Size effects of graphene nanoplatelets on the properties of high-density polyethylene nanocomposites: morphological, thermal, electrical, and mechanical characterization

• Tuba Evgin,
• Alpaslan Turgut,
• Georges Hamaoui,
• Zdenko Spitalsky,
• Nicolas Horny,
• Matej Micusik,
• Mihai Chirtoc,
• Mehmet Sarikanat and
• Maria Omastova

Beilstein J. Nanotechnol. 2020, 11, 167–179, doi:10.3762/bjnano.11.14

• Eylul University, Engineering Faculty, Mechanical Engineering Department, Tinaztepe Campus, 35397, Buca, Izmir, Turkey GRESPI, Multiscale Thermophysics Lab, Université de Reims Champagne-Ardenne URCA, Reims, France Polymer Institute, SAS, Dúbravská cesta 9, 845 41 Bratislava, Slovak Republic Department

• ’ mechanical properties due to poorer dispersion compared to the others. In addition, the size of the GnPs had no considerable effect on the melting and crystallization properties of the HDPE/GnP nanocomposites. Keywords: electrical properties; graphene nanoplatelets; mechanical properties; polymer matrix

• composites (PMCs); thermal properties; Introduction In recent years, electrically and thermally conductive polymer nanocomposites have attracted considerable attention because of their potential use in many industrial applications, such as aerospace, electronics, packaging, automotives, sensors, batteries

Fabrication of Ag-modified hollow titania spheres via controlled silver diffusion in Ag–TiO₂ core–shell nanostructures

• Bartosz Bartosewicz,
• Malwina Liszewska,
• Bogusław Budner,
• Marta Michalska-Domańska,
• Krzysztof Kopczyński and
• Bartłomiej J. Jankiewicz

Beilstein J. Nanotechnol. 2020, 11, 141–146, doi:10.3762/bjnano.11.12

• carbon template was used in a one-pot synthesis of uniform TiO2–Ag hybrid HSs [16], and of Ag/AgCl modified self-doped TiO2 HSs [17]. Finally, polymer spheres were used as hard-templates in a multistep fabrication of tri-modified TiO2 HSs (Ag–C/N–TiO2) [18], and of silver/TiO2 HSs [19]. Many papers

Molecular architectonics of DNA for functional nanoarchitectures

• Debasis Ghosh,
• Lakshmi P. Datta and
• Thimmaiah Govindaraju

Beilstein J. Nanotechnol. 2020, 11, 124–140, doi:10.3762/bjnano.11.11

• from DNA block copolymer micelles [100]. The block copolymer micelles were synthesized through ring-opening polymerization, followed by the integration of DNA oligonucleotides in a postpolymerization modification process. The DNA acted as a polar head group, while the whole polymer system acted as a

A review of demodulation techniques for multifrequency atomic force microscopy

• David M. Harcombe,
• Michael G. Ruppert and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2020, 11, 76–91, doi:10.3762/bjnano.11.8

• ) tracking bandwidths. The input signal is described by Equation 2, where A1 = 500 mV, A2 = 100 mV, A3 = 50 mV and f1 = 50 kHz, f2 = 150 kHz and f3 = 300 kHz. Higher-harmonic amplitude AFM imaging performed with the fundamental mode of a TAP190G cantilever on a PS/LPDE polymer blend. Images shown are the (a

An investigation on the drag reduction performance of bioinspired pipeline surfaces with transverse microgrooves

• Weili Liu,
• Hongjian Ni,
• Peng Wang and
• Yi Zhou

Beilstein J. Nanotechnol. 2020, 11, 24–40, doi:10.3762/bjnano.11.3

• severely hinders the exploration of oil and gas resources in deep wells [4][5][6]; therefore, it is necessary to put additional effort into reducing the skin friction drag. Conventional hydraulic drag reduction methods include the development of high-performance polymer additives to reduce fluid viscosity

• [7][8][9], the injection of gas to modify the turbulent boundary characteristics [10], and the fabrication of superhydrophobic surfaces to reduce the adhesion [11]. However, the application of polymer additives is not economic and the antidrag performance of additives is also instable under some

• flow drag with the bionic pipeline under the same condition. Governing equations A commercial CFD tool, ANSYS Fluent-18.0, was used to calculate the turbulent flow in the pipe and the concentric annulus. Near-wall turbulence characteristics of a drag-reducing polymer fluid flow in the concentric

The different ways to chitosan/hyaluronic acid nanoparticles: templated vs direct complexation. Influence of particle preparation on morphology, cell uptake and silencing efficiency

• Arianna Gennari,
• Julio M. Rios de la Rosa,
• Erwin Hohn,
• Maria Pelliccia,
• Enrique Lallana,
• Roberto Donno,
• Annalisa Tirella and
• Nicola Tirelli

Beilstein J. Nanotechnol. 2019, 10, 2594–2608, doi:10.3762/bjnano.10.250

• for a hard, uniform sphere, 1.0 for vesicles with thin walls (hollow spheres), close to 1.5 for random polymer coil conformations [23][24]. Fractal dimension (D). When applied to particulates, the fractal geometry analysis is another important morphological indicator. For example, aggregation of

• and HA, producing nanoparticles selectively containing one labelled polymer. Following either chitosan- or HA-associated fluorescence (respectively black and red symbols in Figure 5), we observed qualitatively similar uptake kinetics, which is a sign that the two components are mostly internalized

Fully amino acid-based hydrogel as potential scaffold for cell culturing and drug delivery

• Dávid Juriga,
• Evelin Sipos,
• Orsolya Hegedűs,
• Gábor Varga,
• Miklós Zrínyi,
• Krisztina S. Nagy and
• Angéla Jedlovszky-Hajdú

Beilstein J. Nanotechnol. 2019, 10, 2579–2593, doi:10.3762/bjnano.10.249

• , Nagyvarad square 4, Budapest, Hungary 10.3762/bjnano.10.249 Abstract Polymer hydrogels are ideal scaffolds for both tissue engineering and drug delivery. A great advantage of poly(amino acid)-based hydrogels is their high similarity to natural proteins. However, their expensive and complicated synthesis

• often limits their application. The use of poly(aspartic acid) (PASP) seems an appropriate solution for this problem due to the relatively cheap and simple synthesis of PASP. Using amino acids not only as building blocks in the polymer backbone but also as cross-linkers can improve the biocompatibility

• and the biodegradability of the hydrogel. In this paper, PASP cross-linked with cystamine (CYS) and lysine-methylester (LYS) was introduced as fully amino acid-based polymer hydrogel. Gels were synthesized employing six different ratios of CYS and LYS. The pH dependent swelling degree and the

Long-term stability and scale-up of noncovalently bound gold nanoparticle-siRNA suspensions

• Anna V. Epanchintseva,
• Julia E. Poletaeva,
• Dmitrii V. Pyshnyi,
• Elena I. Ryabchikova and
• Inna A. Pyshnaya

Beilstein J. Nanotechnol. 2019, 10, 2568–2578, doi:10.3762/bjnano.10.248

• ; however, it occupies an important place in scientific research. The delivery of therapeutic nucleic acids (TNAs) is of particular importance due to their operation at the genomic level, and various nanoparticles (NPs) have been studied as carriers of TNAs (i.e., metallic, lipid, polymer, and peptide NPs

• structures usually consists of a AuNP, where siRNA is covalently bound to the NP surface through the thiol group, and the core is covered with a lipid or polymer shell [10][11][12][13]. Covalent bonding of siRNA to the surface of AuNPs is carried out in two stages: (1) covalent attachment of one chain of a

Advanced hybrid nanomaterials

• Andreas Taubert,
• Fabrice Leroux,
• Pierre Rabu and
• Verónica de Zea Bermudez

Beilstein J. Nanotechnol. 2019, 10, 2563–2567, doi:10.3762/bjnano.10.247

• .10.247 Keywords: colloidal chemistry; environmental remediation; hybrid nanomaterials; nanocomposite; nanofillers; nanomedicine; nanostructures; polymer fillers; pore templating; smart materials; The Maya blue pigment that was used in Mexico during the VIIIth century is often given as a prototypical

• into a broad scientific and technological subject including important fields such as sol–gel chemistry [4][5], polymer nanocomposites [6][7], and hybrid nanomaterials [8][9]. Nowadays, hybrid materials are almost everywhere and provide a wide range of applications from biology and health, to photonic

• specialized experimental and theoretical techniques. This thematic issue clearly shows that “advanced hybrid nanomaterials” is not just hype, it is a real and powerful toolbox towards advanced materials for highly diverse fields, such as polymer nanocomposite, health and environment. Smart Materials and

Antimony deposition onto Au(111) and insertion of Mg

• Lingxing Zan,
• Da Xing,
• Abdelaziz Ali Abd-El-Latif and
• Helmut Baltruschat

Beilstein J. Nanotechnol. 2019, 10, 2541–2552, doi:10.3762/bjnano.10.245

• small compartment filled with the same electrolyte and separated from main compartment by a capillary. Pt/Ir (90:10) STM tips with a diameter of 0.25 cm were prepared by etching in a 2 M KOH/4 M KSCN bath and coated with hot-melt glue containing different types of polymer (provided by Steinel) to

Small protein sequences can induce cellular uptake of complex nanohybrids

• Jan-Philip Merkl,
• Malak Safi,
• Christian Schmidtke,
• Fadi Aldeek,
• Johannes Ostermann,
• Tatiana Domitrovic,
• Sebastian Gärtner,
• John E. Johnson,
• Horst Weller and
• Hedi Mattoussi

Beilstein J. Nanotechnol. 2019, 10, 2477–2482, doi:10.3762/bjnano.10.238

• on the ability of functional fusion proteins presenting a lytic gamma peptide, to promote interactions with HeLa cells and delivery of large hybrid nanostructures. Keywords: bioconjugation; cellular uptake; nanoparticle hybrids; polymer encapsulation; self-assembly; Introduction Developing hybrid

• hybrid system consisting of self-assembled gold nanoparticles (AuNPs) and polymer-encapsulated QDs. These constructs were further functionalized with polyhistidine-tagged proteins, yielding functional conjugates that exhibit fluorescent and plasmonic properties [8]. Over the last two decades several

• for this study, due to their compact size, enhanced colloidal stability, and reduced non-specific interactions in biological media [22][24][25][26][27][28][29][30][31]. The central QDs used to build up the hybrid assemblies were prepared via encapsulation within a polymer coating made of an amine

Abrupt elastic-to-plastic transition in pentagonal nanowires under bending

• Sergei Vlassov,
• Magnus Mets,
• Boris Polyakov,
• Jianjun Bian,
• Leonid Dorogin and
• Vahur Zadin

Beilstein J. Nanotechnol. 2019, 10, 2468–2476, doi:10.3762/bjnano.10.237

• flexible polymer composite materials. Keywords: finite element method; mechanical properties; molecular dynamics; nanowires; Introduction Nanostructures comprised of noble metals with face centered cubic (FCC) crystal structure (Au, Ag and Cu according to the most common physical definition) prepared via

• electronics [10][11]. In the last case NWs are used as a conductive network in composition with flexible polymer materials such as polydimethylsiloxane (PDMS) [12][13]. The reliability of flexible devices in high-strain conditions will be governed by the mechanical reliability of the individual NWs inside the

• by Russian Science Foundation project grant 18-19-00645 “Adhesion of polymer-based soft materials: from liquid to solid”; mechanical testing and FEM simulations were supported by Estonian Research Council projects PUT1689 and PUT1372.

Self-assembly of a terbium(III) 1D coordination polymer on mica

• Quentin Evrard,
• Giuseppe Cucinotta,
• Felix Houard,
• Guillaume Calvez,
• Yan Suffren,
• Carole Daiguebonne,
• Olivier Guillou,
• Andrea Caneschi,
• Matteo Mannini and
• Kevin Bernot

Beilstein J. Nanotechnol. 2019, 10, 2440–2448, doi:10.3762/bjnano.10.234

• (375 µs) and the CHCl3 solution (13 µs) further reinforces the idea of water-induced growth. Keywords: atomic force microscopy (AFM); luminescence; nanostructuration; polymer; self-assembly; surface; terbium complexes; Introduction The study of materials for the realization of novel magnetic [1][2][3

• the observed objects. Results Coordination polymer growth on mica The [Tb(hfac)3·2H2O]n molecular nanochains have been grown via drop casting of a dilute cyclohexane solution on a freshly air-cleaved mica substrate. The mica substrate was chosen because of its low roughness [23] making it particularly

pH-Controlled fluorescence switching in water-dispersed polymer brushes grafted to modified boron nitride nanotubes for cellular imaging

• Saban Kalay,
• Yurij Stetsyshyn,
• Volodymyr Donchak,
• Khrystyna Harhay,
• Ostap Lishchynskyi,
• Halyna Ohar,
• Yuriy Panchenko,
• Stanislav Voronov and
• Mustafa Çulha

Beilstein J. Nanotechnol. 2019, 10, 2428–2439, doi:10.3762/bjnano.10.233

• (DU145) and are suitable for further evaluation in cellular imaging applications. Keywords: boron nitride nanotubes; cellular imaging; fluorescence; pH switching; polymer brushes; surface modification; Introduction In recent years, considerable effort has been devoted to the development of hybrid

• polymer brushes via polymerization initiated from their surface [12][28]. In particular, BNNTs were covalently modified with hydrophobic polystyrene or poly(glycidyl methacrylate) polymer brushes [28]. The modified nanotubes demonstrated high dispersibility in a large number of organic solvents. In our

• chloroanhydride fragments in oligoperoxide molecules [12]. The second step involved grafting copolymerization of acrylic acid and fluorescein acrylate initiating “from the surface” of oligoperoxide-functionalized BNNTs to fabricate grafted polymer brushes. The functionalized BNNTs were characterized using

Semitransparent Sb₂S₃ thin film solar cells by ultrasonic spray pyrolysis for use in solar windows

• Jako S. Eensalu,
• Atanas Katerski,
• Erki Kärber,
• Lothar Weinhardt,
• Monika Blum,
• Clemens Heske,
• Wanli Yang,
• Ilona Oja Acik and
• Malle Krunks

Beilstein J. Nanotechnol. 2019, 10, 2396–2409, doi:10.3762/bjnano.10.230

• following for reference: dye-sensitized – PCE of 9.2% at 60% AVT [5]; polymer – PCE of 4.0% at 66% AVT [6]; halide perovskite – PCE of 6.4% at 30% AVT [7]. Dye-sensitized, organic, and halide perovskite absorbers are generally sensitive to moisture, especially in combination with sunlight and air [8][9][10

Polyvinylpyrrolidone as additive for perovskite solar cells with water and isopropanol as solvents

• Chen Du,
• Shuo Wang,
• Xu Miao,
• Wenhai Sun,
• Yu Zhu,
• Chengyan Wang and
• Ruixin Ma

Beilstein J. Nanotechnol. 2019, 10, 2374–2382, doi:10.3762/bjnano.10.228

• organic polymers. As a non-ionic polymer compound, polyvinylpyrrolidone (PVP) shows excellent solubility and physiological compatibility and is extensively applied in medicine, food, and cosmetics, which are closely related to the health of people [29]. PVP is commonly integrated in PSCs, which is

• cell (iPSC), Pengcheng Zhou et al. managed to achieve a signifanct boost in efficiency [30]. The photovoltaic properties of inverted polymer solar cells using a PVP-modified indium tin oxide (ITO) layer as the electron-collecting electrode were reported on by J. W. Shim and co-workers [31]. In this

• purchased from Alfa Aesar. Methylammonium iodide (MAI), methylammonium chloride (MACl) and Spiro-OMeTAD were purchased from Xi’an Polymer Light Technology Corp. ITO glasses with a sheet resistance of 8 Ω/sq were also purchased from Xi’an Polymer Light Technology Corp. All chemicals were used as recieved

Integration of sharp silicon nitride tips into high-speed SU8 cantilevers in a batch fabrication process

• Nahid Hosseini,
• Matthias Neuenschwander,
• Oliver Peric,
• Santiago H. Andany,
• Jonathan D. Adams and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2019, 10, 2357–2363, doi:10.3762/bjnano.10.226

• Abstract Employing polymer cantilevers has shown to outperform using their silicon or silicon nitride analogues concerning the imaging speed of atomic force microscopy (AFM) in tapping mode (intermittent contact mode with amplitude modulation) by up to one order of magnitude. However, tips of the

• cantilever made out of a polymer material do not meet the requirements for tip sharpness and durability. Combining the high imaging bandwidth of polymer cantilevers with making sharp and wear-resistant tips is essential for a future adoption of polymer cantilevers in routine AFM use. In this work, we have

• any photo-processable polymer cantilever. Keywords: Atomic force microscopy (AFM); durability; imaging speed; polymer cantilever; silicon nitride tip; Introduction Atomic force microscopy (AFM) cantilevers have been developed for numerous applications since the invention of scanning probe microscopy

A novel method to remove impulse noise from atomic force microscopy images based on Bayesian compressed sensing

• Yingxu Zhang,
• Yingzi Li,
• Zihang Song,
• Zhenyu Wang,
• Jianqiang Qian and
• Junen Yao

Beilstein J. Nanotechnol. 2019, 10, 2346–2356, doi:10.3762/bjnano.10.225

• proposed method, an AFM image with a high density of added impulse noise (Figure 7) and an image of a polymer-blend sample (stiff polystyrene (PS) and soft polybutadiene (PB) polymer, Nanosurf) with noise acquired with a Park Systems XE-100 AFM (Figure 8) are processed by the proposed method. It can be

Design of a nanostructured mucoadhesive system containing curcumin for buccal application: from physicochemical to biological aspects

• Sabrina Barbosa de Souza Ferreira,
• Gustavo Braga,
• Évelin Lemos Oliveira,
• Jéssica Bassi da Silva,
• Hélen Cássia Rosseto,
• Lidiane Vizioli de Castro Hoshino,
• Mauro Luciano Baesso,
• Wilker Caetano,
• Craig Murdoch,
• Helen Elizabeth Colley and
• Marcos Luciano Bruschi

Beilstein J. Nanotechnol. 2019, 10, 2304–2328, doi:10.3762/bjnano.10.222

• nanometer-sized assembly into three-dimensional micelles with a hydrophobic core of PPO and a hydrophilic shell of PEO that can interact by hydrogen bonds with the hydrophilic acrylic-acid derivative polymer. This results in a binary polymeric system with good viscoelasticity, mucoadhesion, softness and

• . Investigation of CUR interaction with the system In order to improve the understanding of these interactions between CUR and the formulations, stability assays using photophysical studies were performed to provide information about the interactions of CUR with the polymer blends under different conditions

• the preparation and before the pH adjustment step, due to the acidic properties of the mucoadhesive polymers [47]. Furthermore, the stability by photophysical studies of polymer blends containing 0.01% (w/w) P407, 1.6 × 10−4% (w/w) C974P and 1.8 × 10−5 mol/L CUR were spectroscopically evaluated using

Microfluidics as tool to prepare size-tunable PLGA nanoparticles with high curcumin encapsulation for efficient mucus penetration

• Nashrawan Lababidi,
• Valentin Sigal,
• Aljoscha Koenneke,
• Konrad Schwarzkopf,
• Andreas Manz and
• Marc Schneider

Beilstein J. Nanotechnol. 2019, 10, 2280–2293, doi:10.3762/bjnano.10.220

• stabilizer (Pluronic), with a tunable hydrodynamic diameter ranging from 40 nm to 160 nm. The size dependence was evaluated by varying different parameters during preparation, namely polymer concentration, stabilizer concentration, solvent nature, the width of the focus mixing channel, flow rate ratio and

• increase in the flow speed of the aqueous phase from 10–100 µL/min led to a reduction in the mean diameter of the NPs from 150 to 70 nm at a flow ratio of 0.05 (Figure 1). This evidence points to the fact that most likely the polymer concentration decreases by increasing the aqueous phase flow rate, thus

• PDI (polydispersity index, respreswenting the size distribution) values always being <0.1 for all particles prepared by microfluidics). Moreover, the particles are easier to redisperse and are more stable within the aqueous suspension. Effect of polymer concentration The nanoprecipitation mechanism is

Four self-made free surface electrospinning devices for high-throughput preparation of high-quality nanofibers

• Yue Fang and
• Lan Xu

Beilstein J. Nanotechnol. 2019, 10, 2261–2274, doi:10.3762/bjnano.10.218

• high-throughput tipless electrospinning via a circular cylindrical electrode. Shin et al. [19] used a multiple vertical rod setup for needleless ES to fabricate submicrometer polymer fibers. Moon et al. developed a syringeless electrospinning technique with a helically probed rotating cylinder for

• -shaped polymer nozzle. Based on the MBE device, three additional self-made devices used for so-called modified free surface electrospinning (MFSE), oblique section free surface electrospinning (OSFSE) and spherical section free surface electrospinning (SSFSE) are introduced in this paper to obtain high

• reservoir as positive pole was a cylinder with a diameter of 40 mm and a height of 30 mm, the bulk conductivity of copper was set to 5.8 × 1011 µs/cm, the electric conductivity of the polymer nozzles in the MBE was 0 µs/cm, the electric conductivity of the PAN-DMF solution with a concentration of 10 wt

Nontoxic pyrite iron sulfide nanocrystals as second electron acceptor in PTB7:PC₇₁BM-based organic photovoltaic cells

• Olivia Amargós-Reyes,
• José-Luis Maldonado,
• Omar Martínez-Alvarez,
• María-Elena Nicho,
• José Santos-Cruz,
• Juan Nicasio-Collazo,
• Irving Caballero-Quintana and
• Concepción Arenas-Arrocena

Beilstein J. Nanotechnol. 2019, 10, 2238–2250, doi:10.3762/bjnano.10.216

• image (Figure S3e, Supporting Information File 1) taken at low voltage (1 kV). These SEM images are complementary to the AFM images shown in Figure 7. Some NCs are highlighted by red circles, however, it is not trivial to unambiguously identify the NCs because they are immersed in the polymer matrix

Mannosylated brush copolymers based on poly(ethylene glycol) and poly(ε-caprolactone) as multivalent lectin-binding nanomaterials

• Stefania Ordanini,
• Wanda Celentano,
• Anna Bernardi and
• Francesco Cellesi

Beilstein J. Nanotechnol. 2019, 10, 2192–2206, doi:10.3762/bjnano.10.212

• polymer that does not promote immune responses. Pegylation reduces the nonspecific binding of nanoparticles to blood proteins and macrophages, making them non-immunogenic and non-antigenic [21]. PEG-PCL copolymers are amphihilic materials that can spontaneously assemble in aqueous media, forming colloidal

• ), targeting a degree of polymerization (DP) equal to 5. Reaction conversions were monitored by means of 1H NMR analysis; almost full monomer conversion (99%) was obtained after 6 h. The dispersity of the purified polymer was 1.19. Subsequent methacrylation of the terminal hydroxy group was accomplished in

• targeted, in order to obtain macromolecules of different valencies, while maintaining relatively short and flexible polymer chains, which minimize steric hindrance during lectin binding. Different percentages of PEG and PCL macromonomers were used, since the number of PCL side chains defined the final

Use of data processing for rapid detection of the prostate-specific antigen biomarker using immunomagnetic sandwich-type sensors

• Camila A. Proença,
• Tayane A. Freitas,
• Thaísa A. Baldo,
• Elsa M. Materón,
• Flávio M. Shimizu,
• Gabriella R. Ferreira,
• Frederico L. F. Soares,
• Ronaldo C. Faria and
• Osvaldo N. Oliveira Jr.

Beilstein J. Nanotechnol. 2019, 10, 2171–2181, doi:10.3762/bjnano.10.210

• polymer-based immunosensor [34][55]. This rather low value is expected for biosensors where the index n is characteristic of heterogeneous adsorption with polyclonal biomolecules that have many active sites with different degrees of affinity and selectivity. Application of the immunosensor in real samples

Liquid crystal tunable claddings for polymer integrated optical waveguides

• José M. Otón,
• Manuel Caño-García,
• Fernando Gordo,
• Eva Otón,
• Morten A. Geday and
• Xabier Quintana

Beilstein J. Nanotechnol. 2019, 10, 2163–2170, doi:10.3762/bjnano.10.209

• explored. Tunable waveguides have been modeled and fabricated using polymers. Optical functions such as variable coupling and optical switching have been demonstrated. Keywords: liquid crystal; organic waveguide; photonic integrated circuit; polymer waveguide; tunable cladding; Introduction Photonic

• are quite close to each other; the second may often lead to complex manufacturing processes and results less manageable for preparing tunable devices. Polymer waveguides (PWGs) are well suited for preparing devices having LC cladding. Indeed, the refractive index of PWGs is typically in the range of

• the cladding index, as in the polymer guides with LC cladding studied here. The effect of cladding on the MMI field profile is boosted by the increment of the evanescent field, which is achieved by reducing the physical dimensions of the waveguide, and the difference between the core and cladding