Ind. Eng. Chem. Res. 1994,33,2789-2794
2789
Co-Ion Behavior at High Concentration Cationic Ion Exchange k FernAndez, M. Rendueles, k Rodrigues, and M. Diaz' Department of Chemical Engineering, University of Oviedo, 33071 Oviedo, Spain
The operation of ion exchange a t high ionic concentration has shown high uptake of the co-ion species in addition to the effect of accumulation in pores giving rise to the possibility of exploitation of a selective co-ion exchange for industrial applications. This phenomenon includes some kind of ion exchange which is the subject of this article; in particular, equilibrium and kinetics were studied in view of the application in fixed bed column operation. Anionic exchange (C1-/S0d2-) was noticed to take place during the recovery of potassium from a concentrated industrial wastewater using a cationic resin and a concentrated solution containing sodium ions for regeneration. The equilibrium of co-ions under the operating conditions was analyzed in terms of constant separation factor, and the kinetics by the pore diffusion model. Both models led to good fits for cation exchange. The co-ion retention in fixed bed could also be predicted from previous results using the axial dispersion model.
Introduction
Table 1. Conditions for Different Column Experiments
The application of ion exchange processes usually takes place in conditions of diluted solutions, where the Donnan principles are applicable. In those conditions, solutions with concentrations lower than 0.1 M are considered ideal, ions are solvated, and there is no interaction between cations and anions in solution (Whitney and Diamond, 1963). Hence, the selectivity of the resin can be viewed as a competition between the fixed groups within the resin and the ions in solution to solvate exchangeable ions (Marinsky, 1966; Meares, 1984). This approximation simplifies the chemical and mathematical treatments, since the activities in solution are assumed to be unity. When the solution concentration increases, some processes can take place such as ionic-pair formation, uncompleted solvated ions, and general selectivity of the resin changing as a function, for instance, of the co-ion present in solution (Mar et al., 1991; Kim and Lee, 1991). Therefore, the behavior of ion exchangers can become much more complex. With high solution concentrations, as are required in industrial processes, Donnan exclusion does not take place, and some accumulation of co-ions within the resin have been noticed (Barret et al., 1968; Kataoka et al., 1978; Nardin, 1971). This effect can be explained based on the considerations previously done of the solution behavior, which becomes more important in these conditions than the Donnan exclusion. The mechanism of co-ion introduction into the resin is not well-known, electrolyte sorption and exchange of complex ions being the most widely accepted theories to explain the process (Meares, 1984; Nardin, 1971). In this work, the exchange of anions that occurs within a cationic resin working at high concentrations was analyzed, and ion exchange models for equilibrium and kinetics were tested to fit the co-ion exchange. The adequacy of the fitting was good, and even enabled an accurate prediction of the co-ion exchange in a fxed bed column operation. The study of co-ions in ion exchange processes with high-concentration solutions can be of fundamental interest for application, in particular when some of the accompanyingco-ions are impurities for the final product, such as in some processes in the fertilizer industry.
* To whom correspondence should be addressed.
run
oper mode
1.a 1.b
batch batch
2
batch
init concn
US ratio ( m u g wet resin)
presatn state of resin
1,2,4,8 1,2,4,8
Nazi304 KCl
1,2,4,8
Na2S04
KCl = 1M NazSO4 = 1.6 M K+ = 0.9 M Na+ = 3.1 M C1- = 3.5 M s04'- = 0.25 M
run
oper mode
3
fxedbed
4
fxedbed
feed concn K+ = 0.7 M Na+=3.2M C1- = 3.0 M Sod2- = 0.45 M K+ = 0.8 M Na+=3.7M C1- = 3.7 M = 0.4 M
bed equilibrated withsoln
flow
(L%)
Na+ = 2.8 M 504'- = 1.4 M
9.7
Na+ = 3.4 M sod2-= 1.7 M
10.2
Experimental Method The system under study was a solution containing NazS04 or KC1 or a mixture of both, and the resin was a strong cationic sulfonic type gel, LEWATIT S-100 manufactured by Bayer. Concentrations are shown in Table 1. Previous batch studies to determine pore concentrations were carried out by contacting an amount of resin presaturated with Na+ (or K+), after washing, with a solution containing the same counterion (Na+ as Nazso4 and K+ as KC1) a t the mentioned concentrations, with the aim of measuring only pore filling but not ion exchange. After equilibrium, the resin was washed again and the counterion concentration measured in the wash solutions. In these experiments, both the counterions and the co-ions are measured. Batch experiments were carried out by contacting a volume of solution with different known mass of resin in order to study the equilibrium and the kinetics of the system. The evolution of concentrations with time until constant concentration was obtained by sampling and measuring the concentration of the solution, the counterions (Na+ and K+) by atomic absorption and the coions (C1-/S042-) by ion chromatography. Experiments in fixed bed column (4 = 10 cm, L = 100 cm) with solutions (Table 1)based on wastewater from
Q888-5885/94/2633-2789$04.50/0 0 1994 American Chemical Society
2790 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994
the fertilizer industry were carried out in order to show the possibility of applying this method to KCl recovery, thanks to the retention of the co-ion, C1-, together with the K+ from a solution also containing a high concentration of NaZS04. A high concentration of pure NaZS04 is currently used as eluent. In fixed bed runs, the load was carried out from the bottom to the top of the column, and elution was in the opposite direction. Runs 3 and 4 were carried out without intermediate washing, as is usual in practice.
Theoretical Considerations Ion Exchange. Several types of equilibrium isotherms have been proposed for ion exchange operation at both low and high concentrations. One of the most commonly used, is the constant separation factor isotherm, represented by eq 1.
Many models have been developed for ion exchange kinetics, some assuming only transport processes and others considering both mass transfer and chemical reaction. One of these models, which applied in this work considers mass transfer and instantaneous equilibrium, is the pore diffusion model, described by eqs 2-8. To apply the model, one must consider that the total concentration of an ion in a particle is calculated as (2) q r. = qer. + €r epi. =qei + q p i where qi is the total concentration in the resin of the ion i, qei is the concentration within the resin due to the true ion exchange, and qpi is the previously measured pore concentration. mass balance in particles.
average concentration in particle.
R:
JRo
R2qi(R,t)dR
initial and boundary conditions. boundary condition in the particle: R = 0 (symmetry condition)
boundary condition a t the interphase:
R =R,
where ai is the activity of species i, zi is the ion valence, II is the swelling pressure, and vi is the partial molar volume of species i (Helfferich, 19621, assumed to be constant. However, at high concentrations, Donnan exclusion does not take place, and the electrolyte can penetrate into the particles. In terms of Donnan theory, the resin capacity for a co-ion increases monotonically with external solution concentration. In general, the massaction product of solution-species activities must equal that of the corresponding pore resin species; thus, in a concentration range where activity coefficients are nearly constant, eq 10 can be assumed. Most authors have studied co-ion uptake as a process of electrolyte sorption and not as an exchange or retention. Studies of kinetics relating the effect of electrolyte penetration on the ion exchange rate have been carried out by Kataoka et al. (1978) using the Nernst-Planck equation; the resin being assumed homogeneous and the particle diameter, the diffusivity, and the activity coefficients taken as constants. Mar et al. (1991) have studied the influence of the co-ion valence on electrolyte sorption and showed that the higher the co-ion valence, the stronger the exclusion is in agreement with Donnan theory.
Results and Discussion
mass balance in solution,
4i(t)=
exchange process was found to be different depending on the ionic environment. At low concentrations, Donnan exclusion takes place, and the electrolyte cannot be sorbed. Therefore, there is no co-ion inside the particles and qi for co-ions must be 0. As a general rule, the exclusion increases as the solution concentration decreases. Thermodynamic formulation of Donnan potential can be obtained from
cpi(Ro,t) = c,(t)
(7)
initial conditions:
cpi(R,O)depends on washing
(8)
Ci(0)= CZT Co-ion Effect. The co-ion behavior during the ion
Previous Study. As previously indicated, at low concentrations, due to Donnan exclusion, qpl must be 0, for both counter and co-ions, of course, qeLmust be 0 for co-ions. However, at high concentrations, qprwill be generally greater than 0; initially qel, true ion exchange, is expected to be 0 for co-ions, while it is the ion exchange capacity for the counterions. In order t o establish the behavior of this system under industrial operating conditions, some previous measurements were carried out. Study of Pore Concentration (qpiMeasuremeill). As was previously indicated, the experimental measurement of qplvalues enables us to distinguish two different phenomena from eq 2: filling of the pores and the interactions with fixed groups. For this aim the resin presaturated with Na+ or K+ was contacted with a solution containing Na2S04 or KC1, respectively, at different liquid to solid (US)ratio. For IJS = 1, 100 g of wet resin were contacted with 100 mL of solution; for other US ratios the volume of solution was kept constant and the weight of resin used was changed. The resin was separated by filtration and washed. The electrolyte in the pores was eliminated by washing and then measured; washing was carried out in batch using a relation milliliters water/gram wet resin of 5 and repeated several times until the ion concentration in the solution was less than 50 mg/mL. Figure 1 shows the
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2791 0.6
0.5
c
0.4
+
m
I-
0.3
0
E
6 0.2 U
0.1 0
0
0
0.4
0.8 1.2 c molil
1.6
2
Figure 2. qezexperimental and predicted values versus czfor K+/ Na+ exchange (run 2: four species in solution).
"
Table 2. Pore and Exchange Concentration of Anions in Cationic Exchanger LEWATIT 5-100at Different Total Concentrations (M) 0.83 1.88
12.0 3.8
25.5 9.8
60
40
c ,gll
Figure 1. Pore concentration of KC1 and Na2S04 as a function of liquid-phase Concentration.
0.35
20
0.20
(M) 0.44 1.0
4.6 4.0
9.2 9.5
CCl-a
CSO~Z-~
~~
qpz(g/L wetresin) qez(g/L wetresin) a
55.4 40.0
15.7 35.0
Equilibrium solution concentration.
results in terms of pore concentration, qpi ( m o a wet resin) where wet resin means the resin with its own humidity (45% for LEWATIT S-loo), as a function of the liquid-phase concentration, ci. The ratio between qpi and ci is the resin porosity (see eq 2) that was estimated to be 0.34 k 0.02. This ratio is a little lower for Na2S04, in agreement with other authors who have found that the smaller the co-ion valence, the higher the electrolyte sorption (Helfferich, 1962; Mar et al., 1991). Ion and Co-Ion Exchange ( q e i Measurement). Total retention (ai) of counterions and co-ions was measured under the previous experimental conditions, contacting different liquid to solid (US) ratios and analyzing ion concentration in the solution after 2 h, i.e., time t o reach equilibrium. For counterions, it was found that qei obtained from eq 2 is larger than the total ion exchange capacity of the resin obtained by titration a t low ionic solution concentration, possibly due to high concentration working solutions. For co-ions (or no exchangeable ions) the obtained qei value was higher than 0, calculated as the difference between total (qj), obtained in the same way as counterions, and pore particle concentration (qpi), obtained from experiencies of electrolyte pore penetration (Figure 1)(Table 2). A conclusion from these results is that some kind of electrolyte retention must be taking place, the most probable way being via the exchange of some ionic association between cation and anion in solution, ion pair, or ionic complex. This assumption can justify both the high values ofqei for cations and different from 0 for anions, both higher than the theoretical at low concentrations. Cationic Exchange. The study of cationic ion exchange is of considerable interest in the analysis of the co-ion exchange, firstly to see if a relation exists between the type of models fitting both schemes, and secondly to evaluate the interactions between the adsorption of counterions and co-ions. Cationic exchange of Na+ and K+ has been treated in a previous
-
0 0
10
20
30
40
t , min
Figure 3. Experimental and theoretical evolution of dimensionless potassium concentration with time (run 1: two species in solution) a t different US ratios. Table 3. Values of Constant Separation Factors for Counterion and Co-ion Exchange under Different Operation Conditions separation factor for counterions (cations) Na+ K+ single solution complex solution
1.26 0.90
1.61 1.09
separation factor for co-ions (anions) c1sod20.60 0.45
0.45 0.30
paper (Fernlndez, 1994) for two different liquid phase compositions of KC1 and Na2S04. The equilibrium of K+/Na+ was represented by the constant separation factor isotherm, giving good fittings as shown in Figure 2 where the experimental and predicted values of qei are plotted as a function of the liquid-phase concentration. The kinetics of the ion exchange K+/Na+was studied in batch experiments, and the results were well fitted with the pore diffusion model, as shown in Figure 3. The values of the diffusivity ratio between potassium and sodium agree well with those obtained a t infinite cm2/s,D " N ~= 1.35 x dilution (D-K = 1.98 x cm2/s). The relation between effective pore diffusivity (D,) and infinite solution diffusivity (D") can be represented by D, = ~pD-/r;obtained effective diffusivities agreed well with a tortuosity value of 5.4. Table 3 summarizes the equilibrium and kinetic parameters obtained in cationic ion exchange analysis. Equilibrium of Co-Ion Exchange. As previously indicated, some kind of electrolyte retention takes place in these systems and experimental conditions, so we have tried to analyze these results in a way analogous to that of ionic (cationic) exchange. Experiments in batch were carried out in order to obtain equilibrium
2792 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 Table 4. Effective Diffusivities for Cations and Anions, Obtained by Fitting of the Experimental Kinetic Results to the Pore Diffusion Model single solution D, (m2/s)
Na+
K+
c1-
SOP
0.90 x 10-10 D-iiD-j = 1.47
1.28 x D p i l D= ~ 1.42
1.90 x 10-10 D-il0-j = 1.88
1.00 x 10-10 Dpi/DM = 1.90
3.00 x
4.50 x 10-lo
complex solution D, (m2/s)
1
0.61
0
0
40
80 c. gli
120
160
I # I
0
40
80
0
30
15 I , min
Figure 4. Experimental and predicted results for the C1-/S042ion exchange (run l(a and b): two species in solution).
8o
;SO
120
160
c, g/l Figure 5. Experimental and predicted results for the c1-/s0d2ion exchange (run 2: four species in solution).
data for different solutions and conditions. From qi results, and those obtained for the electrolyte sorption in pores (qpi), the qei values (eq 2) for anions were determined. If the system is considered as an anion (coion) exchange, an initial suggestion would be to use the same equilibrium analysis used for the cationic (counterion) exchange in the same experiments. This is the constant separation factor that has previously given good results. The first experiments were carried out with solutions containing only one electrolyte (KC1or NazSO4). Figure 4 shows experimental and predicted results of runs 1.a and 1.b (two species in solution). In this figure experimental points were obtained as the difference between qi obtained from eq 4 based on the measured equilibrium solution concentration, ci, and qpi = ~ p ~using i , eq 2; the predicted line was obtained by fitting experimental data with the separation factor isotherm (eq 1). As can be seen, this constant separation factor often used in ion-counter ion exchange can fit the results of co-ion exchange obtained in this 1:l salt exchange. Experiments with a more complex solution containing a mixture of both electrolytes were also studied to assure the applicability of the model. The constant separation model allows also a good simulation of these experimental results, as seen in Figure 5. In this figure, experimental and predicted curves were obtained in the same form as in Figure 4.
Figure 6. Experimental and predicted results of evolution of dimensionless C1- concentration versus time for Cl-/SO& exchange (run 1: two species in solution).
The Ki values are included in Table 3. Differences in the Ki values with single and complex solutions are due to the fact that the total concentration (ionic strength) is very different, and competition may exist between species. The equilibrium constant decreases as ionic strength increases, although the ratio between the two counterions or the two co-ions is quite constant. Kinetics of Co-IonExchange. The pore diffusion model (PDM) used above to model cationic exchange was also applied here in order t o treat experimental results of the exchange rate for co-ions (anions). The system of partial differential equations can be solved by numerical methods using the PDECOL package (Madsen and Sincovec, 1979). Effective diffusivities were obtained from the fitting of the experimental results of kinetic batch sorptions. Figure 6 shows experimental and predicted values of dimensionless decreasing solution concentration of C1- versus time for C1-/So42exchange under conditions of run 1.a (two species in solution), for different US ratios. The PDM model applied for cationic exchange has also given good fittings for the co-ion exchange. On the basis of the PDM model, if there is no other effect, the diffusivities obtained for ions diffusing onto the resin must have a constant ratio equal to the one obtained from the diffusion of the same species in solution at infinite dilution (D-A ) calculated from the ionic mobilities (D"cl= 2.03 x cmz/s,DWso4= 1.08 x cm2/s ) . This ratio is a constant of the resin, a function of the resin porosity, ~ i ,and resin tortuosity, t. Table 4 shows all effective diffisivity values, and the ratio between the infinite dilution diffusivities for all ions and the ratio for the effective ones in single (two species) solution. It can be noticed that the values agree well, showing the validity of the model both for cations and anions. It is interesting to analyze the exchange rate of counterions and co-ions in the resin. The ratios between both diffusivities for co-ion and counterion are shown in Table 5. This ratio is higher for the effective diffisivity than for the infinite dilution diffusivity both for the C1- and S 0 2 - co-ions. This result can be explained in terms of some interaction that must take
Ind. Eng. Chem. Res., Vol. 33,No. 11,1994 2793 Table 5. Diffusivity Ratios between Counterion and Co-ion Diffusivities inside the Resin and at Infinite Dilution
Na+
Kf
1
sop
c1DpCllDpi
,
150
D”Cl1D-i
2.10 1.48
1.50 1.03
Dpso41-fDpi
1.10 0.78
D-SO~~~D-~ 0.80 0.55
place between the counterions and the fixed group in the resin that does not exist in the case of co-ions, making the movement of cations a little slower than that of the anions in the process. This phenomenon was also observed by Meares (1984) and explained on the basis of electrostatic interactions that made the counterions diffuse slower than the co-ions. Application of Co-Ion Sorption to Industrial Processes in Column. The previously studied co-ion exchange effect can be advantageous in fxed bed column separations. To analyze the soundness of the previous studies, additional experiments were carried out in fxed bed columns monitoring simultaneously both counterionic and co-ionic exchange. The co-ion exchange was analyzed, using all the equilibrium constant and effective diffusivity values obtained previously for the coion process. The aim was to test the previous data as well as the applicability of the axial dispersion model for column co-ion exchange in operation. The hydrodynamics of the column was studied by determination of residence time distributions, RTD, using a tracer, and the obtained D, parameter was 0.15 cm2/s (Fernandez, 1994). The basic equations for this model (Fernhdez, 1994; Loureiro et al., 1988; Costa and Rodrigues, 1985; Santacesaria et al., 1982) are
20
0
60
40 t. min
Figure 7. Experimental and theoretical breakthrough curves for anionic exchange (run 3).Parameters used in the simulation: K = 0.30;CT= 3.9 M.
* 150-
. ?
-
100-
0
50 -
20
0
40
60
t , min
Figure 8. Experimental and theoretical breakthrough curves for anionic exchange (run 4). Parameters used in the simulation: K = 0.30;CT = 4.5M.
mass conservation of solute in solution:
mass conservation of solute inside particles:
0
0
0
boundary conditions: in the particles,
initial conditions,
t = 0 c,(z,t) and c,,(z,t) depends on washing (z > 0) (16)
_*
0
10
20
30 . 4 0 t mm
, ... . ,, ,..
50
60
70
Figure 9. Experimental and breakthrough curves calculated in absence of retention term for run4. Conditions used are mentioned in Figure 8 legend.
This system of partial differential equations was also solved by numerical methods using the PDECOL package (Madsen and Sincovec, 1979). Figures 7 and 8 show experimental and predicted breakthrough curves for anionic (co-ion) exchange. Parameters used in this fit were the same obtained in independent equilibrium and kinetic experimets. The predictions of the equilibrium and kinetics results obtained in previous sections have shown good fittings with the column experimental results. Simulations of experimental results shown in Figure 8 without taking into account the retention term qei of
co-ions are displayed in Figure 9 for comparation.
2794 Ind. Eng. Chem. Res., Vol. 33,No. 11, 1994
Conclusions
Greek Symbols
During the ion (cationic) exchange process between KC1 and Na2S04 at high solution concentrations, a coion (anionic) exchange together with the cationic one is noticed. This process, considered different from electrolyte sorption, has been explained in terms of the retention of some ionic pair or ion complex formed in solution due to the high concentration. Considered as a separate phenomenon, this co-ion (anionic) exchange can be analyzed and modeled in the same way as the cationic one. Then the models applied to predict equilibrium and kinetic results of cationic exchange were also applied to the co-ion one. A n adequate fitting of the results was possible in batch experiments, and the calculated parameters were even used for modeling and prediction of experiments carried out in fixed bed at pilot plant scale. The difference between the kinetic parameters for counterion and co-ion exchange obtained gives an indication of the different interactions that occur between the counterions and the fured groups in the polymeric matrix, which do not take place with the coion.
ti €1
Nomenclature
ai = activity of species i in the particles
ai= activity of species i in solution ci = solution concentration of species i cpi = pore solution concentration of species i C ~ T= initial solution concentration of species i in batch runs
or feed solution concentration of species i in column runs CT = total solution concentration in runs with mixed species
co = initial solution concentration
D, = axial dispersion parameter D, = pore diffusivity D-A = diffusivity of species A at infinite dilution F = Faraday constant K = factor separation constant kl = mass transfer coefficient L = length of column qei = exchanged particle concentration of species i qi = particle concentration of species i qi = average particle concentration of species i qpi = pore concentration of species i R = gas constant R = radial coordinate Ro = radius of particle t = time T = temperature ui = interstitial velocity ui = partial molar volume of species i V = volume of solution z = spacial coordinate zi = valence of species i
= resin porosity
= bed porosity ll = osmotic pressure t = resin tortuosity 4 = column diameter Superscript - = average concentrations
Literature Cited Barret, J.; Dalziel, J. A. W.; Rahman, M. K. Co-ion Exchange Between Zirconium Phosphate and Aqueous Solutions. Bull. SOC.Chim. Fr. 1968, 1835-1838. Costa, C.; Rodrigues, A. Design of Cyclic Fixed-Bed Adsorption Processes. Part I: Phenol Adsorption on Polymeric Adsorbents. AIChE J. 19SS,31 (lo),1645-1654. Fernhndez, A.;Rodrigues, A.; Diaz, M. Modeling of N d K Separation in High Concentrated Solutions. Chem. Eng. J. 1994,54, 17-22. Helfferich, F. Zon Exchange; McGraw-Hill: New York, 1962;pp 134- 146. Kataoka, T.; Yoshida, H.; Ikeda, S. Effect of Electrolyte Penetrating from Liquid Phase into Resin Phase on Ion Exchange Rate. J . Chem. Eng. Jpn. 1978,ll(21,156-158. Kim, D. W.; Lee, G. S. Influence of Co-ions in the Eluent on the Separation Factor of Lithium Isotopes. J. Radioanal. Nucl. Chem. 1991,149(11, 73-81. Loureiro, J. M.; Costa, C.; Rodrigues, A. Recovery of Copper, Zinc and Lead from Liquid Streams by Chelating Ion Exchange Resins. Chem. Eng. Sci. 1988,43(5),1115-1123. Madsen, N. K.; Sincovec, R. F. PDECOL: General Collocation Software for Partial Differential Equations. ACM Trans. Math. Software 1979,3(5),326-351. Mar, C.; Larchet, C.; Auclair, B. Etude de l'influence de la valence du co-ion sur la penetration d'un Blectrolite fort dans une membrane Bchangeuse d'ions. (Study of the influence of coion valence on the penetration of a strong electrolyte in a ion exchange membrane.) C. R. Acad. Sci. Paris, Ser. 2 1991,312, 123-128. Marinsky, J. A. Ion Exchange. A Series of Advances; Marcel Dekker: New York, 1966. Meares, P. Transport in Ion-Exchange Polymers. In Diffusion in Polymers; Crank, J., Park, G. S., Eds.; NATO AS1 Series; Plenum: New York, 1984. Nardin, M. Etude de l'adsorption des ions metalliques a forte concentration et des impuretes par les resins. (Study of adsorption of high concentration metallic ions and of impurities by ion exchange.) J. Inorg. Nucl. Chem. 1971,33,3905-3942. Santacesaria, E.; Morbidelli, M.; Servida, A.; Storti, G.; Carra, S. Separation of Xylenes on Y Zeolites. 2. Breakthrough Curves and Their Interpretation. Znd. Eng. Chem. Process Des. Dev. 1982,21,446-451. Whitney, D. C.; Diamond, R. M. Ion Exchange Studies in Concentrated Solutions. I. "he Alkali Cations with a Sulphonic and Carboxylic Acid Resin. Znorg. Chem. 1963,2 (6),1284-1295. Received for review January 4, 1994 Revised manuscript received May 26, 1994 Accepted J u n e 17, 1994@ Abstract published in Advance ACS Abstracts, August 15, 1994. @
