3-dimensional atomic structure model with magnetically attached sub-atomic particle models

Abstract

The invention comprises an atomic structure kit for enabling students to understand how atoms are made of smaller sub-atomic particles, the architecture of these particles in relation to each other, and the forces acting upon the sub-atomic particles that hold an atom together. The kit comprises a central body representing an atomic nucleus attached to a shaft about which concentric circular or elliptical rings are rotatably attached. A plurality of bodies representing protons and neutrons is magnetically attachable to the atomic nucleus, and a plurality of bodies representing electrons is magnetically attachable to the rotatable rings. The properties and geometry of the magnetic materials mimic the strong localised force relationships between sub-atomic particles, specifically the electron-electron, proton-proton repulsion, the electron-nucleus attraction and the very strong attraction between the nucleons that bind the nucleus.

Claims

1. A 3-dimensional model for representing the structure of an atom, the model comprising: a shaft or filament; a central magnetic body connected to the shaft or filament; a plurality of bodies magnetically attachable to the central magnetic body to represent an atomic nucleus, each body representing a proton and/or a neutron; a plurality of concentric rings centres of which substantially coincide with the location of the central magnetic body, the rings connected to the shaft or filament such that the rings can substantially freely rotate around an axis of the shaft or filament; and a plurality of bodies representing electrons magnetically attachable to the rings.

2. A kit for a 3-dimensional model for representing the structure of an atom, the kit comprising: a shaft or filament; a body comprising a central magnetic body connected to the shaft or filament; and a plurality of concentric rings centres of which substantially coincide with the location of the central magnetic body, the rings connected to the shaft or filament such that the rings can substantially freely rotate around an axis of the shaft or filament; a plurality of bodies magnetically attachable to the central magnetic body to represent an atomic nucleus, each spherical body representing a proton and/or a neutron; a plurality of bodies representing electrons magnetically attachable to the rings.

3. The model of claim 1, wherein the shaft or filament is a shaft.

4. The model claim 3, wherein the central body is substantially centrally attached to the shaft.

5. The model of claim 1, wherein the shaft or filament is a filament.

6. The model of claim 5, wherein the central body is attached at or towards an end of the filament.

7. The model of claim 1, wherein each spherical body attachable to the central body represents a proton or a neutron.

8. The model of claim 1, wherein the bodies representing electrons make polar repulsions against each other.

9. The model of claim 1, wherein the bodies representing protons make polar repulsions against each other.

10. The model of claim 1, wherein the bodies representing protons make polar attractions to the bodies representing electrons.

11. The model of claim 1, wherein the bodies representing protons make polar attractions to the central body.

12. The model of claim 1, wherein the respective bodies representing the protons, the neutrons, and the electrons are spheroid bodies.

13. The model of claim 3, wherein movable mounting of the shaft allows for rotation of the rings about two perpendicular axes.

14. The model of claim 13, wherein the shaft is movably mounted to a circular rail at mounting positions at or towards first and second ends of the shaft.

15. The model of claim 14, wherein the substantially circular rail is in a horizontal plane.

16. The model of claim 14, wherein the substantially circular rail is in a vertical plane.

17. The model of claim 1, when used for teaching atomic structure.

18. A method of assembling a model for representing the structure of an atom, including steps of: a) connecting a central magnetic body to a shaft or filament; b) connecting a plurality of concentric rings with the shaft or filament such that centres of the rings substantially coincide with the location of the central body, and the rings can substantially freely rotate around an axis of the shaft or filament; c) magnetically attaching a plurality of bodies to the central body, each of the plurality of bodies representing a proton and/or a neutron; and d) magnetically attaching a plurality of bodies representing electrons to the rings.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0021] FIG. 1 is a side view that shows an overall schema of an embodiment of an atomic structure model according to the invention, showing a supporting frame which holds a horizontal shaft, which in turn holds a central nucleus body and rotatable rings to which electron models are attached.

[0022] FIG. 2 shows another embodiment of an atomic structure model according to the invention. The FIG. 2 embodiment is similar to the FIG. 1 embodiment. However, the means of magnetic attachment between electron models and rings, and between nucleon models and nucleus model are reversed. This is explained in more detail in the description of embodiments section.

[0023] FIG. 3 shows a side view of another embodiment of an atomic structure model according to the invention, in which the rings are rotatable in a similar fashion as a hanging “mobile”, using vertical filaments instead of a rigid shaft. However, the method of attachment of nucleons and electron models use localized magnetic forces rather than contact forces or gravity. This embodiment can allow for improved portability of the model.

[0024] FIG. 4 shows a side view of another embodiment of an atomic structure model according to the invention, in which the holding shaft is supported by vertical posts rather than the frame.

[0025] FIG. 5 shows a side view of another embodiment of an atomic structure model according to the invention, in which the holding shaft is held vertically by being embedded into a hole in the model base. This design avoids the necessity of holding the frame by posts or a frame.

[0026] FIG. 6 shows a side view of another embodiment of an atomic structure model according to the invention, in which the rings are able to rotate around two perpendicular axes. This is achieved by mounting the holding shaft onto a circular rail mounted in a horizontal plane, whereas the rings can rotate about the axis of the shaft.

[0027] FIG. 7 shows a side view another embodiment of an atomic structure model according to the invention. The FIG. 7 embodiment is similar to the FIG. 6 embodiment, however the two perpendicular axes of the FIG. 7 embodiment are perpendicular to those of the FIG. 6 embodiment. In the FIG. 7 embodiment, the rail is oriented in a vertical plane and mounted directly onto the model base. This means that the rail and shaft do not require posts or a frame for support.

[0028] FIG. 8 shows an example of a “dispersed magnet” in which the magnetic field strength is more or less uniform with distance from the magnet, except at the edges where they converge to some extent. This shows the magnetic field pattern for a flat “fridge-magnet” type.

[0029] FIGS. 9, 10 and 11 show side and perspective drawings of three examples of “localized magnets”, in which the magnetic field strength varies significantly with distance from the magnet. This means that the magnetic field line separations also vary significantly. These magnetic line patterns are used as attachment means for embodiments of the atomic structure model according to the invention, to achieve more realistic representation of electric or nuclear forces within atoms.

[0030] FIGS. 12, 13 and 15 show side drawings of electron models of embodiments of the atomic structure model according to the invention in which a localized magnet is embedded into a cavity.

[0031] FIG. 14 shows an electron model in which it is friction-attached by a slot cut into the model.

[0032] FIGS. 16, 17, 18 and 19 show nucleon models of embodiments of the atomic structure model according to the invention. FIGS. 16 and 17 show proton models with embedded magnets, facilitating polar attractions and repulsions. FIG. 18 shows a proton model without an embedded magnet. FIG. 19 shows a neutron model without an embedded magnet.

[0033] FIGS. 20, 21, 22, 23 and 24 show various arrangements of central magnetic bodies of embodiments of the atomic structure model according to the invention, comprising magnet(s) 96 and platform or band 94, wherein proton and neutron models are attached to platform or band 94.

[0034] FIG. 25 shows an arrangement of proton and neutron models attached to a central magnetic body of an embodiment of the atomic structure model according to the invention, wherein the proton models comprise embedded magnets.

DESCRIPTION OF EMBODIMENTS

[0035] Definition of Terms: The term “magnetic material” refers to a substance that is attracted to a magnet, or responds to an external magnetic field. A magnetic material is not itself necessarily a permanent magnet. Such materials include but are not limited to iron, nickel, cobalt, niobium and a few rare earth materials and their alloys.

[0036] The term “magnet” is a magnetic substance that has been magnetized to becomes a source of a permanent magnetic field. These include the above substance that have undergone a magnetizing process that aligns their magnetic domains. A magnet will attract another magnet according to the polarity rules: unlike poles attract; like poles repel. They will also attract a magnetic material such as iron by magnetic induction. They will also align to an external magnetic field if free to do so.

[0037] The term “localized magnet” refers to a magnet in which the North pole and South poles are positioned to produce a magnetic field whose field lines radiate in or out from the magnet at significant angles. For example, a horseshoe-shaped, or rod-shaped magnet, or a ball magnet will produce field lines that emanate away from the north pole in a radial fashion, and into the south pole in a radial fashion. The concentration of field lines, that is, the strength of the magnetic fields, are concentrated at the poles. The poles are regions that have stronger magnetic field strengths than at other points. Magnetic force interactions with magnetic materials will be stronger in the regions where the field lines are concentrated.

[0038] The term “dispersed magnet” refers to a magnet in which the magnetic field lines are uniform. For example, a magnetic film with poles on either side will produce magnetic field lines that emanate as parallel lines away from the north side, and as parallel lines into the south side. The magnetic lines do not congregate to concentrate regions of high magnetic field strength across the surface of the film. That is, one point on the surface of the film has the same magnetic strength as another.

[0039] Provided according to an aspect of the invention is an atomic structure model. Typically, the atomic structure model comprises a plurality of circular orbital rings comprising a magnetic material such as iron or steel, supported by a rigid shaft to which the rings are coupled, so that the rings can rotate freely about the shaft. Typically, the plurality of orbital rings surround a platform or similar containing a magnet-embedded localized nucleus. Exemplary embodiments of the nucleus arrangement are shown in FIGS. 20 to 25.

[0040] Electron models with embedded localized magnets (see, for example, FIGS. 12, 13 and 15), are magnetically attracted to, and can attach to, the magnetic rings. Magnetic nuclear models comprising magnetic material such as iron or steel are magnetically attracted to, and can attach to, the localized magnet-nucleus model (see, for example, FIGS. 20 to 25). The electron models are also embedded with small magnets so that they can attach to a magnetic material such as a steel wire circle representing the electron orbit. The directionality of the magnetic force to the orbital region is an approximate and useful analogue to the probability distribution of electrons within its orbital.

[0041] In some embodiments of the atomic structure model the magnetic material and magnets are reversed e.g. the orbital rings comprising the magnet with the electron models comprising of the magnetic material; and/or the nuclear models comprising the magnetic material and the nucleon models comprising of the magnets.

[0042] The localized magnets embedded into the electron models are arranged so that the same pole protrudes from the model, whereas the opposite pole is embedded so that the magnetic field strength is masked. This allows a net repulsive force to be exerted between any two electron models.

[0043] FIG. 1 shows an embodiment of an atomic structure model according to the invention in which the electron orbital rings 14 are constructed of magnetic material such as iron, and are supported by a horizontal rigid shaft 18 about which rings 14 can rotate. Each ring can rotate independently of each other ring. The rings 14 are attached to couplings [[6]] 20 that thread onto the horizontal shaft 18 so that the rings can rotate about the shaft. The shaft 18 is supported by a U-shaped frame 22 screwed onto a base 24. The nucleus model 10 comprises a localized magnet, such as a strong neodymium rare earth magnet, within it so that it can attract nucleon models 12 which are made of magnetic material such as iron.

[0044] FIG. 2 shows an embodiment of an atomic structure model according to the invention. The FIG. 2 embodiment has similar structure as the FIG. 1 embodiment. However, in the FIG. 2 embodiment, the electron models 36 are made of magnetic material such as iron, whereas the orbital rings 34 are localized magnets. So instead of the electron models possessing a permanent magnetic field and creating the attraction to the rings as in the FIG. 1 embodiment, the rings of the FIG. 2 embodiment instead possess the permanent magnetic field and create the attraction to the electron models. A similar reversal occurs with the nucleons 32, which in the case of the FIG. 2 embodiment are localized magnets, and the nucleus model 30 is made of the magnetic material. The skilled person will readily appreciate that any suitable combination of magnet-magnetic material can be used to create electron ring and nucleon-nucleus attractions, and this principle applies to all subsequent embodiments.

[0045] FIG. 3 shows a side view of a mobile-type suspended embodiment of an atomic structure model according to the invention. In the FIG. 3 embodiment, orbital rings 14 rotate about a filament or thread 38 suspended from an upper point on a frame 23. Each ring can rotate independently of each other ring. The frame is screwed onto the base 24 at points 26.

[0046] FIG. 4 shows a side view of another embodiment of an atomic structure model according to the invention in which the shaft 18 is supported by two posts 40 which are embedded into the base 24.

[0047] FIG. 5 shows a side view of a preferred embodiment of an atomic structure model according to the invention, in which a vertical rigid shaft 18 is embedded into and supported by the base 24 at point 44. The orbital rings 14 are attached to the shaft by couplings or eyelets 20 that allow the rings to rotate. This embodiment avoids the need for a supporting frame.

[0048] FIG. 6 shows a perspective-side view of another embodiment of an atomic structure model according to the invention. The FIG. 6 embodiment allows the orbital rings to rotate around two perpendicular axes. The orbital rings can rotate about the shaft 18, and the shaft can further independently rotate around the circular rail tracks, with bearings 52 located at each end of the shaft. This embodiment allows the electron to orbit around the nucleus in multiple dimensions, not confined to a planar circular pathway. A circular rail 50 is supported by posts 40 at points 54 and embedded into the base 24.

[0049] FIG. 7 shows a perspective-side view of another embodiment of an atomic structure model according to the invention. As for the FIG. 6 embodiment, the FIG. 7 embodiment allows the orbital rings to rotate around two perpendicular axes, although in a different orientation to that of the FIG. 6 embodiment. This advanced version also allows the electron to orbit around the nucleus in multiple dimensions, not confined to a planar circular pathway. A circular rail 50 is rigidly attached to the base 24 at point 56. The rail has a track that supports the rigid shaft 18, which in turn supports the orbital rings 14.

[0050] FIG. 8 shows a perspective-side view of a flat sheet magnet, or “dispersed magnet” similar to a “fridge magnet”. The North and South poles are on either side of the magnet, and the magnetic field lines are generally uniform above and below the magnet surfaces. The magnet field strengths do not vary considerably along at various points located along the magnet surface, except at the edges. Further, the extended lateral shape of the flat magnetic strip means that the region of uniformity is relatively extended as well. The magnetic attractions are very similar at all points of contact between the magnet sheet and a magnetic material, such as a white board.

[0051] FIGS. 9, 10 and 11 show[[s]] side views of 3 examples of localized magnets. [[A]] FIG. 9 represents a bar magnet, [[B]] FIG. 10 represents a horseshoe magnet, and [[C]] FIG. 11 represents a spherical magnet. In each case, the magnetic field lines are convergent or divergent; that is, they are nonuniform. The magnetic force strengths of attraction vary considerably depending on where the magnets are located, and where the magnetic material are attached. For example, when a nucleon model made of a ball of iron is brought close to one end of a bar magnet, the magnetic attraction between the localized magnet and the iron ball increases exponentially as a function of the separation distance, and is directionally oriented towards the magnet. The iron ball will attach to a localized position of the magnet, rather than uniformly to the general region of the nucleus. Similarly, the electron model attracted will be directionally oriented towards the orbital ring, rather than being broadly attracted to the general region of the ring.

[0052] FIGS. 12 to 15 show side views of embodiments of electron models. In FIG. 12, the localized magnet 72 is embedded into the body of the electron model 70, housed within a cavity 74. In this embodiment, the North pole protrudes outside the body of the electron model, while the South pole is masked within the body of the electron model. Other variations are shown in FIGS. 13 and 15. FIG. 14 shows an electron model which is friction-attached by means of a slot, 76.

[0053] Certain advantages of at least typical embodiments of the atomic structure model according to the invention will now be described.

[0054] The present atomic structure model addresses shape problems: The current 3-D invention (along with certain existing 3-D mobile type models) has a compelling advantage over 2-D flat models, whether or not the latter employ either flat dispersed magnet films attached to a flat surface like a whiteboard, or non-magnetic spherical shapes to represent subatomic particles. Any 2-D representation of an atoms is problematic. 3-dimensionality is also important because students find it difficult to reconcile this ‘skeletal’ model of an atom comprised only of its internal sub-atomic particles being visible, with the 3-dimensional models of atoms in which only the ‘surface’ of the atom is visible, as in a solid ball. Normally the student learning progression moves from a ‘solid’ to the ‘skeletal’ model of an atom. Because this progression is a key step, it is useful to make these two versions as similar as possible. In other words, to shift from a 3-D solid ball model to a 2-D sub-atomic model is changing too many variables in a single shift; not withstanding that the 2-D model is also conceptually inaccurate. It is pedagogically preferable for students to compare a 3-D solid ball version with a 3-D sub-atomic skeletal version, so that the only difference is in the visibility of the atom's internal structure. If the dimensionality of the model also changes (from 3-D back to 2D), this adds an unnecessary confusion to the students' understanding. The use of localized magnets, as described herein with reference to FIGS. 8 and 9, also allows for 3-D sphericity in the shape of the sub-atomic particles which, like the atom overall are also spherical. The double-axis embodiments of the present 3-D invention, as shown in FIGS. 6 and 7, are also superior to existing 3-D mobile models in terms of representing electron motion around the nucleus. Whereas existing 3-D mobile models restricts the rotation of the electron orbitals to one axis of rotation—that of the filament—the present 3-D model allows for rotation about two perpendicular axes, which means that the motion of the electron model about the nucleus can be expanded to 3 dimensions, which is a more realistic representation of how real electrons orbit about the nuclei.

[0055] The present atomic structure model addresses force-directionality problems: The force directionality problem with the 2-D flat magnet film type model has been discussed above, in which the flat dispersed magnets whose surfaces attach with uniform force as they are shifted sideways across the white board surface, display no preferential force of attachment to the nucleus region in the case of the nucleons, or to the orbital rings in the case of the electron models. Existing 3-D mobile type models also suffer directionality problems, as the sub-atomic particle models need to be shifted into place, and attached to a sticky substance, then by an external pressing force applied by the user. In other words, there is no inherent force directionality at all without guidance from the user. Indeed, the 3-D mobile type model implies not internal atomic forces-at-a-distance at all. Real atomic nuclei employ a highly localized strong nuclear force to bind the nucleons together, or a nucleon to the existing nucleus, in which the nuclear attractive force is highly directed between two points—the nucleon and the nucleus. A similar force directionality to real atoms is achieved with the present invention because a localized magnet, in which a magnetic material in the geometry of a point, or confined sphere, is attracted to another point, the nucleus-magnet. The present invention also addresses the directionality problem for the electron models, as the localized electron model is specifically attracted to, and attaches to, the magnetic orbital rings. It also addresses the 3-D mobile model type problem, as the magnetic attractions spontaneously attract, and cause attachment, of the sub-atomic particles to their sites on the model without requirement of an external force, except for the original positioning. The lack of effort in binding nucleons to the nucleus more accurately reflects how nuclei actually form in real atoms. In the case of the electrons, orienting the same magnetic pole of the embedded magnet in identical fashion for all electron models will create a net repulsive force between them. For example, if the North pole protrudes to the outside of the embedding material out of which the electron model is composed, while the South pole is embedded and its magnetic field strength is masked at this pole, then the North pole will dominate in any electron-electron interaction, creating a repelling effect. This mimics the repulsive force of interaction between electron-electron pairs as all electrons carry a negative charge. The point-to-point directionality of this force will also be preserved.

[0056] How the present atomic structure model addresses force-distance issues: In the case of the 2-D type model, the force required to pull apart the flat fridge magnet surface from the white board surface is not very sensitive to the separation distance of the surfaces, as a result of the uniform magnetic field patterns associated with flat dispersed magnetic films, and because the magnets are attached to a flat 2-D surface e.g. a whiteboard. However, the nucleon models in the present atomic structure model are attached specifically to, and directed towards, the nuclear region by a localized magnet, in a similar way that the nucleons are contained within the nucleus by a localized strong nuclear force. Force-wise, pulling a nucleon model away from the nucleus model is similar to pulling a nucleon away from the nuclear region, if localized magnets are used. The initial effort is relatively high, but once the nucleon is free from the nucleus, only minimal force is required to fully detach it. This means that the magnetic force of attraction between a localized magnet (especially a strong one like a rare earth magnet) within the nucleus model and a magnetic particle/nucleon is highly sensitive to separation distance. When the particles are close, the magnetic force is very strong because the magnetic field strength is high close to the magnet, but as they are pulled apart, this force diminishes in strength exponentially as the magnetic field strength fades away. This is a better analogue to both electric and nuclear forces of attraction within atoms. Electric forces vary inversely with the square of the distance of separation of the electric charges, showing that the force is disproportionately sensitive to separation distance. In the case of the strong nuclear force, this relationship to separation distance is even more sensitive. Existing 3-D mobile type models have an even more serious flaw in their representation of the force-distance relationships because they rely upon the user to physically guide and press the sub-atomic particle models onto the corresponding sites. Because the binding process is accomplished through the effort of the user, the model suggests that there [[is]] are no internal attractive forces of attraction within atoms at all. The is superior in showing that the attractive force gets much stronger as the sub-atomic particles get closer to their target sites, and that the binding processes within atoms are spontaneous and effortless. Nucleons do not need to be ‘squeezed’ and stuck together by an external agent, and no analogue for such an agent exists within real atoms. All that is required is that the nucleons be proximate, and the natural attractive nuclear force will take over to bind them together. A similar situation exists with electrons that spontaneously and effortlessly attach to atoms through the electric attractive force between oppositely charged particles. No external agent is required. Rather than requiring energy, binding an electron to form an atom instead releases energy, that is, it is an exothermic process, not an effortful endothermic process.

[0057] Other benefits of the present atomic structure model: A further advantage of the present model using localized magnetic forces is that the attachments do not require fine motor skills that younger students often do not possess. Attaching is also instantaneous and more fun so are pedagogically more engaging. Because the user kinesthetically ‘feels’ the attractive forces during attachment and detachment (and repulsions with electron-electron interactions), along with their sensitivity to distance of separation and directionality, learning outcomes are more meaningful. For example, the spontaneous exothermic nature of attaching a nucleon to the nucleus is more understandable if the student can physically feel the models attaching effortlessly. Conversely, the effortful endothermic nature of detaching a nucleon is more understandable if the student needs to physically overcome the magnetic attractions to separate the particles in a hands-on way. The force directionality and distance sensitivity are likewise understood kinesthetically with the localized magnetic forces involved. Kinesthetic learning is acknowledged to be one of the three key modalities of learning: the other two being the visual and auditory modes.

[0058] A key to components in the figures is provided as follows. Note that the numbers used in a figure apply to all subsequent figures, unless otherwise indicated.

[0059] FIG. 1 [0060] 10 nucleus model (localized magnet) [0061] 12 nucleon model (magnetic material) [0062] 14 orbital rings to which electron models are attached (magnetic material) [0063] 16 electron model (localized magnet) [0064] 18 rigid shaft to support orbital rings [0065] 20 orbital ring-shaft coupling [0066] 22 rigid frame [0067] 24 base [0068] 26 hole for screw [0069] 28 screw

[0070] FIG. 2 [0071] 30 nucleus model (magnetic material) [0072] 32 nucleon models (localized magnets) [0073] 34 ring orbitals (localized magnets) [0074] 36 electron models (magnetic material)

[0075] FIG. 3 [0076] 38 filament to suspend ring orbitals

[0077] FIG. 4 [0078] 40 posts to support shaft

[0079] FIG. 5 [0080] 18 vertical shaft [0081] 44 attachment means of shaft to base (e.g. screw and thread)

[0082] FIG. 6 [0083] 50 circular ring rail to support shaft 18 mobile in horizontal plane [0084] 52 attachment means of shaft to rail e.g. wheel or bearing and rut [0085] 54 attachment means of circular rail to supporting posts

[0086] FIG. 7 [0087] 50 circular ring rail to support shaft 18 mobile in vertical plane [0088] 56 attachment means of circular rail to base

[0089] FIG. 8 [0090] 64 uniform magnetic field of flat magnet

[0091] FIGS. 9 to 11

[0092] FIG. 9 represents a bar type magnet

[0093] FIG. 10 represents a horseshoe type magnet

[0094] FIG. 11 represents a spherical ball type magnet [0095] 60 region of strong magnetic field strength [0096] 62 region of weak magnetic field strength

[0097] FIGS. 12 to 15 [0098] 70 body of electron model [0099] 72 in FIGS. 12 and 13 embedded localized magnet, with the North pole protruding for all electron models, while the South pole is located within the body of the electron model. [0100] 78 in FIGS. 12 and 13 cavities to embed localized magnet

[0101] In this specification, the indefinite articles “a” and “an” are not to be read as singular indefinite articles or as otherwise excluding more than one or more than a single subject to which the indefinite article refers. For example, “a” shaft includes one shaft, one or more shafts, and a plurality of shafts.

[0102] In this specification, the terms “comprises”, “comprising”, “includes”, “including”, and similar terms, are intended to denote the inclusion of a stated integer or integers, but not necessarily the exclusion of another integer or other integers, depending on context. That is, a product, composition, or method, etc., that comprises or includes stated integer(s) need not have those integer(s) solely, and may well have at least some other integers not stated, depending on context.

[0103] In this specification, terms such as “above” and “below”; “front” and “back”; “top” and “bottom”; “left” and “right”; “horizontal” and “vertical”, and the like, may be used for descriptive purposes. However, it will be understood that embodiments can potentially be arranged in various orientations, and that such relative terms are not limiting and may be interchangeable in appropriate circumstances.

[0104] In this specification, unless the context requires otherwise, the terms “connection”, “connected”, “connecting”, and the like, are not to be read as limited to direct connections and may also include indirect connections. For example, unless the context requires otherwise, a stated first component “connected” to a stated second component may be connected via, through, or by, one or more unstated components.