**Reactivity Indexes and Structure of Fullerenes**

**Reactivity Indexes and Structure of Fullerenes**

DOI: 10.5772/intechopen.70642

Ernestina Mora Jiménez, Francisco J. Tenorio, David Alejandro Hernández-Velázquez, Jaime Gustavo Rodríguez-Zavala and Gregorio Guzmán-Ramírez David Alejandro Hernández-Velázquez, Jaime Gustavo Rodríguez-Zavala and Gregorio Guzmán-Ramírez Additional information is available at the end of the chapter

Ernestina Mora Jiménez, Francisco J. Tenorio,

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70642

#### **Abstract**

The discovery of fullerenes and their production in measurable quantities launched many studies about their reactivity and possible applications. Their peculiar structure opened possibilities for their study, initially replacing carbon atoms with alternative atoms. The surface also offers the possibility of attaching several species and the interior of their hollow structure represents a challenge because of the possibility of confining elements or molecules that may become less stable when attached to the exterior of the cage. These modifications may considerably affect both chemical and physical properties. In this chapter, we propose the encapsulation of 3–10 nitrogen atoms as aggregates inside the C70 cage. We also study the structures and reactivity indexes and the stabilization conferred as a result of being part of the fullerene. These aggregates are mainly of interest because of their possible application as energetic materials.

**Keywords:** polynitrogen, endohedral fullerenes, Density Functional Theory, reactivity indexes, C70, energetic materials

#### **1. Introduction**

Over the course of time, carbon materials have become important components not only everyday aspects of life, but also vanguard research. The enormous diversity concerning their uses and applications is constantly increasing, representing an area of constant development. Whether as part of a compound or in pure form, carbon has always attracted attention. At least in its purest forms, its structural diversity is extremely attractive (**Figure 1**).

Research on the formation and arrangement of carbon compounds that included long chains of this element in interstellar space lead to the discovery of fullerenes in 1985. Subsequently,

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

**Figure 1.** Allotropic forms of carbon. From left to right and up to down, diamond, graphite, nanotube and fullerene.

been as -BN- pairs, thus ensuring that isoelectronic species are obtained, although this has not necessarily been the only purpose; in the case of silicon, the main motive has been to search for useful applications in electronics [9–21]. Last but not least, endohedral fullerenes exist because of the fact that they are hollow; so they have the potential application of confining or protecting molecules, thus acting as carriers or stabilizers. Particularly, those with metallic atoms inside them—endohedral metallofullerenes—have been attractive for chemistry, physics and interdis-

Considerable interest in nitrogen compounds has emerged, especially those with a high content of this element, because of their particular properties and forms. Apart from the previously

sented a challenge or turned out to be surprisingly simple [27–30]. In spite of this, until now, the species with the highest content of nitrogen produced in measurable quantities has contained 5 nitrogen atoms, meaning that in particular the cyclopentazole anion could be considered as a motivator for theoretical studies on its formation, as well as representing a building block towards more complex structures [31–35]. As species with higher nitrogen content have

numbered experimental ones. Of these, it has been determined that the preferred forms of N4

must be formed from an azide-pentazole (N3

), little was known of species with higher nitrogen content, until

have been discovered or posited, whose synthesis has either repre-

) [26]. However, over time, new polynitrogenated species

–N5

, theoretical studies have out-

Reactivity Indexes and Structure of Fullerenes http://dx.doi.org/10.5772/intechopen.70642 31

) and that more complex

ciplinary areas, such as materials and biological sciences [22–25].

**Figure 2.** Comparison of C60 fullerene with a soccer ball and C70 with a rugby ball.

−

proved to be very unstable with respect to decomposition to N2

**1.2. Polynitrogenated materials**

known molecular nitrogen (N2

, N4 , N5 − and N5 +

are acyclic, N8

such as N3

and N6

the synthesis of the azide anion (N3

they were produced in measurable quantities for use in experiments [1–3]. Even though their study may have evolved accidentally, insufficient effort has been dedicated to understanding their structure, properties and applications. The best known examples of fullerenes are C60 and C70, both of which consist of 12 pentagons, and only differ concerning the number of hexagons in their structure: 20 in the case of the first and 25 in the second. These differences result in the C60 structure, which is more like a soccer ball and C70, which is more like a rugby ball (**Figure 2**). While C60 is more often known as a buckyball, the rest of the hollow structures are inscribed to the general fullerene group.

#### **1.1. Types of fullerenes**

Research into fullerenes has been extremely diverse, but can be categorized according to the structural aspect to be studied. Correspondingly, we have the following: exohedral fullerenes (with external ligands or molecules), endohedrals (with internal atoms or molecules) and heterofullerenes (with one or more carbon atoms in the cage replaced by heteroatoms).

Exohedral fullerenes have essentially resulted from efforts to "decorate" the surface of the fullerenes; mainly achieved by means of chemical functionalization. These types of fullerenes have proved to be extremely interesting, both for medical applications and for their possible applications in material sciences [4–8]. With respect to heterofullerenes, the substitution of carbon atoms by boron, nitrogen and silicon has been proposed; in the case of the first two, these have regularly

**Figure 2.** Comparison of C60 fullerene with a soccer ball and C70 with a rugby ball.

been as -BN- pairs, thus ensuring that isoelectronic species are obtained, although this has not necessarily been the only purpose; in the case of silicon, the main motive has been to search for useful applications in electronics [9–21]. Last but not least, endohedral fullerenes exist because of the fact that they are hollow; so they have the potential application of confining or protecting molecules, thus acting as carriers or stabilizers. Particularly, those with metallic atoms inside them—endohedral metallofullerenes—have been attractive for chemistry, physics and interdisciplinary areas, such as materials and biological sciences [22–25].

### **1.2. Polynitrogenated materials**

they were produced in measurable quantities for use in experiments [1–3]. Even though their study may have evolved accidentally, insufficient effort has been dedicated to understanding their structure, properties and applications. The best known examples of fullerenes are C60 and C70, both of which consist of 12 pentagons, and only differ concerning the number of hexagons in their structure: 20 in the case of the first and 25 in the second. These differences result in the C60 structure, which is more like a soccer ball and C70, which is more like a rugby ball (**Figure 2**). While C60 is more often known as a buckyball, the rest of the hollow structures

**Figure 1.** Allotropic forms of carbon. From left to right and up to down, diamond, graphite, nanotube and fullerene.

Research into fullerenes has been extremely diverse, but can be categorized according to the structural aspect to be studied. Correspondingly, we have the following: exohedral fullerenes (with external ligands or molecules), endohedrals (with internal atoms or molecules) and het-

Exohedral fullerenes have essentially resulted from efforts to "decorate" the surface of the fullerenes; mainly achieved by means of chemical functionalization. These types of fullerenes have proved to be extremely interesting, both for medical applications and for their possible applications in material sciences [4–8]. With respect to heterofullerenes, the substitution of carbon atoms by boron, nitrogen and silicon has been proposed; in the case of the first two, these have regularly

erofullerenes (with one or more carbon atoms in the cage replaced by heteroatoms).

are inscribed to the general fullerene group.

30 Fullerenes and Relative Materials - Properties and Applications

**1.1. Types of fullerenes**

Considerable interest in nitrogen compounds has emerged, especially those with a high content of this element, because of their particular properties and forms. Apart from the previously known molecular nitrogen (N2 ), little was known of species with higher nitrogen content, until the synthesis of the azide anion (N3 − ) [26]. However, over time, new polynitrogenated species such as N3 , N4 , N5 − and N5 + have been discovered or posited, whose synthesis has either represented a challenge or turned out to be surprisingly simple [27–30]. In spite of this, until now, the species with the highest content of nitrogen produced in measurable quantities has contained 5 nitrogen atoms, meaning that in particular the cyclopentazole anion could be considered as a motivator for theoretical studies on its formation, as well as representing a building block towards more complex structures [31–35]. As species with higher nitrogen content have proved to be very unstable with respect to decomposition to N2 , theoretical studies have outnumbered experimental ones. Of these, it has been determined that the preferred forms of N4 and N6 are acyclic, N8 must be formed from an azide-pentazole (N3 –N5 ) and that more complex polynitrogens may exist such as N7 , N12, N18, N20 and a great etcetera [36–42]. Considering larger structures, there is no doubt that polyhedral or fullerene-type structures have provided inspiration, as they are considered as alternative polynitrogenous arrangements with a greater number of nitrogen atoms [18, 19, 21, 41, 43–47]. In this sense, a hollow structure could in principle be useful for storing internal molecules, which is why it is common to find hollow carbon structures as candidates for confining polynitrogenous species. Currently, the most notable examples have been studies of N@C60, N@C70 or even N2 @C60 [48–52], which have extended the use of the C60 cage as a way of confining up to 16 nitrogen atoms [53, 54]. Also recently, the encapsulation of a polymer nitrogen chain in a carbon nanotube was conceived, as in principle this could be stable up to room temperature [55]. This contrasts with other proposed polynitrogenated phases of nitrogen that have been inspired by the analogy to phosphorus and arsenic, all superior in energy to the "cubic gauche" (CG). These have been proposed for extreme conditions and some experimental evidence has even been found for them [56–61]. Therefore, confinement represents an alternative for the stabilization of polynitrogenated species that are not necessarily related to high temperatures and pressure.

Chemical potential was computed by conceptual Density Functional Theory approximation. For an N electron system with an external potential v(r) and total energy E, electronegativity is defined as the partial energy derivative to the number of electrons at constant potential and then by the definition of Mulliken as the mean of IE and EA and the negative of electronega-

> \_\_\_ ∂E ∂N)ν(r)

chemical potential to the number of electrons, also at constant energy potential:

) or detected in experiments (N3

∂2 \_\_\_\_E ∂N2)ν(r)

Chemical hardness was calculated as defined by Parr and Pearson [71], differentiating the

Energies were also obtained for the stabilization reactions for polymer species within the C70 structure, applying the formula: ∆E = ΣE(products) − ΣE(reagents) for two possible schemes. In the first, the stabilization of isolated nitrogen atoms could be analyzed through the reaction *n*N + C70 Nn@C70. In the second scheme, the reagents are substituted with nitrogen as found

It was previously reported that the methodology consisted of an optimization at the PM6 level. As the refinement and electronic structure were performed at the B3LYP/6-311G level,

For the majority of the structures obtained, neutral and charged species correspond to the same arrangement. In cases where it is not observed, it will be mentioned in due course.

the same structure in charged and neutral systems, see **Figure 3**. There is also found a second

"isolated" nitrogen atom. The difference in the relative energies exceeds 40 kcal/mol, leading us to assume that the linear isomer encapsulated in C70 would predominate, if it was ever produced. Distances between nitrogen atoms (1.20 Å) suggest a weaker bond than that observed

Reaction energies were calculated based on various assumptions. First, it is considering only the stabilization due to the encapsulation of nitrogen atoms as reagents. Second, considering

(or not) of 3 isolated nitrogen atoms, compared to placing them within the cage in polymer

@C70 reaction was used to evaluate the role of the C70 box for the stabilization

. The minimum energy structure corresponds to a linear and centered N3

structures that can be found at room temperature as starting materials (**Table 1**).

stable structure that may closely resemble the association between the N2

≈ −\_\_\_\_\_\_ IE + EA

≈ \_\_\_\_\_\_ IE − EA

− , N5 − , etc).

2 (1)

Reactivity Indexes and Structure of Fullerenes http://dx.doi.org/10.5772/intechopen.70642 33

2 (2)

, which shows

molecule and an

tivity is the molecular chemical potential, μ:

μ = −χ = (

η = (

they are presented exclusively in the following.

**3.1. N***n***@C70 structures and reaction energies**

in standard state (N2

**3. Results**

**N3**

for N2

(1.11 Å).

The 3N + C70 → N3

As our work group has studied fullerenes and their reactivity [7, 16, 62–65] and it has been proposed that C60 might be an ideal candidate for trapping nitrogen by a polymer [53, 54], the intention now is to show that C70 might also be an alternative way of storing polynitrogenous species, contributing to the development of new materials in the future.


**1. Introduction**

China is the world's largest emitter of greenhouse gases, and its low-carbon development faces huge challenges. In September 2020, China proposed the climate goal of "carbon peak by 2030 and carbon neutral by 2060" for the first time at the UN General Assembly. The Central Economic Work Conference in December 2020, the Government Work Report in March 2021, and the 14th Five-Year Plan have repeatedly reaffirmed this climate goal.

Tourism has become one of the major sources of global climate change [1]. The carbon emission of tourism accounts for 5% of the total global carbon emission, and the greenhouse effect formed by the carbon emission of tourism accounts for about 14% of the total global effect. By 2035, tourism's carbon emissions are expected to increase by 152%, and its contribution to the greenhouse effect is expected to increase by 188% [2]. In response to this problem, more attention should be given to key issues such as sustainability and adaptation to climate change [3]. Tourism should strive to reduce carbon emissions and improve the

**Citation:** Li, S.; Cheng, Z.; Tong, Y.; He, B. The Interaction Mechanism of Tourism Carbon Emission Efficiency and Tourism Economy High-Quality Development in the Yellow River Basin. *Energies* **2022**, *15*, 6975. https://doi.org/10.3390/en15196975

Academic Editor: Attilio Converti

Received: 29 August 2022 Accepted: 20 September 2022 Published: 23 September 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

efficiency of tourism's carbon emissions, and some actions based on anticipatory action planning are needed in the tourism sector [4]. The availability and sharing of knowledge and information related to tourism's carbon emissions is a basic requirement for the successful planning of the tourism sector regarding this phenomenon [5].

Global tourist arrivals are expected to maintain an annual growth rate of 3.3% between 2010 and 2030 to reach 1.8 billion arrivals [6], generating rapid economic growth for the tourism industry as well as huge challenges. As a pillar industry of China's national economy, the economic development of tourism is also an important issue that requires attention. The China Tourism Economy Blue Book (No. 13) put forward the tourism economy's high-quality development. The development of the tourism economy is closely related to social, economic, and ecological environments [7,8]. Studies have shown that, with the passage of time, tourism consumption and total tourism emissions are roughly 2:1 in direct proportion [9]. Therefore, the next step is to realize how "ecological benefits" and "economic benefits" go hand in hand. It is important to study the interaction mechanism between tourism's carbon emission efficiency and the tourism economy. It helps to realize low-carbon tourism and the high-quality development of tourism.

The Yellow River Basin is an important economic belt and ecological barrier in China. The general secretary's speech in 2019 at the Symposium on Ecological Protection and High-quality Development in the Yellow River Basin, as well as the proposal made at the 6th Meeting of the Financial and Economic Commission of the CPC Central Committee in 2020 to make overall planning and coordinated progress based on the whole Basin and the ecosystem, all illustrate the importance of achieving a win-win situation between economic development and environmental protection in the Yellow River Basin. Therefore, this paper analyzed tourism's carbon emission efficiency (TCEE) and the tourism economy's high-quality development (TEHQD) in nine provinces in the Yellow River Basin from 2010 to 2019. Then, we explored the symbiotic interaction mechanism between TCEE and TEHQD. This is part of the tourism industry's active response to climate change. It provides a basis for the tourism economy's high-quality development, and it also provides ideas and paths for the realization of low-carbon tourism and high-quality economic development in the Yellow River Basin.

There are three main contributions of this paper. Firstly, from a theoretical perspective, this study is conducive to deepening the research on low-carbon tourism, exploring the tourism economy's high-quality development (TEHQD) from a low-carbon perspective, improving the research on the relationship between tourism's carbon emission efficiency (TCEE) and the tourism economy from the symbiotic perspective, enriching the research framework of the interaction mechanism. Secondly, this study adapted to the goal of "Carbon Peak and Carbon Neutral" and the requirements of the tourism economy's highquality development. Research on the carbon emission efficiency of tourism can guide the development of tourism to better assume corresponding responsibilities for carbon reduction. The evaluation system for the tourism economy's high-quality development (TEHQD) was established, which can help to evaluate the development level of the tourism economy comprehensively and provide ideas for the tourism economy's high-quality development. Thirdly, this study contributes to the realization of the Ecological Protection and High-quality Development strategy in the Yellow River Basin. Taking the nine provinces in the Yellow River Basin as the study area, the study of tourism's carbon emission efficiency (TCEE) was used to connect with ecological protection, and the study of the tourism economy's high-quality development was used to correspond with a high-quality development strategy, which can not only promote the development of the two but also contribute to the integration of the two.

The rest of this paper is organized as follows. The second part reviews the relevant literature of this paper. The third part introduces the model, the data source, the specific evaluation index system, and the formula. The fourth part is the empirical analysis of this paper, including the evaluation of TCEE, the evaluation of TEHQD, the evaluation of the symbiosis between TCEE and TEHQD, and the construction of the symbiosis interaction mechanism between TCEE and TEHQD. Following that, the research conclusion, the countermeasure suggestion, the shortage, and the prospect are given in the fifth part.

#### **2. Literature Review**

Tourism's carbon emission efficiency (TCEE) refers to tourism's ecological efficiency based on carbon emissions from the perspective of low carbon, which is used to observe the value that can be achieved by the cost of carbon emissions. At present, research on tourism's ecological efficiency has covered concept [10], mechanism analysis [11], countermeasures and suggestions [12], model building [13,14], and efficiency measurement [15,16]. In terms of the specific content of the research, it mainly includes research on the input and output effect of tourism resources. For example, Jiang (2022) took tourism's CO2 emission efficiency as undesired output, established an index system based on the input and output of tourism's CO2 emission efficiency, and measured the tourism CO2 emission efficiency of Chinese provinces [17]. The application of tourism's ecological efficiency to destination management, as well as the research on energy consumption and carbon emission intensity generated in the process of tourism are also receiving attention. Reilly (2010) studies have shown that tourism traffic is the most important part of energy consumption, and promoting the efficiency of transportation energy will help to enhance the efficiency of tourism ecology [18]. From the perspective of research methods, the current evaluation of tourism's ecological efficiency mostly adopts the single ratio method [19], carbon footprint model [20], life cycle assessment [21], carrying capacity of the low-carbon tourism environment model [22], DEA model [23], and SBM-DEA model [24]. Some researchers who use the single ratio method to measure tourism's carbon emission efficiency usually choose the two indexes of tourism's carbon emissions and tourism's income for accounting [25]. However, most researchers choose to use the "input-output" index and calculate the tourism carbon emission efficiency by establishing a model. From the perspective of the "input" index, it mainly focuses on capital input, labor input, resource input, and energy input [24]. From the perspective of "output" indicators, desirable output indicators such as tourism's income and number of tourists are mainly used [26]. In terms of influencing factors, urbanization, economic development level, government regulation, and tourism development level have an impact on tourism's ecological efficiency [27]. Other researchers analyzed the impact of foreign direct investment [28] and technology embedding [29] on tourism eco-efficiency. It can be seen that, at present, research on the influencing factors of tourism's carbon emission efficiency are mostly focused on the single level of economy, industry, and technology, while the influencing factors of humanities, society, and environment are relatively rare. the exploration of multi-faceted influencing factors has not yet received attention. Researchers mostly use exponential decomposition [24], the regression model [28], or the spatial econometric model [24] to study the influencing factors and analyze the linear relationship between each influencing factor and tourism's ecological efficiency, but they rarely consider the dynamic relationship and interaction mechanism between each influencing factor and tourism's ecological efficiency.

Tourism development is closely related to economy, culture, and ecological environment [30]. With China's requirements of high-quality development, the tourism economy's high-quality development (TEHQD) has also entered the horizon of researchers. Research on the influencing factors of the development quality of the tourism economy has always been the focus of scholars [31]. It has been found that resource conservation, ecological environmental protection, and sustainable development are the important goals of tourism's economic development and the important content of quality improvement [32]. Efficiency improvement, structural optimization, and environmental coordination are the core contents and important ways to promote the development of the tourism economy [33]. Scientific and reasonable arrangements should be made to maximize the adjustment of tourism's resource development and ecological environment protection to improve the sustainable development capacity of the tourism economy [34].

The relationship between the development of the tourism economy and other factors has always been an important issue, such as the relationship between carbon emissions and international tourism growth [35], between tourism investment and energy innovation on carbon dioxide emissions [36], between tourism economy and regional integration [37], and between tourism economic development and government policy [38,39]. With the development of tourism and the improvement of the quality requirements of the tourism economy, the relationship between tourism and the ecological environment is increasingly concerned. Tourism development not only brings economic benefits to the local area, but it also increases the pressure on the local ecological environment [40]. Therefore, it is necessary to take certain measures to promote the coordination between tourism and the environment to realize the sustainable development of tourism [41]. In terms of research content, studies on the tourism economy and ecological environment mainly include their interaction [42], their coupling and coordinated development evaluation [43], influencing factors [44], policies and paths to promote their joint development [45], tourism's ecological footprint measurement [46,47], tourism's ecological efficiency [24], tourism's environmental capacity [48,49], and tourism's ecological security [50]. From the perspective of research methods, in addition to macro qualitative description, spatial data analysis [24], and econometric analysis [28], the coupled coordination model is the most common quantitative study [51].

To sum up, the evaluation of tourism's efficiency from the perspective of ecology is the basis and premise for the realization of the high-quality and sustainable development of tourism, when low carbon tourism has become the goal and mode of tourism development. However, the current research on tourism's carbon emission efficiency usually focuses on the form of tourism's ecological efficiency and less directly considers the more detailed tourism carbon emission efficiency. In the calculation of tourism's carbon emission efficiency, the single ratio method is mainly used, and the research method needs to be expanded urgently. The construction of the "input-output" evaluation index of tourism's carbon emission efficiency rarely considers the undesired output. The few evaluation systems that include an undesired output rarely take tourism's carbon emissions as a specific index. The influencing factors of tourism's carbon efficiency focus on a single aspect, such as economy, industry, technology, society, and environment factors, and multifaceted influence factors are uncommon. Research on the relationship between various influencing factors and tourism's ecological efficiency that gives priority to a linear relationship between the interaction mechanism and dynamic relationship is relatively lacking. The consideration of the development of the tourism economy is mainly based on a single factor, such as industry or technology, and lacks the comprehensive consideration of the tourism economy's high-quality development. Studies on the relationship between the tourism economy and other factors are mainly about social and industrial factors; the relationship between the tourism economy and the ecological environment needs more attention. Most of the studies on tourism's economic development related to the ecological environment are focused on the environment of the whole society, and few of them are detailed towards tourism or even tourism's carbon emission efficiency. The research methods are mainly coupled and coordinated, while other methods should be applied.

#### **3. Research Methods and Data Sources**

*3.1. Modeling and Data Sources*


The turbulence models are summarized in Table 4

Zero equation models

One equation models Two equation models

Smagorinsky-Lilly

RNG – LES model WALLE model

Dynamic subgrid-scale

κ – ε κ – ω

Reynolds Stress Model (RSM)

model

Turbulence is that state of fluid motion which is characterized by random and chaotic threedimensional vorticity. When turbulence is present, it usually dominates all other flow phenomena and results in increased energy dissipation, mixing, heat transfer, and drag. The physical turbulence models provide the solution the closure problem in solving Navier – Stokes equations. While there are ten unknown variables (mean pressure, three velocity components, and six Reynolds stress components), there are only four equations (mass balance equation and three velocity component momentum balance equations). This disparity in number between unknowns and equations make a direct solution of any turbulent flow problem impossible in this formulation. The fundamental problem of turbulence modeling is to relate the six Reynolds stress components to the mean flow

*C H v H T TT H t t*

(11)

Models Description and advantages

model Provides excellent results for all flow systems.

scale motions.

flows.

*r*

(12)

The most widely used models. Its main advantages are short computation time, stable calculations and reasonable results for many

Provides good predictions for all types of flows, including swirl, and separation. Longer calculation times than the RANS models.

LES solves the Navier-Stokes equations for large scale motions of the flow models only the small

**4.1.3 Energy equation**

*H* = Specific enthalpy *T* = Temperature

λ = Thermal conductivity

**4.2 Turbulence models**

Family group

Reynolds – Averaged Navier – Stokes (RANS)

Large Eddy Simulation (LES)

Where

The gas and solid energy equations can be written as:

γ = Interface heat transfer coefficient: / *Nu dp*

$$\frac{\partial}{\partial t}(a\_s \rho\_s) + \nabla \cdot \left(a\_s \rho\_s \vec{v}\_s\right) = 0 \tag{2}$$

Where α, �� and *v* are volume fraction, density and the vector velocity, respectively. No mass transfer is allowed between phases.

#### **4.1.2 Momentum equations**

The gas phase momentum equation may be expressed as:

$$\frac{\partial}{\partial t} \left( a\_g \rho\_g \vec{v}\_g \right) + \nabla \cdot \left( a\_g \rho\_g \vec{v}\_g \vec{v}\_g \right) = -a\_g \nabla p + \nabla \cdot \left[ \pi\_g \right] + a\_g \rho\_g \vec{g} + \mathcal{J} \left( \vec{v}\_s - \vec{v}\_s \right) \tag{3}$$

 *p* and *g* are fluid pressure and gravity acceleration. *β* is the drag coefficient between the phases *g* and *s*. The stress tensor is given by:

$$
\sigma\_{\mathcal{g}} = \alpha\_{\mathcal{g}} \mu\_{\mathcal{g}} \left[ \nabla \vec{v}\_{\mathcal{g}} + \left( \nabla \vec{v}\_{\mathcal{g}} \right)^{T} \right] - \frac{2}{3} \alpha\_{\mathcal{g}} \mu\_{\mathcal{g}} \nabla \vec{v}\_{\mathcal{g}} \tag{4}
$$

The solid phase momentum equation may be written as:

$$\frac{\partial}{\partial t} \left( a\_s \rho\_s \vec{v}\_s \right) + \nabla \cdot \left( a\_s \rho\_s \vec{v}\_s \vec{v}\_s \right) = -a\_s G \nabla a\_s + \nabla \cdot \left[ \tau\_s \right] + a\_s \rho\_s \vec{g} + \mathcal{J} \left( \vec{v}\_g - \vec{v}\_s \right) \tag{5}$$

$$
\sigma\_s = \alpha\_s \mu\_s \left[ \nabla \vec{v}\_s + \left( \nabla \vec{v}\_s \right)^T \right] - \frac{2}{3} \alpha\_s \mu\_s \nabla \vec{v}\_s \tag{6}
$$

*G* is the modulus of elasticity given by:

$$G = \exp\left[C\_G \left(\alpha\_s - \alpha\_{s,\text{max}}\right)\right] \tag{7}$$

Where αs,max is the maximum solid volume fraction and β is the interface momentum transfer proposed by Gidaspow, (1994):

$$\begin{cases} \beta = 150 \frac{\alpha\_s \left(1 - \alpha\_{\mathcal{S}}\right) \mu\_{\mathcal{S}}}{\alpha\_{\mathcal{S}} d\_p^2} + 1.75 \frac{\alpha\_s \rho\_{\mathcal{S}} \left| \vec{v}\_s - \vec{v}\_{\mathcal{S}} \right|}{d\_p} & \left| \alpha\_{\mathcal{S}} \le 0.8 \\\\ \beta = \frac{3}{4} C\_D \frac{\alpha\_s \alpha\_{\mathcal{S}} \rho\_{\mathcal{S}} \left| \vec{v}\_s - \vec{v}\_{\mathcal{S}} \right|}{d\_p} \alpha\_{\mathcal{S}}^{-2.65} & \left| \alpha\_{\mathcal{S}} > 0.8 \end{cases} \tag{8}$$

Where *dp* and *CD* are the particle diameter and the drag coefficient, based in the relative Reynolds number (*Res*)

$$\text{C}\_{D} = \left| \frac{24 \left( 1 + 0.15 \,\text{Re}\_{s}^{0.687} \right)}{\text{Re}\_{s}} \right| \, |\, \text{Re}\_{s} \le 1000 \,\tag{9}$$

$$0.44 \,\qquad \left| \, \text{Re}\_{s} > 1000 \,\right.$$

$$\text{Re}\_s = \frac{\rho\_{\mathcal{g}} \left| \vec{v}\_s - \vec{v}\_{\mathcal{g}} \right|}{\mu\_{\mathcal{g}}} \tag{10}$$

### **4.1.3 Energy equation**

The gas and solid energy equations can be written as:

$$\frac{\partial}{\partial t} \left( a\_g \rho\_g H\_g \right) + \nabla \cdot \left( a\_g \rho\_g \vec{v}\_g H\_g \right) = \nabla \cdot \left( a\_g \lambda\_g \nabla T\_g \right) + \gamma \left( T\_s - T\_g \right) + a\_g \rho\_g \sum\_r \Delta H\_r \frac{\partial \mathcal{C}\_r}{\partial t} \tag{11}$$

$$\frac{\partial}{\partial t}(a\_s \rho\_s H\_s) + \nabla \cdot \left(a\_s \rho\_s \vec{v}\_s H\_s\right) = \nabla \cdot \left(a\_s \lambda\_s \nabla T\_s\right) + \gamma \left(T\_g - T\_s\right) \tag{12}$$

Where

44 Advanced Fluid Dynamics

0 *ss sss v*

*g gg g ggg g v v v p g g gg v v s g t*

 *p* and *g* are fluid pressure and gravity acceleration. *β* is the drag coefficient between the

*s ss s sss s s s s s v vv G g v v g s t*

*G C* exp *Gs s* ,max

is the maximum solid volume fraction and

 2

1

*C*

*C*

2

2

*vv v*

150 1.75 | 0.8

*s g g sg s g*

*g p p*

*d d v v*

*sgg s g*

Where *dp* and *CD* are the particle diameter and the drag coefficient, based in the relative

*s*

Re *g s g*

 *v v*

*g*

*p*

0.687 24 1 0.15Re

*s D s*

*s*

*d*

*T s ss s s ss s*

*vv v*

*T g gg g g gg g*

are volume fraction, density and the vector velocity, respectively. No

3

3

2.65

*s*

*v v*

3 | 0.8 4

*D gg*

(5)

(3)

(4)

(7)

is the interface momentum

(9)

(10)

(6)

β

*g*

(8)

(2)

*t*

The gas phase momentum equation may be expressed as:

The solid phase momentum equation may be written as:

Where α,

Where

αs,max

Reynolds number (*Res*)

��and *v*

**4.1.2 Momentum equations**

mass transfer is allowed between phases.

*G* is the modulus of elasticity given by:

transfer proposed by Gidaspow, (1994):

phases *g* and *s*. The stress tensor is given by:

*H* = Specific enthalpy

*T* = Temperature

γ = Interface heat transfer coefficient: / *Nu dp*

λ = Thermal conductivity

#### **4.2 Turbulence models**

Turbulence is that state of fluid motion which is characterized by random and chaotic threedimensional vorticity. When turbulence is present, it usually dominates all other flow phenomena and results in increased energy dissipation, mixing, heat transfer, and drag. The physical turbulence models provide the solution the closure problem in solving Navier – Stokes equations. While there are ten unknown variables (mean pressure, three velocity components, and six Reynolds stress components), there are only four equations (mass balance equation and three velocity component momentum balance equations). This disparity in number between unknowns and equations make a direct solution of any turbulent flow problem impossible in this formulation. The fundamental problem of turbulence modeling is to relate the six Reynolds stress components to the mean flow quantities and their gradients in some physically plausible manner.

The turbulence models are summarized in Table 4

Fluid Dynamics of Gas – Solid Fluidized Beds 47

Fig. 2. Gas flow over a flat solid surface (left to right) experimental picture, refined mesh

*P P PP C SV S S*

*P* is the value of source term in the center of the cell *P* and *VP* is the volume of

(16)

*P* was suggested by

computational cell centered on node *P.* The method to represent *S*

near the wall and contrast between experiment and discretization.

Fig. 3. Finite volume representation and notation.

**4.4 Source term linearization**

Where *S*

Patankar, 1980

A generic source term may be written as

Table 4. Summary of turbulence models.


**Author details**

Pablo Andrés Crespo Reinoso1 \*, Emilio Ruiz Delgado2 and James Jerez Robalino3

1 Oral and Maxillofacial Surgery. Private practice

2 Department of Prosthodontics and Implantology, Universidad de Cuenca, Ecuador

3 Faculty of Dentistry, Universidad Nacional Autónoma de México, Resident Department of Oral and Maxillofacial Surgery, Ciudad Universitaria, México

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Biomechanics of the Temporomandibular Joint DOI: http://dx.doi.org/10.5772/intechopen.103836*


*Article* **Psychological Health Status of Psychiatric Patients Living in Treatment Communities before and during the COVID-19 Lockdown: A Brief Report**

**Pierluigi Cordellieri 1, Benedetta Barchielli 2, Valeria Masci 3, Francesca Viani 3, Ivan de Pinto 3, Andrea Priori 3, Felice Damiano Torriccelli 3, Chiara Cosmo 4, Stefano Ferracuti 4, Anna Maria Giannini 1 and Jessica Burrai 1,2,\***

**Abstract:** Many studies investigated the psychological impact of lockdown measures on the general population, while few studies focused on the psychiatric population. This study aimed to investigate the role of therapeutic communities in the management and containment of symptoms of patients with psychosis living in psychiatric residential facilities. Data were collected at two different points: November 2019 (Coronavirus disease 19 had not yet spread) and April 2020 (during the lockdown in Italy). Twenty-two study participants were recruited from three residential accredited psychiatric facilities. During lockdown, the patients showed a small increase in symptomatology in terms of emotional isolation. In addition, it was been observed significant differences in certain functional areas of the behavior, measured as lower inclination towards violent behaviors during lockdown, and higher scores in substance abuse and medical impairment. The lockdown condition could represent a form of containment; daily routines, along with adequate social support, are important aspects of the stability and the level of behavioral functioning of psychiatric patients. Social support and continuity of care offered by psychiatric communities can be an effective safeguard against the psychological impact of the COVID-19 epidemic.

**Keywords:** COVID-19; psychiatric patients; mental illness; cognitive function; psychiatric symptoms; risk perception; social support; lockdown


**About the Special Issue Editors**

**Kanji Ono** received a B.Eng. from the Tokyo Institute of Technology and a Ph.D. in materials science from Northwestern University. After a year of postdoctoral research at Northwestern, he joined the faculty of the University of California, Los Angeles, where he became professor of engineering in 1976 and professor emeritus in 2005. He was awarded the HM Howe Medal by ASM International, the Achievement Award by ASNT, the Gold Medal Award by AEWG, and the Kishinoue Award by JSNDI. He is the author of more than 250 publications in materials science, acoustic emission, and non-destructive testing, and was the founding editor of *Journal of Acoustic Emission*. His areas of research have included physical metallurgy, strength and fracture of metallic and composite materials, non-destructive testing, and physical acoustics.

**Tomoki Shiotani** has worked on AE and relevant NDT for the evaluation of civil engineering materials and structures. After graduate study at Tokushima University, he conducted research at a general contractor, then moved to Kyoto University in 2007. In 2014, he founded the Laboratory on Innovative Technology for Infrastructure at Kyoto University, and was promoted to Professor. He has served as chair of AEWG, USA, and of Research and Technical Committee on AE in JSNDI, Japan, and organized International Symposium of AE twice (2008 and 2016) in Kyoto. He was a co-founder of International Institute of Innovative AE. He received Gold Medal of AEWG in 2019, and Best Paper Award of Structural Faults and Repair (Scotland, U.K.) four times.

**Martine Wevers**, Engineer in Metallurgy and Materials Engineering KU Leuven 1981, PhD in Science and Engineering KU Leuven 1987, is a full Professor at the KU Leuven and coordinating the research group "Materials Performance and Non-Destructive Evaluation" at the Department of Metallurgy and Materials Engineering. She is Chair of the Department of Materials Engineering. She is responsible for the NDT research (quality control, defect detection, development of new NDT techniques and data analysis procedures) and the research on the mechanical behavior of materials (fracture mechanics and fatigue). She specializes in in-situ or on-line damage monitoring techniques (acoustic emission, optical fibers, and sensors for structural health monitoring) and the evaluation of microstructural damage in materials using X-ray computed tomography.

**Marvin Hamstad** (Ph.D. ME/Solid Mechanics, University of California, Berkeley) has been continuously involved in acoustic emission research and applications since 1971. This AE work has ranged from nondestructive testing applications to materials characterization. He has worked in the field of composite materials since the 1970s. His various research efforts have resulted in more than 140 papers. From 1971 to 1984, he was at Lawrence Livermore National Laboratory. From 1984 to 2010, Dr. Hamstad was Professor of Engineering at the University of Denver. He is currently Professor Emeritus. Since 1992, Dr. Hamstad has held positions working on AE at the National Institute of Standards and Technology, Boulder, CO. He was chairman of the Committee on Acoustic Emission from Reinforced Plastics for 16 years, where he initiated the AECM international symposiums (1983–1998). Dr. Hamstad was an associate editor of *J. Structural Health Monitoring*, and currently serves as a co-editor of *JAE*.


**5. References**

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© 2013 Sachs et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Sachs et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**ultraMEDIS – Ultra-Wideband**

Ulrich Schwarz, Marko Helbig and Jürgen Sachs

Additional information is available at the end of the chapter

Ingrid Hilger, Katja Dahlke, Gabriella Rimkus, Christiane Geyer, Frank Seifert, Olaf Kosch, Florian Thiel, Matthias Hein, Francesco Scotto di Clemente,

The exploitation of electromagnetic interaction with matter specifically with organic tissues is a powerful method to extract information about the state of biological objects in a fast, continuous and non-destructive (i.e. painless) way. These interactions are mainly based on

One proceeds on an atomic and molecular level, which is typically described by the

reasons of possible interactions may be quite manifold. Here, in connection with ultrawideband sounding, we restrict ourselves to pure electric interactions which affect the permittivity and conductivity via the motion of free charge carriers (free electrons and ions), the Maxwell-Wagner polarization (also Maxwell-Wagner-Sillars polarization) at boundaries, reordering of dipolar molecules or oscillations on an atomic or nuclear level. We assume that

interaction mechanisms for biological tissue is given in [1], and sub-chapter 3 deals with some selected examples. The related effects are scattered over a huge frequency band covering 15…18 decades. In this paper, we limit ourselves to RF and lower microwave frequencies. Water – the key building block of life –shows dipole relaxation within the considered frequency band. Additionally, it has a very high permittivity in comparison with other natural substances. Hence, water will play an important role for UWB-sounding of biological tissue or human and animal subjects. Examples exploiting this fact are discussed in sub-chapter 5 dealing with breast cancer detection or in [2], which refers to lung edema. The frequency bands of our experiments were selected depending on physical requirements (propagation attenuation, relaxation time) and implementation issues of the sensor electrodes (e.g. antennas).

and conductivity

. An overview of relevant

. The physical

, permeability

all involved substances have the permeability of vacuum 0

**Sensing in Medicine**

http://dx.doi.org/10.5772/54987

two groups of phenomena.

macroscopic quantities permittivity

**1. Introduction**


**1. Introduction**

200 New Research on Knowledge Management Technology

Cobos, R. (2003). *Mechanisms for the Crystallisation of Knowledge, a proposal using a collaborative*

Cobos, R., Pifarré, M. (2008). Collaborative knowledge construction in the web supported by

Cobos, R., Claros, I., Moreno, J. (2009). A proposal of Awareness Services for the Construction

Díez, F, Cobos, R. (2007). A Case Study of a Cooperative Learning Experience in Artificial

Echeverria, l., Cobos, R. (2010). A Motivation Booster proposal based on the monitoring of

Gómez, M., Gutiérrez, A., Cobos, R., Alamán, X. (2001). Collaborative Learning with

Luz, C.M., Borges, M.R.S., Campos, M.L.M. (2008) Sofia – A framework for the

Moreno-Llorena, J., Alamán, X. (2006). A Proposal of Design for a Collaborative Knowledge

Moreno-Llorena, J. (2008). *Collaborative Knowledge Management By Means Semantic Information.* Doctoral dissertation. Universidad Autónoma de Madrid. Pifarré, M., Cobos, R. 2009 Evaluation of the Development of Metacognitive Knowledge

*Journal (ETR&D),* Vol. 57, No. 6 (March 2009), pp. 787-799. ISSN 1042-1629. Pifarré, M., Cobos, R. 2010. Promoting Metacognitive Skills through peer scaffolding in a

Schlichter, J., Koch, K. & Chengmao, X. (1998). Awareness The Common Link Between

T. Ishida (Ed), pp. 77–93, Springer Verlag, ISBN 3-540-65475-5, London, UK.

676, ISBN 978-1-4244-6763-1, Shanghai, China, April 14-16, 2010.

315-0, ACM Press, Vancouver, Canada, October 31, 2008.

978-1-4020-4204-1, Dordrecht, The Netherlands.

pp. 365-374, ISBN 978-3-642-02555-6, San Diego, USA, July 19-24, 2009. Cobos, R., Cajías, R., Barros, L., Borges, M.R.S. (2010). Towards the Construction of a

(december 2007), pp. 308-316, ISSN 1061-3773.

the KnowCat system. *Computers & Education*, Vol.50, No. 3, (April 2009), pp. 962-

of Quality Community Knowledge supported by the Knowledge Management system KnowCat. *Proceedings of International Conference Human-Computer Interaction*,

Knowledge Building Environment. *LNCS 6240,* Luo, Y. (Ed.), pp. 27-30. Springer,

Intelligence. *Journal Computer Applications in Engineering Education*. Vol. 15, No. 4,

users' progress in CSCL environments. *Proceedings of the 2010 14th International Conference on Computer Supported Cooperative Work in Design (CSCWD 2010)*, pp. 671-

computer-based support in the design of material for the development of abstract thought in Preschool Education. An Experiment in the teaching of mathematics. *Proceedings of the International Symposium of Computers in Education 2001*, pp. 241-254. Gross, B. M. (1964). *The Managing of Organizations: The Administrative Struggle (Vol. 1)*, New

Development of Group Storytelling Tools, *Proceedings of the ACM Workshop on Story Representation, Mechanism and Context (SRMC 2008)*, pp. 41–47, ISBN 978-1-60558-

Management System by means of Semantic Information. In: *HCI related papers of Interacción 2004, Navarro*-Prieto, R. et al. (Eds.), Springer, pp. 307-319, 2005. ISBN

Supported by the KnowCat system. *Educational Technology Research and Development*

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*system*. Doctoral dissertation. Universidad Autónoma de Madrid.

978, ISSN 0360-1315.

ISSN 0302-9743.

York: Free Press of Glencoe.

ISSN 1556-1607.

Knowledge management (KM) is the collection of processes governing the creation, storage, reuse, maintenance, dissemination and reuse of knowledge. KM refers to the collection of processes controlling the creation, storage and usage of experience in a particular situation or problem solving context. To transfer knowledge between experienced engineers, construction professionals have traditionally used techniques ranging from formal annual meetings to face-to-face interviews. Construction KM focuses on the acquisition and management of important issues and experience from participating engineers.

To enhance the quality of KM gained by engineers involved in construction projects, this study proposes a knowledge flow approach integrated with mind mapping to achieving KM solutions in the construction industry. Combined with web-based technology and mind mapping, this study proposes a Construction Web Topic-based Knowledge Management (CWTKM) system enabling engineers to reuse domain knowledge and experience by dynamically exchanging and managing knowledge during the construction phase of a project. In the proposed CWTKM system, the topic-based experience exchange environment in the mind map enables engineers to illustrate and share their experience with other engineers effectively. Engineers are, thus, invited to exchange and share their knowledge based on their previous experience.

By integrating web-based technology and mind mapping, engineers can obtain problem solutions and experience directly from senior engineers, decreasing the time and reducing the cost of on-the-job training. By exchanging and sharing previous experiences among engineers, similar and related experiences used to execute similar projects can clarify domain knowledge and enable the exchange of knowledge through web KM. The CWTKM system provides a web-based platform for users who can request assistance from selected or all engineers in the enterprise who have relevant experience. The user can also submit knowledge description using mind mapping in CWTKM system. Moreover, senior and junior engineers can effectively and easily exchange knowledge and experience regarding a specific aspect of their current construction project. In this study of a Taiwan construction building project, the survey (questionnaire) results indicated that the CWTKM system, integrated with mind mapping approach is effective for construction knowledge exchange and management.

Enhancing Knowledge Management for Engineers Using Mind Mapping in Construction 203

This study concentrates on new approaches for managing and reusing past specific knowledge for a construction project framework. With the newly proposed TBM approach and integration of mind mapping techniques, service engineers and practitioners can exchange original ideas, experience, knowledge and commands. By integrating TBM and mind mapping techniques, engineers can obtain problem solutions and experience directly from senior engineers, decreasing the time and reducing the cost of on-the-job training. By exchanging and sharing previous knowledge among engineers, similar and related knowledge used to execute similar projects can clarify domain knowledge and enable the

To apply KM to new or other construction projects, the process and content of project knowledge must be collected, recorded and stored effectively in the CWTKM system. To assist the participating engineers in illustrating and managing their own project experience, Topic-based mapping is presented to help them explore their acquired experience. . The main objectives of this study are as follows: (1) enhance the illustration capabilities using the TBM approach and mind mapping techniques of captured experience of engineers and experts related to construction projects; (2) optimize the communication of tacit experience among participating engineers in the exchanging environment; and (3) design an efficient topic-based mapping for users to effectively locate parallel experience from relative engineers. The CWTKM system is then applied in selected case studies of a Taiwan construction building project to verify the proposed approach and demonstrate the value of

**Create Knowledge Map Knowledge**

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Fig. 1. The application of CWTKM in construction projects.

exchange of knowledge through web-based KM platform.

sharing experience in the construction phase.

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**New Project**

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**Reuse Knowledge**

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**Topic-based Maps integrated with Mind Mapping**

**Share Knowledge**

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