1 Chapter 9 Stabilization of Particles

2 Introduction Stabilization ： I. Physical Stabilization II. Chemical Stabilization => Preventing agglomeration => Preventing chemical reaction with solvent or environmental species => Improving compatability with matrix materials (e.g., polymers) when serving as filler.

3 In nanostructure fabrication and processing, it is very important to overcome the huge total surface energy to create the desired nanostructures. As the dimension of nanostructured materials reduces, van der Waals attraction force between nanostructured materials becomes increasingly important. A. Introduction #59#58 I. PHYSICAL STABILIZATION

4 Without appropriate stabilization mechanisms applied, the nanosturctures materials are most likely and readily to form agglomerates. There are two major stabilization mechanism widely used: electrostatic stabilization and steric stabilization A system using electrostatic stabilization kinetically stable, whereas steric stabilization makes the system thermodynamically stable

5 Ven der Waals attraction is created because of the overall interactions between the temporary dipoles of the molecules in the two interacting particles. When particles are small, typically in micrometers or less, and are dispersed in a solvent, ven der Waals attraction force and Brownian motion play important roles, whereas the influence of gravity becomes negligible. The combination of van der Waals attraction force and Brownian motion would result in the formation of agglomeration of the nanoparticles. B. Van der Waals Attraction Potential

6 Integration of all the van der Waals interaction between two molecules over two spherical particles of radius, r, separated by a distance, S, as illstrated on Fig. 2.15, gives the total interaction energy or attraction potential. F2.15T2.3 A: a positive constant termed the Hamaker constant (which has a magnitude on the order of to J,) and depends on the polarization properties of the molecules in the two particles and in the medium which separates them.

7 When the separation distance between two equal sized spherical particles are significantly smaller than the particle radius, i.e. S/r ＜＜ 1, the simplest expression of the van der Waals attraction could be obtained: T2.4 Other simplified expressions of the van der Waals attraction potential are summarized in Table 2.4. Interaction between two molecules are significantly different from that between two particles. Van der Waals interaction energy between two molecules can be simply represented by: 2.16

8 The attraction force between two particles decay much slowly and extends over distances of nanometers. A barrier potential must be developed to prevent agglomeration of particles: electrostatic repulsion and steric exclusion.

9 C. Electrostatic Stabilization (C-1) Surface charge density When a solid emerges in a polar solvent or an electrolyte solution, a surface charge will be developed through one or more of the following mechanisms: (1) Preferential adsorption of ions (2) Dissociation of surface charged species (3) Isomorphic substitution of ions (4) Accumulation or depletion of electrons at the surface (5) Physical adsorption of charged species onto the surface

10 For a given solid surface in a given liquid medium, a fixed surface electrical charge density or electrode potential, E, will be established, which is given by the Nernst equation: E 0 : standard electrode potential when the concentration of ions in unity, n i : valence state of ions, a i : activity of ions T: temperature F: Faraday’s constant

11 the surface potential of a solid varies with the concentration of the ions in the surrounding solution and can be either positive or negative. The focus of the discussion here will be on non- conductive materials or dielectrics, more specifically on oxides. The surface charge in oxides is mainly derived from preferential dissolution or deposition of ions. Ions adsorbed on the solid surface determine the surface charge, and thus are referred to as charge determining ions, also know as co-ions or coions.

12 In the oxide systems, typical charge determining ions are protons (H + ) hydroxyl (OH - ) groups and their concentrations are described by pH (pH= － log[H + ]). The concentration of charge determining ions corresponding to a neutral or zero-charged surface is defined as a point of zero charge or p.z.c. At pH ＞ p.z.c., the oxide surface is negatively charged, since the surface is covered with hydroxyl groups, OH- At pH ＜ p.z.c., H+ is the charge determining ions and the surface is positively charged. T

13 The Nernst equation [Eq.(2.18)] can be written as: At room temperature, (C-2) Electric potential at the proximity of solid surface When a surface charge density of a solid surface is established, there always exist both surface charge determining ions and counter ions.

14 The distributions of both ions are mainly controlled by a combination of the following forces: (1) Coulombic force or electrostatic force, (2) Entropic force or dispersion, (3) Brownian motion. The concentration of counter ions is the highest near the solid surface and decreases as distance from the surface increase, whereas the concentration of determining ions changed in the opposite manner: double layer structure, Stern layer and Gouy layer (also called diffuse double layer), Helmholtz plane. F2.14

15 Stern layer: where the electric potential drops linearly Gouy layer or diffuse double layer: the counter ions diffuse freely and the electric potential does not reduce linearly. The electric potential drops approximately following Where h ≧ H, which is the thickness of the Stern layer, 1/K is known as the Debye-Hückel screening strength and is also used to describe the thickness of double layer,

16 F: Faraday’s constant, ε 0 : the permittivity of vacuum, ε r : dielectric constant of the solvent, Ci and Zi the concentration and valence of the counter ions of type i. This equation clearly indicates that the electric potential at the proximity of solid surface decreases with increased concentration and valence state of counter ions, and increases with an increased dielectric constant of the solvent exponentially. Higher concentration and valence state of counter ions would result in a reduced thickness of both Stern layer and Gouy layer.

17 In theory, the Gouy diffusion layer would end at a point where the electric potential reaches zero. However, in practice, double layer thickness is typically of approximately 10nm or larger.

18 A difference in electrical potential between the surface and the bulk solution can be effected, diffuse electrical double-layer model. Where k -1 is the distance from the charged surface to the plane where and is called the thickness of the double layer. The effective double-layer thickness k -1 is calculated to be about 3 nm. Increasing the concentration or valence of the counterions compresses the double layer and increases the potential gradient. The use of a liquid of a lower dielectric constant or temperature also compresses the double layer.

19 The potental at the slippage plane is called the zeta potential. In system with simple counterions, the zeta potential is an indication of the gradient in electrical potential when the surface potential remains constant. The pH at which the zeta potential is zero is termed the isoelectric point IEP. Raising or lowering the pH from the isoelectric point will initially increase the absolute value of the zeta potential (Fig 10.9). However, a further addition of OH- or H3O- will cause a reduction in the zeta potential because of the compression of the double layer

20 Interactions between particles are complex. When two particles are far apart, there will be no overlap of two double layers and electrostatic repulsion between two particles is zero. However, when two particles approach one another, double layer overlaps and a repulsive force develop. An electrostatic repulsion(i.e.,the repulsive potential, ψ R )between two equally sized spherical particles of radius r, and separated by a distance S, is given by:

21 (C-3) Interactions between two particles: DLVO theory The total interaction between two particles, which are electrostatic stabilized, is the combination of van der Waals attraction and electrostatic repulsion: 2-16

22 The DLVO theory (named after Derjaguin, Landau, Verwey and Overbeek) Important assumption in the DLVO theory: (1) Infinite flat solid surface (2) Uniform surface charge density, (3) No redistribution of surface charge, i.e. the surface electric potential remains constant, (4) No change of concentration profiles of both counter ions and surface charge determining ions, i.e. the electric potential remains uncharged, and (5) Solvent exerts influences via dielectric constant only, i.e. no chemical reactions between the particles and solvent 2-16

23 The DLVO theory works very well in explaining the interactions between two approaching particles, which are electrically charged and thus is widely accepted. The maximum is also known as repulsive barrier. If the barrier is greater than ~10kT, where k is Boltzmann constant, the collisions of two particles produced by Brownian motion will not overcome the barrier and agglomeration will not occur. Brownian motion=>kinetic energy, E k ( ∝ T,~10kT ) =>overcome the energy barrier, V max (?) 2-16

24 Since the electric potential is dependent on the concentration and valence state of counter ions, the overall potential is strongly influenced by the concentration and valence state of counter ions. Ci↑, Zi↑, ε r↓=> K ↑ E↓ ↓ E max (or ) ↓ = f(E,K,ε r )

25 An increase in concentration and valence state of counter ions results in a faster decay of the electric potential as schematically illustrated in Fig As a result, the repulsive barrier is reduced and its position is pushed towards the particle surface. The secondary minimum in Fig is not necessary to exist in all situations, and it is present only when the concentration of counter ions is high enough. If secondary minimum is established, particles are likely to be associated with each other, which is known as flocculation. F2.16 F2.17

26 When the distance between the surfaces of two particles is larger than the combined thickness of two electric double layers of two particles, there would be no interaction. When two particles move closer and the two electric double layer overlap, a repulsion force is developed and reaches the maximum when the distance between two particle surfaces equals the distance between the repulsive barrier and the surface. F2.18 Osmotic flow of solvent Osmotic force

27 (1)Dispersion is very dilute, (each particle is not interfered by other particles.) (2)No other force is present (i.e. the gravity is negligible and no other forces, such as magnetic field.) (3)Geometry of partivles is relativeoy simple, so that the surface preperties are the same over the entire surface. The DLVO theory is valid and has been widely applied in practice, as far as the following conditions are met:

28 (4)The double layer is purely diffusive, so that the distributions of counter ions and charge determining ions are determined by all three forces: electrostatic force, entropic dispersion and Brownian motion.

29 D. Steric Stabilizarion Also called polymeric stabilization. Polymer layer adsorbed on the surface of nanoparticles serves as ： a potential barrier to prevent particles from growth by coagulation. This technique can limit (or prevent) growth of particles by both surface growth and agglomeration. a diffusion barrier to the growth species, resulting in a diffusion-limited growth.

30 A very high concentration can be accommodated, and dispersion medium can be completely depleted. It is not electrolyte sensitive. It is suitable to multiple phase systems Offers several advantages over electrostatic stabilization: It is a thermodynamic stabilization the particles are always redispersible.

31 (D-1) Solvent,polymer and particles Interaction: solvent polymer particles Solvent( polymer interaction) Solvent can be grouped into: aqueous solvent, (H 2 O,) and non-aqueous solvents (organic solvents). Can also be categorized into: protic solvent (can exchange protons, e.g., methanol, CH 3 OH, and ethanl, C 2 H 5 OH) and aprotic solvent (cannot exchange protons, e.g., benzene, C 6 H 6 ). When a solvable polymer dissolves into a solvent, the polymer interacts with the solvent. Such interaction varies with the system as well as temperature. T2.5

32 When polymer in a solvent tends to expand to reduce the overall Gibbs free energy of the system, such a solvent is called a “good solvent”. When polymer in a solvent tends to coil up or collapse to reduce the Gibbs free energy, the solvent is considered to be a “poor solvent”. Whether the solvent is a “good” or “poor” solvent is dependent on the temperature. At high temperature, polymer expands, whereas at low temperatures, polymer collapses. The temperature, at which a poor solvent transfers to a good solvent, is the Flory-Huggins theta temperature, or simply the θ temperature.

33 (1)Anchored polymer: irreversibly binds to solid surface by one end only. => (2)Adsorbing polymer: adsorbs weakly at random points along the polymer backbone. => forming physical (or secondary) bondings (3)Non-adsorbing polymer: which does not attach to solid surface and thus does not contribute to polymer stabilization. Depending on the interaction between polymer and solid surface, a polymer can be grouped into: F2.19 forming chemical (or primary) bonds Polymer( particle surfaces) There is no restriction whether one or multiple bonds are formed.

34 F2.20 (D-2) Interaction between polymer layers Consider two solid particles covered with terminally anchored polymers: the separation distance, H, between the surface of two particles; the thickness, L, of polymer layers. When the distance reduces to less than 2L, but is still larger than L, there will be interactions. (D-2-1) Anchored polymer

35 (a) In a good solvent, in which polymer expands, if the coverage of polymer on the solid surface in not complete, particularly less than 50% coverage, (when the concentration of polymer in the solvent is insufficient,) two polymer layers tend to interpenetrate result in a reduction of the freedom of polymers, which leads to a reduction of entropy, i.e. ΔS ＜ 0. As a result, the Gibbs free energy of the system would increase, assuming the change of enthalpy due to the interpenetration of two polymer layers negligible, i.e. ΔH 0, (a) Good solvent low coverage

36 So two particles repel one another and the distance between two particles must be equal to or larger than twice the thickness of polymer layers. => no agglomeration high coverage When the coverage of polymer is high, particularly approaching 100%, there would be no interpenetration, the two polymer layers will be compressed: △ S ↓ ( △ H 0)=> △ G ↑ The overall Gibbs free energy increases, and repels two particles apart. => no agglomeration F2.21

37 Interpenetration of two polymer layers will promote further coil up of polymers, and result in reduction of the overall Gibbs free energy. Two particles tend to associate with one anther. ○ L ＜ H ＜ 2L △ S 0, △ H ↓ => △ G ↓ ○ H<L △ H 0, △ S ↓ => △ G ↑ high coverage With a high coverage, there would be no penetration and the reduction in distance results in a compressive force, leading to an increase in the overall free energy. H < 2L △ H 0, △ S ↓ => △ G ↑ When the distance between two particles is less than the thickness of the polymer layer, a reduction in distance always produces a repulsive force and an increase in the overall Gibbs free energy. => no agglomeration (b) Poor solvent. low coverage With a low coverage, when L ＜ H ＜ 2L

38 Regardless of the difference in coverage and solvent, two particles covered with polymer layers are prevented from agglomeration by the space exclusion or steric stabilization.

39 The situation of adsorbing polymers is more complicated: First, polymer originally attached to the solid surface of one particle may interact with and adsorb onto another particle surface, and thus form bridges between two particles. Second, given sufficient time, attached polymer can desorb from the surface and migrate out of the polymer layer. When polymers has a strong adsorption and forms a full coverage, the interaction between two polymer layers produces a purely repulsive force and results in an increased free energy. (D-2-2) Adsorbing polymer

40 It is always the case that a repulsive force develops and repels two particles away from each other, when the distance is less than the thickness of polymer layer. When only a partial coverage is achieved, the nature of solvent can have a significant influence. Interaction is very similar to that of anchored polymer layers.

41 (E) Mixed steric and electric interactions Referred to as electrosteric stabilization When polymers are attached to a charged particle surface, a polymer layer would form and an electric potential adjacent to the solid surface would retain. Both electrostatic repulsion and steric restriction would prevent agglomeration. F2.22

42 A.A. Illustration Example aliminum nitride (AIN) in water ( a processing step for wet mixing with additives or to prepare a slurry using water as a solvent.) AINAppl (a) Problems : hydrolysis hydro II. CHEMICAL STABILIZATION Preventing chemical reaction with solvent or environmental species

43 (b) Techniques to prevent hydrolysis : (1) Surface treatment or surface modification (2) coating with SiO 2 on surface AIN SiO 2 ( with surface treatment agents, e.g., H 3 PO 4 ) HDRO

44 B. Illustration Example-1 AIN + Epoxy : high thermal conductivity material ( electronic packaging material, thermal grease,......) affinity ( surface structure or property) compatability mixing technique dispersion state of AIN in epoxy thermal conductivity dielectric property mechanical property electrical properties Composites

45 unever dispersion (agglomerates) good dispersion AIN particles epoxy AIN dispersed along grain boundaries(forming continuously thermally conductive path)

46 (a) Problems ： poor affinity of AIN to epoxy poor affinity formation of pores, flaws between AlN and spoxy formation of agglomerates thermal conductivity ↓ dielectric breakdown ↓ mechanical strength ↓ glass transition temp ↓ (b) Techniques to enhance affinity (1) Coating with SiO 2, Al 2 O 3, or…… AlN AIN SiO 2 or Al 2 O 3

47 (2) Surface treatment with coupling agents (e.g., a class of compounds : silane) coupling agents a class of compounds with two different functional groups, one is reactive to filler (AlN) particle surface and the other is reactive to matrix molecules (epoxy). silane Silane

48 AIN treated with APTS and the composite.

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50 Illustration Example-2 CNT (carbon nanotube) + polymer Surface treatment of CNT Fabrication of composite

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52 Surface charge Determining ions Counter ions (C i, Z i ) Ci ↑, Zi ↑ orε r ↓ K ↑ (1/K ≡double layer thickness ) faster decay doubble layer thickness ↓ repulsive potential ↓

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56 φ ≡V Φ A ≡V A Φ R ≡V R

57 Ci ↑, Zi ↑, εr ↓ =>K ↑ =>K -1 ↓ (double layer thickness) =>E ↓ => ↓ =>E max (or ) ↓

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nanoparticles or nanostructured materials huge surface area & huge surface energy coagulation or (agglomeration) colliding & sticking (Brownian motion & van der Waals attraction) Ostwald ripening (solubility>0 ； vapor pressure>0) or Ostwald ripening agglomerates large particles or structures sintering

72 Brownian Motion Collision (force) averaged over a long enough period of time at any instance Attractive force Collision of particles Particles Brownian motion no attractive force ( Van der waals forces) Brownian motion Particles bouncing back (no agglomerates formation ) agglomeration

73 GROWTH OF PARTICLES Growth Mechanisms (A) Surface Growth (Vapor Deposition) Vapor (or solute) molecules particle number conc: same size : increase shape : sphere By addition (or deposition) of vapor (in gas phase) or solute (in liquid phase) molecules (or atoms or corns) on particle surface Occur when supersaturation S>1 (super saturation s=p/p sat or c/c sat 120

74 GROWTH OF PARTICLES (B) coagulation Coalescent Coagulation particle A ＋ particle B collision, sticking number density : decrease size : increase shape : sphere fusion ＋ particle B collision, sticking no density : decrease size : increase shape : grape-like chain By collision and sticking of particles Occur when there are other particles and they stick when colliding. 121 agglomeration

75 Ⅰ. Properties of AlN high thermal conductivity (w/m-k) Al ： 300 ； Si ： 148 ； AlN ： 130 – 260, SiO 2 ： 1.4 ； Al 2 O 3 ： 20 high electrical resistivity ( cm) Al 2 O 3 ： ； AlN ： low thermal expansion coefficient (PPM/ ℃ ) Si ： 4 ； AlN ： 4.3 ； Al 2 O 3 ： 7.2 ； SiO 2 ： 15 low dieletric constant (8.0 – 9.0) good mechanical strength good corrosion resistance good thermal-shock resistance

76 Ⅱ. Applications of AlN semiconductor or electronic substrates LED substrates, holders, chip submounts or chip carriers IC packages CCL heat sinks thermal grease thermally conductive filler AlN-LTCC heat radiation plates Si-Al-O-N compounds molten metal crucibles and liners corrosion resistant parts components for wafer processing (susceptors, chucks, carriers) subst1 chip3chip2chip1 subst2 crucible

77 P NT Evolution of pH as a function of time for suspensions containing 5 wt% of AlN in distilled water (non-treated powder (NT)), or H 3 PO 4 -treated (P)

78 A. Two Major types of Application for AlN ◎ AlN Powder sintering ◎ AlN Powder Surface High Thermal modification Conductivity Composites e.g., thermal grease, flexible high thermal conductivity LED substrates R S 八. Industrial Applications of AlN slurr y granulatio n tape casting Densified Parts e.g., LED chip carrier, LED lamp housing electronic substrates Q TU Composites Fabrication

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