Chemistry with Refrigerator Magnets: From Modeling of Nanoscale

Chemistry Everyday for Everyone

Chemistry with Refrigerator Magnets: From Modeling of Nanoscale Characterization to Composite Fabrication

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Dean J. Campbell Department of Chemistry, Bradley University, Peoria, IL 61625 Joel A. Olson, Camilo E. Calderon, Patrick W. Doolan, Elizabeth A. Mengelt, and Arthur B. Ellis* Department of Chemistry, University of Wisconsin-Madison, Madison, WI 53706; *[email protected] George C. Lisensky Department of Chemistry, Beloit College, Beloit, WI 53511

Magnets are critical components of an extraordinary range of devices and technologies (1). The basis for many of these applications is the flexible magnet, which is typically a composite material prepared by incorporating magnetic particles into a flexible polymer host. Uses for flexible magnets include auto ignitions, tachometers, magnetic sensors, Hall effect actuators, eddy current devices, synchronous clock and timer motors, bicycle generators, and microwave communication equipment (1). But perhaps the most common place to encounter flexible magnets is on the refrigerator door. The common flexible-sheet refrigerator magnet (RM) has a complex and ingenious magnetic structure maximized for holding power. A sketch of the magnetic fields in a crosssection of an RM is shown in Figure 1A. The field lines in the RM are U-shaped; therefore, the magnetic field is strong on the back side of the magnet and weak on the front side. An RM can be thought of as an array of very small horseshoe magnets (Fig. 1B). The magnetic field structure comprises a striped pattern of alternating north and south poles on the brown, unprinted back side of the RM (Fig. 1C) (2– 5), with a typical stripe width of 1–2 mm. This unusual magnetic topography can be used for a number of interesting demonstrations and experiments. Chemically, RMs are composite materials, typically containing magnetic strontium ferrite (SrFe12O19) particles dispersed in the elastomer Hypalon. Hypalon is a derivative of polyethylene with some hydrogen atoms replaced by Cl and SO2Cl: X = 14.3 % -Cl

X Hypalon 

To manufacture the RM, an array of permanent magnets forms the magnetic stripes as a sheet of the ferrite–Hypalon composite passes by the array. The magnetic fields from the permanent magnets align the magnetic dipoles of the ferrite particles, resulting in the striped pole pattern. Concentrating the magnetic field at the back surface of the magnet enhances

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Figure 2 depicts a model and corresponding layer sequence of a strontium ferrite unit cell (6–8). Strontium ferrite and its analog, barium ferrite, are both referred to as M-type hexagonal magnetoplumbite-type oxides (7 ), and may be thought of as having hexagonal close-packed oxygen layers (the large colorless spheres shown in Fig. 2) with occasional oxygen substitution by M2+ ions such as Sr2+ or Ba2+ (the large yellow spheres shown in Fig. 2).1 The Fe3+ ions occupy tetrahedral, octahedral, and trigonal bipyramidal sites in the close-packed lattice (Fig. 2). The general formula is MFe12O19 (or MO–6Fe2O3), where M is a divalent metal cation (7).

Figure 1. A: A diagram of the orientation of magnetic fields in a cross-section of a RM. B: An array of horseshoe magnets representing the magnetic poles of a RM. C: Arrangement of north and south poles on the back surface of a RM.

JChemEd.chem.wisc.edu • Vol. 76 No. 9 September 1999 • Journal of Chemical Education

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the ability of the RM to cling to a metal surface such as a refrigerator door: The RM poles induce temporary magnetic poles of opposite polarity in the refrigerator door, enabling the RM to stick to the door (2). This paper will explore RM-based demonstrations of magnetic field imaging, scanning probe microscopy, and magnetic read and write processes. Flexible-sheet RMs that are used as promotional items can be used for many of these experiments. RMs are supplied by Edmund Scientific, Barrington, NJ; Magnet Sales & Manufacturing, Culver City, CA; and NADA Scientific LTD., Champlain, NY. RMs with an adhesive surface to attach to business cards are available through office supply stores. Also presented are experiments involving the fabrication of RMs from polydimethylsiloxane (PDMS) elastomer and powdered SrFe12O19, and the reproduction and compression of magnetic patterns from these composite materials. Safety Ferrofluid stains nearly everything with which it comes into contact. Glove use is recommended. The Dow Corning Sylgard Elastomer 184 Kit components are relatively harmless, but should not be ingested or allowed to contact the eye. The use of latex gloves is recommended.

Contact of the unreacted kit components with strong acids, bases, or oxidizing materials may generate hydrogen gas and should be avoided. Strontium ferrite is labeled as an irritant that should not be ingested or allowed to contact the eyes or skin. Latex gloves and a dust mask are recommended. Part A. Macroscopic Imaging of the Magnetic Structure of RMs There are a number of ways to probe the magnetic patterns of RMs. A sensitive technique for imaging magnetic stripes on RMs is the familiar experiment of placing iron powder on a transparent sheet that has been placed over the unprinted back side of the RM and observing the powder as it distributes itself along the magnetic field lines (Fig. 3A) (9). Magnetic field viewing film, such as that available from Edmund Scientific, Barrington, NJ, may also be used. These films typically contain iron particles suspended in oil and sandwiched between two sheets of Mylar (10). The orientation of the particles along the magnetic field lines controls the shading of the film (Fig. 3B). When the field lines are perpendicular to the film surface, alignment of the particles along the field lines reflects little light and causes the film to

Figure 2. A: Model of the unit cell of SrFe12O19 built with the ICE Solid State Model Kit. B: Layer sequence of the unit cell of SrFe12O19. The pink spheres, painted gray tubes, and blue spheres correspond to Fe in tetrahedral, trigonal bipyramidal, and octahedral coordination environments, respectively. The symbols + and { at z = 0.05 and 0.55 indicate, respectively, positions slightly above and below these layers. Layer sequences are described in Campbell, D. J.; Lorenz, J. K.; Ellis, A. B.; Kuech, T. F.; Lisensky, G. C.; Whittingham, M. S. J. Chem. Educ. 1998, 75, 298.

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The striped magnetic pattern results in anisotropic behavior when the unprinted sides of two RMs are dragged across one another. In most cases the magnets slide smoothly across each other, as shown in Figure 4A with a strip cut from one of the magnets. However, when the magnets are aligned so that the stripes on both RMs are parallel and the RMs are dragged in a direction that is not parallel to the stripes, the RMs will “chatter” (Fig. 4B). That is, the RMs will alternately attract and repel each other as their pole stripes alternately attract and repel each other, producing a chattering sound.

The effect is most pronounced when the RMs are dragged in a direction perpendicular to their magnetic pole stripes (3–5). An RM can also be modified to simulate a “checkerboard” pole pattern by cutting the magnet into strips roughly 1 mm wide (Fig. 4C). When the strips are put together in an attempt to re-form the original magnet, the north poles of one strip repel the north poles and attract the south poles of adjacent neighboring strips. The result is that the strips spontaneously assemble into an alternating pole pattern in both horizontal and vertical directions. Magnetically, this staggered array of magnetic strips forms the pattern in Figure 4C. If one of these 1-mm-wide strips is dragged across the assembly of the other strips, it will chatter as it is dragged both parallel and perpendicular to the direction of the strips. These chattering magnet demonstrations are a useful simulation of scanning probe microscopy techniques such as atomic force microscopy (AFM), and of one variant of AFM, magnetic force microscopy (MFM). A thin strip of RM material with magnetic pole stripes perpendicular to the length of the strip will “chatter” when dragged across a large magnetic sheet owing to the alternating attractive and repulsive interactions with the magnetic fields of the large sample or “substrate” magnet. In a similar fashion, in AFM, a small cantilever probe end moves up and down owing to the spatial variation in forces between it and a substrate. A large-scale version of the atomic force microscope utilizing RMs can be built using LEGOs, a mirror, a strong

Figure 3. Imaging the magnetic stripes on RMs by A: iron powder on an overhead transparency that is placed over the RM; B: magnetic field viewing film; and C: a thin layer of ferrofluid in a thinwalled Petri dish placed over the RM.

Figure 4. A: When the probe strip cut from the edge of a RM (an edge perpendicular to the pole stripes) is drawn across the back side of the RM parallel to the pole stripes of the RM, the magnets glide smoothly past each other. B: When the probe strip is drawn perpendicular to the pole stripes of the RM, the magnets “chatter” against each other. C: A checkerboard pole pattern.

appear dark green; when the field lines are parallel to the film surface, the particles align with the field lines to reflect more light and cause the film to appear very pale green. A thin layer of magnetic particles suspended in fluid in a thin-bottomed glass Petri dish placed over the refrigerator magnet will also respond to the underlying magnetic fields by rising up in ridges where the magnetic field lines curve between north and south domains (Fig. 3C). Therefore, the striped north–south pattern on the back of an RM causes the magnetic fluid layer to rise up into a pattern of parallel ridges. Magnetic fluids that work well are ferrofluids (11) or powdered strontium ferrite dispersed in uncured, fluidlike PDMS. Finally, many RMs contain visible stripes or scratches that are parallel to the magnetic pole stripes. Part B. Simulating Probe Microscopy with RMs


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magnet, an RM, and a pocket laser (4, 5). Figure 5A depicts this assembly. A beam from a pocket laser or small flashlight shines onto a small mirror mounted atop the end of a V-shaped cantilever made from LEGOs. The beam is reflected onto a screen or wall. Attached to the underside of the end of the cantilever with double-sided tape is a pair of strong, small magnets (roughly 2 × 2 × 1 mm; see magnet suppliers above). The magnets are oriented so that one of their poles is directed toward the RM located under the cantilever. As the RM is moved on its motor-driven platform, the RM and the magnets alternately repel and attract each other, and the end of the cantilever is deflected up and down, respectively. This causes the reflected laser beam spot to oscillate vertically, an effect that is easily observed by an audience. In the actual AFM experiment, the components are, of

course, much smaller than the LEGO model. The cantilever length is on the order of microns rather than centimeters, and surfaces can be probed at the nanometer scale, rather than the millimeter scale. However, the principle of using a reflected laser beam to detect deflection of the cantilever remains the same. Rather than visually observing a laser beam spot on a wall, AFM uses a pair of photodiodes to detect beam movement. As the beam moves up and down, the intensity of light received by each diode alternately increases and decreases. A computer takes this difference in light received by each photodiode and calculates the cantilever tip deflection. This tip deflection is matched with the location of the cantilever relative to the substrate and used to generate a map of the substrate surface forces. A computer-driven LEGO system (LEGO DACTA, Enfield, CT) may be used as a more detailed model of magnetic force microscopy (Fig. 5B). The model incorporates a built-in light source, a motor-driven substrate, and a light sensor for the reflected beam. The light intensity reaching the sensor may be plotted as a function of time, creating a wavelike pattern. Part C. Modeling Extended Ionic and Metallic Bonding Responses to Applied Forces

Figure 5. A: A scanning probe “macroscope” built from LEGOs and detail of the magnet-containing cantilever tip. B: A computerdriven version of the LEGO scanning probe “macroscope” and the graph of light intensity received by the detector as a function of time. The oscillation in the graph displays the interaction of the cantilever magnet with the RM substrate as the latter is moved back and forth by the LEGO motor assembly.

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In addition to being a model for force microscopy, the interaction of two RMs can also simulate the response of materials to stress. Although the forces are different, the magnetic interactions between two RMs are reminiscent of and may be used as a model for the electrostatic interactions between layers of atoms in metallic and ionic solids. Placing the back sides of two RMs against one another so that they attract and then sliding them against one another in a direction parallel to the pole stripes represents the relatively smooth deformation of a metal: planes of moving metal atoms remain attracted to each other. In contrast, sliding the back sides of the two RMs against one another in a direction perpendicular to the pole stripes will cause the two initially attracted magnets to repel each other, because like poles repel. If the magnets are properly arranged, the repulsive interactions will force the magnets apart before they slide to the point where attractive forces again predominate. This is representative of the process of salt cleavage, in which repulsions between ions of like charge can help fracture an ionic crystal lattice. Figure 6 shows an arrangement for demonstrating this concept to a large group. Each of two RMs is cut to the shape of a ~5-cm square and is glued to a block of about the same size, with the unprinted back side of the RM facing outward. (The business card RMs with an adhesive surface sold in office supply stores are particularly convenient.) One block is clamped in such a position that the plane of its RM is perpendicular to and above the ground. The other is held to it by magnetic attraction between the two RMs on the blocks. A ball is dropped from a specific height onto the unclamped block. If both RMs are arranged so that the lengths of their pole stripes are perpendicular to the ground, the impact of the dropped ball will slide the loose block along the clamped one. If both RMs are arranged so that the lengths of their pole stripes are parallel to the ground, the impact of the dropped ball will knock the loose block away from the clamped one. The height from which the ball is dropped (typically small) depends on its mass, since if the force is too



great, the impact of the ball will push the magnets apart regardless of the orientation of their magnetic poles. Part D. Writing with a Strong Magnet on an RM The magnetic structure of RMs can be modified. If a strong neodymium–iron–boron (Nd2Fe12B) magnet (see magnet suppliers above) is brought into close contact with the refrigerator magnet, it will alter the magnetization pattern of the refrigerator magnet.

Erasing If the poles of the strong magnet are oriented perpendicular to the refrigerator magnet surface, bringing the magnets into contact creates a large perpendicularly magnetized region in the RM (Fig. 7A). When imaged using ferrofluid (see Part A), this new pattern results in a trough or depression in the ferrofluid, bordered by a small ferrofluid ridge (Fig. 7B). There is still almost no field penetration to the front (printed side) of the refrigerator magnet.

strontium ferrite (SrFel2Ol9) powder in freshly mixed, uncured (uncrosslinked) polydimethylsiloxane (PDMS) elastomer, aligning the ferrite particles in a magnetic field, and then curing (crosslinking) the polymer to trap the magnetic pole patterns in the suspended ferrite. We have found that magnetic alignment is much easier before curing than after the polymer structure has become more rigid. Strontium ferrite is available from CERAC, Milwaukee, WI, and Dow Corning Sylgard Elastomer 184 Kit, a two-component PDMS kit, is available from Ellsworth Adhesive Systems, Germantown, WI.2 A composite structure containing the magnetic ferrite–PDMS layer and a white contrast layer, comprising powdered TiO2 in PDMS, may be fabricated and written on with a marker if a “customized” message-bearing RM is desired (Fig. 8).3 The composite structure demonstrates both magnetic and polymer properties, and the total fabrication procedure takes about 1.5 h. This experiment was performed by about 500 students in a general chemistry course at the UW-Madison and was well received.

Writing If the poles of the strong magnet are oriented parallel to the refrigerator magnet surface, bringing the magnets into contact creates a large parallel magnetized region in the refrigerator magnet (Fig. 7C). This new pattern results in a ridge in the ferrofluid (Fig. 7D). This field also penetrates the front surface of the RM, enabling the writing to be imaged as ferrofluid ridges on the front side, as well. These customized magnetic patterns may be imaged (read) by all the techniques described in Parts A and B, and may be used as “unknowns” for these experiments. Part E. Making an RM A flexible RM that contains an alternating magnetic pole structure may be fabricated in the laboratory by suspending

Figure 6. A: Sliding magnet-faced blocks mimicking metal deformation. B: Blocks repelling each other, mimicking salt cleavage.

Figure 7. A: When the poles of a strong magnet in contact with the RM are oriented perpendicular to the RM surface, a large perpendicularly magnetized region is created in the RM. B: When imaged using ferrofluid, the pattern produced in A results in a trough or depression in the ferrofluid, bordered by a small ferrofluid ridge. C: When the poles of a strong magnet in contact with the RM are oriented parallel to the RM surface, a large parallel magnetized region is created in the RM. D: When imaged using ferrofluid, the pattern produced in C results in a ridge in the ferrofluid.


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Although magnetic fields from an RM can magnetically align strontium ferrite particles in PDMS, we have observed that stronger magnets arranged pole-side up on a galvanized steel plate (i.e., the poles are perpendicular to the plate) will more strongly align the suspended ferrite particles. We have found many alternatives to TiO2 for use in the contrast layer, including colored chalk, talc, metal shavings, ZnS powder doped with Cu to make it phosphorescent (yielding a “glow-in-the-dark” RM), and pulverized Drierite containing CoCl 2 as a moisture indicator (the contrast layer can be made to change color between blue and pink by alternately drying it in an oven and allowing it to pick up moisture from the air) (12). Part F. PDMS Magnetic Structure Compression and Replication The process of copying magnetic features with PDMS containing strontium ferrite particles may be repeated; that is, magnetic information may be copied from one PDMS slab to another. This surface magnetic feature copying process is analogous to the surface physical feature copying process developed by Whitesides et al. (13, 14). Their technique of compressing the PDMS to mechanically alter its surface structure may also be used to alter magnetic pole structures (Fig. 9). A recent paper describes the use of a small vise to compress a block of cured PDMS to deform its surface features (15). Epoxy resin is cured against the PDMS surface during compression to copy the deformed surface features. This technique may be easily adapted to magnetic copying by mixing strontium ferrite (1:1 ferrite/polymer by weight) into the uncured PDMS or epoxy resin, depending on which step of the copy cycle is being performed. Instead of copying the physical features of a substrate (e.g., a diffraction grating) onto PDMS, a magnetic pattern is copied onto PDMS–ferrite using an array of magnets. This magnetic pattern may then be compressed and copied to epoxy–ferrite, completing the cycle described in Figure 9. Magnets fabricated using this copy cycle are shown in Figure 10. Nickel powder has been scattered onto the magnets to highlight their poles. The lower epoxy–ferrite magnet has copied the upper PDMS–ferrite magnet while it was compressed; hence, the square checkerboard magnetic array on the PDMS-based magnet has been converted to a rectangular array on the epoxy-based magnet. We have found that the field generated by a PDMS–ferrite magnet is not as strong as that of the array from which the magnetic pole pattern was copied.

Figure 8. Procedure for making a RM. Step 1) Fabrication of the magnetic layer by curing PDMS/ferrite against an array of strong magnets. Step 2) Fabrication of the contrast layer by curing PDMS/ TiO2 over the PDMS ferrite layer. Step 3) Electrical discharge from a Tesla coil makes the top surface hydrophilic. Step 4) Writing on the contrast layer.

Conclusions This paper describes a number of demonstrations and laboratory experiments utilizing flexible sheet refrigerator magnets. The magnetic pole stripes of RMs may be imaged by a variety of simple methods. Atomic force microscopy and magnetic force microscopy may be modeled by using the alternating magnetic pole stripes of RMs. Magnetic pole arrangements of RMs may be altered by contact with strong magnetic fields. RMs are composites that may be prepared from strontium ferrite powder dispersed and magnetically aligned in PDMS. The PDMS-based RM pattern may be copied with compression of the magnetic pole spacings.

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Figure 9. The PDMS/epoxy resin compression and replication cycle: Substrate 1 has surface magnetic features (left side of cycle). PDMS containing ferrite is cast and cured against this substrate (top of cycle), creating a magnetic image of the substrate. Upon removal of the PDMS from the substrate, the PDMS is compressed, reducing the spacing between its magnetic features (right side of cycle). At the bottom of the cycle, epoxy resin containing strontium ferrite is cast and cured against the compressed PDMS, copying the reduced magnetic pole spacing and creating a new substrate, Substrate 2, for which the cycle can be repeated to produce yet smaller magnetic feature spacings.


Chemistry Everyday for Everyone Figure 10. Magnets produced using the magnetic copy and compression cycle shown in Fig. 9. The lower epoxy/ferrite magnetic field pattern has copied that of the upper PDMS/ ferrite magnet while the latter was compressed. Hence, the square magnetic array (6.4 mm × 6.4 mm poles) on the PDMS-based magnet has been converted to a rectangular array (6.8 mm × 5.5 mm poles) on the epoxy-based magnet. Nickel powder has been scattered on the magnets to highlight their field lines.

Acknowledgments We are grateful to the National Science Foundation Materials Research Science and Engineering Center for Nanostructured Materials and Interfaces (DMR-9632527) for generous support of this research. E. Dan Dahlberg and Roger Proksch of the University of Minnesota are gratefully acknowledged for bringing the structure of flexible sheet RMs to our attention. We thank John Moore at UW-Madison for suggesting the RM salt cleavage model to us. We thank the students and teaching assistants in the 1997 Chemistry 109 class at UW-Madison for helping to test these experiments. We also thank Arnold Flexmag Industries, particularly John Omerod, Al Mayforth, and Tom Dziedzic, for their generous donation of strontium ferrite and for sharing their knowledge of flexible sheet RM fabrication. We are grateful to R. G. Neimi and Brian Reno of Dow-Corning Corporation and Barbara Bruce of Ellsworth Adhesive Systems, Inc., for their generous donation of PDMS elastomer components. Notes W The following supplementary material for this article is available on JCE Online at http://jchemed.chem.wisc.edu/Journal/issues/1999/ Sep/abs1205.html: magsup, a Microsoft Word 6.0 document including a student laboratory fabrication of a polydimethylsiloxane-based refrigerator magnet and related instructor notes. The document contains detailed fabrication information. Images and movies of these and other experiments are available at http://mrsec.wisc.edu/edetc/edetc.html. 1. These alkaline earth ions may substitute for oxygen owing to size similarity. The Goldschmidt ionic radii of O2{, Sr2+, and Ba2+ are 132, 127, and 143 pm, respectively (8). 2. Currently, the cost of a 1.1-lb Dow Corning Sylgard Elastomer 184 Kit is $56.00 for a single kit or $38.16 each for five kits.

3. Since PDMS is a hydrophobic material, many markers will not write on its surface. The surface of the elastomer may be modified from hydrophobic to hydrophilic with the electrical discharge of a Tesla coil. The discharge oxidizes the surface, forming oxygen-containing polar species. Marker ink will now “wet” the surface because it is attracted to the hydrophilic surface of the treated polymer.

Literature Cited 1. Dexter Magnetics. Plastalloy Datasheet; Dexter Magnetic Materials Division: Elk Grove Village, IL, 1997. 2. Livingston, J. D. Driving Force: The Natural Magic of Magnets; Harvard University Press: Cambridge, MA, 1996; p 107. 3. Lorenz, J. K.; Olson, J. A.; Campbell, D. J.; Lisensky, G. C.; Ellis, A. B. J. Chem. Educ. 1997, 74, 1032A. 4. Ellis, A. B. J. Chem. Educ. 1997, 74, 1033. 5. Campbell, D. J.; Campbell, K. C; Billmann, J.; Ellis, A. B. University of Wisconsin–Madison MRSEC Education and Outreach; http://mrsec.wisc.edu/edetc/edetc.html; specifically, refrigerator magnets; http://mrsec.wisc.edu/edetc/mfm.html (accessed Jul 1999). 6. Townes, W. D.; Fang, J. H.; Perrota, A. J. Z. Kristallogr. 1967, 125, 437. 7. Chikazumi, S. Physics of Ferromagnetism; Clarendon: Oxford, 1997; p 199. 8. Smit, J.; Wijn, H. P. J. Ferrites; Wiley: New York, 1959; p 178. 9. Krupinsky, K.; Seergae, T. Activity: Producing a Dipole Field Line; http://hurlbut.jhuapl.edu/NEAR/Education/lessonMag/actmag.html (accessed Jul 1999). 10. EMG, Inc., Santa Rosa, CA; Phone 707/525-9941; The EMG Store; http://www.emginc.com/Store.html#magpaper (accessed Jul 1999). 11. Berger, P.; Adelman, N.; Beckman, K. J.; Campbell, D. J.; Ellis, A. B.; Lisensky, G. C. J. Chem. Educ. 1999, 76, 943–948. Commercial ferrofluids may be obtained from Ferrofluidics, Inc., Nashua, NH; http://www.ferrofluidics.com (accessed Jul 1999). 12. Kluiber, R. W. Hydrates: Part B; http://chemistry.rutgers.edu/ genchem/hydrateB.html (accessed Jun 1999). 13. Xia, Y.; Kim, E.; Zhao, X.-M.; Rogers, J. A.; Prentiss, M.; Whitesides, G. M. Science 1996, 273, 347. 14. Xia, Y.; Whitesides, G. M. Langmuir 1997, 13, 2059. 15. Campbell, D. J.; Beckman, K. J.; Calderon, C. E.; Doolan, P. W.; Ottosen, R. M.; Ellis, A. B.; Lisensky, G. C. J. Chem. Educ. 1999, 76, 537–541.

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A Refrigerator Magnet Analog of Scanning-Probe Microscopy by Julie K. Lorenz, Joel A. Olson, Dean J. Campbell, George C. Lisensky, and Arthur B. Ellis. This activity appeared in print on pages 1032 A & B of the September 1997 issue. You can also find it online at http://jchemed.chem.wisc.edu/Journal/Issues/1997/Sep/art1032A.html. A complete list of our Classroom Activities with links to full-text pdf versions can be found online at http://jchemed.chem.wisc.edu/Journal/activity.html. All Activity Sheets may be reproduced for use in the subscriber’s classroom.


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Chemistry with Refrigerator Magnets: From Modeling of Nanoscale

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