粒度对纳米体系相变和化学反应的影响
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摘要
虽然关于纳米粒子和纳米材料物理化学性质方面的研究是目前纳米领域的热门课题之一,但关于粒度对相变和化学反应影响规律方面的研究却不多。
目前的相平衡、化学平衡、化学动力学和电化学理论中均未考虑反应物颗粒的表面影响,因而不能解决纳米体系的相平衡、化学平衡、动力学和电化学中的相关问题。本课题属于表面化学分别与热力学、动力学和电化学等多个学科的交叉,而目前国内外对这些交叉学科的研究不多,在很多方面还处于空白。因此本课题的研究对于建立新的交叉学科和发展物理化学理论有着重要的科学意义和较高的学术价值。
另外,在化工、环保、材料(尤其是功能材料)、能源、电子、农业及生命科学(如血液)等领域中均有许许多多涉及纳米微粒相变和化学反应的问题,本课题的研究成果可为纳米微粒在这些领域中的应用提供理论依据和指导作用。例如应用本研究成果所得到的理论和规律,可预测纳米粒子的相变温度,增大多相反应的平衡常数,提高平衡产率,加快反应速率,降低苛刻的反应条件,减小投资,降低动力消耗和成本,指导有害微粒的防治,产生直接或间接的经济效益和社会效益。可见,本课题的研究还具有广泛的和重要的应用前景。
The researches of nanoparticles and the nano-size materials are one of the current popular topics. Although the investigations of the physical and chemical properties for nanoparticles are a lot of, the studies on regularities of effects of particle size on phases transitions and chemical reactions are less. Since the surface effects are not considered in the current theories of phases transitions, chemical thermodynamics, chemical kinetics and electrochemistry, as a result the theories can't resolve the related problems of the nanosystems. This topic deals with some crossed sciences between surface chemistry and thermodynamics, chemical kinetics and electrochemistry, the crossed sciences are rarely studied and many aspects in the crossed sciences yet are in the blank space. Therefore, The investigations have the important science meaning and academic values to establish the new crossed sciences and to develop the theories of physical chemistry.Moreover, there are a lots of problems involved phase transitions and chemical reactions of nanosystems in many fields such as chemical engineering, environmental protection, material (particularly function
material), energy sources, electronics, agriculture and life science etc, and the studies will provide some theoretical foundations and guidance for applications nanoparticles to these fields. The effort of the study can be applied to predicting the transition temperatures of nanoparticles, increasing the equilibrium constant, the conversion rates and the reaction rate of heterogeneous reactions, lowering the uncharitable reaction conditions and the production costs, decreasing the investment of the apparatus and directing the prevention of the harmful particles, so as to produce the direct or indirect economic performances and social benefits. It is thus clear that, the research still has extensive and important foregrounds of applications.The domestic and international investigations concerning the effects of particle size on the phase transitions, the chemical equilibriums, the reaction kinetics and the galvanic cells have been overviewed in this thesis, and the present status of the topic has been comprehended.The current theory of phase transitions for nanosystems is limited to only melting transitions, and the theories are approximative and can not expound and predict the melting behavior for the particles smaller than 10nm. A universal theory of nanosystem transitions applied to all of phase transitions such as solid-solid (transition of crystal structures), solid-liquid, liquid-gas and solid-gas transitions has not yet been reported. Besides there yet is no the concrete relations between the surface tensions of condensed phases and the particle size, which will have some difficulty in calculating the transition temperatures, the latent heats and the transition entropies of nanoparticles.
At present the investigations of the effects of particle size on the thermodynamic properties and the equilibrium constant in heterogeneous reactions are fewer and still are confined to theoretical aspects, and the reports of the experimental ones are yet not discovered so far.Now the experimental researches to kinetics for heterogeneous reactions are a lot, but the theoretical researches into the regularities of effects of particle size on the kinetics parameters are fewer.Although many models of heterogeneous reaction kinetics was advanced, yet the models can only give expression to relationship between a reaction rate and a extent of reaction or a instantaneous size of particles, and the models only can explain some experimental phenomenon or some kind of experimental results. In other words, these models lack versatility and the universality. The reports that the theoretical studies of effects of particle size on the kinetic parameters in heterogeneous reactions such as the activation energy, the rate constant, the reaction order and the pre-exponential factor are yet discovered.The application study of nanoparticles in the electrochemistry field is more, but the study on regularities of effects of particle size on galvanic cell is less, and especially the study on effect of the size on electrode potential and the electromotive force still is in the blank space. Besides Although the new concept of dispersion cell has been put forward by the author of this thesis in 1997, the cell has yet been prepared to this day.First of all, nanosystems were defined and classified, and the models of the phase transitions, the chemical equilibrium, and the chemistry kinetics
and the electrochemistry of nanosystems were advanced. Then some systems that are fit for the studies were selected out, the models were verified by means of the experiments.In study of the phase transition theory of nanosystems, the classical principle of phase equilibrium is combined with surface chemistry, two universal thermodynamic equations for phase transitions of nanosystems have been derived strictly for the first time by thermodynamic derivations in two approaches, they arewhere pex denotes the external pressure, pα and pβ are the pressures of phase α and phase β, Vα and Vβ are the molar volumes of phase a and phase p, △βαSm and △βκHm are the entropy and the enthalpy of phase transition from phase a to p, and a, A and n are the surface tension, the surface area and the quantity of nanoparticles, separately. Afterwards, the melting temperatures of Au and Sn nanoparticles with different sizes were calculated only by the theories, and were compared with the experimental data. The results show that the calculated melting temperatures are consistent with the experimental ones (even though the diameters of nanoparticles < 10nm).For the first time the effects of reactant sizes on the chemical equilibriums of nanosystems have been researched through the experiments.
The reactions of nanometer sized copper oxide and zinc oxide separately with hydrosulfate of sodium are selected out as the systems that research the size effects on the thermodynamics in heterogeneous reactions. The nanometer-sized copper oxide and nanometer-sized zinc oxide were prepared by the means of the liquid deposition and the solid reaction, and the average diameters of the nanoparticles were characterized by use of X-ray diffraction; then the equilibrium concentrations of some components in the two reaction systems with different sizes of dispersed phases were determined under different temperature; the regularities of effects of particle size on the thermodynamics properties and the equilibrium constant were gained further. The results show that these effect regularities are consistent with the thermodynamic theory of dispersed systems proposed by the author in the 1997.Under the investigations of the kinetics for chemical reactions in nanosystems, a new model of describing the chemical reactions of heterogeneous systems was established for the first time as follows, and both the effects of the specific surface area and the apparent activation energy were simultaneously considered in the model.where r is the reaction rate, A is the pre-exponential factor, E, is the activation energies of a bulk reactant, σ、 M、p and d are the surface tension, the molar mass, the density and the diameter of the reactant with sphericity, separately, Sv is the instantaneous specific area of the reactant, m is the fractional reaction order of Sv, cA、 cB...are the instantaneous concentrations
of reactants or products in a heterogeneous reaction, α, β ...are the fractional reactions of corresponding the reactants or the products. Then the reactions of the nanoparticles of copper oxide and zinc oxide separately with hydrosulfate of sodium are selected out as the systems that research the size effects on the kinetics parameters in heterogeneous reactions. The nanoparticles of copper oxide and zinc oxide were prepared and characterized by the above methods. The instantaneous concentrations of some components in the two reaction systems with different sizes of the particles were determined at different temperatures, and the regularities of effects of the particle size on the rate constant, the reaction order, the activation energy and the pre-exponential factor were obtained further. The regularities are very consistent with the model, and explained satisfactorily by the model.First dispersed electrodes, dispersed cells and dispersion cells are defined and classified in the electrochemistry research, then a nickel dispersed cell and a silver/silver oxide dispersed cell were selected out as the systems of researching the size effects on the electrochemistry. A cell of new concept namely nickel dispersion cell was prepared by the electrochemical technique for the first time, and were characterized by scanning electron microscope. The electromotive force (FMF) of the cell was determined by means of potentiometer, and the regularities of effects of the particle size on the electrode potential and the EMF have been obtained. The nanoparticles of silver oxide was prepared by the means of the liquid deposition and the solid reaction,and the average diameters of the nanoparticles were characterized by
use of X-ray diffraction. The dispersed electrode of silver/silver oxide was prepared out by means of the pressing-sintering, the EMF of the dispersed cell made of the electrode and a calomel electrode was measured by means of the potentiometer. And the regularity of effect of the particle size on the electrode potential has been achieved, and the regularity is the same as that of the model proposed by the author in 1999.The following conclusions can be concluded by the researches in theories and experiments:(1) The nanoparticles of copper oxide, zinc oxide and silver oxide from several to decades nanometers can be obtained by the means of the liquid deposition and the solid reaction, and the advantages of the two methods are that the costs are lower, the operations are more simple, the distribution of the particles are more narrow and the shapes are close to sphericity, and the most shortcoming is very hard to prepare out the ultrafine particles with the mean diameters over the 1 OOnm.(2) In the process of preparing Ni dispersed electrode, there are more influences of current density, temperature, additive and its amount upon the dispersivity of the electrode. The means of preparing Ni dispersed electrode by modes of direct and half wave current have lower cost and more convenient operation, but it is very hard to prepare out the dispersed electrode with the mean diameters from several to decades nm.(3) The means of pressing-sintering is a kind of convenient and higher efficiency method of preparing the electrode, and the method will open up a new approach for preparing some dispersed cells with high performance.
(4) Two exact and universal thermodynamic equations applied to any phase transitions of nanosystems have been derived for the first time. Both Pawlow's model and Reiss' model applied widely to the melting transitions of nanoparticles only are some approximations of the two equations in different extents. The computational values employed the two equations are excellent consistent with experiment results, therefore they can be applied to explain and predict any phase transitions in nanosystems.(5) The relations of the surface tensions of condensed phases and the particle size have been derived for the first time, the relations can commendably describe the regularities that the surface tensions vary with the size. So the relations enable to calculate the thermodynamic properties of phase transitions of nanosystems become feasible.(6) The chemical equilibrium of nanosystems has been experimentalized systematacially in this thesis for the first time, having discovered that the particle size has obvious effects on the standard equilibrium constant, the molar standard Gibbs free energy, the molar standard entropy of reaction and the molar standard enthalpy of reaction in heterogeneous reactions; the standard equilibrium constant increases, the molar standard Gibbs free energy, the molar standard entropy of reaction and the molar standard enthalpy of reaction decrease with the particle diameters of reactants decreasing. Utilizing these regularities, the chemical equilibriums of heterogeneous reactions can be moved towards the expectant direction, increasing the equilibrium inversion rate.(7) The rate equations of reactions of the nanometer-sized copper oxide
and the nanometer-sized zinc oxide separately with hydrosulfate of sodium can be expressed as r = kcn HSO4-(n>1), where r is the reaction rate, k is the rate constant, c is the concentration of HSO4-, and n is the reaction order. The kinetic parameters are related to the particle size of reactant, and the rate constants and the reaction orders of the two heterogeneous reactions increase, the activation energies and the pre-exponential factors decrease with the particle diameters of reactants decreasing, and the rate constants and the apparent activation energies present the linear relations to the reciprocals of the particle size of reactants. The regularities of effects of the particle size on the kinetics parameters have some important directive effects for the investigations of heterogeneous reactions.(8) A new model of describing the chemical reactions of heterogeneous systems was established for the first time, and the effects of both the specific surface area and the apparent activation energy were simultaneously considered in the model. The model has been applied successfully to interpreting the experiment regularities of the effects of the particle size on the rate constants, the reaction orders, the activation energies and the pre-exponential factors. And the model will lay a foundation for establishing the kinetics theory of chemical reactions in nanosystems and provide some conveniences for determining heterogeneous reaction mechanisms.(9) The regularities of effects of electrode dispersivity on the electrode potential and the electromotive force have experimentally been investigated for the first time. It has been discoverd that the electrode dispersivity has obvious effects on the electrode potential and the electromotive force, and
that if a nanometer-sized dispersed phase is a reactant of a electrode reaction or a cell reaction, the electrode potential or the electromotive force increase with the electrode dispersivity decreasing; on the contrary, if the dispersed phase is a product, the electrode potential or the electromotive force decrease with the electrode dispersivity decreasing. These regularities can be applied to researching some high performance cells and to directing manufacture cells.(10) One new concept cell, nickel dispersion cell, has been prepared out for the first time, the results showed that the cell indeed has definite electromotive force. The preparation of the dispersion cell will offer not only some valuable references for its applications but also some directions for preparations of nano-size sensors, controlling of harmful particles, classifications of grains, utilizations of surface energy and so on.Because of the restrictions of the time, the expense of investigation and the experiment conditions, the work still has many shortages. Therefore this topic will need further to be researched.
目前的相平衡、化学平衡、化学动力学和电化学理论中均未考虑反应物颗粒的表面影响,因而不能解决纳米体系的相平衡、化学平衡、动力学和电化学中的相关问题。本课题属于表面化学分别与热力学、动力学和电化学等多个学科的交叉,而目前国内外对这些交叉学科的研究不多,在很多方面还处于空白。因此本课题的研究对于建立新的交叉学科和发展物理化学理论有着重要的科学意义和较高的学术价值。
另外,在化工、环保、材料(尤其是功能材料)、能源、电子、农业及生命科学(如血液)等领域中均有许许多多涉及纳米微粒相变和化学反应的问题,本课题的研究成果可为纳米微粒在这些领域中的应用提供理论依据和指导作用。例如应用本研究成果所得到的理论和规律,可预测纳米粒子的相变温度,增大多相反应的平衡常数,提高平衡产率,加快反应速率,降低苛刻的反应条件,减小投资,降低动力消耗和成本,指导有害微粒的防治,产生直接或间接的经济效益和社会效益。可见,本课题的研究还具有广泛的和重要的应用前景。
The researches of nanoparticles and the nano-size materials are one of the current popular topics. Although the investigations of the physical and chemical properties for nanoparticles are a lot of, the studies on regularities of effects of particle size on phases transitions and chemical reactions are less. Since the surface effects are not considered in the current theories of phases transitions, chemical thermodynamics, chemical kinetics and electrochemistry, as a result the theories can't resolve the related problems of the nanosystems. This topic deals with some crossed sciences between surface chemistry and thermodynamics, chemical kinetics and electrochemistry, the crossed sciences are rarely studied and many aspects in the crossed sciences yet are in the blank space. Therefore, The investigations have the important science meaning and academic values to establish the new crossed sciences and to develop the theories of physical chemistry.Moreover, there are a lots of problems involved phase transitions and chemical reactions of nanosystems in many fields such as chemical engineering, environmental protection, material (particularly function
material), energy sources, electronics, agriculture and life science etc, and the studies will provide some theoretical foundations and guidance for applications nanoparticles to these fields. The effort of the study can be applied to predicting the transition temperatures of nanoparticles, increasing the equilibrium constant, the conversion rates and the reaction rate of heterogeneous reactions, lowering the uncharitable reaction conditions and the production costs, decreasing the investment of the apparatus and directing the prevention of the harmful particles, so as to produce the direct or indirect economic performances and social benefits. It is thus clear that, the research still has extensive and important foregrounds of applications.The domestic and international investigations concerning the effects of particle size on the phase transitions, the chemical equilibriums, the reaction kinetics and the galvanic cells have been overviewed in this thesis, and the present status of the topic has been comprehended.The current theory of phase transitions for nanosystems is limited to only melting transitions, and the theories are approximative and can not expound and predict the melting behavior for the particles smaller than 10nm. A universal theory of nanosystem transitions applied to all of phase transitions such as solid-solid (transition of crystal structures), solid-liquid, liquid-gas and solid-gas transitions has not yet been reported. Besides there yet is no the concrete relations between the surface tensions of condensed phases and the particle size, which will have some difficulty in calculating the transition temperatures, the latent heats and the transition entropies of nanoparticles.
At present the investigations of the effects of particle size on the thermodynamic properties and the equilibrium constant in heterogeneous reactions are fewer and still are confined to theoretical aspects, and the reports of the experimental ones are yet not discovered so far.Now the experimental researches to kinetics for heterogeneous reactions are a lot, but the theoretical researches into the regularities of effects of particle size on the kinetics parameters are fewer.Although many models of heterogeneous reaction kinetics was advanced, yet the models can only give expression to relationship between a reaction rate and a extent of reaction or a instantaneous size of particles, and the models only can explain some experimental phenomenon or some kind of experimental results. In other words, these models lack versatility and the universality. The reports that the theoretical studies of effects of particle size on the kinetic parameters in heterogeneous reactions such as the activation energy, the rate constant, the reaction order and the pre-exponential factor are yet discovered.The application study of nanoparticles in the electrochemistry field is more, but the study on regularities of effects of particle size on galvanic cell is less, and especially the study on effect of the size on electrode potential and the electromotive force still is in the blank space. Besides Although the new concept of dispersion cell has been put forward by the author of this thesis in 1997, the cell has yet been prepared to this day.First of all, nanosystems were defined and classified, and the models of the phase transitions, the chemical equilibrium, and the chemistry kinetics
and the electrochemistry of nanosystems were advanced. Then some systems that are fit for the studies were selected out, the models were verified by means of the experiments.In study of the phase transition theory of nanosystems, the classical principle of phase equilibrium is combined with surface chemistry, two universal thermodynamic equations for phase transitions of nanosystems have been derived strictly for the first time by thermodynamic derivations in two approaches, they arewhere pex denotes the external pressure, pα and pβ are the pressures of phase α and phase β, Vα and Vβ are the molar volumes of phase a and phase p, △βαSm and △βκHm are the entropy and the enthalpy of phase transition from phase a to p, and a, A and n are the surface tension, the surface area and the quantity of nanoparticles, separately. Afterwards, the melting temperatures of Au and Sn nanoparticles with different sizes were calculated only by the theories, and were compared with the experimental data. The results show that the calculated melting temperatures are consistent with the experimental ones (even though the diameters of nanoparticles < 10nm).For the first time the effects of reactant sizes on the chemical equilibriums of nanosystems have been researched through the experiments.
The reactions of nanometer sized copper oxide and zinc oxide separately with hydrosulfate of sodium are selected out as the systems that research the size effects on the thermodynamics in heterogeneous reactions. The nanometer-sized copper oxide and nanometer-sized zinc oxide were prepared by the means of the liquid deposition and the solid reaction, and the average diameters of the nanoparticles were characterized by use of X-ray diffraction; then the equilibrium concentrations of some components in the two reaction systems with different sizes of dispersed phases were determined under different temperature; the regularities of effects of particle size on the thermodynamics properties and the equilibrium constant were gained further. The results show that these effect regularities are consistent with the thermodynamic theory of dispersed systems proposed by the author in the 1997.Under the investigations of the kinetics for chemical reactions in nanosystems, a new model of describing the chemical reactions of heterogeneous systems was established for the first time as follows, and both the effects of the specific surface area and the apparent activation energy were simultaneously considered in the model.where r is the reaction rate, A is the pre-exponential factor, E, is the activation energies of a bulk reactant, σ、 M、p and d are the surface tension, the molar mass, the density and the diameter of the reactant with sphericity, separately, Sv is the instantaneous specific area of the reactant, m is the fractional reaction order of Sv, cA、 cB...are the instantaneous concentrations
of reactants or products in a heterogeneous reaction, α, β ...are the fractional reactions of corresponding the reactants or the products. Then the reactions of the nanoparticles of copper oxide and zinc oxide separately with hydrosulfate of sodium are selected out as the systems that research the size effects on the kinetics parameters in heterogeneous reactions. The nanoparticles of copper oxide and zinc oxide were prepared and characterized by the above methods. The instantaneous concentrations of some components in the two reaction systems with different sizes of the particles were determined at different temperatures, and the regularities of effects of the particle size on the rate constant, the reaction order, the activation energy and the pre-exponential factor were obtained further. The regularities are very consistent with the model, and explained satisfactorily by the model.First dispersed electrodes, dispersed cells and dispersion cells are defined and classified in the electrochemistry research, then a nickel dispersed cell and a silver/silver oxide dispersed cell were selected out as the systems of researching the size effects on the electrochemistry. A cell of new concept namely nickel dispersion cell was prepared by the electrochemical technique for the first time, and were characterized by scanning electron microscope. The electromotive force (FMF) of the cell was determined by means of potentiometer, and the regularities of effects of the particle size on the electrode potential and the EMF have been obtained. The nanoparticles of silver oxide was prepared by the means of the liquid deposition and the solid reaction,and the average diameters of the nanoparticles were characterized by
use of X-ray diffraction. The dispersed electrode of silver/silver oxide was prepared out by means of the pressing-sintering, the EMF of the dispersed cell made of the electrode and a calomel electrode was measured by means of the potentiometer. And the regularity of effect of the particle size on the electrode potential has been achieved, and the regularity is the same as that of the model proposed by the author in 1999.The following conclusions can be concluded by the researches in theories and experiments:(1) The nanoparticles of copper oxide, zinc oxide and silver oxide from several to decades nanometers can be obtained by the means of the liquid deposition and the solid reaction, and the advantages of the two methods are that the costs are lower, the operations are more simple, the distribution of the particles are more narrow and the shapes are close to sphericity, and the most shortcoming is very hard to prepare out the ultrafine particles with the mean diameters over the 1 OOnm.(2) In the process of preparing Ni dispersed electrode, there are more influences of current density, temperature, additive and its amount upon the dispersivity of the electrode. The means of preparing Ni dispersed electrode by modes of direct and half wave current have lower cost and more convenient operation, but it is very hard to prepare out the dispersed electrode with the mean diameters from several to decades nm.(3) The means of pressing-sintering is a kind of convenient and higher efficiency method of preparing the electrode, and the method will open up a new approach for preparing some dispersed cells with high performance.
(4) Two exact and universal thermodynamic equations applied to any phase transitions of nanosystems have been derived for the first time. Both Pawlow's model and Reiss' model applied widely to the melting transitions of nanoparticles only are some approximations of the two equations in different extents. The computational values employed the two equations are excellent consistent with experiment results, therefore they can be applied to explain and predict any phase transitions in nanosystems.(5) The relations of the surface tensions of condensed phases and the particle size have been derived for the first time, the relations can commendably describe the regularities that the surface tensions vary with the size. So the relations enable to calculate the thermodynamic properties of phase transitions of nanosystems become feasible.(6) The chemical equilibrium of nanosystems has been experimentalized systematacially in this thesis for the first time, having discovered that the particle size has obvious effects on the standard equilibrium constant, the molar standard Gibbs free energy, the molar standard entropy of reaction and the molar standard enthalpy of reaction in heterogeneous reactions; the standard equilibrium constant increases, the molar standard Gibbs free energy, the molar standard entropy of reaction and the molar standard enthalpy of reaction decrease with the particle diameters of reactants decreasing. Utilizing these regularities, the chemical equilibriums of heterogeneous reactions can be moved towards the expectant direction, increasing the equilibrium inversion rate.(7) The rate equations of reactions of the nanometer-sized copper oxide
and the nanometer-sized zinc oxide separately with hydrosulfate of sodium can be expressed as r = kcn HSO4-(n>1), where r is the reaction rate, k is the rate constant, c is the concentration of HSO4-, and n is the reaction order. The kinetic parameters are related to the particle size of reactant, and the rate constants and the reaction orders of the two heterogeneous reactions increase, the activation energies and the pre-exponential factors decrease with the particle diameters of reactants decreasing, and the rate constants and the apparent activation energies present the linear relations to the reciprocals of the particle size of reactants. The regularities of effects of the particle size on the kinetics parameters have some important directive effects for the investigations of heterogeneous reactions.(8) A new model of describing the chemical reactions of heterogeneous systems was established for the first time, and the effects of both the specific surface area and the apparent activation energy were simultaneously considered in the model. The model has been applied successfully to interpreting the experiment regularities of the effects of the particle size on the rate constants, the reaction orders, the activation energies and the pre-exponential factors. And the model will lay a foundation for establishing the kinetics theory of chemical reactions in nanosystems and provide some conveniences for determining heterogeneous reaction mechanisms.(9) The regularities of effects of electrode dispersivity on the electrode potential and the electromotive force have experimentally been investigated for the first time. It has been discoverd that the electrode dispersivity has obvious effects on the electrode potential and the electromotive force, and
that if a nanometer-sized dispersed phase is a reactant of a electrode reaction or a cell reaction, the electrode potential or the electromotive force increase with the electrode dispersivity decreasing; on the contrary, if the dispersed phase is a product, the electrode potential or the electromotive force decrease with the electrode dispersivity decreasing. These regularities can be applied to researching some high performance cells and to directing manufacture cells.(10) One new concept cell, nickel dispersion cell, has been prepared out for the first time, the results showed that the cell indeed has definite electromotive force. The preparation of the dispersion cell will offer not only some valuable references for its applications but also some directions for preparations of nano-size sensors, controlling of harmful particles, classifications of grains, utilizations of surface energy and so on.Because of the restrictions of the time, the expense of investigation and the experiment conditions, the work still has many shortages. Therefore this topic will need further to be researched.
引文
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