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Surface Roughness: maximizing surface area

Surface features of fish gills.

Surface features of intestinal villi.

At the microscale and nanoscale, seemingly smooth surfaces becomes very rough and jagged.

Applications of surface area to volume ratio can be found all throughout nature and the body. The way nature has shaped leaves, lungs, intestines, and more, all take advantage of the wonderful benefits surface area to volume ratio provides for reactivity. For example, your intestine comes after your stomach to absorb the nutrients in food into your system. They can only absorb nutrients by coming into contact with them. By making the intestines extremely rough by having small protrusions called villi, the surface area of the intestines is increased several hundred times!

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Purpose

Students will discover that the surface area-to-volume ratio (SA/V) changes with size of an object. When shape is constant but volume changes, SA/V is inversely proportional to size. This ratio affects how an object interacts with its environment and is most dramatic for nanoscale objects.

Introduction

When two chemicals react, they do not immediately react completely. It is the outer boundaries or surface area of the chemicals that react together. For example, if you drop a large chunk of sugar in water, it dissolves slowly. The water rips off molecules from the outside of the chunk of sugar, and does so until it has completely dissolved the water. The more surface area there is, the more places there are to react.

You may think that this means that the bigger an object, the more surface boundary there is, and thus it should react faster. This is actually not true. It has to be taken in relation to the interior of the object. The more surface there is for the total amount of material there is, the faster it will react. Mathematicians and scientists call this the Surface Area-to-Volume Ratio. This is because surface area is the outside of an object (the surface boundary), and volume is the interior space the material occupies. The ratio is the comparison of those two numbers. You can learn more about the mathematics behind this ratio in a short video here.

In actuality, the smaller or flatter an object is, the greater the surface area to volume ratio. Can you imagine why? When you cut up a large object into smaller pieces, you are keeping the same amount of volume (the amount of stuff is the same), but you have a much more surface boundary. This is why smaller particles react faster and better. Now imagine particles at the nanoscale… that makes reactions extraordinarily fast!

The sample activity below deals with: surface area and volume. As an object decreases in size, obviously its volume (V) decreases, and so does its surface area (SA), but not at the same rate. A major reason that the nanoscale is special involves scaling the surface area-to-volume ratio: SA/V. You will explore this ratio for 2 samples of superabsorbent polymer particles, as well as in making delicious marshmallow treats.

Part A Sucking It Up

Set Up and Predictions

right n Gather These Materials

You will get a water-absorbent polymer in two different forms and compare how long it takes them to absorb water.

  • 1. Make a data table to record your predictions and observations of the two polymer samples.
  • 2. Get two small, transparent containers. Label one pellets” and the other “powder.”
  • 3. Get a sample of the pellets, and mass 0.5 g of the pellets in that container. Do likewise for the powder.
  • 4. Record your observations of how the two forms of polymers look different and predict which form will absorb water more quickly. Record your prediction and your reason for making it.

Record Your Predictions

Procedure

  • 1. Predict what will happen and why.
  • 2. Add pellets to container.
  • 3. Add water.
  • 4. Measure time for complete water absorption.
  • 5. Add powders to container.
  • 6. Repeat steps 3-4 with the polymer powder.

Record Data and Observations

 

Reflections

  • How did the results compare with your predictions?
  • How did the form of the polymer material affect its rate of water absorption? Propose a reason for the difference in absorption rate.

Record Reflections

 

more info

Interactive Computational Animation on SAP

Superabsorbent polymers (SAP) are large chain-like molecules that can absorb water up to thousands of times their own weight. Their ability to absorb is strongly related to the surface area of the polymer that is in contact with water. The surface area depends on the polymer particles size. Click the SAP video on the left for a quick guided tutorial of the science behind superabsorbent polymers or click the link below to go through the SAP tutorial at your own pace.

Self-Paced Tutorial

 

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Part B Blowing UP Marshmallows

Now let's try to apply your understanding of the surface area-to-volume ratio concept to making some delicious treats. The goal is to melt some marshmallows in a microwave oven instead of on a camp fire. A microwave oven works by passing energetic high frequency radio waves (at 2.45 gigahertz, GHz) through a sample. For small samples that are a few centimeters thick, the microwave energy is able to penetrate the entire sample and uniformly heat the sample from the inside. In thicker samples, the microwave can only penetrate the surface layers first, and then heat is conducted inside. You can watch the short video below on How Microwaves Work.

How Microwaves Work

Marshmallow is basically a spongy candy molded into a cylindrical shape. It is made of mostly sugar and water. When heated the spongy sugar softens or melts, the air bubbles inside expands, and the marshmallow blows up like a balloon.  

Set Up and Predictions

right n Gather These Materials

Obtain marshmallows in two or three different sizes and compare which sample melts first.

1. Make a data table to record your prediction and observations of the marshmallow samples.
2. Measure the average diameter and height of the different sized marshmallows.
3. Compute the surface area, volume, and surface area-to-volume ratio of the marshmallows.
4. Record your observations of how the marshmallows are different and predict which size will melt (or blow up) more quickly. Record your prediction and your reason for making it.

Record Your Predictions

Procedure

1. Predict what will happen and why.
2. Place marshmallow samples on a paper plate or microwave safe plate.
3. Set power on High (or 100% power) and cook time of 30 seconds.
4. Measure time for first sign of heating (marshmallow puffed up due to internal heat buildup). Optional: use video recorder to capture entire sequence of how each marshmallow heats up.
5. Repeat steps 3-4 with different power settings and cook times with more marshmallows. Note: Heating marshmallows at maximum power for more than 2 minutes will burn them and stink up your house.
6. After the marshmallows have cooled down and the experiment is completed, enjoy the delicious crunchy marshmallow treats.

Record Data and Observations

Reflections

How did the results compare with your predictions?
How did the size of the marshmallow affect how quickly it melts? Propose a reason for the difference in the rate of melting.

Record Reflections

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