Powder Technology 259 (2014) 109–116
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Morphology evolution of exfoliated trimanganese tetroxide nanosheets and mass transfer model of growth kinetics in supercritical N,N-dimethylformamide Lixi Yi a, Guoxin Hu a,⁎, Hao Huang b a b
School of Mechanical & Power Engineering, Shanghai Jiaotong University, Shanghai 200240, China Shanghai Marine Diesel Engine Research Institute, Shanghai 201108, China
a r t i c l e
i n f o
Article history: Received 17 October 2013 Received in revised form 24 March 2014 Accepted 26 March 2014 Available online 1 April 2014 Keywords: Supercritical N,N-dimethylformamide Manganese oxides Accelerated growth Growth kinetics Mass transfer model
a b s t r a c t Trimanganese tetroxide (Mn3O4) nanosheets can evolve into various morphologies in supercritical N,N-dimethylformamide (SC-DMF), including particulate materials, triangle, rhombus, cube, and other regular polyhedrons. The obtained polyhedrons have sizes from hundred nanometers to several micrometers (1–3 μm), along with a growing course. The phases are changed from Mn3O4 to MnO, as the processing time increases. The growth of manganese oxides in SC-DMF has a rate of 28.7–61.5 nm·min−1. The phenomena of accelerated growth for manganese oxides in supercritical ﬂuid are discovered. The growth kinetics of manganese oxides is performed by the classical Lifshitz–Slyozov–Wagner (LSW) model. A mass transfer (MT) model of growth kinetics applicable to supercritical ﬂuid surrounding is proposed. Solubility and diffusion, as main factors, are included in the proposed model. The theoretical model and the ﬁtting curve are in accordance with experimental results. The growth of manganese oxides in SC-DMF satisﬁes the ﬁrst-order kinetics, obeying the exponential law. © 2014 Published by Elsevier B.V.
1. Introduction In nanofabrication and processing, nanomaterials contain nanoparticulate matters, nanorods, nanosheets, and various bulk polyhedrons. Nanomaterials with special shapes and different sizes can give rise to extraordinary properties as reported in many references. Trimanganese tetroxide (Mn3O4) nanosheets can give rise to unique magnetic properties with a low Curie–Weiss temperature (Tc) and a great coercivity, for the special two-dimension structure . Mn3O4 nanoparticles can be applied to a rapid removal of trace pentachlorophenol and phenol [2,3]. Mn3O4 nano-octahedrons can enhance supercapacitor performances  and lead to an unusual property of photodecomposition . Moreover, anomalous magnetic properties of the phase transition, between ferromagnetic and paramagnetic phases at 27 K, exist in manganese monoxide (MnO) nanoclusters . Magnetic properties of Mn3O4 and MnO nanoparticles depend on their sizes as well . Specially, uniform-sized MnO nanospheres and nanorods with nanosizes possess two blocking temperatures . All of these suggest that the morphology control of nanomaterials is important . Nevertheless, the morphology, in shaping and size controlling, is not easy to be achieved in industrial production. Supercritical ﬂuid (SCF) is a kind of ﬂuid with a large compressibility, and a small change near the critical point can give rise to substantial
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http://dx.doi.org/10.1016/j.powtec.2014.03.062 0032-5910/© 2014 Published by Elsevier B.V.
changes in density and the related properties, solubility and diffusion, which can dramatically affect the kinetics of reaction. Consequently, SCF can be used to the exfoliation of graphite to obtain graphene nanosheets [9,10], to the exfoliation of the layered titanate into titania nanosheets  and to the exfoliation of layered manganese oxides for the acquisition of Mn3O4 nanosheets . The synthesis of Fe2O3, Cu2O, Cr2O3 Al2O3, and Ga2O3 in SCF of CO2/ethanol also has been developed since many years ago [13,14]. However, the reaction of manganese oxides in SCF is seldom involved, especially in organic solvents. Compared with normal methods [15–17], special conditions of temperature and pressure are provided in the process of SCF, and therefore the SCF processing can be as a contrast to normal solvothermal methods  and the behavior not under supercritical conditions [15,17]. Supercritical ﬂuid can be utilized to control the morphology of manganese oxides, and unique behaviors of manganese oxides in SCF are desired to be found in the SCF processing of manganese oxides. In SCF processing, the involved Ostwald ripening growth is from the early material investigations , transport properties of ﬂuids belong to chemical engineering, the reactor design depends on mechanical engineering [19,20], and there is a joint of these areas for the procedure of SCF. Therefore, the reaction course in SCF is the result of complex factors, from several aspects of different disciplines. The roles of SCF are taken as the reaction media, the structure-directing agent, to tailor the morphology of manganese oxides for its compressibility and local inhomogeneity, and the agent for an excellent dispersion in reactor, which have superiority distinguished from solvents under normal conditions.
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The high solubility and diffusion of SCF can give rise to the extraordinary evolution of layered manganese oxides (δ-MnO2) after exfoliation. The processing time is a key parameter for manganese oxide growth, and the classical growth rule by Lifshitz–Slyozov–Wagner (LSW) is often applied to a slow growing course, such as the course resulting from electrostatic interaction for the environment of hydrogen ions . However, little discussion involves the growth case for a swift mass transfer course. The supercritical processing is fast course for the swift mass transfer and high diffusion of supercritical ﬂuid. The growth behavior and rule in the swift mass transfer course may be distinguished from the normal growth course. The LSW model is the solution of slow process. Whether this model can be directly applied to the rapid course is undetermined and not attempted. Seeking a growth rule suitable to the rapid growing course is the challenging key problem to understand the rapid growing course. In this article, supercritical N,N-dimethylformamide (SC-DMF) is utilized for the processing of manganese oxides, differently from acid reagents and solvents widely used in normal methods. Considered from production, strong acids are corrosive strongly, which will damage the equipments easily, and therefore DMF is an optimal choice for production. The morphology evolution of Mn3O4 nanosheets in SC-DMF is presented using scanning electron microscopy (SEM) and transmission electron microscopy (TEM), mainly including the manganese oxide crystals for different growth time, after the exfoliation of layered manganese oxides in SC-DMF. The growing course of manganese oxides is clariﬁed. Material phases of manganese oxide are determined using X-ray diffraction (XRD) to show the change of phase structure in crystal growing and shaping course. Sizes of shaped manganese oxides, with different keeping time in SC-DMF, are estimated using TEM. The mixture concentration is related to the mass of source matter provided for growth, which is treated as an indirect intermediate variable; utilizing the relation of intermediate variable, a mass transfer model of the relation between crystal size and growth time is constructed for the crystal growing course. The Lifshitz–Slyozov–Wagner model and the proposed model are performed on the kinetics of crystal growing course. These two models can give an excellent explanation on the crystal growing course qualitatively, but the proposed model is applicable to the supercritical reaction environment, giving an excellent agreement with experimental results. 2. Experimental section 2.1. Materials Potassium hydroxide (KOH) and manganese oxide (Mn2O3) were purchased from commercial products. N,N-dimethylformamide was analytical reagent (Sinopharm Chemical Reagent Co., Ltd, China). 2.2. Preparation of precursors and manipulations According to the scheme in Ref. , layered manganese oxides were obtained by a ﬂux grown method. A stoichiometric mixture of KOH and Mn2O3 was calcined at 1073 K for 60 h under O2 gas ﬂow. The obtained compound manganese oxide, K0.45MnO2 (5 g), was treated with 1 dm3 of HCl solution (1 mol·dm− 3). The acid solution was replaced with a new one daily. Repetition of this acid treatment procedure for 10 days achieved nearly complete removal of interlayer alkali metal ions and expanded the gap between layers. The resulting solid, H0.13MnO2·0.7H2O (HMnO), was washed with copious amounts of water and then air-dried. Supercritical process was realized in a 15 ml sealed stainless-steel reactor. The layered manganese oxides (25 mg) were added to a container and dispersed in 10 ml DMF by low-power sonication (40 kHz, maximum output 180 W) for 15 min. The mixtures were carefully injected into the stainless-steel reactor.
To obtain the samples for the investigation on the evolutional behaviors of manganese oxides in SC-DMF, the sealed reactor was heated up to a preset temperature (400 °C) within 30 min in a tube furnace (DMF critical point: 377 °C, 4.4 MPa). The sample with a short keeping time (labeled as 0 min in collected data) was prepared by putting the hot reactor into an ice-cold water bath to terminate the reaction, as soon as the temperature reached 400 °C. The samples of 5 min, 10 min, 15 min, and 20 min under 400 °C in discussion were acquired by keeping the corresponding time after the temperature reached the preset temperature 400 °C, and then the reaction was terminated with ice-cold water bath. 2.3. Characterization X-ray diffraction (XRD) was performed using a D8 Advance X-ray diffraction apparatus (Cu Kα copper radiation of λ = 0.15405 nm, 40 kV and 40 mA) to examine the samples at the steps of 2θ = 0.02°. Scanning electron microscopy (SEM) images were obtained using a FEI Sirion 200 ﬁeld-emission scanning electron microscope operated at an accelerating voltage of 5.0 kV. The samples of manganese oxides for the observation of SEM were sputtered by Au. Transmission electron microscopy (TEM) images were acquired by a JEM-2100F transmission electron microscope operated at 300 kV. The samples for observation of TEM were prepared by dripping a droplet of suspension with the collected sample on a 300 mesh size micro-grid. 3. Results and discussion 3.1. Morphology 3.1.1. Acquisition of exfoliated sheets for short keeping time in SC-DMF The layered manganese oxide after acid treatment (HMnO), with the birnessite layered structure 1 × ∞, has the phase of δ-MnO2 combined with hydrogen bonding water , which is consistent with reported literatures . After the treatment with SC-DMF, the layered manganese oxide HMnO takes on an obvious change in morphology. Fig. 1(a) is the retrospect view for the sample from SC-DMF with the temperature reaching 400 °C for a short staying time, and 0 min is labeled for this case in discussion. Fig. 1(b) is the cracked sheets from the reactor with the keeping temperature at 400 °C for 5 min before terminating the reaction . The preparation of samples followed the same manipulations; however, the morphologies of the samples, for a short staying time and 5 min, are different enormously. The obtained Mn3O4 nanosheets can be attributed to the exfoliation of layered manganese oxides for the intercalation of SCF [9–12]. The sheets were smashed in the 5 min keeping time, and meanwhile there appear some formed crystals with small size. Therefore, the keeping time in SC-DMF is crucial for the morphology change, and the range from 0 min to 5 min is a transition interval from sheets to small particulate materials for crystal growth . The change of morphology is obvious for the arrival to supercritical state, which demonstrates that the SCF plays important roles for a rapid intercalation and exfoliation in the evolution of morphology [10,11]. Taking the exfoliated sheets as the precursors, the further evolutional behavior of manganese oxide also will behave a distinguishing growth, for the effect of keeping time in SCF. 3.1.2. Morphology evolution of manganese oxides in SC-DMF — from nanosheets to giant polyhedrons To investigate the effect of time on crystal growing behavior in supercritical ﬂuid, the layered manganese oxides, keeping in SCF-DMF for a short time, 5, 10, 15 and 20 min, were prepared, respectively. The observation of morphology with SEM is presented in Fig. 1(a)–(e), corresponding to the above respective cases. The exfoliated sheets and the smashed particulate materials exhibit in Fig. 1(a) and (b), respectively. The crystal volume grows, as indicated from Fig. 1(c) to (e). The
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Fig. 1. Schematic illustrations on the evolution of manganese oxides in supercritical N,N-dimethylformamide. (a)–(e) SEM images of manganese oxides keeping in supercritical N,N-dimethylformamide for a short time, 5, 10, 15, and 20 min, and panels a–e are the corresponding TEM images, with the scales of 100 nm for panels a–b and 0.5 μm for panels c–e.
evolution is from the particulate materials with a few nanometers to the polyhedrons with hundreds of nanometers, and then to the polyhedrons with a few micrometers (1–3 μm). There is a trend that the shape is from a wafery triangular shape to triangular cone, to rhombus, to cubic shape and to other regular polyhedrons. The evolution of geometry is consistent with the rule from the simple form to the complex form, and from the irregular to the regular form, which agrees with the surface energy trending to keep the growing system steady, with an optimal energy . The shape of manganese oxides for the evolution also can be indentiﬁed with the observation of TEM. The pieces in the scope of observation have an increased dark contrast to the background, which shows the shape from thin ﬂakes to bulk shape (Fig. 1 or Fig. S1 of Supplementary information). In addition, the borders of the nanomaterial conﬁguration have a proﬁle from curve to multi-straight-line, as the time increases. There are three, four, and more than four borders, as shown from panel a to panel e in Fig. 1. Though not as intuitionistic as the observation of SEM, it indicates the evolution of the morphology of polyhedrons. All of these results are consistent with the observation of SEM and further conﬁrm the information of manganese oxides from a planar view. 3.1.3. Scheme on the evolution of morphology The scheme on the evolution of layered manganese oxides has been sketched in the middle part of Fig. 1, the path along the direction labeled by arrows. The scheme exhibits the further cracked course of exfoliated Mn3O4 nanosheets, a ﬁerce motion along with the course of nucleation and a growing course for the shape formation. However, these courses could not be seriously divided, and there is an overlapped part between formation of particulate materials and crystal growth, which can be seen from the observation of SEM, as given in Fig. 1 from (a) to (e). The overlapped courses will also be exhibited in the statistical results of TEM in latter section. The crystal volume is determined by the period of the nucleation formation and growth time before the termination of colloid reaction. The overall size of the different shapes is increased. The shapes are formed by virtue of the aggregated particulate materials and the decrease of total energy for two-phase system via the Ostwald ripening mechanism . The various polyhedrons result from a different local environment, the local inhomogeneity of SCF in reactor. The behaviors of supercritical ﬂuid in reactor, especially the
example of cylinder reactor, are extensively simulated in literatures [19,20,24]. Just as the simulated results in literatures [19,20], the gradient and the distribution of temperature, velocity and density, from the cross-section, demonstrate that the ﬁelds can give rise to the local inhomogeneity. The nonuniform ﬁeld for the local inhomogeneity impacts on the shaping course of crystal, and various shapes and different sizes of polyhedrons are formed though within the same growth time. 3.2. Determination on the phases of manganese oxide To conﬁrm the phases and the lattice change of manganese oxide in the growing course, XRD for the samples keeping in the reactor with SC-DMF, for a short time, 5, 10, 15 and 20 min, was performed, and the results are given in Fig. 2. Characteristic peaks of the tetragonal hausmannite Mn3O4 phase  exist in Fig. 2(a) and (b), labeled by triangles (▼). However, according to the XRD spectrum in Fig. 2(c), characteristic peaks of the MnO phase with a rock salt structure [6,25], with an increased intensity, begin to turn up from the case for keeping 10 min. These characteristic peaks of MnO phase are inherited in the cases for 15 min and 20 min, which indicate that the transition from Mn3O4 to MnO took place for the samples keeping more than 10 min, and these characteristic peaks become more sharp for the samples keeping more than 15 min. The increased intensity shows the degree of conversion, so the conversion is enhanced as the reaction time increases. The noises in line shape are decreasing from 0 min to 20 min, and it implies that the degree of crystallization trends to be high. The peaks of XRD are changed from amorphous to sharp peaks, which indicate the formation and growth of crystal as well. The transition is from MnO2 to Mn3O4, and then to MnO. The quantity of oxygen content is reduced in the sequence of MnO2, Mn3O4 and MnO, and therefore there is an oxygen releasing course along with the course of crystal growth. The loss of oxygen is consistent with the fragility of Mn\O bond as comparisons in references . The valence of Mn is changed from +4 for MnO2 to the mixed +3 and +2 for Mn3O4  and +2 for MnO, and there is an electron obtained course for Mn. In addition, the relative content of magnetic Mn is increased, which indicates that the ions of Mn are dense in the growing course. The dense magnetic ions can be attributed to the interior factor of manganese oxide for a rapid formation of crystal. These behaviors of Mn and O also indicate the face ﬂatting in the growing course.
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(d) Intensity (a.u.)
3.4. Growth kinetics of manganese oxides in SC-DMF
112 200 103 211 004
recovers the standard Gaussian shape as demonstrated in Fig. 3(e). Deep information can be revealed from the changes of the proﬁle of the statistical results for the time effect. The skewed proﬁle shape, in the intermediate stages as given in Fig. 3(c) and (d), is consistent with the fact that the cracked course and growing course are mixed. The skewness, trending from the left to the right, indicates that the main aspect is from the cracked course of sheets to the crystal growing course, as demonstrated in the statistical results from Fig. 3(b) to (e). In addition, the center position of the proﬁle is shifted from a small size to a large size, from Fig. 3(b) to (e), which conﬁrms the growing course of crystal. Moreover, on the basis of the above analysis, it suggests that the nucleation mostly takes place in initial stages and the growth is mainly in the following stages.
Fig. 2. X-ray diffraction patterns of manganese oxide from supercritical N,Ndimethylformamide. (a) A short time (0 min), (b) 5 min, (c) 10 min, (d) 15 min and (e) 20 min for manganese oxides kept in supercritical N,N-dimethylformamide. The symbol ▼ labels the suppressed peaks as the increased keeping time, and the symbol ▲ denotes the rising peaks of MnO phase. The labeled peak (▼) in line (e) is the inherited characteristic peak of the Mn3O4 phase.
3.3. Statistical results of sizes from TEM TEM generally can be used to identify the sizes of nanomaterials from a plan view with few inﬂuences from the depth of ﬁeld in photography. To conﬁrm the growth for the effect of time and the size of crystals, TEM observation was performed on the samples kept in SC-DMF for a short time, 5, 10, 15, and 20 min. Many regions were observed, selected images are provided in Fig. S1 of Supplementary information and the statistical results are given in Fig. 3. From the main size distribution in the statistical column charts, it can be found that there is a trend from small to large size, as the keeping time increases. The distribution of sizes is from the magnitude of nanometers to that of micrometers. The width of the distribution above 5%, as the main distribution, is 20–90 nm in Fig. 3(a), 20–90 nm in Fig. 3(b), 0.2–1.5 μm in Fig. 3(c), 0.2–1.1 μm in Fig. 3(d) and 0.6– 2.0 μm in Fig. 3(e), respectively. Nevertheless, there is an inﬂection near 5 min. Comparing the center position of size distribution, the main size distribution in Fig. 3(a) is smaller than that in Fig. 3(b), and therefore the trend of size distribution decreases initially but increases after 5 min keeping time. The inﬂection near 5 min also conﬁrms the cracked courses of sheets after exfoliation pointed out in the previous literature . Scales for the collection of TEM and the direct view of images also reﬂect the change of size and the growth of crystal, as given in the TEM images from panel a to panel e in Fig. 1. The Gaussian distribution of diameter size is obvious in the initial stages for a short keeping time, as demonstrated in Fig. 3(a) and (b). However, as the keeping time in SC-DMF increased, the regular distribution breaks, and the proﬁles exhibit a skewed Gaussian distribution in Fig. 3(c) and (d). As the keeping time increased further, the proﬁle
3.4.1. Rapid growth with accelerated phenomena to giant size The new phase of mixture and the local inhomogeneity in reactor provide the environment for nucleation. When the nucleation exceeds the critical size, the nucleation can give rise to the formation of crystal, and a crystal growing course is followed in SC-DMF. The size of a grain can reach near 3 μm, which is larger than the previous reported sizes in references [15,27,28]. The growth rate is promoted obviously, both from the size increment of Fig. 4(a) and the trend line of growth rate in Fig. 4(b). As for the reported situation, the growth rate is about 1 nm·min−1 within the range of an hour , which is a relatively longer time compared with the situation in this work. Furthermore, in this work, the growth rate reaches up to 61.5 nm·min−1 between 15 min and 20 min in the growing course. Besides the minus value of − 6 nm·min−1 near 5 min for a cracked course, the rate is about 33 nm·min−1 near 10 min and 28.7 nm·min−1 near 15 min, respectively. There exist the phenomena of accelerated growth for manganese oxides in SC-DMF. It indicates that the growth is slow in the mixtures with a high concentration, when the main aspect is nucleation for growth. As the concentration is reduced, the solute in the mixtures can well take part in the growing course around the already existent growth centers. On the other hand, the special magnetic properties can be attributed to the main factor on the rapid formation of crystal, distinguishing from titania and graphite as the comparisons in references , and therefore the enhanced magnet, along with the growing bulk as the growth center, accelerates the growth. The magnetic distance is short in the initial stage for nucleation, and the extended magnetic range as the growing bulk broadens the capture space of solute. In addition, as acquired from XRD, the magnetic Mn contents become dense, which also facilitate the accelerated growth. The shape and size distribution of manganese oxides, including Mn3O4 and MnO reported in literatures, is listed in Table 1 as a comparison. Obviously, there are several shapes and a wide range of sizes for the manganese oxides processed from SC-DMF. The table provides the comparison on morphology, and the morphology comparison exhibits the shapes to be regular for the morphology involution in growing course, agreeing with the growth mechanism by Ostwald. In addition, from the comparison among the cases in literatures, generally the morphology trends to be regular shapes for the preparation with long time and this also agrees with the growth mechanism. Supercritical processing can produce giant manganese oxide grains. The process time for preparation is also listed in Table 1 together. Besides the methods utilizing laser [2,27], most of the methods are slow process mainly for the effect of acid environment. 3.4.2. Classical Lifshitz–Slyozov–Wagner (LSW) theory — growth kinetics of manganese oxides in SC-DMF Lifshitz–Slyozov–Wagner (LSW) model can be employed to a quantity understanding of growth kinetics for transition metal oxides, which has been applied to the growth kinetics of nanoparticles .
L. Yi et al. / Powder Technology 259 (2014) 109–116
Fig. 3. Statistical results of diameter distribution from TEM observation. (a) A short time (0 min), (b) 5 min, (c) 10 min, (d) 15 min, and (e) 20 min for manganese oxides kept in supercritical N,N-dimethylformamide. Height of every rectangle represents the count percentage of corresponding size interval. The increment of statistical interval is 10 nm for panels a–b and 0.1 μm for panels c–e.
Coarsening of crystal is driven by the dependence of solubility of solid phase on the particle size according to Gibbs–Thomson relation [15, 38]. From the theory of coarsening , if the particles are treated in a spherical form, the solubility is cr, and a particle with a radius r satisﬁes the relation  2γV m 1 ; cr ¼ c∞ exp RT r
where c∞ is the solubility at a fat surface, γ is the surface energy of the solid, Vm is the molar volume, R is the gas constant, and T is the temperature. For the case (2γVm / rRT) b 1, the exponential term in Eq. (1) can be linearized. Assuming that the growth rate is determined by the
diffusion of solute from the smaller particles to the larger particles, the rate law for crystal growth can be obtained as
r −r0 ¼
8γDV 2m c∞ t; 9RT
where r is the particle radius at time t, r0 is the particle radius at time zero, and D is the diffusion coefﬁcient. More details can be referred to literatures [23,39]. However, the increment for the law of t1/3 slows down when time increases, which is the character of convex function. The line shape will be upward arch-shaped for the increment slowing down, as the lines given in references [15,38]. The straight line is the limit for the line shape of ﬁtting curve. The ﬁtting curve according to the LSW model is shown in Fig. 4(a) and labeled by LSW. On the contrary, the
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oxides in supercritical ﬂuid. Under an equivalent temperature, the diffusion coefﬁcient for the same ﬂuid under supercritical state is generally larger than that under normal states, and the saturated concentration is enhanced. So the factors, such as c∞ and D as the coefﬁcients in Eq. (2), will be larger for the case in supercritical ﬂuid than the ﬂuid not under supercritical state, and the coefﬁcient characterizing the growing rate before t is larger than normal methods. It is demonstrated that the gradient of growth rate in SCF is more precipitous than the normal method  as shown in Fig. 4(b). So the theoretical explanation can be consistent with the increasing trend of experimental data. The different results between SCF processing and normal methods can be attributed to the enhanced solubility and diffusion of SCF.
Fig. 4. Growth and rate curves. (a) Growth of manganese oxides varying with time in supercritical N,N-dimethylformamide and (b) growth rate compared with the normal method under low temperature . The ﬁtting curves in panel a are given according to the LSW model in the form of Eq. (2) and the mass transfer (MT) model from the concentration in the ﬁrst order. SCF and Ref in panel b label the corresponding rate line for SCF processing and the method in literature, respectively.
trend of experimental data has a down arch-shaped line shape of concave function, and therefore the unsatisﬁed ﬁtting can be accepted. The deep reason is that the construction of LSW model depends on the mathematical solution, and the based assumption is in the case of slow process [23,39]. Some detailed discussion is provided in Supplementary information. Despite of the unsatisﬁed ﬁtting of data by LSW theory, the theoretical explanation is applicable to the growing course of manganese
3.4.3. Mass transfer model for the growth kinetics in supercritical ﬂuid To complete the consistency between the growth kinetics and experimental course, a mass transfer model, applicable to supercritical ﬂuid environment, is proposed. In fact, the mass transfer of particulate matters as the solute in supercritical ﬂuid is discussed often in literatures. The reported cases are considering to make the poorly-soluble active ingredients micronized into nano-particles [40,41], but the crystal growth is a course of aggregation for the already existing solute. The formation of crystal and crystal growing course can be considered as the inversed course as discussed in the pharmaceutics by supercritical processes . In addition, the particle size is related to concentration [42,43]. Starting from this assumption, a mass transfer model for the crystal growth is constructed to give the relation between the size of crystal radius and growth time by virtue of an intermediate variance, the concentration of mixtures. The physical scenario is exhibited in Fig. 5. Fig. 5(a) shows the crystal growing course. Dissolution of small crystals or sol particles and the redeposition of the dissolved species on the surfaces of larger crystals or sol particles realize the crystal growth as described by Ostwald . In the formation course, the surface of the combined particulate matters will shrink as a whole, as shown in Fig. 5(b), to decrease the energy for the new steady system. In the initial stage of nucleation, the new phase of mixtures has a concentration, C(0). As the crystal grows, the concentration will be reduced, and therefore the concentration is the function of time, C(t). Because of the swift mass transfer of supercritical ﬂuid, the global concentration can be adjusted and reach a new equilibrium instantly as the reduction of concentration. On the other hand, the volume of crystal is enlarging, and the radius, r, is also the function of time. The related quantity is the mass reduced from the surrounding solution of nucleated crystal and the increased mass of crystal. Assuming the density, ρ, of the solute before aggregation approximately equals to that after shape formation, the mass, as the related quantity, will be conservative, which is notated as the differential form dm. The changed
Table 1 Shape, size distribution, and process time of manganese oxides reported in literatures. Method
Hydrothermal method (Mn3O4)
Sheets, cubes, rhombohedral shapes, nanorods, octahedron
Synthesis at low temperature in air atmosphere (Mn3O4) Phase separation (Mn3O4) Vapor phase growth (Mn3O4) Thermal decomposition Decomposition of Mn(acac)2 (Mn3O4/MnO) Modiﬁed polyol method (Mn3O4) Laser ablation (Mn3O4) Soft template self-assembly Ultrasonic-assisted synthesis (Mn3O4) This work (Mn3O4/MnO)
Nanoplates, spherical nanocrystals, nanowires and nanokites Nanocrystals (rectangular) Nanocrystals (spherical, cubic) Nanoparticles Microscale supercrystals (cubic), nanocrystals (octahedral) Nanocrystals (cubic and octahedral), spherical nanocrystals Nanocrystals, particles Nanoparticles Nanocrystals, octahedral, quasi-spherical Nanoparticles Flakes, sheets, particle, polyhedron
150 nm 10 nm–180 nm (colloidal sphere ~1 μm) 160 nm 5.5–22 nm
12 h 8h ~24 h 4h ~3 h
    
~125 ± 10 nm (height ~75 ± 5 nm) 5.0–13.4 nm 25–60 nm 15–30 nm
0.1–2 nm·min−1 4h 90 min 45 min–10 h
   
N60 min, 2 h
5–10 nm ~8.2, 7.1, 9.2, 30 nm 7.1–9.2 nm (15–30 nm for aggregation) 5–10 nm 10 nm–3 μm
2h 30 min One day 5h ~20 min
   
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Fig. 5. Crystal growing course. (a) The top part shows the crystal growing course and the concentration reduction, the length of arrows indicates the magnetic range for capture, and the cycle labels a center for nucleation and growth. (b) Geometry and differential relation of the variance of mass are given at the bottom of picture.
quantity of mass dm is assumed to equal to the captured solute in the surface (S) with the radius of r + dr as shown in Fig. 5, where r is the radius of crystal at the time t, and the growing bulk is treated to be a sphere as in the LSW theory. So now, if the average of moving velocity for solute is V, which is related to diffusion coefﬁcient of ﬂuid D, the equal relation of mass, for a single growing crystal, can be obtained as δ V dt S Cðt Þ ρ ¼ dm ¼ S dr ρ:
The coefﬁcient δ is the regulation on the difference of concentration varying within time dt and the correction on the difference of solute between before aggregation and after shape formation with the face ﬂatting. For convenience, δ V is notated by D (V). From the analysis of dimension, the constant D (V) has the unit of (L/T)(L3/M), which includes the factor of velocity related to diffusion and concentration related to solubility, as well as the regulation of difference in growing course. So, D (V) is the characteristic value considered the integrated effect of solubility and diffusion. According to Eq. (3), the differential relation can be given as dr ¼ D V CðtÞ: dt
Therefore, the size of the growing crystal is related to the diffusion of ﬂuid and the solute concentration of particulate matters. The concentration is high for an excellent solubility, and the swift mass transfer results from the high diffusion of supercritical ﬂuid, which are the main factors promoting the rapid growth in supercritical processing. The crystal size is related to the solute mass that can be provided for crystal formation. The high solubility provides a plentiful source for the growth to form a giant bulk. To solve the kinetic equation of crystal growth, the variance of concentration is the key. Generally, the kinetics of concentration in reaction obeys the zero, ﬁrst, second, and third order law . Considering the reaction as the single component of particulate matters, A, converted into the giant block, αA → B;
the product B is the reactants after the formation of shape with face ﬂatting. The discussion on the relation of corresponding order kinetics is provided in Supplementary information.
As evaluated from the shape of ﬁtting curves, the values of parameters, and the coefﬁcient of determination, the ﬁrst order kinetic equation can give a reasonable physical sense and an excellent accordance with experimental data. The concentration of reactants satisﬁes the ﬁrst reaction order relation, −αkt
C ¼ Cð0Þe
Then, the corresponding relation between size and time can be given, in terms of Eq. (4), as
D V Cð0Þ −αkt 1−e : αk
So the growing course is the ﬁrst-order kinetics of concentration. The initial concentration is the necessary parameter in the theoretical ﬁtting, which is related to the kind of solvent. The timely concentration reduction of particulate matter is determined from the phenomenon that sediment is increased in experiments for increasing process time. The ﬁtting result is shown as the curve labeled by MT in Fig. 4(a). The mass transfer theory supports the experimental results, on the rapid and accelerated growth in supercritical ﬂuid. The radius is an increasing function as given in Eq. (7). The stoichiometric coefﬁcient of reactants α is negative, and therefore the rule for the size variation is determined by the exponential term, e−αkt. This exponential law is an increasing function, and its increment is accelerated as time increases. The ﬁtting results, compared with the previous LSW theory, and other details are provided in the Supplementary information. The morphology evolution in supercritical ﬂuid has a general sense. Without loss of generality, the rapid growth phenomena also exist in other common SCFs, such as water and carbon dioxide. These phenomena have been indicated in literatures [14,42,45,46]; however, there is little special discussion on the growth phenomena in SCFs. The model provided here can be taken as a reference for the future work on supercritical processing. The discussion above is also applicable to normal hydrothermal methods that are not under supercritical conditions but with an instant equilibrium of concentration. This model is constructed from the relation of geometry and the concentration of mixtures, and other experiment conditions are not limited. Therefore, a general model for comprehension is provided.
L. Yi et al. / Powder Technology 259 (2014) 109–116
4. Conclusions Exfoliated Mn3O4 nanosheets can be cracked into particulate materials, and a growing course of polyhedron crystals is followed, in supercritical N,N-dimethylformamide. The size of crystals increases with growing time. The phases of manganese oxide are determined to be Mn3O4 and MnO in the processing course. The content of Mn ions becomes dense in the growing course. For the rapid growth, the interior factor is attributed to magnetic properties of manganese oxides, and the exterior factor is attributed to the high solubility and rapid mass transfer of supercritical ﬂuid. The instant equilibrium of concentration, the magnetic Mn ions becoming dense, and the enlarging magnetic growth center promote the accelerated growth. The growth of manganese oxides in supercritical ﬂuid has a higher rate than the normal synthesis reported in literatures. Supercritical ﬂuid processing can give rise to an extraordinary growth of manganese oxides. The classical LSW model is not applicable to the growth of manganese oxides in supercritical ﬂuid anymore, for a rapid growth with an accelerated course. The mass transfer model for the growing course, applicable to supercritical reaction environment, is proposed from the mass conservation. The growth of manganese oxides in SC-DMF is the ﬁrst-order kinetics, and the growth kinetics well agrees with the exponential law, e−αkt. Acknowledgments The authors acknowledge the ﬁnancial support from National Natural Science Foundation of China (51076094) and National Agricultural Science and Technology Achievements Transformation Fund Project from the Ministry of Science and Technology of the People's Republic of China (2013GB23600665), and meanwhile thank the Instrumental Analysis Center of SJTU for the measurements of SEM. Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.powtec.2014.03.062. References  H. Huang, Q. Yu, X. Peng, Z. Ye, Single-unit-cell thick Mn3O4 nanosheets, Chem. Commun. 47 (2011) 12831–12833.  H. Zhang, C. Liang, Z. Tian, G. Wang, W. Cai, Single phase Mn3O4 nanoparticles obtained by pulsed laser ablation in liquid and their application in rapid removal of trace pentachlorophenol, J. Phys. Chem. C 114 (2010) 12524–12528.  C. Chen, G. Ding, D. Zhang, Z. Jiao, M. Wu, C.-H. Shek, C.L. Wu, J.K. Lai, Z. Chen, Microstructure evolution and advanced performance of Mn3O4 nanomorphologies, Nanoscale 4 (2012) 2590–2596.  H. Jiang, T. Zhao, C. Yan, J. Ma, C. Li, Hydrothermal synthesis of novel Mn3O4 nanooctahedrons with enhanced supercapacitors performances, Nanoscale 2 (2010) 2195–2198.  Y. Li, H. Tan, X.Y. Yang, B. Goris, J. Verbeeck, S. Bals, P. Colson, R. Cloots, G. Van Tendeloo, B.L. Su, Well shaped Mn3O4 nano-octahedra with anomalous magnetic behavior and enhanced photodecomposition properties, Small 7 (2011) 475–483.  G.H. Lee, S.H. Huh, J.W. Jeong, B.J. Choi, S.H. Kim, H.-C. Ri, Anomalous magnetic properties of MnO nanoclusters, J. Am. Chem. Soc. 124 (2002) 12094–12095.  W.S. Seo, H.H. Jo, K. Lee, B. Kim, S.J. Oh, J.T. Park, Size-dependent magnetic properties of colloidal Mn3O4 and MnO nanoparticles, Angew. Chem. Int. Ed. 43 (2004) 1115–1117.  J. Park, E. Kang, C.J. Bae, J.-G. Park, H.-J. Noh, J.-Y. Kim, J.-H. Park, H.M. Park, T. Hyeon, Synthesis, characterization, and magnetic properties of uniform-sized MnO nanospheres and nanorods, J. Phys. Chem. B 108 (2004) 13594–13598.  C. Liu, G. Hu, H. Gao, Preparation of few-layer and single-layer graphene by exfoliation of expandable graphite in supercritical N,N-dimethylformamide, J. Supercrit. Fluids 63 (2012) 99–104.  D. Rangappa, K. Sone, M. Wang, U.K. Gautam, D. Golberg, H. Itoh, M. Ichihara, I. Honma, Rapid and direct conversion of graphite crystals into high-yielding, goodquality graphene by supercritical ﬂuid exfoliation, Chem. Eur. J. 16 (2010) 6488–6494.  G. Hu, L. Yi, C. Liu, Supercritical N,N-dimethylformamide exfoliation of the layered bulk titanate material into titania nanosheets, J. Supercrit. Fluids 72 (2012) 59–67.  L. Yi, G. Hu, Supercritical N,N-Dimethylformamide for the exfoliation and phase transition of layered manganese oxide materials to obtain trimanganese tetroxide nanosheets, RSC Adv. 3 (2013) 23461–23469.
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