Water Marbles

Introduction

“Water marbles” are an aqueous polymer gel obtained from a specially designed polyacrylamide polymer. The gel exhibits interesting properties and applications because it has essentially the same refractive index as water. Your students will “swell’ with curiosity at the discrepant events!

Concepts

• Superabsorbent polymers
• Index of refraction
• Discrepant event

Materials

Safety Precautions

Water marbles are nontoxic. However, if ingested, they may harm the gastrointestinal tract. Wear goggles and gloves whenever working with chemicals, heat or glassware in the lab. Wash hands thoroughly with soap and water before leaving the laboratory and follow all laboratory safety guidelines. Please review current Safety Data Sheets for additional safety, handling and disposal information.

Disposal

Please consult your current Flinn Scientific Catalog/Reference Manual for general guidelines and specific procedures, and review all federal, state and local regulations that may apply, before proceeding.Used and unused water marbles may be stored for future use. Used water marbles should be air dried and allowed to return back to their original size before storage. Depending on the temperature and humidity this process may take several days. If disposal is desired, dispose of water marbles in the trash according to Flinn Suggested Disposal Method #26a. The steel ball should be completely dried before storing for future use to limit the possibility of rusting.

Prelab Preparation

The water marbles must be soaked for several hours (overnight is best) before they reach their desired shape and consistency. This step can be performed with or without data collection. Note: Some of the water marbles may split during this process. Pass out copies of the Water Marble Worksheet to each student.

Procedure

Part A. Estimating the Sphere’s Radius

1. Measure the diameter (in mm) of several dry water marbles using a ruler. Have students enter the values and record the average in the data table on the Water Marbles Worksheet.
2. Using a balance, mass 1.00 g of dry water marbles and have students record the exact mass in the data table.
3. Place the water marbles into a 1-L beaker.
4. Add deionized or distilled water to fill the beaker three-quarters full.
5. Let water marbles soak for several hours—overnight is best.
6. Once the water marbles are fully hydrated, tare the weighing dish, and mass the water marbles. Note: Do not transfer water to the weighing dish, only the water marbles. If necessary, let water drain off the water marbles immediately before transfer.
7. Have students record the average mass of a hydrated water marble in the data table. Also, if desired, measure the diameters (in mm) of several other water marbles and record the average diameter in the data table.

8. Gently put four whole and fully hydrated water marbles into a 250-mL beaker.
9. Gently place four more water marbles in a layer on top of the first four water marbles to form an additional intertwining layer (see Figure 1). A third layer may be added if desired—this will float the steel ball closer to the top of the beaker.
   {12165_Procedure_Figure_1}
10. Gently place a steel sphere in the center of the upper layer of the water marbles.
11. Fill the beaker with DI water to the bottom of the steel ball covering all of the water marbles. The steel sphere should appear to be floating in water (see Figure 2).
    {12165_Procedure_Figure_2}

12. Shine a laser light through the area of the beaker containing the water marbles and water. Use paper to show the laser beam is not diffracted.
13. Cautiously remove the steel ball and set aside. Pour all water out of the beaker without removing the water marbles.
14. Shine the laser through the area of the beaker containing only the water marbles. Use paper to show the laser beam is diffracted as light passes through the polymer gel.

15. Write a message, with a maximum length of 7 cm, on a piece of paper.
16. Place the beaker with water marbles on the paper.
17. Have a student volunteer try to read the message—should be unsuccessful.
18. Pour enough DI water into the beaker to cover all of the water marbles and ask the student to again read the message—the message should be easy to read.

Student Worksheet PDF

12165_Student.pdf

Teacher Tips

• This kit contains enough materials to perform the demonstration seven times: water marbles, a laser, ruler and a 3" steel sphere.
• According to the manufacturer, the purer the water the larger the water marbles will become. Therefore, DI water will result in larger spheres than tap water.
• The floating steel ball demonstration can be set up before class. This discrepant event is a good hook to start a class discussion.
• Eight water marbles arranged in two layers of four marbles each will support a 160-g 3" steel sphere well. A third layer (twelve marbles total) may be added if desired allowing the steel sphere to float closer to the top of the beaker. Use different objects related to previous or future demonstration to personalize this demonstration. If an object is too heavy, however, the water marbles will split. Over time the steel ball may also cause water marbles to split. Small items may not give the impression of “floating.” Many small items such as pennies will slip through the cracks between the water marbles and fall to the bottom of the container.
• Ghost crystals, another form of polyacrylamide which also have a similar refractive index to water when swollen with water, take on crystaline shapes. These crystals are available from Flinn Scientific in two sizes: 100 g (Catalog No. G0050) and 500 g (Catalog No. G0052).

Sample Data

Answers to Questions

1. Assuming that the final volume of a hydrated water marble is due to water (the initial volume of the marble is negligible), use the mass of water gained by an average marbled to calculate a) the average volume of the hydrated water marble and b) the average radius and diameter of a hydrated water marble. (Hint: The volume of a sphere is given by V = 4/3 πr³).
   
   1. Initial volume of a sphere with a diameter of 4 mm = (0.4 cm), radius 0.2 cm.

      V_i = 4/3 πr³
      V_i = 4/3 π(0.2 cm)r³
      V_i = 0.034 cm³

      Weight gain per sphere on average

      m₁ = 10.0 g/16 spheres m₂ = 208 g/16 spheres
      Average Δm = 13 g/sphere

      Using an approximation of 1.0 mL/g as the density of water

      {12165_Answers_Equation_2}

      Calculate the final volume, V_f, as:
      V_f = 0.034 cm³ + 13 cm³ = 13 cm³

   2. The radius corresponding to the final volume is calculated using the formula V_f = 4/3πr³.
      

      V_f= 4/3πr³
      13 cm³ = 4/3πr³
      1.46 cm = r

      The diameter is calculated by multiplying the radius by 2.

      1.46 cm x 2

      Converting back to mm the result in the average diameter approximately equal to 29 mm.

2. Compare the calculated diameter of a hydrated water marble with the measured values. Were they relatively equal? Why or why not?

   The measured diameter ranged from 28–31 mm and the calculated value was 29 mm. The results are equal within experimental error.

3. Why are the water marbles relatively invisible in water but not in air?

   The refractive index of the water marbles is almost identical to that of water. The refractive indices of water marbles and air are very different.

4. A scientist is designing a new experiment. The idea is to make a borosilicate glass beaker “disappear” inside a solution.

   What information would be needed before a recommendation can be made as to which solution should be used? The scientist would need to know the refractive index of the borosilicate glass beaker and then identify a solution with a refractive index matching that of the beaker.

Discussion

Water marbles and compounds like “ghost crystals” are composed of a hydrophilic (water-loving), cross-linked polymer called polyacrylamide. The polymer contains thousands of acrylamide units that have been joined together by a polymerization reaction (Equation 1). The numerous polar C=O and –NH₂ groups in polyacrylamide form strong hydrogen bonds to water molecules, and the polymer readily absorbs large amounts of water to form a polymer gel.

The polymer chains in polyacrylamide water marbles are highly cross-linked, which means that they have been “tied together” into a giant, three-dimensional network by the formation of covalent bonds between the individual polymer chains. The network structure is very large, and there is plenty of “empty space” for absorption of water molecules. When the anhydrous water marbles are placed in water, they readily absorb water and swell to many times their original size.

Polyacrylamide and sodium polyacrylate (the material used in disposable diapers) are commercial examples of superabsorbent polymers. The main uses of polyacrylamide are in municipal and industrial water treatment—it is used as a flocculant to clarify water by increasing the rate of settling of suspended solids. “Water gel crystals” such as ghost crystals and water marbles are sold commercially for use in gardening and as watering aids for indoor plants. (A copolymer of polyacrylamide is also used in the popular “Grow Beast” toys.) Polyacrylamide water marbles will absorb approximately 200 times their weight in water to form crystal-clear, gelatinous spherical solids. Because a water marble is made up almost entirely of water, its index of refraction is essentially the same as that of water, and the water marble “disappears” when placed in water. When the swollen water marble is removed from the water, it instantly becomes visible again because the index of refraction of air is much different from that of the marble or water.

When a light ray travels from one transparent medium through another, the light ray bends. The larger the difference of the speed of light in each medium, the more the light ray is bent.

Light travels at different speeds in various transparent media. For example, the speed of light in a vacuum is 3 x 10⁸ m/s, in ice 2.29 x 10⁸ m/s, in glycerin 2.04 x 10⁸ m/s and in rock salt 1.95 x 10⁸ m/s.

To visualize the bending or refraction of light, construct a normal line to the interface between two media and extend the line through the second medium (see Figure 3). If the speed of light is greater in the first medium, the light ray in the second medium will bend towards the normal line (see Figure 4). This bending of light is called refraction. In addition, a fraction of the light will be reflected off the interface between the two media. Objects that are clear can be seen because light is both refracted and reflected at the surface of the object.

The ratio of the speed of light in a vacuum to the speed of light in a specific medium is called its refractive index, n. Because the speed of light in air is so close to that in a vacuum, its refractive index, 1.000293, is usually rounded off to 1.000 for calculations. Water has a refractive index of 1.33 (see Figure 5).

When the two media have the same refractive index, as with water and water marbles, there is neither reflection nor refraction (Figure 6), and the water marbles “disappear” into the water. A further confirmation of this is the observed transmittance of the laser light through the mixture without being refracted.

References

Gore, Gordon. R.: Physics Fun with Jelly Marbles; The Physics Teacher; Dec. 2009; Vol. 47, pp 606–607.