Spatial localization of nanoparticle growth in photoinduced nanocomposites

Anton A. Smirnov; Alexander Pikulin; Nikita Bityurin

doi:10.1007/s00339-017-1539-4

Applied Physics A

February 2018, 124:117 | Cite as

Spatial localization of nanoparticle growth in photoinduced nanocomposites

Authors
Authors and affiliations

Anton A. Smirnov
Alexander Pikulin
Nikita BityurinEmail author

Article

First Online: 11 January 2018

Received: 31 October 2017

Accepted: 28 December 2017

Abstract

Photoinduced nanocomposites are the polymer materials where the nanoparticles can be generated by the light irradiation. The single atoms of metal are formed due to the photoreduction of the metal-containing precursor added to the polymer matrix. Then the atoms precipitate into the nanoparticles (NPs). Similarly, semiconductor NPs are assembled from the monomer species such as CdS, which can be released due to the photodestruction of the appropriate precursor. We analyze theoretically the possibility of spatial confinement of growing nanoparticles in a domain where the elementary species are generated by a three-dimensionally localized source. It is shown that the effective confinement can be achieved only if the size of the generation domain exceeds some critical spatial scale determined by the parameters of the system. The confinement is provided by the trapping of the diffusing elementary species by the growing nanoparticles. The proposed model considers the irreversible particle growth, typical for the noble metals. Both the nucleation and the particle growth processes are suggested to be diffusion controlled.

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Notes

Acknowledgements

This work was supported by the Russian Science Foundation (RSF) under Project No. 14-19-01702.

Appendix

Equations obtained with non-stationary averaging technique

The unknown functions $a(r,\tau )$, $b(r,\tau )$, and $m(r,\tau )$ were substituted in Eqs. (7–9) by the Gaussian probe functions (12) with unknown widths and amplitudes: ${a_0}(\tau )$, ${b_0}(\tau )$, ${m_0}(\tau )$, ${r_{\text{A}}}(\tau )$, ${r_{\text{B}}}(\tau )$, and ${r_{\text{M}}}(\tau )$. The ordinary differential equations for the unknown parameters are obtained by the spatial averaging of the original partial-derivative equations. By applying factor $r$ and then integrating by $r$ of Eqs. (7–9), one gets

$$\frac{{\text{d}}}{{{\text{d}}\tau }}\left( {{a_0}r_{{\text{A}}}^{{\text{2}}}} \right)=1 - 2{a_0} - 0.5\mu a_{0}^{2}r_{{\text{A}}}^{2} - 0.5\delta \mu {a_0}{b_0}r_{{{\text{AB}}}}^{{\text{2}}},$$

(23)

$$\frac{{\text{d}}}{{{\text{d}}\tau }}\left( {{b_0}r_{{\text{B}}}^{{\text{2}}}} \right)=0.25\mu a_{0}^{2}r_{{\text{A}}}^{{\text{2}}},$$

(24)

$$\frac{{\text{d}}}{{{\text{d}}\tau }}\left( {{m_0}r_{{\text{M}}}^{{\text{2}}}} \right)=0.5\mu a_{0}^{2}r_{{\text{A}}}^{{\text{2}}}+0.5\delta \mu {a_0}{b_0}r_{{{\text{AB}}}}^{{\text{2}}}.$$

(25)

By applying factor ${r^2}$ and then integrating by $r$ of Eqs. (7–9), one gets

$$\frac{{\text{d}}}{{{\text{d}}\tau }}\left( {{a_0}r_{{\text{A}}}^{{\text{3}}}} \right)=1 - \frac{1}{{2\sqrt 2 }}\mu a_{0}^{2}r_{{\text{A}}}^{{\text{3}}} - \delta \mu {a_0}{b_0}\frac{1}{{2\sqrt 2 }}r_{{{\text{AB}}}}^{{\text{3}}},$$

(26)

$$\frac{{\text{d}}}{{{\text{d}}\tau }}\left( {{b_0}r_{{\text{B}}}^{{\text{3}}}} \right)=\frac{1}{{4\sqrt 2 }}\mu a_{0}^{2}r_{{\text{A}}}^{{\text{3}}},$$

(27)

$$\frac{{\text{d}}}{{{\text{d}}\tau }}\left( {{m_0}r_{{\text{M}}}^{3}} \right)=\frac{1}{{2\sqrt 2 }}\delta \mu {a_0}{b_0}r_{{{\text{AB}}}}^{{\text{3}}}+\frac{1}{{2\sqrt 2 }}\mu a_{0}^{2}r_{{\text{A}}}^{{\text{3}}}.$$

(28)

Here,

$${r_{{\text{AB}}}}={\left( {\frac{1}{{2r_{{\text{A}}}^{2}}}+\frac{1}{{2r_{{\text{B}}}^{{\text{2}}}}}} \right)^{ - 1/2}}.$$

(29)

Finally, one derives Eqs. (13–18) from (23–28).

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Anton A. Smirnov
- 1
Alexander Pikulin
- 1
Nikita Bityurin
- 1
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1.Institute of Applied Physics Russian Academy of SciencesNizhny NovgorodRussia

Spatial localization of nanoparticle growth in photoinduced nanocomposites

Abstract

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Acknowledgements

References

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