Chemical  Engineering  3  

Lecture  2:  Crystallisa6on  Equilibrium  &  kine6cs  

Crystallisation Solution/melt (liquid phase) Crystals (solid phase)

reaction crystallization filtration drying

(G)

(L)

(S)

(L) (L-S)

(V)

(L)

(S-L)

(S)

product

Crystals: structural periodicity and long-range order (x-ray diffraction patterns) vs. amorphous materials

Related processes (L-S phase transition):

Melt → bulk amorph. solid … casting

Melt → amorphous particles … prilling

Solution → particles … spray drying

Solution → frozen state → solid … freeze drying

Solution → very fine solids … precipitation

Use of crystallisation: 1)  Isolation step (to obtain solid product: e.g. NaCl) 2)  Purification step (to purify product: e.g. pharma)

Overall procedure in crystallisation design:

1)  Thermodynamics (Solid-liquid equilibria)

2)  Kinetics (rate of crystallisation)

3)  Selection of crystalliser type

- mode of achieving super-saturation

4)  Mass, energy and population balances

- to determine operating condition that meet product specification

Solid-liquid phase equilibria - Solubility: saturated concentration vs. T

- often tabulated in the form:

NaCl

KNO3

€

logceq = a1 +a2T

+ a3 logT

or

€

ceq = A + Bθ + Cθ 2 + ...

Solid-liquid phase equilibria - multiple solvents: “drowning out” effect

Compound A soluble in two solvents, e.g H2O and acetone; the two solvents are miscible

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 20 40 60 80

weight % water in acetone

solu

bilit

y [g

/g

]

-  phase diagrams for binary systems forming solid solutions (mixed crystals)

- liquidus line - solidus line

-components are mixed at molecular level

NOT possible to get pure components in a single crystallization step!

-  phase diagrams for eutectic systems (eu tektos = easily melted)

A+Liquid

B+Liquid

AEB - liquidus FG - solidus

F G

It IS possible to crystallize pure components in a single step.

Yield is limited by the eutectic point E.

Below E - physical mixture of A and B domains

- phase diagrams for compound forming systems

Congruent melting point - hydrate (or solvate) can exist in equilibrium with a solution of the same composition (point D)

Phase equilibria for ternary systems

- in general, rich behaviour

Example: KNO3-NaNO3-H2O at 50 °C

Point A = solubility of KNO3 in H2O at 50 °C

Point C = solubility of NaNO3 in H2O at 50 °C

Point B = Eutonic point (drying up point)

Polymorphism = ability to crystallize in more than one crystallographic form

Example: graphite vs. diamond for carbon

or calcite (rhombohedral) vs. aragonite (orthorhombic) for calcium carbonate

Number of polymorphs for some compounds:

Aspirin - 4; TiO2 - 3; CaCO3 - 3; NH4NO3 - 5

Polymorphs:

Enantiotropic - interconvertible (e.g. by T)

Monotropic - incapable of transformation

Solubility curves for polymorphs

temperature

solubility

β -polymorph

α -polymorph

monotropic

temperature

solubility

β -polymorph

α -polymorph

enantiotropic

Ttransition

Alternative solid forms - terminology

Driving force for crystallization: supersaturation

In 1724 Fahrenheit supercooled water to -9.4˚C before freezing

Below solubility curve: undersaturated

Above: supersaturated

Above metastable limit: labile (spontaneous nucleation)

Crystallisation kinetics

Supersaturation ! nucleation (seeding) ! growth

Creating supersaturation: -  by concentration (evaporation of solvent) -  by temperature (cooling) -  by adding antisolvent

Measures of supersaturation:

€

Δc = css − ceq

€

Δcrel =css − ceqceq

€

σ =cssceq

Size-dependent solubility

Gibbs-Thomson effect

⇒  Ostwald ripening (large partciles grow at the expense of small ones)

⇒  Critical radius (smallest crystals that can exist in a solution of given concentration)

(typically 4-10 nm for many solids)

€

c(r) = c∞ exp 2γVm

rRT⎛

⎝ ⎜

⎞

⎠ ⎟

c(r)…solubility of particle with radius r c∞…solubility of macroscopic particle γ…solid-liquid interfacial tension Vm…molar volume of solid R…molar gas constant T…temperature

Nucleation

"  primary nucleation = in the absence of crystals - homogeneous nucleation = clusters of atoms

spontaneously form in the solution

- heterogeneous nucleation = impurities (e.g. dust particles) act as nucleation centres

"  secondary nucleation = in the presence of crystals (‘seeding’ = provision of nuclei) - contact nucleation mechanism (crystal-crystal and

crystal-wall/impeller collisions)

- shear nucleation mechanism (fluid flow over surface creates new nuclei)

Nucleation rate:

€

B = KB exp −16γ3Vm

2 /3R3T 3σ 2( )σ …supersaturation γ  …interfacial tension between crystal and solution Vm …molar volume of the crystal

- primary (theory) - secondary

€

B = KBΔcb

KB=f(agitation rate, equipment type, visocsity, density)

- primary (empirical)

€

B = KBΔcb

Crystal growth

Surface nucleation Spiral growth

Regimes:

Continuous growth (many growth sites on surface)

Surface nucleation (several nuclei on surface)

Spiral growth (single nucleus on surface)

Crystal growth - overall growth rate

expressed as:

1.  mass deposition rate, R [kg m-2 s-1]

2.  linear growth rate G = dx/dt [m s-1]

€

R = KGΔcg =

1Admdt

=3ψVρGψA

€

m =ψVρx3

€

A =ψA x2

ψV, ψA … volume and surface shape factors

Crystal habit

-  Growth rates are generally not identical along crystal facets

-  Specific adsorptionon of foreign species on particular facets can modify crystal growth

Crystallisation in confined geometry

-  crystallisation in pores (e.g. catalyst impregnation, food freezing)

-  crystallisation in emulsions (e.g. ice cream)

-  crystallisation in droplets / vesicles

Mass & Enthalpy balance

Mass balance

Components: A …solute B …solvent C …impurities

In case of solvate:

Volume fraction of crystals in slurry

mF mL

mS

mV

Mass & Enthalpy balance

Enthalpy balance

mF mL

mS

mV

QH

Cooling crystallisation QH = 0, mV = 0Evaporative crystallisation QC = 0

QC

Specific enthalpy