# Accurate Size and Size-Distribution Determination of Polystyrene Latex Nanoparticles in Aqueous Medium Using Dynamic Light Scattering and Asymmetrical Flow Field Flow Fractionation with Multi-Angle Light Scattering

^{*}

## Abstract

**:**

## 1. Introduction

_{r}) of nanoparticles can be predicted by the Giddings equation:

_{0}is the volumetric flow rate through the channel, and V

_{C}is the cross flow rate. Thus, when the cross flow and channel flow rates are constant in the AFFFF system, the separation of nanoparticles by size can achieved and the retention time is proportional to the size of the separated nanoparticles. A drawback to AFFFF separation is band broadening, which results in poor size separation. Band broadening is caused by the different displacement velocities of particles in the flow profile of the AFFFF system. The broadening of particle size bands should therefore be kept to a minimum. One solution to the broadening problem is confinement of particle distribution to a layer whose streamlines have a small velocity range [14]. Such confinement can be accomplished by employing appropriate sample focusing techniques after injection. However, complete elimination of band broadening by controlling the experimental conditions is impossible. Therefore, the effect of band broadening on the apparent size values determined by AFFFF-multi-angle light scattering (MALS) should be estimated by using particles with a known narrow size distribution.

Sample name | Official diameter ^{a)} | CV value ^{b)} |
---|---|---|

(nm) | % | |

^{a)} The official values of official diameter are determined by DMA or TEM; ^{b)} CV values are calculated from the standard deviation of the size distribution by DMA, and the observed size distributions are divided by size. | ||

STADEX SC-0070-D | 70 | 7.30 |

STADEX SC-0080-D | 80 | 4.80 |

STADEX SC-0100-D | 100 | 2.47 |

STADEX SC-0110-D | 107 | 3.10 |

STADEX SC-0140-D | 144 | 1.42 |

STADEX SC-016-S | 152 | 2.46 |

F0223 | 140 | - |

T2112 | 147 | - |

T0622 | 128 | - |

T0021 | 90 | - |

T0118 | 91 | - |

T0408 | 88 | - |

T0625 | 103 | - |

## 2. Experimental Section

#### 2.1. Materials

#### 2.2. DLS Measurements

_{0}is the wavelength of the laser source in vacuum, and n

_{0}is the refractive index of the solvent medium. thus obtained was analyzed by the first cumulant method described in ISO 13321 to determine the average decay rate Γ [19]. The apparent diffusion coefficient obtained from DLS was used in the Stokes–Einstein relation of the following form to determine the hydrodynamic particle size of the PS-latex secondary nanoparticles:

_{B}is the Boltzmann constant, T is the absolute temperature, η is the viscosity of the solvent (0.8902 cP) [20], and d is the calculated hydrodynamic diameter of the nanoparticles.

#### 2.3. AFFFF-MALS Measurement

_{s}) to be measured, the intensity distribution function is given by

## 3. Results and Discussion

#### 3.1. DLS

#### 3.1.1. Calculation Method for Reliable Size Determination by DLS

_{l}of the particles can be calculated from the diffusion coefficient (D) of particles. In principle, the particle concentration in suspension and the optical path length must be sufficiently low to prevent multiple scattering. For a higher concentration suspension, a scattered photon has non-negligible probability of being re-scattered when passing through the suspension. The autocorrelation function for such multiple scattering decays faster than the one for single scattering, resulting in underestimation of particle size. However, if the particle concentration is too low, the scattering is unstable. DLS measurements can also be easily affected by traces of dust. A solution to this problem is to extrapolate the apparent diffusion coefficients observed at a large number of concentrations to infinite dilution. Doing so yields more reliable results than those obtained for measurements at only one concentration. In this study, the measured apparent intensity-average hydrodynamic diameter was therefore extrapolated to infinite dilution and to zero angle in order to determine the true hydrodynamic size in an aqueous medium. We refer to the double extrapolation plot as a Zimm plot in this paper.

#### 3.1.2. Size Determination of PS-Latex by DLS

_{l,app}calculated from the first cumulant of PS-latex against the PS-latex concentration and observed scattering angles is presented in Figure 1b. For the aqueous suspension of PS-latex, we performed 40 independent DLS measurements in the concentration range from 0.009 to 0.044 mg/mL and light scattering was observed at 8 scattering angles from 45° to 150°. In all the measurements, the observed raw photon correlation function showed linear decay similarly to the result in Figure 1a, but the slopes were different for corresponding angles and concentrations of PS-latex suspensions. There was almost a linear dependence of d

_{l,app}on concentration for each investigated concentration andscattering angle.

**Figure 1.**

**a**) Example of observed homodyne photon correlation function for PS-latex (T0625) analyzed by dynamic light scattering ( DLS) (filled circle plots). The concentration of the aqueous PS-latex suspension was 0.009 mg/mL and light scattering was observed at a scattering angle of 90 ° . The red line is the linear least-squares fit of the experimental results. (

**b**) Example of the constructed Zimm plots for PS-latex (T0625) analyzed by DLS at a concentration range from 0.009 to 0.044 mg/mL. Light scattering was observed at 8 different scattering angle s from 45° to 150° . The true d

_{l}was calculated to be 118.2 nm.

_{l}is the true diameter, k

_{c}and k

_{Q}are constants, and c is the concentration of PS-latex nanoparticles in the suspension. The d

_{l}, k

_{c}, and k

_{Q}values for a specific PS-latex concentration and observed scattering angle in Equation 8 are determined by extrapolating the corresponding PS-latex concentration and observed scattering angle to zero in Figure 1b. Cichocki et al. [21] described the relationship between diffusion coefficients and interactions between nanoparticles by using the “effective radius,” which represents not only hydrodynamic interaction but also electrostatic repulsion and attraction at longer distances. Figure 1b and Table S-1 (see Supplementary Information) clearly show that the dynamics of PS-latex in aqueous suspension are dominated by long-range electrostatic interactions between PS-latex nanoparticles since d

_{l,app}shows clear dependence on angle and concentration. The particle scattering factor determined by static light scattering and the existence of electrostatic interactions between particles suggest a large angular distribution, as shown in Figure 1b and Table S-2 (see Supplementary Information). The effect of polydispersity of PS-latex nanoparticles and multiple scattering is not responsible for these dependences because (i) higher polydispersity makes the observed particle sizes larger at lower angles, and (ii) the most concentrated sample with the largest particle size did not exhibit multiple scattering effects at various intensities of the incident beam. Therefore, the double extrapolation of concentration and angular dependences in the DLS results can be used to determine d

_{l}in Equation 8. For example, in the Zimm plot analysis in Figure 2b, the d

_{l}value is estimated to be 118.2 nm. We carried out four independent measurements for Zimm plot analysis and found the average d

_{l}value was 118.5 nm.

**Figure 2.**(

**a**) Example of light scattering intensity fractogram (solid curves) and diameter of the PS-latex nanoparticles measured by AFFFF-MALS. The open circles denote the directly observed diameter determined by MALS. The filled circles denote the size of the PS-latex nanoparticles with narrow size distribution. The separation conditions are as follows: channel flow rate, 1.00 mL/min; cross flow rate, 0.25 mL/min. (

**b**) Example of deconvolution of the fractogram in Figure 3a (black curves). The color curves illustrate the deconvoluted fractograms according to Equation 9.

**Figure 3.**Example of AFFFF-MALS results for PS-latex (SC-0070-D). Channel flow rate, 1.00 mL/min; cross flow rate, 0.22 mL/min. (

**a**) Apparent l ight scattering intensity ( black solid curve) fractogram and fitting curve according to Equation 12 (red solid curve). (

**b**) Apparent diameter of PS-latex (SC-0070-D) nanoparticles measured by MALS at corresponding elution times (filled black circles) and theoretical relationship between diameter and elution time (red line).

#### 3.1.3. Concept of Identifying and Analyzing Sources of Uncertainty in DLS

_{l}) of the PS-latex nanoparticles in an aqueous suspension were determined as shown in the Supplementary Information. The considered sources of uncertainty were the Boltzmann constant ( ) [22], the temperature ( ), the solvent viscosity ( ) [20,23], the delay rate ( ), the solvent refractive index ( ) [24,25], the wavelength ( ), the observed scattering angle ( ), the repeatability of DLS measurements ( ), and the extrapolation to infinite dilution and to zero angle in the Zimm plot ( ).

#### 3.2. AFFFF-MALS

#### 3.2.1. Calculation Method for Determining Size and Size Distribution by AFFFF-MALS

#### 3.2.2. Determination of Size and Size Distribution by AFFFF-MALS

_{b}), and by the standard deviation of the size distribution of PS-latex nanoparticles (σ

_{l}).

**Figure 4.**Example of observed relationship between separated size and elution time, as expressed by Equation 11.

_{l}), the AFFFF-MALS results for PS-latex (SC-0070-D) were theoretically fitted as shown by the red curve and line in Figures 3a and 3b, respectively. The PS-latex (SC-0070-D) has already been well characterized by DMA [18,26]. The standard deviation of the size distribution of the number-average diameter determined by DMA was 5.1 nm, and therefore the standard deviation of the size distribution of the calculated intensity-average diameter assuming a Gaussian size distribution was 4.9 nm. From Equation 10, the appropriate σ

_{b}value for the experimental data was calculated to be 1.17 min. To examine the correctness of this method for estimating σ

_{l}values, we calculated the CV values for five independent PS-latex suspensions in Table 2, respectively. The official CV values are calculated from the standard deviation of the size distribution determined by DMA, and the observed size distributions are grouped by size. The calculated CV values for these PS-latex suspensions were estimated from the standard deviation of the size distribution by AFFFF-MALS. The calculated CV values agreed well with the respective experimental values, indicating that σ

_{b}calculated through this procedure was appropriate.

Sample name | Official CV value | Calculated CV value |
---|---|---|

% | % | |

STADEX SC-0080-D | 4.80 | 4.60 |

STADEX SC-0100-D | 2.47 | 2.20 |

STADEX SC-0110-D | 3.10 | 3.30 |

STADEX SC-0140-D | 1.42 | 1.30 |

STADEX SC-016-S | 2.46 | 2.20 |

_{l}) to have a fixed σ

_{b}value of 1.17 min, the AFFFF-MALS results for PS-latex (T0625) agreed well with theory as shown by the red curve (Figure 5a) and the red line (Figure 5b) in the figures. In Figure 5, the calculated d

_{l}is 117.2 and σ

_{l}is 11.5 nm from Equations 9 and 12. We carried out 12 independent measurements (3 measurements performed under 4 different cross flow rate conditions: 0.18, 0.20, 0.22, and 0.25 mL/min) and the average d

_{l}and σ

_{l}were found to be 117.6 and 10.1 nm, respectively.

**Figure 5.**AFFFF-MALS results for

**PS-latex**(T0625).

**Channel flow rate, 1.00 mL/min; cross flow rate,**

**0.22**

**mL/min.**The calculated d

_{l}is 117.2 and is 11.5 nm from Equation 15. (a) Apparent l

**ight scattering intensity**

**(**

**black**

**solid curve) fractogram**

**and fitting curve expressed by Equation 12 (red solid curve). (**b

**)**

**Apparent**

**diameter of PS-latex**(T0625)

**nanoparticles measured by MALS**

**at corresponding elution times (filled black circles) and theoretical relationship between diameter**

**and elution time (red line)**

**.**

#### 3.2.3. Concept of Identifying and Analyzing Sources of Uncertainty in AFFFF-MALS

_{l}and for PS-latex (T0625) are 3.48 and 0.38 nm, respectively.

#### 3.3. Comparison of DLS and AFFFF-MALS Results

**Figure 6.**Examples of size distribution for PS-latex nanoparticle suspensions determined by DLS using cumulant analytical method. (

**a**) STADEX SC-0110-D and (

**b**) T0625.

**Figure 7.**Examples of size distribution for PS-latex nanoparticle dispersions determined by AFFFF-MALS . (

**a**)STADEX SC-0110-D and (

**b**) T0625.

## 4. Conclusions

## Supplementary Materials

Supplementary File 1## References

- Freund, H.; Shaikhutdinov, S.K.; Doyle, A.M. Surface bonded precursor determines particle size effects for alkene hydrogenation on palladium. Angew. Chem. Int. Ed.
**2005**, 44, 629–631. [Google Scholar] [CrossRef] - Shinoda, K.; Jeyadevan, B.; Tohji, K.; Liu, X.; Perales, O.; Czajka, R.; Barnakov, Y.; Dmitruk, I.; Milczarek, G.; Kasuya, A.; et al. Size- and shape-controls and electronic functions of nanometer-scale semiconductors and oxides. Colloids Surf. A
**2002**, 202, 291–296. [Google Scholar] [CrossRef] - Chan, C.K.; Yue, P.L.; Lee, C.Y.; Yeung, K.L.; Maira, A.J. Size effects in gas-phase photo-oxidation of trichloroethylene using nanometer-sized TiO
_{2}catalysts. J. Catal.**2000**, 192, 185–196. [Google Scholar] [CrossRef] - Talapatra, G.B.; Pal, P.; Sarkar, J. Self-assembly of silver nano-particles on stearic acid Langmuir–Blodgett film: Evidence of fractal growth. Chem. Phys. Lett.
**2005**, 401, 400–404. [Google Scholar] [CrossRef] - Wieckowski, A.; Oldfield, E.; Chung, J.H.; Kobayashi, T.; Babu, P.K.; Watanabe, M.; Uchida, H.; Inukai, J.; Yano, H. Particle-size effect of nanoscale platinum catalysts in oxygen reduction reaction: An electrochemical and
^{195}Pt EC-NMR study. Phys. Chem. Chem. Phys.**2006**, 8, 4932–4939. [Google Scholar] [PubMed] - Grassian, V.H.; Jayaweera, P.M.; Baltrusaitis, J. Sulfur dioxide adsorption on TiO
_{2}nanoparticles: Influence of particle size, co-adsorbates, sample pretreatment, and light on surface speciation and surface coverage. J. Phys. Chem. C**2011**, 115, 492–500. [Google Scholar] [CrossRef] - Nel, A.E.; Xia, T.; Li, N. The role of oxidative stress in ambient particulate matter- induced lung diseases and its implications in the toxicity of engineered nanoparticles. Free Radic. Biol. Med.
**2008**, 44, 1689–1699. [Google Scholar] [CrossRef] [PubMed] - Lyng, F.M.; Byrne, H.J.; Chamber, G.; Cottineau, B.; Casey, A.; Herzog, E.; Davoren, M. In vitro toxicity evaluation of single walled carbon nanotubes on human A549 lung cells. Toxicol. In Vitro
**2007**, 21, 438–448. [Google Scholar] [CrossRef] [PubMed] - Lai, D.; Kreyling, W.; Karn, B.; Carter, J.; Ausman, K.; Fitzpartrick, J.; Castranova, V.; Donaldson, K.; Maynard, A.; Oberdörster, G.; et al. Principles for characterizing the potential human health effects from exposure to nanomaterials: Elements of a screening strategy. Part. Fibre Toxicol.
**2005**, 2, 1–35. [Google Scholar] [CrossRef] [PubMed][Green Version] - Holian, A., Jr.; Hamilton, R.F., Jr.; Buford, M.C. A comparison of dispersing media for various engineered carbon nanoparticles. Part. Fibre Toxicol.
**2007**, 4, 1–9. [Google Scholar] [CrossRef] [PubMed] - Commission Recommendation on the definition of nanomaterial. European Commission Website. 2011. Available online: http://ec.europa.eu/environment/chemicals/nanotech/pdf/commission_recommendation.pdf (accessed on 26 October 2011).
- Pecora, R.; Berne, B.J. Dynamic Light Scattering: With Applications to Chemistry,Biology,and Physics; 2000; Dover Publications: Mineola, NY, USA. [Google Scholar]
- Kinugasa, S.; Nakamura, A.; Takahashi, K.; Iwahashi, H.; Yoshida, Y.; Endoh, S.; Horie, M.; Fujita, K.; Suzuki, M.; Kato, H. Reliable size determination of nanoparticles using dynamic light scattering method for in vitro toxicology assessment. Toxicol. In Vitro
**2009**, 23, 927–934. [Google Scholar] [CrossRef] [PubMed] - Caldwell, J.C.; Schimpf, K. Caldwell,J.C. Giddings Field-Flow Fractionation Handbook; 2000; John Wiley : Hoboken, NJ, USA. [Google Scholar]
- Burchard, W.; Schmidt, M.; Bantle, S. Simultaneous static and dynamic light scattering. Macromolecules
**1982**, 15, 1604–1609. [Google Scholar] [CrossRef] - Schätzel, K.; Burchard, W.; Wenzel, M. Dynamic light scattering from semidilute cellulose-tri-carbanilate solutions. Polymer
**1986**, 27, 195–201. [Google Scholar] [CrossRef] - Kinugasa, S.; Matsuyama, S.; Saito, T.; Kato, H.; Takahashi, K. Precise measurement of the size of nanoparticles by dynamic light scattering with uncertainty analysis. Part. Part. Syst. Charact.
**2008**, 25, 31–38. [Google Scholar] [CrossRef] - Hagwood, R.C.; Mulholland, G.W.; Ehara, K. Determination of arbitrary moments of aerosol size distributions from measurements with a differential mobility analyzer. Aerosol Sci. Technol.
**2000**, 32, 434–452. [Google Scholar] [CrossRef] - Particle size analysis—Photon correlation spectroscopy. ISO 13321. International Organization for Standardization, Geneva, Switzerland, 1996.
- Sakano, T.K.; Bunger, W.B.; Riddick, J.A. Organic Solvents: Physical Properties and methods of Purification1986, 4th ed; John Wiley : New York, NY, USA. [Google Scholar]
- Felderhof, B.U.; Cichocki, B. Self-diffusion of Brownian particles with hydrodynamic interaction and square step or well potential. J. Chem. Phys.
**1991**, 94, 563–568. [Google Scholar] [CrossRef] - Glossary of terms in quantities and units in Clinical Chemistry PAC. Pure Appl. Chem.
**1996**, 68, 957–1000. [CrossRef] - Wakeham, A.; Sokolov, M.; Kestin, J. Viscosity of liquid water in the range −8 °C to 150 °C. J. Phys. Chem. Ref. Data
**1978**, 7, 941–948. [Google Scholar] [CrossRef] - Radwan, M.A.; O’Donohue, S.J.; Huglin, M.B. Refractometric and light scattering parameters at 633 nm for polystyrene solutions. Eur. Polym. J.
**1989**, 25, 543–547. [Google Scholar] [CrossRef] - Finsy, R.; Greef, C.; Moreels, E. Laser light refractometer. Appl. Opt.
**1984**, 23, 3010–3013. [Google Scholar] [CrossRef] [PubMed] - Ehara, K.; Takahata, K. Accurate particle size measurements for development of particle size standards in the range of 30 to 100 nm. In. In Proceedings of the 7th International Aerosol Conference, St. Paul, MI, USA, 10–15 September 2006, Mt. Laurel, NJ, USA, 10–15 September 2006; American Association for Aerosol Reseach, 2006; pp. 395–396. [Google Scholar]
- Kinugasa, S.; Saito, T.; Takahashi, K.; Kato, H. Characterization of nanoparticles in an aqueous solution with bound water molecules using pulsed field gradient nuclear magnetic resonance spectroscopy. Chem. Lett.
**2008**, 37, 1128–1129. [Google Scholar] [CrossRef] - Vass, S.; Grimm, H.; Bányai, I.; Meier G., *REPLACE*; Gilányi, T. Slow water diffusion in micellar solutions. J. Phys. Chem. B
**2005**, 109, 11870–11874. [Google Scholar] [PubMed] - Kullcke, W.; Roessner, D.; Thielking, H. On-line coupling of flow field-flow fractionation and multiangle laser light scattering for the characterization of polystyrene particles. Anal. Chem.
**1995**, 67, 3229–3233. [Google Scholar] [CrossRef] - Giddings, J.C.; Moon, M.H.; Rao, S.P.; Lee, S. Determination of mean diameter and PSD of acrylate latex using flow FFF, PCS, EM. Anal. Chem.
**1996**, 68, 1545–1549. [Google Scholar] [CrossRef] [PubMed] - Maskos, M.; Schmidt, M.; Jungmann, N. Characterization of polyorganosiloxane nanoparticles in aqueous dispersion by asymmetrical flow field-flow fractionation. Macromolecules
**2001**, 34, 8347–8353. [Google Scholar] [CrossRef] - Lee, D.W.; Kim, W.S.; Park, Y.H. Size analysis of industrial carbon blacks by field-flow fractionation. Anal. Bioanal. Chem.
**2003**, 375, 489–495. [Google Scholar] [PubMed]

© 2012 by the authors. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license ( http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Kato, H.; Nakamura, A.; Takahashi, K.; Kinugasa, S. Accurate Size and Size-Distribution Determination of Polystyrene Latex Nanoparticles in Aqueous Medium Using Dynamic Light Scattering and Asymmetrical Flow Field Flow Fractionation with Multi-Angle Light Scattering. *Nanomaterials* **2012**, *2*, 15-30.
https://doi.org/10.3390/nano2010015

**AMA Style**

Kato H, Nakamura A, Takahashi K, Kinugasa S. Accurate Size and Size-Distribution Determination of Polystyrene Latex Nanoparticles in Aqueous Medium Using Dynamic Light Scattering and Asymmetrical Flow Field Flow Fractionation with Multi-Angle Light Scattering. *Nanomaterials*. 2012; 2(1):15-30.
https://doi.org/10.3390/nano2010015

**Chicago/Turabian Style**

Kato, Haruhisa, Ayako Nakamura, Kayori Takahashi, and Shinichi Kinugasa. 2012. "Accurate Size and Size-Distribution Determination of Polystyrene Latex Nanoparticles in Aqueous Medium Using Dynamic Light Scattering and Asymmetrical Flow Field Flow Fractionation with Multi-Angle Light Scattering" *Nanomaterials* 2, no. 1: 15-30.
https://doi.org/10.3390/nano2010015