Inline Particle Sizing in Flow for Demanding Nanosuspension Processes

Carl C.L. Schuurmans, Jan-Piet Wijgergangs, Rut Besseling, Ad Gerich, InProcess-LSP The Netherlands.

Abstract

Non-invasive, fast particle size characterization of concentrated flowing nanosuspensions is a cost-effective and efficient option to improve nanoparticle-based industrial and R&D processes. In this whitepaper, we discuss the use of Spatially Resolved Dynamic Light Scattering (SR-DLS) for rapid inline measurement of both particle size and polydispersity of Silica-based Nanoparticles (Si NPs). We show that using InProcess-LSP’s NanoFlowSizer (NFS) it is possible to accurately measure the hydrodynamic diameter and PolyDispersity Index (PDI) of concentrated Si NPs (5 wt%/v%) in aqueous fluid flows at least up to 300 L/h, and in temperatures ranging from near zero to 70 degrees centigrade. Based on these results, we further elucidate how the NFS uses our SR-DLS technology, and discuss important criteria required to accurately measure nanoparticle hydrodynamic size in flow. 

Image Credit: InProcess-LSP

Direct Quality Control in Industrial Nanoparticle Production and Applications

Nanoparticles (NPs) are ubiquitous in our modern society. The term nanoparticle typically refers to particles with a diameter between 1 and 1000 nm ^[1]. A good example of the range of industrial uses of NPs can be found in nanoparticles based on Silicon Dioxide (Si NPs). Currently, Si NPs are utilized in construction (e.g. concrete or rubber), electronics, as polishing agents, in catalysis, for paints and coatings, in plastics and for use in agriculture ^[2]–[5]. There is also significant research into the potential applications of Si NPs in biomedical engineering ^[6]. In the next decade, the industrial production and use of Si NPs are expected to increase drastically, with an estimated market value in the 2021-2030 time period of 6.4 billion dollars ^[7].

Two of the main essential quality aspects of manufactured NPs are their mean size and polydispersity. In addition, details of the particle size distribution (PSD) can be used as well. Periodic measurement of these size characteristics is common during both the production, storage and use of these materials. Formulation and suspension characteristics can vary wildly depending on the type of NP studied. For instance, typically, Si NPs are formulated as concentrated aqueous slurries, with solid contents up to 50% by weight ^[8]. Due to these high particle concentrations, the quality control during Si NP production or related industrial processes is often laborious, requiring sample preparation (dilution) before a proper analysis can be obtained. These actions often need to be performed in a purpose-equipped laboratory, sometimes far away from the site of production/factory floor.

A new direct, inline method of determining the size of NPs during related processes effectively and efficiently is presented here. Specifically, InProcess-LSP (a Netherlands based Process Analytical Technology [PAT] company) has invented and commercialized a new technology for NP size characterization without the need for dilution ^[9][10]. This technology, named Spatially Resolved Dynamic Light Scattering (SR-DLS), not only provides rapid real-time sizing of highly turbid nanosuspensions, but also allows to perform analysis in many different sample/process environments, even in suspension flows. Currently, this technology based on SR-DLS, the NanoFlowSizer (NFS), is commercially available and able to measure concentrated, turbid, and flowing NP suspensions during both particle formation and processing.

In this whitepaper, we explain how SR-DLS technology of the NFS enables NPs size characterization in previously inaccessible fast flowing conditions, for highly turbid suspensions. We illustrate how these non-invasive measurements can be performed continuously during processing in varying flows and process conditions, without sample extraction or dilution steps.

Spatially-Resolved Dynamic Light Scattering and the NanoFlowSizer

To understand the extent of the improvement in measurement performance and efficiency of the SR-DLS technology in the NFS, it is important to first look at conventional DLS. Standard DLS records fluctuations in laser light as it is scattered from randomly diffusing NPs in a liquid (see Fig. 1A). By characterizing the rate of these fluctuations via the intensity ‘Auto Correlation Function’ (ACF), the diffusion coefficient D of the nanoparticles can be measured. This diffusion coefficient can be used to calculate the NP hydrodynamic diameter (d) via the Stokes-Einstein relation   d = k_BT / (3πηD), whereby k_B is the Boltzmann constant, T the temperature and η the dynamic solvent viscosity. Standard DLS is restricted to low turbidity  (‘single scattering’) NP suspensions, since for highly turbid samples scattering becomes dominated by multiple scattered photons that provide only indirect/limited information on NP diffusion ^[11]. Further, as detailed later, detection methods in standard DLS are ill-suited to measure NP size in inline configurations with significant suspension flow. Considering the typical measurement conditions in R&D or industrial processes, an alternative solution that allows for NP size characterization in turbid, flowing suspensions is needed ^[9].

Figure 1A. Schematic illustration of standard DLS measurement and Spatially Resolved-DLS. 1B. Representation of nanoparticles traveling through a pipe in a laminar flowing suspension. 1C. Autocorrelation functions as measured over a range of sample depths using SR-DLS, the white arrow indicates the increase in local velocity for larger depths. Image Credit: InProcess-LSP

The SR-DLS technology implemented in the NFS uniquely provides the desired extended application ranges for turbid and flowing suspensions (Fig.1A). The instrument employs ‘Fourier-Domain Low Coherence Interferometry’ using broadband NIR light. This technology instantaneously resolves the fluctuations of backscattered light from consecutive (>1000) depth layers (=voxels) in the measured sample, with a few µm depth resolution, up to a few mm total depth in the sample. Auto Correlation functions (ACF’s) are obtained simultaneously for each layer separately, and each ACF yields data on particle motion due to flow and particle diffusion (Fig.1B). This depth-resolved information uniquely enables particle sizing in laminar flows (Fig.1C). The NFS software accurately extracts the diffusive part of the ACFs from the measured data. From this measured data on NP diffusion, the mean particle size (Z_average), polydispersity (PDI) and size distribution (PSD) of the nanosuspension are obtained. Additional spatial filtering also allows to reject multiple scattered light and measure only single scattered light, enabling measurement of highly turbid samples. 

Figure 2A. Picture of the NFS equipped with a 1-inch flowcell filled with a 5 wt% Si NP suspension. 2B. pictures of flow cells with nominal inner diameters ranging from 0.5 to 2.0 inch. Image Credit: InProcess-LSP

These capabilities, combined with a high measurement rate (~2-10 seconds per point) make the NFS uniquely suited as PAT tool, fit for the future of the nanotechnology industry. Process monitoring at flow rates up to hundreds of liters per hour can be achieved by integrating the NanoFlowSizer probe unit ‘inline’ into a process, (see Fig.2A), using dedicated flow cell adaptors ranging from cells with mm scale size up to 2-inch pipes as shown in Fig.2B. Samples can also be analyzed statically in any glass container using other available modules, allowing versatile use in R&D laboratory settings as well. 

NanoFlowSizer Performance for Size Characterization at High Flow Rates

The NFS’s ability to measure inline at demanding flow rates is illustrated in Fig.3AB for a 5 wt% Si NP suspension (Z-Av size: ~101 nm, PDI: ~0.04) pumped through a 1.5-inch flow cell at flow rates Q up to 250 L/h. In Fig.3AB, the blue squares show the Z-av size and PDI obtained using one of the dedicated NFS flow correction algorithms, operating continuously during real-time inline measurements. As observed, the inline method can discern the particle size and PDI with less than 5% deviation from static measurements for the full studied flow range, and with less than 2% deviation for flow rates ≤ 200 L/h. To indicate the unique advantages of the spatial resolution and the flow correction method, the figure also shows the size characteristics obtained when reprocessing the ACF data without application of the flow correction method (green circles in Fig.3AB). As observed, this leads to a significant and progressive underestimation of the mean particle size and PDI. The uncorrected data mimic several literature reports showing the inability of standard DLS to account for the effects of flow when measuring particle diffusion coefficients ^[12], ^[13]. 

As mentioned, the spatial velocity profile is obtained simultaneously from the measurements and used for the flow correction of the ACFs. Averaged velocity profiles within 1 mm of the wall for the different flow rates in Fig.3AB are shown in Fig.3C. A useful characteristic of these velocity profiles is their slope near the wall, known as the wall shear rate (units 1/s). For fully developed laminar flows, the profile follows the well-known parabolic shape of the Hagen-Poiseuille model ^[14]. The present flows mimic a part of such a profile, but as discussed later, due to incomplete flow development, at high flow the match is only approximate.

As a last illustration of the NFS’s sizing capabilities, Fig.3D shows the PSD’s obtained from the measurements for different flowrates. The data show a relatively narrow size distribution, confirming the low polydispersity of the sample. Furthermore, the data is essentially independent of the applied flow rate up to at least 200 L/h.

Figure 3A & 3B. Z-av size and PDI measurements of 5 wt% Si NP suspensions for varying flow rates, using a 1.5-inch flow cell. Mean and error bars are based on 10 measurements each taking ~5 s in real-time analysis mode. Dashed lines in 3A and 3B represent the static results and a deviation of 5% + static measurement error (0.5 nm). 3C. Suspension velocity profiles for the different flow rates shown in 3AB. The inset shows a full parabolic Poiseuille profile in the flow cell. 3D. PSDs corresponding to the different flowrates shown in 3AB. Image Credit: InProcess-LSP

These results show the added benefit of the NanoFlowSizer for non-invasive size measurements of Si NPs in flow. Particle size data as presented above for flows well above 100 L/hr can be routinely obtained with the NFS. This capacity constitutes a breakthrough in inline nanoparticle sizing and process monitoring, especially when regarding ongoing research into DLS methods the last decades ^[13]. The spatial resolution of the method is key to this advancement, as explained in the next paragraph.

SR-DLS’s Key Advantages over Standard DLS 

When DLS is applied in flow, intensity fluctuations from the detection volume (see Fig.1) arise not only from random diffusion of NPs, but also from particle motion due to fluid flow (advection) and from differences in that motion (velocity gradients, see Fig.1C or 3C) within the detection volume. The optics of standard DLS particle sizing severely limit measurements in flow gradients, and options for size-characterization (only to an approximate level) are restricted mostly to the channel center where the flow is approximately uniform ^[13]. When using large channels (for high flow rates), even very modest sample turbidity levels further complicate such measurements due to multiple scattering. Difficulties with standard DLS in flow have recently also been recognized in the context of Asymmetrical Flow Field Flow Fractionation (AF4) applications ^[12].

The breakthrough of the SR-DLS method of the NanoFlowSizer is the ability to accurately measure in flow gradients by dividing the total scattering volume in >1000 slices, enabling measurement along the geometry wall. Looking at the spatially resolved autocorrelation functions (ACF’s) for a flowing NP suspension versus depth in the sample, (See Fig.1B), the combined effect of diffusion and flow is clearly visible: near the wall (blue), the ACF is dominated by diffusion, but at larger depth (green/red) the ACF decreases faster due to increasing flow velocity. The flow and diffusive parts of the ACF are mathematically separated via patented flow correction algorithms. Clearly, when not corrected for, the effect of flow can drastically overestimate the particle diffusion coefficient, and thus underestimate the particle size, as illustrated in Fig.3A. Quantifying local flow on the scale of each few µm per slice (without prior knowledge) and correcting for it is not possible with standard DLS, as it provides only one (averaged) scattering signal over the full measured sample volume.

The Importance of Laminar Flow for Inline Nanoparticle Sizing

SR-DLS offers NP size characterization for much larger flow rates than previously possible. At the same time there are conditions regarding the flow that must be fulfilled for successful measurements. The first concerns the laminarity of the flow; for accurate application of the flow correction algorithms, suspension flow should be laminar without effects from turbulent fluctuations such as temporal ‘swirls‘. Such random fluctuations can also enhance the apparent NP diffusion and bias measured NP size characteristics. The occurrence of turbulence in fluid flows in a pipe is described by the dimensionless Reynolds number ^[15], ^[16]:

(1)

in which ρ is the fluid density and R the inner radius of the flow cell. Turbulence can become relevant for Reynolds numbers beyond a critical value Re_c. This value depends on e.g. wall roughness and geometry details, but practically the onset is described by Re_c ~2000 – 3000 ^[16]. For SR-DLS we observe that Re_c = 2000 represents a conservative limit for the maximum flow where particle sizing results remain accurate within two percent. This is exemplified by the data in Fig.3A, where at the maximum flow rate of Q = 250 L/hr the Reynolds number is Re = 2600, while the measured size is still within 5% of the result without flow. The turbulence related maximum flow rate, expressed using Eq. (1) as Q_max ∝ R ⋅ Re_crit, scales with the flow cell size, allowing to access larger flow rates using larger diameter cells.

What Inline Sizing Limits Apply in the Laminar Flow Regime?

NanoParticle sizing in flow with the NanoFlowSizer requires accurate measurement of the particle diffusion regardless of the non-uniform flow along the flow cell wall. For this diffusion measurement, NPs must diffuse a sufficient fraction of the wavelength of the light¹ λ' in the direction along the light beam, which takes a typical time τ_dif as indicated in Fig.4A. In flow, the particles at a certain depth only spend a certain timespan τ_flow in the measurement beam, as shown in Fig.4B. For accurate measurement, this timespan must be significantly larger than the time required to measure the particle diffusion: τ_flow > τ_dif. The velocity should thus not exceed a maximum value ν_max, which can be expressed as ν_max ∝ w ⋅ (D/λ')², where w is the width of the beam.

¹ The wavelength in the sample, λ', is equal to that in vacuum divided by the sample refractive index, λ' = λ/n_s

Figure 4. Diffusion and flow effects relevant for NFS inline measurements 4A. Random particle diffusion can be accurately measured after a time τ_dif when the diffusive motion has reached a fraction of the wavelength λ'. 4B. Local flow (superimposed on the diffusion) through an NFS measurement voxel. The time for NPs to pass the beam, τ_flow is indicated. Image Credit: InProcess-LSP

Considering that measurements are made over a minimum depth, z_m, the velocity should remain below ν_max over this depth. Thus, the slope of the velocity profile, i.e. the shear rate  (see Fig.4B), must remain limited:  < ν_max / z_m. This can be expressed as:

< max = α D / λ'2

(2)

where α ∝ w / z_m. Since _max is proportional to the diffusion coefficient D, the maximum shear rate is reduced for suspensions with large particles or large solvent viscosity. When Equation 2 is not fulfilled, the quality of the measurement may be compromised, for example in terms of accuracy and precision of the Z-av size and polydispersity.

What does the above limit imply for maximum flow rates? For ideal Poiseuille flow, the wall shear rate for a given flow rate Q is drastically reduced when using larger flow cells:

= 4Q / πR3

(3)

Maintaining optimal measurement quality is thus easily achieved by selecting an appropriate flow cell, as shown below.

NanoFlowSizer Monitoring: Maintaining Data-Quality for Different Scales and Process Conditions

The NFS measures both the shear rate (via the slope of the velocity profile) and the mean diffusion constant D. This means that the quality criterion in Eq.2 is checked automatically during the measurement. For convenient diagnostics, this is done in real-time in the software by calculating the ratio² Pe* = λ'² / αD. When Pe* > 1, the software generates a warning for the occurrence of excessive flow and informs the user about the possibly compromised measurement quality on a per-data point basis.

² This mimics the traditional ‘shear Peclet number Pe = d²/4D ^[18], indicating if NP motion is dominated by diffusion (Pe > 1 or by flow (Pe > 1).

To indicate how the shear rate limit can be fulfilled by appropriate choice of NFS flow cell, Fig.5A shows results of the shear rate as function of the applied flow rate for flow cells with nominal inner diameters ranging from 0.50 to 2.00 inch. The experiments were performed with the same 5 wt% Si NP suspension as used previously. The shear rate increases linearly with flow rate for the smallest cells, while slightly nonlinearly for extreme flow rates > 100 L/hr. Considering a low fixed flow rate, Q ∼30 L/hr, the shear rate decreases very rapidly for increasing cell size, as discussed above. For higher Q, the reduction is less pronounced due to flow development effects described further below. 

Figure 5A. Effects of flow cell diameter on wall shear rate for various available flow cells (T ≃ 22 °C) 5B. relative size deviation as measured for Z_average for a 20 L/h flow measurement using flow cell diameters of 0.50 and 0.75 inch inner diameter. Image Credit: InProcess-LSP

Practically, for every combination of flow cell and particle size, a maximum shear rate (coupled to a maximum flow rate) can be determined. For example, when considering a 20 L/h flow rate through either a 0.50 or 0.75 inch nominal inner diameter flow cell, the deviation in average measured size (ΔZ_average, as compared to a static measurement) can be determined (Fig.5B). This deviation is 2.6% and 0.1% respectively for the 5 wt% Si NP nanosuspension. Thus, using a maximum deviation of 2%, flow cells with an inner diameter starting from 0.75 inch can be considered suitable to measure ~100 nm NPs at a flow rate of 20 L/h.

One of the purposes of inline monitoring is to assess size characteristics in response to changing process conditions. To illustrate the applicability of the NFS for that purpose, the Si suspension was circulated at 100 L/hr, while stepwise changing and stabilizing the temperature between 0 and 75 ⁰C. The temperature was measured inline using a PT100 coupled to the NFS software. Using the temperature dependent solvent viscosity and refractive index incorporated in the software (which may be user specified), the correct analysis parameters are automatically ensured during the experiment. As shown in Fig.6A, both the size and the polydispersity are accurately measured over the entire temperature regime. For the Z_average size, the variation over temperature is less than 2% between 0 and 70 ⁰C.

Figure 6A. NanoFlowSizer inline size characterization a Si suspension circulated at 100 L/hr over a range of temperatures. The data illustrate the capacity to measure inline and simultaneously account for the changes in suspension viscosity when varying temperature. 6B. Wall shear rate associated with the data in 6A, derived from the simultaneously measured velocity profiles. Image Credit: InProcess-LSP

For comparison to the measurement limits discussed above, the mean wall shear rate derived from the measurements at each temperature is also shown in Fig.6B. It is almost constant up to ∼35 °C, but starts to rise at larger temperatures. In ideal Poiseuille flow, the shear rate does not depend on the solvent viscosity (and thus, not on solvent temperature). But in a practical situation with a finite length flow cell (see Fig.2), the flow profile may not be completely developed at large flow rates. This increases the wall shear rate compared to the ideal case, an effect which is enhanced for large Reynold number (Re). Indeed in Fig.6, due to a significant viscosity reduction on increasing temperature, the Reynolds number also increases, see also Eq. (1): for 40 °C, one obtains Re ≃ 1550, rising to Re ≃ 2500 at 70 °C. The enhanced shear rate is consistent with the reduced flow development for such Reynolds numbers ^[17]. While the onset of turbulence may thus begin to play a role at 70 °C, the shear rate stays well within the limit in Eq.(2). This corroborates the excellent quality of the measurements in Fig.6A.

Finding the Right Flow Cell for Each Application

Based on the considerations in this white paper, it can be stated that for most industrial Si NP processes, a suitable flow cell can be found that allows inline NP size measurement. In table 1 below, we offer some indications for maximum flow rate per flow cell and average particle size for Si NPs in water. These values are indicative only and may depend on suspension optical properties. InProcess-LSP can provide custom cell designs to extend the flow range of the various flow cells shown. 

Table 1. Indicative maximum flow rates for different particle sizes and flow cells, for a solvent viscosity of 1 mPa.s. These rates yield comparative data quality as for static sample analysis (deviation <2%). Flowrates limited by shear are marked blue, flowrates limited by turbulence are marked grey. Source: InProcess-LSP

Conclusions

In this whitepaper, the application of the SR-DLS method of the NanoFlowSizer is described for continuous inline monitoring of turbid Si NP suspensions over an unprecedented range of flow speeds. With the NanoFlowSizer, monitoring important quality attributes like the Z_av and PDI can be done continuously and non-invasively in  the industrial production and application of NP suspensions such as the present Silica suspensions.

The two main conditions for which high-quality inline sizing in these new flow regimes can be performed are explained. These conditions are (i) the avoidance of turbulence in the inline measurement configuration and (ii) measuring in flow conditions for which particle motion by Brownian diffusion dominates over the motion induced by flow. Based on these principles and various measurements, it is shown that a careful choice of flow cell type for the intended process flow rate can guarantee high-quality nanoparticle size characterization in demanding process conditions.

By using the NanoFlowSizer in R&D and industrial NP processes, large benefits for process understanding and quality control can be unlocked. The versatile SR-DLS instrument can replace more extensive, laborious, and error-prone methods presently required for nanoparticle size characterization and quality control. 

Materials and Methods

Chemicals

Commercially available Si NPs were acquired (Levasil CS50-33P) and used at a particle concentration of 5 wt%. The batch has an average nanoparticle hydrodynamic diameter ~101 nm and PDI of ~0.04.

Static SR-DLS measurements

NFS measurements without flow were performed as a reference using the vial module and InProcess-LSP’s XsperGo software. Depth scans (1024 pixels) from the vial-suspension interface up to ~3 mm maximum pathlength in the suspension were acquired at 48 kHz during 4 measurement blocks of ~1.3s each. The depth-resolved ACFs (lagtime resolution ~21 µs) and resulting mean correlation function in each block analyzed by XsperGo’s algorithms were averaged over the blocks for optimum statistics and outlier removal, giving a high-quality single scattering autocorrelation function within ~6s for each measurement. For each static measurement, 20 consecutive measurements were performed, and from this, the Z_av and PDI were calculated using the Cumulant method integrated in XsperGo. The solvent viscosity and refractive index required were automatically corrected for that of water at the temperature measured by the dual thermocouples built into the vial module.

SR-DLS Measurements Under Flow

For flow measurements, samples measured at Q>200 L/h were analyzed up to 100 pixels from the flow cell wall, for Q<200 L/h, the full depth range was utilized for analysis. Several commercially available NanoFlowSizer flow cell modules were used (see Fig.2) with nominal inner diameters ranging from 0.5 to 2.0 inch. Using silicone tubing and standard tri-clamp connectors, the flow cells were attached to a quatroflow fluid systems pump (type SN731630), a heat exchanger and a passively cooled suspension reservoir (volume ~ 1 L). The temperature was measured inline using a PT100 thermocouple coupled to Xspergo and suspensions were pumped through this system at flow rates ranging from 0 to 250 L/h and at temperatures between 0 and 75 ⁰C. Residual flow pulsations from the pump were dampened sufficiently via a 1-inch T-junction (with one closed branch partially filled with air), installed just before the flow cell. The NanoFlowSizer was controlled and operated using Xspergo software, velocity profiles were derived from the depth resolved ACFs and employed for flow-correction using the quadratic algorithm representing a parabolic fit. Samples measured at Q>200 L/h were analyzed up to 100 pixels from the flow cell wall, for Q<200 L/h, the full depth range was utilized. For each flow measurement, a total of 15 repeat measurements (as defined in the static measurement section) were performed and analyzed. All data reported in figures 3 and 4 show averaged values with standard deviations (n=15). 

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This information has been sourced, reviewed and adapted from materials provided by InProcess-LSP.

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