Cohesion and Density
Is there a measurable/mathematical relationship between
cohesion and density? It seems like there would be, but I cannot
find an answer anywhere.
'Cohesion' I take to mean any of several interatomic or intermolecular
forces such as chemical bonds, electrostatic attraction/repulsion, van der
Waals forces, etc. Is this what you mean?
Qualitatively, yes, these forces do contribute to the density of a material.
I would point out water as an example, where hydrogen bonding makes it a
liquid at conditions where other low-molecular-weight tri-atomic molecules
(e.g. CO2, SO2) are gases. Conditions also play a huge role. With water as
an example, water's density is low in low pressure/high temp (vapor), high
with moderate temperature and pressure (liquid), and then drops again when
you lower the temperature (ice), and then if you raise the pressure very
high, the density increases again (highly pressurized ice has higher density
than the ice you would find in your freezer).
A quantitative model for density that captures all of the various kinds of
attraction is theoretically possible, but would be extremely complicated.
Much research is being conducted now to model molecules and try to predict
physical and chemical properties, including density. Various models exist
for different kinds of materials -- for instance you can calculate the
density of a crystal based on its atomic composition, impurity level/type,
and other factors. People have also made great progress in studying and
modeling polymers (including synthetic 'plastics' as well as biopolymers
like DNA). For more complicated materials like proteins, the story is even
more challenging. You can use computers to simulate groups of molecules, and
study how they attract or repel each other. Using thermodynamics models, we
can then make predictions about the most probable configuration of a system,
and from that predict density. However, molecular simulations take enormous
amounts of time and huge banks of computers, so usually experiments are used
rather than trying calculations. The computers are getting faster, and our
models better, so that may not be true forever.
In terms of measuring forces between molecules, there are several ways to do
this. Some are purely theoretical, and rely on calculating the various types
of attractions and adding them up. There are also experimental tools to
actually measure the force required to pull apart two molecules (one is a
tool called AFM, or atomic force microscopy). These are probably beyond the
typical high school science curriculum, but if you are interested, you could
visit a nearby engineering college and learn more.
I hope this helps -- if I missed the mark, respond back and I can try again.
There is no direct relationship between cohesion, and density. This is
largely because the main causes of cohesion are not related to the
factors that cause increased density. One of the main influences that
determine density, is an element's nucleus. Elements with high atomic
numbers tend to have high density. Lead and especially Uranium are
good examples of this. Magnesium and Aluminum are examples of the
opposite, namely elements with a low atomic number that have low
But cohesion is largely dependent on attraction between like
molecules, and that can be caused the material's molecules being
strongly polar in nature, or exhibiting strong Van der Waals forces.
These attributes are solely related to the material's electron
arrangement (especially the outer electron shell) and have little to
do with the heavy nucleus.
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Update: June 2012