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1、Synthesis of Nanoparticles Nucleation and GrowthA. IntroductionTechniques for the synthesis of nanoparticles: top-down bottom-up. A-1. Top-down approaches: milling or attrition, repeated quenching, and lithography. Attrition: a relatively broad size distribution, varied particle shape, contain a sig
2、nigicant amount of impurities and defects #6#7#8Two categories: thermodynamic equilibrium approach and kinetic approach. Repeatedthermalcycling(material:verysmallthermalconductivitybutalargevolumechangeasafunctionoftemperature):veryfineparticlescanbeproduced,difficulttodesignandveryfinecontrolA-2.Bo
3、ttom-upapproachesbyhomogeneousnucleationfromliquidorvapor,orbyheterogeneousnucleationonsubstrates.#9lThermodynamic approach: (i) generation of supersaturation, (ii) nucleation, and (iii) subsequent growth. lkinetic approach limiting the amount of precursors available for the growth (e.g., molecular
4、beam epitaxy,) or confining the process in a limited space (micelle synthesis.)#19#20This chapter will take the solution synthesis of nanoparticles as an example.For the fabrication of nanoparticles, a small size is not the only requirement. Other important characteristics: (i) identical size of all
5、 particles, i.e., monosized or with uniform size distribution; (ii) idental shape or morphology; (iii) identical chemical composition and crystal structure; (iv) individually dispersed or monodispersed, i.e., no agglomeration (or readily redispersible.) l Crystalline structure: single crystal, polyc
6、rystalline and amorphous particles l Morphologies: spheres, cubes and platelets.lNanoparticles of single crystalline: nanocrystalslNanoparticles with quantum effects: quantum dotsB. Nanoparticles through Homogeneous Nucleationa supersaturation of growth species must be created, by e.g., a reduction
7、in temperature or in situ chemical reactions. Three mediums: liquid, gas and solidB-1. Fumdamentals of homogeneous nucleationA solution with solute exceeding the solubility or supersaturation possesses a high Gibbs free energy; the overall energy of the system would be reduced by segregation solute
8、from the solution i.e., by forming a solid phase and maintaining an equilibrium concentration in the solution.#2#3#10#11This reduction of Gibbs free energy is the driving force for both nucleation and growth. The change of Gibbs free energy per unit volume of the solid phase, GV, C: concentration of
9、 the solute, C0: equilbrium concentration or solubility, k: Boltzmann constant, T: temperature, : atomic volume, : supersaturation defined by (CC0)/C0.Without supersaturation (i.e. =0), GV is zero, and no nucleation would occur. F3.1When CC0, GV is negative and nucleation occurs spontaneously. Assum
10、ing a spherical nucleus with a radius of r, the change of Gibbs free energy or volume energy, Vincrease in the surface energys: surface energy per unit area. The total change of chemical potentialF3.2the newly formed nucleus is stable only when its radius exceeds a critical size, r.At the critical s
11、ize r=r, dG/dr=0G: energy barrier that a nucleation process must overcomeThe above discussion was based on a supersaturated vapor and a supercooled gas or liquid.critical size represents the limit on how small nanoparticles can be synthesized. To reduce the critical size, one needs to increase the s
12、upersaturation, , e.g., by decreasing temperature. Temperature can also influence surface energy.Surface energy of the solid nucleus can change more significantly near the roughening temperature. Other possibilities include: (i) use of diffierent solvent, (ii) additives in solution, and (iii) incorp
13、oration of impurities into solid phaseThe rate of nucleation (number of nuclei formed per unit volume and per unit time, i.e., nuclei/cm3.sec), RN, is proportional to (i) the probability, PF3.3(ii) the number of growth species per unit volume, n, i.e., the initial concentration, C0, and (iii) the su
14、ccessful jump frequency of growth species, ,: diameter of the growth species, : viscosity of the solution.high initial concentration or supersaturationlow viscosity and low critical energy barrier favor the formation of a large number of nuclei. For a given concentration of solute, a larger number o
15、f nuclei mean smaller sized nuclei.The nucleation occurs only when the supersaturation reaches a certain value above the solubility (critical supersaturation) After the initial nucleation, the concentration or supersaturation of the growth species decreasesF3.4When the concentration decreases below
16、a specific concentration, no more nuclei would form, whereas the growth will proceed until the concentration of growth species has attained the equilibrium concentration or solubility.nucleation occurs when the concentration reaches the minimum saturation (i.e., above the critical supersaturation) r
17、equired to overcome the critical energy barrier, growth rate is above zero for a concentration above its equilibrium solubility.Above the minimum concentration (i.e., above the critical supersaturation) , nucleation and growth are inseparable processes.F3.5For the synthesis of nanoparticles with uni
18、form size distribution, it is best if all nuclei are formed at the same time. In this case, all the nuclei are likely to have the same or similar size, since they are formed under the same conditions.it is highly desirable to have nucleation occur in a very short period of time.to achieve a sharp nu
19、cleation, the concentration of the growth species is increased abruptly to a very high supersaturation and then quickly brought below the minimum concentration for nucleation.The size distribution of nanoparticles can be further altered in the subsequent growth process.B-2.SubsequentGrowthofNuclei#4
20、6#47C-2. Other Classification粉體製備方法粉體製備方法1.breaking down processes (研磨)2. building up processes (化學合成)3. (building up breaking down)2.化學合成方法 (A) 按反應的相分類 氣相反應法 液相反應法 固相反應法 (B) 按反應類別分類evaporation condensation (thermal, laser, electron beam, microwave, plasma)chemical vapor depositionflame synthesisspr
21、ay pyrolysis (spray roasting) solution precipitation co- precipitation hydrothermal precipitation spray drying spray freezing and sublimation alkoxide method sol- gel method combustion synthesis microwave- combustion synthesis 沒有一種方法能合成所有的粉體 有些方法可合成數種粉體(反應物不同、操作條件不同，方法相同) 對某一粉體而言，常有數種方法皆可合成。 選擇最佳方法
22、(powder properties, production cost, raw materials availability, environmental friendly)Preparation of Fine Powders Breaking- down processeslarge particlesFused (liquid)SolidAtomisationComminution ball milling, etc(grinding)GaseousMicronisation Building- up processesreactantsParticle- forming specie
23、s (atoms, molecules)nuclei or initial particlesproduct powdersgrowthnucleationchem. rxn.phys. evaporationExample:Al2O3Bayer ProcessBauxite (Al2O(OH)4=Al2O3.2H2O)(55Al2O3, 7SiO2, Fe2O3鐡礬土)crushed and wet-ground100meshparticlesdigesterNaOH(30)pressure( atm)heat (190)filtrationsolution of sodiumalumina
24、te (NaAlO2)+ wasteseedingwith fineAl(OH)3particleshydrolyzedcoolingTempagitation aluminum gydroxide(precipitated)timefiltration washingAluminum hydroxide(Al(OH)3)calcination1200cooling(size, texture, purity)40100 m particlessize reduction1 m or finerNucleation and Particle GrowthA. Formation Process
25、 of Powder ParticlesreactantsChem. Rxn.Particle Forming SpeciesNucleationNuclei (Initial particles)GrowthProduct ParticlesParticle Forming Species(a) Vapor atoms or molecules in gas phase.(b) Solute atoms, molecules, or ions in liquid solution; pure melt; atoms, molecules, or ions in a melt solution
26、.(c) Solute atoms, molecules, or ions in a solid solution(d) Newly formed phase materials.Phys. Rxn.B. NucleationThe very first step in the formation of a new phaseThe very first step in the formation of a new phase including:including:v v l , v l , v s s, l , l s s, , andand s( s( ) ) s( s( ). ). T
27、he particle size distributionThe particle size distribution, produced during synthesis , produced during synthesis (e.g., precipitation) is a result of the relative (e.g., precipitation) is a result of the relative rates of rates of reaction, nucleation, growthreaction, nucleation, growth, and , and
28、 agglomerationagglomeration, as well , as well as the degree of backmixing in the reactor (e.g., as the degree of backmixing in the reactor (e.g., precipitator). precipitator). B-1 Nucleation and Particle Growth-practical examples Powder Synthesis gas-phase methods (vapor molecular solid particles)
29、solution methods (solute species solid particles) solid-state-reaction-methods (e.g., MgCO3 Mg O; phase phase) others Microstructure Development Materials Heat Treatment Annealing recrystallization and grain growth Coating powder-spray coating CVDB-2 Three main categories of nucleation: homogeneous
30、nucleation: occurs in the absence of a solid interface (production of new particles) heterogeneous nucleation: occurs in the presence of a foreign seed (growth on seed particles, no new particles produced) secondary nucleation: occurs in the presence of solute particle interface. (production of new
31、particles)B-3 Classical Nucleation Theory -thermodynamic approachB-3 Classical Nucleation Theory -thermodynamic approach In very small quantities of matter such as clusters of solute In very small quantities of matter such as clusters of solute molecules, a large fraction of the molecules are at the
32、 surface in a molecules, a large fraction of the molecules are at the surface in a state of higher potential energy than the interior molecules (i.e., state of higher potential energy than the interior molecules (i.e., fewer and weaker bonds).fewer and weaker bonds). A macroscopic body: surface free
33、 energy per unit area, A macroscopic body: surface free energy per unit area, . . In a In a cluster consisting of a small number(10-100) of molecules or cluster consisting of a small number(10-100) of molecules or ions, the definition of surface area and surface free energy is ions, the definition o
34、f surface area and surface free energy is rather ambiguousrather ambiguous. None the less, in the theory presented here, we . None the less, in the theory presented here, we will use the concepts of surface area and surface free energy for will use the concepts of surface area and surface free energ
35、y for convenience. convenience. Classical theories of primary homogeneous nucleation assume that in supersaturated solution solute molecules combine to produce clusters, or ”embryos”, overall free energy per cluster, G, of the aggregates is a result of two terms, the free energy due to the new surfa
36、ce and the free energy due to the formation of new liquid (or solid).B-3-1 Nucleation of Condensation (v l or s) In order for vapor to condense in the absence of free and foreign surfaces it is necessary for small cluster of molecules to form and to grow and finally coalesce to form the bulk phase.
37、This does not happen if the vapor pressure is only slightly higher than the equilibrium vapor pressure because the very small droplets that are formed first have a higher vapor pressure. (kinetics)the thermodynamics of condensation may be discussed in terms of the following two-step process: nA (gas
38、, P)= nA (gas, P)= nA (small liquid droplet of radius r)where n is number of molecules and P is the vapor pressure of the liquid in small droplet. The change in Gibbs free energy for the first step is (8.16)PPP(PP)The change in Gibbs free energy for the second step would be zero if surface effects w
39、ere negligible, but since 4r2 of surface has to be formed, there is an increase in Gibbs free energy of 4r2. Thus the total Gibbs free energy change for the condensation is (8.17)The number of molecules n may also be expressed (8.18)where is the density of the liquid, M its molecular weight and NA i
40、s Avogadros constant. Thus equation 8.17 becomes (8.19)(8.20)(8.21)easier for nucleation to occurFor given degree of supersaturation (S=P/P), the plot of G versus r has the shape indicated in Fig.8.3 At the critical radius rc the Gibbs free energy change becomes smaller as the particle increases in
41、size. Thus a particle of this size grows spontaneously. The critical radius (radius of critical cluster) may be obtained by differentiation B-3-2 Classical Nucleation Theory derived by applying, by amaloy, classical nucleation theory for the condeusation of a vapor. Eq. of nucleation rate from a vap
42、or (Eg. (22) physical no of constant x the concentration moleales surface area of a of critical unclei arriving at critical the surface nuclei per unit area per unit time the equation following Eg. (9),the number density of critical nuclei:B-4 crystal nucleation the free energy of formation for crit
43、ical cluster from a vapor a: geometric pactor S=C/Ce P=P1/Pe crystal nucleation rate K1: has never been fully understood It has been suggested that n: conc. of ionic species v: jump frequency= ?B-4-1 Christiansen and Nielsen Model K: a constant P: 29 J : not a strong function of S, which is inconsis
44、tent with some experimental findings.C. Heterogeneous NucleationIn heterogeneous nucleation, the nuclei are formed at a surface of the container, on the surface of foreign particles, or on structural imperfections of the already present crystal. Such surfaces or impurities are “wet” by both liquid a
45、nd solid lowering of the net energy associated with formation of the nucleation. This situation is illustrated by Fig. 5-10. The heterogeneous nucleus is considered as a spherical cap on a solid, flat substrate. The volume of this cap depends on the contact angle at the nucleus-liquid-substrate junc
46、tion. If the contact angle is less than 180C, a particular surface will serve as nucleation catalyst for that system. By using a substrate of small values of the contact angle at the nucleus-liquid-substrate junction, the value of the surface energy term can be considerably reduced so that the net f
47、ree energy necessary for nucleation is considerably lowered. Thus the change in the free energy associated with formation of the embryo can be given by(5-26)where V= the volume of spherical cap (nucleus) ACL= the interfacial surface area between liquid and cap r= the radius of the cap (nucleus)CL, S
48、C, SL= interfacial surface tensions between cap (nucleus) and liquid, cap and substrate, substrate and liquid, respectively.From Youngs equation we can write CL cos = SLSCand substituting in the Equation 5-26 and rearranging we get0 90 ; r2SCor r2SL(5-27)Note that the volume free energy does not und
49、ergo much change, and the controlling factor is the change in the surface energy which is greatly lowered by the presence of another substrate surface. In homogeneous nucleation the critical size of a nucleus is given by Equation 5-21, and it is independent of contact angle. In heterogeneous nucleat
50、ion, however, the value of CL, the interfacial surface tension, is much smaller; therefore the critical size of the nucleus will be much smaller, as shown by r*= -2CL/G.Thus the number of atoms that must be crystallized before the critical radius size r* is reached is much less for heterogeneous tha
51、n for homogeneous nucleation, and a smaller amount of undercooling is required. Nucleation by cavitation is caused when the cavities collapse, resulting in very high local pressures up to 10 GPa (1450 ksi). This changes the melting temperature according to the Chapeyron equation (Equation 3-7), prod
52、ucing sufficient undercooling for homogeneous nucleation.D. GROWTH OF PARTICLESGrowth Mechanisms(A) Surface Growth (Vapor Deposition)Vapor indeulesparticleparticlenumber conc: samesize : increaseshape : sphere(B) coagulation(1) Coalescent CoagulationparticleAparticleBcollision, sticking, fusionnumber density : decreasesize : increaseshape : sphere(2) Aggregation (Agglomeration)particleAparticleBcollision, stickingno density : decreasesize : increaseshape : grape-like chain
