Morphology Effect on the Kinetic Parameters and Surface Thermodynamic Properties of Ag3PO4 Micro-/Nanocrystals

1Chemical and Environmental Engineering, Baise University, Baise 533000, China 2College of Chemistry and Chemical Engineering, Guangxi University for Nationalities, Nanning 530008, China 3Key Laboratory of Forest Chemistry and Engineering, Guangxi University for Nationalities, Nanning 530008, China 4Guangxi Colleges and Universities Key Laboratory of Food Safety and Pharmaceutical Analytical Chemistry, Guangxi University for Nationalities, Nanning 530008, China


Introduction
Nanomaterials that exhibit high specific surface effect differ from massive materials in terms of physical and chemical properties [1,2].Du et al. [3] explained that the specific surface effect, surface heat capacity, and specific surface energy of nanomaterials cannot be neglected.The overall thermodynamic property of nanoparticles comprises surface and bulk phases [3][4][5][6][7][8][9].Surface thermodynamic properties are the intuitive expression of the special structure-activity relationship of nanomaterial surface, which significantly affects many physical/chemical reactions, including chemical thermodynamics [3,4], chemical kinetics [5], catalysis [10][11][12][13], sense [11], adsorption [14], phase transition [15], and electrochemistry of nanomaterials [16].Theoretical calculation results showed that nanomaterials with different sizes and facets have different surface energies [17][18][19] and that the reactivity of nanomaterials depends on surface energy [11,12].Studying the surface thermodynamic property of nanomaterials and the structure-function relationship between reaction dynamics and size, morphology, and structure is valuable to understand the nature of chemical reactions.
Journal of Nanomaterials [31,32] measured the surface energy of inorganic insoluble salt 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 point produce high and even applied stress-covered surface energies.Hence, theoretical calculation is preferred to measure solid surface energy [23].Nevertheless, theoretical calculation often deviates from the practical ideal model and from many hypotheses.Real surfaces with abundant atom ladders and unsaturated bonds, as well as those with unstable thermodynamics, tend to absorb water [7], gas molecules, and surfactant [11,12]; undergo surface atom reconstruction and aggregation; or even form a protective film layer.The surface energies of these complicated real surfaces are extremely difficult to theoretically calculate.Experimental measurement still faces several challenges.Different experimental methods provide significantly different values for the surface energies of the same material [33]; researchers using the same experimental method also obtain varying results [34,35].A universal method to determine surface energy has yet to be developed.Developing a scientific and universal experimental method to measure the surface energy of nanomaterials is a pressing need in the scientific endeavors on solid surface and in other disciplines.
The visible-light-driven Ag 3 PO 4 photocatalyst has become popular since its introduction in 2010 [36,37].Scientists calculated the surface energies of different facets of Ag 3 PO 4 on the basis of the relationship between included angle of crystal faces and Miller index [38].Other researchers performed the same calculation by using density functional theory [39].Studying the structure-function relationship between the surface energy of micro-/nanomaterial Ag 3 PO 4 and size, morphology, and structure is valuable to understand the natures of chemical reactions.However, the surface energy of this material was rarely calculated using experimental methods.The present study determined the surface energies of Ag 3 PO 4 micro-/nanocrystals with cubic and rhombic dodecahedral morphologies and their kinetic parameters when reacting with HNO 3 by using microcalorimetry.This study also discussed rationally combined thermochemical cycle, transition state theory, basic theory of chemical thermodynamics with thermokinetic principle, morphology dependence of reaction kinetics, and surface thermodynamic properties.

Characterization.
The morphology of the sample was examined under a field-emission scanning electron microscope (Zeiss SUPRA 55 Sapphire, Germany).The X-ray diffraction (XRD) pattern was recorded on an X-ray powder diffractometer (Philips PW 1710 with Cu K radiation,  = 1.5406Å, Holland).Trace amounts of the sample were measured on a XPE analytic balance (Mettler Toledo, Switzerland).Calorimetric experiments were performed using a microcalorimeter (RD496L, Mianyang CP Thermal Analysis Instrument Co., Ltd., China) under constant temperature and pressure.
A small glass tube containing 1.0 mL of 0.36 M HNO 3 solution was placed above a 15 mL glass tube charged with 1.500 mg of Ag 3 PO 4 samples (bulk or the obtained nanocubes).Simultaneously with the establishment of equilibrium, the small glass tube with HNO 3 solution was pushed down.The in situ thermodynamic and kinetic information for this reaction was recorded using the microcalorimeter.

Establishment of Chemical Reaction Kinetic Models for
Cubic and Rhombic Dodecahedron Ag 3 PO 4 Micro-/Nanocrystals.The specific surface area and specific surface energy of the reactant increase after being refined; thus, the mean molar energy of the refined reactant is higher than that of the corresponding bulk reactant.If the reactant particle size is insignificant to the mean energy of the activated molecules, then the difference between the mean molecular activation energy of 1 M of nanoparticles and mean energy of 1 mol super-refined reactant is the chemical activation energy of the nanomaterial [42].Figure 1 shows the transition state theory [8,42,43].In the same chemical reaction, the reactant experiences the same transition state to the final state.Therefore, the apparent activation energy of nanoparticles   is the difference between the activation energy of corresponding bulk material [  (bulk)] and the molar surface energy of nanoparticles (   ): If the dispersion phase in heterogeneous reaction has only one reactant and others belong to the continuous phase, then the relationship between surface energy and apparent activation energy for cubic nanoparticles without inner bores can be expressed as where , , , and  are the surface tension, molar mass, density, and particle size (length of cube edge) of the cubic nanoparticle reactant, respectively.Equation ( 2) provides that the apparent activation energy in the chemical reaction of the nanomaterials is proportional to the particle size of the reactant.

Energy
Reactant Product

Reaction coordinate
Initial state If the heterogeneous reaction follows Arrhenius Law, substituting (2) into it yields the Arrhenius equation of the nanocube: Similarly, the Arrhenius equation of dodecahedron is obtained: where  is the reaction temperature,  is the reaction rate constant, and  is the preexponential factor.Substituting the logarithm on both sides of (4), we obtain the following: ln Therefore, when the particle size is larger than 10 nm, the surface tension slightly changes and can be viewed as a constant [43].On the basis of ( 5) and ( 6), the logarithm of the reaction rate constant is inversely proportional to the particle size of the reactant.

Acquisition of Dynamic Parameters of Ag 3 PO 4
Reacting with HNO 3 .The thermodynamic equation of reversible chemical reaction under constant temperature and pressure can be expressed as [44] ln where  ∞ is the enthalpy change during the whole reaction and may be directly obtained by microcalorimetry, d  /d is the enthalpy change rate,  (s −1 ) is the reaction rate constant expressed by conversion rate, and   is the enthalpy change at reaction time . can be calculated from the linear regression of thermodynamic data: ln where   is Avogadro's constant,   is Boltzmann's constant, ℎ is Planck's constant, and  is the molar gas constant.The diagram of 1/ was drawn with ln .  and  were calculated using (8).

Theoretical Derivation of Molar Surface Gibbs Free Energy, Molar Surface Enthalpy, Molar Surface Entropy, and Molar
Surface Energy.The molar Gibbs free energy of chemical reaction of nanosystem consists of bulk phase (Δ     ) and surface phase (Δ     ) [8,42]: The molar Gibbs free energy of the bulk chemical reaction nearly exhibits bulk phase.The bulk phase of the nanosystem is similar to that of bulk: where Δ    (bulk) is the molar Gibbs free energy of the same chemical reaction bulk material.Therefore, the molar Gibbs free energy difference between the nanosystem and the bulk lies in the molar surface Gibbs free energy of the nanomaterial (excessive Gibbs free energy compared with bulk material).Substituting (12) into (11), we obtain On the basis of ( 13), the thermochemical cycles of nanoand bulk Ag 3 PO 4 were designed (Figure 2).The thermodynamic functions of nano-and bulk Ag 3 PO 4 reactions with HNO 3 were tested.The thermodynamic function of nano-Ag 3 PO 4 conversion 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 Ag 3 PO 4 micro-/nanocrystals with a net reaction of Ag 3 PO 4 (nano) → Ag 3 PO 4 (bulk) is Ag 3 PO 4 (nano) Ag 3 PO 4 (bulk) The same final state In accordance with transition state theory, the relationship between reaction rate constants of Ag 3 PO 4 micro-/ nanocrystals reaction system and bulk Ag 3 PO 4 reaction system and the Gibbs free energy can be expressed as [8,45] where Δ    ̸ = and  are the activation Gibbs free energy and rate constant of Ag 3 PO 4 chemical reaction.
Similarly, molar surface entropy can be deduced from transition state theory: where Δ     , Δ     , Δ    ̸ = , and    are the molar surface reaction entropy, molar reaction entropy, molar activation entropy, and molar surface entropy of Ag 3 PO 4 chemical reaction, respectively.
Apparent activation energy refers to the total energy needed for the material to overcome activation.The essential difference between Ag 3 PO 4 micro-/nanocrystals and bulk Ag 3 PO 4 is the high specific surface effect of the surface phase.After the same transition state to the final state in the same chemical reaction (Figure 1), the surface energy of the nanosystem surface phase (   ) is the energy difference between the nano-reaction system and the bulk reaction system.The molar surface energy in the manuscript cited reference [8] which deduced in our published paper.Its correct form is [8].Consider where Δ   ,   , and   are the molar surface reaction energy, activation energy, and molar surface energy of Ag 3 PO 4 chemical reaction, respectively.

Results and Discussion
3.1.Product Characterization.Figures 3(a)-3(c) show the SEM images of Ag 3 PO 4 micro-/nanocrystals.Cubic Ag 3 PO 4 has six (100) faces, clear and sharp edges and angles, and smooth surfaces; the mean particle size is (695.9 ± 100.2) nm. Figure 3(b) is the rhombic dodecahedral Ag 3 PO 4 with 12 rhombus (110) faces.White spots are scattered on the surfaces; the mean particle size is (647.1 ± 91.8) nm. Figure 3(c) shows the SEM image of the irregularly shaped Ag 3 PO 4 that forms the bulk of the substance; its mean particle size is (6.9 ± 3.9) m.
Figure 4 shows the XRD pattern of the bulk, rhombic dodecahedral, and cubic Ag 3 PO 4 .All diffraction peaks in Figure 4 agree with those of Ag 3 PO 4 with the standard calorie JPCDS (06-0505).No other impurity peak is observed.Moreover, the full width at half maximum of all diffraction peaks is narrow, indicating purity and good crystallinity of the prepared samples.performed using the original thermodynamics data obtained from (7), and the reaction rate constants of Ag 3 PO 4 and HNO 3 under varying temperatures were obtained (Table 1).The curves shown in Figure 5 were drawn on the basis of the reaction rate constants of Ag 3 PO 4 with HNO 3 and the reciprocal of temperature in Table 1.

Effect of Morphology on the Chemical Reaction Rate
Figure 5 shows that the reaction rate is proportional to temperature when the particle size is fixed.Compared with bulk Ag 3 PO 4 , the super-refined materials have significantly more particles of the surface phase.Particles of the surface phase account for a large proportion of the total particles.Atoms of the surface phase have uneven stresses, unsaturated force field, and dangling bonds, which lead to high surface energy.This result explains the faster reaction rate of Ag 3 PO 4 micro-/nanocrystals than bulk Ag 3 PO 4 .As the temperature increases, the surface turbulence and surface energy of Ag 3 PO 4 micro-/nanocrystals increase; consequently, the chemical reaction increases.The effect of morphology on the reaction rate shows that cubic Ag 3 PO 4 has higher reaction rate than dodecahedral Ag 3 PO 4 .the Ag 3 PO 4 micro-/nanocrystals reaction were calculated using (10).Results are listed in Table 2.

Rhombic dodecahedral Bulk
As shown in Table 1, the activation energy, activation Gibbs free energy (as shown in Figure 6), activation enthalpy, and activation entropy of Ag 3 PO 4 micro-/nanocrystals decrease with decreasing particle size.Surface atoms are in metastable state because of the high specific surface effect of micro-/nanomaterials.The nanosystem has higher potential energy than the bulk system because of high specific surface effect.Transition state theory states that the nanosystem has to overcome smaller energy barrier than the bulk system to reach the same transition state.Therefore, smaller particles  14)-( 16), we calculated the surface Gibbs free energy of Ag 3 PO 4 micro-/ nanocrystals on the basis of the activation Gibbs free energy listed in Table 3.
The molar surface Gibbs free energy of Ag 3 PO 4 micro-/ nanocrystals (   ) under different temperatures is shown in Figure 7. Cubic Ag 3 PO 4 has higher    than rhombic dodecahedral Ag 3 PO 4 .Both conditions are inversely proportional to temperature.The uneven stress on the atoms of the surface phase intensifies with increasing reaction temperature.The thermal motion of nanoparticles also intensifies with the increase in unsaturated force field and dangling bonds.The widening particle space weakens their interaction and decreases the surface tension of nanomaterials, thereby reducing the surface Gibbs free energy.

Effect of Morphology on the Molar Surface Enthalpy, Molar Surface Entropy, and Molar Surface Energy of Ag 3 PO 4
Micro-/Nanocrystals.The    ,    , and    of Ag 3 PO 4 micro-/ nanocrystals were calculated using ( 17), (18), and (19), respectively.Table 4 shows that cubic Ag 3 PO 4 micro-/nanocrystals have higher    ,    , and    than rhombic dodecahedral Ag 3 PO 4 .This result agrees with that on surface Gibbs free energy.Molar surface energy is the sum of the kinetic energy, potential energy, and chemical energy of surface phase particles.After super-refinement of the material, atoms of the surface phase suffer from uneven stress, display unsaturated force field, and possess dangling bonds because of strong specific surface effect.Consequently, the interaction of nanoparticles is enhanced.This phenomenon explains why micro-/nanomaterials have high kinetic energy and potential energy.

Conclusion
This study determined the surface energies of Ag 3 PO 4 micro-/nanocrystals and their kinetic parameters when reacting with HNO 3 by using microcalorimetry.It also discussed rationally combined thermochemical cycle, transition state theory, basic theory of chemical thermodynamics with thermokinetic principle, morphology dependence of reaction kinetics, and surface thermodynamic properties.Results show that the molar surface enthalpy, molar surface entropy, molar surface Gibbs free energy, and molar surface energy of cubic Ag 3 PO 4 micro-/nanocrystals are larger than those of rhombic dodecahedral Ag 3 PO 4 micro-/nanocrystals.Compared with rhombic dodecahedral Ag 3 PO 4 , cubic Ag 3 PO 4 with high surface energy exhibits higher reaction rate and lower activation energy, activation Gibbs free energy, activation enthalpy, and activation entropy.These results indicate that cubic Ag 3 PO 4 micro-/nanocrystals possess a much higher reactivity and it is more easily activated than rhombic dodecahedral Ag 3 PO 4 micro-/nanocrystals.This paper presents a novel facile approach to study the surface thermodynamic property of nanomaterials and the structurefunction relationship between reaction dynamics and size, morphology, and structure.

Figure 1 :
Figure 1: Schematic of relationship between surface energy and apparent activation energy.

Figure 5 :
Figure 5: Effect of morphology on the reaction rate constant of Ag 3 PO 4 micro-/nanocrystals with HNO 3 .

Figure 6 :
Figure 6: Morphology effect on the activation Gibbs free energy of Ag 3 PO 4 micro-/nanocrystals.

Figure 7 :
Figure 7: Morphology effect on surface Gibbs free energy of Ag 3 PO 4 micro-/nanocrystals.
Figure 2: Thermochemical cycle of nano-and bulk Ag3 PO 4 reacting with HNO 3 .where Δ   (Ag 3 PO 4 , nano) and Δ   (Ag 3 PO 4 , bulk) are the standard molar Gibbs free energies of the reactions of Ag 3 PO 4 micro-/nanocrystals and bulk Ag 3 PO 4 with HNO 3 , respectively; Δ   (Ag 3 PO 4 , nano) and    (Ag 3 PO 4 , nano) are the molar reaction surface Gibbs free energy and molar surface Gibbs free energy, respectively.

Table 3 :
Surface Gibbs free energy of Ag 3 PO 4 micro-/nanocrystals.PO 4 overcomes smaller energy barrier than dodecahedral Ag 3 PO 4 in the same reaction.Thus, cubic Ag 3 PO 4 requires less activation energy than dodecahedral Ag 3 PO 4 .3.4.Effect of Morphology on the Surface Gibbs Free Energy of Ag 3 PO 4 Micro-/Nanocrystals.Combining (

Table 4 :
Morphology effect on the surface enthalpy, surface entropy, and surface energy of Ag 3 PO 4 micro-/nanocrystals.