Hanbing He,Chang Liu,Xiaohua Lu,*

Catalysis,Kinetics and Reaction Engineering

Kinetics for Preparation of K2Ti2O5Using TiO2Microparticles and Nanoparticles as Precursors☆

Hanbing He1,2,Chang Liu1,Xiaohua Lu1,*

1State Key Laboratory of Materials-Oriented Chemical Engineering,Nanjing University of Technology,Nanjing 210009,China2Division of Energy Science,Lule? University of Technology,Lule? 971 87,Sweden

A R T I C L EI N F O

Article history:

Solid-state

Kinetics

Particle

Reaction

Non-linear regression

The formation mechanism of K2Ti2O5was investigated with TiO2microparticles and nanoparticles as precursors by the thermogravimetric(TG)technique.A method of direct multivariate non-linear regression was applied for simultaneouscalculationofsolid-statereactionkineticparameters fromTGcurves.TGresultsshowmoreregular decrease from initial reaction temperature with TiO2nanoparticles as raw material compared with TiO2microparticles,while mass losses f i nish at similar temperatures under the experimental conditions.From the mechanism and kinetic parameters,the reactions with the two materials are complex consecutive processes,and reaction rate constants increase with temperature and decrease with conversion.The reaction proceedings could be signif i cantly hindered when the diffusion process of reactant species becomes rate-limiting in the later stage of reaction process.The reaction active sites on initial TiO2particles and formation of product layers may be responsible to the changes of reaction rate constant.The calculated results are in good agreement with experimental ones.

?2014TheChemicalIndustry andEngineeringSocietyofChina,andChemicalIndustryPress.Allrightsreserved.

1.Introduction

Material synthesis by solid-state reactions has a long history.In recent years,many synthesis methods such as chemical vapor deposition (CVD)[1,2],solvothermal[3,4],and template methods[5]for preparation of nanomaterials have been developed.Some advanced materials are obtained by a solid-state reaction because of its advantages,including low cost and easy large-scale preparation[6,7].Smaller particle size of raw materials results in lower starting temperature[8].Many methods,such as milling[9]and ultrasonic methods[10],have been used to obtain small particles,though they increase the energy consumption.

Accurate description of reaction rates is of value to determine appropriate process conditions[11].Attempts for incorporating particle-size distribution in the kinetic equation have been made,but the kinetic analysis is oversimplif i ed for solid-state reaction process,which is complex and usually involves multi-step reactions.The kinetic analysis on such solid-state reactions is challenging.Each individual process should be determined for a complete kinetic description of the overall reaction[12].

A large number of analytical methods are available for determining the kinetic parameters of solid-state reactions,including isoconversional or model-free method[13,14],model f i tting procedures[15],master plots[16],nonparametric analysis[17],and combined kinetic analysis [18,19].A method has been proposed by Perejón et al.[12],which involves the deconvolution of individual processes from the overall differential kinetic curves and kinetic analysis for discrete processes using a combined kinetic analysis.In general,for complex reaction processes, nonlinear regression methods are commonly used,in which the overall reaction is the sum of individual reactions with constant activation parameters[20].

Many kinetic parameters of solid-state reactions have been obtained by non-linear regression.Wang et al.[21]showed that the method is applicable for the calculation of kinetic parameters from overlapping processes for the reaction of carbonaceous materials with NO,O2and NO+O2.Ge?wein and Binder[22]investigated the oxidation kinetics of ball milled ZrAl3powder and determined the kinetic parameters.Budrugeac and Segal[23]determined the mechanism and corresponding kinetic parameters,checked the thermo-oxidative degradation of an epoxy resin,and predicted the thermal lifetime of the material.

K2Ti2O5attracts attentions because of its high catalytic activity and photoluminescence[24,25].Our previous study has shown that mesoporous f i brous titania with large specif i c surface area[26]and H2Ti8O17nanorods with high photocatalytic activity[27]can be prepared using K2Ti2O5as a precursor.K2Ti2O5is usually formed by a solid-state reaction,with a layered structure.However,the kinetics forthe preparation of K2Ti2O5has not been reported because of the complexity of process,which is required for understanding the solid-state reaction[28].

Our previous work has exhibited the use of hydrous titanium dioxide(TiO2·nH2O),which transforms to anatase nanoparticles after heatingand decreases theinitialreaction temperaturewith K2CO3compared to the anatase-K2CO3system.Here we take the synthesis of K2Ti2O5as an example to study the kinetic mechanism and equation of solid-state reaction by using TiO2(anatase)nanoparticles and microparticles as starting materials.The non-isothermal kinetics of the solidstate reaction between TiO2and K2CO3is studied by means of thermogravimetric analysis.

2.Theory

2.1.Model-free estimation of activation energy

The kinetic equation for solid-state reaction under non-isothermal conditions is usually expressed as

where α represents the conversion of solid reactant,Eais the activation energy,t is the time,A is the Arrhenius pre-exponential factor,T is the reactiontemperature,Ris thegas constant,andf(α)is a kinetic function related to the reaction mechanism,which depends on particle shapes and driving forces.The most extensively used ones for solid-state processes are given in Table 1[29].

Theconversionαcanbecalculatedfromthemassloss(evolvedCO2)

wherem0isthestartingmass,mtisthemassattimet,andmfisthemass after a complete reaction.

In experiments,different heating ways can be used,the most common ones being isothermal,linear heating,modulated temperature, and sample-controlled[30].The reaction is usually carried out under control with temperature increasing continuously according to a predetermined program so that more information can be obtained[31]. With the heating rate β=dT/dt,Eq.(1)takes the following form

The reaction activation energy is a function of temperature and the extent of conversion for a process involving several steps.The modelfree methods allow for evaluating the Arrhenius parameters without choosing the reaction model and are known as the Flynn-Ozawa-Wall (FWO)method and Friedman method.

The Flynn-Ozawa-Wall equation is[32]

where g(α)is the integral form of mechanism function. The Friedman equation is[33]

where dα/dt is the rate of conversion and f(α)is the differential form of mechanism function.

Thus the activation energy at a constant α value,Ea,can be determined from the slope of curves,the plot of the left-hand side of Eqs.(4)or(5)versus 1/T.

2.2.Determination of kinetic model by means of multiple non-linear regression

Themultiplenon-linearregression(NetzschThermokinetics)makes the assumption that the model parameters are priori identical for all measurements and determines the parameters in a simultaneous analysis.The parameters are determined via a hybrid regularized Gauss-Newton method[30].It allows a direct f i tting of the model to experimental data without a transformation,which would distort the error andconsequentlytheresult[23,30].Ifthequalityoff i ttingisinsuff i cient withthegivenmodel,themodelshouldbeimprovedthroughextension to multi-step reaction processes with different combinations.

3.Experimental

3.1.Sample preparation

Titania(TiO2,anatase)microparticles and potassium carbonate (K2CO3)purchased from Shanghai Linfeng Chemical Reagent Co.,Ltd. (China)andtitania(TiO2,anatase)nanoparticlespurchasedfrom Hangzhou Wanjing New Material Co.,Ltd.(China)were used as raw materials,which were in chemical and reagent grade.Stoichiometric quantity of K2CO3and TiO2particles in two sizes was mixed as a paste-like substance using deionized water and dried in an oven at 60°C for 24 h.The properties of TiO2microparticles and nanoparticles are given in Table 2.

Table 1f(α)functions for common mechanisms in heterogeneous kinetics

Table 2Properties of raw materials

3.2.Measurements

The non-isothermalkineticsofthesolid-statereactionbetweenTiO2and K2CO3was studied by means of thermogravimetric analysis,which iswidelyusedinthef i eldofsolid-statereactionkinetics,withTG/c-DTA (Netzsch,Germany).The mixture of 6-7 mg washeated to 950°Cat 10, 15,20 and 25°C·min-1separately.All TG experiments were performed at a 20 ml/min f l ow rate of N2.

X-ray diffraction(XRD)patterns were collected on a Bruker D8 Advance powder diffractometer using a Ni-f i ltered Cu Kαradiation source at 40 kV and 20 mA.

4.Results and Discussion

4.1.Model-free estimation of activation energy

Fig.1 shows the TG curves of different samples measured in the N2atmosphere with the heating rates of 10,15,20 and 25°C·min-1.Continuous mass loss is observed for the mixtures of A90and K2CO3, which is considered as coupled dehydration and reaction.It is diff i cult to determine the initial reaction temperature directly.The theoretical mass loss can be calculated combined with experimental measurement to obtain the initial reaction temperature.There are two obvious mass loss stages for the mixtures of A10 and K2CO3.The mass loss in 100-200°C is due to the dehydration and that in 500-850°C is by the reaction of A10and K2CO3.The use of nano-TiO2reduces the initial reaction temperature to form K2Ti2O5.Since mass loss processes f i nish at almost the same temperature for both reactions,the complete conversation could be achieved under similar conditions.

A series of dynamic scans with differentheatingrates results in a set of data,which present the same degree of conversion(α)at different temperatures.Eqs.(4)and(5)areusedtodeterminethekinetic parameters without assuming a certain model and the results are shown in Fig.2.For nanoparticles A90,the activation energy increases with the conversion at the beginning of the reaction(α＜0.2)and then changes about the value of 180 kJ·mol-1until α＞0.8.For microparticles A10, the activation energy is almost constant,210 kJ·mol-1,at conversions lessthan0.7andthenincreases.Theloweractivationenergywithnanoparticles suggests that they are easier to form products in the initial reaction.The activation energy has different values and depends on α, which may be due to the mass or heart transfer,or because of parallel and/or successive reactions[34].The weight loss has the same value at different heating rates,so successive reactions occur for both TiO2materials[35].Therefore,the reaction processes are complex.

Fig.1.TG curves of K2CO3-TiO2mixtures under nitrogen atmosphere with different sizes of TiO2.

Fig.2.Dependence of activation energy on conversion with different sizes of TiO2.

4.2.Reaction mechanism and kinetic parameter analysis

The dependence of activation energy on the conversion shows the complexity of the processes.In this case,the kinetic model and parameters are determined by a method of multivariate non-linear regressions.The conversion of 0.05≤α≤0.95 is considered.Among allkinetic models in Table 1,according to the f i tting quality,the kinetic schemeofthereactionofK2CO3withA90andA10as startingmaterials is

respectively.The kinetic parameters for the two reactions are listed in Tables 3 and 4.

The above kinetic scheme shows that,for both reaction processes, reaction Fnis the most probable reaction in the early period,in which experimental conditions,such as temperature and CO2partial pressure at the interface,may have a signif i cant inf l uence on the reaction rate. When the conversion is higher than 0.58,the reaction mechanism of A90and K2CO3is represented by nucleation and growth model [36-41],in which the solid-state reaction proceeds with the formation of new solid phase by nucleation and subsequent nuclei growth, where reaction interfaces increase until growing nuclei overlap extensively and then decrease[42].As the reaction proceeds further,the rate-limiting step is diffusion controlled,indicating that the local product layer may form and chemical reaction with TiO2is on the outer surface of the local product layer by ion diffusion.With TiO2microparticles as starting material,the diffusion is the controlling step when the conversion is between 0.21 and 0.53,with nucleation and growth in the later reaction stage,which implies that the reactants diffuse into reaction sites on the TiO2and reaction interfaces increase.

Forthetworeactions,thevaluesofnare0.88and1.06fornucleation andgrowthprocesses,closeto1.Thevalueof ndependsontheshapeof nuclei,the number of nuclei present at the beginning of reaction and their distribution in the particles[43].The value of n is also related to the morphology or directionality of crystal growth.Lower values of n ref l ect a lower order,such as linear crystal growth[44].It has been reported that K2Ti2O5f i bers could be prepared by low-temperature calcination using amorphous titania and anatase as raw materials[45].It indicatesthatK2Ti2O5maybeapttogrowinone-dimensionalstructure. 4.3.Factors affecting reaction rate

4.3.1.Temperature

The reaction rate constant can be obtained using the Arrhenius equation in the following form

The reaction rate constant k,which depends on temperature and reactionconversionforreactionsinvolvingseveralsteps,canbecalculated by activation energy Eαand pre-exponential factor determined by multiple non-linear regression analysis.

Fig.3 shows that the rate constant k increases with temperature,as commonly known that high temperature is benef i cial in most solidstate reactions.With A90as a raw material k is higher when the conversionislessthan0.58,otherwiseitisratherlow.Rapidformationofproduct layer surrounding the unreacted TiO2core could be the reason. However,for the reaction with A10,higher k value appears only at the beginning of the reaction(α＜0.21).The rate constants are lower in the two reactions when the conversion is higher than a certain value, 0.59 and 0.53 for A90and A10,respectively.In the later stage,k values are almost the same at lower temperature.With increasing temperature,the k value for A10as a raw material is a little higher and the inf l uence of temperature is more signif i cant.

Table 3Non-isothermal kinetic parameters with non-linear regression for the reaction of K2CO3with A90

Table 4Non-isothermal kinetic parameters with non-linear regression for the reaction of K2CO3with A10

Fig.3.Reaction rate constant at different temperatures for A90(a)and A10(b).

4.3.2.Size of raw materials

The specif i c surface area of powders A10and A90is 10 m2·g-1and 90 m2·g-1,respectively corresponding to the equivalent particlediameters of 234 nmand 16 nm,respectively and crystal sizecalculated from the XRD peaks by the Scherrer equation is 44 nm and 18 nm,respectively(Table 2).The equivalent particle diameter is very close to the crystal size of A90.However,the equivalent particle diameter has quite a higher value for A10,compared with its crystal size.The possible reason is that the f i ne crystallites of TiO2powder are pulled together to form large hard particles during the preparation process of A10[46].

The conversion predicted by the kinetic model is shown in Fig.4,for three temperatures in the range of 600-800°C.For solid-state reaction of K2CO3and A90,the conversion is 0.73 at 600°C and 0.96 at 700°C for 60 min,while it takes only about 20 min to react completely at 800°C. Forsolid-statereactionofK2CO3andA10,theconversionis0.50and0.93 at 600°C and 700°C,respectively.For both reaction processes,the conversions increase dramatically in the initial stage of the reaction and then increases slowly with time.The initial reaction rate with A90is higher because of more reaction active sites on smaller particles and lower reaction activation energy.It is worth noting that for both materials the conversion reaches about 0.90 at 60 min at 700°C and the time for complete reaction is almost the same at 800°C.A recent study on the formation of BaTiO3in a solid-state reaction has shown that BaCO3and TiO2may be completely separated from the reaction product and this is likely to correspond to the slowing down of the solid-state reaction because further growth can only proceed by the slower lattice diffusion[47].It indicates that when the solid-state reactionmechanismisiondiffusioninthef i nalstageofthereactionprocess, the reaction rate is rather low and may be related with the thickness of productlayer.Thus thecomplete conversionwill be sensitivetoparticle size during synthesis.It is presumed that this is one of the reasons that cause wide variations in calcination conditions for K2Ti2O5synthesis [45].

Fig.4.The predicted conversion vs calcination time for selected temperatures for A90(a)and A10(b).

Fig.5.X-ray diffraction(XRD)patterns(Cu Kα radiation)of K2CO3-TiO2mixtures for different sizes of TiO2A90(a)and A10(b)calcined at different temperatures for 60 min.?K2CO3;○?TiO2;▽?K2Ti2O5.

4.4.XRD characterization

The K2CO3-TiO2mixtures were heated to different temperatures at 30°C/min and then held at 550,600,650,and 700°C for 60 min in TG equipment.For different sizes of TiO2the XRD patterns of products and raw materials are shown in Fig.5.TiO2characteristic peaks weaken or disappear with a risein temperature,with thecontinuous increase in the intensity of K2Ti2O5characteristic peak at 29.16°.Characteristic peaks of K2Ti2O5exist even at 550°C for both materials,and there is no evident TiO2characteristic peak at 25.34°for the reaction of A90 and K2CO3,which indicates that the main composition is K2Ti2O5.ObviouscharacteristicpeaksofTiO2stillexistat650°CforA10asaprecursor, but only peaks belonging to K2Ti2O5can be observed at 700°C.AccordingtoKlug'sequation[48],theweightfractionisrelatedwithintegrated intensities and mass absorption coeff i cients,and higher integrated intensity suggests a higher content.We can see that as temperature increases,the integrated intensities at 29.16°corresponding to K2Ti2O5phase increase and are higher with A90as a raw material in the temperature range,which means that theconversion may be similar under the condition.This is in agreement with our calculation described above.

5.Conclusions

The kinetic mechanism and parameters can be determined by nonlinear regression for complex solid-state reactions without previous assumption.Kinetic parameters are different for reactions of K2CO3with different sizes of TiO2.The values of n,nearly 1 for nucleation and growth processes,indicate that K2Ti2O5is apt to grow in onedimension,which is in agreement with reported experimental results. With smaller size TiO2as raw material,the initial reaction temperature is lower and the lower activation energy in the initial reaction suggests thatitiseasiertoformproductsinthisstage.However,thereactionrate could signif i cantly decrease when diffusion process of reactant species becomes rate-limiting in the later stage of the reaction process.

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21 January 2013

☆Supported by the Chinese National Key Technology Research and Development Program(2006AA03Z455),the National Natural Science Foundation of China (20976080,21136004)andtheNationalBasicResearchProgramofChina (2009CB226103).

*Corresponding author.

E-mail address:xhlu@njut.edu.cn(X.Lu).

http://dx.doi.org/10.1016/j.cjche.2013.04.001

1004-9541/?2014 The Chemical Industry and Engineering Society of China,and Chemical Industry Press.All rights reserved.

Received in revised form 15 April 2013

Accepted 22 April 2013

Available online 23 August 2014