*2.10. Silence*

Silence enters this discussion not only as music's end, but as its beginning. Augustine can be understood to view the music we hear as coming from a spiritual model, from the music of silence [39]. Joseph Ratzinger, before he became Pope Benedict XVI, in a discussion relying on Philipp Harnoncourt [40], said this:

Faith comes from listening to God's word. But wherever God's word is translated into human words there remains a surplus of the unspoken and unspeakable which calls us to silence—into a silence that in the end lets the unspeakable become song and also calls on all the voices of the cosmos for help so that the unspoken may become audible. This means that church music, coming from the Word and the silence perceived in it, always presupposes a new listening to the whole richness of the Logos [41].


**1. Introduction**

Pancreatic cancer remains one of the most lethal solid organ tumors with a poor 5-year survival rate despite current oncological advances. The poor prognosis is related mostly to the late clinical manifestation. Patients usually are diagnosed in an unresectable stage when metastases are present [1]. 85% of the cases of pancreatic cancer are adenocarcinomas [2]. Pancreatic neuroendocrine tumors (NETs) are rare tumors with highly variable behaviors from nearly benign to extremely aggressive [3]. The early and proper diagnosis of pancreatic cancer is of a great importance for the improvement of the ovSerall prognosis. Symptoms are nonspecific and include progressive weight loss, anorexia, abdominal pain and jaundice. The recent advances and increasing sensitivity of the diagnostic techniques such as multi-detector-row computed tomography (MDCT), magnetic resonance imaging (MRI), positron emission tomography (PET) CT and endoscopic ultrasound (EUS) are promising for the early pancreatic cancer detection, staging and differentiation from other pancreatic diseases [4]. The resectability of the tumor depends on the possible infiltration of vessels and lymph nodes as well as distant metastases. The pancreastic cancer is resectable, borderline resectable, locally advanced or metastatic. Prognosis and treatment depend on the stage of pancreatic cancer as treatment strategies include surgery, ablation, chemotherapy, radiation therapy, and palliative care [5].

### **2. Challenging the pancreatic cancer**

Less than 20% of the patients with pancreatic cancer are diagnosed in an early resectable stage, achieving a negative resection margin (R0) and a significant survival improvement [5, 6]. An adjuvant chemotherapy is mostly recommended after pancreatic resection [5]. A recent metaanalysis highlights the beneficial effect of neoadjuvant therapy in borderline and locally advanced pancreatic tumors, associated with a decreased tumor-stage, higher rates of R0-resections, lower rates of lymphnode invasion, decreased frequency of lymphatic vessel and perineural invasion [7]. After biopsy confirmation, chemotherapy is the treatment of choice for unresectable pancreatic cancer. Different regiments such as gemcitabine / erlotinib, FOLFIRINOX, gemcitabine /NAB-paclitaxel, gemcitabine/capecitabine, and capecitabine/oxaliplatin (XELOX) are recommended according to the patient's performance status [8]. Palliative care relieves symptoms and ensures optimal quality of life [5]. According to the complications of pancreatic cancer, patients might need endoscopic placement of stents for treating biliary obstruction, pancreatic enzyme replacement therapy for pancreatic exocrine insufficiency, insulin for

treating diabetes mellitus, gastrojejunostomy, enteral stent or PEG tube in case of gastric outlet obstruction, as well as pain management and nutritive support [8–11]. Increasing is the interest on the tumor microenvironment and the arising potential future treatment option. Current clinical trials investigate promising treatment strategies for advanced pancreatic cancer such as stroma modifying drugs, platinum chemotherapy, RAS-directed therapies, immunotherapy with pembrolizumab, immune checkpoint inhibitor combinations or natural killer cells [12–14].


**Phylogenomic, Biogeographic, and Evolutionary Research Trends in Arachnology**

Editor

**Matjaz Kuntner ˇ**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

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This is a reprint of articles from the Special Issue published online in the open access journal *Diversity* (ISSN 1424-2818) (available at: https://www.mdpi.com/journal/diversity/special issues/ Evo Arachnology).

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*5.5. Potentiometric Biosensors*

A potentiometric biosensor works on the principle of potential difference between the working electrode and the reference electrode. The measured analytes are not consumed in the same way as in the amperometric biosensor. In this biosensing method, two electrodes galvanic cells immersed in the electrolyte solution generate the electromotive force (e.m.f.) measured by a high impedance voltmeter [127]. One electrode is used as a working electrode, and another is used as a reference electrode. The e.m.f. value is determined by the potential difference between the two electrodes. The analyte's concentration and the potential difference is measured by the Nernst equation [128], which is explained as follows:

$$E\_{cell} = E\_0 - \frac{RT}{zF} \ln Q \tag{2}$$

where *Ecell* is the e.m.f., *E*0 is the potential of the standard electrode, *R* is the gas constant, *T* is the temperature in Kelvin, *z* is no of charge of the electrode reaction, *F* is the Faraday constant, and *Q* is ion concentration ratio of the anode to cathode.

Huang, Mei Rong et al. [129] have reported a membrane based on semi-conducting poly(phenylenediamine) microparticles for Pb2+ detection in natural water. The electrode is selective towards the Pb2+ with the concentration range 3.16 × 10−6 to 0.0316 M with a high sensitivity displaying a near-Nernstian slope of 29.8 mV decade−1. The proposed electrode showed a long lifetime of 5 months, where the short response time was 14 s. Thayyath S. Anirudhan, and S. Alexander [130] have developed a modified multiwalled carbon nanotube (MWCNT) based imprinting polymer for the determination of pesticide 2,4-D (2,4-dichlorophenoxyacetic acid) in natural water. The sensor responds in the range of 1 × 10−9–1 × 10−5 M, where the detection limit is 1.2 × 10−9 M. The developed sensor is stable and can be reusable many times in the first 3 months. Mashhadizadeh, Mohammad Hossein et al. [131] have reported a newly modified carbon electrode to determine the Cu2+ with the presence of other interfering ions. The proposed potentiometric sensor showed a Nernstian slope of 30 (±0.5) mV/decade over a concentration range from 1.0 × 10−8– 1.0 × 10−2 mol L−1. The LOD was 7.0 × 10−9 mol L−1 and the response time was 30 s, which can be used for at least 3 months without sacrificing any quality of the sensor's response without any considerable divergence in responses.


**5. Barrier and facilitators to achieving 90-90-90 among serodiscordant couples**

The possibility of sero-discordant relationships are becoming more common, given the improved quality of life and higher life expectancy for people living with HIV [26]. It is therefore imperative to expand HIV prevention efforts that target sero-discordant couples in the effort to reach the 90-90-90 treatment goals.

In regard to HIV testing and counselling, evidence shows that many of the prevention strategies to reduce the risk of HIV transmission in couples are individual as opposed to couples based. HIV testing and counselling practices, thus far, have only included one partner and encouraged clients to invite their partners to test for HIV. It would be ideal to provide health care services and feasible prevention methods for couples as a unit as opposed to individuals. Furthermore, it is evident that services have been gendered to favour females (e.g. who receive antenatal care) who are perceived to be at greater risk and to whom routine testing is encouraged. It may be important to expand the scope of testing for HIV among men who access health facilities for other health services. It may be suggested that there be more emphasis placed on HIV testing among males and this may speak to a need for male-centred health facilities.

[3] Cluver LD, Orkin MF, Yakubovich AR, Sherr L. Combination social protection for reducing HIV-risk behavior amongst adolescents in South Africa. Journal of Acquired

Achieving 90-90-90: A Focus on Sero-Discordant Couples

http://dx.doi.org/10.5772/intechopen.78313

39

[4] Shisana O, Rehle T, Simbayi LC, Zuma K, Jooste S, Zungu N, Labadarios D, Onoya D et al. South African National HIV Prevalence, Incidence and Behaviour Survey, 2012.

[5] Zuma K, Shisana O, Rehle TM, Simbayi LC, Jooste S, Zungu N, et al. New insights into HIV epidemic in South Africa: Key findings from the national HIV prevalence, incidence

[6] Mashaphu S, Burns JK. Couples-based interventions in the context of HIV discordance.

[7] Kilembe W, Wall KM, Mokgoro M, Mwaanga A, Dissen E, Kamusoko M, et al. Knowledge of HIV serodiscordance, transmission, and prevention among couples in Durban, South

[8] Ndirangu G. Fertility and conception options for HIV-serodiscordant couples in Sub

[9] Wilton J. HIV prevention within serodiscordant couples: A changing paradigm. Prevention in Focus. Canada: Spring; 2015. Available: http://www.catie.ca/en/pif/spring-2015/

[10] Guthrie BL, De Bruyn G, Farquhar C. HIV-1-discordant couples in sub-Saharan Africa: Explanations and implications for high rates of discordancy. Current HIV Research.

[11] Dunkle KL, Stephenson R, Karita E, Chomba E, Kayitenkore K, Vwalika C, et al. New heterosexually transmitted HIV infections in married or cohabiting couples in urban Zambia and Rwanda: An analysis of survey and clinical data. The Lancet. 2008;**371**(9631):

[12] Matthews LT, Crankshaw T, Giddy J, Kaida A, Smit JA, Ware NC, Bangsberg DR. Reproductive decision-making and periconception practices among HIV-positive men and women attending HIV services in Durban, South Africa. AIDS and Behavior. 2013;**17**(2):

[13] Eyawo O, De Walque D, Ford N, Gakii G, Lester RT, Mills EJ. HIV status in discordant couples in sub-Saharan Africa: A systematic review and meta-analysis. The Lancet Infec-

[14] Patel RC, Stanford-Moore G, Odoyo J, Pyra M, Wakhungu I, Anand K, Brown JM. "Since both of us are using antiretrovirals, we have been supportive to each other": Facilitators and barriers of pre-exposure prophylaxis use in heterosexual HIV serodiscordant couples in Kisumu, Kenya. Journal of the International AIDS Society. 2016;**19**(1):1-10

Saharan Africa. Finland: Arcada University of Applied Sciences; 2017

hiv-prevention-within-serodiscordant-couples-changing-paradigm

and behaviour survey, 2012. African Journal of AIDS Research. 2016;**15**(1):67-75

Immune Deficiency Syndromes (1999). 2016;**72**(1):96

South African Journal of Psychiatry. 2017;**23**:a1009

Africa. PLoS One. 2015;**10**(4):e0124548

tious Diseases. 2010;**10**(11):770-777

2007;**5**(4):416-429

2183-2191

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Cape Town: HSRC Press; 2014

In relation to treatment as prevention for sero-discordance, it was found through various clinical trial in South Africa that adherence to using PrEP was a major barrier [29]. This therefore nullifies the excellence of the approach to safeguard the uninfected partner from the transmission of the virus. Furthermore, some of the pre-exposure prophylaxes technologies are yet to be tested. And therefore it is imperative that we explore strategies to increase adherence for ART for the positive partner, more importantly that we should uncover the barriers to adherence for PrEP utilisation.

There are barriers associated with family planning strategies for sero-discordant couples. These include the affordability and accessibility of intrauterine or intravaginal insemination technologies to aid in safe conception. Couples therefore have to rely on manual methods such as timed unprotected sex during fertile periods. This strategy requires health care workers and couples to be cautious and thorough in their actions, so as to reduce the risk of transmission.

Regardless of the existing literature on sero-discordant couples, there is still a need to conduct further research on treatment as prevention and sexual health services that are tailor-made for such couples.


# **Novel Technologies to Enhance Energy Performance and Indoor Environmental Quality of Buildings**

Edited by Alessandro Cannavale, Francesco Martellotta and Francesco Fiorito Printed Edition of the Special Issue Published in *Buildings*

www.mdpi.com/journal/buildings


*6.2.1 Management*

*Cucumber Economic Values and Its Cultivation and Breeding*

airborne dust, soil, water, farm tools and equipment.

spp. Avoidance of overcrowding is also advisable.

**6.1 Striped and spotted cucumber beetles**

from beetle feeding and transmission of bacterial wilt.

**6.2 Aphids (***Myzus persicae* **and** *Aphis gossypii***)**

*<IP_ADDRESS> Management of Pythium spp*

**6. Insect pest of cucumber**

other hand vector viruses.

*6.1.1 Management*

of hydroponically grown crops, including cucumber in South Africa [97]. The infection can occur before or after seeds germination. At pre-emergence, rotting of seed inside seed coat occurs. At post-emergence, damping-off appears as yellow to dark brown and water-soaked lesions are noticed on the root and hypocotyl tissue. With time, further root decay occurs, the hypocotyl shrivels and the seedling wilt. Inoculum of *Pythium* spp. can be transmitted from one place to another through

Chemical treatment, crop rotation, prevention of fruit contact with soil surface, reduction of fruit injury and biological control are being used to manage Pythium

Three insect pests are of high importance to cucumber production. They are cucumber beetle (striped and spotted), green peach and melon aphids. Cucumber beetle cause direct feeding damage and can vector bacterial wilt. Aphids on the

Striped cucumber beetles, Acalymma vittata (Fabricius), and spotted cucumber beetles, *Diabrotica undecimpunctata howardi* (Barber) share a similar life cycle, and inflict similar damage to host plants. Both species of cucumber beetles not only feed on the roots, stems, foliage and fruit of cucumbers they also vector diseases of cucumber [98]. Cucumber beetles vector bacterial wilt and can transmit another important disease, however, spotted cucumber beetles do not vector bacterial wilt disease but can spread squash mosaic virus and there are reports that they can increase the incidence of powdery mildew, black rot, and Fusarium wilt [99]. The feeding injury and disease transmission takes place from emergence until they form runners. Beetle cause growth retardation and destruction of young seedlings causing loss to the farmers.

There is usually a peak in beetle activity each spring that lasts two to four weeks. This is the most important time to control beetles. Monitoring is as important as control which should be done as soon as seedlings emerge because early treatment is essential for beetle management in cucumber fields. Treatment should be carried out at the peak of beetle activity with foliar insecticides to protect cucumber plants

A number of aphid species which include green peach aphid (*Myzus persicae*) and melon aphid (*Aphis gossypii*) feed on cucumber and cause similar damage.  Downward curling and crinkling of the leaves of infested plants is part of the first sign of aphid damage. The aphids are often found on lower leaves, soft-growing tips, flower buds, and in some cases flowers. The feeding activity of the aphids usually causes a variety of symptoms, which can

**190**

The first step to management is early identification. The ability of aphids have to multiply rapidly must be taken into account while monitoring for this pest. Plants should be checked on a regular basis, at least twice a week with special attention to the undersurface of the leaves in most cases problems occur toward the end of the growing season. There are a number of cultural and biological options available depending on environmental factors and available resources. Yellow sticky traps would be helpful in detecting aphids 2–3 weeks prior to planting and can also help in management afterwards. The use of a detergent and vegetable oil solution before destroying old crops can avoid winged virus-infected aphids from getting to nearby crops to overwinter. Chemicals both organic such as potassium soap and petroleum oil or primicarb. Endosulfan, Dimethoate, Lannate, Fulfil, and Actara and inorganic like Cypermethrin (0.01%), acetamiprid (0.01%), bifenthrin (0.01%) and malathion (0.05%) are used to control aphids.


*Article* **Preparation and Photodegradation Properties of Carbon-Nanofiber-Based Catalysts**

**Mingpan Zhang 1,†, Fuli Wang 1,†, Xinran Shi 1 , Jing Wei 1 , Weixia Yan 1 , Yihang Dong 2 , Huiqiang Hu 3,\* and Kai Wei 1,\***

**Abstract:** In this study, an iron oxide/carbon nanofibers (Fe2O3/CNFs) composite was prepared by a combination of electrospinning and hydrothermal methods. The characterization of Fe2O3/CNFs was achieved via scanning electron microscopy (SEM), infrared spectroscopy (IR), X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). It is shown that when the hydrothermal reaction time was 180 ◦C and the reaction time was 1 h, the Fe2O3 nanoparticle size was about 90 nm with uniform distribution. The photodegradation performance applied to decolorize methyl orange (MO) was investigated by forming a heterogeneous Fenton catalytic system with hydrogen peroxide. The reaction conditions for the degradation of MO were optimized with the decolorization rate up to more than 99% within 1 h, which can decompose the dyes in water effectively. The degradation process of MO by Fenton oxidation was analyzed by a UV-visible NIR spectrophotometer, and the reaction mechanism was speculated as well.

**Keywords:** Fe2O3 ; carbon nanofibers; heterogeneous Fenton; methyl orange (MO)

### **1. Introduction**

Dyes are commonly used in modern industries, such as textile, food, paper, printing, leather, and cosmetics. They will cause serious pollution problems and bring risks to human health, such as carcinogenesis and kidney dysfunction, if discharged directly into the natural environment without treatment [1–3]. Therefore, how to remove organic dyes from wastewater effectively has become a hot research issue in recent years [4].

Currently, the treatment of printing and dyeing wastewater can be divided into adsorption technologies [5–7], advanced oxidation technologies, such as Fenton oxidation [8–13] and ozone oxidation [14,15], biological technologies, such as bacterial [16,17], fungal [18,19], and algal [20] treatment, membrane separation technologies, such as ultrafiltration, nanofiltration, reverse osmosis and electrodialysis [21,22], electro-Fenton, anodicoxidation [23], electrocoagulation electrochemical treatment techniques, ion exchange [24–26] and some multiple processes [27–31]. Fenton oxidation is reported to be one of the most widely studied and applied advanced oxidation technologies. It can completely degrade the refractory toxic and hazardous organic compounds into water and carbon dioxide with a short treatment cycle.

The conventional Fenton technique uses ferrous salts, but some iron-containing oxides, such as Fe2O3, can be used instead of ferrous salts. It was shown previously that composites containing Fe2O3 can effectively degrade a large number of organic compounds in wastewater [32–38]. There are kinds of methods that could prepare Fe2O3, mainly the coprecipitation method, solution-gel method, micro-emulsion method, solvothermal method, hydrothermal method, etc. Among them, the hydrothermal method can produce nano

**Citation:** Zhang, M.; Wang, F.; Shi, X.; Wei, J.; Yan, W.; Dong, Y.; Hu, H.; Wei, K. Preparation and Photodegradation Properties of Carbon-Nanofiber-Based Catalysts. *Polymers* **2022**, *14*, 3584. https://doi.org/10.3390/ polym14173584

Academic Editors: Yang Zhou and Zhaoling Li

Received: 24 July 2022 Accepted: 26 August 2022 Published: 30 August 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/).

Fe2O3 with high purity, controllable morphology and particle size under mild synthesis conditions. Electrospinning is a simple technique for the effective production of nanofibers. The device is shown in Figure 1. Since carbon nanofibers (CNFs) have a high specific surface area, few structural defects, low density and high conductivity, they can be used as a catalytic template to prevent the agglomeration of nanoparticles which can solve the problem that nano Fe2O3 is prone to agglomeration. In this study, CNFs were obtained after the carbonization of polymethyl methacrylate/polyacrylonitrile (PAN/PMMA) nanofibers and used as template materials. In addition, Fe2O3/CNFs composites were prepared by the hydrothermal method with high purity, controlled morphological particle size, and uniform dispersibility. Then, the Fe2O3/CNFs composites were used in the Fenton reaction to degrade the MO solution. can produce nano Fe2O3 with high purity, controllable morphology and particle size under mild synthesis conditions. Electrospinning is a simple technique for the effective production of nanofibers. The device is shown in Figure 1. Since carbon nanofibers (CNFs) have a high specific surface area, few structural defects, low density and high conductivity, they can be used as a catalytic template to prevent the agglomeration of nanoparticles which can solve the problem that nano Fe2O3 is prone to agglomeration. In this study, CNFs were obtained after the carbonization of polymethyl methacrylate/polyacrylonitrile (PAN/PMMA) nanofibers and used as template materials. In addition, Fe2O3/CNFs composites were prepared by the hydrothermal method with high purity, controlled morphological particle size, and uniform dispersibility. Then, the Fe2O3/CNFs composites were used in the Fenton reaction to degrade the MO solution.

*Polymers* **2022**, *14*, x FOR PEER REVIEW 2 of 14

mainly the co-precipitation method, solution-gel method, micro-emulsion method, solvothermal method, hydrothermal method, etc. Among them, the hydrothermal method

**Figure 1.** Schematic illustration of fabrication of Fe2O3/CNFs composite nanocatalysts and their deg-**Figure 1.** Schematic illustration of fabrication of Fe2O3/CNFs composite nanocatalysts and their degradation of MO.

### radation of MO. **2. Experimental Methods**

### *2.1. Materials*

*2.1. Materials*  Polyacrylonitrile (PAN) (Mw 150,000) was purchased from Shanghai Maclean. Polymethyl methacrylate (PMMA) (high flow type) was purchased from Shanghai Maclean. N, N-dimethylformamide (DMF) (AR) was purchased from Shanghai SiXin Bio. Ferric chloride hexahydrate (FeCl3·6H2O) (EP) was purchased from 3A chemicals. Urea (AR) was purchased from Genbio. Glycine (AR) was purchased from Genbio. Polyethylene glycol 1000 monomethyl ether was purchased from Aladdin. Ethanol (AR) was purchased from Shanghai Chemical Reagent Procurement and Supply Station. Methyl orange (MO) (AR) was purchased from Shanghai Aladdin Technology & Biochemistry. All reagents Polyacrylonitrile (PAN) (Mw 150,000) was purchased from Shanghai Maclean. Polymethyl methacrylate (PMMA) (high flow type) was purchased from Shanghai Maclean. N, N-dimethylformamide (DMF) (AR) was purchased from Shanghai SiXin Bio. Ferric chloride hexahydrate (FeCl3·6H2O) (EP) was purchased from 3A chemicals. Urea (AR) was purchased from Genbio. Glycine (AR) was purchased from Genbio. Polyethylene glycol 1000 monomethyl ether was purchased from Aladdin. Ethanol (AR) was purchased from Shanghai Chemical Reagent Procurement and Supply Station. Methyl orange (MO) (AR) was purchased from Shanghai Aladdin Technology & Biochemistry. All reagents and solvents were used without further purification.

#### and solvents were used without further purification. *2.2. Preparation of Carbon Nanofiber Membrane*

**2. Experimental Methods**

*2.2. Preparation of Carbon Nanofiber Membrane*  PAN and PMMA were added to DMF for dissolution (the mass ratio of PAN and PMMA was 4:6, and the concentration of the spinning solution was 20%), and the spinning solution was prepared by stirring at room temperature for 24 h. The spinning solution PAN and PMMA were added to DMF for dissolution (the mass ratio of PAN and PMMA was 4:6, and the concentration of the spinning solution was 20%), and the spinning solution was prepared by stirring at room temperature for 24 h. The spinning solution was ultrasonicated for 2 h and spun by an electrospinning machine. The spinning time was 24 h. Then, the above nanofiber film was put into a tube furnace and pre-oxidized in the air for 1 h. After the pre-oxidation, it was continued to be carbonized in nitrogen for 1 h. After the tube furnace was naturally cooled to room temperature, carbon nanofibers were obtained.

### *2.3. Preparation of Fe2O3/CNFs Composites*

The Fe2O3/CNFs were prepared by the hydrothermal method. Firstly, 0.16 g FeCl3·6H2O, 0.2 g polyethylene glycol, 0.484 g urea and 0.03 g glycine were added to 25 mL deionized water. The mixed solution was stirred until it was completely dissolved and then poured into the hydrothermal reactor. Then, 20 mg carbon nanofiber membranes were added to the hydrothermal reactor to make them uniformly dispersed in the solution. The reaction was carried out at a certain temperature for a while to obtain Fe2O3/CNFs composites.

To explore the influence of hydrothermal reaction time and temperature on iron oxide particles, the following experiments were set up:

Under visible light conditions, Fe2O3/CNFs were used as a catalyst for the degradation of MO.

### *2.4. Characterization*

The surface structures of the composites were observed by scanning electron microscopy (SEM, s-4800) (Hitachi Manufacturing, Tokyo, Japan). The crystal structure of the composites was characterized by X-ray diffraction (XRD) (X' Pert-Pro MRD, Panaco, The Netherlands). The functional groups of the composites were determined by infrared spectroscopy (IR) (Nikoli Instruments Manufacturing, Waltham, Massachusetts, USA). The chemical composition of the composites was examined by energy dispersive spectroscopy (EDS) (Hitachi Manufacturing, Tokyo, Japan) and by X-ray photoelectron spectroscopy (XPS) using Axis Ultra HAS equipment.

### *2.5. Degradation Experiments*

A total of 100 mg/L MO solution was prepared, and the pH of the solution was 7.4. Then the degradation experiments were carried out as follows:

### *2.6. Degradation Performance of Fe2O3/CNFs*

MO solutions with the concentration of 4 mg/L, 10 mg/L and 40 mg/L (pH ≈ 7.4) were prepared. The UV-Vis spectrums were measured by Cary 5000 UV-vis-NIR spectrophotometer between the wavelengths of 190–600 nm so as to obtain the maximum absorption wavelength.

MO solutions with the concentrations of 4 mg/L, 6 mg/L, 8 mg/L, 10 mg/L, 20 mg/L, 30 mg/L, 40 mg/L, 50 mg/L and 60 mg/L were prepared. The absorbances of MO solutions with different concentrations at the maximum absorption wavelength were measured, and the absorbance concentration standard curve was obtained.

After the degradation experiment, the absorbance of MO was measured at the maximum absorption wavelength. Then the solution concentration was obtained according to the standard curve of MO. The decolorization rate of MO was calculated.

Determination of the decolorization rate of MO: The absorbance of MO solutions with different concentrations at the maximum absorption wavelength was measured and the absorbance–concentration standard curve was obtained. The concentration of MO before degradation was denoted as C0. After the degradation experiment, the absorbance was measured at the maximum absorption wavelength. Then the solution concentration was obtained according to the standard curve, denoted as C1. The decolorization rate was calculated as follows: fore degradation was denoted as C0. After the degradation experiment, the absorbance was measured at the maximum absorption wavelength. Then the solution concentration was obtained according to the standard curve, denoted as C1. The decolorization rate was calculated as follows: 0 1 0 C C 100% C − × (1)

MO solutions with the concentrations of 4 mg/L, 6 mg/L, 8 mg/L, 10 mg/L, 20 mg/L, 30 mg/L, 40 mg/L, 50 mg/L and 60 mg/L were prepared. The absorbances of MO solutions with different concentrations at the maximum absorption wavelength were measured,

After the degradation experiment, the absorbance of MO was measured at the maximum absorption wavelength. Then the solution concentration was obtained according to

Determination of the decolorization rate of MO: The absorbance of MO solutions with different concentrations at the maximum absorption wavelength was measured and the absorbance–concentration standard curve was obtained. The concentration of MO be-

*Polymers* **2022**, *14*, x FOR PEER REVIEW 4 of 14

and the absorbance concentration standard curve was obtained.

the standard curve of MO. The decolorization rate of MO was calculated.

$$\frac{\mathbf{C}\_0 - \mathbf{C}\_1}{\mathbf{C}\_0} \times 100\% \tag{1}$$

### **3. Results and Discussion 3. Results and Discussion**  *3.1. Characterization of Fe2O3/CNFs*

#### *3.1. Characterization of Fe2O3/CNFs* Figures 2 and 3 are the SEM images of carbon nanofibers and Fe2O3/CNFs prepared

Figures 2 and 3 are the SEM images of carbon nanofibers and Fe2O3/CNFs prepared under different hydrothermal reaction conditions. From the figures, it can be seen that when the reaction temperature rises to 140 ◦C, large amounts of nanoparticles were successfully grown on carbon nanofiber. When the temperature is lower than 150 ◦C, the generated Fe2O3 nanoparticles are uneven, indicating that the hydrothermal reaction temperature affects the fabrication of nanoparticles. Meanwhile, the Fe2O3 particle size gradually increased with the increase in reaction time. It was known that the specific surface area increased as the number of nanoparticles increased, and the particle size became smaller. Furthermore, the catalytic efficiency improved as the specific surface area increased. Therefore, the hydrothermal reaction temperature and time were determined to be 180 ◦C and 1 h. Under this reaction condition, the Fe2O3 nanoparticle size is around 90 nm and grows evenly on carbon nanofibers. under different hydrothermal reaction conditions. From the figures, it can be seen that when the reaction temperature rises to 140 °C, large amounts of nanoparticles were successfully grown on carbon nanofiber. When the temperature is lower than 150 °C, the generated Fe2O3 nanoparticles are uneven, indicating that the hydrothermal reaction temperature affects the fabrication of nanoparticles. Meanwhile, the Fe2O3 particle size gradually increased with the increase in reaction time. It was known that the specific surface area increased as the number of nanoparticles increased, and the particle size became smaller. Furthermore, the catalytic efficiency improved as the specific surface area increased. Therefore, the hydrothermal reaction temperature and time were determined to be 180 °C and 1 h. Under this reaction condition, the Fe2O3 nanoparticle size is around 90 nm and grows evenly on carbon nanofibers.

**Figure 2.** SEM images of Fe2O3/CNFs (effect of temperature): (**a**) 130 °C; (**b**) 140 °C; (**c**) 150 °C; (**d**) 160 °C; (**e**) 170 °C; (**f**) 180 °C. **Figure 2.** SEM images of Fe2O3/CNFs (effect of temperature): (**a**) 130 ◦C; (**b**) 140 ◦C; (**c**) 150 ◦C; (**d**) 160 ◦C; (**e**) 170 ◦C; (**f**) 180 ◦C.

Figure 4 shows the EDS element analysis chart of the Fe2O3/CNFs composites. From the figure, it can be seen that the Fe elements and O elements are uniformly distributed on the carbon fibers, indicating that the Fe2O3/CNFs composites were successfully prepared by the hydrothermal method.

*Polymers* **2022**, *14*, x FOR PEER REVIEW 5 of 14

**Figure 3.** SEM images of Fe2O3/CNFs (effect of time): (**a**) 1 h; (**b**) 2 h; (**c**) 3 h; (**d**) 4 h; (**e**) 5 h; (**f**) 6 h. pared by the hydrothermal method.

**Figure 4.** EDS image of Fe2O3/CNFs. **Figure 4.** EDS image of Fe2O3/CNFs.

**Figure 4.** EDS image of Fe2O3/CNFs. Figure 5 shows the XRD patterns of Fe2O3/CNFs at different reaction temperatures and times. When the hydrothermal reaction temperature raised to 140 °C, characteristic peaks of Fe2O3 appeared at 2θ = 24.2°, 33.2°, 35.6°, 40.9°, 49.5°, 54.1°, 62.4°, and 64.0°, which are consistent with the standard card mapping card JCPDS NO.33-0664, indicating the formation of Fe2O3 particles [39]. Figure 5 shows the XRD patterns of Fe2O3/CNFs at different reaction temperatures and times. When the hydrothermal reaction temperature raised to 140 ◦C, characteristic peaks of Fe2O3 appeared at 2θ = 24.2◦ , 33.2◦ , 35.6◦ , 40.9◦ , 49.5◦ , 54.1◦ , 62.4◦ , and 64.0◦ , which are consistent with the standard card mapping card JCPDS NO.33-0664, indicating the formation of Fe2O3 particles [39].

Figure 5 shows the XRD patterns of Fe2O3/CNFs at different reaction temperatures and times. When the hydrothermal reaction temperature raised to 140 °C, characteristic peaks of Fe2O3 appeared at 2θ = 24.2°, 33.2°, 35.6°, 40.9°, 49.5°, 54.1°, 62.4°, and 64.0°, which are consistent with the standard card mapping card JCPDS NO.33-0664, indicating the formation of Fe2O3 particles [39]. Figure 6 shows the IR spectra of CNFs and Fe2O3/CNFs composites. In the infrared spectrum of CNFs, the characteristic peaks at 3438 cm−1 are caused by −OH bond stretching vibration [40]. The characteristic peaks at 1140 cm−1 and 1537 cm−1 are caused by C−O−C and C=O vibration, respectively [41]. Compared with CNFs, Fe2O3/CNFs composites showed characteristic peaks at 556 cm−1 and 475 cm−1 are caused by the vibrations of Fe-O functional groups [42].

*Polymers* **2022**, *14*, x FOR PEER REVIEW 6 of 14

**Figure 5.** XRD patterns of Fe2O3/CNFs: (**a**) effect of reaction temperature; (**b**) effect of reaction time. **Figure 5.** XRD patterns of Fe2O3/CNFs: (**a**) effect of reaction temperature; (**b**) effect of reaction time. Fe-O functional groups [42].

**Figure 6.** IR image of CNFs and Fe2O3/CNFs. **Figure 6.** IR image of CNFs and Fe2O3/CNFs.

**Figure 6.** IR image of CNFs and Fe2O3/CNFs. Figure 7 shows the XPS spectra analysis of Fe2O3/CNFs composites. The satellite peak of Fe2O3 at 719.2 eV is detected in Figure 7b, which shows the trivalent Fe elemental in the Fe2O3/CNFs composites. Meanwhile, there are two main peaks at 712.5 eV and 725.4 eV Figure 7 shows the XPS spectra analysis of Fe2O3/CNFs composites. The satellite peak of Fe2O3 at 719.2 eV is detected in Figure 7b, which shows the trivalent Fe elemental in the Fe2O3/CNFs composites. Meanwhile, there are two main peaks at 712.5 eV and 725.4 eV corresponding to Fe 2p3/2 and Fe 2p1/2, indicating the existence of Fe2+ and Fe3+ [43]. Furthermore, the energy spectrum of C 1S is shown in Figure 7c. There are three characteristic peaks. The peak at 284.5 eV is caused by the C−C bond, while the peaks at 285.8 eV and 287.9 eV represent C−O and C=O, respectively [44]. Figure 7d shows the energy spectrum of O1 s. The peak at 531.0 eV represents the O element in Fe2O3 and the peak at 532.7 eV represents the O element in CNFs [43,44]. XPS results show that Fe−O−C chemical bonds exist between Fe2O3 and CNFs. Fe2O3 particles grew in situ on the CNFs carrier, and the results were consistent with the XRD and IR analysis. Figure 7 shows the XPS spectra analysis of Fe2O3/CNFs composites. The satellite peak of Fe2O3 at 719.2 eV is detected in Figure 7b, which shows the trivalent Fe elemental in the Fe2O3/CNFs composites. Meanwhile, there are two main peaks at 712.5 eV and 725.4 eV corresponding to Fe 2p3/2 and Fe 2p1/2, indicating the existence of Fe2+ and Fe3+ [43]. Furthermore, the energy spectrum of C 1S is shown in Figure 7c. There are three characteristic peaks. The peak at 284.5 eV is caused by the C−C bond, while the peaks at 285.8 eV and 287.9 eV represent C−O and C=O, respectively [44]. Figure 7d shows the energy spectrum of O1 s. The peak at 531.0 eV represents the O element in Fe2O3 and the peak at 532.7 eV represents the O element in CNFs [43,44]. XPS results show that Fe−O−C chemical bonds exist between Fe2O3 and CNFs. Fe2O3 particles grew in situ on the CNFs carrier, and the results were consistent with the XRD and IR analysis.

corresponding to Fe 2p3/2 and Fe 2p1/2, indicating the existence of Fe2+ and Fe3+ [43]. Furthermore, the energy spectrum of C 1S is shown in Figure 7c. There are three characteristic peaks. The peak at 284.5 eV is caused by the C−C bond, while the peaks at 285.8 eV and 287.9 eV represent C−O and C=O, respectively [44]. Figure 7d shows the energy spectrum of O1 s. The peak at 531.0 eV represents the O element in Fe2O3 and the peak at 532.7 eV represents the O element in CNFs [43,44]. XPS results show that Fe−O−C chemical bonds exist between Fe2O3 and CNFs. Fe2O3 particles grew in situ on the CNFs carrier, and the

results were consistent with the XRD and IR analysis.

*Polymers* **2022**, *14*, x FOR PEER REVIEW 7 of 14

**Figure 7.** XPS spectra of (**a**) Fe2O3/CNFs; (**b**) Fe 2p; (**c**) C 1 s; (**d**) O 1 s. **Figure 7.** XPS spectra of (**a**) Fe2O3/CNFs; (**b**) Fe 2p; (**c**) C 1 s; (**d**) O 1 s.

*3.2. Heterogeneous Fenton Degradation of MO by Fe2O3/CNFs 3.2. Heterogeneous Fenton Degradation of MO by Fe2O3/CNFs*

**Figure 7.** XPS spectra of (**a**) Fe2O3/CNFs; (**b**) Fe 2p; (**c**) C 1 s; (**d**) O 1 s.

*3.2. Heterogeneous Fenton Degradation of MO by Fe2O3/CNFs*  The MO aqueous solution has the characteristics of an acid–base indicator, and its molecular structure will change with the pH value as well colors. When pH < 3.1, it is the quinone structure and the solution is red, and when pH > 4.4, it is an azo structure and the solution is yellow. The structural changes can be expressed as follows: The MO aqueous solution has the characteristics of an acid–base indicator, and its molecular structure will change with the pH value as well colors. When pH < 3.1, it is the quinone structure and the solution is red, and when pH > 4.4, it is an azo structure and the solution is yellow. The structural changes can be expressed as follows: The MO aqueous solution has the characteristics of an acid–base indicator, and its molecular structure will change with the pH value as well colors. When pH < 3.1, it is the quinone structure and the solution is red, and when pH > 4.4, it is an azo structure and the solution is yellow. The structural changes can be expressed as follows:

$$\text{s-}\text{cos}\text{---}\bigvee\_{\text{H}^{+}}\text{-}\text{s-}\text{-}\bigvee\_{\text{H}^{+}}\bigvee\_{\text{H}^{+}}\text{-}\text{s}\text{-}\text{s-}\bigvee\_{\text{H}^{+}}\text{-}\text{s-}\text{s-}\bigvee\_{\text{H}^{+}}\text{-}\text{s-}\text{-}\text{N}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-}\text{s}\text{-$$

Figure 8 shows the UV spectra of MO at a different pH value. When the structure is quinone, the maximum absorption wavelength in the visible region is around 505 nm. When the structure is azo, the maximum absorption wavelength in the visible region is around 465 nm. Figure 8 shows the UV spectra of MO at a different pH value. When the structure is quinone, the maximum absorption wavelength in the visible region is around 505 nm. When the structure is azo, the maximum absorption wavelength in the visible region is around 465 nm. Figure 8 shows the UV spectra of MO at a different pH value. When the structure is quinone, the maximum absorption wavelength in the visible region is around 505 nm. When the structure is azo, the maximum absorption wavelength in the visible region is around 465 nm. *Polymers* **2022**, *14*, x FOR PEER REVIEW 8 of 14

**Figure 8.** UV-vis spectra of MO at different pH value. MO is no longer increased significantly. **Figure 8.** UV-vis spectra of MO at different pH value.

shorten the degradation time.

adsorption per unit area [46,47].

The decolorization effect of Fe2O3/CNFs composites on MO under different pH conditions is shown in Figure 9a. The initial pH of the solution has a great influence on the

Figure 9b shows the effect of reaction temperature on the catalytic effect of MO. The decolorization rate of MO was improved by increasing the reaction temperature. When the temperature increased from 50 °C to 80 °C, the decolorization rate of MO increased from 66.39% to 99.87%. Moreover, the increase in reaction temperature can effectively

The heterogeneous Fenton reaction occurs on the surface of the catalyst, and the amount of catalyst is an important factor, affecting the decolorization effect. The catalytic effect of Fe2O3/CNFs amount on MO is shown in Figure 9c. When the amount of catalyst increased from 0.4 g/L to 0.8 g/L, the decolorization rates of MO increased from 78.5% to 97.31%. Increasing the dosage of Fe2O3/CNFs has a facilitating effect on the decolorization of MO. This is because increasing the amount of catalyst can increase the number of active sites on the surface of the catalyst and accelerate the decomposition rate of H2O2 to produce ·OH. When the amount of catalyst was increased from 0.8 g/L to 1 g/L, the decolorization rate of MO increased slightly because the excessive catalyst will reduce the H2O2

Figure 9d shows the degradation efficiency of MO at different H2O2 concentrations. It can be seen from the figure that within the first 2 h when the concentration of H2O2 increases from 0.097 mol/L to 0.194 mol/L, the degradation rate of MO increases significantly. The degradation rate of MO is related to the amount of ·OH. The higher the hydrogen peroxide concentration, the more that ·OH is produced, and the degradation rate of MO increases. Continuing to increase the concentration of H2O2, the degradation rate of

gradually with the increase in pH. When pH is 6~8, the decolorization rate gradually increases. Furthermore, when pH > 8, the decolorization rate continues to decrease again. The best decolorization of methyl orange was achieved when pH = 2. It may be that the azo bond in the MO molecular structure changes to a quinone structure under the condition of pH < 3, and the destruction of N = N bond leads to the instability of the MO molecular structure, which makes the catalytic reaction easier to proceed. Secondly, due to the over acid condition, Fe2O3 is partially dissolved, more free Fe2+/Fe3+ contacts with H2O2,

and more ·OH is produced, thus improving the decolorization rate of MO [45].

The decolorization effect of Fe2O3/CNFs composites on MO under different pH conditions is shown in Figure 9a. The initial pH of the solution has a great influence on the Fe2O3/CNFs composites catalyzing the degradation of MO by hydrogen peroxide. When pH < 3, the decolorization effect of MO is better, and the decolorization rate decreases gradually with the increase in pH. When pH is 6~8, the decolorization rate gradually increases. Furthermore, when pH > 8, the decolorization rate continues to decrease again. The best decolorization of methyl orange was achieved when pH = 2. It may be that the azo bond in the MO molecular structure changes to a quinone structure under the condition of pH < 3, and the destruction of N = N bond leads to the instability of the MO molecular structure, which makes the catalytic reaction easier to proceed. Secondly, due to the over acid condition, Fe2O3 is partially dissolved, more free Fe2+/Fe3+ contacts with H2O2, and more ·OH is produced, thus improving the decolorization rate of MO [45]. *Polymers* **2022**, *14*, x FOR PEER REVIEW 9 of 14

**Figure 9.** Decolorization effect of MO (**a**) with pH: ([MO]0 =100 mg/L, [Fe2O3/CNFs]0 =0.6 g/L, [H2O2]0 = 0.155 mol/L, T = 80 °C, t = 2 h); (**b**) with temperature: ([MO]0 = 100 mg/L, [Fe2O3/CNFs]0 = 0.8 g/L, [H2O2]0= 0.194 mol/L, pH = 2); (**c**) with Fe2O3/CNFs content: ([MO]0 = 100 mg/L, [H2O2]0 = 0.194 mol/L, pH = 2, T = 80 °C); (**d**) with H2O2 content: ([MO]0 = 100 mg/L, [Fe2O3/CNFs]0 = 0.8 g/L, pH = 2, T = 80 °C). **Figure 9.** Decolorization effect of MO (**a**) with pH: ([MO]0 = 100 mg/L, [Fe2O3/CNFs]0 = 0.6 g/L, [H2O2 ] 0 = 0.155 mol/L, T = 80 ◦C, t = 2 h); (**b**) with temperature: ([MO]0 = 100 mg/L, [Fe2O3/CNFs]0 = 0.8 g/L, [H2O2 ] 0= 0.194 mol/L, pH = 2); (**c**) with Fe2O3/CNFs content: ([MO]0 = 100 mg/L, [H2O2 ] 0 = 0.194 mol/L, pH = 2, T = 80 ◦C); (**d**) with H2O2 content: ([MO]0 = 100 mg/L, [Fe2O3/CNFs]0 = 0.8 g/L, pH = 2, T = 80 ◦C).

It can be observed that the decolorization rate can be up to more than 99% for 100 mg/L MO solution by the Fe2O3/CNFs catalyst. This result was also compared with previous studies reported for the catalytic degradation of MO shown in Table 1. Figure 9b shows the effect of reaction temperature on the catalytic effect of MO. The decolorization rate of MO was improved by increasing the reaction temperature. When the temperature increased from 50 ◦C to 80 ◦C, the decolorization rate of MO increased from 66.39% to 99.87%. Moreover, the increase in reaction temperature can effectively shorten the degradation time.

**Table 1.** Comparison with previous studies reported for catalytic degradation of MO. **Catalysts Initial Concentration Decolorization Rate Reaction Time References**  Fe2O3/CNFs 100 mg/L More than 99% 60 min This work Ti3C2-TiO2 40 mg/L 99% 40 min [48] 10% Co-ZnO 100 mg/L 100% 120 min [49] Ag-PMOS 20 mg/L 81% & 48% 60 min [50] ZnO-PMOS 47% & 57% Ni@FP 15 mg/L 93.40% 5 min [51] The heterogeneous Fenton reaction occurs on the surface of the catalyst, and the amount of catalyst is an important factor, affecting the decolorization effect. The catalytic effect of Fe2O3/CNFs amount on MO is shown in Figure 9c. When the amount of catalyst increased from 0.4 g/L to 0.8 g/L, the decolorization rates of MO increased from 78.5% to 97.31%. Increasing the dosage of Fe2O3/CNFs has a facilitating effect on the decolorization of MO. This is because increasing the amount of catalyst can increase the number of active sites on the surface of the catalyst and accelerate the decomposition rate of H2O2 to produce ·OH. When the amount of catalyst was increased from 0.8 g/L to 1 g/L, the decolorization

TiO2/ZSM-5 20 mg/L 99.55% 180 min [52] PANI(1.5 mol)/ZnO - 98.3% 180 min [53] rate of MO increased slightly because the excessive catalyst will reduce the H2O2 adsorption per unit area [46,47].

Figure 9d shows the degradation efficiency of MO at different H2O2 concentrations. It can be seen from the figure that within the first 2 h when the concentration of H2O2 increases from 0.097 mol/L to 0.194 mol/L, the degradation rate of MO increases significantly. The degradation rate of MO is related to the amount of ·OH. The higher the hydrogen peroxide concentration, the more that ·OH is produced, and the degradation rate of MO increases. Continuing to increase the concentration of H2O2, the degradation rate of MO is no longer increased significantly.

It can be observed that the decolorization rate can be up to more than 99% for 100 mg/L MO solution by the Fe2O3/CNFs catalyst. This result was also compared with previous studies reported for the catalytic degradation of MO shown in Table 1.

**Table 1.** Comparison with previous studies reported for catalytic degradation of MO.

### *3.3. Degradation Mechanism Analysis 3.3. Degradation Mechanism Analysis* The UV-Vis spectra of MO solution before and after degradation are shown in Figure

The UV-Vis spectra of MO solution before and after degradation are shown in Figure 10, from which it can be seen that the absorption peak of MO disappeared, and no other new peaks generated. There are two possible reasons for this phenomenon: (1) the intermediate products of catalytic degradation of MO have no absorption in the range of 190–600 nm; (2) MO is directly degraded to CO2 and H2O without any intermediate products generated. 10, from which it can be seen that the absorption peak of MO disappeared, and no other new peaks generated. There are two possible reasons for this phenomenon: (1) the intermediate products of catalytic degradation of MO have no absorption in the range of 190– 600 nm; (2) MO is directly degraded to CO2 and H2O without any intermediate products generated.

**Figure 10.** UV-vis spectra of MO before and after degradation. **Figure 10.** UV-vis spectra of MO before and after degradation.

Fe2O3/CNFs composites degrade the MO solution under acidic conditions (pH = 2) when MO is a quinone structure and the hydroxyl radical HO· plays a major role in the degradation process. Combined with the Fenton reaction system, it is known that MO is not directly degraded to CO2 and H2O, but certain intermediate products are produced that have no absorption between 190 and 600 nm. It is speculated that there are four possible degradation pathways of MO which are shown in Figure 11. The intermediates produced by path (1) and path (2) will continue to be oxidized to other products in the sub-Fe2O3/CNFs composites degrade the MO solution under acidic conditions (pH = 2) when MO is a quinone structure and the hydroxyl radical HO· plays a major role in the degradation process. Combined with the Fenton reaction system, it is known that MO is not directly degraded to CO2 and H2O, but certain intermediate products are produced that have no absorption between 190 and 600 nm. It is speculated that there are four possible degradation pathways of MO which are shown in Figure 11. The intermediates produced by path (1) and path (2) will continue to be oxidized to other products in the subsequent

sequent reactions. Pathway (3) and pathway (4) are the main mechanisms of this degradation. The quinone structure of MO is decolorized by HO· oxidation, which leads to the

some of the intermediates are completely oxidized to CO2 and H2O as the reaction time

increases.

reactions. Pathway (3) and pathway (4) are the main mechanisms of this degradation. The quinone structure of MO is decolorized by HO· oxidation, which leads to the destruction of the -N=N- group and C-N bond, thus decolorizing the MO solution. Finally, some of the intermediates are completely oxidized to CO2 and H2O as the reaction time increases. *Polymers* **2022**, *14*, x FOR PEER REVIEW 11 of 14

**Figure 11.** Speculation of possible degradation pathways of MO by Fe2O3/CNFs. **Figure 11.** Speculation of possible degradation pathways of MO by Fe2O3/CNFs.

#### **4. Conclusions 4. Conclusions**

In this study, Fe2O3/CNFs composites were prepared by a combination of hydrothermal and electrostatic spinning techniques. The effects of hydrothermal reaction temperature and time on the preparation of the composites were investigated. The Fe2O3/CNFs composites were successfully prepared by a hydrothermal method as proved by SEM, XRD, IR, EDS, and XPS analysis. Meanwhile, the existence of chemical interactions between Fe2O3 nanoparticles and carbon nanofibers was confirmed. When the hydrothermal reaction time was 180 °C and the reaction time was 1 h, the nanoparticle size was about 90 nm with uniform distribution. The degradation efficiency of Fe2O3/CNFs on MO was investigated under the Fenton reaction. Under the optimal reaction conditions, the decolorization rate of MO could reach more than 99% within 60 min reaction. In addition, the degradation mechanism and pathway of the reaction were also speculated. In this study, Fe2O3/CNFs composites were prepared by a combination of hydrothermal and electrostatic spinning techniques. The effects of hydrothermal reaction temperature and time on the preparation of the composites were investigated. The Fe2O3/CNFs composites were successfully prepared by a hydrothermal method as proved by SEM, XRD, IR, EDS, and XPS analysis. Meanwhile, the existence of chemical interactions between Fe2O3 nanoparticles and carbon nanofibers was confirmed. When the hydrothermal reaction time was 180 ◦C and the reaction time was 1 h, the nanoparticle size was about 90 nm with uniform distribution. The degradation efficiency of Fe2O3/CNFs on MO was investigated under the Fenton reaction. Under the optimal reaction conditions, the decolorization rate of MO could reach more than 99% within 60 min reaction. In addition, the degradation mechanism and pathway of the reaction were also speculated.

The prepared Fe2O3/CNFs composite as a heterogeneous catalyst can be separated from water easily. Furthermore, high surface area carbon nanofibers are used as the carrier of the catalysts, which can increase the degradation property. It is known that the

large amounts of surfactants; therefore, the degradation performance of multiple organic

pollutants will be investigated in the future work.

The prepared Fe2O3/CNFs composite as a heterogeneous catalyst can be separated from water easily. Furthermore, high surface area carbon nanofibers are used as the carrier of the catalysts, which can increase the degradation property. It is known that the printing and dyeing wastewater of the textile industry contains not only dyes, but also large amounts of surfactants; therefore, the degradation performance of multiple organic pollutants will be investigated in the future work.

**Author Contributions:** Conceptualization, K.W. and H.H.; methodology, F.W.; software, M.Z.; validation, J.W.; formal analysis, F.W.; investigation, W.Y.; resources, Y.D.; data curation, X.S.; writing original draft preparation, M.Z.; writing—review and editing, K.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Undergraduate Training Program for Innovation and Entrepreneurship, China<PHONE_NUMBER>61E).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** This work was supported by the National Undergraduate Training Program for Innovation and Entrepreneurship, China<PHONE_NUMBER>61E).

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


**2.3.1 Scenario dependency**

The global problem of artificial creation of touch experience is too complex and a simplification can be made developing specific devices that are able to simulate only certain types of scenario. Basically, according to scenario, the device can be simplified in order to be optimized for a certain kind of application. Scenarios can be classified according to the complexity of the interaction starting from one finger interaction on a planar surface getting to spatial interaction with multiple fingers of the same hand:

The user can interact with an artificial surface moving on planar trajectories. According to the type of virtual surface, the speed and the forces exerted by the finger, the tactile display generates distributed stimulus. The kinaesthetic device can apply forces only on directions that are parallel to the plane and can simulate different macroscopic properties of the surface like friction or stiffness. Govindaraj in 2002 realize on planar system presenting a device able to simulate the interaction with a piece of fabric that is lying on a hard planar surface (Govindaraj et al., 2002). Another example of planar device has been realized by Yang(Yang & Zhang, 2009) that choose a cable-driven actuation system for the kinesthetic device.

In the case of planar devices the requirements for the integration of tactile and kinesthetic displays are less demanding. The weight and the encumbrance of the tactile display are less

On the Integration of Tactile and Force Feedback 55

The haptic rendering for object manipulation and exploration has the characteristic of combining the techniques from physics simulation with the principles of control and knowledge about human perception. Without losing generality haptic interaction scenarios can be represented by a physics simulation in which one or more virtual entities have the special role of exchanging haptic information with the user. These entities are called *proxies*. In some scenarios these virtual entities represent a user body part that directly interacts with other objects in the environment. A different type of representation is the one happening when the user interacts by means of a virtual tool as a stylus or a more complex tool. Examples of applications in the former type are exploration of surfaces, grasping, haptic rehabilitation and scenarios in which an avatar is employed. Examples of the latter type are drilling, simulation and even driving simulation. Clearly, the type of proxy depends on the type of haptic interface and the specific attachment to the user body part. For direct contact, like virtual finger exploration, the robotic endeffector applies forces on the fingers of the user using a rigid attachment to the user, or, following an encountered haptic approach. Instead devices in which the user holds a

The type of proxy has effects, for the purpose of our discussion, in terms of the geometry and physical modeling of contact having to simulate, in one case, the contact between the finger or a body part with virtual objects, while in the other the contact of a virtual rigid

The general aim of the proxy is to be respectful of the physical properties of the virtual world, meaning that its behavior will avoid penetration with other objects. There is anyway a caveat. In real world the user moves the haptic interface end-effector specifying in this way a requested virtual position for the proxy. This requested position and orientation is a virtual entity called *haptic handle*. When the proxy touches an object like a virtual wall, the haptic interface produces a force to represent the opposition of the wall to penetration but this force is not always able to prevent the motion of the user in real space into the space where the virtual object is located. The discrepancy between proxy position and haptic handle position is a key element of haptic rendering. The common to rendering approach is to simulate the presence of a virtual spring between the proxy and the handle with a factor proportional to the stiffness of the object in contact. This approach is called penalty based because force is proportional to the penalty of entering with the handle into the object. This spring can introduce some instability and for this reason it can be replaced by a damped spring. Please note how, in this discussion, we have not taken into account the effect of the

Moreover, we have not made distinctions between impedance and admittance interfaces. In the formers the low level controller receives forces to be applied to the user at the endeffector, and in most of the cases such force is computed on the side of the computer performing simulation and collision. In the latters the low level controller specifies a

Contact is a fundamental element of haptic interaction with virtual objects. At large it can be considered as the result of two modeling aspects, first the geometrical aspect then the

position to be held with a given stiffness, up to the maximal force of the device.

stylus or a handle are more suited for tool based proxies.

object that transmits the contact to the user.

force produced by the spring on the proxy.

**3.1 Geometric and physical modeling of contact**

critical since there is no need of gravity compensation. Moreover the single finger interaction puts no strict limits to vertical encumbrance of the display.

One finger device has a superior level of complexity since the weights of the display has to be compensated by the kinaesthetic device. There are various implemented solutions that differ from the type of tactile display that is employed.

Wagner in (Wagner, 2005) proposed the integration of kinaesthetic feedback with a shape display. Kheddar introduced the concept of a multilevel device for the different spatial level of details (Kheddar, 2004).

In the case of multi-finger interaction a major problem has to be considered. For allowing the simulation of grasping of reduced thickness the fingers have to be free to get close each other. This results in very though requirements for the thickness of the tactile display in the palmar area of the fingertip. The display has to be as flat as possible in order to allow the finger of user to get close together during grasps of small virtual objects. There are no experiments that exactly establish what is the exact tolerable thickness of a display for supporting multi-finger interaction, but simple tests can demonstrate that it must be kept in the range of few millimetres.

One possible way to get around this issue is to employ an electro-tactile display that can reach a very flat shape like in (Sato et al.,2007). However, electro-tactile displays show several disadvantages like large variation of perceived stimulus from subject to subject, dependence from wetness of the finger surface, employment of high voltage etc. Those unwanted feature made them hardly usable in the context of a virtual reality simulation.

Other attempts has been done for obtaining mechanical tactile displays with flat shape.

Benali-Khoudja in (Benali-Khoudja et al., 2003) developed a pin-array display based on a multilayer approach that has been conceived for integration with kinesthetic feedback. In the European Project HAPTEX a system composed by a desktop haptic device and a piezo-electric pin-array display have been adapted for the integration and tested (Fontana et al., 2007).

Recently a novel pin-array display based on a customized solenoid transducer has been purposely developed by authors for the integration with a hand exoskeleton (Salsedo et al.,2011).


2. Self-focusing equation for high-intense laser-plasma interaction

### 2.1. High-order paraxial theory

self-defocusing of laser beam occur frequently. In this stage, if the electric field is strong enough, the laser beam will create a dielectric waveguide in the path ahead. This typical waveguide results in reducing or entirely eliminating the divergence of the beam. From an optical perspective, the refractive index of the medium in such situations acts as a convex lens; consequently, the central part of the laser beam would move slower than the edge parts. Therefore, while the beam is propagated through the nonlinear medium, its wave front

Overall, the generation of self-focusing phenomenon could be connected with various physical causes. The basic physical mechanism which is responsible for self-focusing of laser beam is the nonlinearity of the medium which originates in its interaction with the laser field. Therefore, the self-focusing of laser beam through plasma is categorized into three options according

This effect is due to collisional heating of plasma exposed to electromagnetic radiation. In fact, the rise in temperature induces the hydrodynamic expansion, which leads to an

A nonlinear radial ponderomotive force of the focused laser beam pushes electrons out of the propagation axis. It expels the plasma from the beam centre, high-intensity region, and increases the plasma dielectric function, leading to self-focusing of the laser in plasmas.

The increase of electrons' mass traveling by velocity approaching the speed of light modifies the plasma refractive index. This phenomenon has been observed in several experiments and has been proved to be an efficient way to guide a laser pulse over distances

R.W. Boyd et al. [4] reviewed the self-focusing methods, which are recommended by the authors

Figure 1. A schematic showing distortion of the wave-front and self-focusing of a laser beam in plasma.

becomes increasingly distorted, as depicted in Figure 1.

to nonlinear mechanisms that they are listed here:

increase in refractive index and further heating [3].

1. Thermal self-focusing (TS)

198 High Power Laser Systems

2. Ponderomotive self-focusing (PS)

3. Relativistic self-focusing (RS)

for more details on the topic.

much longer than the Rayleigh length.

It is reasonable to assume that the paraxial wave equation presents an accurate description for laser beams propagating near the axis throughout the propagation. Akhmanove et al. [19] illustrated that in a limit when the eikonal term is expanded only up to the second power in r, the shape of the radial intensity profile remains unchanged. However, in the experimental situation with high-intense laser beams, one needs to go beyond the paraxial approximation for which the predictions of such an approximation are often not sufficiently accurate [20]. Thus, it would be interesting, on high-intense laser-plasma interaction, to investigate propagation of laser beams using the extended paraxial approximation. In this case, Liu [21] and Tripathi [22] reported a useful theoretical framework that accounts for the combined several effects of interaction of an intense short pulse laser with plasma, the laser frequency blue shift, self-defocusing, ring formation and self-phase modulation. The expansion of the eikonal term to the fourth power in r makes significant difference in studying laser beam propagating through plasma and even other nonlinear materials.

For more details, the interaction of an intense laser beam with particular plasma is considered. From Maxwell's equations, it is noted that the propagation of such a beam can be investigated by solving the scalar wave equation in the cylindrical coordinate system and along the axis z:

$$\frac{\partial^2}{\partial z^2}E(r,z,t) + \nabla\_\perp^2 E(r,z,t) - \frac{\varepsilon}{c^2} \frac{\partial^2}{\partial t^2} E(r,z,t) = 0\tag{1}$$

b is called the decentred parameter as well as r0 introduced the initial spot size of the laser beam. Two functions a2ð Þz and a4ð Þz , the coefficients of r2 and r4, respectively, are considered as

Furthermore, in the higher-order paraxial theory, the dielectric constant is expanded to the next

ε2ð Þz , and ε4ð Þz corresponding to the nonlinearity play an important role in investigating the selffocusing of laser beam through a nonlinear medium. By substituting both Eqs. (5) and (6) into Eq. (3) and equating the coefficients of r0, r2, and r4 on both sides of the resulting equation, the

differential equations governing the parameters a2, a4, f zð Þ, and S4ð Þz can be given by:

0 f 2

2 þ ð Þ 4 � 8a2 =3 þ 2b6 =15 b2 ε0f

0

propagation distance and an original beam-width parameter, respectively. The first term on the right-hand side of Eq. (8) represents the diffraction effect, while the second term plays a vital role in self-focusing of laser beam. Both of them are nonlinear and responsible for the defocusing and focusing of the ChG laser beam through plasma. The behaviour of laser beam propagating through plasma can be investigated by solving these equations, Eqs. (7)–(9), with the initial

derivative is removed from the wave equation using the independent variable transformation (Z ¼ z, T ¼ t � z=vg) where vg is group velocity. We have presented non-stationary self-focusing of high-intense Gaussian laser beams for different portions of a pulse in classical and quantum plasmas in the weakly relativistic as well as ponderomotive regimes [23, 24]. We have recorded a

As mentioned in the previous section, the refractive index of plasma, the second term in the right-hand side of the self-focusing equation, Eq.(8), depends on nonlinearity mechanisms. Therefore, this term plays an important role in investigation propagation laser beam through a nonlinear medium with a wide variety of nonlinearities. For example, in collisional nonlinearity

> p ω2 þ

ω2 p ω2 αEE∗ =2Te

1 þ αEE∗

=2Te

, (10)

very significant focusing near the peak of the pulse and the rear portion of the pulse.

εð Þ¼ r; z 1 � ω2

 ε0f

0

, a4 ¼ 3a2

=3 � 2a2

3 � ε2

ε2ð Þ� z r4=r4

2 � 4a2

6 � ε4

ε0

2ε0

z and r ¼ r0ω=c are considered as a dimensionless

0 ¼ 0 and a2 ¼ 0 at ξ ¼ 0. In non-stationary situations, the time

r2f � 1 2ε0 dε0 dξ df

> r2 � S4 0 2ε0 dε0 dξ � 4S4

0

ε4ð Þz . The parameters ε0ð Þz ,

dξ (8)

0 f df dξ (9)

=4 (7)

Self-Focusing of High-Power Laser Beam through Plasma

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201

an indicative of the departure of the beam from the Gaussian nature.

da2

dξ ¼ �16S4

2 � 8a2 þ 4 � b2 4 þ b2

a2

higher power in r2 to obtain εð Þ¼ r; z ε0ð Þ� z r2=r2

d2 f dξ2 ¼ 3a2

conditions f ¼ 1, df =dξ ¼ 0, S4

2 � 52a3

8ε0f

2 þ 32a2

6 þ

0 ¼ S4ω=c. Additionally, ξ ¼ c=ωr2

2.2. Importance of nonlinearity in self-focusing equation

dS4 0 dξ ¼ 40a2

where S4

condition:

where α ¼ e2=3δmω2kB

where E shows amplitude of the electric field, c is the speed of light in vacuum and ε is the dielectric constant of plasma. In this stage, we consider the solution of the Eq. (1):

$$E(r,z,t) = A(r,z,t) \exp\left[\mathrm{i}\left(\omega t - \int\_0^z k(z)dz\right)\right] \tag{2}$$

E rð Þ ; z; t can be substituted with Eq. (2) in Eq. (1). This substitution leads to neglecting ∂2 A=∂z2 and ∂2 A=∂t 2 on the assumption that A is a slowly varying function of z and t is compared with ω:

$$-2ik\frac{\partial A}{\partial z} - iA\frac{\partial k}{\partial z} - k^2 A + \frac{\partial^2 A}{\partial r^2} + \frac{1}{r}\frac{\partial A}{\partial r} + \frac{\omega^2}{c^2}\varepsilon A = 0. \tag{3}$$

The complex amplitude of the electric vector A rð Þ ; z; t is expressed as,

$$A(r,z,t) = A\_0(r,z,t) \exp\left[-ik(z)S(r,z)\right] \tag{4}$$

From Eq. (4), it is noticed that the envelope A rð Þ ; z; t has been separated into real amplitude and complex phase terms in which the eikonal function S rð Þ ; z is.

$$\mathcal{S}(r,z) = \mathcal{S}\_0(z) + \left(r^2/r\_0^2\right)\mathcal{S}\_2(z) + \left(r^4/r\_0^4\right)\mathcal{S}\_4(z) \tag{5}$$

where S0ð Þz is the axial phase shift, S2ð Þ¼ z ð Þ df zð Þ=dz =2f zð Þ is indicative of the spherical curvature of the wave front, and S4ð Þz corresponds to its departure from the spherical nature. Moreover, the beam irradiance A∘ð Þ r; z; t of Cosh-Gaussian (ChG) laser beam can be written as:

$$\begin{split} A\_0^2(r, z, t) = EE^\* &= \frac{E\_0^2}{4f^2(z)} \exp\left(\frac{b^2}{2}\right) \left(1 + \frac{r^2}{r\_0^2 f^2(z)} a\_2(z) + \frac{r^4}{r\_0^4 f^4(z)} a\_4(z)\right) \\ &\times \left(\exp\left[-\left(\frac{r}{t\eta(z)} + \frac{b}{2}\right)^2\right] + \exp\left[-\left(\frac{r}{t\eta(z)} - \frac{b}{2}\right)^2\right]\right)^2 \mathbf{g}(t) \end{split} \tag{6}$$

In the near-axis approximation (i.e. a2, a4 ! 0), Eq. (6) converts to a general solution of ChG laser beam. In Eq. (6), the initial laser intensity at the central position r ¼ z ¼ 0 is presented by E0, and the beam-width parameter characterized by f zð Þ depends on z. Temporal shape of the pulse can be considered as a step function, g tðÞ¼ 1 at ti0 and g tðÞ¼ 0 otherwise. In addition, b is called the decentred parameter as well as r0 introduced the initial spot size of the laser beam. Two functions a2ð Þz and a4ð Þz , the coefficients of r2 and r4, respectively, are considered as an indicative of the departure of the beam from the Gaussian nature.

Furthermore, in the higher-order paraxial theory, the dielectric constant is expanded to the next higher power in r2 to obtain εð Þ¼ r; z ε0ð Þ� z r2=r2 0 ε2ð Þ� z r4=r4 0 ε4ð Þz . The parameters ε0ð Þz , ε2ð Þz , and ε4ð Þz corresponding to the nonlinearity play an important role in investigating the selffocusing of laser beam through a nonlinear medium. By substituting both Eqs. (5) and (6) into Eq. (3) and equating the coefficients of r0, r2, and r4 on both sides of the resulting equation, the differential equations governing the parameters a2, a4, f zð Þ, and S4ð Þz can be given by:

$$\frac{da\_2}{d\xi} = -16S\_4/f^2, \ a\_4 = \left(3a\_2^2 - 4a\_2\right)/4\tag{7}$$

$$\frac{d^2f}{d\xi^2} = \frac{\left\{ \left(3a\_2^2 - 8a\_2 + 4\right) - b^2 \left(4 + b^2/3 - 2a\_2\right) \right\}}{\varepsilon\_0 f^3} - \frac{\varepsilon\_2}{\varepsilon\_0} \rho^2 f - \frac{1}{2\varepsilon\_0} \frac{d\varepsilon\_0}{d\xi} \frac{df}{d\xi} \tag{8}$$

$$\frac{dS\_4^{'}}{d\xi} = \frac{40a\_2^2 - 52a\_2^3 + 32a\_2}{8\varepsilon\_0 f^6} + \frac{\left(a\_2^2 + (4 - 8a\_2)/3 + 2b^6/15\right)b^2}{\varepsilon\_0 f^6} - \frac{\varepsilon\_4}{2\varepsilon\_0}\rho^2 - \frac{S\_4^{'}}{2\varepsilon\_0}\frac{d\varepsilon\_0}{d\xi} - \frac{4S\_4^{'}}{f}\frac{df}{d\xi} \tag{9}$$

where S4 0 ¼ S4ω=c. Additionally, ξ ¼ c=ωr2 0 z and r ¼ r0ω=c are considered as a dimensionless propagation distance and an original beam-width parameter, respectively. The first term on the right-hand side of Eq. (8) represents the diffraction effect, while the second term plays a vital role in self-focusing of laser beam. Both of them are nonlinear and responsible for the defocusing and focusing of the ChG laser beam through plasma. The behaviour of laser beam propagating through plasma can be investigated by solving these equations, Eqs. (7)–(9), with the initial conditions f ¼ 1, df =dξ ¼ 0, S4 0 ¼ 0 and a2 ¼ 0 at ξ ¼ 0. In non-stationary situations, the time derivative is removed from the wave equation using the independent variable transformation (Z ¼ z, T ¼ t � z=vg) where vg is group velocity. We have presented non-stationary self-focusing of high-intense Gaussian laser beams for different portions of a pulse in classical and quantum plasmas in the weakly relativistic as well as ponderomotive regimes [23, 24]. We have recorded a very significant focusing near the peak of the pulse and the rear portion of the pulse.

#### 2.2. Importance of nonlinearity in self-focusing equation

As mentioned in the previous section, the refractive index of plasma, the second term in the right-hand side of the self-focusing equation, Eq.(8), depends on nonlinearity mechanisms. Therefore, this term plays an important role in investigation propagation laser beam through a nonlinear medium with a wide variety of nonlinearities. For example, in collisional nonlinearity condition:

$$\varepsilon(r,z) = 1 - \frac{\omega\_p^2}{\omega^2} + \frac{\omega\_p^2}{\omega^2} \frac{a \to E^\*/2T\_e}{1 + a \to E^\*/2T\_e} \tag{10}$$

where α ¼ e2=3δmω2kB

to the fourth power in r makes significant difference in studying laser beam propagating

For more details, the interaction of an intense laser beam with particular plasma is considered. From Maxwell's equations, it is noted that the propagation of such a beam can be investigated by solving the scalar wave equation in the cylindrical coordinate system and along the axis z:

⊥E rð Þ� ; z; t

dielectric constant of plasma. In this stage, we consider the solution of the Eq. (1):

E rð Þ¼ ; z; t A rð Þ ; z; t exp i ωt �

E rð Þ ; z; t can be substituted with Eq. (2) in Eq. (1). This substitution leads to neglecting ∂2

From Eq. (4), it is noticed that the envelope A rð Þ ; z; t has been separated into real amplitude

where S0ð Þz is the axial phase shift, S2ð Þ¼ z ð Þ df zð Þ=dz =2f zð Þ is indicative of the spherical curvature of the wave front, and S4ð Þz corresponds to its departure from the spherical nature. Moreover, the beam irradiance A∘ð Þ r; z; t of Cosh-Gaussian (ChG) laser beam can be written as:

1 þ

r0f zð Þ þ b 2 � �2 � �

In the near-axis approximation (i.e. a2, a4 ! 0), Eq. (6) converts to a general solution of ChG laser beam. In Eq. (6), the initial laser intensity at the central position r ¼ z ¼ 0 is presented by E0, and the beam-width parameter characterized by f zð Þ depends on z. Temporal shape of the pulse can be considered as a step function, g tðÞ¼ 1 at ti0 and g tðÞ¼ 0 otherwise. In addition,

r2 r2 0 f 2 ð Þz

� �2 � � � � 2

2 =r 2 0 � �S2ð Þþ z r

b2 2 � �

where E shows amplitude of the electric field, c is the speed of light in vacuum and ε is the

ε c2 ∂2 ∂t

0 @

2 on the assumption that A is a slowly varying function of z and t is compared with ω:

2 4 ðz

k zð Þdz

A rð Þ¼ ; z; t A0ð Þ r; z; t exp ½ � �ik zð ÞS rð Þ ; z (4)

4 =r 4 0

a2ð Þþ z

þ exp � r

!

r4 r4 0 f 4 ð Þz a4ð Þz

r0f zð Þ � b 2

1 A

3

0

2 E rð Þ¼ ; z; t 0 (1)

5 (2)

c2 εA ¼ 0: (3)

� �S4ð Þz (5)

gð Þt

(6)

A=∂z2

through plasma and even other nonlinear materials.

∂2

�2ik ∂A

∂z � iA ∂k ∂z � k 2 A þ ∂2 A ∂r2 þ 1 r ∂A ∂r þ ω2

The complex amplitude of the electric vector A rð Þ ; z; t is expressed as,

and complex phase terms in which the eikonal function S rð Þ ; z is.

S rð Þ¼ ; z S0ð Þþ z r

0 4f 2 ð Þz exp

� exp � r

and ∂2

A=∂t

200 High Power Laser Systems

A2

0ð Þ¼ r; z; t EE∗ ¼ E2

∂z2 E rð Þþ ; z; t ∇2

or in the ponderomotive regime and in low-intensity laser, it should be expressed like,

$$\varepsilon(r,z) = 1 - \frac{\omega\_p^2}{\omega^2} + \frac{\omega\_p^2}{\omega^2} \left[ 1 - \exp\left(-\frac{\beta E E^\*}{T\_e}\right) \right],\tag{11}$$

plasma density transitions (the so-called ramp density profile), which is usable to investigate several laser-plasma mechanisms such as self-focusing of laser beam, electron acceleration and high harmonic generation. This mathematical model of density transition has been also supported by a wide range of numerical and experimental work [29–35]. For example, Chunyang et al. [36] observed the high harmonics in the reflection spectra from short-intense

laser-pulse interaction with over-dense plasmas the particle-in-cell (PIC) simulations.

3. Relativistic self-focusing of ChG laser beam in quantum plasma

plasma, including higher-order paraxial theory.

power in r4 to obtain εð Þ¼ r; z ε0ð Þ� z r2=r2

ε0ð Þ¼ z 1 � ω2

Γ �2 þ b2 þ a2ð Þz � � 2f 4 ð Þz

> Γ β1f 2 ð Þþ z Γβ2=4 � � 6f 8 ð Þz

> > 2

ð Þþ z 3Γ a2

� �2β1f

ε2ð Þ¼� z

ε4ð Þ¼� z

and ε4ð Þz corresponding to the relativistic nonlinearity are:

Γ f 2 ð Þz

!�1

ω2 p ω2 1 þ

> ω2 p ω2 1 þ

p ω2 1 þ

Theoretical investigations of quantum effects on propagation of Gaussian laser beams are carried out within the framework of quantum approach in dense plasmas [37–40]. Habibi et al. have also shown the effective role of Fermi temperature in improving relativistic self-focusing of short wavelength laser beam (X-ray) through warm quantum plasmas [26]. From a theoretical viewpoint, the relativistic effect would be effective as a result of increasing fermions' number density in dense degenerate plasmas. However, several recent technologies have made it possible to produce plasmas with densities close to solid state. Furthermore, considerable interest has recently been raised in production and propagation of a decentred Gaussian beam on account of their higher efficient power with a flat-top beam shape compared with that of a Gaussian laser beam and their attractive applications in complex optical systems. Generally, focusing of the ChG beam can be analysed like Gaussian beam in plasmas without considering quantum effects. In particular, the present section is devoted to study nonlinear propagation of a ChG laser beam in quantum

The figure for a ChG laser beam makes a substantial contribution with an even stronger selffocusing effect compared with that of a Gaussian laser beam in cold quantum plasma (CQP). In this chapter, the plasma dielectric function, Eq. (13), which is in the relativistic regime, is considered for unmagnetized and collision-less CQP. Then, it is expanded to the next higher

� �ε2ð Þ� z r4=r4

1 � ℏ2 k 4 1 þ

2

2ð Þ� z 2a4ð Þz � � þ 1 þ 4b4 þ ℏ2k4 1 þ Γ

� �

2 4

2

1 � ℏ2 k 4 1 þ

0

Γ f 2 ð Þz

!�1=2

� �ε4ð Þz . The parameters ε0ð Þz , ε2ð Þz ,

Self-Focusing of High-Power Laser Beam through Plasma

http://dx.doi.org/10.5772/intechopen.75036

203

3 5 �1

=4m0 2 ω2

=4m0 2ω2 3 5 �2 (16)

(17)

(18)

=4m0 2 ω2

Γ f 2 ð Þz

f 2ð Þz � ��1=2

!�1=2

0

2

2 4

Γ f 2 ð Þz

> Γ f 2 ð Þz

!�5

!�3

where β ¼ e2 8mω2kB

In addition, in the relativistic regime and high-intense laser-plasma interaction:

$$\varepsilon(r,z) = 1 - \frac{1}{\mathcal{Y}} \frac{a\_p^2}{a^2}, \mathcal{Y} \simeq \left(1 + a\_\*^2/2\right)^{1/2} \\ \text{Circular Polarization, } a\_\* = \frac{\varepsilon E\_\*}{amc} \tag{12}$$

where γ is the Lorentz factor which arises from the quiver motion of the electron in the laser field. The expressions earlier are just three forms of nonlinearities in plasma. In this case, we have investigated relativistic self-focusing of high-intense laser beam in cold and warm quantum plasma [25–28]. From a quantum-mechanical viewpoint, the de Broglie wavelength of the charge particle is comparable to the inter-particle distance. In this situation, the dielectric constant in relativistic cold quantum plasma (CQP) is expressed by:

$$\varepsilon(r,z) = 1 - \frac{1}{\gamma} \frac{\omega\_p^2}{\alpha^2} \left(1 - \hbar^2 k^4 / 4\gamma m\_0^{-2} \alpha^2\right)^{-1} \tag{13}$$

and in the relativistic warm quantum plasma:

$$\varepsilon(r,z) = 1 - \frac{1}{\gamma} \frac{a\_p^2}{a^2} \left( 1 - 2k^2 k\_B T\_{\rm Fe} / m\_0^2 \omega^2 - \hbar^2 k^4 / 4 \gamma m\_0^2 \omega^2 \right)^{-1} \tag{14}$$

#### 2.3. Ramp density profile

Another important parameter in solving the self-focusing equation is plasma density profile. From mathematical and practical perspectives, it can be considered as a uniform or nonuniform function of propagation distance. In inhomogeneous plasmas [12], the propagation of a Gaussian high-intense laser beam in under-dense plasma with an upward increasing density ramp has been investigated. In this chapter, the effect of electron density profile on spot size oscillations of laser beam has been also shown. It leads to further fluctuations in the figure for the spot size of laser beam compared. Therefore, it was confirmed that an improved electron density gradient profile is an important factor in having a good stationary and nonstationary self-focusing in laser-plasma interaction. A mathematical function of non-uniform charge density profile for modelling inhomogeneous plasma can be considered as:

$$n\_e(\xi) = n\_0 F(\xi/d) \tag{15}$$

where ξ ¼ z=Rd is a dimensionless propagation distance, Rd ¼ ωr2 0=c is the Rayleigh length, r0 is the focused laser beam radius, n0 is the density of the plasma at ξ ¼ 0, and Fð Þ¼ ξ 1þ ð Þ n1=n0 tan ð Þ ξ=d is the linear density profile function. The slope of ramp density profile can be determined by changing d and n1 parameters. This model of density is just one kind of plasma density transitions (the so-called ramp density profile), which is usable to investigate several laser-plasma mechanisms such as self-focusing of laser beam, electron acceleration and high harmonic generation. This mathematical model of density transition has been also supported by a wide range of numerical and experimental work [29–35]. For example, Chunyang et al. [36] observed the high harmonics in the reflection spectra from short-intense laser-pulse interaction with over-dense plasmas the particle-in-cell (PIC) simulations.


Leadership for Sustainable and Educational Advancement - Advancing Great Leaders and Leadership

*Edited by Joseph Crawford*

Published in London, United Kingdom

Leadership for Sustainable and Educational Advancement - Advancing Great Leaders and Leadership http://dx.doi.org/10.5772/intechopen.110860 Edited by Joseph Crawford

#### Contributors

Chandra K. Kaye Massner, LeAnne Epling, Nancy Cade, Rachel Breckenridge, Kaone Bakokonyane, MacDonald Isaac Kanyangale, Muhammad Arshad, Chen Kun Yu, Aneela Qadir, Fred Awaah, Emmanuel Ekwam Okyere, Andrew Tetteh, Joseph Seyram Agbenyega, Emmanuel Semanu Asiam, Boy Van Droffelaar, Joseph Crawford, Kristina Berynets, Charles Scott, Michèle Schmidt, Tshimangadzo Selina Mudau, Ndwakhulu Tshishonga, Mavhungu Abel Mafukata, Ahmed Alkaabi, Asma Abdulla, Rashid Alriyami

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