From Aqueous Solutions by Cyanex 923: Transport and Modeling Studies

metals

Article Non-Dispersive Extraction of Ge(IV) from Aqueous Solutions by Cyanex 923: Transport and Modeling Studies

Hossein Kamran Haghighi 1 , Mehdi Irannajad 1,* , Maria Teresa Coll 2 and Ana Maria Sastre 3 1 Department of Mining and Metallurgy, Amirkabir University of Technology, Tehran 1591634311, Iran; [email protected] 2 Department of Chemical Engineering, Universitat Politècnica de Catalunya, EPSEVG, Av. Víctor Balaguer s/n, 08800 Vilanova i la Geltrú, Spain; [email protected] 3 Department of Chemical Engineering, Universitat Politècnica de Catalunya, ESTEIB, Av. Diagonal 647, 08028 Barcelona, Spain; [email protected] * Correspondence: [email protected]; Tel.: +98-21-6454-2937

Received: 27 May 2019; Accepted: 7 June 2019; Published: 11 June 2019

Abstract: Transport process of germanium from an aqueous solution containing oxalic acid and 100 mg/L Ge was studied. Cyanex 923 immobilized in a polytetrafluoroethylene membrane was employed as a carrier in a flat-sheet supported liquid membrane (FSSLM) system. The speciation of the germanium ion in the oxalic acid medium and related diagrams were applied to study the transport of germanium. The effective parameters such as oxalic acid, carrier concentration, and strip reagent composition were evaluated in this study. Based on the experimental data, the oxalic acid and carrier concentrations of 0.075 mol/L and 20% v/v were the condition in which the efficient germanium transport was achieved, respectively. The concentration range of 0.04–0.1 mol/L was selected for sodium hydroxide (NaOH) as a strip reagent providing the best efficiency to transport germanium through the supported liquid membrane (SLM) system. Furthermore, the permeation model was obtained to calculate the mass transfer resistance of the membrane (∆m) and feed (∆f) phases. According to the results, the values of 1 and 1345 s/cm were found for ∆m and ∆f, respectively.

Keywords: germanium; supported liquid membrane; transport; Cyanex 923; modeling

1. Introduction Germanium is a strategic metalloid mainly used in a wide range of high-technology devices [1]. Germanium is found in lead-zinc ores [1] and coal fly ashes [2]. From the perspective of hydrometallurgy, the leach solutions obtained from zinc plant residues and coal fly ashes contain germanium along with the other metals. The most important elements that can be found in these solutions are heavy metals such as zinc, nickel, cobalt, cadmium [3,4]. The germanium separation from these solutions is a vital objective in obtaining purified germanium. Gasification coal fly ashes (GCFAs) containing germanium can be leached with water to dissolve germanium as water-soluble species [5]. Several processes have been developed to recover and separate germanium from impurities such as precipitation [6], flotation [7], ion-exchange [8], distillation [2], adsorption [9], liquid–liquid extraction (LLX) [10], and supported liquid membrane (SLM) [11–13]. Among these techniques, the LLX processes have been extensively applied to separate germanium from aqueous solutions [3,14]. However, some disadvantages such as high loss of extractant, high capital cost, and difficult operation make this method inappropriate for treating low concentrations of ions. The supported liquid membrane techniques have been introduced as alternative methods to

Metals 2019, 9, 676; doi:10.3390/met9060676 www.mdpi.com/journal/metals Metals 2019, 9, 676 2 of 13 overcome these disadvantages [15]. High selectivity, easy operation, low consumption of carrier, and the one-step process are some advantages of SLMs [16–19]. Liu et al. [1] reported oxalic acid as an efficient reagent to dissolve germanium from zinc residues. Therefore, one of the important leachates containing germanium is oxalate solution. To separate germanium from this type of solution, a few studies have been carried out. Liquid–liquid extraction of germanium from zinc leachates containing oxalic acid solutions has been carried out using tertiary amines [20,21]. Since species of germanium oxalates are in the neutral form (H2Ge(C2O4)3)[14], it was anticipated that a neutral extractant could be used to extract germanium. In this regard, Cyanex 923 (a mixture of four trialkylphosphine oxides, alkyl = normal, C6,C8 [22]) with solvation extraction behavior was selected. Solvent extraction experiments using Cyanex 923 showed good efficiency for the extraction of germanium from oxalate solutions [14]. To overcome the challenges mentioned for an LLX system, an SLM system containing Cyanex 923 was firstly developed to transport germanium from an oxalate solution. Cyanex 923 has been widely used in SLM systems. The permeation of cadmium (H(n 2)CdCln) − from wastewater containing chloride anions has been investigated through SLM processes using Cyanex 923 [23]. Chromium(VI) neutral species (H2CrO4) were transported across an FSSLM system using Cyanex 923 from chloride solutions [24]. Zinc(II) species in the form of HnZnCl(2+n) were permeated by a solid-SLM from chloride medium using Cyanex 923 [25]. In addition, an FSSLM system has been used to transport HFeCl4 species through a polyvinylidene difluoride (PVDF) membrane with the carrier of Cyanex 923 from a solution containing chloride ions [26]. Alguacil et al. [27] investigated the transport of Au(III) in the form HAuCl4 through a PVDF membrane film impregnated in Cyanex 923 from an HCl solution. Results showed good transport efficiency for gold species. Neutral complexes of uranium(VI) (UO2(H2PO4)2) were separated through an SLM system from phosphoric acid solutions using the mobile carriers containing 2-ethyl hexyl phosphoric acid mono-2-ethyl hexyl ester (PC88A) and Cyanex 923 [28]. The presented research describes a flat-sheet supported liquid membrane (FSSLM) process with a Cyanex 923 carrier, in which the facilitated transport of germanium species is carried out from a solution containing oxalic acid. Significant parameters affecting the transport of germanium such as germanium concentration in the feed phase, carrier composition, oxalic acid concentration, membrane type, and NaOH concentration in the strip phase have been investigated in detail. Finally, a mass transfer model was developed to find ∆aq and ∆org values which are the resistances corresponding to the species diffusion through the feed–membrane interfacial layer and membrane phase, respectively.

2. Experimental Section

2.1. Materials

Cyanex 923 (93%) consisting of a mixture of four trialkylphosphine oxides (alkyl = normal, C6, C8) was supplied by CYTEC Inc., NJ, USA. Various concentrations of Cyanex 923 (5–30% v/v) as a carrier were prepared by dissolving it in kerosene (Sigma-Aldrich, MO, USA). In all experiments, purified water was supplied through a water purifier (Siemens, Germany). Water solutions used in this study contained 100 mg/L of germanium ion which were prepared by dissolving GeO2 (99.99%) from Sigma-Aldrich. Desired amounts of oxalic acid powder, from Panreac, Barcelona, Spain, were added to the aforementioned solutions to obtain different oxalate concentrations in the range of 0.05–0.2 mol/L. Sodium hydroxide (NaOH) was used to prepare stripping solutions. Poly tetra fluoro ethylene (PTFE) and polyvinylidene difluoride (PVDF) flat-sheet hydrophobic membranes with the characteristics being porosity of about 85%, 47 mm diameter, pore size of 0.45 µm, and diameter of 47 mm from Millipore, KGaA, Darmstadt, Germany, were used in the present study as a liquid membrane support. Metals 2019, 9, 676 3 of 13

Metals 2019, 9, x FOR PEER REVIEW 3 of 12 2.2. Membrane Experiments FSSLM experiments were carried out in a system including two cells attached together with a FSSLM experiments were carried out in a system including two cells attached together with a flanged chamber between the cells in which a membrane filter could be placed. The effective flanged chamber between the cells in which a membrane filter could be placed. The effective membrane membrane area was calculated to be 11 cm2. The configuration of this system has been shown as area was calculated to be 11 cm2. The configuration of this system has been shown as Figure1. Figure 1. To prepare membranes for experiments, PTFE membranes were immersed in Cyanex 923 To prepare membranes for experiments, PTFE membranes were immersed in Cyanex 923 solutions solutions for 30 min. The carrier molecules fill membrane pores by capillarity during this time. for 30 min. The carrier molecules fill membrane pores by capillarity during this time. Afterward, Afterward, the membrane was taken out from a Cyanex 923 solution and it was washed with water the membrane was taken out from a Cyanex 923 solution and it was washed with water to remove to remove the carrier excess. Finally, the membrane was placed between two cells. The samples, the carrier excess. Finally, the membrane was placed between two cells. The samples, with volumes with volumes of 0.5 mL from both cells, were taken to evaluate the concentration of the metal ions of 0.5 mL from both cells, were taken to evaluate the concentration of the metal ions during the during the experiments. The composition of solutions was determined using inductively coupled experiments. The composition of solutions was determined using inductively coupled plasma atomic plasma atomic emission spectroscopy (ICP-AES Agilent, Santa Clara, CA, USA). The emission spectroscopy (ICP-AES Agilent, Santa Clara, CA, USA). The reproducibility of experimental reproducibility of experimental values was calculated in the range of ± 5% and illustrated as error values was calculated in the range of 5% and illustrated as error bars in the next figures. bars in the next figures. ±

FigureFigure 1.1.Flat-sheet Flat-sheet supported supported liquid liquid membrane membrane (FSSLM) (FSSLM) system system used inused the currentin the current study. 1: study. Motors, 1: 2:Motors, agitators, 2: agitators, 3: flat-sheet 3: membraneflat-sheet membrane chamber, 4: chambe feed phase,r, 4: 5:feed strip phase, phase, 5: 6: strip Plexiglass phase, body. 6: Plexiglass body. 2.3. Transport Equations 2.3. TransportTransport Equations phenomena in SLM processes principally occur in three steps including the reaction of speciesTransport with the phenomena carrier at the in feed–membrane SLM processes interface,principall diy ffoccurusion in across three the steps membrane including and the stripping reaction J atof thespecies membrane–strip with the carrier interface. at the According feed–membran to thee literature, interface, the diffusion flux of speciesacross (the) can membrane be found and by disregardingstripping at the the membrane–strip concentration of germaniuminterface. Acco in therding strip to phasethe literature, with respect the flux to Equation of species (1) ( [J16) can]: be found by disregarding the concentration of germanium in the strip phase with respect to Equation J = P C (1) (1) [16]: f f In this equation, P and C represent the permeability= coefficient at the feed–membrane interface f f J Pf C f (1) and the ions concentration in the feed phase, respectively. Furthermore, the flux can be written accordingIn this to Fick’sequation, first lawPf and in a diCfff erentialrepresent form the as permeability Equation (2): coefficient at the feed–membrane interface and the ions concentration in the feed phase, respectively. Furthermore, the flux can be written according to Fick’s first law in a differentialV dCformf as Equation (2): J = ( ) (2) − A dt V dC J = − ( f ) (2) where V and A are the volume of the feed phase andA thedt membrane efficient area, respectively. With respect to Equation (1), the integration form of Equation (2) can be written as Equation (3): where V and A are the volume of the feed phase and the membrane efficient area, respectively.

With respect to Equation (1), the integration form of EquationAP f t (2) can be written as Equation (3): ln(C /C ) = (3) f ,0 f .t −APVt ln(C / C ) = − f (3) f ,0 f .t V

where Cf,0 and Cf,t depict the concentration of ions in the feed phase at the initial time and time of ‘t’, respectively. Hence, the permeability coefficient can be evaluated from the slope corresponding to

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where Cf,0 and Cf,t depict the concentration of ions in the feed phase at the initial time and time of ‘t’, respectively. Hence, the permeability coeﬃcient can be evaluated from the slope corresponding to the plot of ln(C f ,0/C f .t) against t. Furthermore, the transport eﬃciency (%T) of germanium is calculated as Equation (4): C f ,t %T = 100 (4) C f ,0 ×

3. Solution Chemistry Germanium dioxide can be dissolved in water. However, this dissolution is slowly carried out as an intermediate germanium tetra-hydroxide (Ge(OH)4). These species can be converted to germanic 4.5 acid with the solubility product (Ksp) of 2.39 10 as Equation (5) [29]: × −

2H2O(aq) + GeO2 Ge(OH)4(aq) H2GeO3(aq) + H2O(aq) (5)

Germanium can form various complexes with organic acids such as tartaric acid, citric acid, oxalic acid, etc. Oxalic acid is a possible complexant which forms various complexes with germanium ion. According to the literature and observations, the solubility of germanium increases in the presence of oxalic acid [1]. The formation of germanium anionic and neutral species has been reported. For instance, Pokrovski et al. [30] described that germanium (0.02 mol/L) and oxalic acid (0.1 mol/L) form anionic 2 species of Ge(OH)2(ox)2 − (“ox” depicts oxalate) at pHs below 7. Furthermore, Liu et al. [21] introduced 2 Ge(ox)3 − as an anionic complex of germanium and oxalic acid. The concentrations of germanium and oxalic acid in the latter study were reported to be 0.013 and 0.67 mol/L, respectively. However, others [14,29] reported the formation of neutral species of trisoxalato germinates as Equation (6):

3H2C2O4(aq) + GeO2(s) H2Ge(C2O4)3(aq) + 2H2O(aq) (6)

In the current study, germanium neutral species in the form of trisoxalato germinates have been considered as predominant species participated in the reactions. According to the literature review [23,31,32], the probable extraction reaction of germanium using Cyanex 923 can be written as Equation (7) [14]:

+ 2 2H (aq) + 4L(org) + Ge(C2O4)3 −(aq) H2Ge(C2O4)3.4L(org) (7)

4. Results and Discussion

4.1. Determination of Appropriate Oxalic Acid Concentration in the Feed Phase With respect to the “solution chemistry” section, germanium was transported across FSSLM as a neutral complex (trisoxalato germinate) using Cyanex 923. The transport efficiency depends on the complexation of germanium with oxalate. Therefore, the concentration of oxalic acid is a significant parameter for transport. In this regard, a series of experiments were conducted at the oxalic acid concentration in the range of 0.05–0.2 mol/L with the carrier concentration of 20% v/v. Figure2a,b illustrates the obtained results. As can be seen in these figures, the transport efficiency and permeation coefficients decrease at lower and higher values of this range. Moreover, at the oxalic concentration of 0.075 mol/L, the maximum permeation coefficient and transport efficiency were found reaching the values of 9.97 10 4 cm/s and 88%, respectively. The species of germanium for various oxalic × − acid concentrations have been illustrated in Figure3. As can be seen in this figure, at very low oxalic acid concentrations, the dissociation of oxalic acid (H2ox) is not complete and the germanium tetra-hydroxide (Ge(OH)4) is the predominant compound. However, by increasing the oxalic acid concentration (up to 0.1 mol/L), the concentration of oxalate is enhanced and it promotes an increase in the H2Ge(C2O4)3 concentration and consequently the germanium transport improves. However, with Metals 2019, 9, 676 5 of 13

Metals 2019, 9, x FOR PEER REVIEW 5 of 12 Metals 2019, 9, x FOR PEER REVIEW 5 of 12 moreoxalate enhancement decreases of resulting oxalic acid in the concentration, decrease in the germanium concentration transport of germanium at a higher oxalate oxalic decreasesacid oxalate decreases resulting in the decrease in the germanium transport at a higher oxalic acid resultingconcentration in the decrease (>0.1 mol/L). in the germanium transport at a higher oxalic acid concentration (>0.1 mol/L). concentration (>0.1 mol/L).

FigureFigure 2. The 2. The eﬀ ecteffect of of oxalic oxalic acidacid concentration on on (a) ( atransport) transport and and(b) permeability (b) permeability coefficient coe ﬃof cient Figure 2. The effect of oxalic acid concentration on (a) transport and (b) permeability coefficient of of germaniumgermanium on on the the FSSLM FSSLM system system ([Cyanex ([Cyanex 923] = 20% 923] v/v,= temperature20% v/v, of temperature 22 °C, and [NaOH] of 22 =◦ 0.1C, and germanium on the FSSLM system ([Cyanex 923] = 20% v/v, temperature of 22 °C, and [NaOH] = 0.1 [NaOH]mol/L).= 0.1 mol/L). mol/L).

FigureFigure 3. 3. Species of germanium in various oxalic acid concentrations and 100 mg/L Ge (calculated FigureSpecies 3. Species of germanium of germanium in variousin various oxalic oxalic acid acid concentrations concentrations and 100 mg/L mg/L Ge Ge (calculated (calculated by by Medusa software, KTH university, Stockholm, Sweden). Medusaby Medusa software, software, KTH university,KTH university, Stockholm, Stockholm, Sweden). Sweden).

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4.2. Evaluation of Appropriate Carrier Concentration 4.2. Evaluation of Appropriate Carrier Concentration The presence of mobile carriers in a membrane phase is necessary for the transport phenomena;The presence however, of mobile an excess carriers amount in a membrane enhances phase the isviscosity necessary and for thedecreases transport transport phenomena; [33]. however,Therefore, an in excess order amount to obtain enhances efficient the viscositytransport, and determining decreases transportan optimum [33]. Therefore,concentration in order of the to obtaincarrier effiis cientimportant. transport, In the determining present study, an optimum taking concentration in count the ofresults the carrier from is solvent important. extraction In the presentexperiments, study, the taking range in count of 0–30% the results v/v for from the solvent Cyanex extraction 923 concentration experiments, was the selected. range of All 0–30% FSSLM v/v forexperiments the Cyanex were 923 done concentration with 0.075 was mol/L selected. of oxalic All FSSLM acid, at experiments temperature were of 22 done °C, and with using 0.075 0.1 mol mol/L/L of oxalicof NaOH acid, as at temperaturea receiving ofsolution. 22 ◦C, andAccording using 0.1 to mol the/L result of NaOH plotted as a receivingin Figure solution.4a,b, the According complete toreaction the result between plotted Ge(IV) in Figure species4a,b, and the completecarrier molecules reaction betweendoes not Ge(IV)occur at species lower and concentrations carrier molecules of the doescarrier. not The occur germanium at lower transport concentrations efficiency of the rises carrier. to about The 88% germanium when carrier transport concentration efficiency increases rises to aboutfrom 88%10% when v/v carrierto 20% concentration v/v. Moreover, increases with from in 10%creasing v/v to carrier 20% v/ v.concentration, Moreover, with the increasing curves carriercorresponding concentration, to Cyanex the curves 923 of corresponding 30 and 25% tov/ Cyanexv are shifted 923 of 30down, and 25%showing v/v are the shifted decrease down, in showinggermanium the decreasetransport. in In germanium Figure 4b, transport. this behavi In Figureor can4 b,be this observed behavior in can the be reduction observed inof thethe reductionpermeability of the coefficient. permeability The coe mentionedfficient. The reductio mentionedn may reduction be due mayto the be dueenhancement to the enhancement of viscosity of viscosityresulted resultedfrom the from increase the increase in Cyanex in Cyanex 923 conc 923 concentrationentration and and its itsprecipitation precipitation in in pores pores of thethe membranemembrane [34[34].]. According According to to the the aforementioned aforementioned discussion, discussion, the concentration the concentration of 20% of v/ v20% is selected v/v is asselected the optimum as the optimum carrier concentration. carrier concentration.

Figure 4. a b Figure 4. EffectEﬀect of of the the carrier carrier concentration concentration on on (a () )transport transport and and (b) ( permeability) permeability coefficient coeﬃcient of of germanium on the FSSLM system ([Oxalic acid] = 0.075 mol/L, temperature of 22 C, and germanium on the FSSLM system ([Oxalic acid] = 0.075 mol/L, temperature of 22 °C, and [NaOH]◦ = [NaOH] = 0.1 mol/L). 0.1 mol/L).

4.3. Effect of NaOH Concentration as a Strip Reagent on Germanium Transport

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4.3.Metals Eff ect2019 of, 9 NaOH, x FOR PEER Concentration REVIEW as a Strip Reagent on Germanium Transport 7 of 12 StrippingStripping is is an an important important reaction reaction that that takes take places place in the in membrane–strip the membrane–strip phase boundaryphase boundary layer onlayer an SLM.on an For SLM. this For reaction this reaction to occur, to the occur, selection the ofselection an appropriate of an appropriate striping reagent—a striping reagent—a chemical substancechemical suchsubstance as an such acid oras aan base—is acid or important.a base—is im Toportant. select e ffiTocient select reagent efficient/reagents reagent/reagents for stripping for germaniumstripping germanium from the loaded from organic the loaded carrier, organic a series ofcarrier, liquid–liquid a series extraction of liquid–liquid experiments extraction were carriedexperiments out, and were the carried results out, have and been the published results ha elsewhereve been published [14]. Among elsewhere several [14]. reagents Among such several as ammoniumreagents such chloride as ammonium (NH4Cl), chloride sodium hydroxide(NH4Cl), sodium (NaOH), hydroxid catechole (NaOH), (C6H6O2 ),catechol citric acid (C6H (C6O6H2),8 Ocitric7), ammoniaacid (C6H (NH8O73),), ammonia sodium sulfate (NH3), (Na sodium2SO4), andsulfate sulfuric (Na2SO acid4), (H and2SO sulfuric4), NaOH acid was (H selected2SO4), NaOH because was it isselected the most because efficient it reagentis the most for strippingefficient reagent germanium for stripping from 20% germanium v/v Cyanex from 923. 20% Therefore, v/v Cyanex FSSLM 923. experimentsTherefore, FSSLM were carried experiments out to evaluatewere carried the eoutffect to of evaluate the NaOH the concentrationeffect of the NaOH on the concentration germanium transporton the germanium using the carrier transport concentration using the ofcarrier 20% vconcentration/v Cyanex 923 of and 20% an v/v oxalic Cyanex acid 923 concentration and an oxalic of 0.075acid molconcentration/L in the feed of 0.075 solution. mol/L The in resultsthe feed can solution. be seen The in Figure results5a,b. can be seen in Figure 5a,b.

Figure 5. Effect of NaOH concentration on (a) transport and (b) permeability coefficient of germanium onFigure the FSSLM 5. Effect system of ([OxalicNaOH acid]concentration= 0.075 mol on/L, temperature(a) transport of and 22 ◦ C,(b and) permeability [Cyanex 923] coefficient= 20% v/v). of germanium on the FSSLM system ([Oxalic acid] = 0.075 mol/L, temperature of 22 °C, and [Cyanex As923] can = 20% be seen v/v). in these figures, the transport efficiency and the permeability coefficient increase with an enhancement of NaOH concentration. About 87% of germanium was transferred to the strip phaseAs at concentrationscan be seen in thethese range figures, of 0.04–0.1 the transport mol/L NaOH. efficiency The transport and the e ffipermeabilityciency corresponding coefficient toincrease the NaOH with concentration an enhancement of 0.02 of mol NaOH/L is approximatelyconcentration. 66%.About Furthermore, 87% of germanium according was to transferred Figure5b, the permeability coefficient rises to 9.28 10 4 cm/s at the NaOH concentration of 0.1 mol/L. This to the strip phase at concentrations in the× range− of 0.04–0.1 mol/L NaOH. The transport efficiency iscorresponding due to the increase to the in theNaOH amount concentration of OH− anions of 0.02 which mol/L enhances is approximately the de-complexation 66%. Furthermore, rate at the according to Figure 5b, the permeability coefficient rises to 9.28 × 10−4 cm/s at the NaOH concentration of 0.1 mol/L. This is due to the increase in the amount of OH- anions which enhances the de-complexation rate at the interface of the strip side [31]. The probable reaction for stripping species from the loaded carrier can be written as Equation (8) [14]:

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Metals 2019, 9, x FOR PEER REVIEW 8 of 12 interface of the strip side [31]. The probable reaction for stripping species from the loaded carrier can be written as Equation (8) [14]: ⋅ + − + 2− + H 2Ge(C2O4 )3 4L(org) 2OH ⇋ 4L(org) Ge(C2O4 )3 (aq) 2H 2O(org) (8) 2 H Ge(C O ) 4L + 2OH− 4L + Ge(C O ) − + 2H O (8) 2 2 4 3 · (org) (org) 2 4 3 (aq) 2 (org) 4.4. Effect Effect of Membrane Type on Germanium Transport To knowknow the the eff effectect of membraneof membrane type type on the on transport the transport of germanium, of germanium, an experiment an experiment was conducted was conductedat the condition at the of condition 100 mg/L Ge,of 100 oxalic mg/L acid Ge, of oxalic 0.075 molacid/L, of and 0.075 0.1 mol/L, mol/L ofand NaOH. 0.1 mol/L For this of experiment,NaOH. For thisa polyvinylidene experiment, a difluoride polyvinylidene (PVDF) difluoride membrane (PVDF) support membrane was used. support was used. As seen in Figure 66,, therethere isis notnot aa significantsignificant didifferencefference between the transport eefficienciesfficiencies corresponding to the PTFE and PVDF membranes ob obtainedtained from the experiments carried out under a similar condition. However, However, the overall transpor transportt efficiency efficiency of the PTFE membrane is somewhat greater than that of PVDF. The values of the germaniumgermanium permeability coecoefficientsfficients of the PVDF and PTFE membranes were foundfound toto bebe 3.143.14 × 1010−44 andand 9.289.28 × 1010−4 cm/s,cm/s, respectively. Therefore, the × − × − germanium permeabilitypermeability through through the the PTFE PTFE membrane membrane is approximately is approximately three three times times that through that through PVDF. PVDF.Similar Similar results haveresults been have reported been reported by Adnan by et Adnan al. [35 ].et Variousal. [35]. parametersVarious parameters such as higher such tortuosityas higher tortuosityof PVDF membrane of PVDF membrane result in reducing result in their reducing permeability their permeability [36]. [36].

100

50 Cyanex 923-PTFE (0.45 µm) 40 Cyanex 923-PVDF (0.45 µm) 30

Germanium Transport Efficiency, % Efficiency, Transport Germanium 10

0 0 5 10 15 20 25 30 Time, h

Figure 6. Transport efficiency of germanium through polytetrafluoroethylene (PTFE) and Figurepolyvinylidene 6. Transport difluoride efficiency (PVDF) membranesof germanium versus thro timeugh ([Oxalic polytetrafluoroethylene acid] = 0.075 mol/L, temperature(PTFE) and of

polyvinylidene22 ◦C, [Cyanex 923]difluoride= 20% (PVDF) v/v, and membranes [NaOH] = 0.1 versus mol/ L).time ([Oxalic acid] = 0.075 mol/L, temperature of 22 °C, [Cyanex 923] = 20% v/v, and [NaOH] = 0.1 mol/L). 4.5. Permeability Model 4.5. PermeabilityThe permeation Model of germanium ions through the FSSLM (with the PTFE membrane) was modeled to findThe the permeation mass transfer of resistances.germanium Toions model through the mentionedthe FSSLM system, (with itthe was PTFE assumed membrane) that species was modeledtransport to through find the SLM mass was transfer done withresistances. diffusion To and model the the chemical mentioned reactions system, took it place was assumed instantly that [37]. speciesFigure7 illustratestransport howthrough germanium SLM wa oxalates done permeates with diffusion through and a PTFEthe chemical membrane reactions containing took Cyanex place instantly923 based [37]. on the Figure following 7 illustrates steps: how germanium oxalate permeates through a PTFE membrane containing(i) In the Cyanex feed phase,923 based germanium on the following oxalate and steps: protons diffuse to the interface layer. (i)(ii) In Di theffused feed species phase,and germanium Cyanex 923oxalate molecules and protons react together diffuse to in the the interface mentioned layer. layer. (ii)(iii) Diffused The produced species and complexes Cyanex permeate 923 molecules across react the together membrane in the toward mentioned the membrane–strip layer. interface(iii) layer.The produced complexes permeate across the membrane toward the membrane–strip interface layer. (iv) NaOH detaches germanium-Cyanex 923 complexes at the membrane–strip phase interface. Therefore, germanium species are stripped from the organic carrier.

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(iv) NaOH detaches germanium-Cyanex 923 complexes at the membrane–strip phase interface. Metals 2019, 9, x FOR PEER REVIEW 9 of 12 Therefore, germanium species are stripped from the organic carrier. (v)(v) The The unloaded unloaded carrier carrier molecules molecules permeate permeate inversely inversely toward toward the the feed feed phase. phase.

FigureFigure 7. 7.A A schematic schematic transport transport of of germanium germanium ion ion through through FSSLM-Cyanex923. FSSLM-Cyanex923.

TheThe extraction extraction reaction reaction of germanium of germanium by Cyanex by Cyan 923 hasex 923 been has described been described in Equation in (7). Equation According (7). toAccording an LLX modelto an LLX developed model developed by Haghighi by etHaghighi al. [38], et the al. extraction[38], the extraction equilibrium equilibrium constant constant of the aforementionedof the aforementioned reaction wasreaction calculated was calculated to be 2056. to The be germanium2056. The germanium flux can be obtainedflux can usingbe obtained Fick’s firstusing diff Fick’susion law.first Hence,diffusion the law. fluxes Hence, at the the feed–membrane fluxes at the boundaryfeed–membrane layer and boundary the membrane layer and phase the (J and J , respectively) can be presented as Equations (9) and (10): membranef m phase (Jf and Jm, respectively) can be presented as Equations (9) and (10): 11 J == ([([Ge( (IV)])] −[ [Ge( (IV)] )] ) ) J f f Δ Ge IV f f Ge IV bl, fbl, f (9) ∆ f f −

1 J = 1 ([H Ge(ox) .4R] [H Ge(ox) .4R] ) (10) mJ = ([H2 Ge(ox3) .4Rbl], f −[H2 Ge(ox3) .4Rbl],s ) m ∆Δm 2 3 bl, −f 2 3 bl,s (10) m where ∆m and ∆f depict the resistances corresponding to the membrane phase and the feed phase boundarywhere Δm layer, and Δ respectively.f depict the resistances Subscripts fcorresponding, bl, and s are feed, to the boundary membrane layer, phase and and strip, the respectively. feed phase boundary layer, respectively. Subscripts f, bl, and s are feed, boundary layer, and strip, respectively. Moreover, [Ge(IV)]f, [H2Ge(ox)3.4R]bl, f , and [H2Ge(ox)3.4R]bl,s represent the germanium concentrations f inMoreover, the feed phase,[Ge(IV)] the feed–membrane,, [H 2Ge(ox)3.4R] andbl , f the, and strip-membrane [H 2Ge(ox)3 .4 boundaryR]bl,s represent layers, respectively.the germanium It is notedconcentrations that since thein germaniumthe feed phase, concentration the feed–mem in thebrane, strip-membrane and the strip-memb boundary layerrane isboundary lower than layers, that inrespectively. the feed–membrane It is noted boundary that since layer, the [germaniuH2Ge(ox)3m.4 Rconcentration]bl,s has been in neglected. the strip-membrane Hence, Equation boundary (10) can be rewritten as Equation (11): layer is lower than that in the feed–membrane boundary layer, [H 2 Ge(ox) 3 .4R]bl,s has been neglected. Hence, Equation (10) can be rewritten1 as Equation (11): Jm = ([H2Ge(ox)3.4R]bl, f ) (11) ∆1m J = ([H Ge(ox) .4R] ) m Δ 2 3 bl, f (11) Since the chemical reactions took placem instantly, the ﬂux values in the feed–membrane layer and the membrane phase are equal (Jf = Jm = J). Therefore, overall J can be found as Equation (12): Since the chemical reactions took place instantly, the flux values in the feed–membrane layer and the membrane phase are equal (Jf = Jm = +J).2 Therefore,4 overall J can be found as Equation (12): K[H ] [R]org [Ge(IV)] f J = + 2 4 (12) + 2 4 ∆K[+H∆] ([KR[]Horg ][Ge[R(]IV )]) f J = m f aq org (12) Δ + Δ + 2 4 m f (K[H ]aq[R]org )

Regarding Equation (1), the permeability coefficient is also written as Equation (13):

+ 2 4 K[H ] [R]org P = (13) Δ + Δ + 2 4 m f (K[H ]aq[R]org )

By arranging Equation (13), Equation (14) allows us to obtain the mass transfer resistances:

Metals 2019, 9, 676 10 of 13

Regarding Equation (1), the permeability coeﬃcient is also written as Equation (13):

+ 2 4 K[H ] [R]org P = (13) + 2 4 ∆m + ∆ f (K[H ] [R] ) Metals 2019, 9, x FOR PEER REVIEW aq org 10 of 12 By arranging Equation (13), Equation (14) allows us to obtain the mass transfer resistances: Δ 1 = Δ + m 1 f +∆2m 4 (14) P= ∆ f + (K[H ] [R] ) (14) P + 2aq 4org (K[H ]aq[R]org) 1 By plotting versus 1/P, a straight line is obtained. By plotting 1+ 2 4versus 1/P, a straight line is obtained. (K[+H2 ]aq4[R]org ) (K[H ]aq[R]org) The intercept and thethe slopeslope valuesvalues ofof thisthis lineline werewere usedused toto determinedetermine ∆Δff andand ∆Δmm, respectivelyrespectively This plotplot isis shownshown inin Figure Figure8. 8. According According to to the the plot, plot, the the values values of 1of and 1 and 1345 1345 s /cm s/cm were were found found for ∆form andΔm and∆f, respectively.Δf, respectively.

20,000

15,000

10,000 y = x + 1345

1/P, s/cm 1/P, R² = 0.9949 5,000

0 0 5,000 10,000 15,000 20,000

[[HH++]]44 Figure 8. The plot plot of of 1/ 1/PP vsvs. 4 ([Ge] ([Ge]= =100 100 mg mg/L,/L, [Oxalic [Oxalic acid] acid]= = 0.0750.075 molmol/L,/L, temperaturetemperature of (K[R]org4 ) (K[R]org ) 22 ◦C, and [NaOH] = 0.1 mol/L). 22 °C, and [NaOH] = 0.1 mol/L). 5. Conclusions 5. ConclusionThis paper focuses on studying the transport of germanium(IV) through an FSSLM using Cyanex 923 asThis a carrier. paper The focuses main findingon studying of this the study transport is that germanium of germanium(IV) and oxalate through can form an neutralFSSLM species using thatCyanex can be923 extracted as a carrier. and transportedThe main finding by Cyanex of this 923 study through is anthat FSSLM germanium system. and Results oxalate show can that form the oxalicneutral acid species concentration that can be is anextracted essential and parameter transported for the by germanium Cyanex 923 transport through becausean FSSLM extractable system. germaniumResults show oxalate that speciesthe oxalic can acid also formconcentration in a limited is rangean essential of oxalate parameter concentration. for the An germanium optimum concentrationtransport because of oxalic extractable acid for germanium the complete oxalate transport spec ofies germanium can also form is in in the a rangelimited of range 0.075–0.1 of oxalate mol/L. Theconcentration. appropriate An Cyanex optimum 923 concentrationconcentration inof the oxalic liquid acid membrane for the complete phase for transport the complete of germanium germanium is transportin the range is 20% of 0.075–0.1 v/v. Due mol/L. to theopposite The appropriate effect of theCyanex viscosity 923 conc at theentration higher concentrations in the liquid membrane of Cyanex 923phase on for germanium the complete transport, germanium the concentrations transport is 20% over v/ 20%v. Due v/v areto the unsuitable opposite for effect an e ffofective the viscosity process. Inat stripthe higher solutions concentrations with NaOH concentrationsof Cyanex 923 ofon 0.04–0.1 germanium mol/L, transport, the maximum the concentrations germanium transport over 20% is achieved.v/v are unsuitable Finally, a for permeation an effective model process. was developed In strip solutions to find the with mass NaOH transfer concentrations resistances. Asof 0.04–0.1 a result, themol/L, values the ofmaximum 1 and 1345 germanium s/cm were transport found for is∆ achievm anded.∆f, Finally, respectively. a permeation model was developed to find the mass transfer resistances. As a result, the values of 1 and 1345 s/cm were found for Δm Author Contributions: H.K.H. made a significant contribution to every stage of this paper, such as the investigation, analysis,and Δf, respectively. methodology and visualization. M.I. contributed to the conceptualization, project administration, validation and supervision of the paper. M.T.C. contributed to the investigation for the paper. A.M.S. contributed toAuthor the funding Contributions: acquisition, H.K.H. investigation made a andsignificant resources contribution provision forto theevery paper. stage M.I. of andthis H.K.H.paper, finalizedsuch as the paperinvestigation, by a critical analysis, revision. methodology and visualization. M.I. contributed to the conceptualization, project administration, validation and supervision of the paper. M.T.C. contributed to the investigation for the paper. A.M.S. contributed to the funding acquisition, investigation and resources provision for the paper. M.I. and H.K.H. finalized the paper by a critical revision.

Funding: This research was partially funded by THE SPANISH MINISTRY OF ECONOMY AND COMPETITIVENESS, MINECO, grant number CTM2017-83581-R.

Acknowledgments: This research was implemented in the Department of Chemical Engineering, Universitat Politècnica de Catalunya (Barcelona-Tec), Spain. The authors acknowledge Agustin Fortuny for his help. This

Metals 2019, 9, 676 11 of 13

Funding: This research was partially funded by THE SPANISH MINISTRY OF ECONOMY AND COMPETITIVENESS, MINECO, grant number CTM2017-83581-R. Acknowledgments: This research was implemented in the Department of Chemical Engineering, Universitat Politècnica de Catalunya (Barcelona-Tec), Spain. The authors acknowledge Agustin Fortuny for his help. This work has been partially supported by the Spanish Ministry of Economy and Competitiveness, MINECO, through the grant number CTM2017-83581-R. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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