Introduction to Nanotechnology
Module 3
Surface Area to Volume Ratio
The “Big Ideas” of Nanoscale Science*
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Sense of Scale
Surface area to volume ratio
Density, force and pressure
Surface tension
Priority of forces at different size scales
Material/Surface properties
 Understanding of these concepts requires an integration of the disciplines of math,
biology, chemistry, physics and engineering
© Deb Newberry 2008
Surface Area to Volume Ratio
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This ratio is an important factor in understanding many of the straightforward, counter intuitive or unusual properties that can be observed at the
nanoscale.
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Surface Area to Volume ratio (SA/V) changes as the size of the material
changes – it is not constant!!!!
– Not convinced? Do the calculation for a die and a Rubics cube.
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Also – if we keep the total volume of a material constant but divide that
volume into smaller and smaller pieces – the SA does not increase in a
linear fashion.
Surface Area to Volume Ratio
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The SA/V ratio also represents the percentage of the atoms that are on the
surface of the material.
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SA drives chemical, electrical and biological interactions and systems
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V drives weight, cost, inertia, momentum and other factors
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Both SA and V are dependent on a linear dimension (length) but SA goes
as the square and V goes as the cube – this is “rub”
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Ratios of this type are found in many equations – this is the first encounter
to get familiar with this concept – it can be found in all aspects of
nanoscience
Surface area to volume
Sugar Cubes
Basic algebra
Rules of
exponents,
Units conversion
Surface area to
volume
Other shapes
Excel optional
Soap bubbles
Pressure, force
and density
For a cube:
V= a3
Surface area =6 a2
Notice the difference in powers
of the linear dimension
in the ratio of
surface area to volume (SA/V)
a
a
a
Breaking the large cube
into smaller cubes keeps the
Total volume the same but
Increase the total surface area
Impacts:
•Cell sizes
•Surface tension
•Nanotex pants
Ref: NanoInk
SA/V represents the percentage of atoms on
the surface of an entity
 Let’s assume we have a cube that is 1 cm 3
 The SA will then be 6 cm 2
 Assume each atom is 1 nm 3 in size and takes up an area on the
surface of 1 nm 2
 How many atoms in the cube?
 How many atoms on the surface?
 What is the percentage?
 Now break the larger cube into cubes 1 mm on a side
 Percentage of total atoms that are on the surface
 Percentage of atoms on the surface for each smaller cube
Surface area to volume ratio
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Changes for an object as the size of that object changes
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Impacts percentage of atoms on the surface that are available to participate
in reactions
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Changes non linearly as a large object is broken down into smaller objects
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Introduces us to thinking about the dependence of different parameters on
different powers of the linear dimension
Start looking for….
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“Hidden” dimensional dependencies
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At first glance pressure only appears to be dependent on the area aspect of
the length dimension…
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But upon closer inspection – see we have a volume dependence in the
numerator……
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This happens many times in all of the traditional sciences.
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This critical thing concept extends to other parameters (temperature,
material properties etc.)
References
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Poole, Charles P., and Frank J. Owens. Introduction to Nanotechnology. Hoboken,
NJ: J. Wiley, 2003.