Article pubs.acs.org/Langmuir
Improved Metrological Traceability of Particle Size Values Measured with Line-Start Incremental Centrifugal Liquid Sedimentation Vikram Kestens,*,† Victoria A. Coleman,‡ Pieter-Jan De Temmerman,§ Caterina Minelli,∥ Holger Woehlecke,⊥ and Gert Roebben† †
Directorate-General Joint Research Centre, European Commission, 2440 Geel, Belgium Nanometrology Section, National Measurement Institute Australia, 2070 West Lindfield, New South Wales, Australia § Service Trace Elements and Nanomaterials, Veterinary and Agrochemical Research Centre (CODA-CERVA), 1180 Brussels, Belgium ∥ Chemical, Medical and Environmental Science Division, National Physical Laboratory, Middlesex, TW11 0LW, United Kingdom ⊥ Dr. Lerche KG, 12489 Berlin, Germany ‡
S Supporting Information *
ABSTRACT: Line-start incremental centrifugal liquid sedimentation (disc-CLS) is a powerful method to determine particle size based on the principles of Stokes’ law. Because several of the input quantities of the Stokes equation cannot be easily determined for this case of a rotating disc, the disc-CLS approach relies on calibrating the sedimentation time scale with reference particles. To use these calibrant particles for establishing metrological traceability, they must fulfill the same requirements as those imposed on a certified reference material, i.e., their certified Stokes diameter and density value must come with a realistic measurement uncertainty and with a traceability statement. As is the case for several other techniques, the calibrants do not always come with uncertainties for the assigned modal diameter and effective particle density. The lack of such information and the absence of a traceability statement make it difficult for the end-user to estimate the uncertainty of the measurement results and to compare them with results obtained by others. We present the results of a collaborative study that aimed at demonstrating the traceability of particle size results obtained with disc-CLS. For this purpose, the particle size and effective particle density of polyvinyl chloride calibrants were measured using different validated methods, and measurement uncertainties were estimated according to the Guide to the Expression of Uncertainty in Measurement. The results indicate that the modal Stokes diameter and effective particle density that are assigned to the calibrants are accurate within 5% and 3.5%, respectively, and that they can be used to establish traceability of particle size results obtained with disc-CLS. This conclusion has a great impact on the traceability statement of certified particle size reference materials, for which the traceability is limited to the size and density values of the calibrant particles.
■
INTRODUCTION Line-start incremental centrifugal liquid sedimentation, also known as differential or disc centrifugal sedimentation or disc centrifuge photosedimentometry (hence the abbreviation used in this article: disc-CLS), is a technique which is increasingly used to determine the size of particles based on their measured sedimentation rate in a centrifuge filled with a fluid of known density and viscosity. One of the main advantages of CLS is the high size resolving power, enabling populations of single particles to be distinguished from populations of dimers and multimers1−4 for the study of the agglomeration state of suspensions,5 as well as to separate distinct particle populations from each other.6 The disc-CLS consists of a rotating transparent disc, which is partly filled with a liquid density gradient.7 The gradient often consists of a water−sucrose solution of varying sucrose concentration. The particles to be analyzed must be suspended or be brought into a suitable © XXXX American Chemical Society
suspension so that they can be injected in the center of the disc. If the density of the particles exceeds the density of the gradient, then the rotational motion causes the particles to move, through the liquid density gradient, toward the edge of the disc, where they are illuminated by a photodiode, and their light extinction is measured by a photodetector. The measured transit or sedimentation time between the injection of the particles and their detection can be related to a sphereequivalent diameter via Stokes’ law as described in ISO 133181.8 Additional details of the operating and measurement principles of disc-CLS are given in the Supporting Information. To enable the comparison of measurement results obtained in different laboratories and at different times, results must be Received: May 23, 2017 Revised: July 19, 2017 Published: July 21, 2017 A
DOI: 10.1021/acs.langmuir.7b01714 Langmuir XXXX, XXX, XXX−XXX
Article
Langmuir
Standards and Technology (NIST), but no further information about this particle size standard is provided. The limited information about the assigned values for particle size and particle density of the PVC calibrants hampers the metrological traceability and undermines the comparability of particle size and particle density results obtained with discCLS, calibrated with these PVC particles.15−17 The unavailability of uncertainties for the assigned particle size and density values of the calibration particles, furthermore, prevents the establishment of a full uncertainty budget. For example, during the certification campaign of a colloidal silica reference material (ERM-FD102), metrological traceability to the SI unit of length could therefore not be established for the certified Stokes diameter values.18 Instead, traceability had to be limited to the particle size and the particle density values assigned to the PVC calibrants supplied by CPS Instruments, Inc. This limited metrological traceability has a potential consequence that discCLS results obtained after calibration with different types of calibrants cannot be reliably compared. The aim of this article is to improve the metrological traceability of disc-CLS results. It is based on collaborative studies undertaken to assess the trueness of the particle size and particle density values that are assigned to the CPS PVC calibrants. Measurements were conducted using validated measurement procedures, allowing the estimation of measurement uncertainties for particle size and effective particle density. In the last section of the article, we explain how the data presented can be used by users of disc-CLS instruments to establish an uncertainty budget for their disc-CLS method.
traceable to the same metrological reference. Such a reference is ideally an appropriate SI unit (International System of Units).9,10 If the input quantity values of the modified Stokes equation (see eq S1 of the Supporting Information) are known, or measured, and are traceable to the relevant SI units, then the resulting particle size values will be traceable to the SI unit of length (the meter), without the need for a calibration of the sedimentation time scale. However, the accurate determination of the input parameters is challenging. For example, throughout a measurement sequence, the viscosity and density of the gradient change due to the frictional heating of the disc under rotation, the dilution effect originating from repeated injection of samples, and the diffusion of the sucrose which affects the steepness of the gradient. There is no obvious way to measure these parameters as they change during the measurements. Therefore, as an alternative, most manufacturers of disc-CLS instruments recommend a calibration of the instrument setup with reference particles (see eq S2 of the Supporting Information). Particle size measurement results obtained using this alternative method can be traceable to the SI unit of length too, provided that both the particle size and the particle density values of the particle calibrant are traceable to the appropriate SI units. Currently, the main suppliers of disc-CLS instruments, i.e., CPS Instruments, Inc., (Prairieville, LA, USA), also supply calibration particles. The most common consist of highly diluted aqueous suspensions of monodisperse spherical polyvinyl chloride (PVC) particles with assigned particle size and density values. CPS Instruments, Inc. states a common particle density value of 1.385 g/cm3 in the calibration certificates of their PVC calibrants. However, no uncertainty is provided for the density value. According to the supplier, the assigned density value is based on a comparison of particle size results obtained using electron microscopy with size results from calibrated disc-CLS and then back-calculating the particle density. This indirect approach may be suitable for monodisperse nonporous solid particles with a perfectly spherical shape. PVC particles are, however, rather soft, and it has been reported that their size can be altered upon exposure to the electron beam and high vacuum, as applied in electron microscopes.11 Particle size is a method-defined measurand, which means that results obtained with different techniques do not necessarily agree.12,13 Therefore, calibration with particles whose size has been certified by means of a different technique may introduce a systematic bias into the measurement procedure. In 2012, Bell et al.14 experimentally estimated the effective particle density of a PVC calibrant using disc-CLS sedimentation tests in different sucrose density gradients. The average density of the gradients varied from 1.019 g/cm3 to 1.135 g/cm3. The average (n = 5) of the effective particle density results (1.323 g/cm3 ± 0.010 g/ cm3) was 5% lower than the assigned density value of 1.385 g/ cm3. The uncertainty value corresponds to the standard deviation of five replicate results (Minelli, personal communication, 2017). The nominal particle size values assigned to the PVC calibrants and stated in the certificates correspond to the modal value of the main peak in the particle size distributions that stem from size analyses performed by dynamic light scattering, gravitational sedimentation, and disc-CLS. The material certificates also state that the reported size values are traceable to a particle size standard supplied by the National Institute of
■
EXPERIMENTAL SECTION
PVC Test Materials. Calibration materials, consisting of aqueous suspensions of PVC particles with assigned modal particle diameters of 223 nm (PVC-4), 237 nm (PVC-5), 239 nm (PVC-1), 359 nm (PVC6), 372 nm (PVC-7), 377 nm (PVC-8), 460 nm (PVC-9), 476 nm (PVC-3), 479 nm (PVC-10), and 585 nm (PVC-11) were purchased from CPS Instruments, Inc. (Prairieville, LA, USA). All materials came with an assigned particle density of 1.385 g/cm3 and a particle mass fraction of
