298
M. Michaud et al.
This new procedure is numerically stable and uses the unaltered equations with
high accuracy. The typical calculation time for several hour long ripening processes
decreases to a few minutes. Furthermore, processes with dynamically changing temperatures can be modeled with high precision and excellent agreement with experimental data. Due to its predictive nature it saves experimental time and considerably
improves the understanding of continuous colloidal processing [9].
7.5 Systems with Sequential Growth: CdSe@ZnS Quantum
Dots
The bivariate extension of the model was applied to the precipitation and growth of
cadmium selenide—zinc sulfide (CdSe@ZnS) quantum dots. Mathematically these
particles can be represented as a structure growing sequentially from the inner core
to the outer shell in a 2-step process. In order to simplify the complex nucleation
behavior any influence of heterogeneous nucleation of shell material on the core
surface is neglected.
The synthesis of core-shell CdS/ZnS quantum dots is usually done by injecting
shelling agents to seeded core particles by heterogeneous nucleation and growth
of the shell on the core. The so called hot injection technique for the synthesis of
quantum dots is a well-established and widely used method in the lab and was performed using an automated Chemspeed Technologies Swing XL autoplant synthesis
platform. Typically, a Cd-containing stock solution is prepared by introducing CdO
and oleic acid. The hot cadmium oleate solution is injected into a selenium solution
in trioctylphosphene. The high supersaturation induces fast nucleation of CdSe followed by rapid particle growth on a timescale of a few s. The shelling agent, e.g. a
diethylzinc solution, is then injected in a second step to produce the desired core-shell
nanoparticles.
This sequential experimental procedure is a good starting point to introduce bivariate particle simulation, since the temporal separation of the different growth steps
allow for simplification of Eq. 39. The two-step synthesis can be modeled by the
introduction of two Heaviside functions to save calculation time as shown in preceding chapters. Neglecting nucleation and aggregation, the growth terms G 1 and
G 2 can be expressed by distinct growth laws multiplied with a Heaviside function,
ensuring sequential growth (see Eqs. 41 and 42) with T being the injection time of
the shelling agent and log(K SP ) = − 33 being to solubility product [38]. This proves
the bivariate code retains the flexibility of the monovariate model, which is important
to ensure applicability to a wide range of different particulate systems. The code was
tested on experimental data from Mahmoud et al. and showed excellent agreement
as seen in Fig. 14. The shell thickness can be modulated with simulation time and
provides a good basis for future optimization studies.
M. Michaud et al.
This new procedure is numerically stable and uses the unaltered equations with
high accuracy. The typical calculation time for several hour long ripening processes
decreases to a few minutes. Furthermore, processes with dynamically changing temperatures can be modeled with high precision and excellent agreement with experimental data. Due to its predictive nature it saves experimental time and considerably
improves the understanding of continuous colloidal processing [9].
7.5 Systems with Sequential Growth: CdSe@ZnS Quantum
Dots
The bivariate extension of the model was applied to the precipitation and growth of
cadmium selenide—zinc sulfide (CdSe@ZnS) quantum dots. Mathematically these
particles can be represented as a structure growing sequentially from the inner core
to the outer shell in a 2-step process. In order to simplify the complex nucleation
behavior any influence of heterogeneous nucleation of shell material on the core
surface is neglected.
The synthesis of core-shell CdS/ZnS quantum dots is usually done by injecting
shelling agents to seeded core particles by heterogeneous nucleation and growth
of the shell on the core. The so called hot injection technique for the synthesis of
quantum dots is a well-established and widely used method in the lab and was performed using an automated Chemspeed Technologies Swing XL autoplant synthesis
platform. Typically, a Cd-containing stock solution is prepared by introducing CdO
and oleic acid. The hot cadmium oleate solution is injected into a selenium solution
in trioctylphosphene. The high supersaturation induces fast nucleation of CdSe followed by rapid particle growth on a timescale of a few s. The shelling agent, e.g. a
diethylzinc solution, is then injected in a second step to produce the desired core-shell
nanoparticles.
This sequential experimental procedure is a good starting point to introduce bivariate particle simulation, since the temporal separation of the different growth steps
allow for simplification of Eq. 39. The two-step synthesis can be modeled by the
introduction of two Heaviside functions to save calculation time as shown in preceding chapters. Neglecting nucleation and aggregation, the growth terms G 1 and
G 2 can be expressed by distinct growth laws multiplied with a Heaviside function,
ensuring sequential growth (see Eqs. 41 and 42) with T being the injection time of
the shelling agent and log(K SP ) = − 33 being to solubility product [38]. This proves
the bivariate code retains the flexibility of the monovariate model, which is important
to ensure applicability to a wide range of different particulate systems. The code was
tested on experimental data from Mahmoud et al. and showed excellent agreement
as seen in Fig. 14. The shell thickness can be modulated with simulation time and
provides a good basis for future optimization studies.