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Supporting Information

Semi-quantitative structural analysis of highly anisotropic cellulose nanocolloids Kojiro Uetani, Hiroyuki Yano* Division of Creative Research and Development of Humanosphere, Research Institute for Sustainable Humanosphere, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan. Tel: +81 774 38 3669; Fax: +81 774 38 3658; E-mail: uetani-k@rish.kyoto-u.ac.jp, *yano@rish.kyoto-u.ac.jp

In this Supporting Information we describe the technical details of the experiments and models used in the main paper, “Semi-quantitative structural analysis of highly anisotropic cellulose nanocolloids”. In Section 1 we describe the experimental details, and in Section 2 we give a detailed description of the trapezoidal model, and the deviation in the size of sugi nanofibrils (SNFs).

1. Experimental Materials. Filter paper (5 g) was hydrolyzed in 100 mL of 55 wt% H2SO4 aqueous solution at 60°C, for 10 min. The product was washed with Milli-Q water under filtration with a membrane filter, until the pH reached ~4, and was then centrifuged to obtain the purified cotton nanowhiskers (CNWs) from the supernatant.

Wet tunicate of ascidian (40 g) cut into a ~1-cm square was subjected to bleaching treatment using the Wise method, S1,S2 which consisted of a cyclic treatment performed 10 times with sodium chlorite (NaClO2) solution under acidic conditions (pH 4 to 5) at 80°C for 1 h, to remove the matrix proteins. After washing, the product was freeze-dried to obtain ~1.9 g of purified cellulose framework. The aerogel-like tunicin cellulose was then subjected to acid hydrolysis in 100 mL of a 55 wt% H2SO4 solution for 20 min, at 60°C and under vigorous stirring, after which the suspension was washed with Milli-Q water until the pH reached ~4; the suspension was then sonicated for 1 h, at 200 W (24/31 KHz). The diluted supernatant was then centrifuged to obtain the tunicin nanowhiskers (TNWs).

Cedar powders of 30−60 mesh were subjected to a 10 h bleaching treatment by the Wise methodS2 to remove the lignin. After washing, the hemicelluloses were partially removed in a 4 wt% KOH solution, under ambient conditions, to obtain a pulp with an α-cellulose contentS3 of 82wt%. The washed pulp was then passed through the grinder once to obtain the disintegrated SNFs.

Morphology observations. The cellulose nanoparticles (CNPs) negatively stained using 2 wt% uranyl acetate were imaged using a TEM (JEM-2000EXII, JEOL Ltd.). The coffee rings were imaged using an optical microscope (VHX-200, KEYENCE). The structuration of the CNPs in the coffee rings was confirmed using a polarized optical microscope (BX53, Olympus Corp.)0 and an FE-SEM (JSM-6700F, JEOL Ltd.), with a Pt coating (ca. 2 nm) applied in an ion sputter coater (JFC-1600, JEOL Ltd.). The dimensional analyses—including the size distributions of the CNPs and the droplet areas before and after depinning—were performed using ImageJ (NIH).

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Zeta potentials. The equilibrium zeta potential values ζ∞ of the CNPs (at φ＝0.01 vol%) were measured in various KCl solutions via electrophoresis, using an SZ-100 (HORIBA Co., Ltd.). The Smoluchowski equation was applied as follows:

𝜁＝ 𝑈E𝜂𝜀𝑓(𝜅𝑎), (S1)

where the electrophoretic mobility UE = (λΔν)/(2nE sin(θ/2)); η, ε, and n are the viscosity, dielectric constant, and refractive index of the dispersion media, respectively; Henry’s function f(κa)=1; κ is the inverse of the Debye length and a is the major particle radius; λ is the incident wavelength (532 nm); Δv is the frequency shift under the Doppler effect; E is the voltage; and θ is the scattering angle (173°). The cellulose nanofibrils showed a time dependence in the zeta potential, resulting from the swelling of the amorphous polymer located on their surface,S4 so their equilibrium values were determined using successive measurements. The electric conductivity σ was also measured using this device, to allow an estimation of the salt concentration to be made.

Contact angle. The static contact angles θc—and the decrease in the static contact angles after evaporation, normalized by ttotal, the lifetime of the droplets—were measured using the half angle method (which holds for the relation ℎ/𝑅 = tan(𝜃!/2), where h is the central height of a spherical droplet), with a DM500 (Kyowa Interface Science Co., Ltd.). The interval between successive measurements was 5 s.

Coffee ring formation. CNP coffee rings were formed on cover glasses (Matsunami Glass Ind., Ltd.), which were cleaned using ultrasonication in ethanol at 200 W (24/31 KHz); they were dried using an air duster immediately before the experiments were performed. It was necessary to eliminate the watermarks that appeared after the ethanol dried, because they easily interfered with the uniform pinning of the sample droplets. The static contact angle θc of Milli-Q water on this glass was 34.0 ± 0.6°, and the droplet radius R was ~1 mm in the case of a 1 μL droplet. For Milli-Q water, the advancing angle θa and the receding angle θr were 37.3 ± 1.4° and 28.8 ± 1.2°, respectively, so the contact angle hysteresis (θa−θr) was ~9.0 ± 1.0°.S5 Further, the surface free energy of this glass was calculated from the contact angles, which were measured for the two probe liquids Milli-Q water and diiodomethane (Wako Pure Chemical Industries Ltd.), using the Owens-Wendt method.S6 The method divides the surface free energy into two components, dispersive (d) and polar (p), and uses a geometric mean approach to combine their contributions as 𝛾! 1 + cos 𝜃! = 2 𝛾!!𝛾!! +𝛾!!𝛾!! , where γl and γs are the liquid and solid (glass) surface tension, respectively. The total surface free

energy of the glass γs is defined as 𝛾! = 𝛾!! + 𝛾!!. Respective γld and γl

p values of 21.8 and 51.0 for water and 49.5 and 1.3 for diiodomethane were used in the calculations. S6 The θc of diiodomethane was 38.6 ± 0.7°, giving a γs value of 63.1 mJ m-2, with γs

d and γsp values of 30.3 mJ m-2 and 32.8 mJ m-2, respectively.

The droplets of suspensions prepared at various concentrations were placed gently on the glass using a micropipette, while the glass surface was observed using an optical microscope; this was done to avoid places with blemishes or watermarks. These droplets were allowed to evaporate under ambient conditions at 20°C, with a relative humidity of ~30%. When R is smaller than the capillary length 𝛾 𝜌𝑔, where γ is the liquid surface tension, ρ is the density, and g is the acceleration due to gravity, the surface tension overcomes gravity and the droplet remains spherical.S5 The capillary length for water is ~2.7 mm near ambient temperatures; R was varied in this study from approximately 0.3 to 2.6 mm, to ensure that the droplets retained a spherical form.

Gravimetry of drying droplets. The mass reduction in the evaporating droplets was measured on 5-mm square cover glasses (which were cleaned using ultrasonication in ethanol), using a thermogravimetric analyzer (Q50, TA Instruments), with 5 mL/min sample purge, kept at 20°C.

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2-1. Determination of preconditions

Figure S1. Double logarithmic plots of the electric conductivity σ vs the concentration of H2SO4 aqueous solutions (a), and CH3COONa solution (b). The solid lines show the best fit to each plot. Both whisker suspensions, purified from the H2SO4 solution for acid hydrolysis using Milli-Q water, were considered to predominantly contain H3O+ and SO4

2− ions. The thickness of the double layer (Debye screening length κ-1) is non-negligible in colloidal systems with concentrations greater than or equal to semidilute solutions, in which interactions between particles are inevitable.S7 The κ-1 of the CNWs and TNWs were therefore determined from the H2SO4 concentration, which was computed using the various electric conductivities σ [Figure S1a]. The Log  𝜎 values for the CNW and TNW suspensions at φ = 0.01 (vol%), which were 1.763 and 1.924, respectively, gave the H2SO4 concentrations as 2.32 × 10-5 and 4.92 × 10-5 (M). We used these values as the representative salt concentration in each suspension to compute κ-1 as 36.55 nm for the CNWs, and 25.10 nm for the TNWs, using 𝜅!! = 0.176 H!SO! (nm).S8 The dimensions of the whiskers were then determined, as shown in Table S1.

Similarly, the SNF suspension, purified using the Wise method, was thought to largely contain Na＋ and COO− ions. We investigated the σ values of the monovalent salt solution [Figure S1b] to estimate κ-1 as 28.04 nm for the SNFs, using 𝜅!! = 0.304 CH!COONa (nm).S8

Table S1. Dimensions of the whiskers. CNWs TNWs

d 28.03 (nm) 30.57 (nm) L 279.74 (nm) 2312.62 (nm) α 9.98 75.65 κ−1 36.55 (nm) 25.10 (nm) αeff 3.49 29.25

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Figure S2. Optical micrographs of the CNP stains left on the cover glasses after the evaporation of a ~1 μL droplet, with various φ. Note 500 μm scale bars in lower right corners.

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Figure S3. Width of the ring w at the first depinning vs the ring radius R of CNWs (a), TNWs (b), and SNFs (c), at various φ. The lines running through the data show a best fit to power laws. The areas of the droplet bases at the first depinning Ad1 (normalized by the area immediately before depinning) 𝐴!" = 𝜋(𝑅 − 𝑤)! vs w/R for CNWs (d), and TNWs (e). Schematic illustration of a typical CNW coffee ring, with twice depinning (f). For all samples, the ring widths were measured at five points in each ring, for around three to five rings, with a ~1-mm radius in each sample. The single plot shows the mean values calculated from ~15 to 25 points. Each colloid in the droplets was transported near the contact lines to form a clear deposition, in accordance with the coffee ring effect [Figure S2]. The w values of every CNP increased exponentially as R became larger [Figure S3], and as φ increased [Figure 2d]. On the other hand, the Ad1/Ain value remained constant for all CNPs, independent of R or φ. Each CNP seemed to have an equally strong pinning effect, derived from their hydrophilicity, and they also showed continuity in the rings, owing to their anisotropy. This effect was thought to cause the remarkably long pinning that was observed [Figure 3a and 3b], which has rarely been reported in the case of spherical colloids. The volumes of the droplets at the first depinning were thought to be approximately equal, regardless of φ or the type of CNP; the Ad1/Ain values therefore remained constant, at 0.3−0.4.

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2-2. Theoretical details

Figure S4. Explanatory diagrams for the half angle relation (a), the triangular cross-section model for Eq. S6 (b), and the trapezoidal cross-section model for Eq. S9 (c), for coffee rings after evaporation. An SNF unit was taken to be a pseudo-sphere with radius Rg (d). The radius rp of a sphere having the same volume as the effective volume of CNWs, which should form a ring with equal w/R [green line in Figure 4e], was used to estimate Rg (e). The approximations developed in this letter fit well to the data (f). The green and red lines were theoretically determined using Eq. S6, for CNWs and SNFs, respectively. The blue line was calculated using Eq. S9 for TNWs. Though the Oseen approximation to the Navier-Stokes equation was developed for low Reynolds number viscous flow containing fixed anisotropic objects, the direct analysis of hydrodynamic flow is difficult. The hydrodynamic calculation of the movements of floating anisotropic particles (that interact with each other via Brownian motion and inter-surface interactions) in an evaporating droplet is technically difficult. Despite these difficulties, Deegan has estimated w at the first depinning by using φ as a function of t for spherical colloids, without rigorously considering their flowing process.S9 First, a rough estimate of the ring volume Vring is obtained using a cross section in the shape of a right-angled triangle [Figure S4b], as follows:

𝑉!"#$ = 𝜋𝑅𝑤!𝜃!, (S2)

with the approximation of tan 𝜃! ≅ 𝜃!. Meanwhile, the volume of a partial sphere, Vp, is given by

𝑉! =𝜋6 ℎ 3𝑅! + ℎ! , (S3)

with h the droplet height when the droplet is spherical 𝑅 < 𝛾 𝜌𝑔 . Since the half angle method for measuring 𝜃! gives the relation ℎ/𝑅 = tan(𝜃!/2) [Figure 4Sa], Vp is then approximated as

𝑉! ≈𝜋𝑅3𝜃c4 , (S4)

with 𝜃!! 12 ≪ 1. Then, from the initial droplet conditions (in terms of φ), Vring can be expressed as the

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volume of deposited particles with a mean packing fraction p, at time t, as follows:

𝑉!"#$ = 𝑝!! 𝜋𝑅3𝜃c4 𝜙 1 − 1 − 𝑡

𝑡f

34

43

, (S5)

where the prefactor is the total amount of solute in the drop at 𝑡 = 0 multiplied by the inverse of p. By combining Eq. S2 and S5, we obtained

!!= !

!!1 − 1 −

!!!

!!

!!

, (S6)

for 𝑡 ≪ 𝑡!. By focusing on the volumetric relation, w/R can be expressed in terms of φ and p, and our target was to extract the different p due to the different excluded volumes in the samples. Our experiments showed that 𝑡!" 𝑡! ≈ 𝑡!" 𝑡!"!#$ ≈ 1 [Figure 3a, 3b], so we ignored the time term in Eq. S6 and set it to 1. Then, we obtained a good fit to the CNWs data with 𝑝 = 0.656 [the green line in Figure S4f]. The CNW with αeff of ~3.5 was found to form coffee rings with a large p of 0.656, which was equal to that for spheres. We compared the other samples with the results for the CNWs. We hypothesized a novel model with a trapezoidal cross section for the TNWs [Figure S4c]. The nematic region with a large p was approximated as the cross-section of a right-angled triangle using Eq. S6, and the following isotropic region with the smaller p was approximated as a thin film, because ℎ ≪ 𝑅. Then, Vring of an annulus with a trapezoidal cross-section is

𝑉!"#$ = 𝜋𝑅𝑤!!𝜃! + 𝜋𝜃! (𝑅 − 𝑤!)! − 𝑅 − 𝑤! − 𝑤! ! , (S7)

with the approximation tan 𝜃! ≅ 𝜃!. Here, the width of nematic region w1 was negligibly small compared with w2, so we approximated Eq. S7 to

𝑉!"#! = 𝜋𝜃!𝑤 2𝑅 − 𝑤 , (S8)

with 𝑤! ≈ 𝑤. Then, combining Eq. S8 with Eq. S5 produced

!!= !"

!!1 − 1 −

!!!

!!

!!

. (S9)

We kept the time term here only for completeness, and set it to 1. Eq. S9 fit well to the TNW data, with 𝑝 = 7.14×10!! [the blue line in Figure S4f]. SNFs with a random-coil structure in water showed an exponent of logarithmic w/R vs φ similar to that shown by the CNWs [Figure 2d]. The whiskers results described above indicated that the exponent of logarithmic w/R vs φ reflected the p of the particles in the rings. We then considered that the excluded volume of both was apparently small, and assumed a pseudo-sphere for the single unit of coiled SNFs, with a radius Rg [Figure S4d]. Rg differs from the so-called hydrodynamic radius, and contains the thickness of the double layer (κ-1) of the SNFs. Here, we intended to find two parameters; the volume fraction of SNFs accounted for in the pseudo-sphere, φf, and its radius, Rg. Regarding the former, we applied Eq. S6 to the SNF data, and obtained a good fit, with an apparent packing fraction papp = 95 [the red line in Figure S4f]; the p of the pseudo-sphere itself should have been 0.656. The difference between p and papp was considered to represent φf, so 𝜙! = 𝑝 𝑝!"" = 6.905×10!!. Regarding the latter, the w/R value for the SNFs was 7.89 times larger than that

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for the CNWs, as determined using Eq. 1 [red and green line in Figure S4f]. This meant that the Rg was 7.89 times larger than the radius rp of a sphere with a volume equal to the effective volume of the CNWs [Figure S4e]. We calculated the value of rp as

𝑟! = 34𝑑eff2

!𝐿!""

13. (S10)

Under our conditions, rp = 87.86 nm, with the deff and Leff values of the CNWs, and simultaneously, 𝑅! = 7.89×𝑟! = 693.22  nm. We then obtained the volume of the pseudo-sphere Vg as 𝑉! = (4 3)𝜋𝑅!!, and the volume fraction of SNFs in the pseudo-sphere as 𝜙! = 6.905×10!!, so LS was given by

𝐿! =𝑉g𝜙f

𝜋(𝑑 2)2, (S11)

with d being the characteristic diameter of the objective. Under our conditions, LS was tentatively estimated as 11.33 μm, with the arithmetic diameter of the SNFs as d = 32.91 nm (α = 344). References S1. Bercea, M. Macromolecules 2000, 33, 6011–6016. S2. Wise, L. E.; Murphy, M.; D’Addieco, A. A. Pap. Trade J. 1946, 122, 35–43. S3. Loader, N. J.; Robertson, I.; Barker, A. C.; Switsur, V. R.; Waterhouse, J. S. Chem. Geol. 1997, 136, 313–317. S4. Uetani, K.; Yano, H. Langmuir 2012, 28, 818–827. S5. de Gennes, P. –G.; Brochard-Wyart, F.; Quéré, D. Capillary and Wetting Phenomena, Springer: New York, 2003. S6. Owens, D. K.; Wendt, R. C. J. Appl. Polym. Sci. 1969, 13, 1741–1747. S7. Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics, Oxford University Press: New York, 1986. S8. Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed; Academic Press: London, 1992. S9. Deegan, R. D. Phys. Rev. E 2000, 61, 475–485.