Miguel de la Luz-Asunción ,Eduardo E.Pérez-Ramírez ,Ana L.Martínez-Hernández ,Victor M.Castano ,Víctor Sánchez-Mendieta ,Carlos Velasco-Santos ,*

1 Facultad de Química,Universidad Autónoma del Estado de México,Km.12 de la carretera Toluca-Atlacomulco,C.P.50200,San Cayetano,Toluca,Estado de México,Mexico

2 Tecnológico Nacional de México-Instituto Tecnológico de Querétaro,División de Estudios de Posgrado e Investigación,Av.Tecnológico s/n,esq.Gral.Mariano Escobedo,Col.Centro Histórico,C.P.76000 Santiago de Querétaro,Querétaro,Mexico

3 Centro de Física Aplicada y Tecnología Avanzada,Universidad Nacional Autónoma de México,Boulevard Juriquilla 3001,Querétaro 76230,Mexico

Keywords:Carbon nanotubes Graphene Adsorption Hexavalent chromium Kinetic

ABSTRACT The adsorption capacities for the removal of hexavalent chromium from aqueous solutions by six carbon nanomaterials have been evaluated.Single-walled and multi-w alled carbon nanotubes as received and after oxidation treatment,graphene oxide and reduced graphene oxide are the materials w ith different dimension and functionalization compared in thisresearch.Carbon nanotubeshave been modi fi ed using hydrogen peroxide asoxidizing agent under microwave radiation.Theoxidation treatment on carbon nanotubeshasa positive effect increasing the adsorbent-adsorbate interaction.Rate-controlling mechanisms and equilibrium data are analyzed using non-linear models.Non-linear method is proposed as the most suitable method for determining the kinetic and equilibrium parameters.The values of adsorption energy(E)obtained from the Dubinin-Radushkevich isotherm,have been found around 0.371 and 0.870 kJ·mol-1,indicating physical adsorption.Therefore,the pseudo-second order model represents better the kinetic experimental data.The results show that the Langmuir isotherm provides a slightly better fi t to the experimental data compared with the Freundlich isotherm,indicating homogeneous distribution of active sites on carbon nanomaterials and monolayer adsorption.The separation factors R L are found in the range of 0-1,suggesting that the adsorption process is suitable for all adsorbents.The mechanisms for hexavalent chromium removal have been proposed as electrostatic interactions and hydrogen bonding.

1.Introduction

1.1.Heavy metal pollution

Heavy metal pollution is a serious environmental problem due to its harmful effectsand accumulation throughout thefood chain and therefore in the human being.Among the heavy metals contaminants to the environment,chromium is considered as a high priority contaminant[1].The presence of heavy metals in industrial ef fl uents generates a big problem,since they are usually discharged without treatment in the surface water[2].In recent years,the amount of chromium has increased in aquatic ecosystems as a consequence of different anthropogenic activities[3].Chromium is originated from various industrial processes like electroplating,metallurgy,leather tanning,wood preservations,dyes,paints,and petroleum re fi ning processes.The discharge from these industries contain both hexavalent chromium Cr(VI)and trivalent chromium Cr(III)in low and high concentrations.How ever,the hexavalent form is much more harmful than the trivalent one.Moreover,the toxicity of chromium in humans includes skin irritation to lung cancer,as w ell as kidney,liver,and gastric damage[4].Theprotection of water resourcesfrom hexavalent chromium Cr(VI)contamination is extremely important for the life of human beings.Therefore,Cr(VI)must be removed from wastewater before it is discharged into the environment[5].Moreover,Cr(VI)is nonbiodegradable and exists for a long time in the environment.This metal is reported to be potentially harmful even at low concentrations[6].Due to these effects,the discharge of Cr(VI)to surface water is regulated to below 0.05 mg·L-1by the USEPA,while total chromium Cr,including Cr(III),Cr(VI),and itsother formsisregulated to below 2 mg·L-1.Chromium is found in several valence states but only trivalent and hexavalent forms are important from an environmental viewpoint[7].

1.2.Adsorption process in the removal of heavy metals

Several processes have been reported to remove Cr(VI)from aqueous solutions,such as chemical precipitation,photocatalysis,reverse osmosis,ion exchange and adsorption,the latter process is a more useful method for metal removalthan theother processes[8].Most of these methods have high operating costs,but adsorption is an economic and effective method[9].Adsorption process is w idely used to remove heavy metals from water and wastewater.When compared to conventional methods,adsorption process offerstoo many economic and environmental bene fi ts such as low cost,availability,ease of operation,and high removal ef fi ciency.

1.3.Carbon nanomaterials

Different synthetic and natural materialshave been used as Cr(VI)adsorbents including activated carbon(AC),carbon nanotubes(CNTs),zeolites,chitosan,and industrial w astes[10].Nanotechnology has various applications in different areas but recently its application for w astew ater treatment has emerged as a fast-developing.At the nanoscale,materials show unique characteristics and,due to their small size,they possess a large surface area.These characteristics improve the adsorption capacity of the nanomaterials.In addition to a large surface area,these carbon nanomaterials(CNMs)exhibit interesting properties,such as photocatalytic activity and high reactivity,which make them better adsorbentsmaterials than conventional materials[11].Owing to their high surface area,nanomaterials have a greater number of active sites for interaction with different chemical species.To get better resultsfor theremoval of metallic species from wastew ater,nanomaterials are becoming new alternatives to solve the problem of w ater pollution[6].Most of adsorbents have low adsorption capacity and consequently have slow adsorption kinetics.For practical application,it is necessary to develop low cost adsorbent w ith high removal capacity as w ell as relatively faster adsorption rate.In this aspect,recent advances in nanotechnology focuses on the production of nano-sized adsorbentsw ith enhanced sorption capacity and rapid sorption ratefor theremoval of speci fi c contaminants[12].Sincetheir discovery in 1991,nanotubes have been compared as one of the most studied nanomaterials in various areas of science.ACNTis basically a sheet of graphene that hasbeen rolled into a tubular shape.Therearetwo typesof nanotubes that can be differentiated depending on the number of outer layerson thetubular structure.Theseare single-w alled carbon nanotubes(SWNTs)and multi-w alled carbon nanotubes(MWNTs)[13].The nano size of CNTs contributes a high surface area,allow ing higher adsorption capacities.These characteristics have allowed CNTs to become attractive adsorbents in removing contaminants[10].Nanoporous materials possess high surface area,structural and bulk properties that underline their important usesin variousareassuch asion exchange,separation,catalysis and photocatalysis,sensors,biological molecular isolation and puri fi cations.In recent years,considerable effort has been made in the synthesis,characterization,functionalization,molecular modelingand design of nanoporous materials due to the aforementioned properties[14].The CNTsurface may also be chemically modi fi ed to enhance the adsorption properties of speci fi c ions or molecules.Functionalization or defect siteson the nanotube surface could play a role in the adsorption of moleculesand ions[13].Similarly,thin graphene oxide sheets(GEOs)haverecently emerged as a new carbon-based nanoscale material that also provides a path of synthesis to graphene(GE)[15].GEOstructure is assumed to be asheet of GEbonded to oxygenated groupssuch ascarboxyl,hydroxyl or epoxy groups.GEisa fl at singleatomic layer of sp2hybridized carbons[16,17],packed into two dimensional(2D)honeycomb network of carbon[18,19].It has generated great interest due to its unique electrical and thermal conductivity,optical properties,largespeci fi c surfacearea(2630 m2·g-1)and chemical properties[20].There are few reportsthat focus to compare the performance of these nano-adsorbents on the adsorption of Cr(VI).In this research,the adsorption capacities of these nano-adsorbents are compared among them under similar conditions,considering that all possess sp2hybridized structure but the functionalization and dimension play an important role in adsorption process.

1.4.Kinetic and equilibrium modeling

Mathematical models can describe the behavior of the sorption processes.Ow ing to thiskinetic modelsare used to examine the controlling mechanism of the adsorption process.

Chemical kinetic gives information about reaction pathw ays and times to reach equilibrium.Adsorption kinetic shows a large dependence on the physical and/or chemical characteristics of the adsorbent material.The parameters w ere estimated by three non-linear models to understand the mechanism of adsorption.Arelatively high determination coef fi cient(R2)value indicates that the model successfully describes the kinetics of Cr(VI)adsorption on carbon nanomaterials[3].R2hasbeen used to determinetherelationship betw een theexperimental data and the non-linear kinetic models.

In thepresent study,kinetic datahavebeen analyzed using non-linear kinetic models:pseudo-fi rst-order(PFO),pseudo-second-order(PSO),Elovich,and intraparticlediffusion(ID)model.The Langmuir,Freundlich,and Dubinin-Radushkevich(D-R)non-linear models are used to fi t the equilibrium isotherms for these hexavalent chromium-adsorbent systems.Thus,this research is focused to:(i)to study the adsorption kinetics of Cr(VI)on carbon nanomaterials such as SWNT,oxidized singlewalled carbon nanotubes(SWNTOs),MWNT,oxidized multi-walled carbon nanotubes(MWNTOs),GEO,and reduced graphene oxide(RGO),(ii)to analyze the adsorption isotherms of Cr(VI),(iii)to propose the adsorption mechanism of Cr(VI)on carbon nanomaterials and,(iv)to compare the dimensional characteristics and functionalization of these nano-adsorbents on removal of Cr(VI)from aqueous solutions.

2.Materials and Methods

2.1.Materials

The as-received SWNT used in this study w ere purchased from Sigma Aldrich(purity 40%)w ith an average diameter of 0.9-1.2 nm and 10-30μm length,and synthesized by arc-discharge.MWNTs w ere purchased from Sun Nano Company(purity＞80%)with outer diameter of 10-30 nm,and 1-10μm length and produced by chemical vapor deposition(CVD).For the synthesis of graphene materials,graphite powder(No.70230,Electron Microscopy Science/#1686-BA/LOT#1130929)w as used employing the modi fi ed Hummers'method.All solutions w ere prepared using reagent-grade chemicals.

2.2.Adsorbents preparation

For adsorption studies,CNTs w ere oxidized by hydrogen peroxide(H2O2).The methodology used for the oxidation of SWNTand MWNTis reported by a previous study of this research group[21].Likew ise,the synthesis of OGEand RGOis also reported in the aforementioned work.

2.3.Characterization of the carbon nanomaterials

The adsorbents w ere characterized by transmission electron microscope(JEOL JEM-1010)operating at 80 kV.Raman and Fourier transform infrared(FT-IR)spectroscopies w ere analyzed in order to investigatethe presenceof oxygenated functional groupson thesurfaceof CNMs.Raman spectra were obtained using a Dylor LabRam IIequipment(resolution 1 cm-1)w ith an excitation line of He-Ne(632.8 nm)and FT-IRspectra w ere recorded in a spectrometer(Tensor 37,Bruker,resolution 1 cm-1)w ithin the range of 4000-400 cm-1.The surface area w as determined by N2adsorption-desorption isotherms in a BELSORP-minill BELJAPAN and using the BET equation.The point of zero charge(PZC)on the CNMs w as determined from fast titration method[22].The characterization results of these nanomaterials are also reported in the w ork by de la Luz-Asunción et al.[21].In TEM images of as-received CNTs and CNTOs(oxidized carbon nanotubes)w ere observed some changes in amorphous carbon contained on CNTs after oxidation w ith microw aves.The functionalization in CNTOscauses opening up of the tube ends,some defects are generated on the side walls of nanotubes.Likew ise it w as observed that there are no changes in the nanotube diameter after functionalization.The morphological structure of the RGOshowed no difference from the GEO.In Table 1 a summary of the characterizations is show n.

2.4.Adsorption kinetic

The adsorption experiments w ere carried out in a batch system using potassium dichromate(K2Cr2O7,Mallinckrodt)as the source of Cr(VI).A stock solution of 100 mg·L-1w as prepared by dissolving 0.2828 g of K2Cr2O7in 1000 ml of distilled w ater.This stock solution w as diluted to the desired initial concentrations ranging from 10 to 60 mg·L-1.The p H of the Cr(VI)solutions w as adjusted to 2.0 ±0.5 by adding few drops of 1 mol·L-1hydrochloric acid(HCl,Sigma-Aldrich 37%),before mixing with the adsorbents.Cr(VI)concentration wasmeasured using an UV-Visspectrophotometer(DR5000,Hach)at 540 nm by using Diphenylcarbohydrazide spectrophotometric method(ASTM D 1687-02).Prior to analysis,linear calibration curves w ere obtained.

Kinetic experiments w ere performed as follow s:0.050 g of CNMs and 50 ml of Cr(VI)solution(50 mg·L-1)were placed in beakers.The mixture w as ultrasonicated for 5 min.The beakers w ere then covered and the solutions w ere kept in continuous agitation(235 r·min-1)by a magnetic stirred during 180 min at 25°C ± 1°C.Samples w ere taken at predetermined time intervals to determine the residual concentration of the adsorbate and the equilibrium time for Cr(VI)adsorption.Before analysis,samples w ere fi ltered.All adsorption experiments were performed in duplicate under identical conditions and average values w ere used for further calculations.

The uptake of the adsorbate was calculated by the following equation:

where,qtisthe adsorption capacity per gram of the adsorbent at time t,V is the volume of the solution(L),C0is the initial concentration of the adsorbate(mg·L-1),Ctis the concentration of the adsorbate(mg·L-1)in solution at time t,and m is the mass of adsorbent(g)[23].

Kumar reported in his research that it is not suitable to use linear methods for predicting the kinetic rate constants,because the linear method only teststhehypothesisof linear regression instead of verifying the theory of adsorption kinetics.Linear regression supposed that the scatter of points around a line follow s a Gaussian distribution and that the standard deviation is equal in each value of X.These assumptions usually are not true after transforming the experimental data.Sometimes these transformations modify the relation between Y and X.The linear method does not check w hether the process or the kinetic trend is linear or not,instead,it assumes the experimental data are linear.The linear method just reports the slope and intersection for a linear trendlinethat best predictsthe Y valuefor agiven X[24].Kumar also suggeststhat it isnot appropriate to use the linear regression method while using the pseudo-fi rst-order equation.Besidesthepseudo-second-order model may vary depending on the way the kinetic model is linearized.

Similarly Lin and Wang show in their study that the best-fi tting for non-linear forms of the PFOand PSO kinetic models w ere higher than the linear forms[25].

2.5.Equilibrium studies

The equilibrium studies were performed using the following procedureat 25°C±1°C,parallel seriesof batch adsorption testsw erecarried out in 100 ml beakers,50 ml of Cr(VI)solutions(10 mg·L-1,20 mg·L-1,30 mg·L-1,40 mg·L-1,50 mg·L-1,and 60 mg·L-1)wasindependently added to 0.050 g of CNMs.Themixturew asultrasonicated for 5 min and shaken.Preliminary adsorption experiments w ere performed to determine the equilibrium time.Resultsindicated that 60 min w ere suf fi cient to reach the equilibrium in most of the adsorbents.

The uptake of the adsorbate at equilibrium w as calculated by the follow ing equation:

w here,qeis the equilibrium adsorption capacity per gram of adsorbent(mg·g-1),Ceis the equilibrium concentration of adsorbate(mg·L-1),V,C0,and m have the same meaning as before[26].

3.Results

3.1.Effect of pH

In order to understand the mechanism of adsorption of the Cr(VI),it is necessary to know the dominant chemical species of the adsorbate.K2Cr2O7ionizes in w ater to give dichromate ions depending on the p Hand thechromium concentration[27].In aqueoussolution,Cr(VI)exists in the form:chromate(Cr O4-2),dichromate(Cr2O7-2)and hydrogen chromate(HCr O4-).Cr O4-2is predominant in basic solutions,w hile HCr O4-and Cr2O7-2are predominant at p H 1-6(Fig.1).The diagram of species of Cr(VI)w as made using Hydra/Medusa softw are(Make Equilibrium Diagrams Using Sophisticated Algorithms)[28].

Table 1 Characterizations of carbon nanomaterials(de la Luz-Asunción[21])

Fig.1.Diagram of species of chromium(VI)as a function of p H.

According to the p H used in this study,the HCr O4-is the predominant form of hexavalent chromium w hich participated in adsorption process.We consider negligible amount of Cr2O7-2.

3.2.Effect of contact time

Fig.2(a)-(c)show s the effect of contact time on adsorption of Cr(VI)on the CNMs at 50 mg·L-1initial chromium concentration at p H 2.0± 0.5 and temperature 25°C± 1°C.As it can be seen in the aforementioned fi gures the Cr(VI)adsorption rate is high at the beginning and later decreases until saturation levels are achieved at the point of equilibrium(60 min).The data obtained from this experiment were further used to evaluate the kineticsof the adsorption process.

3.3.Kinetic and equilibrium studies

In thisstudy,anon-linear method isused to estimatetheparameters involved in the kinetic and equilibrium data.Non-linear method hasan advantage that the error distribution does not get changed as in linear technique.

All equationsdescribed in Tables2 and 4,except for the intraparticle diffusion model,w ere adjusted using non-linear methods w ith Levenberg-Marquardt algorithm.

The values of the kinetic parameters and R2obtained by non-linear methods are given in Table 3.The values of R2(＞0.965)for the Elovich model areslightly higher than PFOand PSO.Likewise,theadsorption capacities calculated by the PFOand PSOmodels are close to those determined by experiments.In this research,the R2values are very close among PFO,PSOand Elovich,w hereby,the D-Risotherm w as used as a criterion to distinguish between physisorption and chemisorption.Depending on the values of E,the adsorption process can be classi fi ed as chemisorption(8 kJ·mol-1＜ E)and physisorption(E ＜ 8 kJ·mol-1)[29].

The values obtained of adsorption energy show that this process is governed by physisorption.For the aforementioned,the Elovich model is discarded since it represents a process of chemisorption.Therefore,PSO model is more suitable for describing the adsorption kinetics of HCrO4-anions on CNMs.

According to Weber and Morris,if the rate limiting step is the intraparticle diffusion,then the amount adsorbed at any time t should be directly proportional to the square root of contact time t and should pass through the origin[3].How ever,according to Fig.2(d),it can be seen that the ID model has effect on the adsorption process but is not limiting step because the values do not tend to the origin.

Fig.2.Adsorption kinetics of Cr(VI)on CNMs:(a)Pseudo-fi rst-order,(b)Pseudo-second-order,(c)Elovich model,and(d)Intraparticle diffusion(C0=50 mg·L-1,T=25 °C ± 1 °C,p H=2.0±0.5).

Table 2 Nonlinear kinetic models

The oxidation treatment had an in fl uence on the pore size;mean pore diameter increases from 8.74 nm for SWNT to 16.74 nm for SWNTO.Similarly,this effect was observed in MWNTfrom 30.58 nm to 35.33 nm for MWNTO,and fi nally pore size in RGOw ith 18.508 nm is much less than GEOw ith 31.58 nm.

On another hand,the speci fi c surface areas(SSA)w ere calculated using the BET method.The SSA values are 64 m2·g-1,204 m2·g-1,136 m2·g-1,113 m2·g-1,48 m2·g-1,and 186 m2·g-1for SWNT,SWNTO,MWNT,MWNTO,RGO,and GEO,respectively.

The results show that GEOand oxidized nanotubes have a greater adsorption capacity than RGO and unoxidized nanotubes,respectively;this con fi rms that oxygenated groups contained on the surface of these adsorbents contribute to increase the adsorbent-adsorbate interaction.It isalso important to note that GEOand SWNTOhave more surface area than the RGOand SWNT,respectively;which also contributes to increasetheadsorption capacity.On the other hand,MWNTOhasrelatively smaller surface area than MWNT;how ever MWNTO contains higher mean pore diameter,this latter,it isuseful to the adsorbate molecules to get in more easily into the nanotube.

3.4.Adsorption isotherm modeling

An adsorption isotherm is useful to obtain a relationship between the concentration of adsorbate in the solution and the amount of adsorbate adsorbed to the solid phase w hen the two phases are at equilibrium(Fig.3).

3.4.1.Langmuir model

The Langmuir isotherm is used to estimate the adsorption capacity of the adsorbent on a homogeneous surface by monolayer adsorption w ithout interaction betw een adsorbed molecules;assuming that all the adsorption sites are equivalent and that adsorption at one site does not affect adsorption at an adjacent site[3].

Table 3 Adsorption parameters of the kinetic models

3.4.2.Freundlich model

The Freundlich isotherm is based on multilayer adsorption w ith interaction between adsorbed molecules.The Freundlich model describes the equilibrium on heterogeneous surfaces with a uniform energy distribution and reversible adsorption[14].

3.4.3.Dubinin-Radushkevich model

The D-Rmodel is generally used for adsorption mechanism w ith a Gaussian energy distribution onto a heterogeneous surface.Through this isotherm,it is possible to analyze more deeply the type of adsorption,since the application of the isothermsof Langmuir and Freundlich do not provide this type of information[32].

The equilibrium data w ere analyzed w ith non-linear Langmuir,Freundlich,and Dubinin-Radushkevich models(Table 4).

Comparison betw een adsorbents one dimensional(1D):MWNTy MWNTO and tw o dimensional(2D):GEO and RGO,w as realized betw een GEO vs MWNTOand RGO vs MWNT,since these possess similar chemical structures.

It can be seen that GEO(2D)has very high adsorption capacity than itscounterpart MWNTO(1D)becausethe HCrO4-can beadsorbed more easily on theedgesand both sidesof thestacked sheetsof GEO.MWNTO presentsthedisadvantagethat Cr(VI)anionsare not ableto penetrateto some of the interstitial spaces by possible steric effects.

On the other hand,RGO(2D)has less adsorption capacity than its counterpart MWNT(1D);in this case,the factor that has the greatest infl uence in the adsorption processisthe SSA.Since adsorption is a surface phenomenon,the adsorbents w ith higher surface area have greater adsorption capacity in comparison to the adsorbents w ith low er surface area[2].The rate of Cr(VI)removal is higher in the beginning due to large surface area available of the adsorbent.After certain time,these available sitesare saturated and may be dif fi cult to occupy,then adsorption process is slow in the later stages.This con fi rms that the absorbents have a limited number of sites w hich become saturated above a certain time.Once the adsorbate has been absorbed a thick layer is formed over material;thus the capacity of adsorbent is saturated and the uptake rate is controlled by the rate at w hich the adsorbate is transported from the exterior to the interior sites of the adsorbent[14].PZC(the p H at which the electrical charge density on the surface of the adsorbent is zero)is an important parameter for explaining the ef fi ciency of the adsorption process in terms of ion attractions from oppositely charged surfaces.At p H＜p Hpzc,the surface is positively charged,thereby attracting anions and repelling cations or other positively charged particles[10].The PZC values are 6.11,7.01,4.63,6.59,3.17 and 5.24 for MWNTO,MWNT,SWNTO,SWNT,GEOand RGO,respectively.Therefore the surface charges of CNMs are positive at p H values below of PZC.This is because Cr(VI)exists in the form of anions such as HCrO4-,in acidic medium the surface of the adsorbent isprotonated,astrong attraction existsbetween this anions of Cr(VI)and the positively charged surface of the adsorbent.Whereas at high p H there will be abundance of negatively charged ions causing repulsion betw een HCrO4-and negatively charged adsorbent.Thus,hexavalent chromium is removed most effectively in an acidic medium;adsorption increases w ith decreasing p H.This is a common phenomenon observed by many researchers.At low p H,there are a large number of H+ions,which neutralize the negatively charged adsorbent surface,increasing thestrength of interaction between HCrO4-and CNMs.

Fig.3.Adsorption isotherms of Cr(VI)on CNMs(a)Langmuir(b)Freundlich and(c)Dubinin-Radushkevich(T=25°C±1°C,p H=2.0±0.5).

The proposed mechanics w here,negatively charged HCr O4-in the solution attaches through electrostatic interactions to positively charged functional groups,and on thepositivesurfaceof the adsorbents is show n in Fig.4(a).Also,it is suggested that hydrogen bonding occurs between a hydrogen atom and a highly electronegative atom asoxygen,contained in the oxygenated functional groups of the adsorbents and the adsorbate[Fig.4(b)].

According to the above described,the adsorption mechanisms for Cr(VI)on CNMs are a combination of both electrostatic interactions and hydrogen bonding.

The favorable nature of adsorption can be expressed in terms of an equilibrium parameter RL,that is dimensionless,and it is de fi ned as:

w here KLis the Langmuir constant(L·mg-1)and C0is the initial concentration of adsorbate in solution.It establishes that:(i)0＜RL＜1 for favorable adsorption,(ii)RL＞1 for unfavorable adsorption,(iii)RL=1 for linear adsorption and(iv)RL=0 for irreversible adsorption[31].The values of RLfor all adsorbents are listed in Table 5.RLvalues obtained are in the range of 0-1,indicating that the adsorption process is favorable for all adsorbents.It is found that both isotherms(Langmuir and Freundlich)fi t the equilibrium data with high determination coef fi cients(R2≥0.986 and R2≥0.977,respectively),thus indicating both monolayer and heterogeneous surface conditions,the parameter values are presented in Table 5.How ever,the Langmuir model correlated the experimental data slightly better than the Freundlich isotherm,indicating homogeneous distribution of active sites,and monolayer adsorption between HCr O4-and CNMs.The w hole isotherms obtained are type L,according to the Giles'classi fi cation[35],indicating relatively high af fi nity betw een the adsorbate and theadsorbent in the initial phase.Likew ise,thisindicatesmultipleinteractions betw een the adsorbate and the adsorbent,strong molecular attraction betw een the adsorbate and little competition betw een the adsorbate and solvent for adsorption sites.The 1/n values for the whole adsorbents are calculated between 0.304 and 0.427,since these values are less than 1,indicating a favorable adsorption.

Table 4 Nonlinear Langmuir,Freundlich and Dubinin-Radushkevich models

Fig.4.Mechanism of interaction betw een HCrO4ˉand CNMs.

It is w ell know n that,the functionalization on CNTs improves their stability and dispersion in aqueoussolutions.Thus,1Dnanomaterial in its oxidized form has greater adsorption capacity than the unoxidized corresponding 1D form,for the contaminant analyzed in this study.On the other hand,due to stacked graphitic layersof the RGO,adsorbate molecules could have dif fi culty interacting w ith the surface of this adsorbent,w hich considerably reduces their capacity to remove Cr(VI).Comparing 2D nanomaterials,GEO has greater adsorption capacity than RGO,becausethefreespace betw een thegraphitic layersisbroader.Thus,the adsorbate molecules are more easily able to be adsorbed.

These adsorbents also exhibit various advantages such as fast kinetics,and selective adsorption tow ard heavy metals.

4.Conclusions

SWNT,SWNTO,MWNT,MWNTO,RGOand GEOw ere evaluated as adsorbents for Cr(VI)removal.From the kinetic experiment,it is observed that PSOmodel represents the adsorption kinetic of Cr(VI).The Langmuir isotherm model correlated theexperimental dataslightly better than the Freundlich isotherm.The adsorption energy(E)obtained from the D-R isotherm w as found to be betw een 0.371 k J·mol-1and 0.870 kJ·mol-1,indicating that HCrO4-is adsorbed on CNMs by physisorption process.This investigation suggested that the main mechanisms for the removal of Cr(VI)w ere a combination of electrostatic interactions and hydrogen bonding.We found that GEO(2D)w as the most ef fi cient adsorbent follow ed by SWNTO(1D)w ith a slightly lower capacity.It can be concluded that the adsorbent w ith higher adsorption capacity related to functionalization and dimension is GEO.2D nanomaterial in its oxidized form has greater adsorption capacity than 1D counterpart.It is important to mention that GEO(2D)and SWNTO(1D)adsorbents w ith higher adsorption capacity also have greater surface area.It can be seen that the surface area,oxygenated functional groups,pore size and dimension of the CNMsperform an important role on the adsorption process of Cr(VI).Nomenclature

Table 5 Isotherm parameters and the determination coef fi cient for the adsorption of Cr(VI)on CNMs

Ceequilibrium concentration

C0initial concentration

Ctconcentration at time t

D-R dubinin-Radushkevich

ID intraparticle diffusion

KFrelative adsorption capacity

KLLangmuir constant

kidintraparticle diffusion rate constant

k1pseudo-fi rst order rate constant

k2pseudo-second order rate constant

Medusa Make Equilibrium Diagrams Using Sophisticated Algorithms

MWNTO oxidized multi-w alled carbon nanotubes

N2nitrogen

qeequilibrium adsorption capacity per gram of adsorbent

qmaxmaximum adsorption capacity(Langmuir equation)

qsmaximum adsorption capacity(D-Requation)

qtadsorption capacity per gram of the adsorbent at time t

R gas constant

R2determination coef fi cient

RGO reduced graphene oxide

RLequilibrium parameter

RLseparation factor

SWNTO oxidized single-walled carbon nanotubes

T absolute temperature

TEM transmission electron microscopy

t time

V volume

α initial adsorption rate

β activation energy for chemisorption

θ value of the thickness of the boundary layer

1/n intensity of the adsorption

Acknow ledgement

Miguel de la Luz-Asunción is thankful to CONACYT for Grant no.47778 and also to Universidad Autónomadel Estado de México.Authors are grateful w ith the fi nantial support of ITQ-2015-16 research projects.We acknow ledge the partial fi nancial support of the Laboratorio Nacional de Materiales Grafénicos(CIQA)CONACYT Project 250848.In memoriam Dr.Adolfo M.Espíndola-González(1977-2014).