Introduction to Nanoscale Science: Surface Area to Volume Ratio Module

MODULE SUMMARY | ACTIVITY SUMMARIES | RELATED SEMINARS

MODULE SUMMARY

Many intriguing phenomena observed in the "nanoworld" can be attributed to the increase in the surface to volume ratio ( SVR ) at the nanoscale. Understanding the surface area effects to volume changes is thus crucial to the understanding of nanoscale phenomena and nanotechnology applications. As an introduction to the nanoworld, the major goals of this module are to (1) give students a feel for just how small the nanoscale is, (2) give students practice in mathematically communicating nanoscale quantities and relating them to the familiar macroscale, (3) show students that there are different ways to be small (three-, two-, and one-dimensionally), and (4) illustrate the first and foremost property that increases in importance at the nanoscale, viz., surface area. Activity 1 presents some intriguing phenomena that pique student interest in surface area effects, i.e., how physical form of a solid influences the degree to which it interacts with its environment. They find that the more spread out a solid is, the more readily it interacts. In Activity 2, two important mathematical tools are reintroduced into the student scientists' toolbox, namely, powers of 10 and scaling. Students learn to deal with powers of 10 and scale (both linear and the surprises that sometimes result when things do not scale linearly) to represent the magnitudes involved with the nanoscale. In the third activity, students then determine the relationship of the SVR changes with the shape or size of an object. They learn that this ratio changes dramatically in the nanoscale. The challenge in the culminating design project is to introduce a finely divided (high surface area) material in a carbonated beverage that will create the highest liquid geyser possible. The class also has an option to end with playing a "nano-concept" game that will help students review the foundational knowledge about the nanoscale.

ACTIVITY SUMMARIES

Activity 1:  Same Material-Different Behavior

The Activity starts with an attempt by the teacher to burn a nail with a match. When the attempt is repeated with the same material but in a different form (steel wool), the results are different. In Part B, students add water to two different forms of a water-absorbing polymer (pellets and powder), and observe the difference in absorption rates. In Part C, students determine different dissolving times for sugar in different forms (approximately spherical in three sizes, flat, and fibrous).

Activity 2:  Powers of 10 and Scale

Students get a feel for dimensions that are very different from our ordinary experience. A most useful concept for this purpose is scale. First students monitor the nonlinear growth rate of objects in length, area, and volume. They are then introduced to orders of magnitude of length and consider examples in the range 10 9 - 10 -9 m. Students represent some of these lengths graphically and discover the inconvenience of using a linear graph. After their own exploration of a better method, students use semi-log graph paper. They use paper strips to gain a visual sense of what several order of magnitude change look like by laying strips of paper, whose lengths differ by factors of 10, parallel to one another. From this analogy they get a visual grasp of "how small" a nanometer is compared to the width of human hair. Next students try to scale themselves to a large height and then to a small size on the scale of a world map or globe. The activity ends with a poster or Power Point presentation of students illustrating various aspects of an object or system spanning several orders of magnitude, from macroscale to nanoscale. For example, one theme might be circulatory system that includes heart, capillary tubes, and hemoglobin molecules. Another theme might be guitar, showing a macro sized guitar, world's smallest guitar (10 µm long), and diameter of its guitar string (50 nm).

Activity 3:  Surface Area and Volume

To help students realize how and why SVR changes dramatically in the nanometer scale, students begin by looking at two-dimensional (2-D) behavior, perimeter (P) and area (A), which has analogous relationship as surface area and volume. Students learn that the polygon with the maximum ratio of perimeter to area is a triangle (the smallest number of edges that would still be a polygon), and they imagine achieving an even larger ratio by "stretching", approaching a 1-D object. The minimum ratio is achieved by increasing the number of sides, in the limit, approaching a circle. Then in Part B, Students use linking cubes to construct shapes with minimum and maximum SVR of 3-D objects. First, students construct an object with minimum SVR when the volume is fixed. Results are analogous to those for 2-D: This is exhibited by a cube-the most compact shape. The maximum ratio is achieved by "stretching" the cube, again approaching 1-D. Finally, with the shape fixed, students discover that SVR is inversely proportional to size.

Design Project 1:  Designing a Liquid Geyser

Students are challenged to apply the concept of SVR to a real life experiment. They begin by evaluating the familiar "coke fountain" experiment resulting from the heterogeneous nucleation of carbon dioxide gas on the surface of Mentos candy. Their task is to increase the SVR and create a high surface area alternative to Mentos to make the soda "geyser" go higher.

NanoCos Card Game

Combining both the entertainment of popular card games with the educational value of nano-concepts, NanoCos is a highly interactive card game suitable for reviewing module concepts, as well as for a novice to learn the nano-concepts and their role at the nanoscale. To win the game, NanoCos encourages students to apply important concepts, such as orders of magnitude and scale, microscopy tools used in the nanoworld, and SVR changes from macroscopic to nanoscopic scale. Each of the two game players has a deck consisting of Object cards, Action cards, Microscope cards, and Carbon cards. Taking turns, each player selects an Object card to engage with the opponent's Object card; the player with the larger SVR prevails, and he or she gains a Carbon card. The complexity of the game is multiplied by the use of Action and Microscope cards. Some Object cards require the use of Microscope cards in order to be seen. The first player to collect all five Carbon cards, representing the five allotropes of carbon, wins the game. Carbon is emphasized for its prominence in current nanoscale devices and applications. An online version is also available on the NanoEd Resource Portal: » Open NanoCos Card Game

» Sample Activity Pages (PDF)

» Links to Standards (PDF)

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