Hierarchical Incorporation of Reduced Graphene Oxide into Anisotropic Cellulose Nanofiber Foams Improves Their Thermal Insulation

Anisotropic cellulose nanofiber (CNF) foams represent the state-of-the-art in renewable insulation. These foams consist of large (diameter >10 μm) uniaxially aligned macropores with mesoporous pore-walls and aligned CNF. The foams show anisotropic thermal conduction, where heat transports more efficiently in the axial direction (along the aligned CNF and macropores) than in the radial direction (perpendicular to the aligned CNF and macropores). Here we explore the impact on axial and radial thermal conductivity upon depositing a thin film of reduced graphene oxide (rGO) on the macropore walls in anisotropic CNF foams. To obtain rGO films on the foam walls we developed liquid-phase self-assembly to deposit rGO in a layer-by-layer fashion. Using electron and ion microscopy, we thoroughly characterized the resulting rGO-CNF foams and confirmed the successful deposition of rGO. These hierarchical rGO-CNF foams show lower radial thermal conductivity (λr) across a wide range of relative humidity compared to CNF control foams. Our work therefore demonstrates a potential method for improved thermal insulation in anisotropic CNF foams and introduces versatile self-assembly for postmodification of such foams.


Table of Contents
Section S1.Miscellaneous Figures and Tables……………………………………….(C) Production of rGO -CNF foams.A foam was affixed to a Styrofoam plate using needles.The foam was then soaked by dropwise addition from the top, first with methanol, and then with methanol:water mixtures of successively higher water fractions (Table S2).After soaking the foam in 5:1 methanol:water, GO+ in 5:1 methanol:water was added to the foam, followed by GO (in 5:1 methanol:water).The foams were then soaked with methanol:water mixtures of successively lower water content, until the foams were completely soaked in pure methanol (Table S2).The foams were then dried at 55 °C.Finally, the foams were vapor-reduced by hydroiodic acid / acetic acid.(D) CNF control foams were produced exactly as described in (C) (same methanol:water compositions, same added volumes, same drying and reduction protocols), except that GO+ and GO were not added.One batch of native CNF foams were used to make both rGO -CNF foams and CNF control foams.

S-5
Table S1.Comparison of physical properties between rGO -CNF and CNF control foams.
Errors are given with 95 % confidence.Refer to the methods section, main paper, for determination of densities, overall porosities, and specific heat capacities (Cp,dry).Refer to Figure S7 and S8 for determination of average macropore sizes.Refer to Figure S9 and Figure S10 for determination of number density of macropores.Refer to Figure S11 and Figure S12 for determination of BET surface areas.Table S2.Mixtures used in each impregnation step to make rGO -CNF foams.Note that the mixtures were chosen so that the change in surface tension was the same between each step (Δγ ≈ 0.8 mN m -1 ).

Density
We did this to avoid large surface tension gradients in the foams during impregnation, since we surmised that large surface tension gradients potentially could deform the foams.Surface tensions of methanol:water mixtures were taken from reference 1 .

S-6
Table S3.Mixtures used in each impregnation step to make CNF control foams.Note that the mixtures were chosen so that the change in surface tension was the same between each step (Δγ ≈ 0.8 mN m -1 ).The order, volume, and methanol:water composition of each addition is the exact same as for production of rGO -CNF foams (Table S2), except that GO+ and GO were not added.Surface tensions of methanol:water mixtures were taken from reference 1 .The pore-size distribution was obtained by BJH analysis of the isotherms, and is presented in the inset.Note the similarity of the pore-size distribution between CNF control foams (here) and the rGO -CNF foams (Figure S12).The pore-size distribution was obtained by BJH analysis of the isotherms, and is presented in the inset.Note the similarity of the pore-size distribution between the rGO -CNF foams (here) and the CNF control foams (Figure S11).

Section S2. GO and GO+ AFM image statistics
Image statistics for GO and GO+ were generated by depositing GO or GO+ suspensions in 5:1 methanol:water on a SiO2 wafer, followed by AFM characterization.

S-16
Section S3.Statistical significance of difference in thermal conductivity (axial and radial) between rGO -CNF and CNF control foams.
t-tests to judge significance of differences between thermal conductivities at each RH.At each relative humidity, and for each type of sample (rGO -CNF foam or CNF control foam), axial and radial thermal conductivity was measured in three individually produced foam-pairs (one pair is needed for one individual thermal conductivity measurement).Below, we illustrate how, using a two-sided t-test, 22 these measurements are used to determine with which significance the radial thermal conductivity in rGO -CNF foams are lower than in CNF control foams at RH 20 %.The determinations of the respective significances at other relative humidities are analogous.At RH 20 %, we determine the following quantities: The subscript 1 denotes the rGO -CNF foam, 2 denotes the CNF control foam.We then form the null hypothesis (H0), that the true radial thermal conductivities at RH=20% are the same, i.e.

H0: 𝜆
Because the radial thermal conductivities for the rGO -CNF foams and CNF control foams are similar, and because the thermal conductivities are measured on one instrument (TPS 2500 S) by the same procedure, we assume that the variances for the experimental estimations of  ,1 and  ,2 are approximately equal so that a pooled estimation of the standard deviation can be introduced. 22At RH 20%, we have: The degrees of freedom (d.f.) for the pooled standard deviation is: We can now introduce the statistic t: For d.f.= 4, this value for the statistic t, gives a p-value of 0.26.The null hypothesis (H0:  ,1 =  ,2 ) can therefore be rejected at the 74 % level of significance.i.e., at RH 20 %, the radial thermal conductivity of rGO -CNF foams is lower than the radial thermal conductivity of CNF control foams with 74 % significance.At the remaining RHs (35, 50, 65, 80) %, the t-test gave the significances (89, 81, 99, 95) % that the radial thermal conductivity of rGO -CNF foams is lower than the radial thermal conductivity of CNF control foams.
A two-sided t-test was applied to the axial thermal conductivities in an analogous fashion as described above.The p-values for the null hypothesis H0:  ,1 =  ,2 were (0.67, 0.32, 0.62, 0.96, 0.51) at RH (20,35,50,65, 80) %.The null hypothesis is therefore retained at (67, 32, 62, 96, 51) % levels of significance for RH (20,35,50, 65, 80) %, meaning there is no experimental support that the axial thermal conductivity differs between the rGO -CNF foams and the CNF control foams at any RH.Two-sided, paired t-test 22 to judge significance that the radial thermal conductivity overall is lower in rGO -CNF foams than in CNF control foams.At each RH, we form the difference between the estimation of radial thermal conductivity in the CNF control foam ( ,2 ̅̅̅̅̅ ) and the estimation of radial thermal conductivity in the rGO -CNF foam ( ,1 ̅̅̅̅̅ ).This creates a set of differences, in our case  = (4.7,4.6, 2.8, 4.3, 8.0) mW m -1 K -1 .A null hypothesis can then be formed that the estimations  ,1 ̅̅̅̅̅ and  ,2 ̅̅̅̅̅ pairwise (at each RH) are drawn from the same population, or equivalently that the average of the pairwise differences (µ  ) is zero, i.e.: This null hypothesis gives rise to the statistic t: 22

𝑡 = 𝑑 ̅ √𝑛 𝑆 𝑑
where  ̅ is the experimental estimation (calculated from the d-values obtained above) of the true average of the pairwise differences (µ  ), n is the number of pair-wise differences and Sd is the estimation of the standard deviation for the measurement of d.For our set of pair-wise differences, we have  ̅ = 4.9 mW m -1 K -1 , Sd = 1.9 mW m -1 K -1 and n = 5, giving the following t-value:  = 4.9√5 1.9 = 5.8 For d.f.= 5 -1 = 4, this value for the statistic t, gives a (two-sided) p-value of 0.005.Thus, the null hypothesis, H0: µ  = 0 can be rejected with 99.5 % significance, suggesting very strongly that,  ,1 <  ,2 at all considered RHs.I.e., the paired t-test strongly suggests that the radial thermal conductivity of rGO -CNF foams are lower than the radial thermal conductivity in CNF control foams, irrespective of the RH.

S-18
Paired t-test to judge significance that the axial thermal conductivity overall is different in rGO -CNF foams compared to in CNF control foams.This two-sided paired t-test is carried out in analogy with the above-described paired t-test for the radial thermal conductivities.In this case we find that the p-value for the null hypothesis H0: µ  = 0 is p = 0.32.The null hypothesis is therefore retained with a significance of 32 %.Therefore, considering difference in axial thermal conductivities at all RHs, there is no experimental support that the axial thermal conductivity differs between the rGO -CNF foams and the CNF control foams.
Figure S1.CNF Characterization.(A) AFM micrograph of CNF on freshly cleaved mica.(B, C) Image statistics (from AFM micrographs).(B) Distribution of CNF contour heights (average height, <h> = 2 nm).(C) Distribution of CNF contour lengths (average length 800 nm).N = 50 individual fibers were used for image statistics.Fibers that appeared entangled with other fibers were not used for length statistics.The length statistics should therefore be regarded as approximate.

Figure S2 . 3 Figure S4 .
Figure S2.Image statistics to determine macropore size in native, anisotropic CNF foams.(A) Top view of foam.To measure macropore cell-diameters, the projected area (one cell-area marked orange for illustration) of a macropore was measured, then the equivalent disc-diameter was calculated.(B) Distribution of equivalent disc-diameters for native CNF foams.For the distribution, 100 individual cells were measured.

Figure S3 .
Figure S3.Analysis of zeta potentials (ζ) of: GO and GO+ in pure water and in 5:1 methanol:water mixtures, and of CNF in a 5:1 methanol:water mixture.(A) Illustrated by graphical charts.(B) Represented by zeta potential distribution curves.

Figure S6 . 8 Figure S7 .
Figure S6.Typical FIB micrograph of CNF control foam.No film of sheet-like structures was observed (as in rGO -CNF foams, Figure4 E).Imaging was difficult, because of significant charging under the beam, deforming the foam within seconds.In contrast, the rGO -CNF foams were not charging under the beam (Figure4 E), using the same FIB settings.

Figure S8 . 9 Figure S9 .
Figure S8.Image statistics to determine macropore size in rGO -CNF foams.(A) Top view of foam.To measure macropore cell-diameters, the projected area (one cell-area marked orange for illustration) of a macropore was measured, then the equivalent disc-diameter was calculated.(B) Distribution of equivalent disc-diameters for rGO -CNF foams.For the distribution, 100 individual cells were measured.

Figure S10 .Figure S11 .
Figure S10.Illustration of how number density of macropores in CNF control foams was estimated from SEM micrographs.Top view of foam.To measure number-density of macropores, all macropores wholly inside one SEM micrograph was counted, and their total area measured.The number density was then calculated as number of macropores / total cross-sectional area of macropores. 4 micrographs of different foam-regions were used, which resulted in an estimation of the number density of pores of 19.9 mm -2 ± 6.8 mm -2 (95 % confidence).

Figure S12 .
Figure S12.N2 adsorption (crosses) and desorption (open circles) isotherms for the rGO -CNF foams.BET analysis of the data yielded a surface area of 5.0 m 2 g -1 .The pore-size distribution was obtained by BJH analysis of the isotherms, and is presented in the inset.Note the similarity of the pore-size distribution between the rGO -CNF foams (here) and the CNF control foams (FigureS11).
For both height and roughness statistics, 10 individual sheets were measured for both GO and GO+.An illustration of how the height of one individual sheet was measured is given in Figure S13.An illustration of how the roughness of one individual sheet was measured is given in Figure S14.For calculation of 95 % confidence intervals about the mean heights (ℎ  ̅̅̅̅̅ and ℎ + ̅̅̅̅̅̅ ) and mean roughnesses ( , ̅̅̅̅̅̅̅ and  , ̅̅̅̅̅̅̅ ), gaussian distributions of errors were assumed.

Figure S13 . 15 Figure S14 .
Figure S13.Illustration of how height in one individual GO+ sheet was measured.GO sheets were measured in the same fashion.10 individual sheets were used to determine the average sheet height.

Table S4 .
Comparative analysis of thermal conductivity and thermal conductivity anisotropy ratio in 86various materials reported in the literature.87

Table S5 .
Electrical conductivity, in the axial direction, of the rGO-CNF foam, and the CNF control foam.

Table S6 .
Relative humidity (RH) dependent densities (kg m -3 ) of rGO -CNF foams and CNF control foams.Three foams of each type were used for measurement.Errors are given with 95 % confidence.
Estimation of the true radial conductivity ( ,2 ), of the CNF control foam.Given by the average of three individual measurements.At RH 20%, we have  ,2 ̅̅̅̅̅ = 37.9 mW m -1 K -1 .Estimation of standard deviation for the measurement of  ,1 .At RH 20%, we have  ,1 = 5.8 mW m -1 K -1 .