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Accurate determination of the intensity-average diameter of polystyrene latex (PS-latex) by dynamic light scattering (DLS) was carried out through extrapolation of both the concentration of PS-latex and the observed scattering angle. Intensity-average diameter and size distribution were reliably determined by asymmetric flow field flow fractionation (AFFFF) using multi-angle light scattering (MALS) with consideration of band broadening in AFFFF separation. The intensity-average diameter determined by DLS and AFFFF-MALS agreed well within the estimated uncertainties, although the size distribution of PS-latex determined by DLS was less reliable in comparison with that determined by AFFFF-MALS.

Recently, there has been an unprecedented increase in the number of studies related to nanomaterials [

The adverse effects of nanomaterials on human health are a serious issue that has also attracted much attention. Many international organizations and researchers have therefore carried out toxicity assessments of various nanoparticles, such as metals, metal oxides, fullerenes, and carbon nanotubes [

Dynamic light scattering (DLS) is widely used as an effective technique for determining the average secondary particle size of Brownian nanoparticles in colloidal suspensions [

Asymmetric flow field flow fractionation (AFFFF) is an elution technique whereby nanoparticles and macromolecules are separated by flow control in an aqueous medium [_{r}

where _{0}_{C}

The purpose of this study is to establish a robust protocol for determining the size and size distribution of nanoparticles in a liquid phase by DLS and AFFFF. First, the intensity-average size of polystyrene latex (PS-latex) nanoparticles in an aqueous suspension was accurately determined by DLS using extrapolation of both the PS-latex concentration and the observed scattering angle [

Characteristics of PS-latex nano particles used in this study.

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 | - |

Surfactant-free aqueous suspensions of approximately 10 wt % PS-latex nanoparticles were used (T0625, JSR Co., Tokyo, Japan). The suspension was diluted with ultrapure water from a Milli-Q system (Nihon Millipore K.K., Tokyo, Japan) using 0.1 μm filters. The characteristics of the suspension are summarized in

The dynamic light scattering apparatus (DLS7000, Otsuka Electronics Co., Ltd., Kyoto, Japan) used in this study has goniometer equipped with a 35 mW He-Ne laser of 632.8 nm wavelength. A multiple tau digital correlation scheme was used with a minimum sampling time of 0.1 μs. The measurements were performed at a scattering angle of 90°. A quartz sample cell was set in a silicon oil bath such that the refractive indices of the oil and the cell were nearly equal. Light scattering was measured at a regulated temperature of 25.0 ± 0.1 °C. Values reported in this paper are expressed as the mean of three replicates.

Assuming a dilute suspension of monodisperse particles (

Here,

where the modulus of the scattering vector is given by

Here, _{0}_{0}

Here, _{B}

Size determination by AFFFF-MALS was carried out on a system (AF2000 FFF, Postnova, Germany) equipped with a cellulose membrane (Z-MEM-AQU-427N) with a molecular weight cutoff of 10,000 Da and a channel thickness of 350 μm. The main carrier flow and the focusing flow were provided by two double pumps (PN1122, Postnova, Germany). The carrier water was degassed on-line by a vacuum degasser (PN7505, Postnova, Germany). The constant cross flow rate was changed from 0.18 mL/min to 0.25 mL/min, and the channel flow was maintained at a constant 1.0 mL/min. To determine the size of the nanoparticles in each fraction separated by AFFFF, a MALS detector (Dawn EOS, Wyatt Technology Co., USA) was used. Light scattering was detected at 690 nm. The MALS detectors were calibrated using pure toluene, and the detectors at different angles were normalized with respect to a 90° detector measuring bovine serum albumin monomer separated by AFFFF. After AFFFF separation, the nanoparticle sizes in the fractions were determined by the MALS detectors over 11 scattering angular ranges from 34.8° to 152.5°. The intensity distribution function is given by

Assuming spherical particles (the diameter is _{s}

Since the experimental results agree well with calculation results from Equation 7, the assumption of spherical PS-latex nanoparticles is valid. The size of particles was calculated by the ASTRA software particle module analytical method.

Ultrapure water (18.2 MΩ cm electrical resistance, and

According to the Stokes–Einstein relation (Equation 5), the intensity-average hydrodynamic diameter _{l}

A typical example of plots of apparent diameter _{l,app}_{l,app}

_{l}

The observed behavior in

where _{l}_{c}_{Q}_{l}_{c}_{Q}_{l,app}_{l}_{l}_{l}

(

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. (

To estimate the sources of uncertainty, we use the GUM approach since the international guide for the estimation of the uncertainty was published by the standardization bodies. The individual sources of uncertainty in the intensity-average diameter (_{l}

The results of the uncertainty analysis are summarized in Table S-3 (see

To perform deconvolution of the fractogram, the obtained fractogram in

where

In this study, we employed a Gaussian function since the obtained AFFFF-MALS results are in good agreement with the function. In Equation 9,

This result indicates that, to accurately determine the nanoparticle size distribution, the plots of diameter directly observed by MALS (open circles in Figure 2a) cannot be used to form an appropriate calibration curve unless one considers the band broadening effect. In this study, therefore, we first determined

This linear relationship between separated size and elution time in

The standard deviation factor in Equation 10 is caused by band broadening in AFFFF separation (_{b}_{l}

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

By using Equations 9 and 12, and changing the variable value (_{l}_{b}_{l}_{b}

Summary of calculated CV values for various PS-latex nanoparticles by AFFFF-MALS.

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 |

Figure 5 shows the results of AFFFF-MALS for PS-latex (T0625). Figure 5a shows the apparent light scattering intensity fractogram, and Figure 5 b shows the apparent diameter of PS-latex nanoparticles measured by MALS at corresponding elution times. In Figure 5, by using Equation 9 and 12 and by changing the variable value (_{l}_{b}_{l}_{l}_{l}_{l}

AFFFF-MALS results for _{l}

We also identified the sources of uncertainty in AFFFF-MALS as well as those in DLS. Individual sources of uncertainty are described in the _{l}

Having accurately determined the particle size, size distribution, and uncertainties for both DLS and AFFFF-MALS measurements, we next compared the results of DLS and AFFFF-MALS; the uncertainties are necessary to compare the results obtained from different metrological methods. To compare the determined diameters by these two methods, the intensity-average diameter was employed in this study, since the raw particle size determined by the DLS method is the intensity-average diameter. The weight- or number-average diameters of PS-latex nanoparticles determined by DLS are calculated from the average results from light scattering intensity under simple assumptions (size distribution, spherical structure,

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

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

Focusing on the results for T0625, the intensity-average diameter determined by DLS is 118.5 ± 0.69 nm. On the other hand, the value determined by AFFFF-MALS is 117.7 ± 3.48 nm, indicating that the particle size determined by dynamic and static light scattering methods (DLS and AFFFF-MALS) agree well within the estimated uncertainties when using the accurate analytical method established in this study. The values determined by DLS are slightly larger than those determined by AFFFF-MALS. This result might be attributable to the existence of an electrical double layer around the PS-latex particles on account of strongly adsorbed water [

In this study, we investigated a practical protocol for evaluating the size and size distribution of PS-latex nanoparticles in an aqueous suspension by using DLS and AFFFF-MALS analyses. First, we established a novel and practical protocol for accurately determining particle size and size distribution, considering various sources of uncertainty according to the GUM method. The intensity-average diameters determined by DLS and AFFFF-MALS agreed well within the estimated uncertainty, indicating that the particle sizes determined by the dynamic and static light scattering methods were well within the estimated uncertainty when using our analytical protocol. However, the size distribution of PS-latex nanoparticles determined by DLS was less reliable in comparison to the values obtained by AFFFF-MALS. This novel protocol could be a practical method for researchers to achieve some degree of concordance in nanoparticle size determination in industrial and biological research.

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