Page 207 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN004D-ID159 June 8, 2001 15:47

104 Crystallization Processes

a known crystalline species. While not yet uniformly suc- 1. Intrinsic growth rates
cessful on a quantitative basis, the definition and modeling
a. Temperature: The growth rates of individual
of crystal lattice potential energy equations has provided crystal faces depend on temperature, typically
an understanding of crystal growth and morphology on the following an Arrhenius rate law:
molecular level. Derivation of external crystal morphol-

ogy from internal lattice structures via simulation has been E G
G = G 0 exp − (28)
proven possible for several organic compounds. Numeri- RT
cal minimization techniques, coupled with the appropriate If different crystal faces have different activation
valence and nonbonded energy expressions, have enabled energies, variation of the temperature at which
accurate determination of favorable molecular arrange- crystallization takes place modifies individual
ments within a wide variety of molecular crystals. growth rates to varying degrees and results in a
The shape of crystals obtained as a result of following modified crystal shape.
a specific crystallization protocol may be unsatisfactory b. Mixing: The intensity of mixing may determine
and, as a result, methods for modifying the habit of con- the degree to which bulk mass transfer is involved
siderable interest. The predictive capabilities cited in the in growth kinetics, and this can influence the
preceding paragraph are of great utility in such an instance resulting crystal shape.
as they may be used to determine factors leading to the c. Supersaturation: The dependence of growth
unsatisfactory shape and guide subsequent experiments in kinetics on supersaturation may vary from one
which a more desirable shape is sought. Inevitably, such a crystal face to another. Accordingly, different
search involves extensive laboratory or bench-scale exper- prevailing supersaturations can lead to different
iments to determine processing variations that will lead to crystal shapes.
a desired crystal shape.
2. Interfacial behavior
As an example of the variations in shape that can be ex-
hibited by a single crystalline material, consider the forms a. Solvent: Different solvents exhibit different
of potassium sulfate shown in Fig. 8. Clearly, the process- interactions with crystal faces and can alter crystal
ing characteristics and particulate properties of the differ- shape. A change in solvent also can alter the
ently shaped potassium sulfate crystals will vary. stoichiometry of the crystal (e.g., from a hydrated
The mechanisms and variables affecting crystal shape to an anhydrate stoichiometry), which can produce
can be categorized as follows: crystals with quite different morphology.
b. Surfactants: Addition of a surfactant to a
crystallizing system can influence the crystal
shape in a manner illustrated schematically in
Fig. 9. Here, surfactant molecules are shown being
attracted to crystal faces in varying ways; the
hydrophilic head groups favor the horizontal faces,
while the hydrophobic tail groups are
preferentially attracted to the vertical faces. A
growth unit must displace the surfactant to
approach a growing crystal face. As hydrophilic
interactions are typically much stronger than
hydrophobic ones, the growth unit preferentially
enters the vertical faces and growth in the
horizontal direction is favored.
3. Access to growth site
a. Blockage by species attracted to growth site:
Impurities may preferentially locate at a kink or
other favored growth site and block growth at that
site. A difference in the character of the kink or
growth site from one face to another could result
in modification of the crystal shape.
b. Species partially fitting into crystal lattice:In
FIGURE 8 Shapes of K 2 SO 4 crystals. [From Mullin, J. W. (1993).
“Crystallization,” 3rd ed. Butterworth-Heinemann, London. With these instances, an impurity molecule is comprised
permission.] of two parts, one that fits into the crystal lattice