Effects of Gibbs free energy changes and energy barrier on mechanochemical synthesis of LiM
Effects of Gibbs free energy changes and energy
barrier on mechanochemical synthesis of LiMn2O41
Zhongwei Zhao Kingsam Ouyang
School of Metallurgical Science and Engineering School of Metallurgical Science and Engineering Central South University Central South University
Changsha 410083, P. R. China Changsha 410083, P. R. China
zhaozw@https://www.wendangku.net/doc/5e16841130.html, ksouyang@https://www.wendangku.net/doc/5e16841130.html,
Zhaoming Sun Honggui Li
School of Metallurgical Science and Engineering School of Metallurgical Science and Engineering Central South University Central South University
Changsha 410083, P. R. China Changsha 410083, P. R. China
zdszmsm@https://www.wendangku.net/doc/5e16841130.html, hgli@https://www.wendangku.net/doc/5e16841130.html,
Abstract
After grinding in ambient air the mixture of the initial solid-state powder KMnO4
and MnSO4·H2O as Mn sources, and LiOH·H2O as Li source, a quick presence of
LiMn2O4 was found directly at room temperature without subsequent heating process.
The effect of different grinding time on its mechanochemical reaction was
investigated. Most importantly, the effects of the value of Gibbs free energy changes
(?r G) and the other mostly related factor—energy barrier, on its mechanochemical
reaction, were also examined, compared with such other two solid-state reaction
systems as LiOH·H2O–γ-MnO2 and Li2CO3–γ-MnO2. All samples were analyzed by
using X-ray diffraction (XRD) technology. The revealed results show that LiMn2O4
appears only after grinding for 2 min in reaction system
LiOH·H2O–MnSO4·H2O–KMnO4, and in large amounts after 35 min; only a little
LiMn2O4 forms in system LiOH·H2O–γ-MnO2 but no LiMn2O4 yields at all in system
Li2CO3–γ-MnO2, both after grinding for 35 min. Investigation indicates that both ?r G
and energy barrier play a key role in a solid-state reaction under mechanochemical
processing (MCP); and once energy barrier is overcome, ?r G then becomes a
governing factor to mechanochemical reaction during the further grinding.
Keywords:Gibbs free energy; energy barrier; mechanochemical reaction;
mechanochemical processing; LiMn2O4; KMnO4
1Introduction
Lithium manganese oxide LiMn2O4, especially the one with spinel structure, which is one of the cathode materials for secondary lithium batteries, has widely been studied in recent years because of its low cost of raw material, less toxicity and its ordered superstructure providing tunnels to allow the deintercalation and re-intercalation of lithium [1–6]. The preparation of spinel LiMn2O4, as a rule, is based on high-temperature solid-state reactions. However, this high temperature often inevitably results in some side-effects, such as a too fast speed of grain growth, an overall agglomeration of the particles, even other unwanted phases, thus leading to an unstable ability of lithium batteries to recharge. Those disadvantages, to some extent, prevent LiMn2O4 from broadening its commercial use. In order to overcome those defects, especially the too fast speed of grain growth under high temperature, a lot of works have been done to this day. And one of the main approaches is mechanochemical processing (MCP) at low temperature.
According to some literatures [7–10] with MCP, however, lithium manganese oxide has usually been synthesized either by such extreme milling condition as much longer milling time within a high-energy milling or by heating ground products, used as precursors, at a certain heating temperature (400 ℃ or more).
Recently, during grinding the mixture of the initial solid-state powder KMnO4 and MnSO4·H2O as Mn sources, and LiOH·H2O as Li source, a quick presence of LiMn2O4 was found directly at room temperature in ambient air without subsequent heating process. The calculated result shows that the chemical reaction of the synthetic route to LiMn2O4 has a remarkably negative value of Gibbs free energy changes (?r G). In this paper, in addition to investigating the effect of different grinding time, the effects of the value of ?r G and the other mostly related factor—energy barrier on mechanochemical reactions in a solid-state system were mainly discussed by employing such two reaction systems as LiOH·H2O–γ-MnO2 and Li2CO3–γ-MnO2 to synthesize LiMn2O4 to compare with, the former with a less negative value of ?r G and the latter with a considerably positive value of ?r G, than that of reaction system LiOH·H2O–MnSO4·H2O–KMnO4.
2Experimental
Starting solid materials were lithium hydroxide monohydrate (LiOH·H2O) with 99.0% purity (Tianjin Bodi Chemicals Co., Ltd., China) and lithium carbonate (Li2CO3) with 98.0% purity (Shanghai Hengxin Chemical Reagent Co., Ltd., China) as Li sources, potassium permanganate (KMnO4) with 99.5% purity
(Tianjin Kermel Chemical Reagent Development Center, China), manganese sulfate monohydrate
(MnSO4·H2O) with 99.0% purity (Chengdu Jinshan Chemical Industrial Reagent Co., Ltd., China),
electrolytic manganese dioxide (EMD, γ-MnO2) with 91.0% purity (Xiangtan Electric Chemical Group Co.,
Ltd, China) as Mn sources. All three reaction systems are:
(a). LiOH·H2O–MnSO4·H2O–KMnO4;
(b). LiOH·H2O–γ-MnO2;
(c). Li2CO3–γ-MnO2.
And the chemical equations designed to aim at synthesizing LiMn2O4 within reaction systems mentioned
above are as follows:
16/5LiOH·H2O + 7/5MnSO4·H2O + 3/5KMnO4 = LiMn2O4 + 4/5Li2SO4·H2O + 3/5KLiSO4 + 27/5H2O (1)
LiOH·H2O + 2γ-MnO2 = LiMn2O4 + 3/2H2O + 1/4O2↑ (2) 1/2Li2CO3 + 2γ-MnO2 = LiMn2O4 + 1/2CO2↑ + 1/4O2↑ (3)
Starting materials in each reaction system were weighed at a 1:2 molar ratio (Li/Mn), then subjected to
grinding in ambient air using a vibration milling (XZM–100, Wuhan Exploration Machinery Factory, China)
at a rotation speed of 960 rpm, respectively. The grinding time for each system was 35 min, stopped for 2
min to prevent an excessive temperature rise inside the reactor after 5 min, and then every 10 min operation.
For reaction system (a), such different periods of grinding time as 10 sec, 20 sec, 2 min, 8 min, 17 min and
35 min were set, especially to observe the degree of the mechanochemical reaction.
The phase analyses of ground samples were determined by a Rigaku X-Ray Diffractometer
(Dmax/2550VB+, Rigaku Corporation, Japan) using Cu Kα radiation. The tube current is 250 mA and the
voltage 40kV. The scanning rate is 8 degrees per minute, from 10–80 degree (2-Theta) with the step of 0.02
degree. MDI Jade 5 is used as analytical software for X-ray diffraction (XRD).
3Results and Analysis
3.1Effect of grinding time
Fig.1 shows XRD patterns of the ground samples in reaction systems from (a) to (c). As can be seen in this
figure, LiMn2O4 are synthesized after grinding the solid reagents for 35 min in reaction system (a) and (b),
while only peaks of MnO2 left in reaction system (c) along with some unknown peaks. Among the reaction
system (a) and (b), the peaks of LiMn2O4 are more remarkable in the former than in the latter. Besides the
peaks of LiMn2O4, there also exist the peaks of Li2SO4·H2O and KLiSO4 in reaction system (a). To observe
the peaks of LiMn2O4 more clearly, the ground mixture in reaction system (a) was washed quickly by
deionized water, drained by a vacuum filter and then analyzed at once. 1b in Fig. 1 shows only the peaks of
LiMn 2O 4 left. It is notable that at room temperature without subsequent heating process in LiOH·H 2O–MnSO 4·H 2O–KMnO 4 reaction system, grinding the mixed powders could synthesize LiMn 2O 4 directly.
1020304050607080
2-Theta (degree)
I n t e n s i t y (a .u .)
Fig. 1. XRD patterns of 3 reaction systems after ground for 35 min. 1a and 1b are the patterns of the products of reaction (1) before and after washing by distilled water, and 2 to 3 is the corresponding reaction (2) to (3) without any washing.
The fact that the strong peaks of LiMn 2O 4 exist in reaction system (a), that the weak peaks of LiMn 2O 4 exist in reaction system (b) and that none of them can be observed in reaction system (c), implies that the tendency to yield LiMn 2O 4 is various in different reaction systems under the same condition of applying mechanical force.
Since mechanical energy is greatly in favor of synthesizing LiMn 2O 4 in reaction system (a), it makes sense to shorten the grinding time within this system to investigate the degree of its mechanochemical reaction.
Fig. 2 shows XRD patterns of the samples in reaction system (a) ground for 10 sec, 20 sec, 2 min, 8 min, 17 min and 35 min. It is found that the peaks of initial materials LiOH·H 2O, MnSO 4·H 2O and KMnO 4 still exist after ground for 10 sec, and diminish rapidly after ground for 20 sec, then vanish only after 2 min, while some new compounds like KLiSO 4 and Li 2SO 4·H 2O are found after ground for 10 sec, and LiMn 2O 4 appears at once after 2 min. After then, the peak intensity of LiMn 2O 4 becomes stronger gradually along
with the increase of grinding time, while the peak intensities of the other two resultants appear a downtrend. Those obviously varying tendencies can be examined in Fig. 3.
1020304050607080
2-Theta (degree)
I n t e n s i t y (a .u .)
Fig. 2. XRD patterns of the samples of LiOH·H 2O–MnSO 4·H 2O–KMnO 4 reaction system ground for different periods of time .
There is no doubt that the mechanochemical reaction in LiOH·H 2O–MnSO 4·H 2O–KMnO 4 reaction system may take place after grinding for only a very short time, and then go on reacting markedly at a rather quick speed along with the further grinding. The reasons for this are mostly related with the value of ?r G for its
mechanochemical reaction, as well as the energy required to overcome the barrier between reactants during the course of grinding.
1020304050607080
2-Theta (degree)
I n t e n s i t y (a .u .)
Fig. 3 XRD patterns of the samples of LiOH·H 2O–MnSO 4·H 2O–KMnO 4 reaction system ground for 17 min and 35 min. 1a and 2a are the patterns of the ground samples before, and 1b and 2b after washing by deionized water. 3.2 Effect of ?r G and the energy barrier
Table 1 contains the values of ?f G ? of some compounds at 298.15 K (25℃). As the values of ?f G ? of KLiSO 4 and some aqua compounds can not be found in references, the value of ?f G ? of LiOH·H 2O is estimated by the sum of that of LiOH and that of H 2O, the value of ?f G ? of MnSO 4·H 2O approximately the sum of that of MnSO 4 and that of H 2O. As for KLiSO 4, its value of ?f G ? is estimated by the some procedure (see Appendix).
According to the values in standard state in Table 1, the values of standard Gibbs free energy change (?r G ?)
of chemical equation from (1) to (3) are calculated and list in Table 2, based on one mole of LiMn2O4.
Table 1: Thermodynamic data of components at 298.15 K
Component Physical state ?f G? (kJ·mol-1)Reference
CO2gaseous 394.39 11
H2O liquid -237.14 11
KMnO4crystalline solid-737.6 11
K2SO4crystalline solid-1 321.4 11
LiOH crystalline
solid-439 11
LiMn2O4crystalline solid-1 315.61 12
Li2CO3crystalline solid-1 132.12 11
Li2SO4crystalline solid-1 321.7 11
MnO2crystalline solid-465.2 11
MnSO4crystalline solid-957.42 11
KLiSO4crystalline solid-1 323.3 Appendix Table 2: Values of standard Gibbs free energy changes (?r G?) for the mechanochemical reactions
Reaction ?r G?(kJ·mol-1)
16/5LiOH·H2O + 7/5MnSO4·H2O + 3/5KMnO4 = LiMn2O4 + 4/5Li2SO4·H2O +
3/5KLiSO4 + 27/5H2O
-358.63
LiOH·H2O + 2γ-MnO2 = LiMn2O4 + 3/2H2O + 1/4O2↑ -64.78 1/2Li2CO3 + 2γ-MnO2 = LiMn2O4 + 1/2CO2↑ + 1/4O2↑ 378.04
Since it is hard to obtain a precise quantitative value of ?r G under MCP in our test conditions, the
assumption is adopted that the value of ?r G is close to the one of ?r G?, as the grinding was performed at
room temperature. So ?r G is used to discuss in the following discussion, in stead of ?r G?.
In general, the more negative a value of ?r G is, the easier a corresponding chemical reaction will take place
in the same state. ?r G, as the driving force, determines whether a chemical reaction can be able to occur or
not. Besides the value of ?r G, however, there exists another key factor needed to be conquered first in some
situation, especially in a solid-state system. Only simply mixing some initial solid-state materials, for
example, even though the value of ?r G in the chemical reaction is considerably negative, but one can
hardly observe the occurrence of the chemical reaction; yet milling the mixture for a while, the reaction
then may be examined. This existing key factor is some kind of barrier–an energy barrier. A chemical
reaction with a negative value of ?r G can be observed considerably only if available the energy barrier is
removed. Compared with gas phase reaction or liquid phase reaction, usually there exist two main
disadvantages in solid-state reactions. One is the rather less contact area between reactants, and the other is the more lack of diffusion rate of resultants leaving away from the reaction area. What those two limitations often result in when grinding mainly contributes to the energy barrier, which stunts the mechanochemical reactions to start and then carry it through.
Energy needs to obtain to overcome the barrier. During the process of mechanical milling, on the one hand, the decrease of grain size may cause the increase of surface energy of grains; one the other hand, mechanical energy may also be continuously stored in the formation of structural defects and microstrain. Once an accumulated free energy of the reactants exceeds the energy barrier after grinding enough time, all of a sudden the value of ?r G then becomes a governing factor over other ones to a mechanochemical reaction. Now there are two situations regarding the value of ?r G : a negative and a positive one. As for the former, a mechanochemical reaction may take place, then the resultants may be removed quickly and continuously from the reaction area and at the same time leave it available for the rest reactants to keep on reacting, whose reaction rate and degree are strongly dependent on how negative the value of ?r G is. From Table 2 we can find that reaction system (1) and (2) belong to this occasion. And Fig. 4 illustrates the situation.
E 1
Initial materials,
responding to a metastable state
Prospective products, ?r G
E 2
Fig. 4. Schematic of before and after overcoming the energy barrier to bring about a mechanochemical reaction, under the condition of ?r G <0
From (a) in Fig. 4, because of a negative value of ?r G , initial materials such as LiOH·H 2O, MnSO 4·H 2O and KMnO 4 in reaction system (1) and LiOH·H 2O and γ-MnO 2 in system (2), are on a metastable state, where they overcome an energy barrier E 1 (may be a different value) to get to an unstable state. Now
mechanochemical reaction occurs and resultants then form, responding to a stable state (see (b) in Fig. 4). In system (1), as E 2>>E 1, so it is much easier for new initial materials continue to overcome the energy
E
1
Initial materials, ?r G
E 21
Prospective products, responding to a metastable state
F r e e e n e r g y
(c) Occurring of mechanochemical reaction after further grinding
(d) “Reaction cycle” of mechanochemical reaction during grinding
Fig. 5. Schematic of before and after overcoming the energy barrier to bring about a mechanochemical reaction, under the condition of ?r G >0
barrier E1 to react than for resultants to overcome E2 to react. Thus under high-energy milling, E1 can with no doubt make it dominant for the overall mechanochemical reaction to form LiMn2O4. Yet in system (2), the approach of E1 to E2 (here E2 is just a little greater than E1) makes the rate of the reverse reaction close to that of positive reaction, thus resulting in a rather slow rate of the overall mechanochemical reaction to form LiMn2O4. This soundly explains the phenomena in Fig. 1, Fig. 2 and Fig. 3.
But as for the latter situation, i.e. a reaction system with a positive value of ?r G, taking the reaction system (3) for example, it is another case. From (a) in Fig. 5, Li2CO3 and γ-MnO2 as initial materials are in fact in the position of a stable state before grinding. Along with the process of grinding, after overcoming the energy barrier E1 (here E1>>E2 in reaction system (3)), the position of some initial materials reach to an unstable state and then fall into a metastable state, with a spot of temporarily existing products such as LiMn2O4 formed (see (b) in Fig. 5). Those temporarily existed products under the metastable state are easily obtained some energy during further grinding to overcome a rather less barrier E2 to reach the unstable state again, then fall to the stable state, with finial products such as Li2CO3 and γ-MnO2 formed (see (c) in Fig. 5). A “reaction cycle” then finishes. Along with the further grinding, new “reaction cycles” will continue one after another (see (d) in Fig. 5). This multiplestep illustration of simplifying a mechanochemical reaction is mainly to understand the effect of the value of ?r G and the energy barrier. It is most probably the fact of E1>E2 caused by a positive value of ?r G that makes the reverse reaction guide the overall mechanochemical reaction as a whole. Especially when E1>>E2, resultants form first then disappear immediately, so much so that any peaks of LiMn2O4 in XRD patterns are not found in system (3) (see Fig.
1).
4 Conclusions
The following conclusions can be made from the present experiment.
(1)Both ?r G and energy barrier between reactants play a key role in a solid-state reaction under MCP.
Once an energy barrier is overcome, ?r G then becomes a governing factor during the further grinding to decide whether a mechanochemical reaction can take place or not, and at about what a rate the reaction takes place; and by treating in ambient air at room temperature in vibration mill (once energy barrier is overcome):
(2)Reaction system LiOH·H2O–MnSO4·H2O–KMnO4, LiMn2O4 may present at once without any
subsequent heating process only after grinding for 2 min, and yield in large amounts after grinding for 35 min, for there exiting a considerably negative value of ?r G in this system.
(3)Reaction system LiOH·H2O–γ-MnO2, as there exits a less negative value of ?r G in the system,
only a little LiMn2O4 yields after 35 min of grinding.
(4)Reaction system Li2CO3–γ-MnO2, a considerable positive value of ?r G in the system makes it
hard to form LiMn2O4, even grinding for 35 min.
Appendix
The thermodynamic data of compound KLiSO4 is estimated by following procedure. 0.5 mole of K2SO4 is mixed with 0.5 mole of Li2SO4 to compose one mole of KLiSO4, and the value of standard Gibbs free energy ?f G?of KLiSO4 is calculated from those of K2SO4 and Li2SO4, where the thermodynamic date of K2SO4 and Li2SO4 are listed in Table 1.
?f G?(KLiSO4) = (1/2) ?f G?(K2SO4) + (1/2) ?f G?(Li2SO4) + (1/2) RT [ln (1/2) + ln (1/2)]
= (1/2) * (-1 321.4) + (1/2) * (-1 321.7) + 8.314 * 298.15 * ln (1/2) * 10-3
= -1 323.3 (kJ·mol-1)
This estimated result of ?f G?(KLiSO4) is also listed in Table 1.
References
[1]N.V. Kosova, N.F. Uvarov, E.T. Devyatkina, E.G. Avvakumov, Solid State Ionics. 135 (2000) 107.
[2]S. Soiron, A. Rougier, L. Aymard, J-M. Tarascon, J. Power Sources. 97–98 (2001) 402.
[3]N.V. Kosova, E.T. Devyatkina, S.G. Kozlova, J. Power Sources. 97–98 (2001) 406.
[4]Y. Liu, T. Fujiwara, H. Yukawa, M. Morinaga, Electrochimica Acta. 46 (2001) 1151.
[5] A. Eftekhari, Solid State Ionics. 161 (2003) 41.
[6] E. Levi, M.D. Levi, G. Salitra, D. Aurbach, R. Oesten, U. Heider, L. Heider, Solid State Ionics. 126
(1999) 109.
[7]Y. Tanaka, Q. Zhang, F. Saito, Powder Technology. 132 (2003) 74.
[8]N.V. Kosova, I.P. Asanov, E.T. Devyatkina, E.G. Avvakumov, J. Solid State Chem. 146 (1999) 184.
[9]Z. Tang, J. Feng, Y. Peng, Chinese J. Chem. Eng. 12 (2004) 124.
[10]G.M. Song, W.J. Li, Y. Zhou, Materials Chem. and Phys. 87 (2004) 162.
[11]J.A. Dean, Lange’s Handbook of Chemistry (15th Edition). McGraw-Hill Press, New York, 1999, p.
88.
[12]Z.W. Zhao, G.S. Huo, The Chinese J. Nonferrous Metals. 14 (2004) 1926.