Carbide derived carbons investigated by small angle X-ray scattering: Inner surface and porosity vs. graphitization

Carbon 146 (2019) 284e292

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Carbide derived carbons investigated by small angle X-ray scattering: Inner surface and porosity vs. graphitization €rk a, *, Albrecht Petzold a, Günter Goerigk a, Sebastian Risse a, Indrek Tallo b, Eneli Ha €rmas b, Enn Lust b, Matthias Ballauff a Riinu Ha a b

Soft Matter and Functional Materials, Helmholtz-Zentrum für Materialien und Energie GmbH, Hahn-Meitner-Platz 1, 14109, Berlin, Germany Institute of Chemistry, University of Tartu, 14a Ravila Str., 50411, Tartu, Estonia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 October 2018 Received in revised form 18 January 2019 Accepted 21 January 2019 Available online 6 February 2019

Small angle X-ray scattering (SAXS) was used to study the nanostructure of Mo2C derived carbon powders (CDC) synthesized at five different chlorination temperatures. The SAXS-intensities have two contributions: i) a fluctuation contribution from small partially graphitized areas that gives quantitative information about the extent of graphitization, and ii) the scattering from the pores. The fluctuation contribution that scales with q
2 was quantified in term of a length parameter lR and a disorder parameter that can directly be correlated with the increasing graphitization with increasing temperature. The specific inner surface area of the CDC together with the volume fraction f of the pores increases with the chlorination temperature until 900  C, followed by the significant decrease of both parameters at 1000  C. Further analysis led to the conclusion that CDC obtained at 600 and 700  C are ultramicroporous systems with slit pores having an average size of the order of 0.6 nm. CDC obtained at a high chlorination temperature have pores with sizes between 1 and 3 nm that are of the same size as the walls between the pores. A first comparison demonstrates that the stored energy Emax is directly proportional to the anisometry of the pores embodied in the ratio lc =lp obtained by SAXS. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction There is a clear need for modern electrochemical energy storage devices that can deliver discharge electricity with a high power density and low resistance [1e3]. Recently, supercapacitors have been identified as a class of efficient systems for fast storage of energy [4]. Carbide derived carbons (CDC) play a central role in the design of supercapacitors [5e10] because the pore size and the specific surface area may be tuned by varying the chlorination temperature [6,11e13]. The performance of the supercapacitors is predominantly determined by the properties of the carbon [14e16], but it is not yet clear which of the structural features of the carbon, i.e., specific surface area, pore size or pore size distribution is the decisive parameter [17e19]. It is evident, however, that micropores with diameters below 1 nm are necessary to achieve the high loading capacities [10,20]. Hence, a full understanding of the relation between the microstructure of a material and its performance

* Corresponding author. €rk). E-mail address: [email protected] (E. Ha https://doi.org/10.1016/j.carbon.2019.01.076 0008-6223/© 2019 Elsevier Ltd. All rights reserved.

as supercapacitor requires a precise analysis of the structural features from ca. 100 nm down to the subnanometer range. Up to now, most of the studies of carbonaceous materials used for supercapacitors relied on differential pore size distributions derived from gas sorption isotherms [6,11,12,20e25]. While sorption isotherms may give precise information on pores with a size larger than 1 nm, they may lead to much too large specific surface areas for ultramicroporous systems [26e28]. In addition to this, a meaningful analysis of carbonaceous nanomaterials must give information that go beyond data on porosity but also address the state of order in the solid material. The nanostructure of carbons is a well-studied problem with a long tradition and studies by wide-angle X-ray scattering date back to the forties and fifties of the last century [29,30]. This analysis has been extended considerably by Ruland and Smarsly [31] and more recently by Smarsly and coworkers [32e35]. In particular, Faber et al. presented a systematic study of the microstructure of silicon carbide derived carbons [34]. It was shown that carbonaceous materials derived from various sources present overall disordered microporous systems consisting of amorphous regions and regions in which graphene sheets of various size and mutual registry have

€rk et al. / Carbon 146 (2019) 284e292 E. Ha

been formed (cf. the review by Faber et al. [32]). It is interesting to note that this picture has found a qualitative support in recent studies employing transmission electron microscopy [36e38]. TEM-studies, however, are clearly limited by the necessity of the observation of thin samples. Moreover, a quantitative evaluation of structural details in the subnanometer region from TEMmicrographs is a difficult task [34,37]. Small angle X-ray scattering (SAXS) [39e55] and small angle neutron scattering (SANS) [11,55e60] provide the tool for a quantitative analysis of the nanostructure of carbon materials ranging from a few 100 nm down to ca. 0.5 nm. The scattering curves I(q), (q: magnitude of scattering vector) of partially ordered carbon materials as measured by SAXS and SANS, however, contain only few marked features and defy direct interpretation. There is an additional problem: Classical theory predicts that porous systems characterized by sharp interfaces should decay with q
4 (Porod's law; see Refs. [61,62]). However, the scattering intensity measured for numerous carbonaceous materials [31,42,50,54,55,63] exhibit a much smaller exponent of the order of
3. This finding has prompted the interpretation of the local structure of such materials in terms of a fractal [49,51,57]. This modeling, however, has been rejected by Ruland [64]. Moreover, the q-range in which this exponent may be observed is too small for a meaningful assignment to a fractal structure. The pores in carbon materials have also been modeled by assuming a distribution of polydisperse spheres [65,66] or slits [67]. For the present materials, however, a smooth spherical shape of the pores can definitely be ruled out [54]. Moreover, a model-free approach for the evaluation is certainly superior to an approach that assumes a given shape of the pores. At present, most investigations [11,47,52,68,69] of carbon materials using SAXS or SANS follow Kalliat et al. [70] in interpreting the scattering intensity in terms of the correlation function of Debye, Anderson and Brumberger [71]. As already mentioned above, however, most carbon nanomaterials contain graphene-like structures with a typical length scale of ca. 1 nm [32,33]. This fact is also well-established by TEM-studies [37] and by simulations [38]. Therefore, the interpretation of the small-angle scattering by application of the theory by Debye et al. [71] cannot lead to correct results because these features will give additional scattering conring in tributions when probed by SAXS or SANS. Schiller and Me 1967 seem to have been the first to notice this problem and to show that the measured intensity I(q) has an additional term that scales with q
2 [72]. They demonstrated that the additional contribution to I(q) is caused by fluctuations in layer spacing and size of the imperfectly stacked graphene layers. Perret and Ruland used this term when characterizing the microporosity of non-graphitizable and glassy carbons by SAXS [42,50,64,73]. Smarsly et al. have improved this analysis of SAXS-data of carbon materials [44,74]. In particular, these workers [44] introduced the evaluation of the data in terms of the chord length distribution [75]. Recently, we have used this approach for the characterization of microporous carbon materials used for lithium-sulfur batteries [54]. We could demonstrate that analysis of the SAXS-data of such a material leads to their full characterization beyond porosity and internal surface. Here, we present an analysis of five different carbon powders synthesized from molybdenum carbide as a function of the chlorination temperature (from 600  C to 1000  C) [13] by SAXS. It is the main goal to furnish the full set of structural parameters of these CDC that allow us to discuss the porosity and the internal surface in relation to the degree of graphitization. In this way the present comprehensive set of SAXS data may be compared to data obtained by different methods [13,37]. In a final step the structural information obtained here will be compared to electrochemical data [6].

285

2. Materials and methods 2.1. Carbide derived carbon The chlorination of carbides is the most straightforward and scalable method for synthesis of well-defined carbon materials [16e19,21,68]. The preparation of the molybdenum carbide derived carbon powder has been presented in detail elsewhere [6,13]. Five CDC powders were synthesized from molybdenum carbide (Mo2C, r ¼ 9.12 g cm
3, 99.5% purity,
325 mesh powder, Sigma-Aldrich) by high-temperature treatment with Cl2 (99.99% purity, AGA, The Linde Group) at a flow rate of 50 ml min
1, using a stationary bed reactor, according to the simplified reaction scheme eq. (1) [13]:

Mo2 C ðsÞ þ 5Cl2 ðgÞ/2MoCl5 ðgÞ þ CðsÞ

(1)

The CDC carbons thus obtained were thereafter cleaned with hydrogen at 900  C for 1.5 h [6,13]. In the following, all samples are noted in the text as CDC_T where T stands for the chlorination temperature used in the synthesis (600, 700, 800, 900 or 1000  C, respectively). Transmission Electron Micrographs for synthesized carbide derived carbon powders are presented in Supplementary Information Fig. S1. Electrochemical testing for active materials discussed here were previously conducted by various regimes in the two-electrode standard test cell filled with 1M (C2H5)3CH3NBF4 in acetonitrile [6] (see Supplementary Information).

2.2. Small angle X-ray scattering Measurements were performed on an SAXSess (Anton Paar) using slit collimation with monochromatic Cu-Ka radiation with a wavelength of 0.154 nm. The SAXS instrument is equipped with a one dimensional position sensitive detector (Mythen 2R, Dectris). Scattering of the samples was acquired within the range of scattering vectors 0.1 < q < 7 nm
1. The sample chamber was evacuated to 0.5 mbars to avoid air scattering. The desmearing of the data was performed by the Strobl algorithm [76] with improved numerical stability [77] including error propagation. The data are corrected for sample transmission, background scattering detector sensitivity and normalized to the primary flux. The scattering curves are calibrated in units of macroscopic scattering cross section, i.e., cm
1 via measurement of the fluorescence of a Fe-foil (Goodfellow, thickness 20 mm), which was calibrated with water as a primary standard. Thereafter the macroscopic scattering cross-sections have been normalized to the apparent (powder) density of the carbon material rf , giving cm2$g
1 units. The powder density was determined from the sample mass m (balance accuracy 0.1 mg) and the known volume Vcell of the filled powder cell (see Supplementary Information).

2.3. Small angle X-ray Scattering Theory In the following, we use the analysis of the SAXS-data introduced by Ruland and co-workers [42,50,64,73] and applied recently to microporous carbon materials [54,55,60]. Here we gather the main equations necessary for this evaluation. We consider a powder material that does not fill the entire scattering volume. Therefore the differential scattering crosssection is normalized to the mass by dividing the normalized scattering intensity by the apparent filling density rf of the powder, giving units of cm2 $g
1:

€rk et al. / Carbon 146 (2019) 284e292 E. Ha

286

dSm 1 ds ðqÞ ¼ ðqÞ; dU rf dU

(2)

where q ¼ ð4p=lÞsinq is the magnitude of scattering vector with the s ðqÞ represents the wavelength l and the scattering angle 2W. ddU macroscopic cross-section in units of cm
1. In general, the macroscopic scattering cross section of porous carbon represents a superposition of two different scattering contributions [42,72]:

dSpores dSm 1 ds dSfluct ðqÞ ¼ ðqÞ ¼ ðqÞ þ ðqÞ dU r f dU dU dU

(3)

(4)

where Bfl defines the scattering contribution of the carbon phase (dominating at the large q-values) and lR describes the extent of the lateral correlations. It thus provides a measure of the lateral dimensions of the graphene sheets embedded in the material. In order to determine the fluctuation term, a modified Porod's law [42,44,50,54,72] is employed for the large q-values by combining eqs. (3) and (4):

P

¼

Dr2

S ð2pÞ3 m

1


Dr2

00

lP g ðrÞ þ 2p3 PdðrÞ

lSAXS ¼ p

(8)

Qm ¼ ð1
fÞlpore ¼ flsolid 2p3 Pm

(9)

where Qm are the invariant of the system expressed per unit mass, the porosity f and the mean chord length of the pore and solid lpore and lsolid , respectively. The comparison of the average chord length calculated by eq. (8) with the value calculated by eq. (9) may then serve for a consistency check of the data. The mean chord length of the pores lpore and the matrix lsolid are derived from the lp and the porosity by:

lpore ¼

lp lp ; l ¼ 1
f solid f

10

The invariant

Qm ¼

Qm ¼

(6)

where Dr is the scattering contrast of carbon vs. vacuum calculated from the skeletal density [54]. dSfluct After subtraction of dU the chord length distribution (CLD) gðrÞ was calculated from the pore scattering by the approach of Smarsly et al. [44]. It should be emphasised that this analysis makes no assumptions on the shape and structure of the pores [53e55,58,60]. The CLD can be defined as the “well-behaved” part of the second derivative of the autocorrelation function g00 ðrÞ:

gðrÞ ¼

rgðrÞdr

The average chord length was also calculated directly from the scattering data as follows:

(5)

where Pm is the Porod constant and L is the structural length scale. S can be estimated from P : The inner surface area m m

rf

∞ ð

∞ ð

1 ð2pÞ

3 0

dSpores ðqÞ4pq2 dq dU

(11)

is linked to the porosity of the carbon grain f by

dSm ð2pÞ4 Pm Bfl ðqÞ / þ 2 dU qL[1 q4 q

Pm ¼

lCLD ¼ p

0

where dSpores =dU is the scattering of a two phase system with pores embedded in a homogeneous carbon matrix, dSfluct =dU is the fluctuation contribution from the lateral imperfection and finite size of the carbon layers [64,73]. Both scattering contributions are statistically independent and their scattering intensities superimpose [42]. The fluctuation contribution can be approximated by Ref. [54]:


 Bfl l2R 18 þ l2R q2 dSfluct ðqÞ ¼
2 dU 9 þ l2R q2

A finite value of gð0Þ indicates the presence of a significant number of sharp edges at the phase boundary [74,75]. As an example the scattering of spheres will give gð0Þ ¼ 0 meaning absence of any edges. The average chord length is given by the first moment of the CLD:



Dr2 fð1
fÞ rgrain

(12)

where rgrain stands for the overall density of the carbon particles/ grains. Due to the empty pores the particle density is linked to the skeletal density by rgrain ¼ rSk ð1
fÞ. The skeletal density also determines the difference in scattering length density between the carbon matrix and the pores as follows: Dr ¼ ðNA rSk re ZÞ=AC . Here NA is Avogadro's number, re the classical electron radius, Z the number of electrons per carbon atom and AC is the atomic weight of carbon. Thus, combining this with eq. (12) the porosity is given by Ref. [54]:

f¼

Qm

A2C

rSk N2A r2e Z 2

(13)

The weight-averaged chord length lc is calculated through

(7)

where lP is the number-average chord length of the system comprising both chords that go through pores and chords that go through solid material. In the case of higher-ordered porous materials, chords may go through the pores or the solid twice which leads to side maxima and zeros in gðrÞ (see the scheme Fig. S2). The interpretation of gðrÞ measured for such materials becomes a difficult task [74]. However, for the disordered carbon materials under consideration here, these higher order terms may cancel out each other and gðrÞ can be well-approximated by a sum of the chord distributions of the pores and the solid material [75]. The CLD at r ¼ 0 is related to the angularity, i.e., presence of edges of system.

lc ¼

1 2pQm

∞ ð

0

dSpores ðqÞqdq dU

(14)

The combination of the scattering contributions from the lateral imperfections of the carbon layers, Bfl , and the two-phase pore system, Qm , f, gives the degree of the disorder of the carbon by the relation [42]:

Bfl f < D2 a3 > < D 2 lR > ¼ þ 2pa3 Qm < a3 > 2 < lR > 2

(15)

where a3 is the distance of two carbon layers in the graphite crystal

€rk et al. / Carbon 146 (2019) 284e292 E. Ha

structure and corresponds to d002 ¼ 0:335 nm [30,72]. Eq. (15) introduces the degree of disorder in the material via interrelating the two scattering contributions of lateral disorder and pores. 3. Results and discussion 3.1. Analysis by SAXS The SAXS measurements for five CDC samples were conducted. The absolute scattering intensities are presented in Fig. 1a. There are three regions on the scattering curves that are comparable to previous studies on CDC [52,68] (see Fig. 1a): A low q range (q < 0.4 nm
1), an intermediate area with a shoulder (0.4 < q < 3 nm
1) and a high q law range q > 3 nm
1, containing the information on the microporous structure below 2 nm and the scattering intensity due to the fluctuations [42,44,54,72]. This indicates directly the increase in the amount of mesopores in the carbon matrix (i.e., formation of the shoulder in Fig.1a). The scattering curves in the high q-range coincide for CDC synthesized at 600, 700, 800 and 900  C, only the CDC synthesized at 1000  C deviates significantly in the region of highest

287

scattering angles. The modified Porod plots, according to eq. (4) are presented in Fig. 1b. The magnitude of Bfl was determined from the slope of the solid lines, whereas the intercept gives Pm. Evidently, the conm structed plots of q4 dS ðqÞ vs: q2 demonstrate a linear relationship dU and indicating that the determination of the fluctuation contribution is valid as previously demonstrated in the fundamental works ring [72] or Me ring and Tchoubar [75], Perret and of Schiller, Me Ruland and co-workers [31,64]. Following Smarsly et al. [44] this term can be removed by subtracting Bfl =q2 from the scattering curves if the SAXS-intensity is dominated by pore scattering. Fig. 1c shows the application of this procedure to the data obtained from CDC_1000 because in this case the fluctuation scattering only presents a minor contribution to the total scattering intensity and all scattering curves show asymptotic q
4-behaviour. For CDC_600 and CDC_700, however, the fluctuation-induced scattering presents a more significant term as shown in Fig. 1b and c. In this case lR must be estimated as discussed in detail in Ref. [54]: For a given Bfl the length parameter lR is chosen so that the contribution of the fluctuations eq. (4) remains below the scattering curve. In addition, for sufficiently high scattering angles

Fig. 1. (a) Mass normalized scattering curves of CDC powders (noted in the Figure). (b) Modified Porod plot of CDC_600 or CDC_1000, respectively. (c) The fluctuation contribution from the lateral imperfection and finite size of the carbon layers is indicated by solid lines whereas the scattering curves for CDC_600 and CDC_1000 are given as symbols. (d) Scattering due to the pores in a two-phase system for all carbon samples studied after removing the contribution of lateral disorder, as shown in Fig. 1b and c. All corrected scattering curves show the asymptotic q
4-behaviour. (A colour version of this figure can be viewed online.)

€rk et al. / Carbon 146 (2019) 284e292 E. Ha

288

the expression eq. (4) must lead to the modified Porod fit. Fig. 1c displays this estimate which leads to a magnitude of lR in the range of a nanometer (see Table 1). The respective fit is plotted as black solid line for CDC_600 in Fig. 1c. While this determination of lR will entail certainly an error of the order of 10%, we reiterate that the parameter Bfl can be obtained very precisely by the modified Porod fit shown in Fig. 1b. Independent contribution of the fluctuations dSdfluct U ðqÞ and of the dS

pores dpores U ðqÞ are plotted in Fig. S3 a and b for CDC_600 and CDC_1000 powders, respectively. The overall error induced by the correction of the fluctuation term is hence much smaller. As it can dS

be seen in Fig. 1d, the dpores U ðqÞ versus scattering vector curves follow a power law decay with q
4 at high q-range. Therefore, the chord length distribution gðrÞ can now be obtained from these corrected data by the procedure laid out by Smarsly et al. [31]. The respective fits are shown in Fig. 2a in a plot of the intensity times q2 versus q. The area under these curves defines the magnitude of the invariant Qm eq. (11). Fig. 2a demonstrates that this quantity can be obtained in good accuracy: The scattering contribution at the smallest angles lead only to an upturn at low q in this plot which is inconsequential for the areas under the curves and hence for the calculation of Qm . The final slope of
4 allows us to determine the area beyond the measured data in excellent accuracy. Fig. 2b shows the CLDs gðrÞ obtained from this analysis. All structural features and calculated characteristics for synthesized CDC are summarized in Table 1. For comparison, the low temperature N2 adsorption results using Brunauer-Emmett-Teller (BET) multipoint theory and the two-dimensional non-local density functional theory model (2D-NLDFT-HS) for carbons with heterogeneous surfaces implemented in SAIEUS (v2.02, Micromeritics) software for the pore size distribution calculations are given in an extended Table S1. We reiterate that BET will in general give too high values for the internal surface of micropores [78,79]. Hence, we attached more significance to the results of the present analysis by SAXS gathered in Table 1. 3.2. Discussion of the parameters 2

2

First of all, the Ruland length lR and the degree of disorder Da a23 þ 3

D lR give valuable and quantitative information on the increasing 2 lR

degree of graphitization with increasing chlorination temperature.

The latter parameter decreases by approximately one order of magnitude when the chlorination temperature is raised from 600 to 1000  C. The length parameter lR increases markedly for the two smallest temperatures and exceeds 20 nm for temperatures of 800  C and more. This trend is the same as observed by Faber et al. for a series of silicon carbide derived carbons by wide-angle X-ray scattering [34]. The parameter La giving the extent of the graphene sheets derived therefrom is in general smaller [34] than the parameter lR derived here from SAXS, and La seems to attain the magnitude only for similar systems at much higher temperatures (cf. Table 4 of ref. [33]). It should be kept in mind, however, that lR presents an estimate and upper bound of the graphene sheets only whereas La is derived directly from wide-angle scattering. The structural reorganization upon ongoing graphitization is also visible in recent TEM studies [37] showing structural units of the order of a few nanometers. All findings demonstrate that the CDC do not present homogeneous materials at any stage but contain parts in which partial graphitization takes place. These regions give the scattering signal scaling with q
2 which must be subtracted prior to analysing the scattering contributions of the pores. As mentioned in the Small Angle X-ray Scattering Theory section, S and the porosity f can be derived from the the inner surface area m SAXS-curves directly in a model-free manner. Thus, both quantities present reliable information about porous materials as has been shown a long time ago [42,72]. Table 1 demonstrates that both quantities go through a maximum as the function of the chlorination temperature. Obviously, the step from a temperature of 900e1000  C leads to a partial collapse of the pores and to a comitant loss of internal surface area. This finding is in qualitative agreement with earlier findings by J€ anes et al. [13] on very similar materials. Fig. 2b shows that all CLDs extracted from the scattering data of the CDC exhibit only a single peak. This is a clear indication that the chords leading to the gðrÞ shown in Fig. 2b penetrate through the pores or walls only once, ordered structures characterized by chords that penetrate pores or walls twice [53,74] are not contributing to gðrÞ significantly. This finding in turn demonstrates that all CDC present disordered materials with decorrelated pores. Hence, the analysis itself demonstrates its applicability to the present set of materials. Once the lack of order in the material is established, the parameters lpore and lsolid present direct measures for the average

Table 1 S The comparison of the SAXS characteristics: The scattering contribution Bfl (eq. (4)), invariant Qm (eq. (11)), Porod constant Pm (eq. (6)), inner surface area , porosity f (eq. m (13)), number-average chord length lP (eqs.(8) and (9)), mean chord length of the pore l and the carbon matrix l (eq. (10)), weight-averaged chord length lc (eq. (14)), solid D2 a3 poreD2 lR lateral correlation length lR , degree of angularity gð0Þ and a degree of disorder þ 2 (eq. (15)) for carbide derived carbons synthesized at different chlorination 2 a3 lR temperatures. Property
1

2


2

Bfl /cm g nm Q m /cm2 g
1 nm
3 P m /cm2 g
1 nm
4 S /m2 g
1 m f /nm lSAXS p /nm lCLD p lpore /nm lsolid /nm lc /nm lc / lSAXS p lR /nm gð0Þ /nm
1

D2 a3 a3 2

þ

D2 lR lR 2

CDC_600

CDC_700

CDC_800

CDC_900

CDC_1000

10.8 ± 0.2 3.9 ± 0.2 0.112 ± 0.004 965 ± 102

9.7 ± 0.2 4.0 ± 0.2 0.110 ± 0.004 950 ± 100

7.6 ± 0.2 6.8 ± 0.2 0.152 ± 0.005 1310 ± 137

7.9 ± 0.1 9.0 ± 0.2 0.158 ± 0.002 1363 ± 137

2.23 ± 0.03 6.8 ± 0.1 0.072 ± 0.001 621 ± 62

0.27 ± 0.02 0.57 ± 0.04

0.28 ± 0.02 0.59 ± 0.04

0.47 ± 0.03 0.72 ± 0.03

0.63 ± 0.03 0.92 ± 0.02

0.47 ± 0.03 1.52 ± 0.02

0.58 ± 0.1 0.78 ± 0.6 2.1 ± 0.2 4.1 ± 0.3 7.2 ± 0.02 4.0 ± 0.2 1.24 ± 0.04 0.36 ± 0.03

0.63 ± 0.1 0.81 ± 0.05 2.1 ± 0.2 5.2 ± 0.3 8.81 ± 0.09 9.0 ± 0.5 1.16 ± 0.05 0.32 ± 0.03

0.74 ± 0.2 1.35 ± 0.1 1.5 ± 0.1 4.5 ± 0.2 6.25 ± 0.02 >20 1.13 ± 0.03 0.25 ± 0.02

0.93 ± 0.2 2.5 ± 0.2 1.5 ± 0.1 4.9 ± 0.1 5.33 ± 0.01 >20 0.92 ± 0.02 0.26 ± 0.02

1.71 ± 0.1 2.9 ± 0.1 3.2 ± 0.2 9.7 ± 0.1 6.38 ± 0.02 >20 0.25 ± 0.1 0.074 ± 0.004

€rk et al. / Carbon 146 (2019) 284e292 E. Ha

289

or long cylindrical pores. It is fully compatible with the prior conclusion that the pores assume a slit-like shape. At the highest chlorination temperature, however, gð0Þ decreases considerably. Table 1 demonstrates that this structural transition is related to a marked increase of the thickness of the pore walls as indicated by the increase of lpore and a loss of ultramicroporosity as seen from Fig. 2b. Hence, we see a transition from an ultramicro-to a supermicroporous material. Concomitantly, the degree of disorder Da a23 þ 2

3

D2 lR is decreasing markedly which shows the increased degree of 2 lR

graphitization. 3.3. Correlation with the electrochemical parameters

Fig. 2. (a) Kratky plot of the pore scattering data from Fig. 1d). including the corresponding CLD fit (solid lines). (b) Chord length distribution for various nanoporous CDC synthesized at different chlorination temperatures, noted in Figure. (A colour version of this figure can be viewed online.)

pore size and the average thickness of the walls between the pores, respectively. Table 1 shows that lpore is much smaller than lsolid for the two lowermost temperatures. Therefore, gðrÞ displayed in Fig. 2b will be dominated by the contributions of the pores. In both cases the number-average chord length lP is approximately 0.6 nm, that is, we deal with a ultramicroporous system. The average pore size is increasing with higher chlorination temperature as it is obvious from the monotonous increase of lpore (see Table 1). At the same time lsolid is decreasing so that the average size of pores and pore walls are finally more or less equal size. Materials synthesized at 900 and 1000  C, thus are dominated by mesopores. Evidently, gðrÞ defies simple interpretation if the chords through the pores are of the same magnitude as the chords through the walls. Chords near r ¼ 0, however, always refer to features near the surface of the pores and can be interpreted directly. Up to chlorination temperature of 900  C gð0Þ is of appreciable magnitude. This indicates the presence of sharp edges and rules out spherical pores

Up to now, all studies have normalized the measured capacitance by the so-called corrected specific surface area (SSAcorr) determined by the liquid nitrogen or CO2 sorption measurements [10,20,23]. Thus, the analysis was carried out based on the SSAcorr accessible to the ions, that is, only the contribution of pores with sizes above the ultramicropores (lpore > 0.7 nm) has been included [5,10,20,23,25]. In many cases a model assuming flat uniform pores has been applied [24,25,28]. In the present study, we are using the entire internal surface as obtained by SAXS. We found two empirical correlations between the results of SAXS and the maximum gravimetric energy density Emax [6] which is a very sensitive parameter and proportional to capacitance (Table S2). As in previous comparisons [5,10,20,23,24], we choose the pore size as decisive variable. Here we take the number-average pore size lpore as derived from the SAXS analysis. It is important to emphasize that S is derived from the SAXS-curves directly in the inner surface area m a model-free manner, meaning that no further corrections or exclusions of a certain size and shape of the pores are necessary. Fig. 3a shows that Emax correlates very well with the ratio of S over porosity f. This correlation reflects the inner surface area m loss of micropores on the expense of mesopores with increasing temperature of the synthesis (Fig. S4). In other words, the capacitance which contributes to the energy storing is proportional to the S and inversely proportional to the overall porosity at surface area m the same time (Tables 1 and S2). Fig. 3b suggests that Emax is correlated to the anisometry of the pores as embodied in the ratio lc =lp , that is, the ratio of the weightaverage and the number-average size of the pores (see the discussion of Table 1 above). This finding underscores the central role of the micropores for energy storage: We need flat slit-like pores in the submicro-range in which the coordination sphere of the ions is sufficiently distorted [14]. However, if lpore becomes too small, the ions cannot enter anymore which may be the origin of the maximum seen in Fig. 3b (cf. also the discussion of this point in Ref. [10]). In total, the present findings corroborare the previous result that the gravimetric energy density of a supercapacitor is mainly due to the number of microporous pores. Clearly, more data are needed to draw further conclusions in this regard. The present analysis, however, has demonstrated the usefulness of model-free SAXS data for an in-depth understanding of supercapacitors. 4. Conclusion A comprehensive and consistent analysis of a set of carbide derived carbons synthezised by chlorination at different temperatures has been presented. The method employed takes into account the inhomogeneous nanostructure of these carbonaceous materials caused by partially graphitized parts. The scattering intensity at high q (i.e., transition of the q
2 to q
4) is of appreciable magnitude at low chlorination temperatures but diminishes at higher chlorination

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Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.carbon.2019.01.076. References

Fig. 3. Two empirical correlations for the performance prediction of supercapacitors using CDCs synthesized at increasing chlorination temperature: a) The ratio of inner surface area mS over porosity f vs. gravimetric energy density as a function of mean chord length of the pore lpore . b) Correlation between energy density normalized with inner surface area vs. anisotropy as a function of the mean chord length of the pore lpore for various nanoporous CDC synthesized at different chlorination temperatures (Tables S1 and S2). (A colour version of this figure can be viewed online.)

temperatures because of the increasing graphitization. The remaining SAXS-intensity can be evaluated to give the internal surface area and the volume fraction of the pores with high precision. An in-depth analysis of the chord length distribution gðrÞ shows that low chlorination temperatures lead to ultramicroporous materials whereas the ultramicropores are not stable anymore at the highest temperature of 1000  C. As the inner surface area of CDC is increasing with the chlorination temperature until 900  C, followed by the significant decrease at 1000  C the transition from a ultramicro-to a supermicroporous material could be witnessed. The carbon structure collapse was observed as the average pore size of the pores becomes equal or either exceeds the thickness of the pore walls if the higher chlorination temperature was applied. A correlation of these structural data with the stored energy Emax demonstrated that this quantity is directly proportional to the anisometry of the pores embodied in the ratio lc =lp . Further studies along these lines are under way. Acknowledgments A part of this work was supported by the EU through the European Regional Development Fund under project: TK141 “Advanced materials and high-technology devices for energy recuperation systems” (2014-2020.4.01.15-0011), by the Estonian Research Council (institutional research grant No. IUT20-13). Authors thank Dr. Zdravko Kochovski for transmission electron microscopy measurements.

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