SAXS investigation of nanoporous structure of thermalmodified carbon materials
 Bogdan K Ostafiychuk^{1},
 Volodymyr I Mandzyuk^{1}Email author,
 Yuriy O Kulyk^{2} and
 Nadiia I Nagirna^{1}
DOI: 10.1186/1556276X9160
© Ostafiychuk et al.; licensee Springer. 2014
Received: 5 December 2013
Accepted: 27 March 2014
Published: 3 April 2014
Abstract
The article investigates the effect of thermal modification of porous carbon material (PCM), obtained from plant feedstock, on its morphology and fractal structure by smallangle Xray scattering (SAXS) method. The analysis of the scattering intensity curves serve the basis for calculating the parameters of the PCM porous structure: the Porod constant, the Porod invariant, average pore radius, specific surface area, and mass and surface fractal dimensions. It has been found out that the PCMs obtained have fractal structure, formed from mass and surface fractals, the sizes of which increase at the growth of temperature and modification time.
PACS
81.05.Uw; 61.05.cf; 82.47.Aa
Keywords
Porous carbon material Smallangle Xray scattering Mass and surface fractalsBackground
One of the principal ways to improve the existing and create new electrochemical technologies is the development of new electrode materials, possessing necessary properties: high electrocatalytic activity, stability, and abundance of original components [1]. These requirements can be provided by creating electrodes on the porous carbon material (PCM) bases that are actively used as electrode materials for primary and secondary chemical power sources and supercapacitors [2–7]. In particular, we have found out that the specific capacity of lithium power sources on the PCM bases, obtained by hydrothermal carbonization of apricot pits at different temperatures, depends mainly on its specific area and electrical conductivity [8, 9]. The maximum value of specific capacity (1.138 mА · h/g) has the electrochemical system on the basis of PCM, obtained at the carbonization temperature of 750°С. It is evident that to increase the specific energy characteristic of the elements, it is necessary to perform intentional change of PCM structure and morphology by means of different types of processing and modification. The most common ways of modification are thermal, chemical, and laser modifications of PCMs [10–12]. To study changes caused by such modifications a wide range of methods are currently used: Xray diffraction method [13], smallangle Xray scattering (SAXS) [14–16], smallangle neutron scattering [16–18], gas adsorption/desorption [19–21], scanning tunnel microscopy [22], atomic force microscopy [23], and transmission electron microscopy [24]. Each of these methods has its advantages and disadvantages, but they provide a possibility to obtain important information about the porous structure of the materials (specific area, total pore volume, micropore volume, dimensions and forms of pores, their size distribution, fractal structure, etc.). The advantages of SAXS method, in comparison with other methods, may include the following [25, 26]: (1) it is sensitive to both closed and open porosity, (2) SAXS intensity profiles are sensitive to shape and orientation of the scattering, (3) the method can be used to investigate samples that are saturated with liquids, (4) it can be used to investigate the pore texture of materials under operating conditions. Thus, the aim of the work is to perform thermal modification of PCM at different temperatures and times and to investigate the effect of this modification on its morphology and fractal structure using the SAXS method.
Methods
The initial standard was PCM, obtained by method of hydrothermal carbonization of plant material at a temperature of 750°С. It was modified at temperatures Т_{mod} 300°C, 400°C, 500°C (modification time t_{mod} was 0.5, 1, 1.5, 2, 2.5, and 3 h), and 600°С (t_{mod} was 0.25, 0.5, 0.75, and 1 h) in the air in a muffle furnace SNOL40/1300. Less PCM modification times at the temperature 600°С can be explained by the fact that at the given temperature, further thermal treatment leads to the complete material burnoff.
where I^{*}(2θ) is the actual scattering intensity, I_{exp}(2θ) is the experimental scattering intensity, I_{0}(2θ) is the intensity distribution in the primary beam, and T = I_{exp}(0) / I_{0}(0) is the transmission coefficient (intensity proportion of the primary beam, passing through the standard at the zero position of detector). The obtained scattering intensity curves include the collimation adjustment for altitude of the detector receiving slit.
Results and discussion
where ρ_{m} is the actual material density that in turn depends on the structural material density ρ_{ x } and porosity w according to the equation ρ _{m} = (1 − w) ρ _{ x } (structural material density is about 2 g/cm^{3}).
The parameters of porous and fractal structure of PCM modified at 300°C
t_{mod}(h)  Q(nm^{−3})  K_{p}(nm^{−4})  ρ_{m}(g/сm^{3})  w  S_{ n }(m^{2}/g)  R_{p}(nm)  L_{1}(nm)  L_{2}(nm)  D _{v}  D _{s} 

0  2,502  1,640  0.71  0.76  529  1.9  7  16  2.4  2.6 
0.5  2,624  1,860  0.59  0.71  785  1.8  7  16  2.7  2.2 
1  2,657  1,800  0.63  0.69  729  1.9         
1.5  2,698  2,020  0.63  0.69  805  1.7  8  16  2.5  2.3 
2  2,670  1,920  0.63  0.69  773  1.8  7  25  2.5  2.3 
2.5  2,679  1,880  0.63  0.69  755  1.7  4  21  2.55  2.7 
3  2,786  1,990  0.63  0.69  768  1.8  9  25  2.4  2.7 
In addition to the smallscale structure, there forms the largescale cluster structure, formed by clusters with the size of L > L_{1} ≈ 2 π / s_{1}. The scattering from those clusters is observed in the range s < s_{1}. The slope of the linear section at s < s_{1} is in the range 3 < n < 4, which indicates the formation of the fractal surface of largescale carbon clusters.
As can be seen from Table 1, the fractal dimension of the cluster surface increases at the increase of material modification time. It should be noted that there are no linear section on the intensity curve of the sample modified for 1 h; that is probably the evidence of the chaotic (nonfractal) distribution of heterogeneities.
The parameters of porous and fractal structure of PCM modified at 400°C
t_{mod}(h)  Q(nm^{−3})  K_{p}(nm^{−4})  ρ_{m}(g/сm^{3})  w  S_{ n }(m^{2}/g)  R_{p}(nm)  R_{с}(nm)  r_{c}(nm)  D _{v}  D _{s} 

0  2,502  1,640  0.71  0.76  529  1.9      2.4  2.6 
0.5  2,459  1,450  0.63  0.69  634  2.2      2.4  2.8 
1  2,406  1,470  0.63  0.69  657  1.9  13  2.0    2.7 
1.5  2,323  1,500  0.63  0.69  694  1.9  14  2.0    2.4 
2  2,354  1,560  0.59  0.71  734  1.9  15  2.5    2.2 
2.5  2,214  1,630  0.56  0.72  832  1.7  16  2.5    2.1 
3  2,177  1,500  0.53  0.74  795  1.8  16  3.0    2.0 
The parameters of porous and fractal structure of PCM modified at 500°C
t_{mod}(h)  Q(nm^{−3})  K_{p}(nm^{−4})  ρ_{m}(g/сm^{3})  w  S_{ n }(m^{2}/g)  R_{p}(nm)  R_{с}(nm)  r_{c}(nm)  D _{v}  D _{s} 

0  2,502  1,640  0.71  0.76  529  1.9      2.4  2.6 
0.5  2,226  1,310  0.56  0.72  665  2.2  12.5  2.5    2.5 
1  2,237  1,500  0.53  0.74  774  1.9  14.0  3.0    2.4 
1.5  2,273  1,510  0.53  0.74  767  1.9  14.0  2.5    2.2 
2  2,249  1,470  0.43  0.79  806  1.9  14.0  2.0    2.0 
2.5  2,183  1,600  0.41  0.80  915  1.7  15.0  2.0    2.0 
3  2,230  1,610  0.39  0.81  912  1.8  15.0  1.5    2.0 
Let us analyze the changes in the parameters of the PCM fractal structure modified at temperature 400°С (scattering intensity curves in double logarithmic coordinates for PCMs, modified at temperatures 400°С, 500°С, and 600°С, are not provided in the article, as their forms are similar to the dependences lg I(s) = f{lg(s)} in Figure 3).
The intensity curve of the sample, modified for 0.5 h, represents the linear section, the slope of which n_{1} = 2.4 indicates the formation of the volumetric fractal structure with the dimension of D_{v} = 2.4. A similar situation can be observed for the initial standard. One can assume that in the range of wave vectors (s_{1}, s_{2}), there is the scattering of nanoclusters, the sizes of which can be calculated by the formula L_{0} ≈ 2 π / s_{2} ≈ 7 nm. In the range s < s_{1}, the linear section may be observed, the slope of which n_{2} = 2.8 indicates the formation of another system of fractal clusters with the size of L ≈ 2 π / s_{1} ≈ 20 nm, the distribution of which is of the volumetric character.
Thermal modification for 1 h leads to the substantial change of the fractal structure. On the intensity curve in a wide range of scattering angles, there is the linear section with the slope n_{2} = 3.3. Such shape of the scattering intensity is characteristic of the porous twophase system (carbon matrix pore) with fractal interphase surface. In this case, the dimension of the fractal surface is D_{s} = 6 − n_{2} = 2.7 (Table 2). Departure from linearity at small scattering angles (s < s_{1}) is caused by the transition to the Guinier mode, for which the dependence I(s) is described by the formula $\mathit{I}\left(\mathit{s}\right)=\mathit{I}\left(0\right)\cdot exp\left\{{\mathit{R}}_{\phantom{\rule{0.12em}{0ex}}\mathrm{g}}^{\phantom{\rule{0.12em}{0ex}}2}\phantom{\rule{0.12em}{0ex}}{\mathit{s}}^{2}/3\right\}$, where R_{g} is the radius of gyration of the scattering heterogeneities. The Guinier mode corresponds to the independent scattering by carbon clusters with the radius of ${\mathit{R}}_{\phantom{\rule{0.12em}{0ex}}\mathrm{c}}=\sqrt{5/3}{\mathit{R}}_{\phantom{\rule{0.12em}{0ex}}\mathrm{g}}$ in the approximation of their spherical form.
In the range of s > s_{2}, there is scattering of monodisperse heterogeneities with the size of r_{c}. Similarly, the scattering at s > s_{2} is described by the Guinier formula. One can assume that the objects investigated are formed by the carbon clusters with the radius R_{c} and with the extended surface, which in turn, consist of nanoclusters with the radius r_{c}. Thus, the values r_{c} and R_{c} define the lower and upper limits of the selfsimilarity of fractal surface. Further increase of the PCM modification time results in quantitative changes in structural parameters. In particular, the fractal dimension of the interphase surface increases, and modification for 2.5 to 3 h leads to the transition from fractal boundary to smooth one with the dimension of D_{s} = 2. Besides, there is the increase in the sizes of carbon nanoparticles r_{c} and fractal clusters R_{c} (Table 2).
In case of PCM, modified at 500°С, the scattering intensity curves are characterized by the linear section in the wide range of scattering angles, the slope of which changes within the limits 3 < n_{2} < 4. Such values n_{2} indicate on the scattering by the fractal surface with the dimension D_{s} = 6 – n_{2}. In this case, the materials investigated can be also viewed as twophase porous systems with the fractal interphase surface. The increase of the modification time leads to the decrease of the fractal dimension and transition to smooth interphase surface (D_{s} = 2) after modification for 2 h. It should be noted that the shape of the intensity curves for PCMs, modified at 400°С and 500°С, is similar. Thus, thermal modification at those temperatures leads to the formation of PCMs, formed by carbon clusters with the radius R_{c} and fractal surface, which in turn, consist of nanoclusters with the radius r_{c} (Table 3).
The parameters of porous and fractal structure of PCM modified at 600°C
t_{mod}(h)  Q(nm^{−3})  K_{p}(nm^{−4})  ρ_{m}(g/сm^{3})  w  S_{ n }(m^{2}/g)  R_{p}(nm)  R_{с}(nm)  r_{c}(nm)  D _{v}  D _{s} 

0  2,502  1,640  0.71  0.76  529  1.9      2.4  2.6 
0.25  2,496  1,740  0.58  0.71  777  1.8  16  2.0    2.6 
0.5  2,553  1,780  0.56  0.72  788  1.8  15  2.5    2.55 
0.75  2,584  1,950  0.56  0.72  853  1.7  15  2.5    2.6 
1  2,482  1,860  0.56  0.72  847  1.7  15  2.0    2.6 
Conclusions
The thermal modification of the initial material at temperature 300°С results in the formation of PCM with the fractal structure, formed by mass fractals with the dimension D_{v} = 2.4 ÷ 2.7, which combine in the surface fractal aggregates with the dimension D_{s} = 2.2 ÷ 2.7. The increase of the modification time leads to the growth in the sizes of both types of fractals.
The increase of the modification temperature to 400°С and 500°С leads to the increase of the pore volume and pore surface area. PCM, modified for 0.5 and 1 h, was formed by carbon clusters with the radius R_{c}, which consists of the nanoclusters with the radius r_{c}. The increase of the modification duration not only leads to the growth in the sizes of carbon nanoparticles and fractal clusters but also causes the transition from fractal to smooth boundary surface (D_{s} = 2) at t_{mod} = 2.5 to 3 h.
Thermal treatment at 600°С and less process duration leads to more substantial changes in the pore specific volume and surface area, the maximum of which is observed at t_{ mod } = 0.75 h. Besides, PCM are the twophase porous structures, produced by carbon clusters, formed from nanoclusters, and pores with the extended fractal surface. The increase of the modification duration does not change the surface fractal dimension (D_{ s } = 2.55 ÷ 2.60).
Authors’ information
BKO is the corresponding member, a professor at the Physics and Technology Department, Vasyl Stefanyk PreCarpathian National University, IvanoFrankivsk, Ukraine. VIM is an associate professor at the Physics and Technology Department, Vasyl Stefanyk PreCarpathian National University, IvanoFrankivsk, Ukraine. YOK is a senior researcher at the Physics Department, Ivan Franko National University, Lviv, Ukraine. NIN is scientific researcher at the Physics and Technology, Vasyl Stefanyk PreCarpathian National University, IvanoFrankivsk, Ukraine.
Abbreviations
 PCM:

porous carbon material
 SAXS:

smallangle Xray scattering.
Declarations
Acknowledgements
This work was supported by CRDF/USAID (no. UKX29200IF08) and the Ministry of Education of Ukraine (no. М/1302009).
Authors’ Affiliations
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