Non-destructive and Quantitative Viscoelastic-Mapping of Cellulose Nanobrils Using Low-Total-Force Contact Resonance Force Microscopy (LTF-CRFM)1

. Low-total-force contact resonance force microscopy (LTF-CRFM), an atomic force 13 microscopy method, is introduced as a non-destructive means to quantify the local viscoelastic 14 loss tangent ( tan 𝛿) of cellulose nanofibrils (CNFs). The method limits static and dynamic forces 15 during measurement to minimize substrate and geometry effects and to reduce the potential for 16 stress-induced CNF damage. LTF-CRFM uses Brownian motion to achieve the thermally-limited 17 lowest dynamic force, while approaching adhesive pull-off to achieve the low static force. LTF- 18 CRFM measurements were shown to generate analyzable data without evidence of nonlinear 19 artifacts and without damage to the CNF over static forces ranging from 11.6 nN to 84.6 nN. The 20 measured tan 𝛿 of CNFs was 0.015 ± 0.0094, which is the first reported tan 𝛿 measurement of an 21 isolated CNF. Finally, LTF-CRFM successfully mapped tan 𝛿 along the length of CNFs to 22 determine that kink defects along the CNF do not impart a local viscoelastic property change at 23 the length scale of the measurement.

) and mechanically-induced deformations (Ciesielski et al. 2019). CNFs contain 48 alternating highly ordered crystalline regions and disordered amorphous regions (Zhang et al. 49 2013), where the elastic modulus is expected to be greater in the crystalline region compared to 50 the amorphous region since the crystalline cellulose modulus is 5 to 10 times greater than the CNF 51 modulus (Nishiyama 2009). For cellulose derived from plant species, the degree of crystallinity

92
Beyond the elastic CRFM measurements reported in (Wagner et al. 2016), CRFM also allows for 93 the measurement of viscoelastic properties, such as storage modulus ( ′ ), loss modulus ( ′′ ), and 94 loss tangent (tan ). This work seeks to address some of the limitations of prior CRFM work by 95 operating with much lower total forces while simultaneously expanding the materials 96 characterization to include viscoelasticity. Understanding the viscoelastic behavior of a material is 97 important for material development and performance. Notably, the unexpected effects of 98 viscoelastic behavior discovered during the usage of a material can be anticipated and mitigated.

99
As shown in Figure 1a, dynamic mechanical analysis (DMA) is a common technique to measure 100 viscoelastic properties. To summarize, a sinusoidal stress is applied to a sample and the recorded 101 strain response will lag by a phase angle ( ) that is related to the time lag (∆ ). From the stress,

204
Cellulose-β fibrils were dispersed using an aqueous solution on a UV-ozoneand plasma-treated 205 silicon wafer or a UV-ozone-and plasma-treated glass slide.

252
LTF-CRFM measurements were taken in a line of single points (Figure 2)

279
To evaluate the effect of total force on CRFM response, Figure 3 shows the results from Brownian peaks for all dynamic forces are easily detectable. However, the contact resonance peak for the 300 highest dynamic force (∆ 2 ) shows a nonlinear response as evidenced by the asymmetric skew 301 in the peak and the deviation from the DHO fit. At the lower static force of 1.2 nN, the peaks become broader as the dynamic force increases resulting in a reduced capacity for peak detection.

303
In the absence of non-linear effects or varying contact properties (e.g., tip radius and sample 304 viscoelasticity), it is expected that all three excitation techniques would result in identical 1 and 305 1 results as a function of applied force. In the cases shown, the 1 and 1 appear reduced for the 306 low static forces with larger amplitude photothermal excitation compared to the smaller excitation 307 amplitudes. Although this non-linear effect is less pronounced than the skew at higher force, it 308 would directly affect calculated elastic and dissipative material properties. For example, a lower 309 1 will correspond to a lower contact stiffness and thus Young's modulus of the surface. The lower 310 1 , at the same resonance frequency, will correspond to an inversely proportional higher tan for contact.
337 Figure 3c shows 1 as it relates to 1 for mode 1. At a given 1 , tan is inversely proportional 338 to 1 (Figure 1b). Over the range of 1 , the 1 trends higher as the applied dynamic force 339 increases from ∆ to ∆ 1 to ∆ 2 . To further analyze the difference in 1 between the 340 dynamic forces, a power fit was applied to each dynamic force data set. Then, as shown in the 341 inset, the % change in 1 was computed using the power fit to compare ∆ to ∆ 1 and ∆ 2 ,

350
In addition to localizing the stress field, total forces must also be considered in regard to potential  water. When compared to fabricated CNF materials, the quantified tan from this study is lower 432 which is likely due to the influence of the epoxy constituent and cellulose-cellulose interaction.

433
The low value of tan from this study substantiates the crystalline molecular structure that occurs

472
Four CNF arrangements, shown in Figure 6, were identified for tan property mapping to analyze