Solvent-Dependent Dynamics of Cellulose Nanocrystals in Process-Relevant Flow Fields

Flow-assisted alignment of anisotropic nanoparticles is a promising route for the bottom-up assembly of advanced materials with tunable properties. While aligning processes could be optimized by controlling factors such as solvent viscosity, flow deformation, and the structure of the particles themselves, it is necessary to understand the relationship between these factors and their effect on the final orientation. In this study, we investigated the flow of surface-charged cellulose nanocrystals (CNCs) with the shape of a rigid rod dispersed in water and propylene glycol (PG) in an isotropic tactoid state. In situ scanning small-angle X-ray scattering (SAXS) and rheo-optical flow-stop experiments were used to quantify the dynamics, orientation, and structure of the assigned system at the nanometer scale. The effects of both shear and extensional flow fields were revealed in a single experiment by using a flow-focusing channel geometry, which was used as a model flow for nanomaterial assembly. Due to the higher solvent viscosity, CNCs in PG showed much slower Brownian dynamics than CNCs in water and thus could be aligned at lower deformation rates. Moreover, CNCs in PG also formed a characteristic tactoid structure but with less ordering than CNCs in water owing to weaker electrostatic interactions. The results indicate that CNCs in water stay assembled in the mesoscale structure at moderate deformation rates but are broken up at higher flow rates, enhancing rotary diffusion and leading to lower overall alignment. Albeit being a study of cellulose nanoparticles, the fundamental interplay between imposed flow fields, Brownian motion, and electrostatic interactions likely apply to many other anisotropic colloidal systems.


Static SAXS Experiments
The small-angle X-ray scattering (SAXS) experiment for static CNC sample was conducted at LiX beamline (16-ID), Nation Synchrotron Light Source II (NSLS-II), Brookhaven National Lab (BNL).The chosen wavelength of the X-ray was 0.9Å and the sample-to-detector distance was 3.6 m.The sample was injected to a liquid sample holder with mica as the window materials.Five different positions were selected to reduce the experimental errors, and an exposure time of 1 s was set for each position.A polydispersed parallelepiped model was used to fit the scattering curve and extract the cross-sectional dimensions and distributions according to

Post-Processing of Scanning-SAXS Experiments
The scattering invariant was calculated by following: 1 where () is the scattering intensity and  is the scattering vector.The normalized scattering intensity is obtained by  * = / * .The anisotropic factor () was calculated as: 2 where  is the azimuthal angle of the detector plane in polar coordinate.The  range is from 0.25 nm -1 to 0.45 nm -1 and the  range is from −/2 to /2.The idea of the  is that it does not need an aligned reference direction and the degree of the anisotropy could be directly obtained from the original 2D scattering pattern.
The structure parameter ϒ was calculated by the following steps: 1.The normalized form factor  * () is defined as the scattering of dilute CNC(aq) at 0.4 wt% from the work of Rosén et al. 1 normalized with its scattering invariant  * .
2. The structure factor  * () was obtained by dividing  * () with  * (): * () was to illustrate the deviation of CNC structures from a dilute disordered system.
3. The structure parameter ϒ was calculated as follow: where the ϒ is used to quantify the degree of deviation of  * () from a dilute system.
The structure size  was obtained the same way as described by Rosén et.al. 1  * () was firstly smoothed using a spline function and the  position where  * () reached the max value was located within the  range of from 0.06 nm -1 to 0.25 nm -1 (denoted as   ).The value of  was where  is the distance that the light is travelled in the CNC (d was used as the structure size earlier, please change one symbol),  is the wavelength of the light and  0 is the maximum transmitted intensity, which can be obtained at a phase shift of 90 degrees according to the procedure in the main manuscript.The birefringence is directly proportional to the order parameter   = In the present study, the decay is not fully exponential, and some degree of polydisperse dynamics must be considered.The cumulant expansion tool is to re-write a sum of exponential decay functions as a power series expansion according to: where  is the time after the flow was stopped,  0 is the birefringence level when flow was just stopped (a relaxing time of 50 ms is considered to avoid artefacts during the shutting of the valves),   is the mean rotary diffusion coefficient and  is the polydispersity index.
The strong birefringence of the material caused a value of  When combining with the   values of CNC(aq) at corresponding flow rates,   at 50 mL/h became larger than 10 mL/h, with a broader distribution of dynamic time scales.And because   is inversely related to the structural size, it can be concluded that high flow rates could align both small and large tactoids, which contributed to the broader distribution of   .While at the focusing region, CNC(aq) at 50 mL/h gave a smaller  and a larger   .As high flow rates could break up the CNC mesoscopic structure (the hypothesis from the main manuscript), the major population of aligned CNCs was in small size.Here the small size could refer to both individual CNC rod and smaller CNC tactoidal structure.And the fact of the small size contributed to both a small  and a large   at the focusing region and flow rate of 50 mL/h.While for CNC(aq) at 10 mL/h, the mesoscopic structures were present, and they are more easily jammed because of the deceleration accompanied with the compression (Fig 1(a) in main manuscript, region II).Moreover, as smaller tactoids coalesce into bigger ones will also lead to a wider distribution of the   .As a conclusion, larger structures resulted in a smaller   at focusing region and flow rate of 10 mL/h, but the possibilities of small tactoid fusion contributed to a large .
For CNC(PG) at 10 mL/h, the system behaved very differently.The  of CNC(PG) was much larger than CNC(aq) at the same flow rate, meaning a much wider Dmean distribution of the aligned materials.This indicated that a wider size distribution of CNC tactoids was aligned owing to low solvent viscosity.And the  did not show obvious change with channel positions.At the focusing region,  of CNC(PG) exhibits a slight decrease, which may be caused by the flow deceleration accompanied with the compression.

Theoretical Estimation of 𝑫𝑫 𝒓𝒓,𝟎𝟎
The theoretical rotary diffusion coefficient of dilute monodisperse spheroids can be obtained through: 6  ,0 = 3  (2ln   − 1) 2 3 where  ,0 is the rotary diffusion coefficient,   is the Boltzmann constant,  is the temperature in Kelvin,   is the aspect ratio,  is the solvent viscosity and  is the length of the CNCs.From our previous work, 7 we know that the dilute CNCs behave like Brownian spheroids of dimensions  = 150 nm and   = 15.Using  = 293 K,   = 0.042 Pa s and   = 0.00089 Pa s, we estimate that  ,0 = 60.2 rad 2 /s in PG and  ,0 = 2840 rad 2 /s in water.

Computational Fluid Dynamics (CFD)
To illustrate the shear rate distribution in the channel, CFD was conducted on COMSOL Multiphysics software.The geometry of the channel is 5 mm long and 1 mm wide, with a square cross-section shape.A laminar flow was assumed to perform the simulation.
The incompressible steady-state laminar flow in a square channel could be predicted by Navier-Stokes equation in the specific form: where  is the flow velocity,  is the stress tensor,  is the pressure and  is the identity matrix.
For the incompressible fluid, we have the following equation: could be obtained by: where The estimated shear rate at a certain projected channel height was taken as the value from the midplane in the channel, where the system is observed in vorticity direction and contributes more to the signal due to higher projected alignment. 8  where m and n are fitting parameters and ̇ is the shear rate.The fitting results in relationships of  = 0.4253 • ̇− 0.2681 for CNC(aq) and  = 0.0396 • ̇− 0.1823 for CNC(PG).The fitting equations are valid within the range of 0 -150 s -1 , which perfectly covers the achievable shear rates obtained from CFD.

Figure S1 .
Figure S1.Analysis of CNC cross-sections through SAXS; (a) the scattering curve of CNC(PG)

1 2〈3
cos  − 1〉 ∝ Δ, with  being the angle between CNC major axis and flow direction, and the brackets denoting an ensemble average.The decay of Δ after stop will thus reflect the Brownian rotary diffusion of CNCs, which in an ideal dilute case of monodisperse rods decays as Δ ∝   ∝ exp (−6  ), with   being the rotary diffusion coefficient.
, leading to an oscillating intensity during the decay.This phenomenon is illustrated in a supplementary video below.However, by assuming a constant decay of  , the conversion from intensity to birefringence could be easily done through identifications of shifts of 90 ∘ , 180 ∘ , 270 ∘ etc.The procedure is illustrated in Fig S10.

Figure S10 .
Figure S10.The extracted intensity (the upper two figures, blue line is extracted intensities, the () is the apparent dynamic viscosity as function of shear rate ̇ of the suspension obtained by the rheological experiments, (see Fig S14).The resulting shear rate distribution is shown in Fig S12 below.

Figure. S12
Figure.S12 Results from CFD simulations; (a) the velocity distribution in the channel for

Figure S13 .
Figure S13.The plot of   at different positions versus the flow rates for both CNC(aq) (upper left figure) and CNC(PG) (upper right figure); the positions are located: at the wall prior

Figure S14 .
Figure S14.The steady viscosity profile of CNC(aq) and CNC(PG) in log scale at concentration