NUCLEATION and CRYSTAL GROWTH.

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NUCLEATION and CRYSTAL GROWTH. Roger J. Davey,
Molecular Materials Centre, UMIST, Manchester, UK.
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Rojs Golden Triangle
From molecules to crystallizers Roger Davey and
John Garside, Oxford Chemistry Primers, OUP, 2000
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Supersaturation Nucleation of a crystal Molecular
clustering Derivation of a rate equation and its
extension to a polymorphic system. Simple
experiments induction times Crystal Growth a
surface sensitive process
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Quantifying supersaturation ?eq ?0
RTlnxeq ?ss ?0 RTlnxss ? ? ?/RT
ln(xss/xeq)
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Some equations (sorry!!) the critical size
or
hence
define
because
it follows that
Equilibrium between monomers and clusters
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experiments
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SAXS
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Solubility of small crystals
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20 mJ/m2
10 mJ/m2
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The rate equation
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Induction times a simple measure of J.
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Nucleation in polymorphic systems
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with the two values of B being given by the
appropriate values of the term 16?? 3? 2/3R3T 3.
Both KJ,I and KJ,II are functions of xeq and T
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. By defining the dimensionless variables a
?x / BII1/2, b (BI / BII) and c a
/ ln (KJ,II /KJ,I)1/3 a If KJ,I gt KJ,II, then
above some value of supersaturation, the
metastable phase I has the highest nucleation
rate whereas below this value phase II appears
more rapidly. b If KJ,II gt KJ,I and (1 a/c)3 lt
b, the stable phase II has the higher nucleation
rate at all supersaturations. c If KJ,II gt KJ,I
and (1 a/c)3 gt b, the metastable phase has the
higher nucleation rate only over the intermediate
range of supersaturations.
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AI
AII
? J
? ?
b
a
AII
AI
? J
? ?
c
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Solution chemistry polymorphic forms of
2,6,dihydroxybenzoic acid
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Polymorphs 1 and 2 of 2,6 DHB
1 (Toluene)
2 (Chloroform)
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Toluene
1
Chloroform
2
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Crystal Growth
Kinked, stepped and flat faces
Growth in direction 1 gt 2

• Flux of growth units to surface exceeds net loss.
• Integration into lattice dependent, amongst
  others (e.g. molecular recognition) upon strength
  and number of interactions.
• Assume linear growth rate, v, of a face is
  proportional to total binding energy of growth
  unit to surface
• vK gt vS gt vF

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Figure 1. The Morphology of ? glycine taken from
Groth5. b 010, q 011, n 110, m
210
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Saccharin Morphology
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Form 1
Form 2
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Crystal growth the importance of mass transfer,
surface integration and temperature.
When r 1
with
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Concluding remarks You cannot define a
crystallisation experiment without a phase
diagram (solubility curve). In a polymorphic
system the relative nucleation rates of different
structures are not predictable. In a polymorphic
system growth rates of different structures will
be different and appearance depends on J.kG A
structural model for nucleation based on crystal
structure works well see next lecture. Finally
.. The bees in Rojs bonnet
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Concomitant polymorphs and energies Disappearing
polymorphs and control