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Sample Chapter A ABSORPTION Cross-references Agrophysics: Physics Applied to Agriculture The process by which one substance, such as solid or liq- uid, takes up another substance, such as liquid or gas, through minute pores or spaces between its molecules. ADAPTABLE TILLAGE Clay minerals can take water and ions by absorption. See Tillage, Impacts on Soil and Environment ABSORPTIVITY ADHESION Absorbed part of incoming radiation/total incoming radiation. The attraction between different substances, acting at sur- faces of contact between the substances e.g., water and solid, water films and organo-mineral surfaces, soil and ACOUSTIC EMISSION the metal cutting surface. The phenomenon of transient elastic-wave generation due to a rapid release of strain energy caused by a structural ADSORPTION alteration in a solid material. Also known as stress-wave emission. A phenomenon occurring at the boundary between phases, where cohesive and adhesive forces cause the con- Bibliography centration or density of a substance to be greater or smaller McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, than in the interior of the separate phases. Copyright © 2003 by The McGraw-Hill Companies, Inc. Bibliography Introduction to Environmental Soil Physics (First Edition). 2003. ACOUSTIC TOMOGRAPHY Elsevier Inc. Daniel Hillel (ed.) http://www.sciencedirect.com/ science/book/9780123486554 A form of tomography in which information is collected from beams of acoustic radiation that have passed through Cross-references an object (e.g., soil). One can speak of thermo-acoustic Adsorption Energy and Surface Heterogeneity in Soils tomography when the heating is realized by means of Adsorption Energy of Water on Biological Materials microwaves, and of photo-acoustic tomography when Solute Transport in Soils optical heating is used. Surface Properties and Related Phenomena in Soils and Plants Jan Gliński, Józef Horabik & Jerzy Lipiec (eds.), Encyclopedia of Agrophysics, DOI 10.1007/978-90-481-3585-1, # Springer Science+Business Media B.V. 2011 2 ADSORPTION COMPLEX Energetically heterogeneous surfaces can be next clas- ADSORPTION COMPLEX sified into several groups, among which we can distin- guish patchwise and random surfaces. In the case of Collection of organic and inorganic substances in soil that random surfaces e ðx; yÞ varies quite randomly with are capable of adsorbing (absorbing) ions or molecules. ad x; y; for patchwise surfaces eadðx; yÞ¼constant for x; y within consecutive regions Di. Both random and Cross-references patchwise surfaces are two limiting cases of surface topog- Adsorption Energy and Surface Heterogeneity in Soils raphy that is defined by spatial correlations between the Surface Properties and Related Phenomena in Soils and Plants points xi; yi with given values of the energy ead;i. We can distinguish correlations between pairs of sites, triples of sites, and so on (Bulnes et al., 2001). The variation of the energy of adsorption results from ADSORPTION ENERGY AND SURFACE several factors: the presence of different atoms or groups HETEROGENEITY IN SOILS of atoms on the surface; geometrical irregularities includ- ing the presence of pores of different shape and dimen- Zofia Sokołowska1, Stefan Sokołowski2 sions, and so on. Of course, geometrical and energetic 1Institute of Agrophysics, Polish Academy of Sciences, nonuniformities are correlated and the former is one of Lublin, Poland principal sources of energetic heterogeneity. Moreover, 2Department for the Modeling of Physico-Chemical a given adsorbent may be a quite complex mixture of sev- Processes, MCS University, Lublin, Poland eral interacting chemical species. Both energetic and geo- metric heterogeneities have a great impact on the Generalities adsorption process. The potential energy of interaction of a single adsorbate molecule with a solid adsorbent can be described by the Description of adsorption on energetically function UðRÞ, where fRg is a set of coordinates neces- heterogeneous surfaces sary to define the position of the adsorbate molecule. Accurate modeling adsorption on geometrically Assuming that the adsorbate molecule is a sphere of diam- nonuniform surfaces is difficult and only in some cases it eter s, its position is given by the Cartesian coordinates of ; ; is possible to construct an adequate model for a solid. its center, R ¼ r ¼ðx y zÞ. For molecules composed of When it is possible, then computer simulations can be several atoms, one needs to specify a multidimensional employed. However, the structure of great majority of vector fRg that determines the coordinates of all the atoms environmental adsorbents, and soils in particular (see Clay (or groups of atoms) building a given molecule. Formally, Minerals and Organo-Mineral Associates; Organic according to the classical statistical thermodynamics Matter, Effects on Soil Physical Properties and Processes; UðRÞ is the sum of the interactions of Na interaction cen- Parent Material and Soil Physical Properties; Soil ters located within a given adsorbate molecule, with Ns Phases) is extremely complex due to diversified mineral, interaction centers located within a solid, X X organic, and ionic composition. Therefore, the application of approximate approaches is necessary. The most widely UðRÞ¼ uðr Þ; (1) ij used methods are based on the so-called integral adsorp- i2Ns j2Na tion isotherm equation. ; where rij is the distance between the interacting centers. Of Suppose we know the function ylð p eÞ that describes course, when quantum-mechanical treatment is employed, the isotherm (surface coverage) on a uniform surface with UðRÞ is the difference of ground state energies between the adsorption energy e. Then, the isotherm on the molecule at the position fRg and the ground state of a heterogeneous surface can be approximated as a separated molecule. Z emax For a selected adsorbate molecule, say a spherical mol- yð pÞ¼Nm ylð p; eÞwðeÞde; (2) ecule, the potential UðrÞ can be used to characterize the emin surface. For a given set of coordinates x; y in the plane par- allel (or tangential) to the solid the minimum of the func- where p is the pressure, yðp; eÞ is the global (measured) tion UðrÞ with respect to the third coordinate, z, is often adsorption isotherm, N is the monolayer capacity, and called “the adsorption energy,” e .Ife is independent m ad ad w e is the energy distribution function that yields of x; y, the corresponding surface is energetically uniform ð Þ a fraction of the surface characterized by the adsorption (or homogeneous). For crystalline surfaces e (and, of ad energy e. The latter function satisfies the normalization course, UðrÞ) is a periodic function of x; y. However, there condition exists a variety of surfaces that are neither uniform nor ; Z crystalline. In those cases, eadðx yÞ may vary in a quite emax complicated manner with x; y and we call such surfaces de ¼ 1; (3) energetically heterogeneous. emin ADSORPTION ENERGY AND SURFACE HETEROGENEITY IN SOILS 3 where ½emin; emax are the lower and upper integration meaningful results are to be obtained, special care and limits. In many cases, these limits are assumed to be the quality of experimental data are required (Jaroniec ½e0; ?Þ, where e0 is the liquefaction energy of the adsor- and Bräuer, 1986) The easiest way to obtain an approxi- bate. Equation 2 states that the total adsorption is just mate solution of Equation 2 goes through the so-called a weighted average of the isotherms on model, homoge- condensation approximation, according to which neous surfaces, characterized by different values of e. (Rudziński and Everett, 1992) However, it means that the adsorption on each homoge- wðeÞ¼À@y½ pðeÞ=@e: (5) neous surface occurs independently of the adsorption on other surfaces. The last assumption is satisfied only for The condensation approximation replaces the local a patchwise topography, or when the interactions between adsorption isotherm by a step function, i.e., every pressure adsorbed particles are negligibly small. Despite of the is associated with the value of the adsorption energy, above quoted limitations, Equation 2 has been widely p=p0 ¼ expðe=kTÞ, that corresponds to one half of the used to describe adsorption on heterogeneous surfaces. coverage of a given homotattic patch. The basic difficulty Note that a quite similar approach is usually used to in this method is associated with an appropriate numerical describe adsorption by porous solids. In the latter case, differentiation of the total adsorption isotherm, y½pðeÞ. the weight function is just the pore size distribution One of the methods that has been widely used for that pur- function. pose relies on the approximation of the experimental data If the local adsorption isotherm and the energy distribu- by the so-called exponential adsorption isotherm (Jaroniec tion function are given by analytical expressions, Equation 2 and Bräuer, 1986) can be integrated to yield an equation for the total adsorption "# isotherm. For example, if the local isotherm is just given by XN = n ; the Langmuir equation, ylðp; eÞ¼pKðeÞ=½1 þ pKðeÞ, yð pÞ¼exp Bn ðÞkTlnðp pmÞ (6) n 1 where KðeÞ¼K0 exp½e=kT, k is the Boltzmann constant, ¼ T is the temperature, and K0 is a constant, then one can g show that the Temkin isotherm, yðpÞ¼lnð1 þ KpÞ , corre- where fBng are the coefficients and the pressure pm sponds to a constant energy distribution function; the is associated with the minimum adsorption energy via Freundlich isotherm is associated with an exponential emin ¼ kTlnðpmÞ. The distribution function resulting from distribution and the Langmuir–Freundlich isotherm, Equations 5 and 6 is yð pÞ¼Cpg=½1 þ Cpg – with a quasi-Gaussian distribu- "#"# tion (Xia et al., 2006). In the above C; K and g are constants. XN XN nÀ1 n : Numerous analytical expressions for the total adsorption wðeÞ¼ nBnðe À emÞ exp Bnðe À emÞ isotherms obtained from Equation 2 can be found in the n¼1 n¼1 monographs of Rudziński and Everett (1992)andJaroniec (7) and Madey (1988). The above method of derivation of isotherm equations Approximation of the experimental data using Equa- can be also extended to the case of a multilayer adsorption.
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