Kink Rate Model for the General Case of Organic Molecular Crystals

Kim, Seung Ha; Dandekar, Preshit; Lovette, Michael A.; Doherty, Michael F.

doi:10.1021/cg500167a

Cited by 23 publications

(45 citation statements)

References 29 publications

(65 reference statements)

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“…The expression for the step velocity of the ith edge is given by equation 16, where a P,i , u i and ρ i are the distance that the ith edge propagates with the addition of a new row, the net rate of solute attachment to kink sites on the ith edge (kink rate, see section 4.4), and the density of kink sites on the ith edge, respectively [112].…”

Section: Edges and Spiralsmentioning

confidence: 99%

“…Equation 18 is this general expression for the kink rate u i on a step edge of an organic crystal containing n growth units [13,19,112] (n = 1 for centrosymmetric crystals and subscripts k and i correspond to the kink and edge, respectively; note also that the prefactor n was incorrectly omitted in our earlier formulations of equation 18). We use transition state theory (TST) [113] to develop expressions for the attachment and detachment rates to use within equation 18.…”

Section: Kink Rate Model For Spiral Growthmentioning

confidence: 99%

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A design aid for crystal growth engineering

Tilbury

Kim

et al. 2016

Progress in Materials Science

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With the highly competitive development of chemical and pharmaceutical industries, mastering crystal growth is becoming increasingly necessary. Modern industrial manufacturers place high importance on the ability to grow crystals with a specific habit using tailored operating conditions. A detailed understanding of crystal growth is, therefore, vital for researchers in crystallography and crystallization to respond and realize this objective. Various models to predict crystal shape in the literature are reviewed here. The most commonly adopted are usually non-mechanistic and limited in their predictive power and utility, especially for products of industrial interest. Mechanistic models offer far more potential for rational crystal design, but

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Section: Edges and Spiralsmentioning

confidence: 99%

Section: Kink Rate Model For Spiral Growthmentioning

confidence: 99%

A design aid for crystal growth engineering

Tilbury

Kim

et al. 2016

Progress in Materials Science

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“…The kink site potential energies U kink calculated for the obtuse and acute edges of the growth spirals on calcite

(10 \bar{1} 4)

surface are not equal to each other as shown in Table . As the attachment/detachment rate from the kink sites and the step velocity depends on the kink site potential energy, the U kink values suggest that the step velocities of obtuse and acute edges should be different. Therefore, the difference in the solid‐state interaction energies in the kink sites between acute and obtuse spiral edges provides a quantitative explanation for the presence of asymmetric growth spirals on the

(10 \bar{1} 4)

surface of calcite.…”

Section: Kink Site Energiesmentioning

confidence: 99%

A mechanistic growth model for inorganic crystals: Solid‐state interactions

Dandekar

Doherty

2014

AIChE Journal

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Growth shapes of inorganic crystalline solids govern material properties such as catalytic activity and selectivity, solar cell efficiency, and so forth. A systematic understanding of the crystal growth process and the solid‐state interactions within inorganic crystals should help to engineer crystal shapes. A general model that identifies periodic bond chains in inorganic crystals while accounting for the long‐range electrostatic interactions is presented. The variation in the electronic structure and the partial charges of growth units on the inorganic crystal surfaces has been captured using the bond valence model. The electrostatic interaction energies in the kink sites of inorganic crystals were calculated using a space partitioning method that is computationally efficient. This model provides a quantitative explanation for the asymmetric growth spirals formed on the (101¯4) surface of calcite. This methodology for studying solid‐state interactions can be used with a mechanistic growth model to predict the morphology of a wide variety of inorganic crystals. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3707–3719, 2014

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“…Kuvadia and Doherty developed a generalized expression for the kink rate u on a spiral edge on organic crystal surfaces that has n types of kink sites along the edge

u = \frac{{(j^{+})}^{n} - \prod_{k = 1}^{n} j_{k}^{-}}{\sum_{ℓ = 1}^{n} {(j^{+})}^{n - ℓ} {(j^{-})}^{(ℓ - 1)}}

where j + is the attachment flux of growth units into the kink site and

j_{k}^{-}

is the detachment flux from the kink site k . j + is independent of the specific kink site and depends only on supersaturation and solution composition, whereas

j_{k}^{-}

depends on the solution chemistry and the local bonding energies for the kink site k . The quantity

{(j^{-})}^{(ℓ - 1)}

in Eq.…”

Section: Kink Rate For Inorganic Crystalsmentioning

confidence: 99%

“…where j 1 is the attachment flux of growth units into the kink site and j 2 k is the detachment flux from the kink site k. j 1 is independent of the specific kink site and depends only on supersaturation and solution composition, whereas j 2 k depends on the solution chemistry and the local bonding energies for the kink site k. 35,38,39 The quantity ðj 2 Þ ð'21Þ in Eq. 5 is given by…”

Section: New Kink Rate Modelmentioning

confidence: 99%

A mechanistic growth model for inorganic crystals: Growth mechanism

Dandekar

Doherty

2014

AIChE Journal

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Inorganic crystals grown from solution find wide application. A mechanistic growth model based on the spiral growth mechanism that operates at low supersaturation on inorganic crystal surfaces is presented. The long-range electrostatic interactions on inorganic crystal surfaces are captured by methods developed in our previous article (Dandekar and Doherty, AIChE J., in press). The interactions of kink site growth units with the solvent molecules partially determine the growth kinetics. Relevant experimental parameters are systematically accounted for in the expression for the kink incorporation rate along step edges on the crystal surfaces. The growth model accurately predicts the asymmetric growth spirals on the ð10 14Þ surface of calcite crystals. The effect of supersaturation and ionic activity ratio on the step velocities of the acute and obtuse spiral edges is also correctly captured. This model can be used to predict the shapes of solution grown inorganic crystals and to engineer the growth process to design inorganic solids with functionally desirable shapes.

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Kink Rate Model for the General Case of Organic Molecular Crystals

Cited by 23 publications

References 29 publications

A design aid for crystal growth engineering

A design aid for crystal growth engineering

A mechanistic growth model for inorganic crystals: Solid‐state interactions

A mechanistic growth model for inorganic crystals: Growth mechanism

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