Influence of structure of iron nanoparticles in aggregates on their magnetic properties
- Dana Rosická^{1}Email author and
- Jan Šembera^{1}
https://doi.org/10.1186/1556-276X-6-527
© Rosická and Šembera; licensee Springer. 2011
Received: 19 May 2011
Accepted: 14 September 2011
Published: 14 September 2011
Abstract
Zero-valent iron nanoparticles rapidly aggregate. One of the reasons is magnetic forces among the nanoparticles. Magnetic field around particles is caused by composition of the particles. Their core is formed from zero-valent iron, and shell is a layer of magnetite. The magnetic forces contribute to attractive forces among the nanoparticles and that leads to increasing of aggregation of the nanoparticles. This effect is undesirable for decreasing of remediation properties of iron particles and limited transport possibilities. The aggregation of iron nanoparticles was established for consequent processes: Brownian motion, sedimentation, velocity gradient of fluid around particles and electrostatic forces. In our previous work, an introduction of influence of magnetic forces among particles on the aggregation was presented. These forces have significant impact on the rate of aggregation. In this article, a numerical computation of magnetic forces between an aggregate and a nanoparticle and between two aggregates is shown. It is done for random position of nanoparticles in an aggregate and random or arranged directions of magnetic polarizations and for structured aggregates with arranged vectors of polarizations. Statistical computation by Monte Carlo is done, and range of dominant area of magnetic forces around particles is assessed.
Keywords
1 Introduction
Zero-valent iron nanoparticles (nZVI) composed of iron Fe^{0} and its oxides are spherical particles with diameter approximately 40 nm and with a large specific surface. These particles are used for decontamination of groundwater and soil and especially for decontamination of organic pollutants such as halogenated hydrocarbons [1]. Nanoparticles migrate through the soil and can reach the contamination in situ. Properties of the nZVI and remediation possibilities depend on methods of production [2]. At the Technical University of Liberec, experiments with iron nanoparticles TODA, produced by the company Toda Kogyo Corp. [3], and with the nanoparticles NANOFER, produced by the company NANO IRON s.r.o. [4], are made. During a remedial intervention, transport of the iron nanoparticles is slowed down due to rapid aggregation of them. The rate of aggregation increases with growing concentration of particles in solution and with growing ionic strength of the solution [5]. With the word particle we mean both nanoparticles and aggregates. For preservation of the transport properties, it is advisable to stabilize the particles. A lot of methods of stabilization were published [6–10]. We simulate the transport of the iron nanoparticles and that is why we examine the interactions among them causing the aggregation. Models of aggregation of small particles were published in many articles (e.g., [11–13]). They are mostly based on the publications [14] and [15]. However, this generally used model is insufficient for our case. A surface charge established on the surface of particles causes repulsive electrostatic forces between them. The influence on the aggregation into the known aggregation model was implemented in submitted article [Rosicka and Sembera (2009)]. The iron particles corrode in the water, and this process causes change of the surface charge as well as the change of the rate of aggregation [16]. Because the particles are made from iron, they also have magnetic properties, which significantly affects the rate of aggregation [2, 17–20]. In the previous work, the influence of magnetic forces on rate of aggregation of iron particles was assessed [21]. The magnetic forces have significant effect on aggregation. Size of this effect is dependent on the magnitude of polarization of nanoparticles, their directions and distances among nanoparticles or aggregates. We suppose same magnitude of vectors of polarization of all nanoparticles. Hence, there is presented evaluation of magnetic forces among particles depending only on the structure of aggregates, respectively, on directions of the vectors of polarization and distances between particles in this paper. In the future, the extended model of the aggregation of iron nanoparticles will be included into a solver of particle transport in groundwater. It would allow to simulate the transport of iron nanoparticles and to predict effciency of the remedial intervention. That could be useful for proposal of optimal remedial intervention which would enable to decontaminate an affected area effciently and economically.
2 Methods and models
2.1 Magnetic properties of nanoparticles
where M is the vector of magnetic polarization at the point dV , the vector R is the difference between the source of magnetic field dV and the point r, R is the length of R.
where a is the radius of the nanoparticle, and [x _{1}, x _{2}, x _{3}] are the coordinates of the point r. Here, the direction of the vector of polarization M is set to the direction x _{3}, M is the magnitude of the vector M.
2.2 Unstructured model of aggregates
2.3 Structured model of aggregates
3 Results and discussion
3.1 Unstructured model of aggregates
3.1.1 Random directions of polarization of nanoparticles in aggregates
Table of magnitudes of magnetic forces between interacting nanoparticle and aggregate
i | Averaged F _{mg} | Deviation | Summed F _{mg} | Deviation |
---|---|---|---|---|
1 | 1.4·10^{-9} | 2.5·10^{-9} | 6.3·10^{-9} | 1.1·10^{-9} |
10 | 4.4·10^{-10} | 1.9·10^{-10} | 6.3·10^{-9} | 8.4·10^{-9} |
100 | 7.2·10^{-11} | 2.7·10^{-11} | 4.6·10^{-9} | 5.4·10^{-9} |
1,000 | 1.1·10^{-11} | 3.0·10^{-12} | 7.4·10^{-8} | 1.1·10^{-7} |
10,000 | 1.9·10^{-12} | 6.0·10^{-13} | 5.9·10^{-8} | 7.0·10^{-8} |
1,000,000 | 2.8·10^{-13} | 1.1·10^{-13} | 8.7·10^{-9} | 1.0·10^{-8} |
1,000,000 | 5.4·10^{-14} | 2.2·10^{-14} | 3.0·10^{-8} | 4.9·10^{-8} |
Table of magnitudes of magnetic forces between interacting nanoparticle and aggregate
i | Averaged F _{mg} | Deviation | Summed F _{mg} | Deviation |
---|---|---|---|---|
1 | 2.0·10^{-20} | 1.0·10^{-20} | 3.1·10^{-20} | 5.5·10^{-21} |
10 | 3.3·10^{-21} | 2.3·10^{-21} | 6.5·10^{-21} | 4.0·10^{-21} |
100 | 4.7·10^{-22} | 2.8·10^{-22} | 5.9·10^{-22} | 2.2·10^{-22} |
1,000 | 4.7·10^{-23} | 1.7·10^{-23} | 5.1·10^{-23} | 3.0·10^{-23} |
10,000 | 7.9·10^{-24} | 4.0·10^{-24} | 1.5·10^{-23} | 8.5·10^{-24} |
1,000,000 | 1.1·10^{-24} | 5.6·10^{-25} | 1.5·10^{-24} | 1.1·10^{-24} |
1,000,000 | 1.4·10^{-25} | 7.1·10^{-26} | 4.1·10^{-25} | 2.0·10^{-25} |
On the basis of known concentration of particles, we are able to estimate the approximate distances among particles and to choose the right model of computation of magnetic forces and limit distances among the particles.
3.1.2 The same directions of polarization of all nanoparticles in aggregates
3.2 Structured model of aggregates
Table of magnetic forces between one nanoparticle and cubic aggregate
i | |F _{mg}| | |F _{ g } | |
---|---|---|
1 | 2.4·10^{-38} | 2.0·10^{-18} |
8 | 4.1·10^{-38} | 1.6·10^{-17} |
125 | 6.6·10^{-40} | 2.5·10^{-16} |
1,000 | 7.7·10^{-41} | 2.0·10^{-15} |
10,648 | 8.4·10^{-42} | 2.2·10^{-14} |
97,336 | 5.7·10^{-42} | 2.0·10^{-13} |
1,000,000 | 5.0·10^{-42} | 2.0·10^{-12} |
Even though the distance between the particles is the smallest possible, the magnetic forces between the particles are negligible in comparison with gravitation forces. For structured aggregates with polarization of nanoparticles respecting the structure, the magnetic forces have insignificant influence on the rate of aggregation of the particles.
4 Conclusion
We examined the influence of structure of nanoparticles in aggregates on the resulting magnetic field around the aggregates. The comparing parameter was size of magnetic forces among particles and the limit distance. According to these two connected parameters, we are able to estimate the degree of influence of the magnetic forces on rate of aggregation of particles. We analyzed magnetic properties of unstructured aggregates with randomly distributed nanoparticles with random direction of polarization in the aggregates and of structured model of aggregates with orderly distributed nanoparticles and with arranged directions of polarization. In the case of structured model, resulting magnetic forces approach to zero. Since we suppose that magnetic field of iron particles has significant influence on the rate of aggregation [19], the structured model is not sufficient. Hence, we assume damaged structure of aggregates. In our future work, the unstructured model will be compared with experimental data of aggregation of iron particles.
Declarations
Acknowledgements
This result was realized under the state subsidy of the Czech Republic within the research and development project "Advanced Remedial Technologies and Processes Centre" 1M0554--Programme of Research Centres supported by Ministry of Education and within the research project FR-TI1/456 "Development and implementation of the tools additively modulating soil and water bioremediation"--Programme MPO-TIP supported by Ministry of Industry and Trade.
Authors’ Affiliations
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