# Establishing SI-Traceability of Nanoparticle Size Values Measured with Line-Start Incremental Centrifugal Liquid Sedimentation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{St,p}is the Stokes diameter of a particle detected after a transit time t

_{p}; M and S are, respectively, the ending (detection) and starting (inner liquid surface) radii of rotation; η and ρ

_{f}are, respectively, the average dynamic viscosity and the average density of the carrier fluid between S and M; ρ

_{p}is the effective particle density; and ω is the angular frequency of the disc. If the particles have morphologies which differ from ideally spherical, solid particles, which is mostly the case for industrially relevant materials, then d

_{St,p}is the equivalent Stokes diameter (i.e., the diameter of a solid sphere with the same settling velocity).

^{3}or less. The equation for sedimentation in a linear gradient is provided in the Supplementary Information.

_{cal}and ρ

_{cal}are the particle size and the mean effective particle density values assigned to the calibration material, and t

_{cal}is the sedimentation time of the calibration particles.

^{3}), and, on the other hand, they also demonstrated that the assigned modal particle diameter and particle density values are accurate within 5% and 3.5% respectively (at a 95% confidence level). Thanks to the use of these PVC calibration particles, the disc-CLS method [7] has now become an important part of today’s nanoparticle characterization toolbox. Although the reliability of the PVC calibration materials has thus been demonstrated [6], the actual comparability of the measured particle size results obtained for routine test samples is; however, limited because the critical properties (i.e., particle size and particle density) of the used calibration particles (PVC or other), have often not been characterized in a metrologically sound manner. For example, the “particle size” measurand is not always unambiguously defined, and uncertainties and traceability statements are often not given by the calibrant manufacturer. As a result, particle size measurement results obtained by the commonly used disc-CLS method (Equation (2)) are mostly only traceable to the property values of the calibrant used and not to the SI unit of length (Figure 1), which is the ultimate metrological reference of the particle size traceability network.

## 2. Materials and Methods

#### 2.1. Chemicals

#### 2.2. Calibration Material

^{3}. The indicated uncertainties, which correspond to a confidence level of about 95%, were estimated during a previous study [6]. 50 μL of calibration material was injected before each sample measurement.

#### 2.3. Certified Reference Materials

^{®}-FD102 and ERM

^{®}-FD304, were provided by the European Commission’s Joint Research Centre, JRC (Geel, Belgium). Both CRMs are aqueous suspensions of near-spherical silica nanoparticles that come with certified values and uncertainties for different measurands, including light extinction-weighted modal Stokes diameters obtained by line-start and homogeneous incremental CLS. ERM-FD102 has a distinct bimodal size distribution and the certified equivalent diameter values of (23.9 ± 2.0) nm and (88 ± 7) nm are valid for a mean effective (buoyant) particle density of 2.0 g/cm

^{3}. ERM-FD304 has a monomodal size distribution, and its certified equivalent diameter value of (33.0 ± 3.0) nm is valid for a particle density of 2.305 g/cm

^{3}. The assigned uncertainty values correspond to a confidence level of about 95%. For each disc-CLS measurement, sub-samples of 200 μL were taken from the undiluted CRMs using plastic syringes. The exact volume injected was determined by weighing the syringe before and after injection.

#### 2.4. Disc-CLS Conditions and Method

^{TM}model DC20000 (CPS Instruments, Inc., Prairieville, LA, USA). The instrument was operated at a rotational speed of 20,000 revolutions per minute. The optically transparent disc has an inner diameter of 95.15 mm and an inner width of 6.4 mm. Due to the assembly tolerances and a slight outward bulge of the disc’s faces at high rotational speed, the inner width of the disc typically expands to 6.5 mm (personal communication CPS Instruments, Inc.). A metal rim attached to the outside edge of the disc provides reinforcement against radial expansion, leaving an uncertainty of the inner radius of 12.5 μm, which purely reflects the machining tolerance. The optical system consisted of a photodetector and a laser diode with a nominal wavelength of 405 nm. The photodiode was positioned at a radial distance of (43.0 ± 0.5) mm from the center of the disc. The radial position of the photodiode was determined experimentally by injecting known volumes of water into the empty disc while constantly rotating at 20,000 revolutions per minute. The signal response of the detector changed significantly when the water, accumulating in the disc, reached the position of the detector. Based on the total volume of water injected, and on the inner dimensions of the disc, the radial position of the detector could be determined. The carrier fluid contained a density gradient constructed from sucrose solutions of (20.0 ± 0.1) g/kg and (80.0 ± 0.1) g/kg, respectively.

^{3}, respectively. These values, which have been assigned by CPS Instruments, Inc., are based on particle size measurements conducted with disc-CLS, gravitational sedimentation and dynamic light scattering. Six independent replicates of each colloidal silica CRM were analyzed under repeatability conditions within a time frame of maximum 5 h to ensure optimal conditions of the gradient during measurement. The raw measurement data were plotted as light extinction-weighted particle size distributions with a linearly scaled abscissa. The modal value of the Stokes diameter distribution was used as the characteristic value.

## 3. Results and Discussion

#### 3.1. Particle Size Analysis by Disc-CLS

_{f}〉, of the carrier fluid, consisting of the sucrose gradient and the water layer, through which the particles travel. For each subsequent measurement, the new position of the inner liquid surface was calculated from the known volume of sample and calibrant injected, and the variable method parameters 〈η〉 and 〈ρ

_{f}〉 were re-assessed using the method of linear extrapolation (Equation (S5)). The initial properties of the density gradient, together with all other key method parameters and calculated Stokes diameters, are listed in Table 1. A complete overview of all replicates is given in Table S1 of the Supplementary Information.

#### 3.2. Metrological Traceability

#### 3.2.1. Measurand Definition

#### 3.2.2. Traceability Network

- The density of the sucrose solutions was measured using an oscillating-type density meter. The working principle of this technique is based on the well-known law of harmonic oscillation [14]. The glass U-tube is excited to vibrate at the resonance or characteristic frequency of the introduced sample, which depends on its mass. The density of the sample under investigation is calculated using cell constants previously determined by measuring resonance frequencies when the sample cell is filled with a calibrant (e.g., water, ethanol, iso-octane, toluene), which are certified for density [15]. Measurement results obtained with an oscillating-type density meter are traceable to the SI units of length and mass through calibration with suitable SI-traceable calibrants [16]. The cell constants used in the calculation of the density are temperature and pressure dependent. However, the uncertainties of the temperature and pressure calibrations are assumed to be negligible compared to the uncertainties of the input quantities of the Stokes’ equation. Hence, the traceability chains of the temperature and pressure calibrations are omitted from the disc-CLS traceability network in Figure 4.
- The average dynamic viscosity values of the density gradient (between the detector’s position M and the inner liquid surface S) were calculated from the inner disc dimensions, the viscosity results that were obtained experimentally for the individual sucrose solutions (Figure S2) and from the known volumes of each sucrose carrier fluid component used for constructing the density gradient. Viscosity results are temperature dependent, and it can be assumed that the uncertainty mainly depends on the accuracy of the temperature controller. The viscosity measurements were performed at controlled temperatures using a rotational viscometer. The temperature controller of the viscometer was SI-traceably calibrated by the manufacturer with ITS-90 fixed points [17].
- The angular frequency of the disc-CLS instrument was verified by the manufacturer using an SI-traceably calibrated tachometer.
- The radial position of the photodetector (distance M) was measured using a paper strip with integrated SI-traceable length scale that was especially designed by the manufacturer for the given purpose. The measured distance was confirmed experimentally based on the inner dimensions of the disc (personal communication CPS Instruments, Inc.) and by injecting known volumes of water until a significant change of the signal response of the detector was recorded.
- The radial positions of the inner liquid surface (distance S) were determined based on the inner dimensions of the disc, the known volume of the sucrose density gradient and the known volumes of sample (+calibrant) injected during a measurement sequence. The effective volumes were determined gravimetrically using an SI-traceably calibrated balance and using the known density of water at 20 °C.
- The effective (buoyant) density of the silica nanoparticles was determined experimentally using isopycnic velocity interpolation and multi-velocity sedimentation approaches [6,18,19]. The measurement principle is based on the creation of a density gradient in an optically transparent cell. The particles to be analyzed migrate through the density gradient until they reach the zone where the density of the gradient matches the effective density of the particles. The zone of particle accumulation is detected optically. The density gradient can be constructed in an SI-traceable manner (temperature controlled, liquids of known density); hence, the effective density of the nanoparticles can also be considered to be SI-traceable.
- The sedimentation times of the particles, which are measured using the integrated computer clock, correspond to the time intervals between the start of measurement and the detection of a particle population (e.g., modal value of a PSD). SI-traceability of these time interval measurements can be established, for example, by accessing an SI-traceable Network Time Protocol service over a data network or by using a calibrated stopwatch.

#### 3.2.3. Measurement Uncertainties for Results of CRMs

_{c}(d

_{St,p}), of the output quantity or the measurand, d

_{St,p}, are arranged in the fishbone diagram shown in Figure 5. The relative uncertainties related to the main branches of the fishbone diagram are estimated according to the procedures described in the Guide to the Expression of Uncertainty in Measurement (GUM) [20]. Considerations for estimating each uncertainty component are discussed below.

- For similar types of disc-CLS instruments, Kamiti and co-workers have demonstrated, using a tachometer, that the rotational speed is accurate within 0.4% [21]. This value is considered to be a realistic estimate of the relative standard uncertainty for the angular frequency, u(ω).
- Among the different uncertainty sources shown in the fishbone diagram, temperature is considered to be the most important factor affecting the average viscosity of the gradient. The instrument, however, does not allow for the on-line monitoring of the gradient’s temperature during sample analysis. Instead, the temperature of the gradient can only be measured manually by immersing a temperature sensor in the carrier fluid immediately after having stopped the instrument. We conservatively consider that the measured temperature agrees with the temperature of the equilibrated gradient (during operation) within ±0.5 °C. For the given temperature variation, and using the experimental viscosity data shown in Figure S2, the average viscosity of the pristine gradient has a range of 0.018 mPa s. The experimental viscosity measurements were performed under intermediate precision conditions (different days). For both types of sucrose solutions, the standard deviation calculated from the replicate results at 30 °C was 0.043 mPa s. Considering that the effect of temperature on the viscosity follows a rectangular probability distribution (with a half-width of 0.009 mPa s), the absolute standard uncertainty for the average viscosity of the sucrose gradient, u(η), is estimated according to Equation (3),$$u\left(\eta \right)=\sqrt{{0.043}^{2}+{\frac{0.009}{\sqrt{3}}}^{2}}$$For an average viscosity of 0.907 mPa s, the relative standard uncertainty corresponds to 4.8%.
- Using the approach explained for estimating the uncertainty of the average viscosity, a standard combined uncertainty of 0.0002 g/cm
^{3}was estimated for the average density of the sucrose gradient by combining the standard deviation (0.0001 g/cm^{3}) of the density results at 30 °C and the half-width (0.0001 g/cm^{3}) of the rectangular distribution when assuming a temperature fluctuation of ±0.5 °C. For an average density of the sucrose gradient of 1.0067 g/cm^{3}, the relative standard uncertainty, u(ρ_{f})/ρ_{f}, corresponds to 0.01%. - The radial position of the photodetector (M) was determined to be located 4.25 cm from the center of the disc. The distance was confirmed using a paper strip specifically designed by the manufacturer for this purpose. A standard uncertainty, u(M), of 0.05 cm, or 1.18% in relative terms, is considered realistic.
- The radial position of the inner liquid surface (S) of the sucrose gradient depends on the total volume of the two sucrose solutions injected and on the injected volumes of the samples. The gradient is created by injecting nine 1.6 mL volumes of a mixture of 20 g/kg and 80 g/kg sucrose solutions and one 0.5 mL volume of n-dodecane.The sucrose solutions were injected using disposable plastic syringes with a volume scale graduated in 0.1 mL intervals. If the syringes are carefully filled with liquid, i.e., by avoiding air bubbles, then a volume accuracy of ±0.05 mL can be achieved for each injection. In this case, the effective volume of the sucrose gradient (+0.5 mL of n-dodecane) in the disc is expected to be between 14.40 mL and 15.40 mL, corresponding to S values of 3.93 cm and 3.87 cm, respectively. Based on the half-width (0.06 cm) calculated from the values for S, and assuming a triangular probability distribution, the relative standard uncertainty is about 0.6%.Sub-sampling and sample injection were performed using disposable plastic syringes with a volume scale graduated in 0.01 mL intervals. For each measurement, a nominal volume of 0.20 mL of the undiluted silica CRM was injected. Based on repeated sampling and injection experiments, the uncertainty associated with the effective sample volume has been estimated to be 3.43% or 0.01 mL. The relative standard uncertainty, u(S)/S, is estimated according to Equation (4):$$u\left(S\right)/S=\sqrt{{3.43}^{2}+{0.6}^{2}}$$
- A relative standard uncertainty, u(ρ
_{p})/ρ_{p}, of 2.50% for the effective density of silica nanoparticles has been determined in a previous study [6]. - The uncertainty associated with the sedimentation time, u(t
_{p}), of the silica nanoparticles is assumed to comprise a contribution related to the actual start of the time recording (time lag between manually starting the measurement and sample injection) and a contribution related to the measurement of the time at which the modal value occurs. The time lag between sample injection and the start of the measurement is estimated to be in the range of 0.1 s to 0.5 s. Compared to the relatively long measurement time required for silica nanoparticles, this short time lag can be assumed negligible, and the uncertainty mainly depends on the repeatability of the time measurements of the modal value. Throughout a measurement sequence, the volume of the carrier fluid increases and thus also the sedimentation times. The relationship between sedimentation time and the number of injected replicates is linear. To estimate the uncertainty, u(t_{p}), the sedimentation times are normalized using the slope of the linear relationship. Based on the half-width (0.4 s and 12.4 s for the large and small nanoparticle populations of ERM-FD102), and by considering a triangular probability distribution, the relative standard uncertainties of the sedimentation time are 0.3% and 0.7%, respectively for the large and small nanoparticle populations.

_{St,p}, and the input quantities, ω, η, ρ

_{p}, M, S, ρ

_{f}, and t

_{p}, can be expressed as in Equation (5):

_{c}(d

_{St,p}), the GUM applies the law of propagation of uncorrelated uncertainties as follows (Equation (6)):

_{i}is the so-called sensitivity coefficient for the input quantities x

_{i}, which is the partial derivative of d

_{St,p}with respect to x

_{i}. It is a measure of how much the measurement result of the measurand d

_{St,p}is affected by changes in the input quantity, x

_{i}. An overview of the standard uncertainties that contribute to the combined uncertainty of a single measurement result of ERM-FD102, obtained by the reference disc-CSL method, is given in Table 4 (population of small particles) and Table 5 (population of large particles). A similar uncertainty budget for ERM-FD304 is given in Table S2 of the Supplementary Information. It must be noted that the tabulated quantity values are only applicable to the very first sample injected in a pristine sucrose gradient. After the first sample injection, the average viscosity and density of the carrier fluid, as well as the distance between the inner liquid surface and the center of the disc, need to be adjusted according to the sample and calibrant volume(s) injected. In relative terms, both combined uncertainties correspond to about 5.5%. In expressing the uncertainty at a confidence level of about 95%, the latter is multiplied by a coverage factor, k = 2, resulting in a relative expanded uncertainty of about 11%. The relative expanded (k = 2) uncertainty of a single replicate result of ERM-FD304 is about 8%.

#### 3.2.4. Implications for End Users

_{CRM}, of the certified value of the CRM (Equations (8) and (9)):

_{CRM}. For example, the uncertainty of the disc-CLS certified value of ERM-FD102 contains relative standard uncertainty contributions of 2.5% and 2.2% for the effective density of silica nanoparticles and for the use of different PVC calibrants, respectively. As explicitly stated in Section 4.3.10 of the GUM [20], double-counting of uncertainty components must be avoided. As a result, the corresponding individual standard uncertainties (u(ρ

_{cal}), u(d

_{cal}) and u(ρ

_{p})) should, in this example, be taken out of Equation (7).

## 4. Conclusions

^{3}to 2.3 g/cm

^{3}. The certified values for disc-CLS embodied in the CRMs are the result of intercomparison studies among expert laboratories. Since most of these laboratories used the routine disc-CLS method in combination with non-traceable PVC calibrants, the certified values are only traceable to those PVC calibrants and not the SI. The data presented now show that the results obtained with the reference method agree with the certified values. On that basis, the metrological traceability statement of the certified values for the particle size measured by disc-CLS could be upgraded from traceable to “the size values provided for the PVC calibrants supplied by CPS Instruments, Inc.” to “the International System of Units (SI)” for the colloidal silica CRMs.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations and Symbols

CRM | certified reference material |

d_{cal} | assigned particle size of calibrant |

d_{St,p} | Stokes diameter of test particles |

Disc-CLS | disc centrifugal liquid sedimentation |

GUM | Guide to the Expression of Uncertainty in Measurement |

ISO | International Organization for Standardization |

ITS-90 | International Temperature Scale of 1990 |

JRC | Joint Research Centre of the European Commission |

k | coverage factor |

M | radial position of the detector |

N | normal distribution |

PSD | particle size distribution |

PVC | polyvinyl chloride |

R | rectangular distribution |

S | radius of the inner liquid surface |

SI | International System of Units |

t_{cal} | sedimentation time of the calibration particles |

t_{p} | sedimentation time of the test particles |

T | triangular distribution |

u | standard uncertainty (confidence level 68%) |

u_{c} | combined uncertainty (confidence level 68%) |

U | expanded uncertainty (confidence level 95%) |

VIM | Vocabulary of Metrology |

x_{i} | quantity |

η | average dynamic viscosity between M and S |

ρ_{cal} | assigned mean effective particle density of calibrant |

ρ_{f} | average density of the carrier fluid between M and S |

ρ_{p} | effective particle density |

ω | angular frequency of the disc |

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**Figure 1.**Metrological traceability network linking a particle size measurement result of a test sample obtained by the routine disc-CLS method (after calibration with PVC reference particles) to the particle size and particle density values assigned to the PVC calibration material. In this network, and in other schemes further discussed in this manuscript, the dotted rounded groups indicate measurement procedures, while the square boxes represent tools, reference materials and accepted literature/reference values. The different input quantities of the measurement functions are grouped in rounded shaded boxes with solid borders.

**Figure 2.**Overlay of representative light extinction-weighted PSDs of colloidal silica ERM-FD102 (

**a**) and ERM-FD304 (

**b**) obtained by the routine (black curves) and reference (gray curves) disc-CLS methods. The vertical dashed lines correspond to the certified ranges of the modal diameters for the two CRMs. The ordinates correspond to the natural logarithm of the ratio of the incident (I

_{0}) and transmitted light intensity (I).

**Figure 3.**A simplified representation of different traceability chains, each providing a different level of traceability.

**Figure 4.**Metrological traceability network linking a particle size measurement result of a test sample obtained by the routine disc-CLS method (after calibration with PVC reference particles) to the SI unit of length (meter) via particle size results of silica CRMs obtained by the reference disc-CLS method.

**Figure 5.**Fishbone diagram illustrating the potential sources of uncertainty for particle size measurements performed with the reference disc-CLS method.

**Table 1.**Overview of key parameters (first replicate) for the direct calculation of Stokes diameter results using the reference disc-CLS method.

CRM | d_{st,p}^{1} | 〈η〉 ^{2} | 〈ρ_{f}〉 ^{2} | ρ_{p}^{3} | M | S | ω | t_{p} |
---|---|---|---|---|---|---|---|---|

[nm] | [Pa s] | [g/cm^{3}] | [g/cm^{3}] | [cm] | [cm] | [rad/s] | [s] | |

ERM-FD102 | ||||||||

Population 1 | 22.5 | 0.0091 | 1.0070 | 2.0 | 4.25 | 3.87 | 2094 | 688 |

Population 2 | 83.7 | 0.0091 | 1.0070 | 2.0 | 4.25 | 3.87 | 2094 | 50 |

ERM-FD304 | 31.0 | 0.0095 | 1.0079 | 2.3 | 4.25 | 3.88 | 2094 | 285 |

^{1}Light extinction-weighted modal Stokes diameter.

^{2}At a temperature of 30.0 °C (ERM-FD102) and 27.8 °C (ERM-FD304).

^{3}As stated on the CRM certificates.

**Table 2.**Comparison of particle size results (mean ± expanded uncertainty) determined by routine and reference disc-CLS methods.

CRM | Particle Size ^{1} [nm] | |
---|---|---|

Routine | Reference | |

ERM-FD102 | ||

Population 1 | 24.7 ± 2.5 | 23.1 ± 2.8 |

Population 2 | 90.1 ± 9.0 | 84.2 ± 10.1 |

ERM-FD304 | 33.3 ± 3.1 | 31.1 ± 3.6 |

^{1}Light extinction-weighted modal Stokes diameter.

Feature | Description |
---|---|

Physical principle | Sedimentation rate measurement |

Technique | Disc-CLS (line-start incremental mode) |

Detection system | Turbidity of an ensemble of particles with the same sedimentation rate |

Data analysis | Routine method: conversion of time to particle size through sedimentation time scale calibration Reference method: conversion of sedimentation time to particle size through Stokes’ law |

Type of diameter | Sphere-equivalent Stokes diameter |

Type of weighting | Light extinction |

Type of distribution | Density distribution |

Representative value | Mode |

**Table 4.**Uncertainty budget for a single disc-CLS measurement (reference method) of nominally 80 nm silica nanoparticles (ERM-FD102).

Quantity, x_{i} [unit] | Quantity Value | Standard Uncertainty, u(x_{i}) | Distribution Type ^{1} | Contribution ∂f/∂x_{i}·u(x_{i}) [nm] |
---|---|---|---|---|

Angular frequency, ω [rad/s] | 2094 | 9 | N | −0.34 |

Average viscosity of the carrier fluid between M and S, η [Pa s] | 0.0091 | 0.0004 | N & R | 2.05 |

Average density of the carrier fluid between M and S, ρ_{f} [g/cm^{3}] | 1.0070 | 0.0001 | N & R | <0.01 |

Radial position photodetector, M [cm] | 4.25 | 0.05 | N | 1.39 |

Radial position of inner liquid surface, S [cm] | 3.87 | 0.03 | T & N | 3.76 |

Density silica, ρ_{p} [g/cm^{3}] | 2.0 | 0.05 | N | −2.14 |

Sedimentation time silica, t_{p} [s] | 48.2 | 0.2 | T | −0.15 |

Stokes diameter, d_{St,p} [nm] | 83.7 | Combined measurement uncertainty, u_{c}(d_{St,p}) [nm] | 5.0 | |

Expanded (k = 2) measurement uncertainty, U [nm] | 10.0 |

^{1}N, normal; R, rectangular; T, triangular.

**Table 5.**Uncertainty budget for a single disc-CLS measurement (reference method) of nominally 20 nm silica nanoparticles (ERM-FD102).

Input Quantity, x_{i} [unit] | Quantity Value | Standard Uncertainty, u(x_{i}) | Distribution Type ^{1} | Contribution ∂f/∂x_{i}·u(x_{i}) [nm] |
---|---|---|---|---|

Angular frequency, ω [rad/s] | 2094 | 9 | N | −0.09 |

Average viscosity of the carrier fluid between M and S, η [Pa s] | 0.0091 | 0.0004 | N & R | 0.55 |

Average density of the carrier fluid between M and S, ρ_{f} [g/cm^{3}] | 1.0070 | 0.0001 | N & R | <0.01 |

Radial position photodetector, M [cm] | 4.25 | 0.05 | N | 0.37 |

Radial position of inner liquid surface, S [cm] | 3.87 | 0.03 | T & N | −0.84 |

Density silica, ρ_{p} [g/cm^{3}] | 2.0 | 0.05 | N | −0.57 |

Sedimentation time silica, t_{p} [s] | 675 | 5.1 | T | −0.09 |

Stokes diameter, d_{St,p} [nm] | 22.5 | Combined measurement uncertainty, u_{c}(d_{St,p}) [nm] | 1.3 | |

Expanded (k = 2) measurement uncertainty, U [nm] | 2.7 |

^{1}N, normal; R, rectangular; T, triangular.

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## Share and Cite

**MDPI and ACS Style**

Kestens, V.; A. Coleman, V.; Herrmann, J.; Minelli, C.; G. Shard, A.; Roebben, G.
Establishing SI-Traceability of Nanoparticle Size Values Measured with Line-Start Incremental Centrifugal Liquid Sedimentation. *Separations* **2019**, *6*, 15.
https://doi.org/10.3390/separations6010015

**AMA Style**

Kestens V, A. Coleman V, Herrmann J, Minelli C, G. Shard A, Roebben G.
Establishing SI-Traceability of Nanoparticle Size Values Measured with Line-Start Incremental Centrifugal Liquid Sedimentation. *Separations*. 2019; 6(1):15.
https://doi.org/10.3390/separations6010015

**Chicago/Turabian Style**

Kestens, Vikram, Victoria A. Coleman, Jan Herrmann, Caterina Minelli, Alex G. Shard, and Gert Roebben.
2019. "Establishing SI-Traceability of Nanoparticle Size Values Measured with Line-Start Incremental Centrifugal Liquid Sedimentation" *Separations* 6, no. 1: 15.
https://doi.org/10.3390/separations6010015