lecture 2 - nucleation and growth of nanomaterials

7/27/2019 Lecture 2 - Nucleation and Growth of Nanomaterials

1/17

Lecture 2

Nucleation and Growth


2/17

Importance - Nucleation and Growth

Important controlling Parameters:

Selection of Precursors

Purity of precursors

Precursor Concentration

Mixing Sequence

Reaction Temperature

Reaction Time

Precursor

Solution/Vapor

Ostwald

Ripening

Formation of Nuclei

Growth of

Nuclei

Agglomeration

Precipitation

Homogenous Heterogeneous

1. Variation of Particle Size Distribution

2. Hard agglomeration

3. Nano size change to micron

SIZE is an important phenomenon for NANOMATERIALS


3/17

Monosize and Wide Size Distribution Nanoparticles!!

20nm

T. Hyeon et al, Nature Materials, 3, 2004, 891-95D. Sarkar et al, J American Ceramic Society, 92 [12], 2877 2882, 2009

Iron Oxide

5, 9, 12,16 and 22nm

Titanium Carbide

84nm


4/17

Particle Size Distribution

Particle Size (nm)

VolumeFraction(

%)

monosize

narrow size

wide size

= Shape , b = Scale,g = location,x = particle size and f(x) = Cumulative undersize

Effect of Nucleation and Growth on particle size distribution

D. Sarkar et al, J American Ceramic Society, 92 [12] 2877 2882, 2009

Cumulative undersize mass distribution

gives the amount of particle smaller than

the defined size.


5/17


6/17

Nucleation

Nucleation, the first step

First process is for microscopic clusters (nuclei) ofatoms or ions to form

Nuclei possess the beginnings of the structure of the crystal

Only limited diffusion is necessary

Thermodynamic driving force for crystallization must bepresent

Homogeneous - random accumulation of mother molecules

Heterogeneous -small particles present in the solution act as nuclei

Two Type:


7/17

The change in free energy is balanced by

the energy gain of creating a new volume,

and the energy cost due to creation of a

new interface.

When the overall change in free energy,DG is negative, nucleation is favored

In the classic case of a spherical cluster

that liberates -Gv J/cc during formation, but

which must pay the positive cost of J/cm2

of surface interfacing with the surrounding

Homogenous Nucleation

Free Energy needed to form a cluster of radius r is ;

J/cc)

First term shows the energy gain of creating a new volume

Second term shows the energy loss due to surface tension of the new interface

Solid particle

G1 G2

DG = 4/3r3Gv + 4r2

orDG = 4/3r3Gv 4r2

G2 G1 = - DG


8/17

Free energy to add molecules to this cluster, until the radius reaches Critical

radius

Homogenous NucleationContd

Addition of new molecules to clusters larger than this critical radius is no longer

l imited by nucleat ion, but perhaps by diffusion (i.e. the supply of molecules) or

cont inuous growth of nuc lei

The free energy needed to form this critical radius can be found by

which occurs at the maximum DG where dG / dr = 0

As the phase transformation becomes more and more favorable, the

formation of a given volume of nucleus frees enough energy to form an

increasingly large surface

r* =2

GvdGdr = 0Where,

DG* =163

3(Gv)2

Surface energy related to Gibbs free energy during nucleation !!

For Ti, DGv = 50J/cm3 and = 50mJ/m2

r* = 2nm (5-10times larger than single unit cell)


9/17

Heterogeneous Nucleation

Heterogeneous nucleation occurs much more often than homogeneous nucleation

It forms at preferential sites such as phase boundaries or impurities like dust and

requires less energy than homogeneous nucleation.

At such preferential sites, the effective surface energy is lower, thus diminished the

free energy barrier and facilitating nucleation.

Surfaces promote nucleation because of wetting contact angles greater than zero

between phases encourage particles to nucleate

The free energy needed for heterogeneous nucleation is equal to the product of

homogeneous nucleation and a function of the contact angle :

DGheterogeneous = DGhomogenous x f(q)

f(q) = + Cosq Cos3q

Energy needed for heterogeneous nucleation is reduced

Wetting angle determines the ease of nucleation byreducing the energy needed.

Hetero

Homo

DGr

r*


10/17

Formation of Nuclei

formation favor: high initial concentration or supersaturation

low viscosity

low critical energy barrier

uniform nanoparticle size:

same time formation

abruptly high supersaturation

Growth of Nuclei Growth processes then enlarge existing nuclei

Smallest nuclei often redissolve

Larger nuclei can get larger through diffusion and adsorption

Thermodynamics favors the formation of larger nuclei

Nucleation and Growth Process


11/17

Strong overlap of growth and

nucleation rates

Nucleation rate is high

Growth rate is highBoth are high at the same

temperature

No overlap of growth and

nucleation rates Nucleation rate is small

Growth rate is small

At any one temperature one of the

two is zero

RateTemperature

Nucleation Rate

Growth Rate

Nucleation Rate

Growth Rate


12/17

Nucleation

(critical size)

Agglomeration

Clusters

Crystallites

Primary particlesParticles

Growth

Typical precipitation reaction:

Reactant 1 + Reactant 2 Product + By-productT, t

Stabilizer

Nucleation & Growth


13/17

Precipitation has generally been shown to occur in four steps:

(a) nucleation

(b) crystal growth

(c) agglomeration and

(d) ripening of the solids

(a) Nucleation: a nucleus is a fine particle on which the

spontaneous formation or precipitation of a solid phase can

take place in a supersaturated solution.

Homogeneousnucleation occurs when the nuclei is formed

from component ions of the precipitate; if foreign particles are

the nuclei, heterogeneousnucleation occurs.

Precipitation


14/17

(b) Crystal growth: crystals form by the deposition of the precipitate

constituent ions onto nuclei.

Crystal growth rate can be expressed as:

where

C* = saturation concentration (mole/L)

C = actual concentration of limiting ion (mole/L)

k = rate constant (Ln / time mg)

S = surface area available for precipitation (mg/L of a givenparticle size)

n = constant

When the diffusion rate of ions to the surface of the crystal controls

the crystal growth rate, exponent n = 1; when other processes such asthe reaction rate at the crystal surface are rate limiting, n 1

dC

dtkS C C

n= ( *)

Precipitation.Contd


15/17

(c) Agglomeration : conversion of small particles into larger

particles is enhance by agglomeration of particles to form

larger particles, which is the continual growth until equilibrium

is reached. The changes in crystal structure that take place

over time are often called aging.

(d) Ostwald Ripening : A phenomenon called ripeningmayalso take place whereby the crystal size of the precipitate

increases.

Precipitation.Contd

Growth of Protein Crystal

Day 6 Day 10 Day 13 Day 16


16/17

Ostwald ripeningOstwald ripening is an observed phenomenon in solid (or liquid) solutions

which describes the change of an inhomogeneous structure over time. The

phenomenon was first described by Wilhelm Ostwald in 1896

It is a spontaneous process that occurs because largercrystals are more energetically favored than smaller crystals.

While the formation of many small crystals is kineticallyfavored, (i.e. theynucleate more easily) large crystals are thermodynamicallyfavored.

Thus, from a standpoint of kinetics, it is easier to nucleate many smallcrystals. However, small crystals have a larger surface area to volume ratiothan large crystals.

Molecules on the surface are energetically less stable than the ones

already well ordered and packed in the interior.

Large crystals, with their greater volume to surface area ratio, represent alower energy state.

Thus, many small crystals will attain a lower energy state if transformedinto large crystals and this is what we see in Ostwald ripening.


17/17

Conclusion

To achieve monodispersity, these two stages must be separated and nucleation

should be avoided during the period of growth (Curve I)

Curve III represents self-sharpening growth process, i.e Ostwald ripening

Uniform particles can be obtained due to aggregation of much smaller subunits

rather than continuous growth by diffusion (Curve II)

In a homogenous precipitation, a short single burst of nucleation occurs when the

concentration of constituent species reaches critical supersaturation

The nuclei so obtained are allowed to grow uniformly by diffusion of solutes from thesolution to their surface until the final size is attained

lecture 2 - nucleation and growth of nanomaterials

Documents