Introduction to Nanotechnology Module 4 Pressure, Force and Density

© Deb Newberry 2008 The “Big Ideas” of Nanoscale Science* 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

Review: Surface area to volume ratio Changes for an object as the size of that object changes Impacts percentage of atoms on the surface that are available to participate in reactions Changes non linearly as a large object is broken down into smaller objects Introduces us to thinking about the dependence of different parameters on different powers of the linear dimension – This module is an example of this non-equal dependence

An example: Relationship between pressure, force and density Relatively simple equations, easy mathematical manipulation

Some ants can carry items times their body weight The reason that ants can lift so much is because of scaling: ant muscles are no stronger than human muscles on a pull-for-pull basis, but the small size of ants gives them an advantage on how much muscle force they can produce. A muscle is basically a bundle of fibers which can contract and create a pulling force- the amount of force produced by a muscle is proportional to the cross sectional area of that bundle of fibers. Consider a bundle of bungee cords- one bungee cord has a small cross sectional area, and doesn't exert much force (you wouldn't jump off a bridge with just one bungee cord to stop you!); a bundle of bungee cords, such as is used for bungee jumping, has a much greater cross sectional area, and exerts much more force (enough force to stop a bungee jumper from hitting the ground!). In human terms, you can think of a human bicep- the bigger the bicep, the larger the cross-sectional area, and the more force (or strength) that can be applied by that bicep. A fellow by the name of Wigglesworth, in 1972, looked at the strength of insect and vertebrate muscles, in terms of force per square centimeter, and found that they both exerted similar forces, so it's not that ant muscles are somehow stronger. The reason that ants can lift so much is because body size (in terms of volume, which is closely related to mass) increases as a cube of length- while the cross sectional area of muscles increases as the square of length. So, as the size of an organism increases, its mass increases at a much greater rate than the cross-sectional area of its muscles, so those muscles have proportionately more mass to lift. So, the reason ants can lift so much is because their small size means they don't have a large body mass that they must carry around- they have proportionately more muscle (in terms of that cross-sectional area) that they can use to lift heavy things. Conversely, humans are proportionately more massive, and have less muscle that can be applied to lifting heavy things. Ypsite.net/blog

Start looking for…. “ Hidden” dimensional dependencies At first glance pressure only appears to be dependent on the area aspect of the length dimension… But upon closer inspection – see we have a volume dependence in the numerator…… This happens many times in all of the traditional sciences. This critical thing concept extends to other parameters (temperature, material properties etc.)

An example: Viscosity Equation for viscosity: We know that viscosity is temperature dependent based on our experience with pancake syrup. Where is the temperature dependence in the above equation?

An example: Viscosity Equation for viscosity: We know that viscosity is temperature dependent based on our experience with pancake syrup. Where is the temperature dependence in the above equation? Answer: In the density parameter When looking at tables of “constants” like density– take note of the values are specified at a particular temperature or pressure. This implies an inherent dependency on that environmental (or other)constraint on that value (the ‘constant”)

References Poole, Charles P., and Frank J. Owens. Introduction to Nanotechnology. Hoboken, NJ: J. Wiley, 2003.