Microfluidic in-line Dynamic Light Scattering with a Commercial Fibre Optic System

We report the coupling of dynamic light scattering (DLS) in microfluidics, using a contact-free fibre-optic system, enabling the under-flow characterisation of a range of solutions, dispersions, and structured fluids. The system is evaluated and validated with model systems, specifically micellar and (dilute) polymer solutions, and colloidal dispersions of different radii (∼1-100 nm). A systematic method of flow-DLS analysis is examined as a function of flow velocity (0-16 cm s-1), and considerations of the relative contribution of 'transit' and 'Brownian' terms enable the identification of regions where (i) a quiescent approximation suffices, (ii) the flow-DLS framework holds, as well as (iii) where deviations are found, until eventually (iv) the convection dominates. We investigate practically relevant, robust setups, namely that of a capillary connected to microdevice, as well as direct measurement on a glass microdevice, examining the role of capillary dimensions and challenges of optical alignment. We conclude with a demonstration of a continuous flow measurement of a binary surfactant/salt solution, whose micellar dimensions vary with composition, characterised with hundreds of data points (every ∼5 s) and adequate statistics, within a few minutes.

Electronic Supplementary Material (ESI) for Lab on a Chip.This journal is © The Royal Society of Chemistry 2023 Various aspects of our experimental setup are depicted in Fig. S1 and were used in different arrangements throughout this work: (i) For quiescent measurements, a pump was connected directly onto the FEP tubing to fill up the capillary; flow was switched off and measurements were carried out on the filled capillary as shown in figure S1a-b.(ii) For under flow measurements, the solution was displaced at a constant flow rate, after a ∼ 10 s stabilisation time to ensure steady-state flow conditions.(iii) Measurements on capillaries of ID = 0.4 and 0.2 nm were carried out with the setup and procedure in (i) using different 3D printed capillary holders.(iv) For direct measurements on the microfluidic chip (Fig. S1d), the ≈ 5 m long serpentine channel was filled, and the rectangular glass chip was secured to another 3D printed holder and a single channel was aligned with the optics using the xz-transition stage.Subsequently, measurements were carried out under quiescent conditions.(v) For the composition ramp experiments, 2 pumps were connected to the inputs of the micromixer chip in Fig. S1c using the 4-way linear connector shown, with one of the inputs blocked.The output of the chip was then connected via the FEP tubing to the capillary in Fig. S1a-b and measurements were taken under flow with changing composition.

Beam dimensions
Beam profile measurements were carried out using a Beamage-3.0beam profiling camera, to extract both the beam waist (1/e2 ) and the full width half maximum (FWHM) diameter, both shown in Fig. S2.The data agree well with our calculated value of 25 µm for the beam radius, w from the transit correlation function, using the model solutions or dispersions as secondary calibration standards.

Concentration limits of DLS measurements
Measurements were carried out to estimate the lower concentration limit for detection in a the fiber optic capillary setup (and benchmarked against a Malvern Zetasizer for comparison).We selected the DDAD surfactant system as it forms micelles of small dimensions (∼5 nm), and has a refractive index of ∼1.376 making it a challenging system to test the detection limits of our DLS setup.Figure S3 shows that our fibre optic system is sensitive down to the critical micelle concentration (CMC) of this system, namely ∼ 0.02% w/w.These values are commensurate with the results of a conventional 'sizer', such as the Malvern Zetasizer, also included in the figure.In practical terms, capillaries or microchannels of greater dimensions provide more robust measurements, likely due to the ease of alignment of the illuminated volume within the cross-section.The evolution of fitting parameters with sampling time (corresponding to the time taken to collect scattering data), agree well with the magnitude of fluctuations of the extracted R H values shown in Fig. 4 of the main paper.From these data combined, we estimate that ∼ 3 s is the minimum measurement time appropriate for a 1% w/w DDAO solution in water to acquire sufficient statistics, estimated from the broad invariance of χ 2 or R 2 beyond this sampling time.This minimum time, however, will dependent on the specific system, including size, refractive index contrast with the solvent, concentration of particles, scattering angle, etc.However, our demonstration using 1% w/w DDAO/H 2 O can be considered as a benchmark low-scattering system due to a similar refractive index to water and small micelle sizes, and we have thus employed 3 s as a reasonable minimum time for all other systems investigated.From the rearrangement of the modified correlation function shown in Eq. 9 of the main paper, one could incorrectly assume that the correlograms are transformed to a linear function over the full range of delay times.This is absolutely not the case, as shown in Fig. S5, and strong deviations are observed for 'sufficiently low' or 'high' delay times.Mathematically, the explanation for this is due to the normalised g 2 correlation function being ≈ 1 for low delay times and ≈ 0 at high delay times, while the MCF is proportional to 1/τ.In these regions, where the normalised correlation function is approximately constant, but the delay time is changing by orders of magnitude, the dependence on 1/τ dominates.By carefully considering the full MCF profile, we observe that the function is only linear in the region where g 2 is decaying significantly, i.e. for delay times close to where g 2 ≈ 0.5.For this reason, we have therefore decided to follow a simple, yet robust procedure of only fitting the MCF to data points corresponding to 0.2 > (g 2 − B)/Bβ > 0.8 where the MCF follows the expected linear relation.This criterion was validated for different v and R H in the main paper.
In order to determine the actual size of PS NP without relying solely on the manufacturer-provided 'nominal' dimension (obtained by the use of a CPS DISC Centrifuge 24000), SEM was carried out on PS NP of various size ranges.

Figure S6.
Histograms showing the distribution of diameters of 80, 100, and 200 nm (nominal) PS NPs obtained from processing the SEM data shown in ImageJ using the particle analyser tool and accounting for the thickness of the gold coating on the particles.The histograms were fitted with a normalised Gaussian distribution and the mean diameter and standard deviations are given.By cross-referencing these diameters with the measured R H values for the systems, there is a reasonably good agreement between the two experimental methods.
The map provided in Fig 8 of the main paper provides estimates for boundaries of applicable data analysis procedures for flow-DLS.The map was computed with the set of parameters for the system, namely scattering angle θ = 130 • , laser wavelength λ = 638 nm, temperature T = 25 • C, solvent refractive index n = 1.33, and viscosity η = 8.9 ×10 −4 Pa.s (water), as well as beam radius ω = 25 µm.While the main results of the map hold in general, here we adjust the estimates for different, plausible, system parameters.For clarity, we provide only the boundary between the range where the MCF approach holds, and the region where deviations become pronounced and cannot be modelled by the theory.This corresponds to the boundary between the light green ('transit theory') and orange ('deviations') ranges of Fig. 8 of the main paper modeled by v = 2Dq 2 ω ∝ 1/R H and g 2,T ≈ 0.75.The boundaries between the 'transit DLS' and 'deviation' regimes are based on the proportionality between v = 2Dq 2 ω ∝ 1/R H , arising from the relative magnitudes of the Brownian and transit terms.The boundaries therefore shift to higher velocities by increasing the scattering angle (Fig. S7a) and thus increasing q; or by a lower viscosity of the medium (the main contribution in Fig. S7b) increasing the value of the diffusion coefficient, D; or increasing the temperature and thus simultaneously reducing the viscosity (Fig. S7c); or by increasing the beam width ω (Fig. S7d).The dependence of the regime boundaries with experimental parameters can be understood, in simple terms, as follows.While it is trivial that correlograms shift with angle, when measuring particles of the same size due to the intrinsic dependence of Γ = Dq 2 in wavenumber q (and thus angle θ ), given D H ∝ 1/R H , the size-dependence of the decorrelation time also results in slightly different boundaries when compared against the transit term.Modifications to the DLS setup may be carried out to expand the v-R H parameter space where the transit correlation function holds, namely by increasing the scattering angle, using solvents of lower viscosities, or increasing the beam width.The latter, however, imposes greater constraints on the azimuthal angle between the wavevector and perpendicular to the velocity (expressed in Eq. 6), and an increase in the shear rate gradient in the scattering volume that also increases the constraint on the azimuthal angle, and hence shear correlation function models may need to be considered.Increasing the scattering angle would alleviate restrictions on the azimuthal angle (Eq.6), and widen the region of applicability for transit theory.However, in our setup, a reduction in the spacial coherence factor, β , was observed, indicating a tension between data quality and increasing the v-R H parameter space where theory applies.
One of the benefits of our proposed flow-DLS setup, employing a fibre optic, contact-free arrangement, is the ease in changing the flow cell for different measurements and applications, which only requires the design and printing of new holders.Figure S8 shows the data obtained within different flow cells: capillaries with reduced ID from 1 mm to 0.4 and 0.2 mm shown in Fig. S8a, and direct measurements on a microchannel of a microfluidic deviced shown in Fig. S1d, with data shown in Fig. S8b.Illustrative data were collected for both 3% w/w DDAO and 0.01% v/v 100 nm PS NP (nominal size) samples under quiescent conditions.The correlograms and extracted R H values for the ID reduction experiments are commensurate within the repeatability error of the instrument, suggesting that a reduction in the flow cell dimensions is feasible, if required/beneficial.Furthermore, the direct measurement on the microfluidic channel also showed consistent data with measurements on the 1 mm capillary for the PS NP sample.For measurements on DDAO micellar solutions, we observe an apparent increase of ∼0.9 nm in R H .We believe this could be due to two things: interference between incident and scattered light from the flat surface of the chip leading to a change in the scattering angle and hence wavevector that was not accounted for by the correlator, and the misalignment of the optics on the channel and potential clipping of the curved channel walls leading to parasitic scattering.The former would need to be accounted for on a case by case basis depending on the microdevice, while the latter could be remedied by designing a holder specifically for the dimensions and alignment required for the chip.
Size measurements of particle dispersions and solutions by DLS generally assume dilute and weakly interactions conditions, as crowding effects or strong interactions cause departures in the Brownian models for analysis, which is thus replaced by appropriate models.Measurements of SDS micelles in Fig. 9d show an apparent R H of ∼0.5 nm at 0.4 M (10% w/w) SDS and ∼10 mM NaCl.This apparent R H does not correspond to the actual micellar dimensions and is impacted by electrostatic effects discussed in the main paper.In short, these increase the diffusion coefficient which then appears as a lower R H in the Stokes-Einstein framework.At sufficiently low SDS concentrations, the apparent R H becomes the actual R H as shown in Fig. S9.Addition of electrolytes can thus mitigate these additional contributions, providing a means to recovering actual R H , albeit other structural changes can be inadvertently caused.Since DDAO is a non-ionic (amphoteric) surfactant, this effects are not observed in this system, as seen in Fig. S3 and S8.

1
Figure S1.a) Custom capillary-DLS setup.The fibre optic laser and detector are mechanically aligned to the same plane, while the 3D printed capillary holder is aligned using the xz translation stage.b) A close up of the microfluidic fittings and capillary in the holder.o-rings are used to seal the connection between the 3D printed part and the threaded conical port (Idex Flangeless Fitting, Cole-Parmer UY-02020-76).c) Microfluidic mixer used in the ramp experiments, whose output connects onto the capillary.d) Microreactor chip used for direct DLS measurements where the optics were aligned with a single channel.

Figure S2 .
Figure S2.The X-profile (a) and Y-profile (b) of the incident laser beam used in our setup.A Gaussian fit was implemented to determine the FWHM diameter and the beam waist (1/e 2 ).

Figure S3 .
Figure S3.Measurements of D H (•) and the average mean value (×) for DDAO solutions of different concentrations from the Malvern Zetasizer (Sizer) and the fiber optic capillary setup with capillaries of different diameters.The error bars display the standard deviation.

Figure
Figure S4.a) Correlograms obtained for different sampling times of a 1% DDAO aqueous solution.b) Evolution of the reduced χ 2v and adjusted R 2 associated with fitting g 2 = B 1 + β e −2Γτ to the correlograms at different sample times.Above ∼ 3 s sampling time, the quality of fits remains largely unchanged, in agreement with Fig.4of the main paper.we take this as an estimate for minimum integration time for our system to ensure robust R H estimates.

5
Figure S5.Correlation functions in the MCF rearrangement over the whole range of delay times (in log scale) and linear scale near the region of linearity (inset).

Figure S7 .
Figure S7.Effect of (a) scattering angle, (b) solvent properties (including changes in refractive index and viscosity), (c) temperature, and (d) beam radius, on the estimated boundary between transit-DLS theory being applicable and deviations from invariant R H with increasing v behvaviour.

Figure S8 .
Figure S8.Normalised correlograms acquired for 3% w/w DDAO (blue) and 0.01% v/v PS NP of 100 nm (nominal, red) in water, measured in (a) capillaries of internal diameters 1, 0.4, and 0.2 mm under quiescent conditions, and (b) in a microfluidic channel of cross-section 250 µm depth × 400 µm width compared to correlograms obtained within a 1 mm capillary under quiescent conditions.

Figure S9 .
Figure S9.Apparent R H of SDS micelles with concentration, measurements taken with a Malvern Zetasizer.