# Characterization of magnetic nanoparticle by dynamic light scattering

- JitKang Lim
^{1, 2}Email author, - Swee Pin Yeap
^{1}, - Hui Xin Che
^{1}and - Siew Chun Low
^{1}

**8**:381

https://doi.org/10.1186/1556-276X-8-381

© Lim et al.; licensee Springer. 2013

**Received: **7 August 2013

**Accepted: **30 August 2013

**Published: **8 September 2013

## Abstract

Here we provide a complete review on the use of dynamic light scattering (DLS) to study the size distribution and colloidal stability of magnetic nanoparticles (MNPs). The mathematical analysis involved in obtaining size information from the correlation function and the calculation of *Z*-average are introduced. Contributions from various variables, such as surface coating, size differences, and concentration of particles, are elaborated within the context of measurement data. Comparison with other sizing techniques, such as transmission electron microscopy and dark-field microscopy, revealed both the advantages and disadvantages of DLS in measuring the size of magnetic nanoparticles. The self-assembly process of MNP with anisotropic structure can also be monitored effectively by DLS.

### Keywords

Dynamic light scattering Magnetic nanoparticles Colloidal stability Surface functionalization Review## Review

### Introduction

Magnetic nanoparticles (MNPs) with a diameter between 1 to 100 nm have found uses in many applications [1, 2]. This nanoscale magnetic material has several advantages that provide many exciting opportunities or even a solution to various biomedically [3–5] and environmentally [6–8] related problems. Firstly, it is possible to synthesize a wide range of MNPs with well-defined structures and size which can be easily matched with the interest of targeted applications. Secondly, the MNP itself can be manipulated by an externally applied magnetic force. The capability to control the spatial evolution of MNPs within a confined space provides great benefits for the development of sensing and diagnostic system/techniques [9, 10]. Moreover MNPs, such as Fe^{0} and Fe_{3}O_{4}, that exhibit a strong catalytic function can be employed as an effective nanoagent to remove a number of persistent pollutants from water resources [11, 12]. In addition to all the aforementioned advantages, the recent development of various techniques and procedures for producing highly monodispersed and size-controllable MNPs [13, 14] has played a pivotal role in promoting the active explorations and research of MNPs.

In all of the applications involving the use of MNPs, the particle size remained as the most important parameter as many of the chemical and physical properties associated to MNPs are strongly dependent upon the nanoparticle diameter. In particular, one of the unique features of a MNP is its high-surface-to-volume ratio, and this property is inversely proportional to the diameter of the MNP. The smaller the MNP is, the larger its surface area and, hence, the more loading sites are available for applications such as drug delivery and heavy metal removal. Furthermore, nanoparticle size also determines the magnetophoretic forces (*F*_{mag}) experienced by a MNP since *F*_{mag} is directly proportional to the volume of the particles [15]. In this regard, having size information is crucial as at nanoregime, the MNP is extremely susceptible to Stoke’s drag [16] and thermal randomization energy [17]. The successful manipulation of MNP can only be achieved if the *F*_{mag} introduced is sufficient to overcome both thermal and viscous hindrances [18]. In addition, evidences on the (eco)toxicological impacts of nanomaterials have recently surfaced [19]. The contributing factors of nanotoxicity are still a subject of debate; however, it is very likely due to either (1) the characteristic small dimensional effects of nanomaterials that are not shared by their bulk counterparts with the same chemical composition [20] or (2) biophysicochemical interactions at the nano-bio interface dictated by colloidal forces [21]. For either reason, the MNP’s size is one of the determining factors.

The technique of dynamic light scattering (DLS) has been widely employed for sizing MNPs in liquid phase [22, 23]. However, the precision of the determined particle size is not completely understood due to a number of unevaluated effects, such as concentration of particle suspension, scattering angle, and shape anisotropy of nanoparticles [24]. In this review, the underlying working principle of DLS is first provided to familiarize the readers with the mathematical analysis involved for correct interpretation of DLS data. Later, the contribution from various factors, such as suspension concentration, particle shape, colloidal stability, and surface coating of MNPs, in dictating the sizing of MNPs by DLS is discussed in detail. It is the intention of this review to summarize some of the important considerations in using DLS as an analytical tool for the characterization of MNPs.

### Overview of sizing techniques for MNPs

^{10}to 10

^{15}particles/mL and the size analysis by measuring thousands or even tens of thousands of particles still give a relatively small sample pool to draw statistically conclusive remarks.

**Common analytical techniques and the associated range scale involved for nanoparticle sizing**

Techniques | Approximated working size range |
---|---|

Dynamic light scattering | 1 nm to approximately 5 μm |

Transmission electron microscopy | 0.5 nm to approximately 1 μm |

Atomic force microscopy | 1 nm to approximately 1 μm |

Dark-field microscopy | 5 to 200 nm |

Thermomagnetic measurement | 10 to approximately 50 nm |

Thermomagnetic measurement extracts the size distribution of an ensemble of superparamagnetic nanoparticles from zero-field cooling (ZFC) magnetic moment, *m*_{ZFC}(T), data based on the Néel model [27]. This method is an indirect measurement of particle size and relies on the underlying assumption of the mathematical model used to calculate the size distribution. In addition, another limitation of this analytical method includes the magnetic field applied for ZFC measurements which must be small compared to the anisotropy field of the MNPs [30], and it also neglects particle-particle dipolar interactions which increase the apparent blocking temperature [31]. This technique, however, could give a very reliable magnetic size of the nanoparticle analyzed.

Dark-field microscopy relies on direct visual inspection of the optical signal emitted from the MNP while it undergoes Brownian motion. After the trajectories of each MNP over time *t* are recorded, the two-dimensional mean-squared displacement *<r*^{
2
}*> =* 4*Dt* is used to calculate the diffusion coefficient *D* for each particle. Later on, the hydrodynamic diameters can be estimated via the Stokes-Einstein equation for the diffusion coefficients calculated for individual particles, averaging over multiple time steps [18]. Successful implementation of this technique depends on the ability to trace the particle optically by coating the MNP with a noble metal that exhibits surface Plasmon resonance within a visible wavelength. This extra synthesis step has significantly restricted the use of this technique as a standard route for sizing MNPs. The size of an MNP obtained through dark-field microscopy is normally larger than the TEM and DLS results [17]. It should be noted that dark-field microscopy can also be employed for direct visualization of a particle flocculation event [32]. As for AFM, besides the usual topographic analysis, magnetic imaging of a submicron-sized MNP grown on GaAs substrate has been performed with magnetic force microscopy equipment [33]. Despite all the recent breakthroughs, sample preparation and artifact observation are still the limiting aspect for the wider use of this technology for sizing MNPs [34].

The particle size and size distribution can also be measured with an acoustic spectrometer which utilizes the sound pulses transmitted through a particle suspension to extract the size-related information [29]. Based on the combined effect of absorption and scattering of acoustic energy, an acoustic sensor measures attenuation frequency spectra in the sample. This attenuation spectrum is used to calculate the particle size distribution. This technique has advantages over the light scattering method in studying samples with high polydispersity as the raw data for calculating particle size depend on only the third power of the particle size. This scenario makes contribution of the small (nano) and larger particles more even and the method potentially more sensitive to the nanoparticle content even in the very broad size distributions [35].

DLS, also known as photon correlation spectroscopy, is one of the most popular methods used to determine the size of MNPs. During the DLS measurement, the MNP suspension is exposed to a light beam (electromagnetic wave), and as the incident light impinges on the MNP, the direction and intensity of the light beam are both altered due to a process known as scattering [36]. Since the MNPs are in constant random motion due to their kinetic energy, the variation of the intensity with time, therefore, contains information on that random motion and can be used to measure the diffusion coefficient of the particles [37]. Depending on the shape of the MNP, for spherical particles, the hydrodynamic radius of the particle *R*_{H} can be calculated from its diffusion coefficient by the Stokes-Einstein equation *D*_{
f
}*= k*_{B}*T/* 6*πηR*_{H}, where *k*_{B} is the Boltzmann constant, *T* is the temperature of the suspension, and *η* is the viscosity of the surrounding media. Image analysis on the TEM micrographs gives the ‘true radius’ of the particles (though determined on a statistically small sample), and DLS provides the hydrodynamic radius on an ensemble average [38]. The hydrodynamic radius is the radius of a sphere that has the same diffusion coefficient within the same viscous environment of the particles being measured. It is directly related to the diffusive motion of the particles.

**Hydrodynamic diameter of different MNPs determined by DLS**

Type of MNPs | Surface coating | Hydrodynamic diameter by DLS (nm) | Reference |
---|---|---|---|

Fe | Carboxymethyl cellulose | 15-19 | [39] |

Guar gum | 350-700 | [40] | |

Poly(methacrylic acid)-poly(methyl methacrylate)-poly(styrenesulfonate) triblock copolymer | 100-600 | [41] | |

Poly(styrene sulfonate) | 30-90 | [22] | |

γ-Fe | Oleylamine or oleic acid | 5-20 | [42] |

Poly( | 55-614 | [43] | |

Poly(ethylene oxide)-block-poly(glutamic acid) | 42-68 | [44] | |

Poly(ethylene imine) | 20-75 | [45] | |

Poly(ϵ-caprolactone) | 193 ± 7 | [46] | |

Fe | Phospholipid-PEG | 14.7 ± 1.4 | [47] |

Polydimethylsiloxane | 41.2 ± 0.4 | [48] | |

Oleic acid-pluronic | 50-600 | [49] | |

Polyethylenimine (PEI) | 50-150 | ||

Polythylene glycol | 10-100 | [51] | |

Triethylene glycol | 16.5 ± 3.5 | [52] | |

Poly( | 15-60 | [53] | |

Pluronic F127 | 36 | [54] | |

Poly(sodium 4-styrene sulfonate) | ~200 | [55] | |

Poly(diallyldimethylammonium chloride) | 107.4 ± 53.7 | [56] | |

FePt | Poly(diallyldimethylammonium chloride) | 30-100 | [57] |

NiO | Cetyltrimethyl ammonium bromide | 10-80 | [58] |

Fetal bovine serum | 39.05 | [59] | |

Not specified | 750 ± 30 | [60] | |

CoO, Co | Poly(methyl methacrylate) | 59-85 | [61] |

CoFe | Hydroxamic and phosphonic acids | 6.5-458.7 | [62] |

### The underlying principle of DLS

The interaction of very small particles with light defined the most fundamental observations such as why is the sky blue. From a technological perspective, this interaction also formed the underlying working principle of DLS. It is the purpose of this section to describe the mathematical analysis involved to extract size-related information from light scattering experiments.

#### The correlation function

*θ*

_{dls}for a given time

*t*

_{ k }in time steps ∆

*t*. The time-dependent intensity

*I*(

*q*,

*t*) fluctuates around the average intensity

*I*(

*q*) due to the Brownian motion of the particles [38]:

*I(q)*] represents the time average of

*I(q)*. Here, it is assumed that

*t*

_{ k }, the total duration of the time step measurements, is sufficiently large such that

*I(q)*represents average of the MNP system. In a scattering experiment, normally,

*θ*

_{dls}(see Figure 1) is expressed as the magnitude of the scattering wave vector

*q*as

*n*is the refractive index of the solution and

*λ*is the wavelength in vacuum of the incident light. Figure 2a illustrates typical intensity fluctuation arising from a dispersion of large particles and a dispersion of small particles. As the small particles are more susceptible to random forces, the small particles cause the intensity to fluctuate more rapidly than the large ones.

*τ*=

*i*∆

*t*is the delay time, which represents the time delay between two signals

*I*(

*q*,

*i Δt*) and

*I*(

*q*,(

*i*+

*j*)

*Δt*). The function

*C*(

*q*,

*τ*) is obtained for a series of

*τ*and represents the correlation between the intensity at

*t*

_{1}(

*I*(

*q*,

*t*

_{1})) and the intensity after a time delay of

*τ*(

*I*(

*q*,

*t*

_{1}+

*τ*)). The last part of the equation shows how the autocorrelation function is calculated experimentally when the intensity is measured in discrete time steps [37]. As for nanoparticle dispersion, the autocorrelation function decays more rapidly for small particles than for the large particles as depicted in Figure 2b. The autocorrelation function has its highest value of [

*I*(

*q*,

*0*)]

^{2}at

*τ*= 0. As

*τ*becomes sufficiently large at long time scales, the fluctuations becomes uncorrelated and

*C*(

*q*,

*τ*) decreases to [

*I*(

*q*)]

^{2}. For non-periodic

*I*(

*q*,

*t*), a monotonic decay of

*C*(

*q*,

*τ*) is observed as

*τ*increases from zero to infinity and

*ξ*is an instrument constant approximately equal to unity and

*g*

^{(1)}(

*q*,

*τ*) is the normalized electric field correlation function [63]. Equation 4 is known as the Siegert relation and is valid except in the case of scattering volume with a very small number of scatterers or when the motion of the scatterers is limited. For monodisperse, spherical particles,

*g*

^{(1)}(

*τ*) is given by

*D*

_{ f }is obtained, the hydrodynamic diameter of a perfectly monodisperse dispersion composed of spherical particles can be inferred from the Stokes-Einstein equation. Practically, the correlation function observed is not a single exponential decay but can be expressed as

*G*(

*Γ*) is the distribution of decay rates

*Γ*. For a narrowly distributed decay rate, cumulant method can be used to analyze the correlation function. A properly normalized correlation function can be expressed as

*Γ*〉 is the average decay rate and can be defined as

*μ*

_{2}= 〈

*Γ*〉

^{2}− 〈

*Γ*〉

^{2}is the variance of the decay rate distribution. Then, the polydispersity index (PI) is defined as PI = μ

_{2}/〈

*Γ*〉

^{2}. The average hydrodynamic radius is obtained from the average decay rate 〈

*Γ*〉 using the relation

#### Z-average

*Z*-average. Since the

*Z*-average arises when DLS data are analyzed through the use of the cumulant technique [64], it is also known as the “cumulant mean.” Under Rayleigh scattering, the amount of light scattered by a single particle is proportional to the sixth power of its radius (volume squared). This scenario causes the averaged hydrodynamic radius determined by DLS to be also weighted by volume squared. Such an averaged property is called the

*Z*-average. For particle suspension with discrete size distribution, the

*Z*-average of some arbitrary property

*y*would be calculated as

*n*

_{ i }is the number of particles of type

*i*having a hydrodynamic radius of

*R*

_{H,i}and property

*y*. If we assume that this particle dispersion consists of exactly two sizes of particles 1 and 2, then Equation 10 yields

*R*

_{H,i}and

*y*

_{ i }are the volume and arbitrary property for particle 1 (

*i*= 1) and particle 2 (

*i*= 2). Suppose that two particles 1 combined to form one particle 2 and assume that we start with

*n*

_{0}total of particle 1, some of which combined to form

*n*

_{2}number of particle 2. With this assumption, we have

*n*

_{1}=

*n*

_{0}

*– n*

_{2}number of particle 1. Moreover, under this assumption

*R*

_{H,2}= 2

*R*

_{H,1}. Substitute these relations into Equation 11; then, the

*Z*-average of property

*y*becomes

*2n*

_{2}/

*n*

_{0}is the fraction of total particle 1 existing as particle 2. Solving this fraction, we obtained

*Z*-average should only be employed to provide the characteristic size of the particles if the suspension is monomodal (only one peak), spherical, and monodisperse. As shown in Figure 3, for a mixture of particles with obvious size difference (bimodal distribution), the calculated

*Z*-average carries irrelevant size information.

### DLS measurement of MNPs

*R*

_{H}of particles. This increase in

*R*

_{H}is a convenient measure of the thickness of the adsorbed macromolecules [65]. This section is dedicated to the scrutiny of these two phenomena and also suspension concentration effect in dictating the DLS measurement of MNPs. All DLS measurements were performed with a Malvern Instrument Zetasizer Nano Series (Malvern Instruments, Westborough, MA, USA) equipped with a He-Ne laser (

*λ*= 633 nm, max 5 mW) and operated at a scattering angle of 173°. In all measurements, 1 mL of particle suspensions was employed and placed in a 10 mm × 10 mm quartz cuvette. The iron oxide MNP used in this study was synthesized by a high-temperature decomposition method [17].

#### Size dependency of MNP in DLS measurement

_{3}O

_{4}MNPs produced by high-temperature decomposition method which are surface modified with oleic acid/oleylamine in toluene (Figure 5). The TEM image analyses performed on micrographs shown in Figure 5 (from top to bottom) indicate that the diameter of each particle species is 7.2 ± 0.9 nm, 14.5 ± 1.8 nm, and 20.1 ± 4.3 nm, respectively. The diameters of these particles obtained from TEM and DLS are tabulated in Table 3. It is very likely that the main differences between the measured diameters from these two techniques are due to the presence of an adsorbing layer, which is composed of oleic acid (OA) and oleylamine (OY), on the surface of the particle. Small molecular size organic compounds, such as OA and OY, are electron transparent, and therefore, they did not show up in the TEM micrograph (Figure 5). Given that the chain lengths of OA and OY are approximately 2 nm [66, 67], the best match of DLS and TEM, in terms of measured diameter, can be observed from middle-sized Fe

_{3}O

_{4}MNPs.

**Diameter of Fe**
_{
3
}
**O**
_{
4
}
**MNP determined by TEM and DLS (**
Z
**-average)**

Particle | TEM (nm) | DLS (nm) | Difference (nm) |
---|---|---|---|

Fe | 7.2 | 16.9 | 9.7 |

14.5 | 21.1 | 6.6 | |

20.1 | 43.1 | 23.0 |

For small-sized MNPs, the radius of curvature effect is the main contributing factor for the large difference observed on the averaged diameter from DLS and TEM. This observation has at least suggested that for any inference of layer thickness from DLS measurement, the particles with a radius much larger than the layer thickness should be employed. In this measurement, the fractional error in the layer thickness can be much larger than the fractional error in the radius with the measurement standard deviation of only 0.9 nm for TEM but at a relatively high value of 5.2 nm for DLS. At a very large MNP size of around 20 nm (bottom image of Figure 5), the *Z*-average hydrodynamic diameter is 23 nm larger than the TEM size. Moreover, the standard deviation of the DLS measurement of this particle also increased significantly to 14.9 nm compared to 5.2 and 5.5 nm for small- and middle-sized MNPs, respectively. This trend of increment observed in standard deviation is consistent with TEM measurement. Both the shape irregularity and polydispersity, which are the intrinsic properties that can be found in a MNP with a diameter of 20 nm or above, contribute to this observation. For a particle larger than 100 nm, other factors such as electroviscous and surface roughness effects should be taken into consideration for the interpretation of DLS results [68].

#### MNP concentration effects

In DLS, the range of sample concentration for optimal measurements is highly dependent on the sample materials and their size. If the sample is too dilute, there may be not enough scattering events to make a proper measurement. On the other hand, if the sample is too concentrated, then multiple scattering can occur. Moreover, at high concentration, the particle might not be freely mobile with its spatial displacement driven solely by Brownian motion but with the strong influences of particle interactions. This scenario is especially true for the case of MNPs with interparticle magnetic dipole-dipole interactions.

^{20}particles (pts)/m

^{3}and 6.3 × 10

^{18}pts/m

^{3}by assuming that the composition material is magnetite with a density of 5.3 g/cm

^{3}. This concentration translated to a collision frequency of 85,608 s

^{−1}and 1,056 s

^{−1}. So, at the same mass concentration, it is more likely for small particles to experience the non-self-diffusion motions.

For both species of particles, the upward trends of hydrodynamic diameter, which associates to the decrement of diffusion coefficient, reflect the presence of a strong interaction between the particles as MNP concentration increases. Furthermore, since the aggregation rate has a second-order dependency on particle concentration [69], the sample with high MNP concentration has higher tendency to aggregate, leading to the formation of large particle clusters. Therefore, the initial efforts for MNP characterization by using DLS should focus on the determination of the optimal working concentration.

#### Colloidal stability of MNPs

As shown in Figure 7, both polyethylene glycol (PEG) 6k and PEG 10k are capable of tentatively stabilizing the MNPs in PBS for the first 24 and 48 h. Aggregation is observed with the detection of particle clusters with a diameter of more than 500 nm. After this period of relative stability, aggregation accelerated to produce micron-sized aggregates by day 3. Actually, the continuous monitoring of MNP size by DLS after this point is less meaningful as the dominating motion is the sedimentation of large aggregates [71]. For PEG 6k and PEG 10k that have a rather low degree of polymerization, the loss of stability over a day or two could have been due to slow PEG desorption that would not be expected of larger polymers. Nevertheless, PEG 100k-coated MNPs were not as well stabilized as the PEG 6k- or PEG 10k-coated ones, despite the higher degree of polymerization that one might expect to produce greater adsorbed layer thicknesses and therefore longer-ranged steric forces. In addition to the degree of polymerization, as discussed by Golas and coworkers [72], the colloidal stability of polymeric stabilized MNPs is also dependent on other structural differences of the polymer employed, such as the chain architecture and the identity of the charged functional unit. In their work, DLS was used to confirm the nanoparticle suspensions that displayed the least sedimentation which was indeed stable against aggregation.

_{3}O

_{4}) MNP, and 40-nm hematite (α-Fe

_{2}O

_{3}) MNP [73]. Phenrat and coworkers have demonstrated that DLS can be an effective tool to probe the aggregation behavior of MNPs (Figure 8a). The time evolution of the hydrodynamic radius of these particles from monomodal to bimodal distribution revealed the aggregation kinetic of the particles. Together with the in situ optical microscopy observation, the mechanism of aggregation is proposed as the transitions from rapidly moving individual MNPs to the formation of submicron clusters that lead to chain formation and gelation (Figure 8b). By the combination of small-angle neutron scattering and cryo-TEM measurements, DLS can also be used as an effective tool to understand the fractal structure of this aggregate [78].

### DLS measurement of non-spherical MNPs

*Γ*vs

*q*

^{ 2 }, the value of rotational diffusion

*D*

_{R}can be obtained directly by an extrapolation of

*q*to zero and the value of translational diffusion

*D*

_{T}from the slope of the curve [79]. For rigid non-interacting rods at infinite dilution with an aspect ratio (

*L*/

*d*) greater than 5,

*D*

_{R}and

*D*

_{T}can be expressed using Broersma’s relations [82, 83] or the stick hydrodynamic theory [84]. By performing angle-dependent DLS analysis on rod-like β-FeOOH nanorods as shown in Figure 9a, we found that the decay rate is linearly proportional to

*q*

^{ 2 }and passes through the origin (Figure 9b), suggesting that the nanorod motion is dominated by translational diffusion [85]. From Figure 9b, the slope of the graph yields the translational diffusion coefficient,

*D*

_{T}= 7 × 10

^{−12}m

^{2}/s. This value of

*D*

_{T}corresponds to an equivalent spherical hydrodynamic diameter of 62.33 nm, suggesting that the DLS results with a single fixed angle of 173° overestimated the true diameter [86]. By taking the length and width of the nanorods as 119.7 and 17.5 nm (approximated from TEM images in Figure 9a), the

*D*

_{T}calculated by the stick hydrodynamic theory and Broersma’s relationship is 7.09 × 10

^{−12}m

^{2}/s and 6.84 × 10

^{−12}m

^{2}/s, respectively, consistent with the DLS results.

## Conclusion

Dynamic light scattering is employed to monitor the hydrodynamic size and colloidal stability of the magnetic nanoparticles with either spherical or anisotropic structures. This analytical method cannot be employed solely to give feedbacks on the structural information; however, by combining with other electron microscopy techniques, DLS provides statistical representative data about the hydrodynamic size of nanomaterials. In situ, real-time monitoring of MNP suspension by DLS provides useful information regarding the kinetics of the aggregation process and, at the same time, gives quantitative measurement on the size of the particle clusters formed. In addition, DLS can be a powerful technique to probe the layer thickness of the macromolecules adsorbed onto the MNP. However, the interpretation of DLS data involves the interplay of a few parameters, such as the size, concentration, shape, polydispersity, and surface properties of the MNPs involved; hence, careful analysis is needed to extract the right information.

## Declarations

### Acknowledgements

This material is based on the work supported by Research University (RU) (grant no. 1001/PJKIMIA/811219) from Universiti Sains Malaysia (USM), Exploratory Research Grants Scheme (ERGS) (grant no. 203/PJKIMIA/6730013) from the Ministry of Higher Education of Malaysia, and eScience Fund (grant no. 205/PJKIMIA/6013412) from MOSTI Malaysia. JKL and SWL are affiliated to the Membrane Science and Technology Cluster of USM.

## Authors’ Affiliations

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