Small Angle X-Ray Scattering (SAXS)

The representation of the intensity recorded during a SAXS experiment against the scattering vector (q2_{) after proper corrections and background subtraction as}

presented in the annex (A1.2) gives the SAXS profile of the samples. In Figure 2.18 a, the SAXS profiles of the lignin derived hard carbons synthesized according to the second synthetic methodology are shown. This series of samples was chosen because the range of temperatures of pyrolysis used (700- 1000 ºC) allows the study of the evolution of the porosity with the temperature. Figure 2.18 b shows the comparison of the SAXS profile of the lignin derived hard carbon sample showing best electrochemical performance among the samples synthesized through methodology B (as will be further discussed) and a sugar derived hard carbon (HC-SA) and a soft carbon synthesized from PVC (SC- PVCHM).

Figure 2.18 a) I vs. Q profiles of lignin derived carbons synthesized through method B, b)

comparison of the I vs. Q profiles of lignin derived hard carbon synthesized at 900 ºC (HC-L900-07), of sugar derived hard carbon (HC-SA) and PVC-derived soft carbon (SC-PVCHM).

All the samples show an intensity profile typical of porous materials with a large intensity at low q decaying as q-4_.

77 Intensity (I) can be defined by as follows:

𝐼 (𝑄) = (∆𝜌)2_{∑ 𝑛}

𝑖𝑉𝑝𝑖2𝑃𝑖(𝑄)

𝑖 (a.u.) Eq.2.2

The intensity I(Q) is a sum of all the contributions of the objects (particles or pores). Δρ is the contrast of scattering length between carbon and vacuum, ni is

the amount of particles, Vpi their volume, and Pi(Q) is the form factor which

depends on the shape and size of the particles and whose value is normalized to 1 at low Q and decreases as Q increases. The form factor Pi(Q) can be

approximated by a Gaussian curve at small angles. According to Guinier68_{, the}

curvature of this Gaussian is due to the overall size of the particles so that: 𝑃(𝑄) ≈ 𝑎0 exp (−𝑅𝐺2

𝑞2

3) Eq.2.3

RG is the radius of gyration and can be used to calculate particle dimensions.

Assuming that the particles are spherical with an equal density, the average radius can be calculated by

𝑅 = √5/3 𝑅𝐺 Eq.2.4

The parameter a0 is the extrapolated zero-angle intensity. In the equation above

a0=1 because P(0)=1 by definition, but if ΔI(q) is used instead, then a0=ΔI(0),

which can be used to represent the Guinier plot. In the Guinier plot, the logarithm of the intensity is plotted vs. the square of the length of the scattering vector (q2_).

ln[∆𝐼(𝑞)] = ln[𝑎0] − 𝑅𝐺2

3 𝑞

2 _Eq.2.5

The RG and a0 are determined by straight-line fitting from the slope (-R2G/3) and

from the intercept (ln(a0)) as shown in Figure 2. 19.

68 _{Schnablegger, H. and Sing, Y., The SAXS guide: getting acquainted with the principles, 2011,}

78

Figure 2. 19 Linear fit of the Guinier plots of lignin derived carbons synthesized through method B

(a) and PVC derived soft carbon (SC-PVCHM) and sugar hard carbon (HC-SA)

The determination of RG allows the calculation of the radius of the pores.

Although both carbon particles and pores give rise to SAXS intensity, it happens at different Q ranges since particles are typically micrometric while pores can be as small as a fraction of nanometers. SAXS does not make any distinction if the pores are open or buried and thus inaccessible from the surface by a gas or an electrolyte.

The scattering contrast (Δρ) between carbon and vacuum has been calculated on the basis of a scattering length of 8,504· 1010 _cm.g-1 _{for carbon}69 _{multiplied by}

the density of the carbons.

∆𝜌 (𝑐𝑚−2) = 𝜌 (𝑐𝑚 · 𝑔−1) · 𝑑(𝑔 · 𝑐𝑚−3_{) Eq. 2.6} The density of the carbons (dcarbon) was calculated considering the density of

graphite (dgraphite =2.2676 g·cm3), the interplanar distance of graphite (d002graphite)

and interplanar distance of carbons (d002carbon)

79

𝑑𝑐𝑎𝑟𝑏𝑜𝑛(𝑔 · 𝑐𝑚3) =

𝑑𝑔𝑟𝑎𝑝ℎ𝑖𝑡𝑒 (𝑔 · 𝑐𝑚−3) · 𝑑002 𝑔𝑟𝑎𝑝ℎ𝑖𝑡𝑒

𝑑002 𝑐𝑎𝑟𝑏𝑜𝑛

Eq. 2.7

The interplanar distance of carbons (d002carbon) was calculated by obtaining the

position of the 002 peak in the XRD patterns through mathematical fitting using a pseudo-Voigt function (Figure 2.20).

Figure 2.20 Fitting of the XRD patterns of lignin derived hard carbons (a) and sugar hard carbon

and PVC soft carbon (b) with a pseudo-Voigt function.

The porous volume (Vp) can be calculated from the following equation

considering the scattering contrast (Δρ), the zero-angle intensity (I0) and the

average pore radius (R). 𝑉𝑃(𝑐𝑚3· 𝑔−1) =

𝐼0 (𝑐𝑚2· 𝑔−1) (∆𝜌)2_(𝑐𝑚−4

) · 4 3⁄ 𝜋𝑅3_(𝑐𝑚) Eq. 2.8

In Figure 2.21, the average pore diameter and pore volume of lignin derived hard carbons synthesized through B methodology are represented vs. the temperature of pyrolysis together with sugar derived hard carbon (HC-SA) and PVC derived soft carbon.

80

Figure 2.21 Average pore diameter and pore volume vs. temperature of pyrolysis of lignin derived

hard carbons synthesized following B methodology at different temperatures (squares), of sugar derived hard carbon (HS-SA, circles) and PVC derived soft carbon (SC-PVCHM, triangles).

It is observed that for lignin derived hard carbons the pore diameter increases with the temperature of pyrolysis. This is consistent with the “falling cards model” (Figure 2.22) proposed by Buiel et al.70 _{According to this model, micropores}

separated by a single graphene sheet coalesce when a single layer becomes mobile at high temperature and aligns with neighboring layers in a process similar to graphitization on a very small scale.

Figure 2.22 The “falling card model” for hard carbon. Solid lines represent graphene sheets.

The fact that pore volume remains more or less constant with increasing temperature of pyrolysis while the pore diameter increases, suggests that no new microporosity is created upon heating at higher temperatures.

70 _{Buiel, E.; George, A. E. and Dahn, J. R.; On the reduction of lithium insertion capacity in hard}

carbon anode materials with increasing heat-treatment temperature, J. Electrochem. Soc.,1998, 145 (7), 2252-2257.

81

The average pore volume is similar to that of sugar derived hard carbons at high temperatures of pyrolysis whereas it is more similar to that of PVC- soft carbons at low temperatures. These similarities in the pore diameter of carbons that have been synthesized at similar temperatures may indicate that the temperature of pyrolysis has a stronger effect on the development of the porosity than the nature of the precursor.