research article morphology effect on the kinetic...
TRANSCRIPT
Research ArticleMorphology Effect on the Kinetic Parameters and SurfaceThermodynamic Properties of Ag3PO4 Micro-/Nanocrystals
Zai-Yin Huang,1,2,3,4 Xing-Xing Li,2 Zuo-Jiao Liu,2 Liang-Ming He,2 and Xue-Cai Tan2,3,4
1Chemical and Environmental Engineering, Baise University, Baise 533000, China2College of Chemistry and Chemical Engineering, Guangxi University for Nationalities, Nanning 530008, China3Key Laboratory of Forest Chemistry and Engineering, Guangxi University for Nationalities, Nanning 530008, China4Guangxi Colleges and Universities Key Laboratory of Food Safety and Pharmaceutical Analytical Chemistry,Guangxi University for Nationalities, Nanning 530008, China
Correspondence should be addressed to Zai-Yin Huang; [email protected]
Received 28 April 2015; Accepted 1 October 2015
Academic Editor: Yu-Lun Chueh
Copyright © 2015 Zai-Yin Huang et al.This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Considerable effort has been exerted using theoretical calculations to determine solid surface energies. Nanomaterials with highsurface energy depending on morphology and size exhibit enhanced reactivity. Thus, investigating the effects of morphology,size, and nanostructure on the surface energies and kinetics of nanomaterials is important. This study determined the surfaceenergies of silver phosphate (Ag
3PO4) micro-/nanocrystals and their kinetic parameters when reacting with HNO
3by using
microcalorimetry. This study also discussed rationally combined thermochemical cycle, transition state theory, basic theory ofchemical thermodynamicswith thermokinetic principle,morphology dependence of reaction kinetics, and surface thermodynamicproperties. Results show that the molar surface enthalpy, molar surface entropy, molar surface Gibbs free energy, and molarsurface energy of cubic Ag
3PO4micro-/nanocrystals are larger than those of rhombic dodecahedral Ag
3PO4micro-/nanocrystals.
Compared with rhombic dodecahedral Ag3PO4, cubic Ag
3PO4with high surface energy exhibits higher reaction rate and lower
activation energy, activationGibbs free energy, activation enthalpy, and activation entropy.These results indicate that cubic Ag3PO4
micro-/nanocrystals can overcome small energy barrier faster than rhombic dodecahedral Ag3PO4micro-/nanocrystals and thus
require lower activation energy.
1. Introduction
Nanomaterials that exhibit high specific surface effect differfrom massive materials in terms of physical and chemicalproperties [1, 2]. Du et al. [3] explained that the specificsurface effect, surface heat capacity, and specific surfaceenergy of nanomaterials cannot be neglected. The overallthermodynamic property of nanoparticles comprises surfaceand bulk phases [3–9]. Surface thermodynamic propertiesare the intuitive expression of the special structure-activityrelationship of nanomaterial surface, which significantlyaffects many physical/chemical reactions, including chemicalthermodynamics [3, 4], chemical kinetics [5], catalysis [10–13], sense [11], adsorption [14], phase transition [15], and elec-trochemistry of nanomaterials [16]. Theoretical calculationresults showed that nanomaterials with different sizes and
facets have different surface energies [17–19] and that thereactivity of nanomaterials depends on surface energy [11,12]. Studying the surface thermodynamic property of nano-materials and the structure-function relationship betweenreaction dynamics and size, morphology, and structure isvaluable to understand the nature of chemical reactions.
Calorimetry [7, 8, 20, 21], contact angle [22], Youngmodulus [23, 24], balance crystal shape [3, 25], zero creep,and field-emission microscopic method [26] are commonmethods of measuring solid surface energy. Hulett [27, 28]reported that the surface energies of BaSO
4andCaSO
4⋅2H2O
obtained using the Ostwald-Freundlich formula are within1000–3000mJ⋅m−1. However, Tang et al. [29–32] discoveredthat results obtained using the Ostwald-Freundlich formulafor nanoparticles with far higher solubility than commoncrystals contradict with experimental facts. Thus, Tang et al.
Hindawi Publishing CorporationJournal of NanomaterialsVolume 2015, Article ID 743121, 9 pageshttp://dx.doi.org/10.1155/2015/743121
2 Journal of Nanomaterials
[31, 32] measured the surface energy of inorganic insolublesalt indirectly through crystal growth or dissolution kinetics.Methods commonly used in Young modulus (e.g., tearing)and other methods involving compression, solubilization,high-temperature dissolution, or lowering of melting pointproduce high and even applied stress-covered surface ener-gies. Hence, theoretical calculation is preferred to measuresolid surface energy [23]. Nevertheless, theoretical calcu-lation often deviates from the practical ideal model andfrom many hypotheses. Real surfaces with abundant atomladders and unsaturated bonds, as well as those with unstablethermodynamics, tend to absorb water [7], gas molecules,and surfactant [11, 12]; undergo surface atom reconstruc-tion and aggregation; or even form a protective film layer.The surface energies of these complicated real surfaces areextremely difficult to theoretically calculate. Experimentalmeasurement still faces several challenges. Different exper-imental methods provide significantly different values forthe surface energies of the same material [33]; researchersusing the same experimental method also obtain varyingresults [34, 35]. A universal method to determine surfaceenergy has yet to be developed. Developing a scientificand universal experimental method to measure the surfaceenergy of nanomaterials is a pressing need in the scientificendeavors on solid surface and in other disciplines.
The visible-light-driven Ag3PO4photocatalyst has become
popular since its introduction in 2010 [36, 37]. Scientists cal-culated the surface energies of different facets of Ag
3PO4on
the basis of the relationship between included angle of crystalfaces and Miller index [38]. Other researchers performedthe same calculation by using density functional theory [39].Studying the structure-function relationship between the sur-face energy of micro-/nanomaterial Ag
3PO4and size, mor-
phology, and structure is valuable to understand the naturesof chemical reactions. However, the surface energy of thismaterial was rarely calculated using experimental methods.The present study determined the surface energies of Ag
3PO4
micro-/nanocrystals with cubic and rhombic dodecahedralmorphologies and their kinetic parameters when reactingwith HNO
3by using microcalorimetry. This study also dis-
cussed rationally combined thermochemical cycle, transitionstate theory, basic theory of chemical thermodynamics withthermokinetic principle,morphology dependence of reactionkinetics, and surface thermodynamic properties.
2. Experiments
2.1.Materials. Analytical-grade sodiumdihydrogen phosphatedihydrate (NaH
2PO4⋅2H2O), disodiumphosphate dodecahy-
drate (NaH2PO4⋅12H2O), silver nitrate (AgNO
3), ammonium
hydroxide (NH3⋅H2O), potassium chloride (KCl), and nitric
acid were purchased from Sinopharm Chemical Reagent Co.Ltd. and used without further purification. Deionized waterwith a resistivity of 18.2MΩ⋅cm was used in all experiments.
2.2. Characterization. The morphology of the sample wasexamined under a field-emission scanning electron micro-scope (Zeiss SUPRA 55 Sapphire, Germany). The X-raydiffraction (XRD) pattern was recorded on an X-ray powder
diffractometer (Philips PW 1710 with Cu K𝛼 radiation, 𝜆 =1.5406 A, Holland). Trace amounts of the sample were mea-sured on a XPE analytic balance (Mettler Toledo, Switzer-land). Calorimetric experiments were performed using amicrocalorimeter (RD496L, Mianyang CPThermal AnalysisInstrument Co., Ltd., China) under constant temperature andpressure.
2.3.Calorimetric Experiment. Rhombic dodecahedrons, cubes,and bulk Ag
3PO4were prepared by a simple ion-exchange
method at room temperature [40].Themicrocalorimeter wascalibrated by Joule effect, and its calorimetric constant was(69.91±0.56) 𝜇V⋅mW−1 at 298.15 K.The dissolution enthalpyof KCl in deionized water (1 : 1110, 𝑚KCl/𝑚de-water) was(17.792 ± 0.029) kJ⋅mol−1. This value agrees with the previ-ously published value of (17.524±0.028) [41].This agreementindicates that the calorimetric system is accurate and reliable.
A small glass tube containing 1.0mL of 0.36M HNO3
solution was placed above a 15mL glass tube chargedwith 1.500mg of Ag
3PO4samples (bulk or the obtained
nanocubes). Simultaneously with the establishment of equi-librium, the small glass tube with HNO
3solution was pushed
down. The in situ thermodynamic and kinetic informationfor this reaction was recorded using the microcalorimeter.
2.4. Establishment of Chemical Reaction Kinetic Models forCubic and Rhombic Dodecahedron Ag
3PO4Micro-/Nanocrys-
tals. The specific surface area and specific surface energyof the reactant increase after being refined; thus, the meanmolar energy of the refined reactant is higher than that ofthe corresponding bulk reactant. If the reactant particle size isinsignificant to the mean energy of the activated molecules,then the difference between the mean molecular activationenergy of 1M of nanoparticles and mean energy of 1molsuper-refined reactant is the chemical activation energy ofthe nanomaterial [42]. Figure 1 shows the transition statetheory [8, 42, 43]. In the same chemical reaction, the reactantexperiences the same transition state to the final state. There-fore, the apparent activation energy of nanoparticles 𝐸
𝑎is the
difference between the activation energy of correspondingbulk material [𝐸
𝑎(bulk)] and the molar surface energy of
nanoparticles (𝐸𝑆𝑚):
𝐸
𝑎 (nano) = 𝐸
𝑎 (bulk) − 𝐸
𝑆
𝑚. (1)
If the dispersion phase in heterogeneous reaction hasonly one reactant and others belong to the continuous phase,then the relationship between surface energy and apparentactivation energy for cubic nanoparticles without inner borescan be expressed as
𝐸
𝑎 (nano) = 𝐸
𝑎 (bulk) − 𝐸
𝑆
𝑚= 𝐸
𝑎 (bulk) − 4𝜎𝑀
𝜌𝑙
, (2)
where 𝜎, 𝑀, 𝜌, and 𝑙 are the surface tension, molar mass,density, and particle size (length of cube edge) of the cubicnanoparticle reactant, respectively. Equation (2) provides thatthe apparent activation energy in the chemical reaction ofthe nanomaterials is proportional to the particle size of thereactant.
Journal of Nanomaterials 3
Ener
gy
Reactant ProductReaction coordinate
Initial state
Ea (bulk) Ea (nano)
E (bulk) E (nano)
Bulk
Nano
Transient state
Final state
Figure 1: Schematic of relationship between surface energy andapparent activation energy.
If the heterogeneous reaction follows Arrhenius Law,substituting (2) into it yields the Arrhenius equation of thenanocube:
𝑘 = 𝐴 exp[−
𝐸
𝑏
𝑎
𝑅𝑇
+
4𝜎𝑀
𝑅𝑇𝜌𝑙
] .(3)
Similarly, the Arrhenius equation of dodecahedron isobtained:
𝑘 = 𝐴 exp[−
𝐸
𝑏
𝑎
𝑅𝑇
+
√6𝜎𝑀
𝑅𝑇𝜌𝑙
] ,(4)
where 𝑇 is the reaction temperature, 𝑘 is the reaction rateconstant, and 𝐴 is the preexponential factor.
Substituting the logarithm on both sides of (4), we obtainthe following:
Cube:
ln 𝑘 = ln𝐴 −
𝐸
𝑏
𝑎
𝑅𝑇
+
4𝜎𝑀
𝜌𝑙
.(5)
Dodecahedron:
ln 𝑘 = ln𝐴 −
𝐸
𝑏
𝑎
𝑅𝑇
+
√6𝜎𝑀
𝜌𝑙
.(6)
Therefore, when the particle size is larger than 10 nm,the surface tension slightly changes and can be viewed as aconstant [43]. On the basis of (5) and (6), the logarithm of thereaction rate constant is inversely proportional to the particlesize of the reactant.
2.5. Acquisition of Dynamic Parameters of Ag3PO4React-
ing with HNO3. The thermodynamic equation of reversible
chemical reaction under constant temperature and pressurecan be expressed as [44]
ln [
1
𝐻
∞
d𝐻𝑖
d𝑡] = ln 𝑘 + 𝑛 ln [1 −
𝐻
𝑖
𝐻
∞
] , (7)
where 𝐻
∞is the enthalpy change during the whole reaction
and may be directly obtained by microcalorimetry, d𝐻𝑖/d𝑡 is
the enthalpy change rate, 𝑘 (s−1) is the reaction rate constantexpressed by conversion rate, and𝐻
𝑖is the enthalpy change at
reaction time 𝑡. 𝑘 can be calculated from the linear regressionof thermodynamic data:
ln 𝑘 = ln𝐴 −
𝐸
𝑎
𝑅𝑇
(8)
Δ𝐺
𝜃
== 𝑅𝑇 ln [
𝑅𝑇
𝑁
𝐴ℎ𝑘
] (9)
ln 𝑘
𝑇
= ln 𝑘
𝐵
ℎ
+
Δ𝑆
𝜃
=
𝑅
−
Δ𝐻
𝜃
=
𝑅𝑇
,
(10)
where𝑁
𝐴is Avogadro’s constant, 𝑘
𝐵is Boltzmann’s constant,
ℎ is Planck’s constant, and 𝑅 is the molar gas constant. Thediagramof 1/𝑇was drawnwith ln 𝑘.𝐸
𝑎and𝐴were calculated
using (8). Δ𝐺
𝜃
=, Δ𝐻
𝜃
=, and Δ𝑆
𝜃
=were calculated from (9) and
(10).
2.6.Theoretical Derivation ofMolar Surface Gibbs Free Energy,Molar Surface Enthalpy, Molar Surface Entropy, and MolarSurface Energy. The molar Gibbs free energy of chemicalreaction of nanosystem consists of bulk phase (Δ
𝑟𝐺
𝐵
𝑚) and
surface phase (Δ𝑟𝐺
𝑆
𝑚) [8, 42]:
Δ
𝑟𝐺
𝑚 (nano) = Δ
𝑟𝐺
𝐵
𝑚+ Δ
𝑟𝐺
𝑆
𝑚. (11)
ThemolarGibbs free energy of the bulk chemical reactionnearly exhibits bulk phase.The bulk phase of the nanosystemis similar to that of bulk:
Δ
𝑟𝐺
𝐵
𝑚= Δ
𝑟𝐺
𝑚(bulk) , (12)
whereΔ𝑟𝐺
𝑚(bulk) is themolarGibbs free energy of the same
chemical reaction bulk material.Therefore, themolarGibbs free energy difference between
the nanosystem and the bulk lies in the molar surface Gibbsfree energy of the nanomaterial (excessive Gibbs free energycompared with bulk material). Substituting (12) into (11), weobtain
Δ
𝑟𝐺
𝑆
𝑚= Δ
𝑟𝐺
𝑚(nano) − Δ
𝑟𝐺
𝑚(bulk) . (13)
On the basis of (13), the thermochemical cycles of nano-and bulk Ag
3PO4were designed (Figure 2). The thermody-
namic functions of nano- and bulk Ag3PO4reactions with
HNO3were tested. The thermodynamic function of nano-
Ag3PO4conversion into the bulk one was calculated on the
basis of their difference.On the basis of (12), the chemical reaction for the molar
surface Gibbs of Ag3PO4micro-/nanocrystals with a net
reaction of Ag3PO4(nano) → Ag
3PO4(bulk) is
Δ
𝑟𝐺
𝜃
𝑚= Δ
𝑟𝐺
𝜃
𝑚(Ag3PO4, nano)
− Δ
𝑟𝐺
𝜃
𝑚(Ag3PO4, bulk)
= Δ
𝑟𝐺
𝑆
𝑚(Ag3PO4, nano)
= −𝐺
𝑆
𝑚(Ag3PO4, nano) ,
(14)
4 Journal of Nanomaterials
Ag3PO4 (nano) Ag3PO4 (bulk)
+HNO3 +HNO3
The same final state(Ag+,HPO4
−2,NO3−)
ΔG 𝜃m (nano),
ΔH𝜃m (nano),
ΔS 𝜃m (nano) Δ
G𝜃
m(b
ulk),
ΔH
𝜃m
(bulk
),ΔS𝜃
m(b
ulk)
ΔG𝜃m, ΔH
𝜃m, ΔS
𝜃m
Figure 2:Thermochemical cycle of nano- and bulkAg3PO4reacting
with HNO3.
where Δ𝐺
𝜃
𝑚(Ag3PO4, nano) and Δ𝐺
𝜃
𝑚(Ag3PO4, bulk) are the
standard molar Gibbs free energies of the reactions ofAg3PO4micro-/nanocrystals and bulk Ag
3PO4with HNO
3,
respectively; Δ𝐺
𝑆
𝑚(Ag3PO4, nano) and 𝐺
𝑆
𝑚(Ag3PO4, nano)
are the molar reaction surface Gibbs free energy and molarsurface Gibbs free energy, respectively.
In accordance with transition state theory, the relation-ship between reaction rate constants of Ag
3PO4micro-/
nanocrystals reaction system and bulk Ag3PO4reaction
system and the Gibbs free energy can be expressed as [8, 45]
Δ
𝑟𝐺
𝜃
𝑚(Ag3PO4, nano) − Δ
𝑟𝐺
𝜃
𝑚(Ag3PO4, bulk)
= Δ
𝑟𝐺
𝜃
=(bulk) − Δ
𝑟𝐺
𝜃
=(nano)
= 𝑅𝑇 (ln 𝑘bulk − ln 𝑘nano) ,
(15)
where Δ
𝑟𝐺
𝜃
=and 𝑘 are the activation Gibbs free energy and
rate constant of Ag3PO4chemical reaction.
On the basis of (14) and (15),
𝐺
𝑆
𝑚(Ag3PO4, nano) = −Δ
𝑟𝐺
𝑆
𝑚(Ag3PO4, nano)
= −𝑅𝑇 (ln 𝑘bulk − ln 𝑘nano) .(16)
Similarly, Δ𝐻
𝜃
=can be calculated from (10). Molar surface
enthalpy can be deduced from transition state theory:
Δ
𝑟𝐻
𝑆
𝑚= Δ
𝑟𝐻
𝜃
𝑚(nano) − Δ
𝑟𝐻
𝜃
𝑚(bulk)
= Δ
𝑟𝐻
𝜃
=(bulk) − Δ
𝑟𝐻
𝜃
=(nano)
Δ
𝑟𝐻
𝑆
𝑚= 𝐻
𝑚(Ag3PO4, nano) − 𝐻
𝑚(Ag3PO4, bulk)
= −𝐻
𝑆
𝑚(Ag3PO4) ,
(17)
where Δ
𝑟𝐻
𝑆
𝑚, Δ𝑟𝐻
𝜃
𝑚, Δ𝑟𝐻
𝜃
=, and 𝐻
𝑆
𝑚are the molar surface
reaction enthalpy, molar reaction enthalpy, molar activationenthalpy, and molar surface enthalpy of Ag
3PO4chemical
reaction, respectively.
Similarly, molar surface entropy can be deduced fromtransition state theory:
Δ
𝑟𝑆
𝑆
𝑚= Δ
𝑟𝑆
𝜃
𝑚(nano) − Δ
𝑟𝑆
𝜃
𝑚(bulk)
= Δ
𝑟𝑆
𝜃
=(bulk) − Δ
𝑟𝑆
𝜃
=(nano)
Δ
𝑟𝑆
𝑆
𝑚= 𝑆
𝑚(Ag3PO4, nano) − 𝑆
𝑚(Ag3PO4, bulk)
= −𝑆
𝑆
𝑚(Ag3PO4) ,
(18)
where Δ
𝑟𝑆
𝑆
𝑚, Δ
𝑟𝑆
𝜃
𝑚, Δ
𝑟𝑆
𝜃
=, and 𝑆
𝑆
𝑚are the molar surface
reaction entropy, molar reaction entropy, molar activationentropy, and molar surface entropy of Ag
3PO4chemical
reaction, respectively.Apparent activation energy refers to the total energy
needed for the material to overcome activation.The essentialdifference between Ag
3PO4micro-/nanocrystals and bulk
Ag3PO4is the high specific surface effect of the surface
phase. After the same transition state to the final state inthe same chemical reaction (Figure 1), the surface energy ofthe nanosystem surface phase (𝐸𝑆
𝑚) is the energy difference
between the nano-reaction system and the bulk reactionsystem. The molar surface energy in the manuscript citedreference [8] which deduced in our published paper. Itscorrect form is [8]. Consider
Δ𝐸
𝑆
𝑚= 𝐸 (nano) − 𝐸 (bulk) = 𝐸
𝑎(bulk) − 𝐸
𝑎(nano)
Δ
𝑟𝐸
𝑆
𝑚= 𝐸
𝑚(Ag3PO4, nano) − 𝐸
𝑚(Ag3PO4, bulk)
= −𝐸
𝑆
𝑚(Ag3PO4) ,
(19)
whereΔ𝐸
𝑆
𝑚,𝐸𝑎, and𝐸
𝑚are themolar surface reaction energy,
activation energy, and molar surface energy of Ag3PO4
chemical reaction, respectively.
3. Results and Discussion
3.1. Product Characterization. Figures 3(a)–3(c) show theSEM images of Ag
3PO4micro-/nanocrystals. Cubic Ag
3PO4
has six (100) faces, clear and sharp edges and angles, andsmooth surfaces; the mean particle size is (695.9±100.2) nm.Figure 3(b) is the rhombic dodecahedral Ag
3PO4with 12
rhombus (110) faces.White spots are scattered on the surfaces;the mean particle size is (647.1 ± 91.8) nm. Figure 3(c) showsthe SEM image of the irregularly shaped Ag
3PO4that forms
the bulk of the substance; its mean particle size is (6.9 ±
3.9) 𝜇m.Figure 4 shows the XRD pattern of the bulk, rhombic
dodecahedral, and cubic Ag3PO4. All diffraction peaks in
Figure 4 agreewith those of Ag3PO4with the standard calorie
JPCDS (06-0505). No other impurity peak is observed.Moreover, the full width at half maximum of all diffractionpeaks is narrow, indicating purity and good crystallinity ofthe prepared samples.
3.2. Effect of Morphology on the Chemical Reaction Rate Con-stant of Ag
3PO4Micro-/Nanocrystals. Linear regression was
Journal of Nanomaterials 5
2𝜇m
(a)
2𝜇m
(b)
20𝜇m
(c)
Figure 3: SEM images of cubic (a), rhombic dodecahedral (b), and bulk (c) Ag3PO4micro-/nanocrystals.
(c)
(b)
Inte
nsity
(a.u
.)
(421
)(3
32)
(420
)
(400
)(3
21)
(320
)(2
22)
(310
)
(220
)(211
)(210
)
(200
)
(110
)
(a)
8040 50 60 703020
2𝜃 (deg.)
Figure 4: XRD patterns of bulk (a), rhombic dodecahedral (b), andcubic (c) Ag
3PO4micro-/nanocrystals.
performed using the original thermodynamics data obtainedfrom (7), and the reaction rate constants of Ag
3PO4and
HNO3under varying temperatures were obtained (Table 1).
The curves shown in Figure 5 were drawn on the basis ofthe reaction rate constants of Ag
3PO4with HNO
3and the
reciprocal of temperature in Table 1.Figure 5 shows that the reaction rate is proportional to
temperature when the particle size is fixed. Compared withbulk Ag
3PO4, the super-refined materials have significantly
more particles of the surface phase. Particles of the surfacephase account for a large proportion of the total particles.Atoms of the surface phase have uneven stresses, unsaturatedforce field, and dangling bonds, which lead to high surfaceenergy.This result explains the faster reaction rate of Ag
3PO4
micro-/nanocrystals than bulk Ag3PO4. As the tempera-
ture increases, the surface turbulence and surface energyof Ag
3PO4micro-/nanocrystals increase; consequently, the
chemical reaction increases. The effect of morphology on thereaction rate shows that cubic Ag
3PO4has higher reaction
rate than dodecahedral Ag3PO4.
CubesRhombic dodecahedralBulk
−5.85
−5.80
−5.75
−5.70
−5.65
−5.60
−5.55
−5.50
−5.45
ln k
0.00325 0.00320 0.003150.003300.00335
1/T (K−1)
Figure 5: Effect of morphology on the reaction rate constant ofAg3PO4micro-/nanocrystals with HNO
3.
Table 1: Reaction rate constant of Ag3PO4micro-/nanocrystals with
HNO3.
𝑇 (K) 298.15 303.15 308.15 313.15 318.15𝑘 ⋅ 10
−3 (s−1)Cube 3.37 3.53 3.77 3.99 4.17Rhombic dodecahedra 3.25 3.44 3.64 3.86 4.08Bulk 2.95 3.25 3.48 3.71 3.98
3.3. Effect of Morphology on the Activation Energy, Activa-tion Gibbs Free Energy, Activation Enthalpy, and ActivationEntropy of Ag3PO4 Micro-/Nanocrystals. Linear regression oflogarithmic reaction rate constant and temperature recipro-cal (slope and intercept in Figure 4) was performed using(8), and the 𝐸
𝑎of the Ag
3PO4micro-/nanocrystals reaction
was obtained. The Δ𝐺
𝜃
=of the Ag
3PO4micro-/nanocrystals
reaction was calculated using (9). The Δ𝐻
𝜃
=and Δ𝑆
𝜃
=of
6 Journal of Nanomaterials
Table 2: Activation energy, activation Gibbs free energy, activation enthalpy, and activation entropy of Ag3PO4micro-/nanocrystals.
Ag3PO4
Micro-/nanocrystals T (K) Δ𝐺
𝜃
=(kJ⋅mol−1) 𝐸
𝑎(kJ⋅mol−1) Δ𝐻
𝜃
=(kJ⋅mol−1) Δ𝑆
𝜃
=(J⋅K−1⋅mol−1)
Cube
298.15 87.132
8.653 6.093 −271.831303.15 88.518308.15 89.852313.15 91.204318.15 92.585
Rhombicdodecahedra
298.15 87.222
8.990 6.430 −270.987303.15 88.583308.15 89.941313.15 91.290318.15 92.643
Bulk
298.15 87.462
11.548 8.988 −263.123303.15 88.726308.15 90.056313.15 91.393318.15 92.708
87
88
89
90
91
92
93
300 305 310 315 320295
T (K)
CubesRhombic dodecahedralBulk
ΔG𝜃 ≠(k
Jmol
−1 )
Figure 6: Morphology effect on the activation Gibbs free energy ofAg3PO4micro-/nanocrystals.
the Ag3PO4micro-/nanocrystals reaction were calculated
using (10). Results are listed in Table 2.As shown in Table 1, the activation energy, activation
Gibbs free energy (as shown in Figure 6), activation enthalpy,and activation entropy of Ag
3PO4
micro-/nanocrystalsdecrease with decreasing particle size. Surface atoms are inmetastable state because of the high specific surface effect ofmicro-/nanomaterials. The nanosystem has higher potentialenergy than the bulk system because of high specific surfaceeffect. Transition state theory states that the nanosystem hasto overcome smaller energy barrier than the bulk system toreach the same transition state. Therefore, smaller particles
Table 3: Surface Gibbs free energy of Ag3PO4micro-/nanocrystals.
𝑇 (K) 298.15 303.15 308.15 313.15 318.15𝐺
𝑆 (kJ⋅mol−1)Cube 0.330 0.208 0.205 0.189 0.123Rhombic dodecahedra 0.240 0.143 0.115 0.103 0.066
require less activation energy. The effect of morphology on𝐸
𝑎, Δ𝐺
𝜃
=, Δ𝐻
𝜃
=, and Δ𝑆
𝜃
=demonstrates that cubic Ag
3PO4
overcomes smaller energy barrier than dodecahedral Ag3PO4
in the same reaction. Thus, cubic Ag3PO4requires less
activation energy than dodecahedral Ag3PO4.
3.4. Effect of Morphology on the Surface Gibbs Free Energyof Ag3PO4 Micro-/Nanocrystals. Combining (14)–(16), wecalculated the surface Gibbs free energy of Ag
3PO4micro-/
nanocrystals on the basis of the activation Gibbs free energylisted in Table 3.
The molar surface Gibbs free energy of Ag3PO4micro-/
nanocrystals (𝐺𝑆𝑚) under different temperatures is shown
in Figure 7. Cubic Ag3PO4has higher 𝐺
𝑆
𝑚than rhombic
dodecahedral Ag3PO4. Both conditions are inversely propor-
tional to temperature. The uneven stress on the atoms of thesurface phase intensifies with increasing reaction tempera-ture. The thermal motion of nanoparticles also intensifieswith the increase in unsaturated force field and danglingbonds.The widening particle space weakens their interactionand decreases the surface tension of nanomaterials, therebyreducing the surface Gibbs free energy.
3.5. Effect of Morphology on the Molar Surface Enthalpy,Molar Surface Entropy, and Molar Surface Energy of Ag
3PO4
Micro-/Nanocrystals. The𝐻𝑆𝑚, 𝑆𝑆𝑚, and𝐸
𝑆
𝑚ofAg3PO4micro-/
nanocrystals were calculated using (17), (18), and (19), respec-tively.
Journal of Nanomaterials 7
Table 4:Morphology effect on the surface enthalpy, surface entropy,and surface energy of Ag
3PO4micro-/nanocrystals.
Surface energies Ag3PO4micro-/nanocrystals
Cube Rhombic dodecahedron𝐻
𝑆
𝑚(kJ⋅mol−1) 2.895 2.558
𝑆
𝑆
𝑚(kJ⋅mol−1) 8.708 7.864
𝐸
𝑆
𝑚(kJ⋅mol−1) 2.895 2.558
GS
(kJ m
ol−1)
300 305 310 315 320295
T (K)
0.05
0.10
0.15
0.20
0.25
0.30
0.35
CubesRhombic dodecahedral
Figure 7: Morphology effect on surface Gibbs free energy ofAg3PO4micro-/nanocrystals.
Table 4 shows that cubic Ag3PO4micro-/nanocrystals
have higher 𝐻
𝑆
𝑚, 𝑆
𝑆
𝑚, and 𝐸
𝑆
𝑚than rhombic dodecahedral
Ag3PO4. This result agrees with that on surface Gibbs free
energy. Molar surface energy is the sum of the kineticenergy, potential energy, and chemical energy of surfacephase particles. After super-refinement of thematerial, atomsof the surface phase suffer from uneven stress, displayunsaturated force field, and possess dangling bonds becauseof strong specific surface effect. Consequently, the interactionof nanoparticles is enhanced.This phenomenon explains whymicro-/nanomaterials have high kinetic energy and potentialenergy.
4. Conclusion
This study determined the surface energies of Ag3PO4micro-
/nanocrystals and their kinetic parameters when reactingwith HNO
3by using microcalorimetry. It also discussed
rationally combined thermochemical cycle, transition statetheory, basic theory of chemical thermodynamics withthermokinetic principle,morphology dependence of reactionkinetics, and surface thermodynamic properties. Resultsshow that the molar surface enthalpy, molar surface entropy,molar surface Gibbs free energy, and molar surface energy ofcubic Ag
3PO4micro-/nanocrystals are larger than those of
rhombic dodecahedral Ag3PO4micro-/nanocrystals. Com-
pared with rhombic dodecahedral Ag3PO4, cubic Ag
3PO4
with high surface energy exhibits higher reaction rateand lower activation energy, activation Gibbs free energy,activation enthalpy, and activation entropy. These resultsindicate that cubic Ag
3PO4micro-/nanocrystals possess a
much higher reactivity and it is more easily activated thanrhombic dodecahedral Ag
3PO4micro-/nanocrystals. This
paper presents a novel facile approach to study the surfacethermodynamic property of nanomaterials and the structure-function relationship between reaction dynamics and size,morphology, and structure.
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
Acknowledgments
The authors are thankful for the financial support from theNational Natural Science Foundation of China (21273050,21573048), high level innovation teams and academic excel-lence scheme of colleges and universities in Guangxi(Guangxi teach [2014]7), the Reform of Postgraduate Cul-tivation Mechanism from 2013 (Chemical Engineering,113000100030001), and Innovation Projects of PostgraduateEducation of Guangxi University for Nationalities (gxun-chxs2015086). The authors would like to express their greatappreciation to Guangxi Colleges and Universities Key Labo-ratory of Food Safety and Pharmaceutical Analytical Chem-istry (Guangxi University for Nationalities).
References
[1] L. D. Zhang, The Preparation and Application of SuperfinePowders, China Petrochemical Press, Beijing, China, 2001.
[2] L. D. Zhang and J. M. Mou, Nanomaterials and Nanostructures,Science Press, Beijing, China, 2001.
[3] J. Du, R. Zhao, and Y. Q. Xue, “Effects of sizes of nano-copper oxide on the equilibrium constant and thermodynamicproperties for the reaction in nanosystem,” Journal of ChemicalThermodynamics, vol. 45, no. 1, pp. 48–52, 2012.
[4] Y. Q. Xue, B. J. Gao, and J. F. Gao, “The theory of thermodynam-ics for chemical reactions in dispersed heterogeneous systems,”Journal of Colloid and Interface Science, vol. 191, no. 1, pp. 81–85,1997.
[5] J. P. Du, H. Y. Wang, and R. H. Zhao, “Size-dependent ther-modynamic properties and equilibrium constant of chemicalreaction in nanosystem: an experimental study (II),” Journal ofChemical Thermodynamics, vol. 65, pp. 29–33, 2013.
[6] L. Mazeina, S. Deore, and A. Navrotsky, “Energetics of bulkand nano-akaganeite,𝛽-FeOOH: enthalpy of formation, surfaceenthalpy, and enthalpy of water adsorption,” Chemistry ofMaterials, vol. 18, no. 7, pp. 1830–1838, 2006.
[7] L. Mazeina and A. Navrotsky, “Enthalpy of water adsorptionand surface enthalpy of goethite (𝛼-FeOOH) and hematite (𝛼-Fe2O3),”Chemistry of Materials, vol. 19, no. 4, pp. 825–833, 2007.
[8] X. X. Li, Z. Y. Huang, L. Y. Zhong, T. H. Wang, and X. C. Tan,“Size effect on reaction kinetics and surface thermodynamic
8 Journal of Nanomaterials
properties of nano-octahedral cadmium molybdate,” ChineseScience Bulletin, vol. 59, pp. 2490–2498, 2014.
[9] T. H. Wang, L. D. Wang, Y. X. Guo, Y. F. Li, G. C. Fan, and Z.Y. Huang, “Standard molar enthalpy of formation of uniformCdMoO
4nano-octahedra,” Chinese Science Bulletin, vol. 58, no.
26, pp. 3208–3212, 2013.[10] D. Fernandez-Canoto and J. Z. Larese, “Thermodynamic and
modeling study of thin n-heptane films adsorbed on magne-sium oxide (100) surfaces,”The Journal of Physical Chemistry C,vol. 118, no. 7, pp. 3451–3458, 2014.
[11] Z.-Y. Zhou, N. Tian, J.-T. Li, I. Broadwell, and S.-G. Sun, “Nano-materials of high surface energy with exceptional properties incatalysis and energy storage,” Chemical Society Reviews, vol. 40,no. 7, pp. 4167–4185, 2011.
[12] Q. Kuang, X. Wang, Z. Jiang, Z. Xie, and L. Zheng, “High-energy-surface engineered metal oxide micro- and nanocrys-tallites and their applications,” Accounts of Chemical Research,vol. 47, no. 2, pp. 308–318, 2014.
[13] L. H. Hu, Q. Peng, and Y. Li, “Selective synthesis of Co3O4
nanocrystal with different shape and crystal plane effect oncatalytic property for methane combustion,” Journal of theAmerican Chemical Society, vol. 130, no. 48, pp. 16136–16137,2008.
[14] Y.-Z. Wen, Y.-Q. Xue, Z.-X. Cui, and Y. Wang, “Thermo-dynamics of nanoadsorption from solution: theoretical andexperimental research,” Journal of Chemical Thermodynamics,vol. 80, pp. 112–118, 2014.
[15] Z.-X. Cui, M.-Z. Zhao, W.-P. Lai, and Y.-Q. Xue, “Thermo-dynamics of size effect on phase transition temperatures ofdispersed phases,” Journal of Physical Chemistry C, vol. 115, no.46, pp. 22796–22803, 2011.
[16] Y. Yunfeng, X. Yongqiang, C. Zixiang, and Z. Miaozhi, “Effectof particle size on electrode potential and thermodynamics ofnanoparticles electrode in theory and experiment,”Electrochim-ica Acta, vol. 136, pp. 565–571, 2014.
[17] B. Slater, C. Richard, A. Catlow, D. H. Gay, D. E. Williams, andV. Dusastre, “Study of surface segregation of antimony on SnO
2
surfaces by computer simulation techniques,” Journal of PhysicalChemistry B, vol. 103, no. 48, pp. 10644–10650, 1999.
[18] M. Lazzeri, A. Vittadini, and A. Selloni, “Structure and ener-getics of stoichiometric TiO
2anatase surfaces,” Physica B:
Condensed Matter, vol. 63, no. 15, Article ID 155409, 2001.[19] M. Lazzeri, A. Vittadini, and A. Selloni, “Erratum: structure
and energetics of stoichiometric TiO2anatase surfaces,”Physical
Review B: Condensed Matter, vol. 65, Article ID 119901, 2002.[20] J. M. McHale, A. Auroux, A. J. Perrotta, and A. Navrot-
sky, “Surface energies and thermodynamic phase stability innanocrystalline aluminas,” Science, vol. 277, no. 5327, pp. 788–789, 1997.
[21] A. V. Radha, O. Bomati-Miguel, S. V. Ushakov, A. Navrotsky,and P. Tartaj, “Surface enthalpy, enthalpy of water adsorption,and phase stability in nanocrystalline monoclinic zirconia,”Journal of the American Ceramic Society, vol. 92, no. 1, pp. 133–140, 2009.
[22] M. K. Chaudhury and G. M. Whitesides, “Correlation betweensurface free energy and surface constitution,” Science, vol. 255,no. 5049, pp. 1230–1232, 1992.
[23] K. Kendall, N. M. Alford, and J. D. Birchall, “A new method formeasuring the surface energy of solids,” Nature, vol. 325, no.6107, pp. 794–796, 1987.
[24] V. M. Huxter, A. Lee, S. S. Lo, and G. D. Scholes, “CdSenanoparticle elasticity and surface energy,” Nano Letters, vol. 9,no. 1, pp. 405–409, 2009.
[25] Q. Wu, M. Liu, Z. Wu, Y. Li, and L. Piao, “Is photooxidationactivity of 001 facets truly lower than that of 101 facets for anataseTiO2crystals?”The Journal of Physical Chemistry C, vol. 116, no.
51, pp. 26800–26804, 2012.[26] W. H. Luo,Molecular dynamic calculation of free energy and its
application in nanostructured materials [Ph.D. thesis], HunanUniversity, Changsha, China, 2008.
[27] G. A. Hulett, “The solubility of gypsum as affected by size ofparticles and by different crystal-lographic surfaces,” Journal ofthe American Chemical Society, vol. 27, no. 1, pp. 49–56, 1995.
[28] W. J. Jones, “Uber die beziehung zwischen geometrischer formund dampfdruck, loslichkeit, und formenstabilitat,” Annalender Physik, vol. 346, no. 7, pp. 441–448, 1913.
[29] R. K. Tang, G. H. Nancollas, and C. A. Orme, “Mechanismof dissolution of sparingly soluble electrolytes,” Journal of theAmericanChemical Society, vol. 123, no. 23, pp. 5437–5443, 2001.
[30] R. K. Tang, L. Wang, C. A. Orme, T. Bonstein, P. J. Bush, and G.H. Nancollas, “Dissolution at the nanoscale: self-preservationof biominerals,” Angewandte Chemie, vol. 43, no. 20, pp. 2697–2701, 2004.
[31] R. Tang, W. Wu, M. Haas, and G. H. Nancollas, “Kinetics ofdissolution of 𝛽-tricalcium phosphate,” Langmuir, vol. 17, no. 11,pp. 3480–3485, 2001.
[32] R. K. Tang, “Progress in the studies of interfacial energy andkinetics of crystal growth/dissolution,” Progress in Chemistry,vol. 17, no. 2, pp. 369–376, 2005.
[33] V. K. Kumikov and K. B. Khokonov, “On the measurement ofsurface free energy and surface tension of solid metals,” Journalof Applied Physics, vol. 54, no. 3, pp. 1346–1350, 1983.
[34] H. P. Bonzel and M. Nowicki, “Absolute surface free energies ofperfect low-index orientations of metals and semiconductors,”Physical Review B, vol. 70, no. 24, Article ID 245430, 2004.
[35] H. P. Bonzel and A. Emundts, “Absolute values of surface andstep free energies from equilibrium crystal shapes,” PhysicalReview Letters, vol. 84, no. 25, pp. 5804–5807, 2000.
[36] Z. Yi, J. Ye, N. Kikugawa et al., “An orthophosphate semi-conductor with photooxidation properties under visible-lightirradiation,” Nature Materials, vol. 9, no. 7, pp. 559–564, 2010.
[37] Y. Bi, H. Hu, S. Ouyang, G. Lu, J. Cao, and J. Ye, “Photo-catalytic and photoelectric properties of cubic Ag
3PO4sub-
microcrystals with sharp corners and edges,”Chemical Commu-nications, vol. 48, no. 31, pp. 3748–3750, 2012.
[38] Z. Jiao, Y. Zhang, H. Yu, G. Lu, J. Ye, and Y. Bi, “Concavetrisoctahedral Ag
3PO4microcrystals with high-index facets
and enhanced photocatalytic properties,” Chemical Communi-cations, vol. 49, no. 6, pp. 636–638, 2013.
[39] Y. Bi, S. Ouyang, N. Umezawa, J. Cao, and J. Ye, “Facet effect ofsingle-crystalline Ag
3PO4sub-microcrystals on photocatalytic
properties,” Journal of the American Chemical Society, vol. 133,no. 17, pp. 6490–6492, 2011.
[40] Z. J. Liu, G. C. Fan, and Z. Y. Huang, “Catalytic processthermodynamics, kinetics and surface thermodynamic effectof different morphologies Ag
3PO4,” Science in China Series B:
Chemistry, vol. 45, no. 8, pp. 855–862, 2015.[41] R. Rychly and V. Pekarek, “The use of potassium chloride and
tris (hydroxymethyl) aminomethane as standard substances forsolution calorimetry,”The Journal of ChemicalThermodynamics,vol. 9, no. 4, pp. 391–396, 1977.
Journal of Nanomaterials 9
[42] Y.-Q. Xue, J.-P. Du, P.-D. Wang, and Z.-Z. Wang, “Effectof particle size on kinetic parameters of the heterogeneousreactions,” Acta Physico—Chimica Sinica, vol. 21, no. 7, pp. 758–762, 2005.
[43] Y. Q. Xue, Effects of particle size on phase transitions andreactions of nanosystems [Ph.D. thesis], Taiyuan University ofTechnology, Taiyuan, China, 2005.
[44] R. Z. Hu, Q. F. Zhao, and H. X. Gao, Calorimetry Fundamentalsand Application, Science Press, Beijing, China, 2011.
[45] L. D.Wang, S. G. Liu, X. L. Liu, Z. J. Liu, Z.Ma, and Z. Y. Huang,“Thermodynamic functions and growth constants of web-likeZnO nanostructures,” Chinese Science Bulletin, vol. 58, no. 27,pp. 3380–3384, 2013.
Submit your manuscripts athttp://www.hindawi.com
ScientificaHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation http://www.hindawi.com Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Nano
materials
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Journal ofNanomaterials