chemical)engineering)3) - vscht.czuchi.vscht.cz/uploads/pedagogika/chi3/lectures/lecture-2... ·...
Post on 19-Jul-2018
217 Views
Preview:
TRANSCRIPT
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
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
top related