obey the same laws. The diffusion rate is proportional to the cross-sectional area of the sample, as well as the difference in concentrations, temperatures or charges (in the case of relatively small values of these parameters). Thus, heat will travel four times faster through a rod two centimeters in diameter than through a rod one centimeter in diameter. This heat will spread faster if the temperature difference per centimeter is 10°C instead of 5°C. The diffusion rate is also proportional to the parameter characterizing a specific material. In the case of thermal diffusion, this parameter is called thermal conductivity, in the case of a flow of electric charges - electrical conductivity. The amount of a substance that diffuses in a given time and the distance traveled by the diffusing substance are proportional to the square root of the diffusion time.

Diffusion is a process at the molecular level and is determined by the random nature of the movement of individual molecules. The diffusion rate is therefore proportional to the average velocity of the molecules. In the case of gases, the average speed of small molecules is greater, namely, it is inversely proportional to the square root of the mass of the molecule and increases with increasing temperature. Diffusion processes in solids at high temperatures often find practical application. For example, certain types of cathode ray tubes (CRTs) use metallic thorium diffused through metallic tungsten at 2000°C.

If in a mixture of gases the mass of one molecule is four times greater than the other, then such a molecule moves twice as slowly compared to its movement in a pure gas. Accordingly, its diffusion rate is also lower. This difference in diffusion rates between light and heavy molecules is used to separate substances with different molecular weights. An example is isotope separation. If a gas containing two isotopes is passed through a porous membrane, the lighter isotopes penetrate the membrane faster than the heavier ones. For better separation, the process is carried out in several stages. This process has been widely used for the separation of uranium isotopes (separation of 235 U from the bulk of 238 U). Since this separation method is energy intensive, other, more economical separation methods have been developed. For example, the use of thermal diffusion in a gaseous medium is widely developed. A gas containing a mixture of isotopes is placed in a chamber in which a spatial temperature difference (gradient) is maintained. In this case, heavy isotopes are concentrated over time in the cold region.

Fick's equations

From the point of view of thermodynamics, the driving potential of any leveling process is the growth of entropy. At constant pressure and temperature, the role of such a potential is played by the chemical potential µ , causing the maintenance of the flow of matter. The flux of substance particles is proportional to the potential gradient

In most practical cases, the concentration is used instead of the chemical potential C. Direct Replacement µ on the C becomes incorrect in the case of high concentrations, since the chemical potential ceases to be related to the concentration according to the logarithmic law. If we do not consider such cases, then the above formula can be replaced by the following:

which shows that the flux density of matter J proportional to diffusion coefficient D[()] and the concentration gradient. This equation expresses Fick's first law. Fick's second law relates spatial and temporal changes in concentration (diffusion equation):

Diffusion coefficient D temperature dependent. In a number of cases, in a wide temperature range, this dependence is the Arrhenius equation.

An additional field applied parallel to the chemical potential gradient breaks the steady state. In this case, diffusion processes are described by the non-linear Fokker-Planck equation. Diffusion processes are of great importance in nature:

Nutrition, respiration of animals and plants;
The penetration of oxygen from the blood into human tissues.

Geometric description of the Fick equation

In the second Fick equation, on the left side is the rate of change of concentration over time, and on the right side of the equation is the second partial derivative, which expresses the spatial distribution of concentration, in particular, the convexity of the temperature distribution function projected onto the x-axis.

Notes

Literature

Bokshtein B.S. Atoms wander through the crystal. - M .: Nauka, 1984. - 208 p. - (Library "Quantum", Issue 28). - 150,000 copies.

Links

Diffusion (video lesson, 7th grade program)
Diffusion of impurity atoms on the surface of a single crystal

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Synonyms:

See what "Diffusion" is in other dictionaries:

- [lat. diffusio distribution, spreading] physical, chemical. the penetration of molecules of one substance (gas, liquid, solid) into another upon their direct contact or through a porous partition. Dictionary of foreign words. Komlev N.G.,… … Dictionary of foreign words of the Russian language

Diffusion- is the penetration into the medium of particles of one substance of particles of another substance, which occurs as a result of thermal motion in the direction of decreasing the concentration of another substance. [Blum E.E. Dictionary of basic metallurgical terms. Yekaterinburg … Encyclopedia of terms, definitions and explanations of building materials

Modern Encyclopedia

- (from Latin diffusio spreading spreading, scattering), the movement of particles of the medium, leading to the transfer of matter and the alignment of concentrations or to the establishment of an equilibrium distribution of concentrations of particles of a given type in the medium. In the absence of… … Big Encyclopedic Dictionary

DIFFUSION, the movement of a substance in a mixture from an area of high concentration to an area of low concentration, caused by the random movement of individual atoms or molecules. Diffusion stops when the concentration gradient disappears. Speed… … Scientific and technical encyclopedic dictionary

diffusion- and, well. diffusion f., German. Diffusion lat. diffusio spreading, spreading. Mutual penetration of adjoining substances into each other due to the thermal movement of molecules and atoms. Diffusion of gases, liquids. BAS 2. || trans. They… … Historical Dictionary of Gallicisms of the Russian Language

Diffusion- (from the Latin diffusio distribution, spreading, dispersion), the movement of particles of the medium, leading to the transfer of matter and the alignment of concentrations or the establishment of their equilibrium distribution. Diffusion is usually determined by thermal motion ... ... Illustrated Encyclopedic Dictionary

The movement of particles in the direction of decreasing their concentration, due to thermal motion. D. leads to the alignment of the concentrations of the diffusing substance and the uniform filling of the volume with particles. ... ... Geological Encyclopedia

Diffusion (Latin diffusio - spreading, spreading, dispersion, interaction) is the process of mutual penetration of molecules of one substance between the molecules of another, leading to spontaneous alignment of their concentrations throughout the occupied volume. In some situations, one of the substances already has an equal concentration and one speaks of the diffusion of one substance in another. In this case, the transfer of a substance occurs from an area with a high concentration to an area with a low concentration (against the concentration gradient)

An example of diffusion is the mixing of gases (for example, the spread of odors) or liquids (if you drop ink into water, the liquid will become uniformly colored after a while). Another example is connected with a solid body: atoms of adjoining metals, diffusion of particles plays in plasma physics.

Usually, diffusion is understood as processes accompanied by the transfer of matter, but sometimes other transfer processes are also called diffusion: thermal conductivity, viscous friction, etc.

Rice.

The diffusion rate depends on many factors. So, in the case of a metal rod, thermal diffusion takes place very quickly. If the rod is made of synthetic material, thermal diffusion proceeds slowly. Diffusion of molecules in the general case proceeds even more slowly. For example, if a piece of sugar is lowered to the bottom of a glass of water and the water is not stirred, it will take several weeks before the solution becomes homogeneous. Even slower is the diffusion of one solid into another. For example, if copper is covered with gold, then gold will diffuse into copper, but under normal conditions (room temperature and atmospheric pressure), the gold-bearing layer will reach a thickness of several microns only after several thousand years.

The physical meaning of the phenomenon of diffusion

If in a mixture of gases the mass of one molecule is four times greater than the other, then such a molecule moves twice as slowly compared to its movement in a pure gas. Accordingly, its diffusion rate is also lower. This difference in diffusion rates between light and heavy molecules is used to separate substances with different molecular weights. An example is the separation of isotopes. If a gas containing two isotopes is passed through a porous membrane, the lighter isotopes penetrate the membrane faster than the heavier ones. For better separation, the process is carried out in several stages. This process has been widely used to separate uranium isotopes (separation of 235U from the bulk of 238U). Since this separation method is energy intensive, other, more economical separation methods have been developed. For example, the use of thermal diffusion in a gaseous medium is widely developed. A gas containing a mixture of isotopes is placed in a chamber in which a spatial temperature difference (gradient) is maintained. In this case, heavy isotopes are concentrated over time in the cold region.

Fick's equation.

From the point of view of thermodynamics, the driving potential of any leveling process is the growth of entropy. At constant pressure and temperature, the role of such a potential is played by the chemical potential µ, which determines the maintenance of substance flows. The flow of matter particles is proportional to the potential gradient:

In most practical cases, the concentration C is used instead of the chemical potential. The direct replacement of µ by C becomes incorrect in the case of high concentrations, since the chemical potential is related to the concentration according to a logarithmic law. If we do not consider such cases, then the above formula can be replaced by the following:

which shows that the flux density of the substance J is proportional to the diffusion coefficient D [()] and the concentration gradient. This equation expresses Fick's first law (Adolf Fick is a German physiologist who established the laws of diffusion in 1855). Fick's second law relates spatial and temporal changes in concentration (diffusion equation):

The diffusion coefficient D depends on the temperature. In a number of cases, in a wide temperature range, this dependence is the Arrhenius equation.

An additional field applied parallel to the chemical potential gradient breaks the steady state. In this case, diffusion processes are described by the nonlinear Fokker-Planck equation. Diffusion processes are of great importance in nature:

Nutrition, respiration of animals and plants;

The penetration of oxygen from the blood into human tissues.

Geometric description of the Fick equation.

In the second Fick equation, on the left side is the rate of temperature change over time, and on the right side of the equation is the second partial derivative, which expresses the spatial distribution of temperatures, in particular, the convexity of the temperature distribution function projected onto the x-axis.

Lesson Objectives:

Educational: to consolidate the knowledge of students on a given topic, to teach them to understand and describe the behavior of the molecules of a substance in various states of aggregation, to explain the significance of the diffusion process in nature and human life.

Educational: to continue the formation of students' ability to scientific thinking.

Educational: to instill in students the ability to compare phenomena seen in nature with the knowledge gained about various physical laws.

Basic terms:

Aggregate state of matter- this is a state of matter that can be characterized by a set of specific properties (for example, preservation or inability to preserve volume, shape, etc.).

Diffusion

The concept of the aggregate state of matter.

The world around us is complex and changing. At the same time, we are able to see that the limitless diversity of the world is not so limitless. We often see the same substances in different states.

The simplest example on which I can prove the veracity of my words is water. It is easiest to see it in different states - it's steam, or fog, it's ice or snow, it's liquid running from the tap in the kitchen. Whatever the characteristics of water in one form or another, it always remains water - its composition does not change. These are the same 2 hydrogen molecules and 1 oxygen molecule.

If we continue to use the example we have taken, then we can trace that these 3 states of water depend on certain external conditions. So, water freezes at 0 degrees, turning into ice, and water boils at 100 degrees, turning into steam. This photo clearly demonstrates all 3 states of water:

Rice. 1: 3 states of aggregation of water

So what conclusions can we draw from thinking carefully about our example? They will be like this:

Aggregate state of matter is a state of matter that can be characterized by a set of specific properties (for example, preservation or inability to preserve volume, shape, etc.) under certain conditions.

Not only water can be in three states of aggregation: solid, liquid and gaseous. This is true for all substances.

Sometimes, in addition to the above three states of aggregation, a fourth one is added - plasma. You can get an idea of what a plasma looks like from the following figure:

Rice. 2: plasma lamp

but you will learn more about plasma in the lessons of physics and chemistry in high school.

Diffusion process

As we all have already learned, all substances consist of the smallest particles - ions, atoms, molecules, which are in constant motion. It is this movement that becomes the reason why the diffusion process occurs.

Diffusion is a process consisting in the mutual penetration of molecules of substances into the gaps between molecules in other substances.

Let's take a closer look at diffusion in various aggregate states.

Diffusion in gases

Let's give examples of the process of diffusion in gases together. Variants of manifestation of this phenomenon can be as follows:

Spreading the smell of flowers;

Tears from cutting onions;

A trail of perfume that can be felt in the air.

The gaps between the particles in the air are quite large, the particles move randomly, so the diffusion of gaseous substances occurs quite quickly.

Let's watch a video demonstrating this process:

Diffusion in liquids.

Particles of substances in liquids, and these are most often ions of substances, interact with each other quite strongly. At the same time, the distance between the ions is large enough to allow the particles to mix easily.

The following video picture shows how the diffusion process in liquids takes place. Particles of paint, falling on the surface of the water, easily diffuse, that is, they penetrate into the water.

Rice. 3: paint particles spread in water.

The same process, but already in dynamics, you can observe in the video using the example of the dissolution of potassium permanganate crystals:

Diffusion in solids.

Solids can have a different structure and consist of molecules, atoms or ions. In any case, regardless of what microparticles the body consists of, the interaction of these particles with each other is very strong. Despite the fact that they, these particles, are still moving, but these movements are very insignificant. The gaps between the particles are small, so it is difficult for other substances to penetrate between them. The diffusion process in solids is very slow and imperceptible to the naked eye.

Let's watch a video about it:

Having learned about the features of the diffusion process in various aggregate states, we saw that the process is not equally fast. What does the diffusion rate depend on? We already have one of the answers to this question - the rate of the diffusion process depends on the state of aggregation of the substance.

You and I also know that particles of matter begin to move faster with increasing temperature. Does this mean that the diffusion process will also accelerate with increasing temperature? The answer is obvious. To confirm, let's watch the video:

The intensity of diffusion of one substance into another also depends on the concentration of these substances and on external influences (for example, if you just drop a solution of iodine into water and if you also mix it, then the rate of acquiring a uniform color by the solution will be different).

conclusions

1. Aggregate state of matter is a state of matter that can be characterized by a set of specific properties (for example, preservation or inability to preserve volume, shape, etc.) under certain conditions. Not only water can be in three states of aggregation: solid, liquid and gaseous. This is true for all substances.

2. Diffusion is a process consisting in the mutual penetration of molecules of substances into the gaps between molecules in other substances.

3. The diffusion rate depends on: temperature, concentration, external influences, state of aggregation of the substance.

It is difficult to overestimate the process of diffusion in human life. For example, the penetration of oxygen through the thinnest wall of the alveoli into the capillaries of the lungs is carried out precisely due to diffusion. The walls of the alveoli are very thin, from a physical point of view, the alveolar wall is a semi-permeable membrane. The concentration of oxygen in atmospheric air is much higher than its concentration and capillary blood, which is why oxygen droops through a semi-permeable membrane - to where it is less. Diffusion allows us to breathe.

Also, this process partially ensures the penetration of nutrients from the digestive system into the blood and the action of many drugs.

The figure shows schematically how nutrients are absorbed in the human intestine.

Rice. 4: mammalian small intestine