Competitive Adsorption as a Physicochemical Ground for Self-Sufficient Decontamination Areas from Radioactive Pollutants

Abstract

A theory of competitive sorption as an instrument for predicting the conditions for desorption of radionuclides, Sr(II) in particular, from “contaminated solid–water” systems is formulated in this chapter. Typical isotherms of competitive sorption are presented. Based on the sorption isotherm we analyze the possibility of desorption of traces of Sr(II) and Sr-90 from ion-exchange materials. The role of humic acid (HA) in Sr(II) mass transfer in river water and the possibilities of strontium ion desorption from solids with the help of HA solutions are discussed in detail. We describe finally new competitive sorption techniques based on concurrent sorption of the aimed microelement from the contaminated material to the sorbent placed into a specially made pocketed membrane mini-reactor.

1 Introduction

The contamination of natural objects, soil and surface water with technogenic radionuclides is a result of global fallout induced by nuclear tests and the use of nuclear weapons in the twentieth century (González 1998), as well as by imperfect and becoming ever more sophisticated atomic power engineering (Gonzalez 1996; Yadigaroglu 2012). In response to the threat of worldwide radioactive contamination, there appeared approaches to the decontamination of natural objects, first of all, fresh water and soil. By now, vast experience in removal of radionuclides from aqueous media has been gained. However, the decontamination of solid materials is still a rather difficult economic and technological problem (Warner and Нarrison 1993; Ding et al. 2016). A number of methods for the removal of radionuclides and heavy metals from soil have been proposed: reagent less (Nikulina 2016), chemical reagent treating methods (Hamby 1996; Streletskaya 2003) and their combination (Valcke et al. 1997; Maslova et al. 2013). However, no efficient and relatively cheap green chemistry friendly decontamination technology has been created hitherto (Ding et al. 2016). The most promising in this respect techniques are the reagent less methods, by using which it is possible to purify clayey soils with a decontamination index of ~10 by concentrating the most sorption-active clay fraction (its content is up to 15% of the total mass of soil) (Nikulina 2016). At a low level of radiation pollution, ploughing and digging-in of topsoil are used. In order to reduce the transfer of long-lived radionuclides into plants, soil is limed (fixation of Sr-90), and enhanced quantities of potassium fertilizers are introduced (suppression of ion-exchange sorption of Cs-137) (Guillen et al. 2008). The chemical reagent treating methods include high-pressure water handling of soil (Kato 2015); flotation treatment of soils with surface-active substances and electro migration separation of radionuclides from soils (Veshev et al. 1996; Chirkst et al. 2001; Sanzharova et al. 2005). Since ⁹⁰Sr and ¹³⁷Cs radionuclides are fixed mainly by clay minerals, of interest is the deactivation technique based on ion-exchange desorption of these radionuclides with salt solutions containing cations with a high exchange capability (for example, Fe(III)) (Chirkst et al. 2001; Streletskaya 2003). There are examples of using microbe strains and phyto-sorbents in the processes of bioaccumulation of radionuclides in soils (Vandana et al. 2000; Sasaki and Takeno 2014). Because of the large scale of soil deactivation technologies, of increasingly greater importance for radionuclide behavior control in soils is the method of sorption fixation of radionuclides by introduction of an additional sorbent into soil (Wauters et al. 1996a, b; Valcke et al. 1997).

The role of sorbent here is to provide a sorption competition with plants for the absorption of radionuclides in the system “soil material – soil solution – sorbent – plant root age”. To understand the quantitative processes in such multiphase and multicomponent system, physicochemical modeling of equilibrium (stationary) and dynamic interactions is used. The modeling is based on the application of heterogeneous ion exchange laws, selectivity constants, as well as the notions about sorption inhomogeneity of minerals – sorbents in the framework of the Langmuir theory (Langmuir 1916; Brunauer et al. 1938; Sips 1948; Elovich and Larionov 1962).

The development of countermeasures against radioactive contamination is based on the understanding of sorption phenomena with participation of soil components. The works (Cremers et al. 1988; Wauters et al. 1996a, b) gave an important insight into the sorption regularities in the distribution of radioactive pollutants in the natural environment. They are based on the generalization of sorption properties of different types of soils, which allowed an a priori estimation of the cesium distribution coefficient value in soils (Cremers et al. 1988). The selectivity discreteness of sorption centers of soils and the existence of highly selective sorption centers toward cesium ions in illite let them introduce the notion of ¹³⁷Cs radiocesium interception potential – RIP (Cremers et al. 1988). RIP is a product of the capacity of silicates relative to the high selectivity centers and the selectivity coefficient of Cs(I) with respect to K(I) during the exchange on common and high selectivity centers (Cremers et al. 1988; Wauters et al. 1996a; Sanzharova et al. 2005). Using RIP it is possible to estimate the distribution coefficient (Kd) of cesium ions between the soil solution and soil on the basis of their chemical composition. RIP characterizes the competition of cations (Cs⁺-K⁺, Cs⁺-NH₄⁺) for the sorption centers, generally highly selective centers (Wauters et al. 1996b). This allows one to consider the decontamination processes in terms of competitive sorption of microelement in a sorption system containing several competitive sorbents: soil (sorbent 1) – bentonite (sorbent 2) – soil solution of cesium radionuclides – plant (Vandenhove et al. 2005). In order to avoid the transfer of radionuclides from soil to plants, a competitive sorbent (bentonite) is introduced into contaminated soil, which is superior to the competitive sorbents (soil and plants) in the RIP value of (Cs/K) pair. The competitive sorbent suppresses the transfer of radionuclides (“intercepts” it) in the chain “soil – solution – plant”.

The “price” for the positive effect of sorption suppression by plants is deeper radioactive contamination of soil. After such decontamination, for the removal of radionuclide from soil it is necessary to separate bentonite particles with adsorbed radionuclide from soil. Inevitable degradation of sorbent particles in soil (dispersion, variation in the phase and chemical composition under the action of humic and microbial species of soil, atmospheric moisture and fertilizers) can lead to secondary contamination of the soil. The separation of radionuclide from sorbent with a high sorption affinity is a more complicated sorption problem than decontamination at the initial stage of this scheme (Vandenhove et al. 2005).

In order to make a general idea of the potential of the competitive sorption method as an instrument of decontamination of materials, natural soils or artificial materials, it is expedient to consider the decontamination of solid in terms of heterogeneous equilibria and kinetics of microelement transfer in the simplest model of competitive system. The model includes material with sorbed microelement, aqueous solution of electrolyte providing the transport of microelement from the material to ambient environment, artificial sorbent capable of competing with contaminated material for the microelement. The use of the decontamination factor as a dependent variable will allow simulating competitive processes in this and more complicated systems and will provide a more comprehensive insight into the organization of natural and synthetic ion-exchange material decontamination technologies on self-sustained competitive sorption and green-chemistry principles (Polyakov 2012; Polyakov et al. 2015a).

2 Competitive Sorption: Statics

Consider as a model the statics and kinetics of competitive sorption in a system, for which the interphase distribution of microelement obeys the Henry’s distribution law, and follows the Langmuir equation for medium and high sorbate concentration, Fig. 1 (Langmuir 1916; Egorov 1975; Benes and Majer 1980; Polyakov 2003). The contamination of a material with microelement ions we will consider as a reversible sorption process that can be arbitrarily close to thermodynamic equilibrium. According to the mass action law, the condition for effective desorption of microelement ions from contaminated material by an arbitrary competitive sorbent is a higher value of the distribution coefficient, Kd*, of the sorbent in comparison with the material, Kd^m. We consider a competitive sorption in the system: “material (for example, illite) with sorbed ions – sorbate (desorbing solution containing electrolyte, simple and complex ions, true, and/or adsorption colloids of this microelement) – sorbent (for example, bentonite, Prussian blue, KU2 (Dowex-50)”. The desorbing solution in the considered scheme acts as both complex solution and transport medium. It provides the interphase transfer of sorbate ions between the material and the sorbents. The introduction of a complexing agent (for example, humic acid, НА) or a competitive ion (for example, K(I) ions) into this solution displaces the equilibrium in the sorption system. This provides deeper desorption of both this microelement and other microelements sorbed by contaminated material owing to their transfer onto sorbate (Valcke and Cremers 1994; Polyakov et al. 2015b).

Fig. 1

The scheme of equilibrium competitive sorption of arbitrary microelement in the system “material – sorbate – sorbent”: (a) the initial state, contaminated material; (b) the final state, the contaminated material is brought into contact with the sorbent. Designations: long yellow arrow –a particle of the material; short blue arrow –a particle of the sorbent; double-headed yellow arrow –microelement М. Combination of arrows, respectively: the state of contaminated material with sorbed microelement (green–yellow) and the state of microelement absorbed by the sorbent (blue–yellow); background–electrolyte solution. (Adopted from Polyakov et al. 2015b)

Represent an elementary model of desorption of a microelement from material onto foreign sorbent as an equilibrium competitive system “material – sorbate – sorbent” (1) (Polyakov et al. 2015b).

$$ A\overset{K^m}{\rightleftarrows }B\overset{K^{\ast }}{\rightleftarrows }C. $$

(1)

Here, A is the state of adsorbed microelement М in material “А”; В is the state of microelement М in the sorbate, which is a solution of electrolyte “В” contacting with material “А” and artificially introduced sorbent “С”; and С is the state of adsorbed microelement M in the sorbent (Polyakov 2003). Let the coefficients K^m and K^∗ characterize the concentration constants of sorption equilibria of microelement М with participation of material (index m) and sorbent (index*), Fig. 1.

The driving force for the chemical distribution of desorbed microelement in (1) is the difference in its chemical potentials (constants K^m, K^∗, distribution coefficients Kd^m, Kd^∗) in each of the contacting equilibrium subsystems “material – sorbate”, “sorbent – sorbate”. The microelement distribution coefficient value can be additionally affected by introducing a competitive ion (Valcke and Cremers 1994), or a complexing agent like НА (Polyakov et al. 2015a; Volkov et al. 2013), into the suspension. The scheme in Fig. 1 differs from the schemes of desorption by a homogeneous solution of complexing agent in the fact that the result of competitive sorption here is the accumulation of microelement ions in the competitive sorbent phase, rather than in the solution phase. After completion of desorption, the sorbent can be left in the medium of the decontaminated material (Vandenhove et al. 2005) or can be removed from it and used as the final form for subsequent long-term storage (Polyakov et al. 2015a; Nikulina 2016). The latter possibility considerably improves the efficiency and ecological safety of the whole decontamination process. Soils, samples of building, roadway, fabric and other materials possessing surface ion-exchange groups can be considering as decontamination objects (Cremers et al. 1988; Sanzharova et al. 2005; Stepina et al. 2013). If a microelement in contaminated material is not in the ionic form but in the form of true or adsorption colloid, ultrafiltration and colloid-chemical extraction can be used for competitive sorption (Polyakov et al. 2000; Polyakov 2000).

From the methodological standpoint, there is a good reason to compare the results of thermodynamic estimation of the consequences of chemical desorption of microelement М from sorption-decontaminated material due to complexing and sorption of sorbent suspensions in the solution on the basis of the decontamination coefficient K _o (Maslova et al. 2013; Cremers et al. 1988; Stepina et al. 2013; Polyakov et al. 2015b). By definition, the decontamination coefficient K _o of a material is the ratio

$$ {K}_o=\frac{M^{in}}{M^m}\kern1em \mathrm{rel}.\mathrm{units}., $$

(2)

where Mⁱⁿ and M^m are the initial and equilibrium mass of a microelement in the material after desorption, mol. (Moskvin 2004).

Below we consider a heterogeneous equilibrium (1) for the case when sorption of a microelement by the material is accompanied by a complex formation in the solution. This is a known case of the sorption, which was first formulated in (Shubert 1948) and analyzed in detail in (Egorov 1975). In the framework of this approach, the evaluation of the decontamination efficiency of a material can be reduced to the description of competitive sorption of microelement M by this material in the presence of competitors for this microelement – monodentate complexing agent (HA) and monofunctional sorbent (index *) – in the Henry’s law region, Fig. 1. Write the independent conditions of microelement distribution between material, solution and sorbent as the sorption ratio (ε) for the whole system (1) and for its subsystems: “material – sorbate” (ε^m), “sorbent – sorbate” (ε^*):

$$ \varepsilon =\frac{M^m}{M+{M}^{\ast }}=\frac{\varepsilon^m}{1+{\varepsilon}^{\ast }},\kern1em {\varepsilon}^m=\frac{M^m}{M},\kern1em {\varepsilon}^{\ast }=\frac{M^{\ast }}{M},\kern1em {M}^{tot}=M+{M}^m+{M}^{\ast }, $$

(3)

$$ \varepsilon =\frac{Kd^m\left[{m}^m\right]}{1+{Kd}^{\ast}\left[{m}^{\ast}\right]}, $$

$$ \left[{m}^m\right]=\frac{m^m}{V},\left[{m}^{\ast}\right]=\frac{m^{\ast }}{V},\kern1em {Kd}^m=\frac{\left[{M}^m/{m}^m\right]}{\left[M/V\right]},\kern1em {Kd}^{\ast }=\frac{\left[{M}^{\ast }/{m}^{\ast}\right]}{\left[M/V\right]}. $$

Here, M is the equilibrium mass of microelement in solution of volume V, ml. M^m and M^∗are the equilibrium masses of microelement in material (index m) and sorbent (index *). M^tot is the total mass of microelement in system (1), mol; m and m^∗ are the masses of material and sorbent, respectively, g (a sorbate solution may contain both a microelement and a complexing agent HA); Kd^m, Kd^∗ are the microelement distribution coefficients between material and solution (index m) and between sorbent and solution (index*), ml g⁻¹. The square brackets are the symbol of microelement concentration in phases.

Isotherm (3) describes the simplest situation of competitive sorption of a microelement in a system with two competitive sorbents and allows one to estimate at what ratio of the sorption affinity of the material and the sorbent to adsorbed microelement (Kd^m, Kd^∗) the desired decontamination degree of this material should be achieved.

At the initial stage of analysis of competitive system (2, 3) it is interesting to evaluate the role of complexing agent НА as a desorbing agent in (1) in the absence of sorbent. Write the equation of the complexing reaction of microelement М with НА molecule as a homogeneous reaction

$$ M+ HA+ MHA,\operatorname{}\beta =\frac{\left[ MHA\right]}{\left[M\right]\left[ HA\right]}, $$

Assuming that the molecules of complexing agent НА and complex МНА are not adsorbed by the material, we write the microelement distribution coefficient dependence between the material and the solution (Kd^m) as a function of the equilibrium concentration of the complexing agent [НА]

$$ {Kd}^m=\frac{Kd_0^m}{\left(1+\beta \left[ HA\right]\right)},\kern1em {\varepsilon}^m={Kd}^m\left[m\right]. $$

(4)

Here, ${Kd}_0^m$ is the distribution coefficient for a material in the absence of a complexing agent. When desorption is due to chemical binding of the microelement by a complexing agent HA according to (2), the decontamination coefficient of the material is:

$$ {K}_o=\frac{M^{in}}{M^m}=\frac{M+{M}^m}{M^m}=\frac{1+{\varepsilon}^m}{\varepsilon^m},\kern1em {Kd}^{\ast }=0. $$

(5)

It is obvious that the decontamination coefficient will be greater than unity only if desorption leads to reduction of Kd^m as compared with ${Kd}_0^m$ when the complexing agent concentration grows according to (4). The expression for the decontamination coefficient during homogeneous sorption by a complexing agent solution (5) takes on the form:

$$ {K}_o=\frac{1+{\varepsilon}^m}{\varepsilon^m}=\frac{1+{Kd}^m\left[m\right]}{Kd^m\left[m\right]}. $$

(6)

Figure 2 displays the characteristic dependences of the decontamination coefficient according to (6) for three different values of the microelement distribution coefficient ${Kd}_0^m$ between a material and a sorbate solution. Desorption efficiency growth with increasing concentration of complexing agent in desorbing solution [HA]. This dependence characterizes the methods for chemical decontamination (Moskvin 2004).

Fig. 2

The dependence between the decontamination coefficient of a material (K _o , rel. units), complexing agent concentration ([HA], rel. units) and sorption properties of decontaminated material (${Kd}_0^m$, rel. units) according to Eqs. (2, 6, and 8). The values in the inset are used in the calculation of ${Kd}_0^m$ at β = 0.3

The application of complexing agent solutions in the practice of decontamination gives rise to secondary radioactive solutions having a high concentration of desorbed microelement in a chemically more stable state. This leads to incremental costs for hardening of desorbing solution and for its transformation into the form suitable for long-term storage of isolated microelement (radionuclide). The modern methods of surface decontamination by polymer coatings also have some restrictions as to the decontamination of powder materials (Hamby 1996).

In terms of technology, a more appropriate procedure is desorption, when a contaminated material is brought into contact with a competitive sorbent suspension in solution according to Scheme (1) (Valcke et al. 1997; Polyakov et al. 2015b). Due to a high difference in chemical potentials, the sorbent concentrates the microelement absorbed by the material. After the required decontamination coefficient has been attained, the sorbent is left together with the material (Valcke et al. 1997) or is removed from it by any convenient phase separation method (Chirkst et al. 2001; Streletskaya 2003; Ioshin et al. 2016; Nikulina 2016).

Consider the microelement sorption equilibrium according to Eq. (1). Expression (2) for the decontamination coefficient K _o in this case takes the form:

$$ {K}_o=\frac{M^{in}}{M^m}=\frac{M+{M}^m+{M}^{\ast }}{M^m}. $$

(7)

The difference between (5) and (7) is in the term M* which expresses mass balance after the contaminated material is brought to sorption equilibrium with the sorbent suspension. For convenience of analysis, we assume that there is no complexing agent HA in the solution and the distribution coefficient Kd^∗ is not already equal to zero. The expression for the decontamination coefficient (7) is written as

$$ {K}_o=\frac{1+{M}^m/M+{M}^{\ast }/M}{M^m/M}=\frac{1+{Kd}^m\left[m\right]+{Kd}^{\ast}\left[{m}^{\ast}\right]}{Kd^m\left[m\right]}. $$

(8)

$$ {K}_o=\frac{1}{Kd^m\left[m\right]}+1+\frac{Kd^{\ast}\left[{m}^{\ast}\right]}{Kd^m\left[m\right]}. $$

(9)

This relation is the desired form of the decontamination coefficient dependence on the sorption parameters of contaminated material, sorbent and solution. The first term in (9) determines the sorption contribution of the material to the expression for K _o . The higher is the distribution coefficient for a material, the smaller is its decontamination coefficient as a result of contacting of the material with a certain volume of desorbing solution. When the distribution coefficient and the mass of the material (Kd^m ⋅ [m]) increase, the first term of the decontamination coefficient asymptotically tends to zero. It is obvious that the effect of sorbent on sorption-contaminated material according to (9) is analogous to the action of complexing agent in model (4, 5 and 6). The decontamination coefficient increases with the concentration of complexing agent [HA] or the sorbent mass [m*], Fig. 3. However, in the context of technological consequences, the effect of a liquid desorbing substance and of sorbent in the form of an aqueous suspension is different. In the former case, desorption of a microelement from the material is due to the formation of a more stable ion-molecular complex with НА molecules in the solution and a transfer of the microelement from the material to the solute. This solution is left for storage or is decontaminated, with the desorbed microelement being transferred into solid state. In the latter case, the microelement transfers, with the participation of the solution, from the material to a more thermodynamically stable sorption form in the sorbent and then it can be stored as a solid product.

Fig. 3

The variation in the decontamination coefficient (K _o ) with the sorbent distribution coefficient (Kd*) growth in model (9) as a function of the sorbent mass per unit volume of solution [m*] (rel. u.). The results of simulation for Kd^m = 1, m = 1 and Kd^∗ = 10, 10³, 10⁵ in (9), respectively, are given

Isotherm (9) shows that the third term – the ration of microelement distribution coefficients between the material and the sorbent, Kd^∗[m^∗]/Kd^m[m] – plays the most important role in the considered decontamination model. It determines the technologically acceptable strategy of sorbent application as a decontaminating suspension, the attainment of a specified decontamination coefficient and the mass ratio of sorbent and decontaminated material at the same volume of desorbing solution. For example, according to (9), the decontamination coefficient 10² can be reached for a contaminated material with Kd^m = 10 rel. u. at the sorbent to material mass ratio 0.1 rel. u. if a sorbent with Kd^∗ = 10³ rel. u. is used (Fig. 3).

Soils are one of the most difficult objects in terms of technology for Cs(I) and Sr(II) radionuclide decontamination (Sanzharova et al. 2005). According to the modern concepts about the sorption character of contamination of soils with microelements, in particular ¹³⁷Cs radionuclides, soils as natural sorbents have three types of exchange centers , whose distribution coefficients with respect to cesium ions differ approximately by an order of magnitude (Cremers et al. 1988). Type (I) is represented by low-selectivity exchange centers constituting the greatest fraction in the total exchange capacity of soil, ~95–98%. They are characterized by Kd^m(I) ~ 10² ml g⁻¹. The centers of the second type (II) have intermediate selectivity with respect to cesium ions. Their fraction in the total capacity is ~2–5% and the distribution coefficient is Kd^m(II) ~ 10⁴ ml g⁻¹. Finally, there are super-selective centers (III), the fraction of which in the total capacity is about 0.02–0.06%, and Kd^m(III)~10⁵ ml g⁻¹. The presence of exchange centers with Kd^m(II) and Kd^m(III) in soils is attributed to the presence of illite mineral from hydromica subgroup and to a special crystal structure of “frayed-edge” sites of hydromica microcrystals (Cremers et al. 1988).

In the considered model, the ratio between the distribution coefficients of the soil (material) and competitive sorbent mass, Kd^∗[m^∗]/Kd^m[m], determines the decontamination coefficient value. Estimate the result of equilibrium sorption interaction in the competitive system “soil – Cs(I) – Prussian blue (PB)”. Let a sample with exchange centers of chosen types (Kd^m(I) ~ 10² ml g⁻¹, Kd^m(II) ~ 10⁴ ml g⁻¹ and Kd^m(III) ~ 10⁵ ml g⁻¹) and mass [m] is brought to equilibrium with the sorbent, for example, PB powder, having a distribution coefficient of Kd* = 6.3^.10⁶ ml g⁻¹ and sorbent mass [m^∗] (Polyakov et al. 2015b). The process of sorption with participation of soil, PB and soil solution includes competitive sorption equilibria of Cs(I) and ion analogues, in particular, K(I), NH₄⁺, Mg(II), Ca(II) and their HA-complexes (Valcke and Cremers 1994; Vandenhove et al. 2005; Polyakov et al. 2015a). Further, for the sake of simplicity, we assume that the electrolyte composition remains constant, the sorbent capacity changes insignificantly as a result of sorption (Henry’s region) and the ratio of the concentrations of Cs(I) and competitive cations in the solution and in the sorbents is considered in the Kd^∗, Kd^m distribution coefficient values. From the soil decontamination coefficient (for example, K ₀  = 3 or 50) it is possible, using (9), to estimate the fraction of soil decontaminated by the sorbent to a preset decontamination degree in equilibrium conditions.

According to the estimated results, if soil is characterized only by nonselective centers of the type (I), the unit mass of the sorbent can provide the specified decontamination degree for 100 (K _o  = 50) and 2600 (K _o  = 3) mass units of soil, respectively (Polyakov et al. 2015b). The introduction of competitive cations, for example potassium or ammonium ions , into the decontaminated solution makes it possible to additionally decrease the cesium distribution coefficient by soil, thereby increasing the decontaminated mass (Sanzharova et al. 2005; Stepina et al. 2013). Considering that the estimation of Kd^* of ¹³⁷Cs for construction materials, such as concrete, granite, limestone, brick, asphalt, keeps within 10³ ml g⁻¹ (Stepina et al. 2013), the decontamination effectiveness of these materials will be similar to our estimates obtained for soil with nonselective exchange centers of type (I). So, the cesium ion decontamination coefficient K _o  = 3, according to (9), for soil with nonselective exchange centers, Kd^m(I), leads to the decontaminated soil to sorbent mass ratio of ~2^.10³ kg kg⁻¹ if a sorbent with Kd* = 6.3^.10⁶ ml g⁻¹ (PB) is used. Assuming the mass of a 10 cm layer of soil with an area of 1 m² and a volume density of ~1.1 g cm⁻³ (Yu et al. 2000) to be ~110 kg, we find that almost 20 m² soil can be decontaminated with the use of one kg of the chosen sorbent. Accordingly, the decontamination of 1 ha of soil at a depth of 10 cm requires ~ 500 kg of sorbent.

Sr(II) ions are characterized by reversible sorption on low-specificity (RES) functional groups of clay particles (Cremers et al. 1988). The yield of ⁹⁰Sr(II) into soil solution and the ⁹⁰Sr(II)/Са(II) ratio in soil solutions varies from 0.49 to 0.78 of their ratio in soil and is due to more stable sorption of Sr(II) compared with Са(II). The cation (⁹⁰Sr/Ca) exchange selectivity coefficient for most soils changes in the range 1–2 (Wauters et al. 1996a; Sanzharova et al. 2005; Comans et al. 1997). The estimation of the possibility of sorption decontamination of soil from ⁹⁰Sr radionuclides with the use of a highly selective sorbent gives the result similar to that for the system “soil – Cs(I) – PB”. We can use Kd^m (~20 ml g⁻¹) for the system “illite – ⁸⁵Sr – 0.01M CaCl₂” at pH = 4–7 (Wissocqa et al. 2017) and Kd^* (~10⁶ ml g⁻¹) for the sorbent – polyantimonous acid Sb₂O₅∙nH₂O (PAA) (Belinskaya and Militsina 1980; Zhang et al. 2016). It can be shown, that for the decontamination of 1 ha of soil from ⁹⁰Sr with K _o  = 3 and K _o  = 50 at a depth of 10 cm one needs 43 and ~1100 kg of PAA respectively, Fig. 4.

Fig. 4

The mass ratio [m]/[m^∗] of decontaminated soil to a mass unit of sorbent as a function of the Kd^m of soil and of decontamination coefficient K _o according to Eq. (9). Figures above the bars denote a set of sorption centers of the soil toward the radionuclide: 1–3: soil –¹³⁷CsCl – PB, Kd* = 6.3*10⁶ ml g⁻¹; 4: – “illite –⁸⁵Sr – 0.01 M CaCl₂ Sb₂O₅nH₂O (PAA), pH = 4–7, Kd^* = 10⁶, ml g⁻¹. (Adopted from Belinskaya and Militsina 1980; Zhang et al. 2016)

From the foregoing it is seen that the desorption of Cs(I) and Sr(II) radionuclides by selective sorbents (for example, (Belinskaya and Militsina 1980; Zhang et al. 2016; Remez 1994) is a technologically feasible method for the remediation of areas with a high level of radionuclide contamination (50 Cu km⁻² and more (Kryshev et al. 2013). The high distribution coefficients are necessary, but not sufficient for radionuclide desorption. For successful application, the sorption technique shall have proper kinetics. It is necessary to have the information about the kinetic regularities of competitive sorption, as well as the time, during which the equilibrium decontamination coefficients are achieved in an elementary system (Eqs. 1, 7, and 9).

3 Competitive Sorption: Kinetics

In the previous section, we discussed the decontamination processes based on competitive sorption of radionuclides from contaminated material (material) on decontaminating sorbent (sorbent). The statics of desorption of a microelement from the adsorbed state in material is considered as a spontaneous process of competitive sorption in the system “material – aqueous solution – sorbent”. The thermodynamics of equilibria in this system is indicative of formal equivalence of the achieved decontamination coefficients of material during equilibrium desorption by a complexing agent solution and sorbent aqueous suspension. The potential of competitive sorption as a processing method for the decontamination of soils was shown on the example of cesium ion sorption by iron-potassium cyanoferrate (PB) (Polyakov et al. 2015a). As one of possible options for the realization of competitive sorption, we proposed to use a new method for the decontamination of solutions and solid materials, which consists in the application of hermetic pockets with a sorbent having semi-permeable track membrane walls. Such sorption “mini-reactors” allow combining the spontaneous decontamination of material on the principles of competitive sorption and the possibility of facile removal of mini-reactors with the sorbent from decontaminated material powder both in natural and men-made conditions (Ioshin et al. 2016).

The driving force of the interphase transfer of contaminant microelement ions from material (sorbent “А”, Fig. 1) via ionic state in aqueous solution “В” to the adsorbed state in sorbent (sorbent “С”) is the difference in the chemical potentials of the microelement in sorbents “А” and “С”. The time necessary for the achievement of equilibrium values of distribution coefficients of microelement “В” between “А” and “С” phases (relaxation time) should be technologically admissible for the decontamination in static or dynamic states in different-scale sorption systems.

To estimate the order of the relaxation time values of the reaction presented in Fig. 1, analyze the kinetic model of a competitive sorption system

$$ A\underset{b1}{\overset{k1}{\rightleftarrows }}B\underset{b2}{\overset{k2}{\rightleftarrows }}C, $$

(10)

which will be considered as first-order consecutive chemical reactions between the ions of microelement М in an ultra-diluted solution and the sorption positions in material and sorbent in the framework of the Henry’s law. When equilibrium in the reaction chain (10) is achieved, the system transfers to state (1) (Yablonskii et al. 1983; Polyakov and Betenekov 1988).

Kinetic model (10) is an elementary model (with the minimal number of components) of chemical kinetics of interphase transfer of microelement ions from material “А” via ionic state in aqueous solution “В” to the adsorbed state “С (Polyakov 2003). The chosen model has an advantage – it allows one to take into account the effect of the composition of solution “В” and the side-reactions of microelement complexing on the rate of elementary stages of competitive sorption. It can be used also for diffusion-controlled sorption in solution (Kokotov and Pasechnik 1970; Betenekov et al. 1999). As in previous section, we assume that the sorption behavior of system (1, 10) obeys the Henry’s law; i.e. the microelement forms an ideal diluted solution in all phases.

The coefficients k_1,2 and b_1,2 of linear adsorption mechanism (10) characterize the specific microelement transformation rates in direct (k_1,2) and inverse direction (b_1,2) in competitive sorption kinetics. Analytical solution of the system of equations characterizing the kinetic mechanism (10) is given for the initial conditions, when the microelement concentration in material “A” at t = 0 is equal to C₀, and in solution “В” and sorbent “С” it is equal to zero (Rodigin and Rodigina 1960). As with the equilibrium system (1), consider the dependence of the kinetic analogue of the decontamination coefficient K _o (t) on the independent sorption parameters of model (10): masses [m], [m*], coefficients of direct and inverse reaction rates. For this purpose, we turn from equilibrium sorption characteristics Kd^m, Kd^∗ to their non-equilibrium analogues depending on the phase contact time, Kd^m(t), Kd^∗(t). We use the known analytic solution of kinetics equations for mechanism (10) having a form of the time (t) dependence of the microelement concentration in “А, В, С” states (Rodigin and Rodigina 1960). Represent (9) in the form (11):

$$ {K}_o(t)=\frac{1}{Kd^m(t)\left[m\right]}+1+\frac{Kd^{\ast }(t)\left[{m}^{\ast}\right]}{Kd^m(t)\left[m\right]}. $$

(11)

In (11), K _o (t) is a non-equilibrium decontamination coefficient, whose dependence on the phase contact time (t) is determined by mechanism (10) and gives an equilibrium decontamination coefficient, K _o  = K _o (t → ∞). Equation (11) solution with the initial conditions A(t = 0) = A₀, B(t = 0) = C(t = 0) = 0 can be finding in the analytical form elsewhere (Rodigin and Rodigina 1960). We present the obtained results omitting the conclusion and analysis of sorption–desorption kinetics equations.

The dependences of the non-equilibrium decontamination coefficient K _o (t) and non-equilibrium microelement distribution coefficients in “material – sorbate” and “sorbent – sorbate” subsystems on variables [m], [m*], k _1,2 , b _1,2 have the form

$$ {Kd}^m(t)=\frac{A(t)}{B(t)},\kern1em {Kd}^m\left(t\to \infty \right)={Kd}^m,\kern1em {Kd}^{\ast }(t)=\frac{C(t)}{B(t)},\kern1em {Kd}^{\ast}\left(t\to \infty \right)={Kd}^{\ast }. $$

(12)

Their numerical analysis performed with the use of the Mathcad 14 program showed the following.

We consider a situation when a material is saturated with a microelement to the concentration A₀ (contamination stage) and then it is brought into contact with a suspension of sorbent “С” in solution “В”. The kinetic process of decontamination of the material takes place spontaneously due to competitive interaction of the sorbate with the sorbent and the material. Typical isotherms of microelement concentration variation in the material, solution and sorbent versus the contact time according to (10, 11, and 12) are shown in Fig. 5. The reduction in the М concentration in the material caused by competitive sorption on sorbent leads to the non-equilibrium concentration B(t) in the solution, which is sometimes much higher than the equilibrium one and passes through the maximum. The dependence of the non-equilibrium distribution coefficients on the contact time is generally monotonic reaching equilibrium Kd^m, Kd^∗ values in time ~10∙t∙k₁. The non-equilibrium decontamination coefficient increases with time also monotonically, Fig. 6.

Fig. 5

An example of the dependence between the concentration of microelement М in “А”, “В” and “С” states and the relative time of phase contact t/τ₁ = t ⋅ k₁ according to linear mechanism (10). In Eqs. (11 and 12), the initial microelement concentration in material, A _o  = 1, the rate coefficients (rel. u.): k ₁  = 0.2, k ₂  = 0.1, b ₁  = 0.001, b ₂  = 0.01, [m] = 1, [m*] = 0.1; equilibrium distribution coefficients (rel. u.) Kd^m = 5 ⋅ 10⁻⁴, Kd^∗ = 10

Fig. 6

An example of variation of the distribution coefficients and decontamination coefficients Kd^m(t), Kd^∗(t), K₀(t) with the relative phase contact time (t.k ₁ ) in model (11 and 12). The parameter values (rel. u.) are similar to those in Fig. 5, except [m] = 0.1 = [m*]

Equations (12) are complex functions of direct and inverse elementary reaction rate coefficients. The exponential factors in these equations contain two kinetic coefficients, −х_1,2, which can be determined from the experimental data on microelement sorption by the material and/or sorbent (Emanuel and Knorre 1984). The numerical analysis of the dependences of coefficients х_1,2 on the elementary stage rate constants k₁, k₂, b₁, b₂ according to (11 and 12) revealed that both the direct and inverse reaction constants affect х_1,2 if they differ in each elementary stage by more than one order of magnitude. The coefficients х_1,2 increase with the growth of the constants of any inverse reaction. If the direct reaction constants are larger than the inverse reaction constants, the coefficient х₁ no longer differs from k₁ and х₂ no longer depends on k₂.

The K _o (t)-t isotherms feature the possibility of appearance of an inflection point, when in time (3–5)∙t∙k₁ the non-equilibrium decontamination coefficient reaches the stationary value and further the equilibrium value, Fig. 7. The reasons are the intermediate stage “B” in mechanism (10), when microelement aqua-complexes are formed and accumulated in the solution, and the effect of reversibility of stages in kinetic mechanism (10). The degree of reversibility of elementary stages is an important factor of decontamination effectiveness in kinetic mode. It affects the decontamination coefficient value. When the mass of the material changes by one or two orders of magnitude with the sorbent mass, remaining constant, the kinetic isotherms retain their shape. The results of numerical analysis (10) reveal that increasing irreversibility leads to enhancement both of non-equilibrium and equilibrium decontamination coefficients.

Fig. 7

An example of the kinetics of variation of the non-equilibrium decontamination coefficient K₀(t, [m], [m^∗]) with time (t∙k ₂ ) calculated by Eqs. (11 and 12) for competitive system “material (SiO₂) – CsCl – sorbent (PB)”. The figures in brackets at K ₀ are the values of the “mass concentration” of material [m] and sorbent [m*], ml g⁻¹, in Eq. (12); Kd^m = 50 ml g⁻¹, Kd* = 1∙10⁵ ml g⁻¹; (t∙k ₂ ) is the relative phase contact time

To compare the model results with the behavior of a real sorption system, we used the data on the statics and kinetics of Cs(I) ion sorption on two sorption materials. First of them is silica SiO₂, 200–500 μm fraction (Silica Pearl) we considered as a model contaminated material. The second one is sorbent (PB, 40–80 μm fractions) (Polyakov et al. 2015a). A silica gel powder was preliminarily washed with distilled water and dried in air. High purity CsCl stock solution and 0.1 mmol l⁻¹ HCl solutions were used for the preparation of solutions. The sorption isotherms were obtained in polyethylene test tubes with a phase contact time of 24 h and stirring of the suspensions at 50 min⁻¹. The sorbent mass in each test tube and the solution volume corresponded to [m] = 20.0 g l⁻¹ (SiO₂) and [m*] = 4.0 g l⁻¹ (PB). Sorption and separation of the sorbent powder by filtration followed by solutions analysis by the ICP-MS method on an Elan 9000 (Perkin Elmer) device in quantitative mode to determine the cesium content. The sorption statics isotherms in the form of the logarithmic Langmuir equation were used to estimate K _d and the concentration region, in which the Henry’s law was fulfilled, Table 1 (Volkov et al. 2017). The sorption kinetics isotherms of cesium ions in SiO₂ and PB are well approximated by the first-order reversible reaction with respect to Cs(I) cations, which allowed us to determine the constants of these reactions for the material and sorbent, Table 1 and Fig. 7 displays the decontamination kinetics isotherms of material (silicon oxide) on sorbent – PB in a closed system described by Eqs. (10, 11, and 12) with sorption parameters taken from the Table 1 for individual subsystems. The non-equilibrium decontamination coefficient K _o (t) depends considerably on the material to sorbent mass ratio ([m*]/[m]) and the phases contact time. In the range [m*]/[m] = 20/0.2–20/40, K _o reaches 400–8000 in a time of ~10∙t∙k ₂ , i.e. in 3–5 h under laboratory conditions. This is close to the modeling results on real soils (Valcke and Cremers 1994; Johnson and Dortch 2014). Such are the preliminary estimates of the behavior of competitive system (10) containing silica gel, electrolyte and Prussian blue solutions in the conditions close to the chemical or mixed-diffusion sorption kinetics mode. In order to establish the real kinetic peculiarities of the competitive sorption mechanism in static and dynamic systems, further studies are required.

Table 1 Initial data for modeling of competitive sorption kinetics in the system SiO₂-CsCl-PB in the region of Henry’s law; rel. error < 0.4

4 Strontium (II) Mass Transfer in the System “HA-Water”

Humic acids (HA) play an important role in the mass transfer of microelements and radionuclides in the environment. They largely determine the mobility of radionuclides in geochemical systems, the ability to bind metal ions and to assimilate them by plants (Twardowska and Kyziol 2003). This provides the biological protective action of HA, reduces the toxicity of elements (Hg, Cd, Pb, As) due to complexing (Varshal and Buachidze 1983; Varshal et al. 1993) and promotes the transfer and fixation of ions of contaminated aqueous media by soils (Orlov 1990).

The adsorption regularities in the chemistry of humate complexes of metal ions have not been exhaustively examined because of objective complexity and dual nature of НА and their salts. Depending on the рН, ionic composition of chemical components of solution and the concentration of HA, they can transfer from mainly anionic state into colloidal state due to protonation, dimerization (Bergelin 2001) and interaction with cations (Davis et al. 2002). НА are able to coexist in the natural рН range in both molecular-ionic and colloidal states. The transfer from the molecular state of НА into the colloidal state begins, depending on the total concentration, at рН 3–4, when the anion protonation degree approaches 0.5 mol mol⁻¹ (Fukushima et al. 1996).

The acid-base properties of НА play a major role in binding technogenic radionuclides, first of all Sr(II) ions, in natural aqueous solutions (Nash et al. 1981; Paulenova et al. 2000; Ozaki et al. 2003; Qiu et al. 2013). Strontium ions form stable complexes with НА in neutral and alkaline media. Their durability lowers with the growth of acidity (Paulenova et al. 2000). Complexing with natural organic ligands suppresses strontium sorption on minerals in neutral and alkaline media, but intensifies strontium transfer into solid phase together with solid НА (Paulenova et al. 2000; Qiu et al. 2013; Yu et al. 2015). The sorption isotherm of cesium (Cs-137) and strontium (Sr-85) ions on K and Ca forms of montmorillonite in humate solutions is a combination of Langmuir and Freundlich equations (Shaban and Macasek 1988; Sips 1948, 1950). Here, the stability constant of ⁸⁵Sr(II) – HA complex according to (Shaban and Macasek 1988) differs considerably (by three orders of magnitude) from the stability constants of humate complexes of other alkaline-earth element ions (Paulenova et al. 2000).

The information about the sorption behavior of humate complexes concerns mainly mineral or synthetic types of НА (Choppin 1999) produced by thermal or chemical treatment of НА (Kemdorff and Schnitzer 1980; Čežíková et al. 2001; Celebi et al. 2009). Although the processes of coprecipitation of Sr(II) with НА determine strontium transfer into bottom sediment, they are less well understood (Volkov et al. 2017).

The experimental data characterizing the sorption equilibria “⁹⁰Sr – НА” at variable sorbent (НА) and sorbate (Sr(II) + ⁹⁰Sr) concentrations showed that the sorption capacity (E, mg Sr g⁻¹) and the distribution coefficient (Kd, ml g⁻¹) during coprecipitation of humate complexes of Sr(II) with НА at рН = 2 depend on the concentration of НА, but do not depend on the initial рН of the sorbate. Strontium ion sorption during coprecipitation with НА (Fig. 8) obeys the behavior of the sorbent with two energetically non-equivalent sorption centers according to Langmuir isotherm (Kassandrova and Lebedev 1970; Adamson 1979; Čežíková et al. 2001; Volkov et al. 2017). This is confirmed by the data of IR and NMR spectroscopy of НА precipitates and by the acid-base properties of НА (Polyakov et al. 2015a). The “two-position” Langmuir isotherm determines the overall concentration of Sr(II) in the sorbent phase С(s) as a sum of element concentrations in each of the two i-th energetically and sorption non-equivalent and chemically unbound to each other positions С(s) _i , mg g⁻¹, in the form of (13) (Volkov et al. 2017):

$$ {\displaystyle \begin{array}{l}C(s)=\sum \limits_iC{(s)}_i,\kern0.5em C{(s)}_i={a}_i/{\left(1+{b}_i\mathrm{C}\left({Sr}_{aq}\right)\right)}_i,i=1,2.\\ {}Y=X-\log \left(a1/\left(1+b1\cdot {10}^X\right)+a2/\left(1+b2\cdot {10}^X\right)\right).\end{array}} $$

(13)

Fig. 8

The sorption isotherms of Sr(II) ions onto fresh HA precipitate (I) at рН = 2.0 ± 0.3, 22 C. Y = log(C(Sr, HA)), X = log(C(Sr, aq.)). C(Sr, HA) is the strontium concentration in HA, mg g⁻¹. C(Sr, aq.) is the strontium concentration in solution over HA precipitate, mg l⁻¹. The regression line is the Langmuir sorption equation on energetically homogeneous centers of two types, Eq. (13)

In (13), the coefficients a_1,2 (ml g⁻¹) = Kd(1,2) are the distribution coefficients of the centers with indices “1” and “2”; the ratio of coefficients (a_1,2/b_1,2) = E(1,2) is the sorption capacity of centers “1” and “2”, mmol g⁻¹.

The validity of model (13) was proved by ANOVA techniques. The model parameters values calculated from the experimental data showed that at Sr(II) ion concentrations <0.1–1.0 mg l⁻¹ the sorption of complex Sr(HA) by solid НА is characterized by the distribution coefficient log(Kd(1), ml g⁻¹) = 3.3 ± 0.6, the fraction of total capacity of НА is less than 0.02 wt.%, (Fig. 9). Kd(1) The remaining part of the HA precipitate capacity is characterized by log(Kd(2), ml g⁻¹) = 2.8 ± 0.2 (Volkov et al. 2017).

Fig. 9

The sorption isotherm of Sr(II) onto as-precipitated HA versus its equilibrium concentration; pH = 6.7–8.9, the initial concentration of Sr(II) – 20.0 μg l⁻¹, 22 °С. (Adopted from Volkov et al. 2017)

Considering the energy inhomogeneity of solid НА during co-precipitation of Sr(II), the distribution coefficient dependence on the НА concentration was studied at two initial concentrations of Sr(II) in solution – 20.0 μg l⁻¹ and 1 mg l⁻¹. In the former concentration region, sorption is determined by “1” centers, while in the latter region – mainly by “2” centers, Fig. 9 (Volkov et al. 2017). The sorption interaction of strontium ions with НА during co-precipitation was simulated by the Shubert method considering that Kd(1) at low НА concentrations is determined by sorption of Sr(HA)_aq complex (Paulenova et al. 2000), while at high concentrations – by Sr(HA)_aq,2 complex (Paulenova et al. 2000; Kostić et al. 2013). The latter complex was treated as non-sorbable:

$$ Sr{(HA)}_{aq}=\overline{Sr(HA),}\kern2em K1=\left[\overline{Sr(HA)}\right]/\left[ Sr{(HA)}_{aq}\right], $$

(14)

$$ Sr{(HA)}_{aq}+ HA= Sr{(HA)}_{2, aq},\kern2em \beta =\left[ Sr{(HA)}_{2, aq}\right]/\left[ Sr(HA)\right]\cdot \left[ HA\right], $$

(15)

Here, K1 is the concentration constant of strontium ion sorption onto НА, and β is the concentration constant of formation of nonsorbable complex Sr(HA)_aq,2. The dependence of the overall distribution coefficient Kd of НА complexes Sr(HA)_aq and Sr(HA)_aq,2 between the solid phase of НА (symbols with vinculum) and the solution according to model (14, 15, 16 and 17) in the concentration approximation has the form:

$$ Kd=\left[\overline{Sr(HA)}\right]/\left(\left[ Sr{(HA)}_{aq}\right]+\left[ Sr{(HA)}_{2, aq}\right]\right)=K1/1\left(1+\beta \left[(HA)\right]\right). $$

(16)

In the logarithmical form Eq. (16) is written as

$$ {\displaystyle \begin{array}{c}\log (Kd)=\log (K1)-\log \left(1+\beta {\left[ HA\right]}^c\right)=a-\log \left(1+b{\left[ HA\right]}^c\right),\\ {}a=\log (K1),\kern2em b=\beta, \end{array}} $$

(17)

and the index с at the independent variable – the concentration of free humic acid [HA] – was used as an additional parameter (с = 1 according to (16–17)) to verify eqs. (14–17). The comparison of the model coefficients performed by the least square method for sorption isotherms at two different initial concentrations of Sr(II) is given in Fig. 10. It is seen that for the isotherm at different Sr(II) concentrations, only the coefficients а exhibit a statistically significant difference, in agreement with the results of modeling of Sr(II) sorption by (16–17). The average value of the coefficient b = (4.0 ± 3.5) and the average value of c = (1.8 ± 1.3), which is a nonsignificant difference from 1. The value of the stability constant b of the strontium complex Sr(HA)_aq,2 determined by (17) is three orders of magnitude smaller than the formation constants of the Sr(HA)_aq complex (Paulenova et al. 2000) suggesting a small stability of the Sr(HA)_aq,2 complex in concentrated НА solutions.

Fig. 10

The results of verification of Sr(II) sorption model onto humic acid in the co-precipitation mode in experiment with a variable concentration of HA, Eqs. (14 and 15). (HA) is the concentration of humic acid, g l⁻¹. The initial concentration of Sr(II) is 20.0 μg l⁻¹ (A) and 1.0 mg l⁻¹ (B). a = log(K1), b = β, c = c in (16). (Adopted from Volkov et al. 2017)

Thus, the sorption properties of freshly precipitated НА with respect to Sr(II) ions are affected by the strontium concentration in solution and the energy inhomogeneity of HA sorption centers. When strontium ions are co-precipitated onto НА, the distribution coefficient log(Kd(1), ml g⁻¹) = 3.3 ± 0.6 in ultradiluted solutions of Sr(II) and log(Kd(2), ml g⁻¹) = 2.8 ± 0.2 in solutions with a high ion content. In acid solutions, НА has a high affinity to the humate complex Sr(HA)_aq and forms an unsorbed complex of the composition Sr(HA)_aq,2. This shows that it is possible to desorb Sr(II) radionuclides from soil and subsequently to isolate strontium from humate solution onto solid HA by co-precipitation. Since solutions of natural НА are relatively cheap and available in comparison with other, more selective, but toxic sorbents (polyantimonic acid and its salts), the sorption properties of НА with respect to Sr(II) can be used to develop the countermeasures against contamination of soils with ⁹⁰Sr as a result of technogenic accidents in the future (Davis et al. 2002).

5 New Competitive Sorption Techniques

The ways to realize the sorption extraction of microelements and their radionuclides from solutions are diverse: sorption in a limited-volume reactor, a flow-type reactor or in a sorption column. Of much importance for the decontamination practice are the efforts in creating new methods for sorption concentration of microelements as applied to decontamination of soil and other natural objects? The use of competitive sorption for the decontamination of materials requires a technique for its implementation, which would allow one to enjoy the advantage of selective sorption providing facile separation of sorbent from material after the desired decontamination coefficient has been attained. For this purpose we have proposed a new method for the decontamination of aqueous solutions from heavy metals and radionuclides, in which the sorbent and the reactor enclosing it are united in one isolated pocket – a thin-walled airtight mini-reactor, whose walls are made of a membrane material (for example, Nuclear Track Membranes) (Ioshin et al. 2016), Fig. 11. A sorbent/extractant or their solution is placed inside the mini-reactor. To prepare a pocketed membrane reactor, a track membrane is used to form a pocket (Fig. 11, stage I), a sorbent/extractant is brought into the pocket creating a mini-reactor with semipermeable walls (stage II), then the mini-reactor is made airtight (stage III) and is used for the sorption from liquid phase/soil (stage IV). Figure 11, at the right, shows a pocketed mini-reactor with PB powder placed into the aqueous electrolyte solution. If there were no membrane walls, PB would form a stable colloidal solution in the whole volume. In the offered design, the sorbent/liquid extractant and membrane pocket are integrated since the sorbent is isolated from the outside by the membrane material. Sorption by means of a mini-reactor creates some advantages. Among them are the simplification of the sorption process and the possibility of sorption concentration in the diffusion-kinetic mode. The latter it is especially important for the decontamination of large volumes of soil, basin and river water under natural conditions, when time is not the decisive factor in comparison with the scale and degree of decontamination. There is no longer any need to use special chromatographic equipment, sorbate solution injection and ejection systems or sorbent loading/unloading procedures. In terms of technical results, of considerable importance are the performance characteristics of track membranes. The comparison of the sorption properties of mini-reactors filled with granular sorbents or extractants (silica gel, fraction 0.50–1.5 μm; KU2 cation exchanger, fraction 200–500 μm; Prussian blue (PB), fraction 0.2–0.9 μm, TBP, DEHPA, ТОА) with individual sorbents revealed a similarity of their decontamination, distribution and separation coefficients for the majority of microelement ions. Figure 11 shows as an example a variation in cesium ion sorption from electrolyte solution (S) on a mini-reactor filled with PB sorbent versus solution contact time. The diffusion mass transfer mode determines the time, in the course of which the equilibrium characteristics are established if the membrane mini-reactor in the sorbate solution is not stirred. We have shown that the mass transfer rate in the conditions of Fig. 12 depends on the pocketed reactor area, the pore size of membrane wall and the stirring rate of the solution with the reactor. The time, during which the equilibrium sorption characteristics are reached, is units of months. These sorption relaxation time values are relatively high, but quite admissible in taking countermeasures to remedy the effects of man-made accidents on large areas. The described functional properties of mini-reactors with semipermeable walls, in our opinion, can be used in the competitive sorption technology for the decontamination of soil and ground from toxic/radioactive microelements (Ioshin et al. 2016).

Fig. 11

A diagram of preparation (at the left); a view of a pocketed membrane mini-reactor with sorbent/extractant (at the center); a mini-reactor in a glass with a solution (at the right). Reactor walls – Nuclear Track Membranes with pore size 0.1 μm [Flerov Laboratory of Nuclear Reaction, Russian Federation (FLNR JINR, Dubna, RF)], sorbent – Prussian blue powder of mass 56.0 mg (PB) and size 0.2–0.9 μm

Fig. 12

The sorption kinetics of Cs((I) from tap water on a membrane mini-reactor filled with PB as a function of the ratio between the sorbent mass and the external solution volume [m] (shown in the inset, g ml⁻¹). The initial concentration Cs = 6.03 mg ml⁻¹. The sorption conditions are the same as in Fig. 8. Mixing was carried out by shaking up the vessel with the mini-reactor with a frequency of 0.1 min⁻¹. During the experiment, log(Kd, ml g⁻¹) = 5.0 ± 0.2 was reached, 22 °С

6 Conclusion

The discussed model of microelement desorption from adsorbed state in material shows that the use of a competitive sorbent having a high selectivity with respect to cesium and strontium radionuclides can, under equilibrium conditions, be just as effective as desorption by complexing agents solutions. The kinetic properties of an elementary competitive system “material – sorbate – sorbent” considered on the example of cesium ion sorption reveal that during convective mass transport the region of equilibrium can be reached in hours or days depending on the material to sorbent mass ratio. This is comparable with the cesium ion spontaneous mass transfer rate in soil in the diffusion mode. The application of НА as a complexing agent for radionuclides with their subsequent co-precipitation concentrating together with a selective material, such as PB, allows one to localize as much as possible the level of interference of the sorption process in the physicochemical state of sorbate and to organize the decontamination as a self-sustaining process. The use of sorbents as part of pocketed mini-reactors with semipermeable walls offers additional advantages promoting self-sustaining sorbate mass transfer, as well as material and sorbate phase separation, which can considerably facilitate sorption decontamination of large soil, ground and water areas.