Crystallization Theory
What is Crystallization?
Crystallization is a separation and purification process where a solid crystalline phase is formed from a homogeneous solution, melt, or vapor. It is one of the oldest and most important unit operations in chemical engineering, widely used in pharmaceutical, chemical, food, and mineral processing industries.
Crystallization serves multiple purposes: product purification, solid formation for handling and storage, and recovery of valuable materials. The process is driven by supersaturation - the excess concentration above the equilibrium solubility.
Solubility and Supersaturation
Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at equilibrium at a specific temperature. The solubility curve shows how solubility varies with temperature.
S = C - C*
where S = supersaturation, C = actual concentration, C* = saturation concentration
Supersaturation ratio: σ = C/C* or σ = (C - C*)/C*
- σ < 1: Undersaturated - no crystallization
- σ = 1: Saturated - equilibrium, no net crystallization
- σ > 1: Supersaturated - driving force for crystallization
- Higher supersaturation → faster nucleation and growth
Nucleation
Nucleation is the formation of small crystal nuclei from the supersaturated solution. It is the initial step in crystallization.
Primary Nucleation
Homogeneous nucleation: Spontaneous formation without foreign particles. Requires very high supersaturation. Rare in industrial practice.
Bhom = kh exp(-ΔG*/kT)
where ΔG* is the critical free energy barrier
Heterogeneous nucleation: Nucleation on foreign surfaces (dust, impurities, vessel walls). Requires lower supersaturation. Most common in industrial crystallizers.
Secondary Nucleation
Formation of nuclei from existing crystals through:
- Contact nucleation: Crystal-crystal or crystal-impeller collisions
- Shear nucleation: Fluid shear forces on crystal surfaces
- Needle breeding: Dendrite breakage
Secondary nucleation dominates in well-mixed crystallizers with existing crystals.
Crystal Growth
Once nuclei form, they grow by incorporating solute molecules from the solution. Crystal growth rate is typically expressed as:
G = dL/dt = kg(C - C*)g
where G = linear growth rate, L = crystal size, kg = growth rate constant, g = growth order
Growth Mechanisms
- Diffusion: Mass transfer of solute molecules through the boundary layer to the crystal surface
- Surface integration: Incorporation of molecules into the crystal lattice at the surface
- Volume diffusion: (For growth from melts) Diffusion within the crystal structure
The slowest step is rate-limiting. At low supersaturation, surface integration often limits; at high supersaturation, diffusion may dominate.
Metastable Zone Width (MSZW)
The metastable zone is the region between the saturation curve and the spontaneous nucleation curve. Within this zone:
- Existing crystals can grow
- New nuclei do not form spontaneously (or form very slowly)
- The solution is supersaturated but kinetically stable
Practical Importance: Operating within the MSZW allows controlled crystal growth with minimal nucleation, producing larger, more uniform crystals. Exceeding the MSZW causes nucleation bursts and small, irregular crystals.
MSZW depends on cooling rate, agitation, impurities, and the presence of seed crystals. Slower cooling and seeding can widen the effective operating range.
Crystal Size Distribution (CSD)
The crystal size distribution describes the size range and population of crystals in the product. CSD affects:
- Product purity and quality
- Filterability and washing efficiency
- Flowability and bulk density
- Dissolution rate (important for pharmaceuticals)
Narrow CSD is often desired for consistent product performance. Controlling nucleation and growth rates, using seeding, and optimizing residence time help achieve desired CSD.
Population balance equation (for continuous crystallizers):
∂n/∂t + ∂(Gn)/∂L = B(0)δ(L) - n/τ
where n = population density, G = growth rate, B(0) = nucleation rate, τ = residence time
MSMPR Crystallizer Model
The Mixed Suspension, Mixed Product Removal (MSMPR) crystallizer is a fundamental model for continuous crystallization:
- Perfect mixing of crystals and solution
- Steady-state operation
- Crystals of all sizes are removed at equal rates
- Constant supersaturation throughout the vessel
Steady-state population density:
n(L) = n0 exp(-L/Gτ)
where n0 = nuclei population density, τ = residence time
The MSMPR model predicts an exponential CSD. Dominant crystal size ≈ 3.67Gτ for this distribution. Residence time is a key design parameter.
Crystallization Methods
| Method | Principle | Applications |
|---|---|---|
| Cooling | Lower temperature reduces solubility | Organic compounds, salts with positive solubility-temperature slope |
| Evaporation | Remove solvent to increase concentration | Salts with weak temperature dependence, sugar |
| Vacuum | Combined cooling and evaporation at low pressure | Heat-sensitive materials, large-scale salt production |
| Drowning-out | Add anti-solvent to reduce solubility | Pharmaceutical APIs, proteins |
| Reactive | Chemical reaction produces insoluble product | Precipitation, calcium carbonate, hydroxides |
Yield Calculation
The theoretical crystal yield is calculated from mass balance:
Mass balance (for cooling crystallization):
Mfeed × Cinitial = Mcrystal + Mmother liquor × Cfinal
Yield = Mcrystal / (Mfeed × Cinitial) × 100%
Important considerations:
- Actual yield < theoretical yield due to losses, incomplete separation
- Mother liquor contains dissolved solute at final temperature solubility
- Crystal purity depends on washing efficiency and impurity incorporation
- Lower final temperature = higher yield but may be limited by eutectic point
Design Strategies for High-Quality Crystals
1. Seeding
Add small seed crystals at controlled supersaturation to avoid spontaneous nucleation. Provides control over final CSD.
2. Controlled Cooling Profile
Linear, natural, or optimized cooling rates. Slower cooling produces larger crystals. Programmed cooling maintains constant supersaturation.
3. Agitation Optimization
Sufficient mixing prevents settling and ensures uniform supersaturation, but excessive agitation causes crystal breakage and secondary nucleation.
4. Fines Dissolution
Remove and dissolve small crystals to shift CSD toward larger sizes. Improves product uniformity.
5. Residence Time Control
For continuous crystallizers, τ = V/Q where V is volume and Q is flow rate. Longer residence time allows larger crystal growth.
Common Industrial Applications
Pharmaceutical Industry
- • API (Active Pharmaceutical Ingredient) purification
- • Polymorphic form control
- • Protein crystallization
- • Chiral separation
Chemical Industry
- • Salt production (NaCl, KCl, etc.)
- • Fertilizer manufacturing
- • Organic chemical purification
- • Specialty chemical synthesis
Food Industry
- • Sugar refining
- • Salt production
- • Lactose production
- • Citric acid crystallization
Mineral Processing
- • Metal salt recovery
- • Lithium extraction
- • Rare earth purification
- • Wastewater treatment (struvite)
References
- Mullin, J.W., "Crystallization", 4th Edition, Butterworth-Heinemann (2001)
- Myerson, A.S., "Handbook of Industrial Crystallization", 2nd Edition, Butterworth-Heinemann (2002)
- Randolph, A.D., Larson, M.A., "Theory of Particulate Processes", 2nd Edition, Academic Press (1988)
- Mersmann, A., "Crystallization Technology Handbook", 2nd Edition, Marcel Dekker (2001)
- Lewis, A.E., Seckler, M., Kramer, H., van Rosmalen, G., "Industrial Crystallization: Fundamentals and Applications", Cambridge University Press (2015)