### Abstract

The effects of sensitivity and resolution of a nucleation detector on induction time were mathematically analysed. The induction time was defined here as the time at which the number density of crystals nucleated under isothermal conditions had reached the minimum detectable number density of crystals (N/M)_{det}. The value of (N/M)_{det} depends on the detector used, and therefore can be called the detector sensitivity. Meanwhile, the detector resolution is defined as the minimum detectable crystal size L _{d}. The equation for induction time t_{ind} was derived for a simplified case wherein secondary nucleation and concentration reduction were both neglected. For a more general case where such a simplification cannot be made, the induction time t_{ind} was calculated numerically. The sensitivity and resolution had effects on induction time. The induction time increased as the sensitivity decreased (i.e., the value of (N/M)_{det} increased). It also increased with a decrease in the resolution (i.e., an increase in the minimum detectable size L_{d}). The effect of nucleus size L_{0} on induction time t_{ind} was also analysed. The analysis suggested that the induction time in an actual experiment, where the minimum detectable size L_{d} would be much larger than the nucleus size L_{0}, was independent of nucleus size itself but was affected by the resolution L_{d}. The interfacial energy of a crystal nucleus in solution that is deduced from the widely used plot of ln t_{ind}vs. 1/(ln S)^{2} (S: supersaturation ratio) was pointed out to be questionable. The effect of agitation rate (or stirrer speed) on induction time was also discussed. This journal is

Original language | English |
---|---|

Pages (from-to) | 1103-1112 |

Number of pages | 10 |

Journal | CrystEngComm |

Volume | 16 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2014 Feb 14 |

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### ASJC Scopus subject areas

- Chemistry(all)
- Materials Science(all)
- Condensed Matter Physics

### Cite this

*CrystEngComm*,

*16*(6), 1103-1112. https://doi.org/10.1039/c3ce42019a

**Effects of detector sensitivity and resolution on induction time reading.** / Kubota, Noriaki; Kobari, Masanori; Hirasawa, Izumi.

Research output: Contribution to journal › Article

*CrystEngComm*, vol. 16, no. 6, pp. 1103-1112. https://doi.org/10.1039/c3ce42019a

}

TY - JOUR

T1 - Effects of detector sensitivity and resolution on induction time reading

AU - Kubota, Noriaki

AU - Kobari, Masanori

AU - Hirasawa, Izumi

PY - 2014/2/14

Y1 - 2014/2/14

N2 - The effects of sensitivity and resolution of a nucleation detector on induction time were mathematically analysed. The induction time was defined here as the time at which the number density of crystals nucleated under isothermal conditions had reached the minimum detectable number density of crystals (N/M)det. The value of (N/M)det depends on the detector used, and therefore can be called the detector sensitivity. Meanwhile, the detector resolution is defined as the minimum detectable crystal size L d. The equation for induction time tind was derived for a simplified case wherein secondary nucleation and concentration reduction were both neglected. For a more general case where such a simplification cannot be made, the induction time tind was calculated numerically. The sensitivity and resolution had effects on induction time. The induction time increased as the sensitivity decreased (i.e., the value of (N/M)det increased). It also increased with a decrease in the resolution (i.e., an increase in the minimum detectable size Ld). The effect of nucleus size L0 on induction time tind was also analysed. The analysis suggested that the induction time in an actual experiment, where the minimum detectable size Ld would be much larger than the nucleus size L0, was independent of nucleus size itself but was affected by the resolution Ld. The interfacial energy of a crystal nucleus in solution that is deduced from the widely used plot of ln tindvs. 1/(ln S)2 (S: supersaturation ratio) was pointed out to be questionable. The effect of agitation rate (or stirrer speed) on induction time was also discussed. This journal is

AB - The effects of sensitivity and resolution of a nucleation detector on induction time were mathematically analysed. The induction time was defined here as the time at which the number density of crystals nucleated under isothermal conditions had reached the minimum detectable number density of crystals (N/M)det. The value of (N/M)det depends on the detector used, and therefore can be called the detector sensitivity. Meanwhile, the detector resolution is defined as the minimum detectable crystal size L d. The equation for induction time tind was derived for a simplified case wherein secondary nucleation and concentration reduction were both neglected. For a more general case where such a simplification cannot be made, the induction time tind was calculated numerically. The sensitivity and resolution had effects on induction time. The induction time increased as the sensitivity decreased (i.e., the value of (N/M)det increased). It also increased with a decrease in the resolution (i.e., an increase in the minimum detectable size Ld). The effect of nucleus size L0 on induction time tind was also analysed. The analysis suggested that the induction time in an actual experiment, where the minimum detectable size Ld would be much larger than the nucleus size L0, was independent of nucleus size itself but was affected by the resolution Ld. The interfacial energy of a crystal nucleus in solution that is deduced from the widely used plot of ln tindvs. 1/(ln S)2 (S: supersaturation ratio) was pointed out to be questionable. The effect of agitation rate (or stirrer speed) on induction time was also discussed. This journal is

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U2 - 10.1039/c3ce42019a

DO - 10.1039/c3ce42019a

M3 - Article

VL - 16

SP - 1103

EP - 1112

JO - CrystEngComm

JF - CrystEngComm

SN - 1466-8033

IS - 6

ER -