Thermodynamics of adsorption. Thermodynamics of adsorption according to Gibbs Rules for writing colloidal micelles
Kuznetsova E.S. and Buryak A.K. compared the thermodynamic characteristics of the adsorption of amino acids and their associates. In this work, the influence of the structure of amino acids, their dimers and associates with eluent components on their adsorption on the surface of carbon materials was studied. A molecular-statistical calculation of the thermodynamic characteristics of adsorption (TXA) for aromatic amino acids (phenylalanine, tyrosine), heterocyclic amino acids (tryptophan) and their dimers with trifluoroacetic acid (TFA) on the surface of graphitized thermal carbon black (GTC) has been carried out. The obtained data are compared with the patterns of amino acid retention on porous graphite carbon Hypercarb under conditions of reversed-phase high-performance liquid chromatography (RP HPLC). It has been shown that TCA and amino acid retention values increase with the increase in the carbon chain of these compounds.
Shkolin A.V., and Fomkin A.A. analyzed the behavior of thermodynamic functions (differential molar isosteric heat of adsorption, entropy, enthalpy and heat capacity) of the adsorption system methane-microporous carbon adsorbent AUK depending on the parameters of adsorption equilibrium in the temperature range from 177.65 up to 393 K and pressures from 1 Pa to 6 MPa. Taking into account the influence of nonideality of the gas phase and the noninertness of the adsorbent led to the appearance of a temperature dependence of the isosteric heat of adsorption, especially in the region of high pressures of the adsorbent. For the system under study, the thermodynamic functions of the adsorption system are mainly affected by the imperfection of the gas phase. The correction for the non-inertia of the adsorbent in this range of parameters of the adsorption system is no more than 2.5%.
At the Institute of General and Inorganic Chemistry of the Academy of Sciences of the Republic of Uzbekistan Muminov S.Z. In his work, he studied changes in the surface properties and porous structure of montmorillonite upon replacement of exchangeable cations of the mineral with polyhydroxyaluminum cations. Preliminary thermal vacuum has a significant effect on the adsorption properties of polyhydroxyaluminum montmorillonite with respect to methyl alcohol. According to the series of CH3 adsorption isosteres on dehydrated sodium and modified montmorillonites, measured in a wide temperature range, the dependences of the heat of adsorption on the amount of adsorbed substance were established.
N.S. Kazbanov, A.V. Matveeva and O.K. Krasilnikova conducted a study of the adsorption of phenol from aqueous solutions with activated carbons such as FAS, PAH and carbon felt at temperatures of 293, 313 and 343K in the concentration range of 5 - 250 mmol/l. A series of samples of successively activated carbon FAS, characterized by a narrow pore size distribution, was obtained by carbonization of furfural-based polymers. PAH is a microporous polymeric activated carbon. Carbon felt is a fibrous material based on hydrated cellulose fibers. The parameters of the porous structure of the adsorbents were determined from nitrogen vapor adsorption isotherms at 77 K (ASAP-2020, Micromeritics, USA). The adsorption of solutions was studied by the ampoule method in a thermostat. The selected samples were analyzed by spectrophotometry. The analysis of the obtained isotherms of liquid-phase adsorption was carried out using the theory of volumetric filling of micropores (TOZM) according to the Dubinin-Radushkevich (DR) equation.
The effect of temperature on sorption from liquid solutions is ambiguous. On the one hand, for microporous adsorbents, the penetration of molecules into pores comparable in size to these molecules depends on the kinetic energy and, accordingly, increases with temperature. On the other hand, physical adsorption is an exothermic process and adsorption decreases with temperature. The ratio of these factors for each system determines the course of the temperature dependence of adsorption.
The uniqueness of the adsorbent - phenol system is that it has an inverse temperature dependence of adsorption isotherms, since with an increase in temperature from 293 to 313 K, the limiting value of adsorption increases, which is apparently associated with the molecular sieve effect: with an increase in temperature, phenol molecules are able to penetrate into narrower pores of carbon materials. Adsorption occurs mainly in micropores, since adsorbents have a small number of mesopores. As the size of micropores increases, the values of limiting adsorption increase significantly, reaching 2.9 mmol/g for PAHs, 8.5 mmol/g for FAS, and 12.7 mmol/g for felt. The resulting adsorption isotherms are well described by the DD equation with the exponent equal to 2.
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34. Nature of adsorption forces
The interaction between the molecules of the adsorbent with the surface of the adsorbent at the so-called. physical adsorption can be due to various reasons. Then the potential that determines the interaction of one adsorbent molecule with one atom of a nonpolar adsorptive can be expressed as follows:
θ = −Cr 6 +Br 12 ,
where r is the distance between particle centers; C is the dispersion attraction constant; B is a constant that characterizes the energy of the repulsive forces.
It is quite obvious that at relatively distant distances, attractive forces should prevail, and at close distances, repulsive forces. Also, at certain distances, these forces must be equal, which will correspond to the minimum free energy. But it is important to note that during adsorption, dispersion forces act simultaneously between each nonpolar particle.
Since the interaction energy of particles can rapidly decrease with distance, it suffices to perform summation on the nearest adsorbent atoms to determine the potential of adsorption forces. It is important that, in the case of adsorption of complex nonpolar molecules, the potential energy can be approximately calculated as the sum of all potential adsorption energies of the units of the molecule.
If the adsorbent consists of ions, then the action of already known dispersion forces can be supplemented by the action of induction forces of attraction of dipoles, which are induced in the molecules of the adsorbent by an electric field, which, in turn, is created by the ions of the adsorbent lattice.
With such an interaction, the share of inductive forces in the adsorption interaction can be proportional to the polarizability of the adsorptive molecule and the square of the field strength on this adsorbent surface.
If, on the other hand, polar adsorbent molecules are adsorbed on a polar adsorbent, then the dipoles in this case polarize the atoms of the adsorbent, i.e., as if they induce electric moments in them. Due to this influence, the inductive interaction is added to the dispersion one.
The inductive interaction itself is usually small and, depending on the dipole of the adsorptive molecule and the polarizability of the adsorbent, can reach large values. In the event that molecules are adsorbed on an adsorbent that has ions or dipoles on the surface, a so-called. interaction of ions or dipoles of the adsorbent with the electrostatic field of the adsorbent itself.
In this case, the adsorptive molecules can even orient themselves in the field of the adsorbent, and orientational Coulomb interaction occurs. It usually happens that the energies of inductive and orientational interactions are less than the energy of dispersion interactions, and therefore it is assumed that the energy of intermolecular attraction is determined by the energy of dispersion attraction.
Also, the formation of a hydrogen bond can serve as a cause of adsorption. A bond of this type can arise during adsorption on adsorbents that contain hydroxyl groups of molecules such as water, alcohols, ammonia, and amines on the surface. When a hydrogen bond is formed, the interaction energy of the adsorbent with the adsorbent can be quite large, and the heat that is released during such adsorption is much greater than the heat of adsorption of substances that are similar in shape and size of molecules, but do not form a hydrogen bond.
It is important to note that, knowing the thermodynamic description of the surface layer at the "adsorbent - adsorbent" boundary, its structure, the nature of various types of forces, the dynamics of the process, one can proceed to the study of more complex adsorption processes.
35. Adsorption as spontaneous concentration on the phase interface of substances that reduce interfacial tension
Surfactants are divided into two large groups: active and inactive substances.
Surfactants are able to accumulate in the surface layer, and in this case, positive adsorption occurs. G > 0.
Such kinds of substances must have a surface tension which, in turn, must be less than the surface tension of the solvent, otherwise the accumulation of the substance in the surface layer would be unfavorable, and must have a relatively low solubility. With sufficiently good solubility, surfactant molecules tend to leave the surface deep into the solution. Therefore, surfactants will preferentially be pushed out of the bulk of the liquid to the surface.
But with the accumulation of substances at the boundary of the solution in the molecules of these substances, which weakly interact with each other, the intermolecular interaction in the surface layer will decrease, and the surface tension will fall.
Surfactants relative to the water layer are many types of organic compounds, fatty acids with a sufficiently large hydrocarbon radical, salts of these acids (soaps), sulfonic acids and their salts, as well as various types of alcohols and amines. A characteristic feature of most molecules is their amphiphilicity: the molecule consists of two parts of a polar group and a non-polar hydrocarbon radical. Possessing a significant dipole moment and well hydrating polar group can determine the affinity of the surfactant for the aqueous environment. But the hydrocarbon radical is the cause that lowers the solubility of these compounds.
Surface inactive surfactants- these types of substances, tending to leave the surface of the liquid into its volume, as a result, the so-called. negative adsorption G < 0. Поверностно-инактивные вещества также обладают значительным поверхностным натяжением, значительно большим, чем натяжение у растворителя (иначе эти вещества способны самопроизвольно накапливаться в поверхностном слое), также обладают высокой растворимостью, что способствует их стремлению уйти с поверхности жидкости в объем. Взаимодействие между молекулами поверхностно-инактивного вещества и растворителя всегда больше, чем взаимодействие между самими молекулами растворителя, поэтому они и стремятся перейти в объем раствора. Surface-inactive substances in relation to water are many inorganic electrolytes: acids, alkalis, salts. Molecules of surface-inactive substances do not have a hydrophobic part and can decompose in water into highly hydrating ions.
Examples surface-inactive substances are also some organic compounds in which the non-polar part of the molecule is absent or very small. These substances include formic, aminoacetic acids.
In non-aqueous solvents, inorganic electrolytes are also capable of increasing the surface tension, and this depends on the solvent.
For example, when sodium iodide is introduced into methanol, the surface tension greatly increases; for ethanol, the surface tension is approximately 2 times greater. The surface activity of substances can depend not only on the nature of the substance, but also on the properties of the solvent. If any solvent has a high surface tension, then this solute may exhibit significant surface activity.
36. Adsorption theories
Let us consider the most common adsorption theories that describe individual types of adsorption on the “solid-gas” or “solid-solution” interface.
The theory of monomolecular adsorption by I. Langmuir.
1. Adsorption is localized and is caused by forces close to chemical ones.
2. Adsorption occurs only on active centers - protrusions or depressions on the surface of the adsorbent, characterized by the presence of free valences. Active centers are considered independent and identical.
3. Each active center is able to interact with only one adsorbate molecule; only one layer of adsorbed molecules can form on the surface.
4. The process of adsorption is reversible and equilibrium; the adsorbed molecule is retained by the active center for some time, after which it is desorbed; After some time, a dynamic equilibrium is established.
The maximum possible adsorption value G o is achieved under the condition that all active centers are occupied by adsorbate molecules. Monomolecular adsorption isotherm equation relating the adsorption value G with adsorbate concentration FROM, looks like:
where b- a constant for a given pair of "adsorbent - adsorbate" value (the ratio of the rate constants of desorption and adsorption), numerically equal to the concentration of the adsorbate, at which half of the active centers are occupied.
The graph of the Langmuir adsorption isotherm is shown in Figure 2. The constant b we define graphically by drawing a tangent to the adsorption isotherm at the point FROM= 0. When describing the process of adsorption of gases in the equation, the concentration can be replaced by a proportional value of the partial pressure. Theory of monomolecular adsorption I. Langmuir applicable to describe the processes of adsorption of gases and dissolved substances at low pressures (concentrations) of the adsorbate.
Polanyi's theory of polymolecular adsorption describes s-shaped adsorption isotherms, the shape of which indicates the possible interaction of adsorbed molecules with the adsorbate.
1. Adsorption is caused by physical forces.
2. The surface of the adsorbent is homogeneous, there are no active centers; adsorption forces form a continuous force field near the surface of the adsorbent.
3. Adsorption forces act at a distance greater than the size of the adsorbate molecule, i.e., there is a certain adsorption volume near the surface of the adsorbent, which is filled with adsorbate molecules during adsorption.
4. The attraction of an adsorbate molecule by the adsorbent surface does not depend on the presence of other molecules in the adsorption volume, as a result of which polymolecular adsorption is possible.
5. Adsorption forces do not depend on temperature, and, therefore, with a change in temperature, the adsorption volume does not change.
Freundlich equation. The surface of the adsorbent is inhomogeneous, interaction occurs between adsorbed particles, active centers are not completely independent of each other. G. Freindlich suggested that the number of moles of adsorbed gas or solute per unit mass of the adsorbent (the so-called specific adsorption X/m), should be proportional to the equilibrium pressure (for gas) or the equilibrium concentration (for substances adsorbed from solution) of the adsorbent raised to a certain power, which is always less than unity:
x / m = aP n x / m = aC n.
exponents n and proportionality factor a determined experimentally.
37. Thermodynamics of the adsorption process. Gibbs adsorption equation
To study the phenomenon of adsorption at the "solution - gas" boundary, it is necessary to establish a relationship between the excess of the adsorbed substance in the layer on the surface ( G), surfactant concentration in solution ( With) and surface tension ( σ ) at the “solution-gas” phase boundary. It is more expedient to consider the phenomena from the thermodynamic standpoint and relate the adsorption of a solute to a change in the free energy of the surface or its surface tension. This connection was made W. Gibbs in 1876, which was named "Gibbs adsorption equation":
G = – With / RT x dσ/dc.
You can still imagine Gibbs Equation, based on thermodynamics, using isobaric-isothermal potential G, chemical potentials μ 1 and μ 2 , and also using n 1 and n 2 the number of moles of the components. Having analyzed it taking into account the entropy S, volume V and pressure P, we can write the following equation:
dG=– SDT+VdP+σds+ μ 1 d n 1 + μ 2 days 2 .
We equate it to zero, and taking into account constant temperature and pressure, it simplifies into an equation of the form:
sd σ + n 1 d μ 1 + n2d μ 1 = 0.
Taking into account the fact that for dilute solutions the chemical potential of the second component is expressed as follows:
μ 2 = μ 2 0 +RT ln c,
and given that the temperature is constant
dμ 2 =rtdnc,
substituting this equation into
we obtain the desired Gibbs adsorption equation. Based on the equation, it can be seen that if the surface tension σ increases with concentration With, then the concentration of the dissolved substance on the surface layer is less than in the volume of the solution (the so-called negative adsorption), and if the surface tension σ decreases with increasing concentration With, then the concentration in the layer is greater than in the volume (positive adsorption), and, finally, if σ does not depend on With, then the concentration of the substance in the layer on the surface and in the volume is the same. The Gibbs equation was derived using thermodynamics. It is difficult to verify this equation in practice, which is due to the complexity of determining the concentration of a dissolved substance in a layered surface. Experienced B. McBen found that a very thin layer of liquid was cut off from the surface of the solution using the device. Further determination of all parameters of the Gibbs equation showed that the experimentally found values of adsorption coincided with the values calculated using the Gibbs equation within the experimental error. Due to the homogeneity and smoothness of the surface of any liquid, when studying adsorption on its surface, the usual ideas about active centers are completely inapplicable. At the critical temperature, the difference between the adjacent phases disappears, and the surface tension, as a rule, becomes equal to zero. The adsorption of gases and vapors has such a large practical application that in the literature, especially in the technical one, you can find this concept, which is used only in relation to processes on the surface of solids.
This concept, as well as the most general patterns of adsorption, as the considered Gibbs equation, is applicable to all phase boundaries. Using the Gibbs equation and all the provisions arising from it, having determined the value of Г, it is possible to construct an adsorption isotherm.
38. Peculiarities of adsorption on microporous materials. Polan's potential theory. Adsorption potential
Glade's theory considers non-localized physical adsorption, which is directly due to van der Waals forces between the adsorbent and adsorbate (this can be considered the first position). The second position of this theory is the concept of the force (or potential) field of the adsorbent, which extends over a considerable distance from the surface; the adsorption layer that appears in this field is polymolecular. If we consider the adsorption of gases, then the density of this layer decreases along a certain normal from the surface. If we consider vapor adsorption, then a liquid layer of a certain thickness is formed on the surface. The field in Polanyi's theory is considered as a series of equipotential surfaces, each surface corresponds to a certain value of the potential ε , and each subsequent surface will be smaller than the previous one. Each such surface in space cuts out layers of a certain volume, designated as v i. The task of Polanyi's theory is to find the transition from the usual coordinates of the isotherm ( x, p) to field parameters ε i and v i, with further establishment of the connection between these main parameters. The first part of the problem, which Polanyi laid down, is rather complicated, and in many cases cannot have definite solutions, but for the case of vapor adsorption, this part of the problem is solved in the first approximation very simply. For a liquid adsorption layer, the filled part of the volume will be equal to:
v i \u003d x (M / d),
where d is the density of the substance in the liquid state.
In his theory, M. Polyany introduces another provision about the absence of the so-called. field screening in the process of adsorption, the value ε in this theory of space is a constant value (something like a gravitational potential) regardless of whether there are certain adsorbate molecules between a given point and a solid surface, or whether all space is free. Polyani introduces the concept adsorption potential ε , which is the isothermal work of compressing the vapor when it is transferred from the equilibrium pressure R in the bulk phase far from the surface to the region of the surface layer with saturated vapor pressure p 0 then the expression for determining the potential will look like:
ε = RT ln R 0 / R.
With the help of such an equation, one can go from the coordinates x, p to the coordinates ε and v and get a curve, which is called "characteristic". Polanyi discovered in his experiments that such curves, constructed from the experimental data of the obtained isotherms, have the following property: they are invariant with respect to T, or, in other words, all curves of this type can lie on one curve ε −ε .
M. Polyany accepted this position as a postulate, i.e.:
This property of Polyani is of great practical importance; it can construct a family of isotherms from one experimental adsorption isotherm.
Polanyi's theory does not give an analytic expression for the isotherm or the function of potential versus volume, but allows one to calculate the coordinate for any given temperature if at least one isotherm is known. This result is very important for technological calculations, because for similar gases on the same adsorbent, the adsorption curves can turn out to be close to each other and can in many cases be superimposed.
39. Characteristic curve of adsorption. Temperature invariance and affinity of characteristic curves
The force field that appears at the surface of the adsorbent can be similar in many respects to the gravitational field. In the adsorption field, potential surfaces can be represented, i.e., surfaces for which the same adsorption potential is characteristic. Under the concept of adsorption potential θ should be understood as nothing more than the work done against the forces of adsorption when moving 1 mole of the adsorbate from a certain point in the field to a certain gas phase. The maximum adsorption potential will exist at the “adsorbent – adsorption volume” boundary. But at the boundary "volume - gas phase" (this is where the action of adsorption forces ends), the adsorption potential must be equal to zero. The change in the adsorption potential with a change in the adsorption volume can be represented in the form of curves. This was first done by M. Polyani. Such types of curves do not depend on temperature and can be characteristic of each particular adsorbent; such types of curves are usually called characteristic curves of adsorption. The theory of polymolecular adsorption assumes that the equation of state of the gas applies to the amount of adsorption. Consequently, the isotherms that characterize the dependence of the density of the adsorbate on the volume for different temperatures resemble the isotherms of the dependence of the pressure on the volume. At low temperatures, adsorption forces on the surface can cause the vapor to condense into a liquid of a certain density. At temperatures lower than the critical one, during condensation, the entire adsorption volume will be filled with liquid. In this case, the adsorption curve will run almost parallel to the abscissa axis, which is related to the low compressibility of the liquid. Then the adsorption curve at the “volume – gas phase” boundary drops sharply down, and, accordingly, the density of the adsorbate reaches the value of a certain density of the gas phase. At temperatures higher than critical, the adsorbent may behave like an ideal gas, and the graph will be expressed as an isotherm of the dependence for an ideal gas, provided that pV = RT. Under such conditions, the adsorbed gas will have a maximum density at the very surface of the adsorbent and have a minimum density in the immediate vicinity of the gas phase. Moreover, in this case it is important to note that the density of the adsorbate in the adsorption layer nowhere reaches the density of the liquid itself. And if the temperature is very close to critical, the dependence of density on volume will be expressed by a curve close in appearance to the isotherm, which is described van der Waals equation. In this scenario, part of the adsorbed substance will be in the adsorbed volume in a liquid state, and part of the adsorbed substance will be in a gaseous state. Then the curve will decrease most sharply in the section that corresponds to the transition from liquid to gas. If a characteristic curve is constructed from the experimental adsorption isotherm of one of the adsorptives, and knowing the corresponding affinity coefficients for some other adsorptive, one can find the adsorption isotherm and construct it for another adsorptive. The potential theory of adsorption makes it possible to calculate different adsorption isotherms of different vapors on the same adsorbent, moreover, using the characteristic curve obtained from the adsorption isotherm of one vapor, since the ratio of the adsorption potential does not depend on the adsorption volumes.
affinity(from Latin affinis - “related”) - affinity chromatography. The method of purification and separation of proteins is based on their selective interaction with a ligand covalently bound to an inert carrier (affinity chromatography). Measuring the affinity of a toxicant for a receptor, in fact, is an experimental study of the relationship between the amount of a substance added to the incubation medium and the amount of the toxicant-receptor complex formed as a result of the interaction.
Thermodynamics of adsorption processes.
| Parameter name | Meaning |
| Article subject: | Thermodynamics of adsorption processes. |
| Rubric (thematic category) | Education |
Basic definitions and methods for classifying adsorption processes.
Adsorption refers to phenomena occurring as a result of a spontaneous decrease in surface energy.
Adsorption- the process of spontaneous reversible or irreversible redistribution of the components of a heterogeneous system between the surface layer and the volume of a homogeneous phase.
In multicomponent systems, the component that lowers the interfacial tension is preferable to the surface layer. In single-component systems, during the formation of a surface layer, its structure changes (a certain orientation of atoms and molecules, polarization), called autoadsorption.
The denser phase on which adsorption interactions are localized is called adsorbent. The substance redistributed between the volume of the homogeneous phase and the surface layer is denoted by the term ʼʼ adsorbateʼʼ.
In some cases, the adsorption process is reversible. In this case, under certain conditions, part of the adsorbed molecules can pass from the surface layer into the volume of the phase as a result of molecular kinetic phenomena. The reverse process of adsorption is called desorption.
Methods for classifying adsorption processes.
Classification of adsorption processes according to the state of aggregation of the interacting phases. Taking into account the dependence on the aggregate state of adjacent phases, the following types of adsorption processes are distinguished:
Adsorption of gases on solid adsorbents;
Adsorption of dissolved substances at the ʼʼsolid-liquidʼʼ and ʼʼliquid-liquidʼʼ interfaces;
Adsorption of surfactants at the ʼʼliquid-gasʼʼ interface.
Classification of adsorption processes according to the mechanism of interaction of the adsorbent and adsorbate. Adsorption can be considered as the interaction of adsorbate molecules with the active centers of the adsorbent. According to the mechanism of their interaction, the following types of adsorption are subdivided:
1) physical (molecular) adsorption- the interaction between the molecules of the adsorbate and the adsorbent is carried out due to the van der Waals forces, hydrogen bonds (without the occurrence of chemical reactions);
2) chemical adsorption (chemisorption)– the attachment of adsorbate molecules to the active sites of the adsorbent occurs as a result of chemical reactions of various types (with the exception of ion exchange reactions);
3) ion-exchange adsorption (ion exchange) - the redistribution of the adsorbate substance between the solution and the solid phase (ion exchanger) according to the mechanism of ion exchange reactions.
For a quantitative description of adsorption processes, two quantities are used.
1) Absolute adsorption is the amount (mol) or mass (kg) of the adsorbate per unit surface area or mass of the adsorbent. Designation - A; unit: mol/m 2 , mol/kg, kg/m 2 , kg/kᴦ.
2) Gibbs (excess) adsorption is the excess of the adsorbate substance in the surface layer of a certain thickness compared to its amount in the volume of the homogeneous phase, per unit surface area or mass of the adsorbent. Designation - G; unit: mol/m 2 , mol/kᴦ.
The relationship between absolute and excess adsorption can be illustrated using the equation:
G \u003d A - c * h (3.1)
where c is the equilibrium concentration of the substance in the volume of the phase, mol/m3;
h is the thickness of the surface layer, conditionally taken equal to 10 -9 m.
In multicomponent heterogeneous systems, when one or another component is redistributed between the volume of a homogeneous phase and the surface layer, the equation for the excess internal energy of the surface is valid:
U = T * S + s * s + Sm i * n i (3.2)
Bringing all the terms of the equation to the unit area of the interfacial surface, we obtain:
U s = T * S s + s + Sm i * Г i (3.3)
where Г i = n i / s is the excess of the i-th component in the surface layer, that is, Gibbs adsorption.
For a one-component system, equation (3.3) takes the form:
G s = s + m * Г (3.4)
where G s = U s - T * S s is the Gibbs energy of the surface or the work of creating a unit area of the surface;
m * Г - compaction of the substance of the adsorbed substance in the surface layer.
Based on equation (3.4), we can conclude that during adsorption, the work to create an interfacial surface consists of the work of forming a surface (breaking cohesive bonds in the bulk of the adsorbate phase) and compacting the substance in the surface layer.
In a state of dynamic equilibrium between the adsorbent and adsorbate, the change in the Gibbs energy of a heterogeneous system ΔG = 0, the thermodynamics of the adsorption process is described by an equation called Gibbs fundamental adsorption equation:
Ds = SГ i * dm i (3.5)
This equation is universal, since it is valid for all types of adsorption processes
Particular cases of the Gibbs adsorption equation.
1) Adsorption from solutions.
For the chemical potential of the i-th component of the system during adsorption at the interfaces "liquid - solid adsorbent" and "liquid - gas" the equations are valid:
m i = m i 0 + R*T*ln a i (3.6)
dm i = R*T* d ln a i (3.7)
where m i 0 is the chemical potential of the i-th component of the system under standard conditions;
a i – activity of the i-th component of the system under standard conditions.
Based on this, the Gibbs adsorption equation will take the form:
Г i = - a i / R*T * (ds / da i) (3.8)
For non-electrolyte solutions, we take a i \u003d c i, then:
Г i \u003d - s / R * T * (ds / ds) (3.9)
For electrolyte solutions:
Г i = - с ± n / R*T * (ds / dс ± n) (3.10)
where c ± is the average ionic concentration of the solution;
n is the stoichiometric coefficient.
2) Adsorption of substances from the gas phase.
In accordance with the Mendeleev-Claiperon equation:
P \u003d c * R * T (3.11)
In this regard, the Gibbs equation for the adsorption of gases on solid adsorbents is written in the following form:
Г i = - Р / R*T * (ds / dР) (3.12)
In practice, the Gibbs adsorption equation makes it possible to calculate the amount of adsorption of substances in the interfacial layer, for which the surface tension is determined, based on the measurement of surface tension at various values of liquid concentration or equilibrium gas pressure.
Thermodynamics of adsorption processes. - concept and types. Classification and features of the category "Thermodynamics of adsorption processes." 2017, 2018.
"EDUCATIONAL AND METHODOLOGICAL MANUAL" THERMODYNAMICS OF ADSORPTION OF GASES, VAPOR AND SOLUTIONS (SPECIAL COURSE). A. M. TOLMACHEV 2012 Annotation The lectures analyze in detail the description of adsorption ...»
-- [ Page 1 ] --
Faculty of Chemistry of Moscow
state university
them. M. V. Lomonosov
EDUCATIONAL AND METHODOLOGICAL AID
«THERMODYNAMICS OF GAS ADSORPTION,
VAPOR AND SOLUTIONS
(SPECIAL COURSE).
A. M. TOLMACHEV
annotation
The lectures analyze in detail the description
adsorption equilibria on macro- and microporous
adsorbents both within the framework of the "Gibbs excess method" and within the framework of the "total content method". In the latter case, the consideration was carried out on the basis of the thermodynamic theory of stoichiometric adsorption of individual substances and binary and multicomponent solutions developed by the author.
The methods of theoretical (a priori) calculation of adsorption equilibria and the description of isotherms of "absolute" and "excessive" adsorption of gases, vapors and components of binary solutions of non-electrolytes by various equations obtained within the framework of phenomenological, lattice and empirical models are considered in detail.
The methods of quantitative description of adsorption isotherms and topological analysis of supramolecular structures of adsorbates on microporous active carbons by the method of molecular dynamics are considered.
Based on a comparison of numerical and physical experiments, the possibility of using the equations of the theory of volumetric filling of micropores (Dubinin Radushkevich, Dubinin-Astakhov), equations of lattice models, etc. at supercritical temperatures is proved.
A computer data bank on adsorption developed under the guidance of the author is presented.
This development is a presentation of the material of a special course of lectures, which the author has been reading for a number of years to students, graduate students and graduate students specializing in the field of adsorption. The author hopes that this teaching aid will fill the gap that exists in the scientific and educational literature on the topic under consideration, and will help novice researchers to get acquainted with the main problems and achievements of the science of adsorption, this most complex section of thermodynamics.
The proposed development option does not consider such important sections as adsorption on mesoporous adsorbents, accompanied by capillary condensation processes, and quantum chemical methods for analyzing adsorption phenomena. The author hopes to make the necessary additions in the future and will be grateful for all comments and suggestions for improving this manual.
Email: [email protected], [email protected] Honored Professor of Moscow State University A.M. Tolmachev Table of contents.
Lecture 1. Gibbs excess method
Lecture 2
Lecture 3. Thermodynamics of adsorption.
Stoichiometric theory of adsorption...............52 Lecture 4. Thermodynamics of adsorbed solutions
Lecture 5. Description of adsorption equilibria of solutions, gases and vapors on macro and microporous adsorbents
Lecture 7. Study of adsorption on microporous carbon adsorbents by numerical methods.
Adsorption isotherms and molecular nanostructures of sorbates ..........178 Lecture 8. Computer data bank on adsorption ......226.
– – –
A quantitative description of the adsorption isotherms of individual substances and components of fluid mixtures on adsorbents of various types and a priori calculation of adsorption equilibria in such systems, which are widely used in various processes of separation and deep purification of substances in chemical technology, medicine, and in solving environmental problems, is one of the most complex and, at the same time, important problems of the theory of adsorption, since the experimental search for the corresponding highly selective systems is quite laborious.
The main difficulty in constructing a rigorous thermodynamic model of adsorption systems is the problem of dividing the system into two phases, more precisely, determining the coordinates of the surface separating the bulk and adsorption phases. Precise drawing of the separating surface is impossible, therefore, two approaches are considered in theoretical works: the thermodynamically rigorous, but little informative Gibbs excess method, which does not separate the system into bulk and adsorption phases and allows one to analyze only the properties of the system as a whole, and the Langmuir total content method, based on the chosen in one way or another, models (dimensions, capacity) of the adsorption phase and the use of real (absolute) concentrations of components in this phase. Although the latter method is less rigorous, it is significantly more informative, since
considers the adsorption system as a two-phase one and allows one to analyze the properties of each of the phases separately and, in particular, to compare the results obtained by thermodynamic and molecular-statistical (or based on molecular models) methods, since the latter always require specifying the “structure” of the adsorption phase. The term "full content" appeared in the literature in the last quarter of the last century, however, according to the author, its foundations were first formulated by Langmuir, although he did not use this terminology.
Indeed, the well-known classical Langmuir model of ideal adsorption was based on two defining principles: setting the capacity of the adsorption phase limited by the monolayer, considered precisely as a separate phase of the adsorption system, and considering the adsorbent as a component of this phase, the concentration of which changed during adsorption due to the transition of free adsorption surface centers into adsorption complexes adsorbate – adsorbent.
Adsorption is a thickening of a substance at the phase boundary, due to the unsaturation of the bonds of surface atoms or molecules and, as a consequence, the existence of an adsorption field that propagates, strictly speaking, to points infinitely distant from the surface of the adsorbent in the bulk phase. This circumstance leads to the need to take into account the following features of such systems:
1. The separation of the system into adsorption and bulk phases cannot be carried out strictly.
2. The adsorption phase isolated on the basis of some additional (always approximate) considerations will be energetically inhomogeneous (it will be in an inhomogeneous adsorption field) and, since this inhomogeneity cannot be taken into account within the framework of phenomenological thermodynamics, the description of the properties of the adsorption phase has to be carried out using phase-averaged parameter values (concentrations, chemical potentials, etc.) .
Parameters of the adsorption phase: concentrations - c, x, activity coefficients -, chemical potentials - are marked either by a bar above the corresponding symbol, or by the subscript R.
3. The presence of the adsorption field must be taken into account in the expression for the chemical potential, i.e., use the full chemical potentials for the components of the adsorption phase:
For bulk gas or vapor phase:
– – –
where: surface (pore volume) of the adsorbent, W surface tension (internal pressure).
Using Maxwell's equations, we get:
– – –
It is useful to pay attention to two forms of the Gibbs-Duhem equation, which are widely used for adsorption solutions in the framework of the total content method. In older models, the adsorbent was often not considered as a component of the adsorption solution, but only as a source of the adsorption field (surface energy). In this case, for example, during the adsorption of a one-component vapor, the equation
Gibbs-Duhem has the form (P,T=const.):
c i d i Wd 0 (1.7) (W is the surface area of the adsorbent, i is the total chemical potential of the adsorbate).
In modern models, the adsorbent (R) is a component of the adsorption solution. It is introduced either in the form of adsorption centers (as in the Langmuir and Tolmachev models) or in the form of vacancies (free voids of certain sizes in the adsorption solution).
In this case, the Gibbs-Duhem equation can be represented in two equivalent forms (single-component vapor, P,T=const.):
with i d i c R d R Wd 0 (1.8) and since s(st.), then within the framework of the “hard” solution model (the molar areas of the components - s=const., s i +sR=W) (1.8) reduces to the form:
c i d i c R d R (si sR)d Wd c i d iR c R d R 0 .
The above features of adsorption systems led to the development of two versions of their thermodynamic description:
1. The Gibbs excess method - a thermodynamically rigorous description of the change in the properties of the entire system during adsorption on the basis of experimentally determined excess adsorption values (see below) without its separation into two phases. This method, obviously, does not allow obtaining any information about the properties of the adsorption phase and, therefore, is not informative enough, especially when solving practical problems, since it does not provide information about the capacity of the adsorbent with respect to the components of the bulk phase, about its structure, properties, and etc..
2. Total content method, based on the separation of the system into two phases (see below) and the description of its properties as a heterogeneous system using the absolute concentrations of the components in each of the equilibrium phases. Thermodynamically, this method is less rigorous, because it is based on a model approximation that determines the interface between the bulk and adsorption phases, but it is obviously much more informative, because
allows one to obtain the characteristics of the adsorption phase, which is extremely important from a practical point of view, and, in addition, allows one to compare them with those calculated on the basis of various molecular models, which are necessarily associated with specifying a specific arrangement of molecules near the surface of the adsorbent.
In this regard, a significant part of modern information on adsorption is presented within the framework of the total content method, and the excess method is used to obtain primary information and as a criterion (see below) when choosing a model for switching to the total content method. For a long time, the attention of researchers was drawn to the study of the adsorption of gases and vapors at relatively low pressures, at which the values of excess and absolute adsorption practically coincided, and the problem of choosing a method for the thermodynamic analysis of adsorption phenomena was not actively discussed.
Interest in this problem reappeared in the last quarter of the last century in connection with the active use in industry of adsorption processes at high pressures. During this period, a significant number of works appeared devoted to the experimental and theoretical study of adsorption equilibria in wide ranges of temperature and pressure changes and a detailed analysis of the ways of converting experimentally determined values of excess adsorption into absolute ones.
Since our task does not include a detailed analysis of various options for the thermodynamic consideration of adsorption phenomena, we will restrict ourselves to a brief comparison of the two approaches noted above, focusing on the problems of the total content method, within the framework of which almost all methods for describing and a priori calculation of adsorption equilibria have been developed.
Gibbs excess method.
A brief summary of the fundamentals of the "Gibbs Excess Method" will begin with two quotations that fairly fully set out the main idea of the method and reflect two approaches to assessing the significance of this method in the modern theory of adsorption phenomena:
“A feature of Gibbs' approach is that he immediately abandoned the attempt to characterize adsorption by any absolute values, i.e., to consider the interfacial layer as some physical object that has natural boundaries and, therefore, contains a certain amount of substance in a certain volume, which could be equated with the measured value of adsorption. Such a consideration would be contrary to the principles of adsorption measurement. The advantage of excess quantities is that they are directly measured in the experiment and therefore are not associated with any models. With their help, it is possible to construct a thermodynamic theory that will include only experimental quantities”;
“Some features of the thermodynamic formalism proposed in the description of adsorption phenomena are, it seems to us, in sharp discrepancy with the current state of the theory of adsorption. The excess adsorption value is determined directly from the adsorption experiment, and in any equation of the Gibbs adsorption theory it is allowed to use only this value.
From our point of view, the use of only excess adsorption in all cases brought the Gibbs method into irreconcilable contradiction with adsorption science at the end of the 20th century. Indeed, any equation of the adsorption isotherm (for example, the Langmuir equation) or the equation of state of the adsorption phase, based on molecular kinetic concepts, includes not the number of excess molecules, but the total number of real molecules in the region of inhomogeneity. The heats of adsorption determined experimentally are associated with a change in enthalpy when all, and not just excess, molecules enter the adsorbent field. Not only excess, but all adsorbed molecules participate in two-dimensional phase transitions. Finally, when applying the method of statistical thermodynamics to describe adsorption phenomena, it should be remembered that in statistical physics there are no "excess" molecules at all. Thus, in almost any modern study of adsorption, it is necessary to take into account all the molecules of the adsorbate, while in the Gibbs thermodynamic equations, in the name of ephemeral "strictness", only excess adsorption should be taken into account.
Sharing, in the main, the point of view stated in the second quote, we note that the Gibbs method has retained its significance for the analysis of surface phenomena at the gas-liquid and liquid-liquid interfaces, for which it was originally developed, since in these cases the surface tension () , which is included in the famous Gibbs adsorption equation, is an experimentally measured quantity.
Let us first consider the essence of this method using the adsorption of a one-component gas as an example.
We introduce into three (I, II, III) identical vessels (Fig. 1.1) with volumes V0 the same number of moles of gas n0. Let the walls of vessel I absolutely do not adsorb this gas - then its pressure in vessel I will be Р0, molar density 0, and the number of moles n0=0V0. Let the lower wall in vessel II be an adsorbing surface. Then, near the surface, the density of the gas will increase, and away from the surface in the volume of the vessel, it will decrease to.
– – –
Since the adsorption phase is not released, the volume of the vessel does not change, and the amount of gas in this volume decreases to V0, if we assume that the density extends up to the lower adsorbing surface (the adsorption phase is identified with the geometric surface located on the lower wall of the vessel II).
Change in the amount of gas in the volume of vessel II compared to vessel I:
ne V00 V0 (1.10),
– – –
Since at low (up to several atmospheres) pressures, the last terms on the right-hand sides of equations (1.13) and (1.14) are vanishingly small compared to excess adsorption, when describing the adsorption of gases and vapors, there is often no distinction between absolute and excess values. Only in experiments with high pressures of adsorptives do these differences become noticeable.
Indeed, the absolute values of adsorption increase with increasing pressure, tending to a certain limit:
– – –
where v is the molar volume of the adsorbate in the adsorption phase (usually it is taken equal to the molar volume of a pure liquid adsorptive). At the same time, excess adsorption passes through a maximum with increasing pressure and then decreases to zero, since the density of the bulk phase becomes the same , as well as near the surface.
Rice. 1.2. Isotherms of excessive adsorption of methane on activated carbon at different temperatures.
In some cases, the density in the bulk phase may even exceed the density near the surface due to the limitation of the mobility of molecules near the surface and, as a consequence, their less compact packing (excess adsorption will be negative in this case). Examples of excess adsorption isotherms are shown in Figs. 1.2, while total content isotherms in fig. 1.3:
– – –
Rice. 1.3. Adsorption isotherms of hydrocarbons and CO2 on Nuxit activated carbon at 293K. Designations: - methane, - ethylene, - ethane, - propylene, - propane, - CO2.
Let us now consider the adsorption of one of the components of a binary liquid solution:
If the excess adsorption of a solution component is determined similarly to the excess adsorption of a gas, then it is necessary to take into account the change in the volume of the solution due to its compression in the adsorption field (without dividing the volume of the system into
– – –
Based on (1.24), the Gibbs adsorption equation, which is the basis of the thermodynamic description of adsorption systems in the framework of the excess method, can be, taking into account (1.17) and (1.18), as well as the relations obviously following from the Gibbs-Duhem equation written for a bulk solution with using molar concentrations or mole fractions:
– – –
The lower integration limits in (1.25) and (1.26) are determined by the choice of adsorption values at which the surface tension is assumed to be 0. For example,
– – –
surface active) is an important characteristic of such systems.
Since a change in surface tension during adsorption leads to a change in the total chemical potentials of adsorbates and, consequently, in thermodynamic functions, from (1.25) and (1.26) one can obtain (we will not consider the corresponding conclusions) relations for calculating the excess thermodynamic functions of adsorption (Ge, He, Se) characterizing the change in the corresponding properties of the entire system as a whole as a result of the adsorption process in comparison with the corresponding comparison system. It is important to emphasize that these calculations are carried out using experimentally determined excess adsorption values and are not related to the choice of any model of the adsorption phase.
As applied to adsorption on solid adsorbents, equations (1.25) and (1.26) are not widely used, and the Gibbs excess method is used mainly as a criterion when choosing a thermodynamically permissible volume of the adsorption phase in the total content method.
The most useful in this sense were the equations describing the dependences of the excess thermodynamic functions for the adsorption system as a whole on the composition of two-component bulk (mainly liquid) phases. If we choose an adsorbent wetted with a pure second component as a reference state, then the corresponding equation for changing the excess isobaric potential
Gibbs (G e) has the form:
– – –
If there are experimental data on the temperature dependence of adsorption, then equations for the corresponding dependences of the excess enthalpies and entropies of the system can be easily obtained from (1.27).
Attempts to represent the dependences of the corresponding “isosteric” thermodynamic functions on the values of andexcess adsorption clearly demonstrate the difficulties of their physical interpretation, which is clearly seen in the example of the corresponding dependence for the differential isosteric excess heats of methane adsorption on Rho zeolite on the filling and adsorption temperature shown in Fig. 1.3.
As follows from the figure, under "isosteric" conditions, with increasing temperature, the differential excess heats of adsorption are at first constant (curves 1,2,3), and then sharply increase, fanning out due to the imperfection of the gas phase. The heat value reaches values exceeding 150 kJ/mol.
Fig.1.4. Temperature dependence of the isosteric excess heat of methane adsorption on Rho zeolite at Г 1 (mmol/g): 0.5 (1.4); 0.535 (2.5); 0.645 (3.6).
x The further course of the heats of adsorption is due to the presence of a maximum on the excess adsorption isotherms and the manifestation of a break in the derivative to the isostere when passing through this point. The heats acquire a negative sign and in the region of high pressures gradually approach the abscissa axis.
It is clear that a comparison of these results with the experimentally observed calorimetric heats of adsorption, which depend on the total amount of adsorbed molecules, is at least difficult.
However, despite these difficulties, the Gibbs excess method has been repeatedly analyzed and refined. "Geometric"
Gibbs' formalism was developed by Guggenheim and Adam, later Hansen and Goodrich developed an "algebraic" formalism that did not explicitly require the introduction of a geometric interface for the liquid-liquid boundary. An important stage in the development of the Gibbs method was the work of Tikodi and, especially, Shai, in which adsorption on solid adsorbents was considered. The result of these many years of research was summed up in the fundamental monograph by Lopatkin, who analyzed in detail and clarified all the problems of applying the "excess method" to the analysis of adsorption equilibria on solid adsorbents of various structures.
Literature.
1. Gibbs J.W. //Thermodynamics. Statistical mechanics.
The science. Moscow,.
2. Lopatkin A.A. // Theoretical foundations of physical adsorption, Publishing House of Moscow State University, 1983.
3. Tolmachev A.M.// Langmuir, 1991, No. 7, p.1400;
Tolmachev A.M. // Vestn.Mosk. University. Series 2. Chemistry, 1990, vol. 31, no. 6, p. 529; Tolmachev A.M. //Vestn. Moscow University.
Ser. 2. Chemistry, 1994, vol. 35, no. 2, p. 115.
4. Larionov O.G. /Dis. dr. chem. Sciences. Institute of Chemistry of the Academy of Sciences of the USSR, Moscow, 1975.
5. V. V. Serpinsky and T. S. Yakubov, Izv. Academy of Sciences of the USSR. Ser.chem., 1985, p.12.
6. Fomkin A.A. //Dis. dr. physics and mathematics Sciences. IPC RAS, Moscow, 1993.
7. A. A. Pribylov, T. S. Yakubov, G. F. Stekli, L. Curry, I. A. Kalinnikova, and L. G. Shekhovtsova, Russ. //Izv. AN. Ser.chem.
8. Szepesy L., Illes V.// Acta Chim. Hung., 1963, vol. 35, pp. 37, 54, 245, 373.
9. Guggengeim E.A.// Modern Thermodynamics Stated According to Gibbs Method), Moscow-Leningrad: GNTI, 1941.
10 Guggenheim E.A., Adam N.K. //Proc. Roy. Soc., 1933, vol.
11. Hansen R.S. // J. Phys. Chem., 1962, vol. 66, p. 410.
12. Goodrich F.C. // Trans. Faraday Soc., 1968, vol. 64, p. 3403.
13. Tykodi R.J. // J. Chem. Phys., 1954, vol. 22, p. 1647.
14. Shay G.A. // Pure Apple. Chem., 1976, vol. 48, p. 393.
Lecture 2. Full content method.
Introduction.
Insufficient information content of the Gibbs excess method, difficulties in interpreting the thermodynamic characteristics of adsorption systems obtained on its basis, the practical need to analyze the properties of the region of inhomogeneity (adsorption phase) led to the emergence of a series of studies in which the mathematical Gibbs interface was replaced by a real phase with its own physical and thermodynamic characteristics .
Initially, these studies were developed within the framework of the finite thickness layer method, and later developed within the framework of the total content method.
Consideration of the transition region of inhomogeneity as a certain layer of finite thickness, separated from homogeneous bulk phases by two surfaces, i.e. as a separate phase with its own energy, entropy, mass and volume, with real, "absolute" concentrations of components, was started in the works, and also in .
A detailed development and detailed analysis of this approach was carried out in the works of A.I. Rusanov, who, following mainly the Gibbs method, derived all the necessary relationships for the thermodynamic analysis of surface phenomena and properties of a layer of finite thickness (both with flat and curved surfaces) using not excess, but total concentrations of components in the layer. So for the adsorption of a binary liquid solution on a flat surface of a solid adsorbent, a strict thermodynamic equation (2.1) was obtained:
– – –
where: x 1, x 1 - equilibrium mole fractions of the first component in a layer of finite thickness and in a bulk solution; i, i corresponding chemical potentials of components in equilibrium phases; A is the interface per mole of the mixture.
Integration (2.1) for the simplest case, when both phases are assumed to be ideal, and A is an additive function of the areas of each of the components (s 0 i), leads to an equilibrium equation like the law of mass action:
x 1 (1 x 1) K (2.2), x 1 (1 x 1) s 01 where: K is a constant; - stoichiometric coefficient s 02 of mutual displacement of components.
As part of the finite thickness layer method, the most stringent and accurate methods for determining its thickness (capacity) have not been developed. In addition, it has been developed mainly for binary (and multicomponent) bulk phases and analysis of the properties of surface phases. Therefore, for the analysis of adsorption equilibria proper, the total content method is widely used, which does not fundamentally differ from the finite thickness layer method, but relies on the developed methods for determining the “sizes” (capacity) of the adsorption phase and the use of the chemical potential apparatus, which makes it possible to obtain the ratios in a simpler way similar to (2.2), including those for adsorption from one-component bulk phases. Within the framework of the total content method, almost all known equations of adsorption isotherms from single- and multi-component bulk phases were obtained; therefore, we will consider the main features of this method in more detail.
full content method.
The first work in which the full content method was introduced is, as already noted, the work of Langmuir. However, the consideration of the problem in general terms and the thermodynamic justification of the method were carried out in the second half of the last century in a series of studies that considered methods for determining the "dimensions"
(volume, capacity) of the adsorption phase and methods for converting excess adsorption values into total (absolute), as well as adsorption thermodynamics within the framework of the total content method.
To calculate the absolute values of adsorption in the total content method, it is necessary to choose the volume or limiting capacity of the adsorption phase.
The very possibility of such a choice was called into question on the basis of the following reasoning:
Since the adsorption potential tends to zero at an infinite distance from the surface, the total content of individual gases during adsorption should be defined as a definite integral:
– – –
converges.
However, one can always choose the distance from the surface (z0) at which the increase in fluid density due to the adsorption field is compensated by the equilibrium fluctuation of the fluid density, i.e. adsorption is zero. Taking this circumstance into account, the total content should be defined in the form of a convergent integral
– – –
Since the choice of the size of the adsorption phase in the transition to the total content method is different for different types of adsorbents, let us consider the main types of adsorbents:
– – –
In accordance with the widely used classification of adsorbent types proposed by M.M. Dubinin, all adsorbents are divided into three groups:
microporous adsorbents with a narrow size distribution of micropores (0.5 - 1.5 nm): active carbons, zeolites.
microporous adsorbents with a bimodal micropore size distribution (0.5 - 1.5 and 1.5 - 2.0 nm.): some types of active carbons.
mesoporous adsorbents (2.0 - 20 nm.): silica gels, oxides of aluminum, iron, etc.
macroporous adsorbents (r 20 nm.): graphite soot, silica gels, surfaces of single crystals, etc.
In accordance with the theory of volumetric filling of micropores (TOSM), adsorbate molecules at any point in a micropore are in the zone of action of the adsorption potential of the pore walls and, therefore, unlike mesopores, phase transitions of the first order (liquid adsorbate - vapor) are impossible in them. In this regard, we note that quantum chemical calculations show that the adsorption potential sharply decreases with distance from the adsorbing surface and, as is clearly seen from Fig. 2.1, noticeably manifests itself at distances up to 0.8–1 nm, which corresponds to the accepted maximum micropore sizes of 1.6–2.0 nm. In classical thermodynamics, it is usually assumed that the adsorbate-adsorbent interaction potential decreases with the adsorption layer number (n) in accordance with the formula:
– – –
4.0 Fig. 2.1. Interaction energy profiles between propene (0), benzene (1), and methanol (2) molecules with a carbon surface, calculated by the quantum chemical method (DFT PBE0/6 311G).
Before considering the problem of determining the volume of the adsorption phase, we obtain relations similar to (1.13, 1.14) for adsorption from binary liquid solutions.
The corresponding calculation formulas can easily be obtained on the basis of balance ratios.
– – –
Various choices of values V or c i are discussed in detail in the literature. We will briefly consider the most widely used methods in relation to adsorption on adsorbents of various structures.
Adsorption on smooth surfaces (macroporous and mesoporous adsorbents).
In accordance with (2.6), in the adsorption of gases, the adsorption phase always represents a monolayer. However, to determine the limiting adsorption (capacity of the monolayer c i a m mol.cm-2), it is necessary to know the surface area of the adsorbent (A) and the area per adsorbate molecule ():
am A / Na (2.11) At the same time, equation (2.11) is used to determine the surface area from the “experimental” values of a m found as a parameter of the equations describing the isotherms of polymolecular vapor adsorption (we will consider these equations in detail below), while no satisfactory equations have yet been proposed to describe gas adsorption isotherms (the classical Langmuir equation is inapplicable in real systems). Further, based on various estimates (quantum chemical calculations, van der Waals radii, etc.), taking into account possible orientations of molecules near the surface, values are found and a m is calculated for gas adsorption. Thus, in the thermodynamic analysis of gas adsorption on macroporous adsorbents within the framework of the total content method, one should take into account the difficulties of accurately determining a m, as well as the possibility of changing the orientation of molecules during the adsorption of gas mixtures.
In the case of polymolecular adsorption of vapors on macroporous adsorbents, the volume of the sorption phase is variable, since the condensation of the adsorbent in the second and subsequent layers due to the presence of an adsorption field (although sharply decreasing with distance from the surface) occurs at pressures lower than the saturation vapor pressure (Ps). In this regard, thermodynamic analysis in the framework of the total content method for such systems is difficult and is limited to using the equations of excess adsorption isotherms (mainly for determining the surface of adsorbents) in cases where the values of Ps are small and excess adsorption can be equated to absolute:
The two-parameter BET and Aranovich equations are most widely used (see Lecture 5 for details), one of the parameters of which is a m. It should be emphasized that during the adsorption of gases, it is not the volume of the adsorption phase that is determined - the volume of the monolayer, which during the adsorption of gas mixtures can be a variable value due to the difference in the effective radii of the molecules, but a thermodynamically more important value - the capacity of the monolayer at a constant surface area (see lecture 3), i.e.
a two-dimensional problem is considered.
In the case of adsorption of liquid solutions on macroporous adsorbents, the adsorption phase, as a rule, is also limited to a monolayer; it is much less often necessary to consider it as a two-layer one. In this case, two methods are used to determine the volume (capacity) of the adsorption phase:
1. Universal thermodynamic method O. G.
Larionova,
2. A method based on the Aranovich-Tolmachev equation.
The first one is based on the comparison of changes
– – –
and, in the presence of the corresponding data for different temperatures, H e, S e during the transition from the adsorbent wetted with pure component 2 to solutions of composition x 1, for the adsorption system as a whole, i.e. within the framework of the Gibbs excess method, with similar dependences calculated within the framework of the total content method. Since in the latter case, the change in the thermodynamic functions of the system as a whole will depend on the separation of the system into two phases (into the volume of the adsorption phase V and the volume of the solution phase V-V):
G(x 1) (VG ads. (V V)G vol.)(x 1) (2.13), then by varying the values of V, one can find the volume (capacity) of the adsorption phase, at which the corresponding dependences in the excess method and in the total content method will match.
Analysis of a large number of adsorption systems by this method showed that the adsorption phase, as a rule, is a monolayer and, relatively rarely, two layers (for example, in the case of alcohols characterized by a strong adsorbate–adsorbate interaction).
The second method, based on the use of the Ono-Kondo lattice model and the Aranovich-Tolmachev equation obtained within the framework of this model, was proposed in .
In this work, it is shown that a quantitative description of the isotherms of excess adsorption of components of nonelectrolyte solutions on macroporous adsorbents with physically reliable values of parameters (interaction energies, monolayer capacity, layer composition) can be obtained based on the system of Aranovich Tolmachev equations.
The corresponding equations will be presented in Lecture 5.
The parameters of the equations (a1,m, / kT, B) are found by a numerical method (by minimizing the deviations of the calculated and experimental values of Г1). Then, using a special program, the compositions of the first two layers of the adsorbate are calculated. The results are presented in table 2.1. It can be seen from the table that for systems with / kT, which characterize the differences in the interaction energies of identical and different solution molecules, less than 0.04 (the majority of such systems!) the composition of only the first layer X1(n=1) differs from the composition of the bulk phase X1(oo), those. the adsorption phase is monolayer, which agrees with the conclusions obtained by the Larionov method.
Table 2.1 Dependence of X1(n) on X1() at 303K for systems:
I-CCl4-iso-C8H18-graphite. carbon black (/kT theor.=0.01), II- C6H5CH3C6H5Cl-silica gel (/kT theor.=0.04), III- c-C6H12-С6H5NO2Al2O3 (/kT theor.=0.16) – – –
Adsorption on microporous adsorbents (active carbons, zeolites) has been studied and continues to be intensively studied, since the widespread use of adsorption technologies for the separation and deep purification of substances, environmental protection, and in various catalytic processes is based on the use of microporous adsorbents.
On the other hand, microporous adsorbents are a convenient object for various theoretical studies. Thus, the interests of fundamental science and practice are successfully combined.
In particular, the total content method is most strictly and successfully used specifically for studying adsorption on microporous adsorbents, since the volume (capacity) of the adsorption phase in this case is determined quite strictly.
Determination of the volume (capacity) of the adsorption phase:
The simplest is the "limiting" capacity of adsorption 1.
phase, which it is natural to take the volume of micropores, is determined using equations describing the vapor adsorption isotherms, of which it is a parameter.
These are, first of all, the equations of the theory of volumetric filling of micropores (TOZM): Dubinin - Radushkevich (microporous coals) and Dubinin - Astakhov (zeolites) and the Tolmachev-Aranovich equation (microporous coals and zeolites), one of the parameters of which is the limiting capacity of the adsorption phase at adsorbate pressure equal to the pressure of its saturated vapor (Ps). Of course, it is necessary to use adsorptives having saturated vapor pressures less than one atmosphere at the temperature of the experiment, so that the excess and absolute adsorption coincide. A detailed analysis of these and other equations will be considered in Chapter 5.
2. When adsorbing solutions, the volume (capacity) of the adsorption phase can be determined by the Larionov method described above. The application of this method in all cases leads to the volume (capacity) of the adsorption phase, which practically coincides with the volume (capacity) of micropores, determined by vapor adsorption.
3. An interesting way to determine absolute adsorption in the framework of the total content method was proposed by Fomkin. This method, which requires special equipment for the experimental determination of excess liquid and vapor adsorption at a pressure equal to Ps, shows the possibility of a fairly accurate determination of absolute adsorption without determining the volume of micropores.
– – –
Rice. 2.2. Scheme for determining absolute adsorption.
At the first stage, a sample of a microporous adsorbent is placed in an adsorption vessel of volume V (the scheme is shown in Fig. 2.2) and the usual calibration is carried out using helium at a high temperature (400-500K), when its adsorption can be neglected. In this case, it is not the true volume of the adsorbent with micropores that is determined, but a somewhat larger volume V (shown by a dotted line in the figure), since helium atoms have their own volume.
At the second stage, the determination of excess adsorption from saturated vapor and liquid is carried out. Obviously, the absolute adsorption is the same in both cases, and therefore
– – –
which makes it possible to calculate the absolute adsorption without determining the true volume of micropores. Estimates that can be made in the case of zeolites, for which the geometric micropore volume can be calculated from X-ray analysis data, show that the available micropore volume is 20-30% less than the geometric one.
In connection with the consideration of this method, we emphasize that in the total content method, it is the capacity (limiting capacity) of the adsorption phase, which can be calculated quite accurately, that is the main characteristic used in thermodynamic analysis. The constancy of the volume of micropores or the surface in the case of macroporous adsorbents is an important condition that makes it possible to characterize the adsorption phase as a phase of limited capacity with respect to the components of the system. In this case, it is often not necessary to accurately determine the volume of micropores or the surface.
In conclusion, we note that the absolute adsorption of vapor or pure liquid at saturated vapor pressure is usually taken as the limiting capacity or limiting filling of the adsorption phase.
However, in accordance with the Langmuir-Tolmachev quasi-chemical model, the limiting saturation of the adsorption phase can be achieved only at a pressure tending to infinity. In addition, it has been experimentally shown that with an increase in the hydrostatic pressure on a liquid, the limiting adsorption in micropores can increase by 10-15% due to the rearrangement of the adsorbate structure.
Therefore, in the thermodynamic analysis of adsorption systems, it is necessary to accurately define the concept of the limiting capacity of the adsorption phase.
The change in the limiting adsorption with a change in the composition of the adsorbed solution during the adsorption of liquid solutions is calculated using the "hard" solution model.
As already noted, this is a forced approximation, since there are practically no data on partial molar volumes.
However, if we assume that the volume of the adsorption phase during adsorption on zeolites is equal to the volume of the cavities, then the “absolute” adsorption in the total content method can be found not by calculation using equations (2.10), but experimentally during adsorption from solutions (by the pycnometric method) as for pure adsorptives, and for solutions.
Obviously, the rigid solution model should lead to a linear dependence of the absolute total adsorption
– – –
Of the five systems studied so far, the corresponding linear dependences with a good approximation are fulfilled for four (see, for example, Fig.
2.3a), however, in one system, deviations from linearity are noticeable (see Fig. 2.3b)
– – –
In thermodynamic analysis, such deviations from the rigid solution model are formally taken into account in the activity coefficients of the components of the adsorbed solution, which, according to the apt expression of V.S. Soldatov, in this case become "the coefficients of our ignorance".
In conclusion, we note that the total content method turns out to be necessary and very fruitful in the analysis of the adsorption of gases, vapors, and liquids on microporous adsorbents in wide temperature and pressure ranges.
Peculiarities of adsorption in micropores.
Physical adsorption of gases, vapors, and liquids on microporous adsorbents differs significantly from adsorption on an open surface. In micropores, the adsorption potential greatly increases due to the superimposition of adsorption fields of opposite walls. These features of the microporous system of the adsorbent dramatically change the properties of the substance in the adsorbed state. The adsorption field of a microporous adsorbent imposes its structure and disperses the substance in such a way that there are no first-order phase transitions of the condensation type in the adsorbate. However, with an increase in adsorption in it, processes of restructuring similar to second-order phase transitions become possible.
The adsorption interaction of adsorbate molecules with the surface of a solid body in the general case always leads to a change in the state of the solid body itself. This change can be more or less significant, depending on how strongly the surface of the solid body is developed, whether it has high-energy adsorption centers that exhibit specific interaction, and whether the energies of intermolecular bonds of atoms or molecules that make up the solid body are high. When adsorbed on microporous adsorbents, the adsorbent and adsorbate are equal participants in the adsorption process.
Features of the properties of adsorption systems and the adsorbate in microporous adsorbents are especially noticeable in the behavior of adsorption isotherms and isosteres, adsorption deformation of the adsorbent, and thermodynamic functions of adsorption systems when studied in wide ranges of pressures and temperatures.
A detailed study of these processes was carried out in the works of A.A. Fomkin and colleagues. .In these works it was shown:
The adsorption of gases, vapors, and liquids in microporous adsorbents increases smoothly with increasing pressure when passing through the critical temperature and during phase transitions in the adsorbent.
Rice. 2.4. Adsorption isotherms of water (1-3) and benzene (4.5) on NaX zeolite at T (K): 1-303; 2-313; 3-323; 4-303, 5-323.
– – –
hydrostatic pressure up to 100 MPa), and in fig. 2.5 isotherms of methane at temperatures lower and higher Tcr.
As follows from Fig. 2.5, the adsorption isotherms change symbatically with increasing temperature when passing through the temperature of the critical point of the adsorptive: Tcrit. = 190.55 K, which indicates the absence of condensation effects in the adsorbate.
a[mmol.g-1]
1 0 1 2 3 4 5 6 logP(P[ Pa]) 2.5. CH4 adsorption isotherms on the microporous carbon adsorbent PAU-10, at T, K: 1 - 120; 2 - 130; 3 Adsorption isosteres in the coordinates lnP=f(1/T)a remain linear in wide ranges of pressures and temperatures and do not change their slope when passing through the critical temperature of the gas phase. This is clearly seen from the data shown in Fig. 2.6.
From fig. It can be seen from Fig. 2.6 that isosteres remain linear over the entire studied pressure and temperature range, and, what is especially important, isosteres that terminate at the saturated vapor pressure line continue linearly in the supercritical region, and adsorption isosteres that begin in the vapor region continue linearly in the region state of compressed fluid.
Rice. 2.6. Xe adsorption isosteres on NaX zeolite during adsorption, mmol/g: 1 – 0.1; 2 - 0.2; 3-0.4; 4 - 1.0; 5 - 2.5; 6 - 3.5;
7 - 4.0; 8-4.5:9-4.7; 10-4.9; 11-5.15; 12-5.3; 13 - 5.5; 14 - 5.8. ln Ps
– saturated steam pressure line.
The linearity of adsorption isosteres in the region where gases have significant deviations from ideality, their linear continuation in the region of the liquid state of the adsorbent and in the supercritical region - all this indicates that the adsorbate in the microporous adsorbent is a special state of matter.
This position is also confirmed by studies of the adsorption of various liquids on NaX zeolite along the saturated vapor pressure line, carried out by M.M. Dubinin et al. С9Н20, СF3Cl) and inert gases (Xe, Kr, Ar) at low temperatures - less, and near the critical temperature - more liquid adsorptive density. The temperature at which they are equal is approximately 0.8 Tcr. The average densities of adsorbed polar substances (H2O, C6H6, C2H5OH) in the studied temperature range of 273–473 K are higher than the liquid density and change much more slowly with temperature. It is significant that the density curve for adsorbed water does not have a maximum at 277.15 K, which is characteristic of ordinary water.
The differential molar isosteric heat of adsorption at high pressures depends on temperature both due to the nonideality of the gas phase and the noninertness of the adsorbent, i.e. the intensity of its temperature and adsorption deformation (Fig. 2.7.). Similar results were also obtained for other systems.
Differential molar isosteric heat capacities of adsorption systems (Fig. 2.8.) at high adsorption values have maxima, indicating the presence of structural rearrangement processes (second-order phase transitions) in the adsorbate.
Similar dependences of the isosteric heat capacity have also been obtained for other adsorption systems. The main reason for the appearance of maxima on the curves of isosteric heat capacity, apparently, is the properties of the adsorbed substance in the micropores of adsorbents. This is indicated, first of all, by the temperature intervals in which extreme phenomena develop. From fig. 2.8 it follows that the maxima begin to appear in the temperature range approximately 100–200K higher than the critical temperature of the sorbed gas. Similar dependences were also obtained for other studied systems. With an increase in adsorption and, consequently, the average number of molecules in the cavities of microporous adsorbents, the maxima of the isosteric heat capacity become more pronounced and shift to the region of low temperatures.
Rice. 2.7. Dependence of the differential molar heat of Xe adsorption on NaX zeolite, taking into account the adsorption deformation, on the adsorption value at T(K): 1-150; 2–210; 3 The dashes show the shape of the curves without regard to adsorption deformation).
Fig.2.8. Temperature dependences of the differential molar isosteric heat capacity of the adsorption system "Xe - zeolite NaX" at different adsorption values, mmol/g: 1-1.0; 2 - 2.0; 3 - 4.0; 4 - 4.5; 5 - 4.7; 6 - 4.9; 7 - 5.0; 8 - 5.15; 9 – 5.30 a.m.
At low fillings, according to the calculations of the potential energy maps of interaction in the pores of the adsorbent, the molecules are in deep potential "wells". However, with an increase in temperature under isosteric conditions at medium and high fillings, due to an increase in the kinetic energy of molecules, the process of transition of molecules from adsorption centers to the volume of micropores with the formation of associates becomes more and more likely. In particular, such an adsorption mechanism, that is, the transition from partially localized to delocalized adsorption, was discovered by A.A. Fomkin et al. in the analysis of helium adsorption in NaX zeolite.
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Adsorption as a spontaneous concentration of molecules on the surface is accompanied by a decrease in the entropy of the system. Since the criterion for the spontaneity of the process is
∆N - T · ∆S = ∆G< 0,
then adsorption is possible only at ∆Н< 0 (экзотермический процесс). Равновесие определяется условием ∆Н = T· ∆S. With an increase in temperature, the equilibrium shifts towards the endothermic process, i.e., desorption.
Adsorption on a solid surface
1. monomolecular adsorption.
According to Langmuir's theory, adsorbate molecules interact with the adsorbent surface, eventually forming a monomolecular layer. In this case, the degree of filling () of the surface with the adsorbed substance during adsorption from the gas phase
from liquid
where K is the equilibrium constant (adsorption constant);
p is the partial pressure of the adsorbed gas;
c is the concentration of the adsorbed substance.
The dependence of β on p (or c) is represented by a graph (adsorption isotherm, Т = const) in Fig. 1. 1.3.
Rice. 1.3. Degree of filling of the surface with adsorbed substance
At low concentrations and partial pressures, adsorption is proportional to the concentration or partial pressure:
R<< 1, β ≈ К· r oris<< 1, β ≈ К· s, i.e. the initial section of the isotherm is approximately linear, and tan α \u003d K (tg α is determined by the slope of the curve at p (or c) → 0: or ).
If - the number of moles of the adsorbed substance per 1 g of the adsorbent; - the maximum possible number of moles of the adsorbed substance per 1 g of the adsorbent ("monolayer capacity"), then
Substituting β into equation (1.3) (for the case of adsorption from the gas phase, the concentration With in the equations should be replaced by pressure R), we get:
(1.6)
Since and K in this pair of adsorbent-adsorbent are constants (at T= const), then the dependence can be found and To(Fig. 1.4).
Rice. 1.4. Graphical solution of the adsorption equation
obtained by extrapolating the experimental linear dependence to () = 0; and, since , then , .
The value can be used to determine the specific surface area of the adsorbent UD (in m 2 per 1 g of adsorbent), if the area ω occupied on the surface by one molecule of the adsorbent is known (determined from the size of the molecule):
UD = · ω · Na, (1.7)
where Na is Avogadro's number (Na = 6.02 10 23).
In turn, the known value of SD can be used to calculate or ω of any substance by its adsorption on a given adsorbent.
2. Polymolecular adsorption.
Equation (1.5) describes a curve with saturation, i.e. at
p (or c) → ∞ tends to the limit value equal to (Fig. 1.5, a).
Fig.1.5. Adsorption isotherms:
a – adsorption with saturation; b – polymolecular adsorption
However, in some cases adsorption isotherms look like those shown in Fig. 1.5b, i.e. does not reach the limit even at high p (or c).
Dependencies of the type shown in fig. 1.5b correspond to polymolecular adsorption. As a rule, such isotherms are characteristic of substances with strong intermolecular interactions (for example, water). When the adsorption centers on the surface of the adsorbent are occupied (the monomolecular layer is saturated), the "landing" of the next adsorbate molecules occurs due to intermolecular interactions with already adsorbed molecules (Fig. 1.6). The heat of such adsorption is close in absolute value, but opposite in sign, to the heat of evaporation of the corresponding liquid (think why).
Fig.1.6. Adsorption scheme:
a - monomolecular adsorption; b - polymolecular adsorption
As you get closer R to the saturated vapor pressure of the adsorbed substance, it begins to condense on the surface of the adsorbent; as a result, it rapidly increases with increasing R.
