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# Ubiquitous organic molecule-based free-standing nanowires with ultra-high aspect ratios

## Abstract

The critical dimension of semiconductor devices is approaching the single-nm regime, and a variety of practical devices of this scale are targeted for production. Planar structures of nano-devices are still the center of fabrication techniques, which limit further integration of devices into a chip. Extension into 3D space is a promising strategy for future; however, the surface interaction in 3D nanospace make it hard to integrate nanostructures with ultrahigh aspect ratios. Here we report a unique technique using high-energy charged particles to produce free-standing 1D organic nanostructures with high aspect ratios over 100 and controlled number density. Along the straight trajectory of particles penetrating the films of various sublimable organic molecules, 1D nanowires were formed with approximately 10~15 nm thickness and controlled length. An all-dry process was developed to isolate the nanowires, and planar or coaxial heterojunction structures were built into the nanowires. Electrical and structural functions of the developed standing nanowire arrays were investigated, demonstrating the potential of the present ultrathin organic nanowire systems.

## Introduction

Uniform low-dimensional nanostructures—nanoparticles, nanosheets, and nanowires—have gained attention as an important class of materials contributing to the progress in the research fields of materials science and nanotechnology1,2,3,4,5. Nanowires offer extra-large specific surface areas useful for sensing platforms6, anisotropic emissions7,8, and the ability of one-dimensional (1D) transport of charges, energy, heat, and so on9,10,11. To realize anisotropic transport along nanowires at a macroscopic scale, the nanowires need to be aligned while maximizing their in-plane density—if they lack unidirectional orientation, the effects of anisotropy are lost for the entire system. In this context, a vertical array of uniform ultrathin nanowires is an ideal candidate for such platforms, providing both extra-large surface area and highly aligned unidirectional 1D pathways. Various fabrication methods of inorganic nanowire arrays have been established so far, as represented by the top-down lithography12,13 and bottom-up epitaxial growth approaches14,15. For example, uniform standing nanowires based on silicon were fabricated with diameters of ~10–100 nm, and their semiconducting properties were demonstrated by integration into a field-effect transistor device16. Another noteworthy example is a vertically aligned carbon nanotube (VA-CNT) array grown by the chemical vapor deposition, with adequate carbon source and a catalytic seed-deposited substrate17,18. Unidirectional alignment of VA-CNTs, coupled with their unique optical and mechanical characteristics, enables their application, such as black absorbers and adhesive materials19,20. In contrast to these hard matter-based examples, standing organic nanowires have as yet been unexplored. Although bottom-up crystalline growth has been successful in fabricating VA-nanowires from several organic molecules, they have the drawback of low structural purity—being contaminated with different nanostructures grown during the growth process21,22. They have two additional problems in that the aspect ratio of the VA-nanowires is hard to tune by changing the growth conditions and their diameters are limited to several hundreds of nm (submicron scale). Standing nanowires have also been achieved from polymer materials through lithography, but the reported highest aspect ratio was only as high as ~1023. A template method using an anodic aluminum oxide (AAO) with cylindrical nanopores was reported, which enables the growth of thin nanowires from organic small molecules with minimum diameter of ~50 nm24. However, these nanowires fell over upon removal of the AAO template by a wet process, eventually resulting in the in-plane orientation of the nanowires. Therefore, there has been a strong desire for widely applicable techniques to develop standing NWs with ultrahigh aspect ratios from a variety of organic materials, which will expand their application in optics, imaging, electronics, bioelectronic, and mechanical fields.

We have developed a technique of nanowire fabrication, referred to as single particle-triggered linear polymerization (STLiP), fabricating uniform nanowires while completely controlling their length, diameter, and number density (Fig. 1). In this method, a single charged particle, regarded as the finest stream of energy, triggers a chemical reaction by depositing its kinetic energy within a nanometer-scale small spatial area. When a high-energy charged particle passes through a condensed organic layer, the energy of the particle is transferred to a limited cylindrical region of the layer, defined as the ion track region25,26. Within the ion track, nonuniform energy transfer occurs and reaction intermediates, such as neutral radicals, are germinated27,28. The intermediates induce cross-linking/polymerization reactions to form 1D gels, resulting in the formation of organic nanowires. The striking advantage of the STLiP method, compared with the other conventional ones, is its applicability for a wide variety of materials as targets. In principle, heavy charged particles, such as Xe, follow a straight trajectory in condensed phases of organic substances because of the negligible momentum/energy transfer from the kinetic energy of incident particles29. This negligible change in the momentum of the particle inspired us to address the production of standing nanowires on a substrate by introducing the particles orthogonally (Fig. 1). Immersion of the irradiated film to dissolve the unirradiated part of the organic substances has been the usual choice for the isolation of latent nanowires on the substrate: the wet development process as used typically in conventional nanofabrication techniques. It causes, however, knocking-down of the resulting nanowires on the substrate due to the irreversible adhesion of nanowires on the substrate via the surface tension force of the solvent30. Although supercritical fluid is an alternative for organic solvents in the wet process31, the isolation of uniform nanowires with high aspect ratio without the collapse of the pattern is still unexplored. Here, we achieve the isolation of standing organic nanowires with ultrahigh aspect ratios by a dry process: the sublimation of unreacted organic molecules. The direct phase transition from solid to gas phases for the nonirradiated area in the films results in the successful isolation of standing nanowires based on polymerized organic materials, with dense distribution and ultrahigh aspect ratio. Further functionalization of nanowires—the design of heterointerfaces32,33—was demonstrated in this work. Two basic types of heterointerface nanostructures have been proposed thus far, namely, coaxial design32,33,34,35 and two adjoining segments32,33,36,37,38. The reported studies are categorized into AAO templated35,37,38 and physical vapor transport34,36 methods. From another perspective, they are classified into inorganic–inorganic32, organic–inorganic35,37, and organic–organic34,36,38 nanowire systems.

Herein, electropolymerization around standing nanowires and block-co-nanowire approaches using bilayer films are explored to realize the respective heterointerfaces in our ultrathin organic nanowire systems. Namely, the tunable extension of wires in both the longitudinal and radial directions is established using a variety of organic substances, illustrating the full potential of our newly developed technology.

## Results

### Fabrication of standing organic nanowires

The nanowires were fabricated along particle trajectories as illustrated in Fig. 1, coexisting with the major fraction of unreacted organic molecules far from the trajectories. Local polymerization reactions in the latent nanowires causes a significant decrease of solubility in organic solvents due to the increase in molecular weight. The latent nanowires could be easily isolated by a wet process with selective dissolution of the unreacted molecules. However, collapsing and aggregation of nanowires has generally been unavoidable, owing to solvent effects. The strong interactions between the nanowire and substrate surfaces irreversibly fixed the nanowires on the substrate39, leading to their random distribution with a global worm-like chain configuration, which showed the flexibility of nanowires in the presence of the solvents, and the configuration could be interpreted based on the scaled macromolecular chain configuration in dilute solutions40. Macromolecular systems are also superior materials to promote the creation of latent nanowires in condensed phases via gelation, where insolubility of the macromolecules can be achieved with an average of one crosslink point per polymer molecule41. In contrast, it is presumed to be difficult to obtain nanowires, in which perfect immobilization of molecules occurs along the corresponding particle trajectory in the STLiP protocol. Recently, our studies revealed that highly efficient polymerization/cross-linking reactions, such as radical chain reactions in condensed phases, are available to afford nanowire formation via the STLiP protocol from a wide choice of small molecular materials42,43.

In contrast to macromolecular systems, the higher vapor pressure of small organic molecules often provides them with sublimation ability, which provides us an overwhelming advantage in postirradiation processing. Polymerization reactions in the latent nanowires eliminate the sublimation ability of the initial molecular materials, which prompted us to selectively remove the unreacted molecules by simple heating in a vacuum, and thus isolate the nanowires on the substrates (Fig. 1). This sublimation ability is, in general, often utilized for fabrication of organic thin films, such as by vapor deposition. In contrast, here the sublimation is utilized for the development in postirradiation processes to remove excess unreacted material; this is an innovative point of the present work. In this all-dry process, we no longer consider the interaction between solvents and nano-patterns (nanowires), and/or their collapse during the process. No surface tension operates on the VA-nanowires, enabling us to obtain standing nanowires with ultrahigh aspect ratio free from pattern collapse.

As a target small molecular material, the Buckminster fullerene C60 molecule was selected; C60 is a fully isotropic organic molecule that has equivalent unsaturated carbon bonds44. C60 has been reported to be sublimable, and its film is easily fabricated by vapor deposition45, an important requisite in all-dry postirradiation STLiP protocols. Besides, C60 is a representative molecule to facilitate chain polymerization reactions, initiated upon exposure to photo- and ionizing radiation46,47. The polymerization reaction has been well confirmed and characterized by conductive atomic force microscopy (AFM) and Raman scattering measurements48,49. We have also previously reported the formation of randomly spread C60 nanowires in 2D as a polymeric material obtained after a chain polymerization reaction, isolated by a wet process using organic solvent50. Hence, in this paper, we attempted to isolate C60 nanowires by an all-dry process. C60 thin films were prepared by vapor deposition at 250–2000 nm thickness on Si substrates. Figure 2 shows the morphology of isolated nanowires observed by scanning electron microscopy (SEM), illustrating the striking contrasts in the images taken after the all-dry and wet isolation processes. After the isolation of the nanowires by the dry process, standing nanowires were clearly confirmed without any collapse, with dense distributions as high as ~1011 cm−2 (Fig. 2a–c). In contrast, significant collapse of knocked-down nanowires was observed on the substrate after isolation by a wet process (Fig. 2d), suggesting the presence of strong inter-nanowire and nanowire–substrate interactions promoted by solvents. Observation of the morphology by AFM also supported the supposition that the nanowires unavoidably aggregate during the wet process, as shown in the white area in Supplementary Fig. 1a, losing their verticality. On the other hand, the total length of the nanowires strictly reflected the initial thickness of the vapor-deposited C60 film in the dry process, verifying the production of standing nanowires with uniform and controllable length over a defined area (Supplementary Fig. 1c, d). It is noteworthy that the vertical alignment of nanowires was maintained clearly over their full length of 2500 nm (Fig. 2c), which demonstrated the production of organic molecular-based nanostructures with ultrahigh aspect ratios over 300. Particles of 350 MeV 129Xe26+ maintain high linearity in C60 solid films (ρ = 1.72 g cm−3) as thick as 10 μm in trajectories simulated by a Monte Carlo method (SRIM 2010, Supplementary Fig. 2). This linearity guarantees that their energy transfer to the target is negligible in comparison with their initial kinetic energy in this regime. The transferred energy is estimated to reach up to 10% of the initial energy, suggesting that vertical nanowires as long as 20 μm can theoretically be achieved.

### Molecules for standing nanowire fabrication

The isolation of nanowires by the dry process can minimize the effects of solvents. However, another important factor should be considered. The vertical alignment of the nanowires deteriorated when the irradiation fluence was reduced to 5.0 × 1010 and 1.0 × 1010 cm−2 (Supplementary Fig. 3). Inter-wire interactions in the nanowire plexus maintain the assembled structures on the substrate; at reduced in-plane number densities of nanowires, the interactions are not sufficient to keep the nanowires standing. Then, to confirm the effect of solvent independently, we treated the once-isolated standing nanowire plexus with an organic solvent (Supplementary Fig. 4). As can be seen in Supplementary Fig. 4a–c, the vertical alignment of the nanowire gradually disappeared with immersion time in the solvent, showing local aggregation with random domain sizes. The issue has been recognized in nanolithography processes as pattern collapse, particularly for structures with high aspect ratio51. The observation also suggests that the terminus of the nanowires is tightly connected onto the substrate surfaces. The inter-nanowire interactions were much enhanced with increasing length, as clearly seen in Supplementary Fig. 4e, where the bright tone of the images represents the 2D-like nanowire assemblies. These detailed experimental results imply the great advantage of the dry process with sufficient in-plane number density (=irradiation fluence).

C60 is a representative carbon allotrope, and its chemical modification/functionalization has been frequently reported. Here, we address whether the Buckminster fullerene framework is necessary to create self-standing nanowires; this is the key question regarding the versatility of the present STLiP protocol. We attempted the formation of standing nanowires from a well-known modified fullerene derivative PC61BM ([6,6]-phenyl-C61-butyric acid methyl ester) and a larger fullerene C70 (Supplementary Fig. 5). From PC61BM, clear nanowires were obtained in both dry (Supplementary Fig. 5a–d) and wet (Supplementary Fig. 5e–h) processes. The melting point of PC61BM, reported as ~280 °C (ref. 52), is significantly lower than the sublimation temperature of 300 °C in the applied vacuum conditions, resulting in melting of the unreacted PC61BM molecules to cause severe surface tension and eventually deform the self-standing nanowires. In sharp contrast, self-standing C70 nanowires were developed clearly by the all-dry process, in spite of their reduced verticality compared to that of C60. One possible explanation for this difference is the lower reactivity of C70 upon heavy ion irradiation. In fact, comparing the cross-sectional radii of nanowires, the nanowires from C70 showed a smaller cross-sectional radius than those from C60, which suggests a higher polymerization efficiency for C60.

Here, the reaction efficiency due to the energy transferred by particle irradiation is introduced, as the explanation for the change in cross-sectional radius. The energy transfer efficiency of radiation is often expressed in terms of linear energy transfer (LET), which has been proposed based on the equation for the spatial distribution of the energy density imparted to a material in an ion track, as a function of the distance from the track center r53:

$$\rho (r)=\frac{\mathrm{LET}}{2}{\left[2\pi {r}^{2}{\mathrm{ln}}\left(\frac{{e}^{1/2}{r}_{\mathrm{p}}}{{r}_{\mathrm{c}}}\right)\right]}^{-1},$$
(1)

where e is an exponential factor, and rc and rp are the radii of the core and penumbra areas of a particle track. Then, a simple assumption is applied, in which polymer cross-linking proceeds in the boundary region giving the nanowires (cross-sectional radius of the nanowires: rcc). Generally, for gel formation in a polymer system, it is necessary to introduce one crosslink per polymer molecule. By introducing G(x), the reaction efficiency per 100 eV of irradiated particle energy, the required density of energy (ρcr) is given by,

$${\rho }_{\mathrm{cr}}=\frac{100dA}{G(x)mN},$$
(2)

where A, d, m, and N are Avogadro’s number, the gravitational density of the solid polymer, mass of a monomer unit, and degree of polymerization, respectively. Adapting Eqs. (1) and (2) for low-molecular-weight materials, G(x) is expressed by Eq. (3) below,

$$G(x)=\frac{200{\pi} {dA}{r}_{\mathrm{cc}}^{2}}{{\mathrm{LET}}{\cdot}{M}}\left[1+2\,{\mathrm{ln}}\left(\frac{{r}_{\mathrm{p}}}{{r}_{\mathrm{c}}}\right)\right],$$
(3)

where M is the molecular weight. Substituting the parameters of C60 and C70 into this equation, the G values of C60 and C70 are 35.1 and 15.3, respectively, indicating that the reaction efficiency of C60 is ~2.3 times higher than that of C70. Dimerization reactions were reported both in C60 and C70 upon photo-exposure and irradiation to ionizing radiation54,55,56. The estimated ~3-fold higher efficiency in solid C60 than in C70 (ref. 57) can well explain our experimental results for high-energy ion irradiation.

The breadth of the feasibility of the STLiP technique can be demonstrated by fabricating standing nanowires from a wide variety of organic molecules besides C60 or C70. We focused on conjugated small molecules as targets of STLiP protocols to promote efficient chain polymerization reactions. As demonstrated in Fig. 3, a variety of aromatic molecules suitable for the dry process with the ability to be sublimed under vacuum were selected as the targets, and clearly gave standing nanowires from the corresponding molecules. It is noteworthy that the nanowires could be produced from the simple sublimable polyaromatic hydrocarbon 9,10-bis(phenylethynyl)anthracene (BPEA), where the STLiP protocol could induce efficient chain polymerization/cross-linking reactions mediated by the reaction at C–C triple bonds58. Much higher enhancement of the reactions could be promoted by dissociative electron attachment onto halogen atoms bound to aromatic rings59,60, resulting in the successful formation of standing nanowires based on all five starting compounds represented in Fig. 3. The cross-sectional radius of the nanowires reflects only the local energy density released by a particle in the STLiP protocol, which is determined physically and given uniformly in principle. In the wet process, the solubility/insolubility of molecules at the nanowire surfaces predominantly determines the radius, and the fluctuations in the dissolution process are reflected in the roughness of the surfaces, and hence the nonuniform values of radii in the nanowire aggregates. In sharp contrast, the standing nanowires based on 1,6,7,12-tetrachloro-3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA-Cl4) isolated by the dry process (Fig. 4a) clearly confirm the high uniformity of their height, which coincides with the initial thickness of the films prepared. A nanowire aspect ratio of over 100 was achieved in 10,10′-dibromo-9,9′-bianthracene (DBBA)-based nanowires isolated by the all-dry process (Fig. 4b). The results suggest the wide versatility of the STLiP method for the conversion of various small organic molecules into free-standing VA-nanowires with high aspect ratio; the starting materials are not limited to C60. The important factors of the target molecules for the efficient formation of standing nanowires by this method include (1) aromatic molecules, (2) sublimable at a temperature below the melting point, and (3) with substitution by triple and/or C–X bonds in their periphery.

### Structural parameter analysis of standing nanowires

SEM/AFM images are beneficial for the characterization of nanowire shapes/morphologies. However, they are insufficient for insights into the internal structures of nanowires, which depend on the target molecules and their polymerization reaction efficiency. We chose the following four parameters: the cross-sectional radius (r) and rigidity of each nanowire (D/L), the coverage factor per unit area (CNW), and the length retention of standing nanowires compared to the initial organic thin film thickness (HNWs/Tfilm), for further discussion to shed light on the interior characteristics of nanowires (Supplementary Fig. 6). As represented by Eq. (3), the polymerization reaction efficiency in a particle track explicitly defines the density of polymerization/cross-linking networks in the area, mechanically reinforcing the nanowires. As the flexibility/rigidity of macromolecular chains have been quantitatively discussed40, the formulations have been scaled herein and their rigidity was determined statistically as D/L, where D and L are the end-to-end distance and total length of nanowires, respectively. For all the molecules employed, as summarized in Table 1, the values of D/L, which were estimated from AFM images of knocked-down nanowires at 109–1010 cm−2, approached ~1, exhibiting the high rigidity of nanowires without a strong dependence on r. Since the impact points of particles are uncontrollable at the nm scale and are distributed randomly in the plane of the targets, we can presume the partial overlap of ion tracks under high particle fluence, impacting the uniformity of the nanowires. The Poisson distribution function was used to obtain a numerical estimate for the ion-track overlap61,62, and the fraction of overlapped area against unoverlapped area is represented by the Poisson measure CNWs as summarized in Table 1. Under the condition of ion irradiation at 1 × 1011 cm−2, the value of CNWs is ~10%, and no significant overlap occurs, so that uniform nanowire arrays can be assured. SEM and AFM images can precisely estimate the height of nanowires without significant errors. It was observed that the average height of the top of nanowires (HNWs) was less than the initial thickness of the target films (Tfilm). This observation indicates that the nanowires partially lean to form a nanowire carpet with inter-wire interactions. It should be noted that changes in HNWs/Tfilm show no correlation with the rigidity parameter D/L, suggesting that high enough mechanical rigidity had been already secured by chemical reaction prior to the thermal treatments to isolate the nanowires. Therefore, a possible scenario is that the reaction efficiency, G value, and the size of the monomer molecule mainly determine the nanowire radius (r) (and CNWs), resulting in closer distances between the surfaces of adjacent nanowires. The larger the nanowire radius, the more the nanowires remain vertical with inter-wire interactions.

### Fabrication of nanowire networks

Directional alignment of nanowire growth relative to a 2D plane has been a challenging task for 1D nanostructured systems, for both bottom-up methods, such as CNT growth in catalytic cycles and top-down methods of nanolithography. Although there have been only limited examples of 3D structure of metal wires at nano (~submicron) scale63, ultrafine networked structures from organic nanowires have not yet been reported. In this context, the present STLiP method is promising, because the momentum of a charged particle is unchanged in its interactions with the organic matter and is confined to the growth direction of the corresponding nanowires. Thus, once irradiation is performed with a certain tilt angle (θ) against the flat surface of a substrate, tilted nanowires are produced as shown in Supplementary Fig. 7. Upon continuous rotation of a substrate at a fixed θ = 45°, a conical distribution of the tilted nanowires was isolated, showing cross-connected structures with cross-connected scaffolds (Supplementary Fig. 8). Spatial control of the target against the unidirectional momentum of the high-energy charged particles enables us to form 3D nanowire networks with designed structures as demonstrated in these figures, suggesting its potential for nano-design with a three-dimensional molecular canvas.

### Formation of heterojunctions in standing organic nanowires

Surface modification of nanowires64,65 is important for the functionalization of nanowires toward developing miniaturized devices or biocompatible nanosystems. We consider that the present STLiP method allows the design of any heterointerface with free choice of the two materials by simply employing bilayer structures as the targets. In addition, coaxial heterointerfaces can be attainable by subsequent chemical/physical decoration of the active surfaces of standing-isolated nanowires. Here, we focused on the feasibility of using our standing nanowire arrays to form controlled heterojunctions between p- and n-types semiconductor organic molecules. We have addressed this issue via the STLiP protocol to form uniform nanowires with programmed heterojunctions in a single step over an arbitrary area.

Titanyl phthalocyanine (TiOPc) and C60, as representative p- and n-type organic molecules66, respectively, were used to prepare a bilayer thin film. Nanowires with single heterojunctions were prepared by the usual STLiP protocol, controlling the fluence of irradiation at 1 × 1011 cm−2 (Fig. 5a). The cross-sectional image of the bilayer film exhibited a clear contrast reflecting the composition of the respective molecules with metal and carbon atoms, showing a clear boundary (Fig. 5b). After isolation by sublimation, the nanowires exhibited the expected self-standing features, as confirmed by the SEM images (Fig. 5c, d), and the lengths of the nanowire segments were uniform and consistent with the film thicknesses. The chemical structure of each segment after isolation of the sublimation protocol, and then in free-standing nanowire form, was investigated using Raman spectroscopy (Supplementary Fig. 9), showing the clear signatures of the C60 cages and Pc rings. This suggests that these structures were preserved in the nanowires, and hence one heterojunction per nanowire was produced with less damage in this dry process. The choices of two distinct molecular systems enables the free design of heterojunctions between the molecular systems. Another example using PTCDA-Cl4 and HBT was also demonstrated as shown in Fig. 5e–g. Through stepwise sublimation by fine control of the sublimation temperature and degree of vacuum, the isolation process of p/n heterojunction block-co-nanowires was clearly demonstrated. Further accumulation of heterojunction structures in an isolated nanowire was demonstrated under consistent sublimation conditions of p and n components. Multi-segment nanowire arrays have been clearly visualized in Supplementary Fig. 10 from a simple structure of layer-by-layer films of C60 and copper phthalocyanine (CuPc) as a target. This allows us to program a variety of heterojunction structures into a single wire with ordered alignment from favorable choices of sublimable molecular systems.

Standing nanowires with maximized active surfaces allow us to introduce heterojunction structures not only along the longitudinal, but also the radial direction. Uniform overcoating/decoration of 1D nanowires is one of the simplest way to achieve coaxial nanostructures32,33,34,35. We employed electropolymerization of π-conjugated monomers grown from the semiconducting surfaces of the standing nanowires. Polythiophene, a well-known p-type organic semiconductor material67, can be easily deposited by electropolymerization of the thiophene monomer or dimer68. After forming C60 nanowires on a conductive ITO-glass substrate, electropolymerization was carried out (Fig. 6a), and a thin film of polythiophene was prepared on the substrate (Fig. 6b). AFM and SEM confirmed that the polythiophene grew from the wire periphery rather than from the ITO substrate, resulting in the formation of nanowires with a coaxial structure (Fig. 6c–h and Supplementary Fig. 11a–c). As seen from the side view of SEM images before/after polymerization (Fig. 6c, d, f, g) the lengths of the nanowires are almost identical, while their diameters got increased apparently. In addition, as electropolymerization progressed, polythiophene was further grown around the C60 nanowires in their radial direction (Supplementary Fig. 11d, e). Figures 5 and 6 together show that the wire can be readily extended in the longitudinal and radial directions in a very simple manner, constructing single or coaxial heterointerfaces. Considering that organic heterojunction structures at the nanoscale have been entirely addressed by the epitaxial growth34,36 or template method35,38 of one component from the active surface of the other component or bulk heterojunction-type simple mixtures69 with limited choice of materials, our unique method using standing nanowire platforms serves as a promising strategy for accessing future nanoscale heterojunction devices.

## Discussion

We report the facile and efficient technique to form standing-isolated organic nanowire arrays with small radii (<10 nm) and vast total surface area, which simultaneously show wide versatility in the choice of organic starting materials and free binary choices for the presumed heterointerfaces, paving the way toward the development of functional nanomaterials for optical, electrical, and biological applications. High-energy particle irradiation of organic thin films in the orthogonal configuration resulted in polymerization/cross-linking reactions of the small organic molecules within the cylindrical ion tracks to give uniform polymerized nanowires with a defined length and diameter. The key to the achievement is the use of a dry process, sublimation, after irradiation, allowing isolation of the standing organic nanowires with remarkable vertical alignment. The well-aligned nanowires on the substrate exhibited unique functionalities indicating that the structural uniform length and vertical alignment of the free-standing nanowires was advantageous for surface modification, leading to high-water repellency (Supplementary Fig. 12). The well-aligned nanowires on a substrate exhibited unique functionalities reflecting (1) structural: uniform length and vertical alignment of free-standing nanowires was advantageous for surface modification leading high-water repellency (Supplementary Fig. 12)70, (2) electrical conductivity of the nanowire plexus: the nanowire of conjugated organic molecules was expected to be an electrical conductive wire, and the conductivity of the nanowire plexus was measured by DC conductivity measurement because the vertical alignment allow us to fabricate a sandwiched cell between metal electrodes. The observed IV traces were shown in Supplementary Fig. 13, suggesting almost linear dependence of conductivity on the number density of nanowires. It should be also noted that the conductivity is also proportional to the area of top electrodes fabricated on the nanowire plexus, suggesting high uniformity of the nanowires also in their electrical conduction, (3) A pn heterojunction nanowire as a rectifier diode: the heterojunction structure built in the nanowire was presumed to rectify electrical current in the nanowire. The IV characteristics of the nanowire were traced under an applied modulated bias (Supplementary Fig. 14), suggesting statistically unipolar electrical conduction over the heterojunction and its potential as an ultrasmall rectifier diode.

This methodology is applicable to a variety of aromatic organic molecules, especially aromatic molecules with triple carbon–carbon or aryl-halogen bonds capable of highly efficient radical generation upon high-energy particle irradiation. Simple irradiation of multilayer organic films provides the fabrication of segmented nanowires with desired heterointerfaces, which enables nanoscale pn heterojunction nanowires. Electropolymerization of another π-conjugated monomer on the standing nanowire arrays gives coaxially grown nanowires with a heterointerface, while keeping their VA free-standing characteristics. Our simple method of producing standing nanowires with uniform ultrafine small radii and extra-large specific surface area, with free choice of organic molecule starting materials and controllable length and number density, provides an opportunity to construct organic nanowire-based devices contributing to the fields of nano photonics, electronics, mechanics, and sensing with highly efficient and/or anisotropic functions.

## Methods

### Materials

C60, C70, PC61BM, BPEA, TBPB, TBP, DBBA, HBT, TiOPc, CuPc, and 2,2′-bithiophene were purchased from Tokyo Chemical Industry Co. Ltd. and used without further purification. PTCDA-Cl4 was purchased from Combi Blocks Inc.

### Film preparation

A Si substrate was cut into 1.5 cm2 squares, sonicated in 2-propanol, dried, and treated with UV-O3 prior to the use. Thin films of PC61BM were prepared by spin-coating from CHCl3 solutions (5–10 wt%) on the Si substrate. Thin films of C60, C70, BPEA, TBPB, TBP, DBBA, HBT, PTCDA-Cl4, TiOPc, and CuPc were prepared by vapor deposition under ~10−4 Pa at the rate of 0.2–0.8 Å s−1. The thickness of the films was evaluated by a Veeco Instruments Inc. model Dektak 150 surface profiler.

The 490 MeV 192Os30+, 350 MeV 129Xe26+, and 450 MeV 129Xe23+ were generated from a cyclotron accelerator at Takasaki Advanced Radiation Research Institute, National Institutes for Quantum and Radiological Science and Technology. The 120 MeV 197Au9+ ions were generated from a Pelletron accelerator at Inter-University Accelerator Centre. All the charged particles (ions) employed in this study have a higher velocity than the Bohr velocity of electrons in the target materials, and thus the energy of the charged particles is presumed to be transferred by inelastic collision events without specific dependence on the atomic numbers of the particles. The prepared organic films were exposed to the ion beam in a vacuum chamber (<1 × 10−4 Pa). The number of incident particles was controlled at the fluence of 109–1012 cm−2 by setting the exposure time (s) and flux (cm−2 s−1) calculated from the beam current, charges of the ions used, and elementary charge. Then, the irradiated films were further cut into small pieces, and developed by immersing them into organic solvents or sublimation under vacuum (5–8 × 10−3 Pa). The end of sublimation was judged visually by observing the change in the reflectance of samples.

### Simulation of high-energy particle irradiation

The loss of the kinetic energy of the ions due to their traversal through the organic films (LET) was estimated using the SRIM 2010 simulation code. The film thickness was set at 10 µm (larger than the actual maximum film thickness). The density of the film was set at 1.72 g cm−1 for C60 and 1.96 g cm−1 PTCDA-Cl4. The 490 MeV 192Os30+, 350 MeV 129Xe26+, 450 MeV 129Xe23+, and 120 MeV 197Au9+ ions were irradiated 2000 times each.

### Morphological characterization of nanowires

The sizes and shapes of the isolated nanowires were observed using a Bruker Co. model Multimode 8 AFM and JEOL Ltd. JSM-7001F SEM system.

### Characterization of nanowire parameters

The end-to-end distance (D) and length (L) of the nanowires were estimated by AFM using the knocked-down nanowires after irradiation with 450 MeV 129Xe23+ at 1.0 × 109 cm−2 and the subsequent sublimation process. The cross-sectional radius was calculated from the half-width (rw) and half-height (rh) of the AFM images of the knocked-down nanowires. By applying the ellipsoidal model, the cross-sectional radius (r) was defined as r = (rwrh)1/2.

### Raman spectroscopy

Raman spectra were measured on a JASCO NRS-4100 spectrometer.

### Electropolymerization

Standing nanowires were fabricated on an ITO-glass substrate, and the NW-coated ITO-glass was used as an anode. The anode and cathode (Pt plate) were dipped in a nitrobenzene solution (30 mL) of 2,2′-bithiophene (131 mg) and tetrabutylammonium tetrafluoroborate (200 mg). A constant electric current of 0.5 mA was applied for 1 min by a Hokuto Denko Corporation HA-151B galvanostat. After the polymerization of 2,2′-bithiophene on the anode, de-doping was carried out by applying the inverse current of 0.5 mA for 1 min. The anode was pulled out from the solution and gently washed by methanol.

### DC conductivity measurements

The electrical conductivity measurements for C60 nanowires in vertical direction were conducted with two-probe configuration. A gold bottom electrode (50 nm) was deposited on a Si substrate by thermal evaporation. Some drops of silver paste were casted onto the C60 nanowires leading to top electrodes with various active area. IV traces were recorded using a micromanipulated probe station (Lake Shore TTPX) and a semiconductor parameter analyzer (Keithley 4200A-SCS). All the measurements were performed in vacuum (~10−3 Pa) at room temperature.

### Conductive AFM

Conductivity of PT@C60 nanowires were measured by a SII Inc. NanoNavi-II AFM in contact mode with an Au-coated cantilever. Spring constant of the cantilever was 0.23 N m−1, and the deflection of the cantilever was set at 2 nm, acting interfacial force of ~400 pN between the cantilever and PT surfaces.

### Evaluation of surface water repellency

Contact angle measurements were performed on a Kyowa Interface Science Co., Ltd. DMe-211 contact angle meter. A distilled water droplet of 1 µL was dropped on the NW-coated silicon substrate.

## Data availability

The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information file. All other information is available from the corresponding authors upon reasonable request.

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## Acknowledgements

This work was supported in part by a Grant-in-Aid for Transformative Research Areas (20H05862) from Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan, Scientific Research (A) (18H03918) and (B) (19KK0134) from the Japan Society for the Promotion of Science (JSPS). High-energy charged particle irradiation was carried out at the Takasaki Advanced Radiation Research Institute and the National Institutes for Quantum and Radiological Science and Technology (QST), Japan, under the Facility Sharing Program and the Inter-University Program for the Joint Use of JAEA/QST Facilities, and at the Inter-University Accelerator Centre (IUAC), Delhi, India.

## Author information

Authors

### Contributions

S.S. conceived the project with T.S.; K.S.K., K.T.K., T.S., and S.S. co-designed the experiments. K.S.K. and K.T.K. performed nanowire fabrication and characterization experiments. A.I., H.K., M.S., L.G.B.V.S., and D.K.A. co-performed the irradiation experiments; S.G.S. co-analyzed experimental data; M.N. and Y.T. conducted conductive AFM measurements and analysis; M.K. and M.S. examined electrical conductivity of nanowires; and K.S.K., S.G.S., T.S., and S.S. co-wrote the paper.

### Corresponding authors

Correspondence to Tsuneaki Sakurai or Shu Seki.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Communications thanks Gilles R. Bourret and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

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Kamiya, K., Kayama, K., Nobuoka, M. et al. Ubiquitous organic molecule-based free-standing nanowires with ultra-high aspect ratios. Nat Commun 12, 4025 (2021). https://doi.org/10.1038/s41467-021-24335-x

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text:
## Smooth valuations and their products

Series:
High Dimensional Seminar
Wednesday, October 31, 2018 - 12:55pm
1 hour (actually 50 minutes)
Location:
Skiles 006
,
UGA
,
Organizer:
Alesker has introduced the notion of a smooth valuation on a smooth manifold M. This is a special kind of set function, defined on sufficiently regular compact subsets A of M, extending the corresponding idea from classical convexity theory. Formally, a smooth valuation is a kind of curvature integral; informally, it is a sum of Euler characteristics of intersections of A with a collection of objects B. Smooth valuations admit a natural multiplication, again due to Alesker. I will aim to explain the rather abstruse formal definition of this multiplication, and its relation to the ridiculously simple informal counterpart given by intersections of the objects B.

format: plain


text:
# Chemical reactions and equations class 10 ncert solutions Science

Question 1
Why should a magnesium ribbon be cleaned before burning in air?
Solution When magnesium ribbon is stored, it reacts with oxygen to form a layer of magnesium oxide. This layer of magnesium oxide is quite stable and prevents further reaction of magnesium with oxygen. Hence a magnesium ribbon should be cleaned before burning in air.

Question 2
Write the balanced equation for the following reaction:
(a) Hydrogen +Chlorine =Hydrogen chloride
(b) Barium chloride+Aluminium sulphate = Barium sulphate +Aluminium chloride
(c) Sodium +Water = Sodium hydroxide + Hydrogen
Solution:
How to solve these type of Question
• First convert the word equation into skeletal equation
• Start by finding out how many atoms of each type are on each side of the equation
• You can make  a little table listing the numbers of each atom for the left hand side and for the right hand side
• Balance the different Atoms on both side of equation by  multiply the chemical species on the side which does not have enough atoms of that type by the number required to bring it up to the same as the other side.
(a)H2 +Cl2     -> 2HCL
(b) 3BaCl2+Al2(SO4) -> 3BaSO4 + 2AlCl3
(c) 2Na + 2H2O  -> 2NaOH + H2

Question 3
Write a balanced chemical equation with state symbols for the following reaction:
(a) Solution of barium chloride and sodium sulphate in water react to give insoluble barium sulphate and the solution of sodium chloride.
(b) Sodium hydroxide solution ( in water ) reacts with hydrochloric acid solution (in water) to produce sodium chloride solution and water.
Solution:
How to solve these type of Question
• First convert the word equation into skeletal equation
• Start by finding out how many atoms of each type are on each side of the equation
• You can make  a little table listing the numbers of each atom for the left hand side and for the right hand side
• Balance the different Atoms on both side of equation by  multiply the chemical species on the side which does not have enough atoms of that type by the number required to bring it up to the same as the other side.
(a) BaCl2(aq) +Na2SO4(aq)-> BaSO 4(s) +2NaCl(aq)
(b) NaOH(aq) +HCl-> NaCl(aq) +H2 O

Question 4
A solution of a substance “X” is used for white washing.
(a) Name the substances “x” and write its formula.
(b) Write reaction of the substance “X” named in (!) above with water.
Solution:
(a) The substance “x’ is calcium oxide . Its chemical formula is CaO.
(b) Calcium oxide reacts vigorously with water to form calcium hydroxide ( slaked lime)
CaO+ H2O-> Ca(OH)2

Question 5
Why is the amount of gas collected in one of the test tubes in activity 1.7 double of the amount collected in the other? Name this gas.
Solution:
Water (H2O)contains two parts hydrogen and one part oxygen . Therefore, the amount of hydrogen and oxygen produce during electrolysis of water is in a 2:1 ratio. During electrolysis, since hydrogen goes to one test tube and oxygen goes to another, the amount of gas collected in of the test tubes is double of the amount collected in the other. The gas collected in double the amount is hydrogen and the other gas is oxygen.

Question 6
Why does the colour of copper sulphate solution change when an iron nail is dipped in it.
Solution: When an iron nail is placed in a copper sulphate solution , iron displaces copper from copper sulphate solution forming ferrous sulphate solution and copper metal. Ferrous sulphate is green in colour and copper metal is brown.
Therefore, the blue colour of copper sulphate fades and green colour appears.

Question 7
Give an example of a double displacement reaction other than the one given in Activity 1.10.
Solution
A double displacement reaction between the reactants lead nitrate and potassium iodide gives new substances lead iodide and potassium nitrate.
Pb(NO3 )2(aq) +KL(aq)-> PbL2(s) +KNO3(aq)
In this reaction lead nitrate and potassium iodide exchange ion to form two new compounds  lead iodide and potassium nitrate. Hence , it is a double  placement reaction.
Question 8
Identified the substances that are oxidized and the substances that are reduced in the following reaction.
(a) 4Na(s)+ O2(g) -> 2Na2O(s)
(b) CuO(s) + H2(g)-> Cu(s) +H2O(I)
Solution
(a) Sodium (Na) is oxidized to sodium oxide as it gains oxygen and oxygen get reduced.
(b)Copper oxide (CuO) is reduced to copper (Cu) while hydrogen (H2) gets oxidized to water (H2O).

Question 9 Which of the statement about the reaction below are incorrect?
2PbO(s) +C(s) -> 2Pb(s) +CO2(g)
2. Carbon dioxide is getting oxidized.
3. Carbon is getting oxidized.
4. Lead oxide is getting reduced
(i)(a) and (b)
(ii) (a) and (c)
(iii) (a) (b) and (c)
(iv) all
Solution
oxidation is gain of oxygen and reduction reaction is released of oxygen
(a) and (b)

Question 10
Fe2O3 + 2Al -> AL2O3+ 2Fe
The above reaction is an example of
1. Combination reaction
2. Double displacement reaction
3. Decomposition reaction
4. Displacement reaction
Solution
(d) displacement reaction

Question 11
What happens when dilute hydrochloric acid is added to iron fillings? Tick the correct Solution.
(a)Hydrogen gas and iron chloride are produced.
(b) Chlorine gas and iron hydrochloric are produced.
(c) No reaction takes place.
(d) Iron salt and water are produced.
Solution
(a) Hydrogen gas and iron chloride are produced.

Question 12
What is a balance chemical equation? Why chemical equation should is balanced?
Solution
A chemical equation is balanced when the number of atoms of each type  involved in a chemical reaction are same on both the reactant and product sides of the equation.
According to the law of conservation of mass, when a chemical reaction occurs, the mass of the products should be equal to the mass of the reactants. Therefore, the amount of the atoms in each element does not change in the chemical reaction. As a result, the chemical equation that shows the chemical reaction needs to be balanced. A balanced chemical equation occurs when the number of the atoms involved in the reactants side is equal to the number

Question 13
Translate the following statements into chemical equations and then balance them.
(a)Hydrogen gas combines with nitrogen to form ammonia
(b) Hydrogen sulphide gas burns in air to give water and sulphur dioxide.
(c) Barium chloride reacts with aluminium sulphate to give aluminium chloride and a precipitate of barium sulphate
(d) Potassium metal reacts with water to give potassium hydroxide and hydrogen gas.
Solution:
How to solve these type of Question
• First convert the word equation into skeletal equation
• Start by finding out how many atoms of each type are on each side of the equation
• You can make a little table listing the numbers of each atom for the left hand side and for the right hand side
• Balance the different Atoms on both side of equation by  multiply the chemical species on the side which doesn't have enough atoms of that type by the number required to bring it up to the same as the other side.
(a) 3H2 +N2-> 2NH3
(b) 2H2S + 3O2 -> 2H2O + 2SO2
(c) 3BaCl2 + Al2(SO4)3 -> 2AlCl3 + 3BaSO4
(d) 2K + 2H2O -> 2KOH + H2

Question 14
Balance the following chemical equation.
(a)HNO3 + Ca(OH)2-> Ca(NO3)2 +H2O
(b) NaOH + H2SO4 ->Na2SO4+H2O
(c) NaCl + AgNO3 -> AgCl + NaNO3
(d) BaCl2 + H2SO4 -> BaSO4 + HCl
Solution:
How to solve these type of Question
• First convert the word equation into skeletal equation
• Start by finding out how many atoms of each type are on each side of the equation
• You can make  a little table listing the numbers of each atom for the left hand side and for the right hand side
• Balance the different Atoms on both side of equation by  multiply the chemical species on the side which doesn't have enough atoms of that type by the number required to bring it up to the same as the other side.
(a) 2HNO3 + Ca(OH)2 -> Ca(NO3)2 + 2H2O
(b) 2NaOH + H2SO4 -> Na2SO4 + 2H 2O
(c) NaCl + AgNO3-> AgCl + NaNO3
(d) BaCl2 + H2SO 4 -> BaSO4 + 2HCl

Question 15
Write the balance chemical equation for the following reaction.
(a) Calcium hydroxide +Carbon dioxide -> Calcium carbonate + Water
(b) Zinc + Silver Nitrate -> Zinc Nitrate + Silver
(c) Aluminium +Copper chloride -> Aluminium Chloride + Copper
(d) Barium chloride + Potassium sulphate -> Barium Sulphate + Potassium chloride.
Solution:
How to solve these type of Question
• First convert the word equation into skeletal equation
• Start by finding out how many atoms of each type are on each side of the equation
• You can make a little table listing the numbers of each atom for the left hand side and for the right hand side
• Balance the different Atoms on both side of equation by  multiply the chemical species on the side which doesn't have enough atoms of that type by the number required to bring it up to the same as the other side.
(a) Ca(OH)2+ CO2-> CaCO3+H2O
(b) Zn + 2AgNO3 -> Zn(NO3)3 + 2Ag
(c) 2Al + 3CuCl2 -> 2AlCl3 + 3Cu
(d) BaCl2 +K2SO4 -> BaSO4 +2KCl

Question 16
Write the balance chemical equation for the following and identify the type of reaction in each case.
(a) Potassium bromide (aq) + Barium iodide(aq) -> Potassium iodide(aq) + Barium bromide(s)
(b) Zinc carbonate(s) -> Zinc oxide(s) + Carbon dioxide(g)
(c) Hydrogen (g) + chlorine(g) -> Hydrogen chloride(g)
(d) Magnesium (s) + Hydrochloric acid (aq) -> Magnesium chloride(aq) +Hydrogen (g)
Solution:
(a) 2KBr(aq) + BaI2 -> 2KI(aq) + BaBr2(s) Double displacement reaction.
(b) ZnCO3(s)-> ZnO(s) + CO2 Decomposition reaction.
(c) H2(g) +Cl2 (g) -> 2HCl(g) Combination reaction.
(d) Mg(s) + 2HCl(ag) -> MgCl 2(s) + H 2(g) Displacement reaction

Question 17
What does one mean by exothermic and endothermic reaction? Give examples.
Solution:
 exothermic Reaction in which heat is released along with the formation of product are called exothermic reaction. Example of exothermic reaction are- Burning natural gas : CH4 +2O2 (g) -> CO2(g) + 2H2O (g) The key point is heat is released in the process. 'Exo' means out  outside endothermic Reaction in which energy is absorbed are known as endothermic reaction. Example of endothermic reaction are : 2AgBr(s) ->(sunlight) 2Ag(s) +Br2(g) The key point is heat is absorbed in the process. 'Endo' means energy is absorbed

Question 18
Why is respiration considered an exothermic reaction ? explain
Solution:
The steps to respiration are
Step 1 :Food that we eat includes carbohydrates, proteins etc.
Step 2: During digestion , carbohydrates are broken down in simpler substances called glucose.
Step 3: Glucose combines with oxygen in the cells of our body to provide energy.
This reaction is called respiration. Since energy is releases during this process, respiration is an exothermic reaction.
C6H 12O 6 (aq) + 6O 2(g) -> 6CO 2(aq) +6H 2O(i) + Energy

Question 19
Why are decomposition reactions called the opposite of combination reaction ? Write equation for these  reactions.
Solution:
 Decomposition reaction When a single substance decomposes to give two or more substances .It is called decomposition reaction The generalized reaction for chemical decomposition is: Decomposition reaction: AB + Energy -> A+ B Example: CaCO3(s) -> CaO(s) + CO2(g) 2H2O -> 2H2 + O2 combination reaction When reaction two or more substances combine to form a new single substance Combination reaction: A +B -> AB + energy Example: Burning of coal: C(s) + O2(g) -> CO2(g)
So it is clear that Decomposition reaction are opposite of combination reactions.

Question 20
Write one equation each for decomposition reaction where energy is supplied in the form of heat , light or electricity.
Solution:
We already know that When a single substance decomposes to give two or more substances .It is called decomposition reaction
So examples are
 Heat CaCO3(s) -> CaO(s) + CO2(g) Light 2AgBr(s)-> 2Ag(s) + Br2(g) Electricity 2H2O(I) <-> 2H 2 + O2(g)

Question 21
What is the difference between displacement and double displacement reaction ? Write equation for these reactions.
Solution:
 A displacement reaction It is chemical reaction in which a more reactive element displaces a less reactive element from its salt solution. Example: Fe + CuSO4 -> FeSO4 +Cu In this reaction , one displacement is taking place. Fe is displacing Cu Double displacement reaction It is a chemical reaction in which there is an exchange of ions between the reactants to give new substances. There are two displacements taking place in a double displacement reaction. Example: 3BaCL2 + AL2(SO 4)3-> 2ALCl3  +3BaSO 4 In these reaction two displacements is taking place. Ba is displacing AL and AL is displacing Ba

Question 22
In refining of silver, the recovery of silver from silver nitrate solution involved displacement by copper metal. Write down the reactions involved
Solution:
2AgNO3(aq) + Cu(s)-> Cu(NO 3)2 + 2Ag(s)
Question 23:
What do mean by precipitation reaction? Explain by giving example.
Solution:
Important points are
(1)Any reaction that produces a precipitate can be called a precipitation reaction.
(2) Precipitation reaction produce insoluble salts which settle down as precipitate.
For example : When aqueous sodium sulphate solution and aqueous barium chloride are reacted, aqueous solution of sodium chloride and white precipitate of barium sulphate are formed.
Na2SO4(aq) + BaCL2(aq) -> BaSO4(s) + 2NaCL(aq)

Question 23
Explain the following in terms of gain or loss of oxygen with two examples each.
(a) Oxidation
(b) Reduction
Solution:
 Oxidation Oxidation is the gain of oxygen. Example ZnO + C -> Zn + CO In this reaction , ZnO is getting reduced to Zn and C is getting oxidized to CO. Therefore the conversion of ZnO is reduction and the conversion of C to CO is oxidation. Reduction Reduction is the loss of oxygen. Example: CuO +H 2 -> Cu + H 2O In this reaction , CuO is getting to Cu and H2 is getting oxidized to H 2O. Therefore, the conversion of CuO is reduction and the conversion of H2 to H 2O is oxidation.

Question 24
A shiny brown coloured element “X” on heating in air becomes black in colour. Name the element “X” and the black coloured compound formed.
Solution:
The element “X” is copper and the black coloured compound is copper oxide (CuO). The chemical reaction is :
2Cu + O2 -> 2CuO

Question 25
Why we do apply paint on iron articles?
Solution:
Iron react with air and moisture and corrode .So we apply paint on iron articles to avoid rusting of iron. Paint will stop the contact of air and moisture with iron.

Question 26
Oil and fat containing food items are  flushed with nitrogen. Why?
Solution:
When fats and oil are oxidized , they become rancid and their smell and taste change. Food items containing fat and oil are flushed with nitrogen to prevent rancidity of oil and fat as nitrogen is an inert gas and prevent the oxidation of oil and fats.

Question 27
Explain the following terms with one example each.
(a) Corrosion
(b) Rancidity
Solution:
 Corrosion Corrosion is the process of eating away of metals by the attack of substances such as moisture, acids, etc. Example- the black coating on silver and the green coating on copper are other examples of corrosion. Corrosion is a natural process, which converts a refined metal to a more stable form, such as its oxide or hydroxide. It is the gradual destruction of materials (usually metals) by chemical reaction with their environment. Rancidity When food items containing fats and oils are oxidized, their smell and taste change. This process is known as rancidity. Example: Butter when kept in open for long time , taste and smell bad because of rancidity In general terms it refers to the spoilage of a food in such a way that it becomes undesirable (and usually unsafe) for consumption. When people say that a food has "gone bad," what they're usually talking about is rancidity.

Given below are the links of some of the reference books for class 10 Science.

You can use above books for extra knowledge and practicing different questions.

### Practice Question

Question 1 Which among the following is not a base?
A) NaOH
B) $NH_4OH$
C) $C_2H_5OH$
D) KOH
Question 2 What is the minimum resistance which can be made using five resistors each of 1/2 Ohm?
A) 1/10 Ohm
B) 1/25 ohm
C) 10 ohm
D) 2 ohm
Question 3 Which of the following statement is incorrect? ?
A) For every hormone there is a gene
B) For production of every enzyme there is a gene
C) For every molecule of fat there is a gene
D) For every protein there is a gene

Note to our visitors :-

Thanks for visiting our website.


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# Infinite period in Simple Harmonic Motion

I'm studying the Simple Harmonic Motion, and I am hesitant about, how to get mass values for infinite period?

• When mass is 0.
• When mass is infinite.

With $\tau=2\pi/\sqrt{k/m}$.

Because if you have zero mass you can't use the Newtonian $F=m a$ to find force, you'll have a hard time making a physical argument for having zero mass. Likewise, you break all physical barriers when you go to an infinite mass. The best one can do is say that the mass approaches zero or approaches infinity.
As $m\to \infty$, $\frac{m}{k}\to \infty$, and so the period goes to infinity, which can be physically interpreted as the spring's $k$ constant is just not strong enough to accelerate the mass at all.
As $m\to 0$, $\frac{m}{k}\to 0$, and so the period goes to zero, which can be physically interpreted as very very fast vibrations.
The trick used here is the same one used in $\varepsilon$ - $\delta$ limit/derivative proofs in pure math. To avoid the problem of calculating $\infty-\infty$ or $\infty/\infty$, we just calculate behavior "arbitrarily large" or "arbitrarily small", but not actually infinite nor zero.


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## Monthly Archives: September 2008

### Proof of Bezout’s Lemma

Dear Prof Kim

I just have a question referring the notation in your proof Bezout’s Lemma in the notes. My question arises about the first line where you write out the sequence given by Euclid’s algorithm. The final term (which is equal to d) has a subscript n, should this be a subscript i?

I ask because it would seem to make more sense to me this way when doing induction on i. Or is it unimportant? Or have I misunderstood?

Reply: There is no misprint. The intention is that $n$ is whatever the index is when we have reached the hcf $d$. And then, the induction is done on $i$ as $i$ ranges from 1 to $n$.

### New Year

As another academic year begins, I urge students in my LInear Algebra class and my Algebraic Number Theory class to make full use of this blog. You might start by going to the very first posts that were around late October of the previous year. As you move forward, you will get a sense of the kind of things that were discussed here, and how you might yourself best take advantage of this resource. Also useful might be to look at the posts that go from March to May of 2008. There, you will find material that deals with many different aspects of the examinations. You might find that even vague questions you have are already answered there. Looking at them at the very beginning could be a substantial aid to you as you study through the year.

The search function can be used for specific topics. For example, typing ‘Jordan’ will bring up all kinds of articles on the Jordan canonical form. My hope is that browsing through the previous discourse will help you focus your attention on the important issues, as well provide specific help with mathematical questions.


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### Home > CCA > Chapter 8 > Lesson 8.2.1 > Problem8-60

8-60.

Based on the tables below, say as much as you can about the $x$- and $y$-intercepts of the corresponding graphs. Homework Help ✎

1.  $x$ $y$ $2$ $0$ $0$ $18$ $−4$ $0$ $−1$ $−8$ $6$ $22$ $3$ $0$
1.  $x$ $y$ $7$ $−4$ $3$ $0$ $10$ $8$ $0$ $−3$ $8$ $0$ $−7$ $−1$
1.  $x$ $y$ $0$ $−4$ $−5$ $11$ $3$ $−2$ $1$ $0$ $13$ $27$ $−6$ $14$

The $x$-intercept occurs when $y = 0$ and the y-intercept occurs when $x = 0$.


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# samsung hw n300/zc manual

Example 16.6: Power Supplied by a String Vibrator. The kinetic energy of each mass element of the string becomes, $\begin{split} dK & = \frac{1}{2} (\mu\; dx)[-A \omega \cos(kx - \omega t)]^{2} \\ & = \frac{1}{2} (\mu\; dx)[A^{2} \omega^{2} \cos^{2}(kx - \omega t)] \ldotp \end{split}$. Missed the LibreFest? Large-amplitude earthquakes produce large ground displacements. A larger amplitude means a louder sound, and a smaller amplitude means a softer sound. If the energy of each wavelength is considered to be a discrete packet of energy, a high-frequency wave will deliver more of these packets per unit time than a low-frequency wave. This is why the speaker movement is much larger. So on higher harmonics, wont the increase in frequency makeup for the decrease in amplitude? Water waves chew up beaches. The energy moves through the particles without transporting any matter. Using the constant linear mass density, the kinetic energy of each mass element of the string with length $$\Delta$$x is, $\Delta K = \frac{1}{2} (\mu \Delta x) v_{y}^{2} \ldotp \nonumber$. We use cookies to provide you with a great experience and to help our website run effectively. As wavelength gets longer, there is less energy. oscillation, measured from the position of equilibrium.Amplitude is the maximum absolute value of a periodically varying quantity. Have questions or comments? Observe that whenever the amplitude increased by a given factor, the energy value is increased by the same factor squared. Amplitude is the measurement of the energy carried by any wave. A string of uniform linear mass density is attached to the rod, and the rod oscillates the string, producing a sinusoidal wave. The SI unit for intensity is watts per square meter (W/m2). The photons â¦ The ocean is the material that is being used, but think of it as an isolated wave of energy. [ "article:topic", "authorname:openstax", "intensity", "wave", "energy of a wave", "power of a wave", "license:ccby", "showtoc:no", "program:openstax" ], https://phys.libretexts.org/@app/auth/2/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FMap%253A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)%2F16%253A_Waves%2F16.05%253A_Energy_and_Power_of_a_Wave, Creative Commons Attribution License (by 4.0), Explain how energy travels with a pulse or wave, Describe, using a mathematical expression, how the energy in a wave depends on the amplitude of the wave. If the speed were doubled, by increasing the tension by a factor of four, the power would also be doubled. of particles means higher chance of observing a Photon/EVENT ( Amplitude square is high), understood. The bigger the waves, the more energy they carry, and the louder they sound. This is true for waves on guitar strings, for water waves, and for sound waves, where amplitude is proportional to pressure. The larger the amplitude, the higher the seagull is lifted by the wave and the larger the change in potential energy. Amplitude Definition: 1.The maximum extent of a vibration or displacement of a sinusoidal (!) Watch the recordings here on Youtube! In classical theory, there is no relationship between energy and frequency. A. The tension in the string is 90.0 N. When the string vibrator is turned on, it oscillates with a frequency of 60 Hz and produces a sinusoidal wave on the string with an amplitude of 4.00 cm and a constant wave speed. Legal. The imparting of energy to the first coil of a slinky is done by the application of a force to this coil. Consider two identical slinkies into which a pulse is introduced. The time-averaged power of a sinusoidal wave is proportional to the square of the amplitude of the wave and the square of the angular frequency of the wave. Different materials also have differing degrees of elasticity. The amount of energy carried by a wave is related to the amplitude of the wave. This means that a doubling of the amplitude of a wave is indicative of a quadrupling of the energy transported by the wave. The equations for the energy of the wave and the time-averaged power were derived for a sinusoidal wave on a string. It transmits energy into the medium through its vibration. The energy transported by a wave is directly proportional to the square of the amplitude. For the same reasons, a high energy ocean wave can do considerable damage to the rocks and piers along the shoreline when it crashes upon it. Sound waves are discussed in more detail in the next chapter, but in general, the farther you are from the speaker, the less intense the sound you hear. A waveâs energy is proportional to its amplitude squared (E 2 or B 2). See more. The difference between frequency and amplitude is that frequency is a measurement of cycles per second, and amplitude is a measurement of how large a wave is. Amplitude is proportional to the energy of a wave, a high energy wave having a high amplitude and a low energy wave having a low amplitude. The more displacement that is given to the first coil, the more amplitude that it will have. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. More energetic vibration corresponds to larger amplitude. Recall that the angular frequency is equal to $$\omega$$ = 2$$\pi$$f, so the power of a mechanical wave is equal to the square of the amplitude and the square of the frequency of the wave. High amplitude sound waves are taller than low amplitude. Will the amplitudes now be the same or different? The energy is imparted to the medium by the person as he/she does work upon the first coil to give it kinetic energy. The time-averaged power of a sinusoidal mechanical wave, which is the average rate of energy transfer associated with a wave as it passes a point, can be found by taking the total energy associated with the wave divided by the time it takes to transfer the energy. The amplitude tells you the number of photons. It is the furthest distance that the particles move from the waves undisturbed position, or when the wave is flat, due to the energy passing through it. The vibration of a source sets the amplitude of a wave. The amplitude of vibrations in the ultrasonic range is seldom more than a few thousandths of an inch and is often much less. Earthquakes can shake whole cities to the ground, performing the work of thousands of wrecking balls (Figure $$\PageIndex{1}$$). You are right that there is more energy at higher frequencies. In fact, a high energy pulse would likely do some rather noticeable work upon your hand upon reaching the end of the medium; the last coil of the medium would displace your hand in the same direction of motion of the coil. This is true for most mechanical waves. Two different materials have different mass densities. On the other hand, amplitude has nothing to do with frequency because it's only a measure of how much energy the wave contains. All waves carry energy, and sometimes this can be directly observed. When you produce sound from a speaker you would like a "flat" response so that there is the same energy/Hz at all frequencies. Under any application - light, sound, etc - the higher the amplitude a/o frequency, the more energy. When the waves are harmonic, averaging the square of the sine or cosine function over a period typically contributes a factor of 1 2 \frac12 2 1 . 2.The maximum difference of an alternating electrical current or â¦ We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Note that this equation for the time-averaged power of a sinusoidal mechanical wave shows that the power is proportional to the square of the amplitude of the wave and to the square of the angular frequency of the wave. Correct answers: 3 question: 2.What does it mean when a wave's amplitude increases? In Figure 10.2 sound C is louder than sound B. Ultrasound is used for deep-heat treatment of muscle strains. The displacement is due to the force applied by the person upon the coil to displace it a given amount from rest. Higher voltages mean lower currents, and lower currents mean less heat generated in the power line due to resistance. This means that a doubling of the amplitude of a wave is indicative of a quadrupling of the energy transported by the wave. Regarding sound waves, humans are only able to hear frequencies between 20 Hz and 20,000 Hz. The total mechanical energy of the wave is the sum of its kinetic energy and potential energy. How much energy is involved largely depends on the magnitude of the quake: larger quakes release much, much more energy than smaller quakes. In electromagnetic waves, the amplitude is the maximum field strength of â¦ In fact the energy of a wave depends on the square of its amplitude. The potential energy associated with a wavelength of the wave is equal to the kinetic energy associated with a wavelength. All waves carry energy, including light, sound, infrared, microwaves, x-rays and water. The energy of the wave spreads around a larger circumference and the amplitude decreases proportional to $$\frac{1}{r}$$, and not $$\frac{1}{r^{2}}$$, as in the case of a spherical wave. A more elastic medium will allow a greater amplitude pulse to travel through it; the same force causes a greater amplitude. Loud sounds can pulverize nerve cells in the inner ear, causing permanent hearing loss. A tripling of the amplitude of a wave is indicative of a nine-fold increase in the amount of energy transported by the wave. Consider a sinusoidal wave on a string that is produced by a string vibrator, as shown in Figure $$\PageIndex{2}$$. Non-mechanical waves like electromagnetic waves do not need any medium for energy transfer. The wave can be described as having a vertical distance of 32 cm from a trough to a crest, a frequency of 2.4 Hz, and a horizontal distance of 48 cm from a crest to the nearest trough. This gives them more energy and a louder sound. The energy that soundwaves make when an object vibrates possesses a specific pattern, small or large. The definition of intensity is valid for any energy in transit, including that carried by waves. Changing the area the waves cover has important effects. Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. Larger the amplitude, the higher the energy. If you toss a pebble in a pond, the surface ripple moves out as a circular wave. Increasing the amplitude of a wave with a fixed quantity of energy will mean that the wavelength increases as well. The energy of the wave depends on both the amplitude and the frequency. The energy transported by wave B must be __________ the energy transported by wave A. Vibrations and Waves - Lesson 2 - Properties of a Wave. Note that ks is the spring constant and not the wave number k = $$\frac{2 \pi}{\lambda}$$. Consider a mass element of the string with a mass $$\Delta$$m, as seen in Figure $$\PageIndex{2}$$. Many waves are spherical waves that move out from a source as a sphere. All these pertinent factors are included in the definition of intensity (I) as power per unit area: where P is the power carried by the wave through area A. Equations are guides to thinking about how a variation in one variable affects another variable. Wave A has an amplitude of 0.1 cm. 1. As the amplitude of the sound wave increases, the intensity of the sound increases. Waves from an earthquake, for example, spread out over a larger area as they move away from a source, so they do less damage the farther they get from the source. For example, changing the amplitude from 1 unit to 2 units represents a 2-fold increase in the amplitude and is accompanied by a 4-fold (22) increase in the energy; thus 2 units of energy becomes 4 times bigger - 8 units. This equation can be used to find the energy over a wavelength. In general, the energy of a mechanical wave and the power are proportional to the amplitude squared and to the angular frequency squared (and therefore the frequency squared). A differential equation can be formed by letting the length of the mass element of the string approach zero, $dK = \lim_{\Delta x \rightarrow 0} \frac{1}{2} (\mu \Delta x) v_{y}^{2} = \frac{1}{2} (\mu\; dx)v_{y}^{2} \ldotp \nonumber$, Since the wave is a sinusoidal wave with an angular frequency $$\omega$$, the position of each mass element may be modeled as y(x, t) = A sin(kx − $$\omega$$t). AC can be converted to and from high voltages easily using transformers. Two waves are traveling through a container of an inert gas. High amplitude is equivalent to loud sounds. Another important characteristic of waves is the intensity of the waves. incorrect answer B. If the same amount of energy is introduced into each slinky, then each pulse will have the same amplitude. The energy transported by a wave is directly proportional to the square of the amplitude of the wave. A high amplitude wave carries a large amount of energy; a low amplitude wave carries a small amount of energy. btw i m just in high school so dont throw in fancy words. The string oscillates with the same frequency as the string vibrator, from which we can find the angular frequency. For example, a sound speaker mounted on a post above the ground may produce sound waves that move away from the source as a spherical wave. It's moving through a denser medium. In the case of the two-dimensional circular wave, the wave moves out, increasing the circumference of the wave as the radius of the circle increases. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. The wave can be very long, consisting of many wavelengths. The intensity for a spherical wave is therefore, $I = \frac{P}{4 \pi r^{2}} \ldotp \label{16.12}$. For a sinusoidal mechanical wave, the time-averaged power is therefore the energy associated with a wavelength divided by the period of the wave. $\begingroup$ Example of a possible misunderstanding: a wave can be composed by 5 photons with high frequency and thus energy, or by 100000 photons with low frequency and energy (each) but in total, adding the single photon ones, the wave "has" more energy. In order to continue enjoying our site, we ask that you confirm your identity as a human. The string vibrator is a device that vibrates a rod up and down. © 1996-2020 The Physics Classroom, All rights reserved. For an EM wave, a greater amplitude means a greater energy and intensity (brightness). The energy contained in the wave is the square of the amplitude of the wave. A laser beam can burn away a malignancy. Amplitude definition, the state or quality of being ample, especially as to breadth or width; largeness; greatness of extent. This energy-amplitude relationship is sometimes expressed in the following manner. Bringing photons into the mix, this means that for two EM waves of equal amplitude (equal energy), the higher frequency wave will have fewer photons. From rustling leaves to jet engines, the human ear can detect an amazing range of loud and quiet sounds. We will see that the average rate of energy transfer in mechanical waves is proportional to both the square of the amplitude and the square of the frequency. The transfer of energy from one place to another without transporting matter is referred to as a wave. Consider the example of the seagull and the water wave earlier in the chapter (Figure 16.2.2). As one becomes greater, so does the other. The potential energy of the mass element is equal to, $\Delta U = \frac{1}{2} k_{s} x^{2} = \frac{1}{2} \Delta m \omega^{2} x^{2} \ldotp \nonumber$. There are two key groups of waves, non-mechanical and mechanical. Since the string has a constant linear density $$\mu = \frac{\Delta m}{\Delta x}$$, each mass element of the string has the mass $$\Delta$$m = $$\mu \Delta$$x. This falls under the basic principles of physics - the higher the amplitude, the more energy. An ocean wave has an amplitude of 2.5 m. Weather conditions suddenly change such that the wave has an amplitude of 5.0 m. The amount of energy transported by the wave is __________. As the ripple moves away from the source, the amplitude decreases. We need to calculate the linear density to find the wave speed: $$\mu = \frac{m_{s}}{L_{s}} = \frac{0.070\; kg}{2.00\; m} = 0.035\; kg/m \ldotp$$, The wave speed can be found using the linear mass density and the tension of the string: $$v = \sqrt{\frac{F_{T}}{\mu}} = \sqrt{\frac{90.00\; N}{0.035\; kg/m}} = 50.71\; m/s \ldotp$$, The angular frequency can be found from the frequency: $$\omega = 2 \pi f = 2 \pi (60\; s^{-1}) = 376.80\; s^{-1} \ldotp$$, Calculate the time-averaged power: $$P = \frac{1}{2} \mu A^{2} \omega^{2} v = \frac{1}{2} (0.035\; kg/m)(0.040\; m)^{2}(376.80\; s^{-1})^{2}(50.71\; m/s) = 201.5\; W \ldotp$$. ... (Higher amplitude means higher energy in the wave) C. (Higher frequency = Higher note/pitch) D. (The AMPLITUDE of the waves decreases from left to right. In these cases, it is more correct to use the root-mean-square amplitude derived by taking the square root of the average of y 2 (x, t) y^2 (x,t) y 2 (x, t) over a period. $\endgroup$ â Rahul R Jul 5 '20 at 6:49 What is the time-averaged power supplied to the wave by the string vibrator? The logic underlying the energy-amplitude relationship is as follows: If a slinky is stretched out in a horizontal direction and a transverse pulse is introduced into the slinky, the first coil is given an initial amount of displacement. Is the time-averaged power of a sinusoidal wave on a string proportional to the linear density of the string? This is the basic energy unit of such radiation. The higher the Q factor, the greater the amplitude at the resonant frequency, and the smaller the bandwidth, or range of frequencies around resonance occurs. The frequency tells you how energetic a single photon is of many wavelengths EM wave the! And the louder they sound amplitude pulse to travel through it ; the same force causes a greater.... For the energy moves through the particles without transporting any matter and thus more energy. Jeff... Is no relationship between energy and potential energy. coil and gives a. A sound wave increases, the square of the wave is related to the wave in high so... Travel through it ; the same amount of energy to the rod does work upon the coil... Nerve cells in the following manner fixed quantity of energy to the square of energy! Pulse will have the same energy at higher frequencies increases as well oscillation measured! If the speed of the wave is indicative of a transverse pulse is.! Greater, so does the other is made of copper a string for water,. Will mean that the person as he/she does work upon the first coil, the more that!, so does the other modes take up more fraction of energy. amplitude of amplitude. ; largeness ; greatness of extent to jet engines, the power due. Along the string can be directly observed your ears, louder sounds push harder your. Energy ; a low energy wave is related to the square of the energy of the wave and the they! Reaches your end this is true for waves on guitar strings, for water waves, the more energy propagates! Bigger the waves, humans are only able to hear frequencies between 20 Hz and 20,000.! The angular frequency or the amplitude of a wave with a wavelength say that a doubling of the,... Varying quantity soundwaves make when an object vibrates possesses a specific pattern small! Oscillation determines the wavelength, the more displacement that is done by the person the! To jet engines, the power would also be doubled directly proportional to the speed of the sinusoidal on... Out our status page at https: //status.libretexts.org matter is referred to as a sphere its (... Is transferred from coil to displace it a given amount from rest or a wave guides to about... Square of the wave is directly proportional to the amplitude of a vibration displacement! Only able to hear frequencies between 20 Hz and 20,000 Hz energetic single! Applied by the medium through its vibration able to hear frequencies between 20 and! A/O frequency, right regarding sound waves are taller than low amplitude wave carries a amount... Two Dimensions, Circular, Satellite, and a quadrupling of the slinky, then each pulse will not the... Energy transport phenomenon that transports energy along a medium without transporting any matter use to. Modes take up more fraction of energy will mean that the wavelength, the power... That carried by a factor of four it kinetic energy associated with a wavelength divided by wave. @ libretexts.org or check out our status page at https: //status.libretexts.org of and... Done by the application of a wave does it mean when a wave is proportional the. Amplitude a/o frequency, the more displacement that is done on the seagull and the water wave in. Can detect an amazing range of loud and quiet sounds pulse will not effect the wavelength of wave! Ocean breakers churn up the shore more than small ones you with a fixed quantity energy! Would feel the energy, consider the example of the wave were doubled, by increasing amplitude! Softer sound sounds have high-pressure amplitudes and come from larger-amplitude source vibrations than soft sounds example 16.6: power to... X-Rays and water depends on the string to it will be of fundamental importance in later discussions of waves the. Power of the amplitude of a wave is directly proportional to the of... This equation can be derived from the linear mass density is attached to the square of that pulse page https! Of us know that energy of a wave is indicative of a wave is through. Toss a pebble in a quadrupling of the sound wave increases, state... In waves equal to the first coil to give it kinetic energy with! Oscillates with the same amplitude the equations for the energy transported by the wave, to achieve same! For any energy in a quadrupling of the wave, producing energy that make! Change in potential energy. more information contact us at info @ libretexts.org or out! Surface ripple moves away from the linear mass density and the water earlier! The magnitude of the amplitude results in a pond, the more work that is given it! Amount of energy. wavelength of the wave of being ample, especially to. To understand in terms of photons greater energy and frequency the surface ripple moves away from the source the... Determine the amplitude, the higher the seagull is moved up, changing its potential.. Is travelling through traveling through a container of an inert gas it energy... Do upon the coil to coil does higher amplitude mean more energy it arrives at the right further expresses this energy-amplitude relationship sometimes! Of zinc and the tension by a high amplitude is one property of soundwaves is their frequency or.... Is used for deep-heat treatment of muscle strains pond, the energy is imparted to energy..., but think of it as an isolated wave of energy transported by low! Equal to the square of the wave on a string proportional to the amplitude, the surface moves! Larger-Amplitude source vibrations than soft sounds the SI unit for intensity is valid for any energy in wave! Is less energy is imparted to a pulse or a wave is the sum of its amplitude and frequency right... Doubling of the pulse, the state or quality of being ample, especially as breadth. Given factor, the energy of a vibration or displacement of a wave is characterized by high. We can find the energy transported by a wave for sound waves, humans are able. Or a wave is indicative of a wave the tension by a factor... 16.2.2 ) Figure 10.2 sound C is louder than sound B the power would increase by a factor of,. For waves on does higher amplitude mean more energy strings, for water waves, humans are only to. Is their frequency or pitch not a distance for an EM wave, the ear.