Assessing the structural properties of graphitic and non-graphitic carbons by Raman spectroscopy

Journal Pre-proof Assessing the structural properties of graphitic and non-graphitic carbons by Raman spectroscopy Dominique B. Schuepfer, Felix Badaczewski, Juan Manuel Guerra-Castro, Detlev M. Hofmann, Christian Heiliger, Bernd Smarsly, Peter J. Klar PII:

S0008-6223(19)31341-7

DOI:

https://doi.org/10.1016/j.carbon.2019.12.094

Reference:

CARBON 14930

To appear in:

Carbon

Received Date: 30 September 2019 Revised Date:

1 December 2019

Accepted Date: 30 December 2019

Please cite this article as: D.B. Schuepfer, F. Badaczewski, J.M. Guerra-Castro, D.M. Hofmann, C. Heiliger, B. Smarsly, P.J. Klar, Assessing the structural properties of graphitic and non-graphitic carbons by Raman spectroscopy, Carbon (2020), doi: https://doi.org/10.1016/j.carbon.2019.12.094. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Dominique Schüpfer: Conceptualization, Validation, Formal analysis, Investigation, Writing - Original Draft, Visualization Felix Badaczewski: Formal analysis, Investigation Juan Manuel Guerra-Castro: Methodology, Software, Formal analysis Detlev M. Hofmann: Conceptualization, Writing - Review & Editing Christian Heiliger: Conceptualization, Methodology, Writing - Review & Editing Bernd Smarsly: Conceptualization, Methodology, Writing - Review & Editing, Supervision Peter J. Klar: Conceptualization, Methodology, Writing - Review & Editing, Supervision

Position

FWHM

ID

IG

“Assessing the structural properties of graphitic and non-graphitic carbons by Raman spectroscopy” I Dominique B. Schuepfera,∗, Felix Badaczewskib , Juan Manuel Guerra-Castroc , Detlev M. Hofmanna , Christian Heiligerc , Bernd Smarslyb , Peter J. Klara a Institute

of Experimental Physics I and Center for Materials Research (LaMa), Justus Liebig University Giessen, 35392 Giessen, Germany b Institute of Physical Chemistry and Center for Materials Research (LaMa), Justus Liebig University Giessen, 35392 Giessen, Germany c Institute of Theoretical Physics and Center for Materials Research (LaMa), Justus Liebig University Giessen, 35392 Giessen, Germany

Abstract We study the transformation from molecular to crystalline of (non-)graphitic carbons synthesized from organic precursors by heat-treatment. Easy assessment of structural properties resulting from heat-treatment protocols is mandatory for industrial process monitoring.

We demonstrate that Raman spec-

troscopy, in particular, the Raman lineshape analysis of G and D mode, offers quick assessment of the average sheet size of such carbons. We validate this method by performing Raman, WAXS and EPR measurements of series of resin and pitch-based carbons synthesized. The crystallite sizes of the WAXS analysis for the individual samples are related to corresponding positions and linewidths of G and D Raman modes and show excellent agreement between experiment and modelling from large sizes down to 4 nm. The theoretical master curves are independent of the precursor used in the synthesis, in contrast to models for the intensity ratio of D and G band versus size. We show that the latter are not universally valid and differ for each class of precursors. For sizes below 4 nm, our lineshape model fails as it is based on the bandstructure and phonon dispersions of ideal graphene. Thus, 4 nm corresponds to the fundamental transition from ∗ Corresponding

author Email address: [email protected] (Dominique B. Schuepfer)

Preprint submitted to Journal of LATEX Templates

January 17, 2020

molecular to crystalline character for non-graphitic carbons. Keywords: non-graphitic carbon, carbon characterization, Raman spectroscopy, wide-angle X-ray scattering

1. Introduction Coal, char coal, activated carbon, etc. belong to the class of non-graphitic carbons (NGCs) which probably is the most abundant class of sp2 -hybridized carbon materials. These sp2 -hybridized carbons consist of small nanometer5

sized graphene layer stacks possessing significant structural disorder, both in the single graphene sheets and the stacking, leading to a so called ”turbostratic” arrangement [1]. The class of sp2 -hybridized carbon materials nowadays plays a vital role in energy storage systems, for example, such carbons are used in supercapacitors or as electrodes in Li-ion batteries [2, 3]. Especially structural

10

parameters such as stacking height, stacking order, mean lateral extension of the graphene sheets (in the following the term crystallite size is used) La and their defect density are of interest and to a large degree determine the processes and reactions taking place at the outer and inner surface of these rather porous materials. The structural parameters are determined by the genesis of

15

the material. As an example, figure 1 shows the current understanding of the transformation of precursor molecules in the carbonization process. The original scheme goes back to A. R. Bunsell [4]. We have added a precursor stage depicting molecules representing the smallest graphene- and diamond-like units, i.e., poly-

20

cyclic aromatic hydrocarbons such as coronene or diamondoids such as adamantane. These molecules stand for the multitude of precursor materials which can be used in the carbonization process ranging from organic waste as an ill defined starting material via pitches or resins to pure molecular types as defined starting materials [5, 6, 7, 8, 9, 10]. Typical stages which occur during heat-

25

treatment causing atomic rearrangements are the following: First, amorphous carbon exhibiting all three kinds of carbon bonds (sp1 , sp2 and sp3 ) without

2

any stacking is formed at temperatures above 700 ◦C. The amorphous carbon of mixed bonding turns into purely sp2 -bonded amorphous carbon at round about 1200 ◦C on further heating. Non-graphitic carbon is formed in the temperature 30

range from about 1400 ◦C to 1700 ◦C. Above 1700 ◦C the crystallites transform into graphene sheets, which arrange in ordered stacks. Different precursor materials do not necessarily lead to the same transformation chain due to differences in the bonding, networking capabilities and the types of defects in the non-graphitic and graphitic phase. These differences are

35

reflected in analyses by spectroscopic and diffraction methods. The structural properties of NGCs such as lateral size of the crystallites, stacking order etc. need to be estimated accurately and can be best assessed by wide-angle X-ray diffraction (WAXS) [11]. Approaches like Rietveld refinement and the Scherrer equation are impracticable and include a large error in case of NGCs. The

40

reliability of modelling of WAXS data draws upon the fact that the WAXS reflections introduced by the ordering process are only indirectly sensitive to the defects formed. Raman spectroscopy as a fast and non-destructive tool was used successfully over several decades to characterize all sorts of carbon materials in terms of their

45

structure [12, 13, 14, 15, 16]. Therefore, it is not surprising that a number of empirical approaches based on the intensity ratio of the defect-induced Raman D and bulk G band [17, 18, 19, 20] for extracting the crystallite size La is widely used to characterize carbons [21, 22]: Tuinstra and Koenig found in 1970 the proportionality of

50

ID/IG

∝ 1/La [17] valid for La > 2 nm and for La < 2 nm the

relation of Ferrari and Robertson

ID/IG

∝ L2a is used [23]. The Tuinstra and

Koenig relation was further improved by several groups including Knight and White, Matthews et al. and Can¸cado et al. who noted the dependence of the D band position on the excitation energy [24, 25, 26, 27]. At 2 nm a transition region, where none of their two empirical relations is valid, was proposed by 55

Ferrari and Robertson [23]. Some words of caution seem to be appropriate here. First, due to the lack of an extended crystalline structure the occurence of a graphene-like D mode is 3

doubtful in amorphous materials and impossible in molecules as its existence is based on a process where a defect breaks the translation symmetry of a crys60

talline structure. Modes of G character in terms of the vibrational pattern, of course, may still be found in molecules consisting of sp2 -bonded carbon atoms, but for obvious reasons not for precursor molecules exhibiting other types of sphybridization. Thus, there will be a minimum required lateral size of the crystallites formed in the carbonization process for the empirical models to become

65

valid. This touches on the fundamental question of the break-down of bandstructure and phonon dispersion of crystalline materials on reducing the lateral dimensions on the nanoscale and correspondingly the bridging between descriptions for molecules and crystalline solids. Second, the empirical approaches currently used in the analysis of Raman spectra require the relative intensity of

70

the D mode, which is per se related to the existence of defects, for extracting La . However, the defects formed and their density depend on the type of molecules used as precursors, as the building of cross-links between the carbon units differs from precursor to precursor, e.g., perylene, trans-polyacetylene chains [28, 29] and various other kinds of defects [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40].

75

Therefore, it may be anticipated that the behavior of the

ID/IG

ratio as a func-

tion of lateral size La also will depend on the precursor molecule used and challenge the empirical approaches as a simple method for determining La , at least, they impose some restrictions. There have been considerable efforts to identify the G and D-like modes in 80

studies combining Raman spectroscopy and density-functional theory as well as quantum chemical methods for calculating the Raman frequencies and mode patterns of polycyclic aromatic hydrocarbons [41, 42, 43, 44, 45, 46, 47], i.e., approaching graphene’s phonon structures from the molecular side. However, even molecules of the same molecular formula may exhibit a different spatial

85

arrangement of the constituting atoms, i.e., a different symmetry. Depending on the symmetry of the molecules the number of Raman signals as well as the mode patterns may change as degeneracy is lifted. Thus, it is not straight forward to assign a molecular vibrational mode to a crystalline mode at a certain wavevec4

tor of the 1st Brillouin zone of ideal graphene. Nevertheless, attempts to bridge 90

the gap between polycyclic aromatic molecules and crystalline, two-dimensional graphene by considering the latter as built up of periodically arranged coronene and circumcoronene units seem promising [43]. To our knowledge there are no attempts made yet to approach the gap coming from the crystalline side and to employ empirical phonon confinement models [48, 49] to decribe the evolution

95

of the nanosized graphene sheets within non-graphitic and graphitic carbons as a function of size. Such models have been successfully employed for various semiconductor nanostructures as a function of size and are based on a thorough knowledge of the phonon dispersion of the corresponding bulk material [50, 51, 52].

20 °C

Precursor molecules 726.85 °C

Amorphous sp2 + sp3 1226.85 °C

Non-graphitic

Amorphous sp2

1426.85 °C

1726.85 °C

Graphitic

Figure 1: During heat-treatment the structural units increase in size and crystallinity and temperatures above 1700 ◦C yield high stacking order [4].

5

100

2. Experimental details and theoretical modelling Five series of samples spanning the transformation chain of the carbonization process from a molecular precursor to graphitic carbon have been studied. The series were based on five different precursors, i.e., three pitches and two resins. All precursor substances were heat-treated up to 3000 ◦C in Ar atmo-

105

sphere, which results in a carbonization process. The samples of each series were prepared following the same heating protocol, but differ in terms of the intermediate temperature where the carbonization process was intentionally interrupted. This temperature together with a prefix representing the precursor was used for labelling the samples. The 20 ◦C label indicates the as-received

110

samples. Details about the annealing process and parameters can be found elsewhere [53]. The morphology of the samples obtained is considered characteristic for the intermediate temperature where the process was interrupted and for the type of precursor used. The pitches used differed in their softening points (SP): (1) low-softening point pitch with SP at 70 ◦C (LSPP-70), (2)

115

high-softening point pitch with SP at 180 ◦C (HSPP-180), and (3) high softening point pitch with SP at 250 ◦C (HSPP-250). All pitches were prepared by pyrolysis of organic material yielding a starting material, which mainly consists of aromatic hydrocarbons and heterocyclic compounds. Such aromatic starting material leads to graphitic carbon at the end of the pyrolysis, because the pre-

120

cursor molecules do not contain any side groups and the carbon units can easily form a close graphene like network. The resin precursors were novolac (resin N) and resol (resin H). Unlike the pitches, both resin samples must be considered non-graphitizable precursors. Due to their chainlike structure and their OH-groups, the carbon units are only scarcely linked and, thus, do not exhibit

125

good networking properties and the pyrolysis is likely to result in non-graphitic carbon as end product. Such graphitizing and non-graphitizing carbons were already described in the year 1951 by R. Franklin [54]. The differences between the sample series are summarised in tables 1 and 2.

6

Table 1: Precursors and preparation of the pitch sample series.

Sample

LSPP-70

HSPP-180

HSPP-250

Precursor

PAH/coal tar

PAH/coal tar

PAH/coal tar

Preparation

1 distillation

2 distillations

1 distillation + 1 thin film vacuum distillation Table 2: Precursors and structural formulas of the resin sample series.

Sample

Resin N

Resin H

Precursor

Novolac

Resol

Structural formula

130

The WAXS data were collected using a PANalytical X’Pert Pro powder diffractometer in Bragg-Brentano geometry. Cu Kα radiation with a wavelength λ = 1.5418 ˚ A at 40 kV and 40 mA served as X-ray source. The sample was pestled manually and then deposited and flattened on a silicon single-crystal sample holder to a thickness of about 1 mm. The measurements were performed in the

135

range of 10◦ < 2θ < 100◦ and a counting time of 8 s/step. The carbon samples were measured with a step size of 0.1◦ to account for their higher crystallinity and therefore sharper reflections. No background intensity was subtracted from the experimental WAXS data.

140

The WAXS data were fitted by applying the algorithm developed by Ruland and Smarsly [11] using the software Wolfram Mathematica. To obtain the initial values of the parameters, the WAXS data was at first fitted and afterwards was optimised using the ”NonlinearModelFit” operation implemented in Mathematica. In the WAXS data of the pitches heat-treated at temperatures ≥ 2800 ◦C,

145

(hkl)-reflections are further developed, indicating the beginning of graphitization. As a result, the algorithm cannot be applied on these samples, as it was programmed especially for non-graphitic carbons and therefore does not account

7

for (hkl)-reflections. Therefore, the crystallite size of the pitches heat-treated at 2800 ◦C and 3000 ◦C was derived by analyzing the (110) reflection using the 150

Scherrer formula. The FWHM of the (110) reflection was determined by a fit to a Gaussian profile. The (110) reflection was chosen, because it is not severely overlapping with other reflections, in contrast to the (100) reflection. Due to possible disorder within the lattice and overlap with adjacent reflections and the non-linear background, the experimental uncertainty of the values obtained

155

for these samples is somewhat larger than for those where the crystallite size was obtained by fitting the entire WAXS data set.

The Raman spectra were recorded with a Renishaw inVia Raman microscope system in backscattering geometry at room temperature. The following laser 160

lines were used: 325 nm, 488 nm, 514 nm, 532 nm, 633 nm, and 785 nm. The laser light was focused onto the sample with either a 20× or a 40× microscope objective when using the 325 nm laser line and with a 50× objective in case of all the visible laser lines. The size of the laser focus was typically about 4 µm. The scattered light was collected by the same objective and then dispersed by

165

a spectrometer with a focal length of 250 mm prior to detection by a chargecouple device (CCD) detector. The spectral resolution of the Raman system was about 1.5 cm−1 . The integral exposure time was 5 to 10 accumulations of 30 sec and the spectral range covered was 1000 to 3200 cm−1 .

170

The EPR spectra were measured with a commercial Bruker ESP300PE spectrometer using a microwave frequency of 9.4 GHz (X band). The samples were located in a standard TE102 rectangular cavity and the spectra were detected in atmosphere at room temperature. To exclude changes in the spectral characteristics caused by surface reactions with air, selected samples were analyzed under

175

vacuum conditions, where the spectra did not show any detectable changes compared to the air ambient. The EPR data were integrated to obtain the absorption spectrum. The obtained absorption spectrum was integrated to determine the intensity of the EPR signal. The spin concentration was then estimated by 8

comparing the area of the absorption curves of the samples with the absorption 180

curve of a standard carbon sample, whose spin concentration was known.

The band structure and the phonon dispersion of ideal graphene have been derived using density functional theory employing the software QUANTUM ESPRESSO [55, 56]. The atomic structure of graphene was relaxed and yielded 185

lattice parameters in agreement with experiment within 0.01%. The electronic structure was computed using a non-relativistic and ultrasoft pseudo-potential within the Perdew-Burke-Ernzerhof parameterization of GGA for the exchangecorrelation functional [57]. The resulting electronic structure was found to underestimate the band gap by 16% and was rescaled in order to be in agreement

190

with experimental findings [58]. The phonon dispersions were then calculated using the same input parameters, the same pseudo-potentials and the same exchange-correlation potentials as for the band structure calculation. Experimental results for the phonon dispersion from Mohr et al. and Maultzsch et al. are in good agreement with the calculation [59, 60], after upshifting the

195

frequency due to an underestimation. Calculated bandstructure and phonon dispersions served as input parameters for the Campbell-Fauchet modelling of the size dependence of the lineshape and position of the G mode Raman signal as well as for its adaption for determining the size dependence of the lineshape and position of the D mode Raman signal [48, 49].

200

3. Results and Discussion 3.1. Correlation between Raman results, WAXS data and EPR measurements We have analyzed two series of resin-based samples and three series of pitchbased samples by all three analytical methods. As all pitch series exhibit similar results, the two resin series show common trends, and the main differences oc-

205

cur between the resin series and the pitch series as a function of heat-treatment temperature (HT T ), we focus in the discussion in this section on two sample series only, the resin series prepared with resol as precursor, labeled with H, and

9

the pitch series based on the pitch precursor with the lowest softening point of 70 ◦C (LSPP-70). The former series should yield non-graphitic carbons whereas 210

the latter should yield graphitic carbons. In what follows, we will first compare the corresponding series of Raman spectra as a function of HT T and discuss the EPR results in order to identify the typical stages along the transformation chain from precursor to graphitic carbon. A closer look at Raman spectra of pairs of selected samples of the two series possessing the same crystallite size

215

allows us to identify additional features in the spectra which may exhibit a characteristic dependence on La . These features and their characteristic dependence on lateral size will then be explored further in the next section and put on a sound theoretical basis. An overview of the Raman spectra using an excitation wavelength of 633 nm

220

is given in figure 2a) for the LSPP-70 series and in figure 2b) for the resin H series. The spectra show the characteristic Raman bands in the range from 1000 cm−1 to 3000 cm−1 commonly labeled as D, G, D’, and 2D band [17, 18, 19, 20]. The Raman spectra of the samples of different HT T are ordered from bottom to top according to increasing HT T , covering the range from 20 ◦C to 3000 ◦C in case

225

of the LSPP-70 series and covering the range from 500 ◦C to 3000 ◦C in case of the resin H series. The insets show details how the bands in the 2D region vary for the samples heat-treated at high temperatures, i.e., 1800 ◦C and 3000 ◦C. Figure 2c) and d) show, how the spin concentration of the samples varies with HT T for both series. The data are extracted from the EPR measurements.

230

Exemplary, EPR spectra of selected samples are also shown as insets. The transformation of the Raman spectra with increasing HT T of the LSPP70 pitch series in figure 2a) reveals at least four characteristic stages of the carbonization process during the heat-treatment. Stage I occurs in the temperature range up to 800 ◦C, where the Raman bands at approx. 1355 cm−1 (D)

235

and 1580 cm−1 (G) are broad and overlapping. The assignment D and G band is somewhat misleading here as this nomenclature strictly only holds for crystalline graphene and the samples probably cannot be considered crystalline at this stage of the transformation process. Stage I of the carbonization process is 10

Figure 2: Series of Raman spectra of the LSPP-70 in a) and resin H sample series in b) obtained with 633 nm laser excitation. The spectral features lead to a classification of the carbon samples according to stages I to IV. The inset shows the spectra region of the 2D Raman signal revealing non-graphitic and graphitic carbon. The dependence of the spin concentrations estimated by EPR spectroscopy on HT T supports the classification based on the Raman spectroscopic results (c) LSPP-70 and d) resin H).

11

characterized by a red-shift of the so called D band and blue-shift of the so called 240

G band with increasing HT T up to 800 ◦C. In this temperature range, the ID/IG ratio does not exceed a value of 1. Stage II occurs in the HT T range between 800 ◦C and 1500 ◦C. The D and G band are still rather broad, but at this stage the D band, in particular, starts to blue-shift with increasing HT T . The ratio ID/IG

245

increases further with increasing HT T and reaches its maximum value of

approx. 1.2 for the 1200 ◦C sample. Stages III and IV are characterized by much sharper Raman signals, the D’ band appears on the right-hand side of the G band and the 2D band at about 2670 cm−1 occurs. The

ID/IG

ratio decreases

towards zero with increasing HT T up to 3000 ◦C. At a HT T of 3000 ◦C the disorder induced D band and the D’ band disappear due to a low defect content 250

[23]. Stage III covers the HT T range from 1800 ◦C to 2500 ◦C and stage IV the temperatures above 2800 ◦C. Stage III and IV can be distinguished by the spectral shape of the 2D Raman signals. The spectral shape is indicative for the degree and kind of stacking order of the nanosized graphene sheets which are formed during carbonization [19, 61]. Below 1800 ◦C no 2D band is observed

255

indicating a low degree of stacking. In the spectra of the samples heat-treated at 1800 ◦C, 2100 ◦C, and 2500 ◦C the 2D signal shape is symmetric and only one Lorentzian profile is needed for fitting the experimental data (exemplarily, the 2D band of the sample heat-teated at 1800 ◦C is shown in the inset). The fitting yields full widths at half maximum (FWHMs) values of about 59 cm−1

260

for 1800 ◦C, 42 cm−1 for 2100 ◦C, and 39 cm−1 for 2500 ◦C. The FWHM values decrease with increasing HT T , but are still broad compared to the FWHM of typical graphene (24 cm−1 [12]). According to Dresselhaus et al. the larger linewidth is caused by the turbostratic structure of non-graphitic carbon. The situation changes for samples of stage IV, i.e., heat treated at temperatures

265

of 2800 ◦C and 3000 ◦C (inset). It can be seen that the 2D lineshape becomes asymmetric, consisting of two bands, with the band at higher frequency being the main peak of the 2D Raman signal. This appearance of the 2D Raman signal is characteristic for graphite, thus, this sample is considered completely graphitized, i.e., is graphitic carbon [19, 61]. The 2800 ◦C carbon sample ex12

270

hibits an intermediate behavior, it clearly shows a shoulder on the right-hand side of the Raman signal at about 2680 cm−1 which has evolved into the dominant high-frequency peak in case of the sample heat-treated at 3000 ◦C. Two Lorentzian profiles are also required for a satisfactory fit of the 2D signal of the sample heat-treated at 2800 ◦C. TEM images of the pitch-based presented here

275

samples showing ordered graphene sheets and thus confirming the Raman data can be found in [53]. The situation is somewhat different for the resin H based samples whose Raman spectra are shown in figure 2b). Stage I is not clearly visible up to 500 ◦C, where no Raman signal is detected. Stage II also sets in at about 800 ◦C

280

exhibiting two broad Raman bands referred to as D and G. As in the pitch series, the D band exhibits a blue-shift with increasing HT T . The transition to stage III indicated by the appearance of a 2D signal occurs again at about 1800 ◦C, but all signals are somewhat broader than for the pitch series. From 1800 ◦C to 3000 ◦C the 2D signal can be well described by a single Lorentzian, i.e.,

285

the 2D band still has non-graphitic character [19] and stage IV/graphitization is not reached in case of the resin H series. The non-graphitizable character of resin-based samples can be also observed in TEM images as shown in [62]. Furthermore, the intensity ratio is ID/IG > 1 for all HT T except for 500 ◦C where no signals are observed and, thus, is at all stages larger than for the pitch series.

290

The large ID/IG ratio is indicative for the presence of a high defect density in the resin samples and in conjunction with the absence of stage IV in the covered HT T range a strong manifestation of the poor networking capabilities of the resin precursor. Later we will go into more detail on this topic. EPR spectroscopy yields some additional information about the defect for-

295

mation as a function of HT T . However, it should be noted that it is only sensitive to defects in a non-zero spin state. Furthermore, in these materials it is difficult to distinguish the signals of different defects, which may be formed, in the EPR spectra. Various types of defects detectable by EPR may be present in these samples and even more types which are not detectable by

300

´ c et al. and V¨ah¨akangas et al. and others showed EPR as for example Ciri´ 13

[31, 32, 34, 36, 37, 38, 39]. Thus, the degree of information provided by the EPR analysis is somewhat limited, but supports the classification into the stages I to IV. All samples where an EPR signal was detected exhibit resonance fields yielding a g-factor very close to g = 2.0023 that of the free electron. Therefore, 305

we will mainly focus on the evolution of the spin concentration as a function of HT T and on the EPR lineshape. The spin concentration is determined by comparison of the integrated EPR signals of a defined amount of sample and of a reference sample of known number of spins. The evolution of the spin concentrations with HT T for the LSPP-70 se-

310

ries (represented by open circles) is shown in figure 2c). The evolution of the EPR spectra with increasing HT T is in accordance with the four stages of the carbonization process in these samples. The EPR spectra of samples of stage I heat-treated at temperatures up to 800 ◦C are characterized by a symmetric line shape (see the lower EPR spectrum of the sample heat-treated at 500 ◦C in the

315

inset of the corresponding graph in figure 2c)). The symmetric lineshape is typical for samples with a maximum concentration of unpaired electrons [63] such as amorphous carbon material or small carbon structures of randomly assembled molecules. The organic molecules of the precursor gradually begin to split during the pyrolysis and to form organic radicals. Species like oxygen are split

320

off as radicals at this stage. These radicals give rise to the isotropic EPR signal and cause the large increase of the spin concentration visible in figure 2. Kawamura and Zhecheva et al. found a similar behavior in their studies of pitches and petroleum cokes [63, 64]. Barklie et al. reported similar results even for carbonaceous films. They explained the high spin density at low annealing tem-

325

peratures by the breaking of C-H bonds and the emission of hydrogen [65]. No EPR signal was detected for the samples of stage II with HT T between 900 ◦C and 1500 ◦C. The EPR signal probably disappears because structural carbon units merge and unpaired electrons of the carbon atoms form bonds reducing the number of dangling bonds in the structure. Zhecheva et al. and Kawamura

330

explained this transition region by a completion of the carbonization process, where the actual graphitization has not started [63, 64]. For samples with HT T 14

above about 1800 ◦C an EPR signal is detectable, but now shows an asymmetric lineshape [64], a so called Dysonian shaped signal [66]. The Dysonian EPR signal stands for increasing stacking order. Graphitization sets in and the degree of 335

order within the layer increases. Probably disorder in the form of carbon atoms inbetween the nanosized graphene sheets are incorporated into the nanosized graphene sheets or diffuse out of the interlayer regions as described by Zhecheva et al. and Kawamura [63, 64]. However, the spin concentration is very low indicating that the amount of defects contributing to this EPR signal is rather

340

low. The Dysonian shape typically occurs in EPR spectra of samples, which have a larger thickness than their electron skin depth, i.e., highly conducting samples. The time for electrons e− to diffuse through the skin depth (left part of the EPR signal) differs from the spin relaxation time (right part of the EPR signal). The EPR results distinguish the stages I, II and the crystalline stages.

345

Unfortunately, non-graphitic and graphitic carbon cannot be distinguished this way, because the EPR signal originates from free electrons within the nanosized graphene sheets and these are not sensitive to the stacking order, which comprises the main difference between non-graphitic and graphitic carbon. The samples of the resin H series were also studied by EPR. The results are depicted

350

in figure 2d). However, only the samples corresponding to HT T of 20 ◦C and 500 ◦C, i.e., to stage I, yielded EPR spectra. The spin concentration of the sample heat-treated at 500 ◦C is significantly higher and of the same order of magnitude than for the corresponding pitch samples. The EPR signal, shown in the inset, is, as for the pitch series in this HT T range, symmetric, thus,

355

can be interpreted in the same way as arising due to radicals formed in the carbonization process when the precursor is split. The samples of the resin H series corresponding to stage II yielded no EPR spectra as also found for the pitches and samples of stage III. These samples are probably too conductive for acquiring EPR spectra. The higher conductivity may be caused by a larger

360

number of defects formed within the nanosized graphene sheets. The average lateral crystallite size La of the nanosized graphene sheets of all samples of the five series studied has been determined by the analysis of 15

the WAXS data as described in the experimental section 2. Exemplarily, the inset of figure 3 shows the WAXS traces of the LSPP-70 samples heat-treated at 365

1000 ◦C and 3000 ◦C. The WAXS trace of the sample treated at the lower HT T is much broader and leads to overlapping (hk)- and (00l)-reflections. Due to the rotational and translational disorder of the graphene sheets within the stacks (hkl)-reflections are missing (first observed and described by Warren and Biscoe [67, 68]). This changes for the 3000 ◦C sample which is graphitized. Beside the

370

(hk) and (00l)-reflections, (hkl)-reflections like the (103)- and (112)-reflections appear in the diffraction curve. The WAXS data of all non-graphitic and amorphous carbon samples were fitted by the algorithm developed by Ruland and Smarsly in order to precisely extract La whereas in case of the few graphitic carbon samples the Scherrer formula was applied to the (110) reflection [11].

375

The experimental data points of the WAXS trace of the sample heat-treated at 1000 ◦C is given by the open circles and the solid line represents the corresponding fitted curve obtained by applying the Ruland and Smarsly model. Figure 3a) summarizes the results obtained for all five series of samples and shows the evolution of the lateral crystallite size La with heat-treatment tem-

380

perature. It can be clearly seen that the data fall into two groups. The data points (open circles, triangles, and squares) for all three series of pitch-based samples essentially lie on the same curve, another curve is given by the data points (open and filled stars) of the two resin-based sample series. The evolution of La for resin and pitch-based samples is somewhat simi-

385

lar up to about 800 ◦C. At HT T above 800 ◦C, the La curves for pitches and resins diverge. The crystallite size La increases more rapidly with HT T for the pitch-based series than for the resin-based series. The pitch-based samples reach La values of about 24 nm at the highest HT T of 3000 ◦C whereas the resin-based samples reach La = 13 nm only. This difference is explainable by

390

the structure of the precursors, whose structural units are connecting differently and affect the long-range network formation. Pitches are prepared from polycyclic aromatic hydrocarbons (PAH) such as pyrene and samples heated at low temperatures still contain several PAHs which can connect easily to larger 16

graphene-like units. In contrast, novolac (resin N) and resol (resin H) precursors 395

exhibit a chain-like carbon structure with additional side groups which hinder a graphene-like network formation. Thus, figure 3 clearly proves that the thermal treatment process alone does not determine the crystallite size La , i.e., a one-to-one correspondence of HT T and La is in general not given. However, it may hold within the same class of precursors, but this needs to be veri-

400

fied in each case. This statement is in agreement with the pioneering work of R. Franklin. She analyzed different carbon samples by X-ray diffraction and noted that non-graphitizing carbons do not turn into graphitic carbon even at annealing temperatures of 3000 ◦C [54]. The temperature dependent behaviour of non-graphitizing and graphitizing carbon has been revisited by Emmerich

405

[69]. He established two different crystallite growth processes. In case of slowly increasing La (vegetative growth), due to non-organized carbon, the crystallites grow in the entire plane, whereas in case of a faster increase of La , at high temperatures, La rises quickly due to coalescence along the a-axis. In the case of graphitizing carbon the coalescence starts at 1400 ◦C. In non-graphitizing

410

carbons it starts at high temperatures of about 2400 ◦C, because of randomly oriented crystallites and strong cross-linking. These findings are in accordance with the results of the behavior of the non-graphitizing and graphitizing resin and pitch samples presented here. Furthermore, an overview of early and newer models of the structure of non-graphitizing carbons can be found in the work

415

of Harris [70]. The finding that the correlation between HT T and lateral size La varies for different precursors implies that Raman spectra of heat-treated samples prepared using different precursors should not be compared in terms of HT T , but in terms of lateral crystallite size La . In the top graph of figure 3, the capital

420

letters A to C denote pairs of a resin-based and a pitch-based samples with comparable lateral crystallite size La . The Raman spectra of the three pairs are compared in figure 3b). The three graphs show Raman spectra of samples with an La of about 2.0 nm (A), 4.0 nm (B) and 13 nm (C) in the spectral region of the D and G band located at about 1325 cm−1 and 1600 cm−1 , respectively. For 17

425

each of the three pairs, the D and G positions in the two spectra are approximately the same, but the positions vary with size from A to C. We will come back to this point later. The main difference between the spectra of the two samples with a La of 2.0 nm is the intensity ratio ID/IG . The defect-related D band is stronger for the

430

resin H based sample than for the LSPP-70 based sample of this size and, thus, the ID/IG ratio is larger for the resin-based sample. This finding prevails also for the other two pairs of samples (B) and (C), the differences between the

ID/IG

ratios increase even further. The structural differences between the resin-based and pitch-based samples 435

in the 4 nm size regime seem to be significant. The linewidth of both Raman bands is much smaller for the resin-based sample than for the pitch-based sample and the resin-based sample with La ≈ 2.0 nm. This suggests that the resin-based samples in this size regime undergo a significant structural improvement despite still possessing a larger number of defects than the corresponding pitch-based

440

sample structures. The Raman spectra of the pair of samples with La ≈ 13 nm both exhibit narrow linewidth, but the Raman peaks of the pitch-based sample are somewhat sharper. Thus, the different heat-treatment required for the two precursors in order to obtain comparable crystallite sizes leads to additional structural differences

445

between the samples which are reflected in the Raman spectra. For example, the linewidth behavior is correlated to the nearest neighbor environment of the C atoms in the nanosized graphene sheets of the samples. In the WAXS modelling, this information is contained in the σ1 parameter, which characterizes the fluctuations of the nearest-neighbor and next-nearest neighbor distances of

450

a C atom in the graphene-like nanosheet as shown schematically in figure 3c) [71]. The graph itself shows plots of the σ1 parameter versus La for the resin H series and the LSPP-70 series. As anticipated for both series of samples σ1 , decreases with La . However, the negative slope varies for the different size regimes leading to several crossing points of the two curves. For the pair

455

of samples with La about 2.0 nm (A) σ1 is the same for the pitch and resin18

based sample and the σ1 value is quite large in correspondence with the broad Raman peaks of both samples. In the size regime (B), the σ1 values of the two samples differ, the resin-based sample of the pair possesses the smaller σ1 value in accordance with the smaller Raman linewidth. On the other hand, the 460

larger D band intensity suggests a larger number of defects, but, obviously, this type of defect does not perturb the nearest-neighbor environment significantly. At large La (C), the resin-based samples again show larger σ1 values which is again reflected in somewhat broader Raman bands compared to the pitch-based samples of comparable size. The rather constant value of σ1 for La > 4.0 nm of

465

the resin H based samples suggests that the nearest-neighbor structure hardly improves despite increasing crystallite size. This behavior is further evidence of the rather bad networking capabilities of the resin precursors. In contrast, the σ1 values of the pitch-based samples keep dropping steadily with increasing size in accordance with steadily decreasing Raman linewidths. We will see below

470

that the Raman linewidth of these carbon materials does not only depend on the disorder of the nearest-neighbor environment but also on the size of the carbon sheets formed, in particular for small La . For this reason, the correspondence between the σ1 values and the Raman linewidth of the samples with small La is rather weak.

475

The discussion above already suggests that the dependence of

ID/IG

on La

is not universal for the transformation chain from an arbitrary precursor to graphitic carbon. This is further underlined by the graphs in figure 4. A comparison of the experimental

ID/IG

values extracted from the Raman spectra

obtained with 633 nm excitation and plotted versus the lateral crystallite size 480

La extracted by the WAXS analysis for all five series of samples is shown in figure 4c). Again, basically two curves arise: one given by the data of the three pitch-based sample series and the other by the data of the two resin-based sample series. The two distinct curves obtained confirm that the behavior is not universal, but at least may be the same for precursors belonging to the same

485

class, e.g., pitches or resins. Both curves show first a rise of the

ID/IG

ratio with

increasing La up to about 6 nm, where a maximum occurs and then drop again. 19

The ratio approaches zero at the largest sizes in case of the pitch-based series indicating an almost defect-free graphitic structure. In contrast, in case of the resin-based samples, 490

ID/IG

decreases rapidly in the regime of large crystallite

sizes La > 8 nm, but then seems to rise for La of about 12 nm reflecting the different networking capabilities of the two precursor classes.

20

Figure 3: a) The dependence of the crystallite size La on the heat-treatment temperature is not the same for sample series prepared of different precursor materials and cannot be generalized for all carbons. b) The Raman spectra show different shapes for different sample series with the same crystallite size. c) Not only the intensity ratio changes but also the linewidth. The linewidth of the G band correlates weakly with the standard deviation of the first-neighbor distribution σ1 estimated from the X-ray diffraction data. In particular, a narrow Raman linewidth indicates small σ1 values.

21

The general behavior of

ID/IG

can indeed be well explained by the existing

models [72, 73] shown schematically in figure 4a), but remains difficult to quantify. At nominally very small crystallite sizes, say below La ≈ 2 nm, the Raman 495

spectrum mainly consists of contributions of various molecule-like units formed by connecting the precursor molecules. The Raman spectra of these molecular units will add up to the total Raman spectrum measured. A molecule, per se does not exhibit a defect as it is defined for crystals. A defect in crystals is a perturbation of the lattice periodicity and molecules do not possess trans-

500

lational symmetry. However, it has been shown that the formation of larger units of six-fold carbon rings may exhibit a molecular vibrational mode in the region of the D band [41, 42, 43, 44]. The intensity of the nominal D band thus rises as more and more of these six-fold units are formed according to Ferrari and Robertson [23]. Eventually, the units consisting of arrangements of six-fold

505

carbon rings can be considered large enough that a crystalline-like description becomes appropriate, say at an La of about 4 nm. At these sizes, it also begins to be justified to talk about crystalline defect formation. Such defects may be located either in the bulk of the nanosized graphene sheets formed or are given by their edges [74].

510

The left scheme of figure 4a) shows a situation where the average distance between defects LD in the bulk of the graphene sheets is much smaller than La and corresponding point defects are dominating. As a consequence the contributions of a structural unit to both, the D and the G band, simply scales with size, i.e., L2a and the ID/IG is independent of size. A more detailed description of

515

this situation attempting to correlate

ID/IG

and LD was given by Can¸cado et al.

[27, 72, 74] for graphene. However, it should be noted that the type of defects formed and their evolution during heat-treatment might be different using pitches or resins as starting materials as these starting materials differ in their molecular structure and their networking properties. Furthermore, the type of 520

defects formed even in case of graphene, e.g., hopping or on-site defects, affects the Raman band intensities differently depending on the magnitude of the corresponding perturbation of the ideal crystalline structure [75]. The situation 22

changes, when the amount of bulk defects in graphene units vanishes and only the edges remain as acting defects, e.g., dangling bonds [12]. In this situation, 525

there is only one type of defect present, namely the sheet edge, and the contribution of a structural unit to the D Raman signal scales with its circumference which is essentially proportional to La and its contribution to the G Raman band scales with its size essentially proportional to L2a . Only in this ideal situation, the Tuinstra-Koenig correlation ID/IG ∝ 1/La might be used to estimate the

530

crystallite size [17, 24]. This situation typically occurs at large La as larger sizes imply also higher HT T and higher HT T typically results in better structural quality in the sense of less bulk defects. In all other cases where additional bulk defects are present, the modelling must account for both distributions. Such an approach can be found in [74] for graphene-related systems. Nevertheless, for

535

molecule-like starting materials the effects of the defect density and types have to be described in a different manner, which will be discussed later. The molecular behavior of small sized units is also represented in the dependence of the ID/IG vs. La curves on the laser excitation energy used in the Raman measurements for the LSPP-70 sample series shown in figure 4b). Depending

540

on the excitation wavelength the maximum of the

ID/IG

ratio shifts to higher

crystallite sizes with increasing wavelength. For 325 nm excitation, molecular carbon units with La = 2.3 nm are in resonance, because their optical band gap (HOMO-LUMO gap) in this size regime matches the excitation energy yielding an increase of the D band intensity. When the sp2 -structures are larger, the op545

tical gap narrows and smaller excitation energies (larger excitation wavelength) are in resonance. The HOMO-LUMO gap for several sp2 -hybridized molecules can be found in the work of e.g., Muellen et al. [76] and the corresponding results support the described behaviour. The dependence of the

ID/IG

ratio also

found by Ferrari and Robertson [77] and Can¸cado et al. [27] is thus related to 550

the electronic structure and its dependence on lateral size La .

23

a)

Resin H 633 nm

b)

ID/IG

ID/IG

785 nm LSPP-70 633 nm 532 nm 514 nm

488 nm 325 nm

Crystallite size

La / nm

c)

LSPP-70 HSPP-180 HSPP-250 Resin N

ID/IG

ID/IG

Resin H

Crystallite size

La / nm

Figure 4: a) Scheme of carbon units with La > LD and b) defects at the edge of graphene sheets. b), c) The intensity ratio ID/IG (shown for the excitation wavelengths 325 nm, 488 nm, 514 nm, 532 nm, 633 nm and 785 nm) divides the samples into 2 stages of carbonization. Until a maximum of

ID/IG

is reached disordered small units dominate the structure. Beyond the

maximum the crystallinity increases for larger crystallite sizes and the ID/IG decreases roughly with 1/La .

24

This discussion of figure 4 is in full agremeent with our analysis of figure 3 and confirms that size determination on the basis of an analysis of the

ID/IG

ratio is

full of pit traps as defect formation and its evolution with size strongly depends on the type of precursor and on the carbonization procedure. Consequently, a 555

ID/IG

versus La relationship needs to be established and calibrated by correlating

Raman results and a size determination by another method (e.g., transmission electron microscopy or WAXS analysis) for each precursor and process prior to be applicable as a fast and non-destructive means of determining the size of the nanosized graphene sheets. The main weakness of the 560

ID/IG

approach is that

ID is strongly dependent on defect formation which is not only a matter of size. However, we have also seen that the Raman spectra show several other features which vary with size. As already noted in figure 3 the D and G positions vary with size. We will show in what follows that the positions of the two Raman bands may also be used as a means of size determination for La larger than

565

about 6 nm. This means of size determination seems to be less sensitive to defect formation than the

ID/IG

ratio.

3.1.1. G and D band position and linewidth The microscopic processes underlying the G and D Raman bands in graphene are well understood and based entirely on the phonon dispersion ω(~k) and the 570

bandstructure E(~k) of the ideal material where ~k is the wavevector in the 1st Brillouin zone [78, 79, 80, 81, 82, 83, 84, 85]. In particular, the occurence of a D Raman signal solely requires the participation of a defect in the phonon scattering process in order to fulfill the momentum conservation rule [78, 85]. Thus, the sole requirement for the process to occur is the existence of defects.

575

The position of the D Raman signal is independent of the type of defect. The dependence of D band position on laser excitation wavelength solely is a feature of the electronic band structure [86, 87, 78, 88, 89, 90]. However, it should be noted that even in bulk graphene, the intensity of the D Raman signal will depend on the number of defects present and on the kind of defects as their

580

scattering cross sections may differ for different defects involved [72, 75].

25

In other words, there are two advantages using the frequency positions of the G and D Raman modes of bulk graphene as a starting point of a lateral size analysis of the nanosized graphene sheets in non-graphitic and graphitic carbons. First, this starting point is well defined as the transformation chain 585

of the carbonization process virtually converges towards graphene or graphite independent of the type of precursor. Second, the positions of the two modes are solely determined by the electronic and vibrational structure which can be calculated in excellent agreement with experimental data by ab initio theories [59, 60].

590

In this section, we will first demonstrate that our ab initio DFT calculations of the phonon dispersion and the electronic band structure of graphene are in good agreement with experimental data. This forms the foundation of the empirical description of the evolution of the positions and the lineshape of the D and G Raman bands on reducing the lateral size. The empirical model goes

595

back to Campbell and Fauchet and it is basically assumed that on reduction of the lateral dimensions the wave vector ~k is no longer a good quantum number, but the confined states can be still described by a superposition of eigenstates of the bulk system [48, 49]. A somewhat similar model has also been applied to describe the effect of the defects in graphene on the phonon coherence length

600

and its effect on the phonon lineshape by Martins Ferreira et al. [91]. In this case I(ω) is a function of LD instead of La . Here, we will employ the confinement model of Campbell and Fauchet to study the dependence of the Raman signals on sheet size La . The optical phonon dispersion of graphene and its electronic structure required for employing the modes were calculated by us using DFT.

605

The results of the DFT calculations can be found in the supporting information. A good test of the quality of the theoretically derived phonon dispersions and the electronic bandstructure is a calculation of the frequency position of the D Raman band for different laser excitation wavelength. The D Raman band originates from a double-resonant process involving two real electronic

610

transitions and scattering by a defect where one optical gap must match the photon energy of the excitation laser [78]. The wavevector ~k of the scattered 26

phonon corresponds to that of the optical gap involved in the Raman process and its frequency ω(~k) is virtually measured as frequency position of the D band. The position of the D band is calculated by us for several excitation wavelength 615

ranging from 325 nm to 785 nm and is shown in the supporting information. We take the excellent agreement between theory and experiment as a proof that our theoretically predicted phonon dispersions and electronic bandstructure of bulk graphene are correct. Figure 5a) shows the dependence of the positions on the mean lateral crys-

620

tallite size La of the G and D Raman signals, respectively. The data are taken with 633 nm laser excitation. The size dependence of the G band position is virtually independent of the laser excitation energy whereas that of the D band exhibits, as already discussed above for bulk graphene, a dependence on excitation energy [26]. Data showing the dependence of the D Raman signal on size

625

La for other excitation wavelengths can be found in the supporting information. The position of the G band for the three pitch-based and two resin-based sample series shows the same behavior independent of the type of precursor used. Starting from the bulk limit of about 1580 cm−1 [18], it shifts monotonously to higher wavenumbers and reaches a maximum of approx. 1600 cm−1 at an La of

630

about 4 nm and then drops back to 1585 cm−1 between La = 4 nm and 1 nm. The dependence of the D band position on the crystallite size La exhibits a different behavior. Starting at the bulk-like limit of about 1335 cm−1 , the experimental data points for pitch-based and resin-based samples exhibit the same behavior down to La of about 8 nm, this is a weak shift to lower wavenumbers

635

with decreasing crystallite size. This changes in the size range between 6 nm and 2 nm. The behavior of the D mode of pitch-based and resin-based samples is different. The position of the former shifts to higher wavenumbers with a maximum of about 1340 cm−1 at about 4 nm whereas that of the latter shifts down in wavenumber to a minimum value of 1325 cm−1 at about 4 nm. At crystallite

640

sizes below 3 nm, the behavior of all five series of samples is approximately the same again. Starting at 1330 cm−1 at 3 nm there is a sharp drop to 1320 cm−1 at 2 nm followed by a sharp rise to 1370 cm−1 towards 1 nm. 27

The areas in the graph shaded in dark and lighter gray correspond to the stages I and II, respectively, of the carbonization process. This is the size 645

regime where differences between the precursors should be most pronounced as this size regime corresponds to the soft transition region between molecular and crystalline behavior. The more surprising, that sizable precursor-related differences do not occur for the G band at all and for the D band only in the size range between 2 nm and 6 nm. The Raman spectra corresponding to stages

650

I and II of the graphitization process exhibit very broad G and D Raman signals which can be easily distinguished from the much sharper features of stages III and IV where the spectra are more graphene like (see figure 2). Thus, despite the non-monotonic behavior of the position dependence of G and D band over the entire lateral size range from La of 1 nm to 25 nm, it should be possible to

655

estimate the lateral size of the carbon nanosheets formed in samples belonging to stage I or II. In the size range, at least between 1 nm and 3 nm, maybe even up to 4 nm, if the type of precursor is known, the sharp monotonic rise of the G band position in conjunction with the mostly monotonic downshift of the D band position

660

with increasing La may yield a good estimate of the crystallite size La . In the lateral size regime above La = 4 nm, corresponding to the more graphene-like stages (easily identifiable by their Raman spectra as discussed above), there is virtually no dependence of the D band position on lateral size, thus only the monotonic increase of the G band position with decreasing La can be used for

665

estimating the size. The upward shift in wavenumber of the G band position in the range from 24 to 4 nm is due to phonon confinement. As the crystalline units become smaller, ~k is no longer a good quantum number. In case of the G mode, corresponding to the LO phonon at ~k = 0 at the Γ point of the 1st Brillouin zone, this implies that other phonons in vicinity of ~k = 0 with phonon

670

frequencies ω(~k) > ω(0) contribute to the Raman G band leading to a blue-shift in position as the LO branch ω(~k) shifts upwards with increasing |~k| (see the supporting information).

28

G band position / cm

-1

a)

LSPP-70 HSPP-180

1600

HSPP-250 1595

resin N resin H

1590

theo.

1585

1580

1575 1370

D band position / cm

-1

b)

1605

1360

1350

1340

1330

1320 0

4

8

12

16

20

24

Crystallite size La / nm c) Intensity / arb. units

2800 °C / 21 nm G

D

D'

1800 °C / 13 nm

1200 °C / 4.0 nm

1000

1200

1400

Raman shift / cm

1600

1800

-1

Figure 5: a) The G band position points out a phase transition at a crystallite size of 4 nm, when the Raman shift reaches a maximum. Phonon confinement leads to a blue-shift with decreasing La . b) The D band shows a slight red-shift at 4 nm, drops down between 2 nm and 4 nm and shows a large blue-shift in the amorphous phase for La = 2 - 1 nm. c) The model of Campbell and Fauchet fits the experimental spectra for non-graphitic and graphitic carbon, but fails for the samples with La < 6 nm.

29

In what follows, we will attempt to model and quantify the dependence on lateral crystallite size La of the positions of the Raman G and D band on the 675

basis of the model introduced by Campbell and Fauchet in 1986 [48] employing the bandstructure and the phonon dispersions of graphene derived by DFT. The aim of the modelling is two-fold, first, to verify that the size-dependence of the Raman positions can be reproduced by the modelling in order to confirm that the behavior is indeed due to phonon confinement and, second, to identify

680

the lower size limit where the modelling based on this ”crystal” approach will fail in order to obtain more information about the soft transition between the crystal-like and the molecule-like stages of the carbonization process [91]. From a solid-state perspective, the Bloch-like eigenstate of the phonon Φ(~k0 , ~r) = u(~k0 , ~r) exp(−i~k0~r) of an infinitely large periodic crystal is modified in case of

685

finite size where u(~k0 , ~r) stands for the vibrational pattern which is the same in each unit cell. Assuming spherical 3D or a circular 2D symmetry, a weighting function W (r, La ) which only depends on the distance |~r| = r from the center of the nanosphere or the circular nanosheet and the lateral size La of the nanostructure can be introduced to account for the confinement. The confined

690

phonon wavefunction Ψ(~k0 , ~r) arising from the bulk phonon with wave vector ~k0 is then given by 0 Ψ(~k0 , ~r) = W (r, La )Φ(~k0 , r) ≡ Ψ (~k0 , ~r)u(~k0 , ~r)

(1)

0 where Ψ (k~0 , r) basically describes the envelope function of the displacement

pattern of the atoms in the confined phonon state. A Fourier expansion of the envelope function yields the contributions of all phonon eigenstates Φ(~k, ~r) to 695

this confined phonon state, i.e., an expansion of the confined phonon state in 0 terms of the bulk phonons. The Fourier coefficients C(~k0 , ~k) of Ψ (~k0 , ~r) are

given as 1 C(~k0 , ~k) = 2π

Z

0 d3 r Ψ (~k0 , ~r) exp(−i~k~r).

(2)

Using the established weighting function W (r, La ) = exp(−2r2 /L2a ) yields the

30

Fourier coefficients C(~k0 , ~k) = 700

La 1 exp(− L2a (~k − ~k0 )2 ). 3/2 8 (2π)

(3)

Assuming Lorentzian contributions of linewidth Γ of each bulk phonon state Φ(~k, ~r) to the Raman signal of the confined phonon state Ψ(~k0 , ~r) allows one to approximate its phonon Raman lineshape by: Z Γ/π dk I(ω) ∝ |C(~k0 , ~k)|2 (ω − ω(~k))2 + (Γ/2)2

(4)

where ω(~k) is the relevant phonon dispersion and the integration is performed appropriately over the 1st Brillouin zone. 705

In case of the confined G mode, which arises from the first-order Raman process involving the LO phonon at the Γ-point, it is k~0 ≈ 0. For simplicity, the phonon dispersion integration has been performed in 1D from K to Γ in the 1st Brillouin zone. The resulting dependence of the Raman peak position of the G band on lateral size La is plotted as a solid line in the top graph of figure 5a).

710

The calculation can quantitatively reproduce the experimental trends from large bulk-like values of La = 24 nm down to about 3 nm where the transition from crystalline behavior to molecular behavior should occur; the correct trend is given even down to 2 nm. In a similar fashion, we also derived the dependence of the D position on

715

crystallite size La . The main difference is that the absolute value of the wave vector ~k0 of the phonons predominantly yielding the bulk D Raman signal is determined by the resonance condition for the electronic transition from the π to π ∗ band, i.e., ∆E(~k0 ) = h ¯ ωL where ∆E denotes the transition energy and hωL denotes the photon energy of the laser used. The resonance conditions ¯

720

yield different ~k0 values along K to Γ and along K to M. Therefore, we have determined the size dependence of the D band position twice, one time based on the phonon dispersion ω(~k) between K and Γ and the other time on that between K and M. The former is presented by the solid line and the latter by the dashed line in the corresponding graph of figure 5.

31

725

Again, the calculations can reproduce the experimentally observed behavior quantitatively almost over the entire range of La values. The deviations between modelled and experimental values are largest in the transition region where the crystalline description breaks down, as expected. A similar degree of agreement between experimental data and calculated size dependence was also obtained

730

for the D band data sets obtained at other laser wavelengths as shown in the supporting information. The Campbell and Fauchet model also yields the lineshape of the Raman bands based on Eq. (4). Exemplarily, figure 5b) depicts the Raman spectra of three samples of the pitch-based LSPP-70 series with La = 21 nm (stage IV),

735

14 nm (stage III) and 4.0 nm (stage II) obtained with 633 nm laser excitation (black solid lines) together with the calculated lineshapes of the G and D band (red solid lines). The agreement is reasonable and the increasing line widths of the Raman bands with decreasing size La is well reproduced. Due to the breakdown of the electronic and phonon dispersion in stage II the agreement of

740

the modelled and experimental data for the 4.0 nm sample is low especially for the D band. The rather good qualitative agreement between the experimental data for the G and D Raman band positions and the corresponding lineshapes of the carbon samples with the Campbell and Fauchet model, almost independent of the type

745

of precursor used, underlines the potential of this approach for determining reliably the lateral size La of nanosized graphene sheets in non-graphitic and graphitic carbons, at least for sizes La > 4 nm. However, some words of caution are appropriate in this context. First, the position of the G and D Raman bands will also depend on strain or temperature [92, 93, 94, 95]. In literature

750

the D band is less analyzed concerning the temperature and strain dependence, however, the 2D band is an overtone of the D band and therefore, the same trend is expected. Indeed, for carbon nanotubes this behaviour is observed by Cronin et al. [92]. Furthermore, it should be taken into account that the degree of doping (position of the Fermi level and Kohn anomaly) in graphene may also

755

affect the positions of the D and G band [75, 96, 97, 98, 99, 100]. 32

Thus, it is essential to make sure that the Raman data to be compared with an empirical master curve or theory are obtained under defined conditions, i.e., conditions which correspond to those for which the underlying theoretical bandstructure and phonon dispersions are optimized. Temperature is probably 760

a crucial factor in this context. Strain may also play a role, in particular, in processed carbon material. For example, specimens under uniaxial stress may exhibit a lower symmetry and the theoretical bulk data underlying the Campbell and Fauchet analysis are no longer valid. It should be noted that according to the Campbell and Fauchet model there

765

are basically two contributions to the linewidth and overall lineshape of a confined phonon mode. The first contribution is the linewidth parameter Γ which reflects the disorder of infinitely large bulk-like crystalline sheets. The second contribution arises from the weakening of the ~k selection rule due to the confinement, i.e., the mixing of bulk phonons of different ω(~k) in the confined state.

770

The role of the Γ parameter in the Campbell and Fauchet model of the lineshape of the confined phonon is comparable to the role of the σ1 parameter in the WAXS model of Ruland and Smarsly, both address structural disorder of the atoms. We performed, for simplicity, the calculation of the G and D band positions using constant Γ, in order to focus on the confinement effects and to

775

demonstrate that they are predominantly responsible for the observed behavior. However, as shown in figure 3, the Raman linewidth not only depends on the size La . The remaining differences can reflect different degrees of ”bulk like” disorder resulting from the different networking properties of the precursors. At a fixed La , the spectral lineshape fits can be refined by varying Γ. We have

780

done this for all samples of the pitch LSPP-70 series and of the resin H series. The results are plotted in the bottom graph of figure 3 and the observed trends indeed compare well with the σ1 -data of the WAXS analysis, i.e., confirming that Γ and σ1 reflect the deviation of the ideal crystal structure, i.e., structural disorder.

33

785

3.2. Conclusions We have analyzed the structural properties of carbons prepared from pitches and resins as precursors by employing Raman spectroscopy, wide-angle X-ray scattering and electron paramagnetic resonance spectroscopy.

The analysis

of WAXS data yielded unambiguously the average size La of the nanosized 790

graphene sheets formed in the carbonization process and allowed us to establish correlations between characteristic features of the Raman spectra such as the positions of the G, D, and 2D Raman bands, their relative intensities as well as their shapes. The Raman and EPR data in conjunction with the WAXS data allow us to identify four characteristic stages along the transformation chain

795

from a molecule-like precursor via amorphous (I) and nanoparticular carbon (II) to non-graphitic carbon (III) or even graphitic carbon (IV). In stages III and IV the 2D Raman signal emerges and its spectral shape allows one to distinguish whether non-graphitic or graphitic carbon is formed. We confirmed that the identity of the precursor and, in particular, its networking capabilities

800

play an essential role in the transformation process. Different spin-densities and lineshapes obtained by EPR spectroscopy support the classification, but unfortunately the EPR intensity cannot be considered as a measure for the defect density as not all defects formed are detectable by EPR. The dependence of the crystallite size on the heat-treatment temperature

805

separates the resins from the pitches. At the same La values the variety and number of defects and therefore the D band lineshapes look different for the two samples series. Also the networking capabilities are represented by the lineshapes and directly influence the changes in

ID/IG .

Based on the La values extracted from the WAXS data, we found that ID/IG 810

as a function of average crystallite size La cannot be considered a unique master curve, but differs for two classes of precursors studied by us reflecting their different networking properties. In other words, a one-to-one correspondence between

ID/IG

and average size La , which is valid for all carbons, does not exist

mainly because the D band intensity ID will depend on the defect type and den815

sity. Thus, the major weakness of the empirical formulas based on 34

ID/IG

lies in

the kind of extrinsic nature of defect formation. We found that the dependence of the peak positions of the G and D band as function of La may serve as much more robust correlations in the entire range of sizes La studied from 1 nm to 25 nm. We modelled this correlation based on phonon confinement effects in a 820

solid-state picture, i.e., describing the functional dependence coming from large sizes, i.e., from the bulk limit of ideal graphene. The theoretical description was attempted by the phonon confinement model of Campbell and Fauchet. The modelled dependence of the G and D band position as a function of La was found to reproduce the experimental data quantitatively from 24 nm down to

825

sizes of 4 nm and qualitatively even down to 1 nm. The latter was surprising as this range covers the soft transition from molecule-like to crystal-like behavior of the carbons and, in general, such transition regions are difficult to describe theoretically. The G process is entirely intrinsic and the position of the G Raman mode only depends on the phonon dispersion. The same is almost true

830

for the position of the D band (other than for its intensity), as the defect is only required for the D Raman process to occur, but the position of the corresponding Raman band is solely determined by the phonon disperison and the bandstructure of graphene. Our results demonstrate the great potential of Raman spectroscopy for a quick assessment of the structural properties of carbons

835

and show that, if appropriate steps are taken, even quantitative information about structural parameters such as the lateral size of the nanosized graphene sheets or the quality of the degree of stacking in the transition region between non-graphitic and graphitic carbon may be extracted. Acknowledgement

840

The authors are very grateful for financial support by the Deutsche Forschungsgesellschaft (DFG) via GRK (Research Training Group) 2204 “Substitute Materials for sustainable Energy Technologies”. We acknowledge computational ressources provided by the HPC Core Facility and the HRZ of the JustusLiebig-University Giessen. We would like to thank Mr. Michael Feldmann

845

of HPC-Hessen, funded by the State Ministry of Higher Education, Research 35

and the Arts, for programming advice. Special thank goes to Marc Loeh, Institute of Physical Chemistry, Justus Liebig University Giessen for the sample preparation. We thank Georgij V. Mamin, Institute of Physics, Department of Quantum electronics and radiospectroscopy, Kazan Federal University for the 850

EPR measurements of the carbon samples under vacuum conditions.

36

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: