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Diagrammatical

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I just finished going over the online proofs of my images and text for Diagram magazine.  Sorry – not allowed to share the proofs page (you’ll just have to wait).  I enjoy popping in to the Diagram online presence.  It’s an art and literary magazine organized around odd diagrams and everything diagram like.  It’s about the most fun I’ve had reading a journal online (though I wish the one with the gumballs hadn’t gone kaput).  I’ve found that most of the small press editors are pretty good-natured, and I’ve learned something about Arizona’s experiment in camel mail.  Perhaps even something true.

My personal favorite diagram has yet to make an appearance in the Diagram magazine.  I’ve always had a strange fondness for the sunset diagram (but not for the underlying math – ouch).  The sunset diagram is one of the simplest diagrams for describing fields where the polymer paths or the particle paths (or whatever you’re studying paths) are no longer independent.  It introduces coupling of interactions, and it’s an oddly poetic little beastie.

Image

Here’s a picture of something (an ink drawing) NOT appearing in Diagram (spoiler avoidance!)

entropic-repulsion

It’s called Entropic Repulsions, and is a few tweaks away from an acceptable technical diagram on entropic repulsion.  It’s also quite small, around 5×7 inches.  Purchase the original through Art Venue, or a giclee through Fine Art America

At some point I’ll have to post about “Acceptable” technical graphics and the hidden semiotics of science imagery.  Need more coffee for that though.   After the gap – a bit of nerdliness.  Click an arrow or something if you’re phobic about science (no math here yet – haven’t figured out WordPress equations)

What are entropic repulsions?  You really want to know? You really want to know.  Oh so warm and fuzzy-happy!  Let me explain…  Entropy is popularly defined as “chaos and disorder”.  A somewhat more accurate way to describe entropy is “number of configurations”.  There are different flavors of entropy too – different entropic contributions to free energy.  In high school and college chemistry we all learn about a mysterious “chemical” entropy fudge factor. In a dedicated Thermodynamics class you might see mixing entropy and the entropy associated with phase transitions (water to steam is common).  In polymers, there are additional contributions to entropy.  These arise because a polymer is made of a bunch of smaller molecules linked together to form a floppy chain.  The floppiness of the polymer chain allows it to take many distinct floppy shapes or conformations.  More shapes = more configurations = more entropy (simply stated).

So how can this type of entropy be used to push things apart?  How does conformational entropy translate into an “entropic repulsion”? Think about what happens to a floppy molecule in different circumstances.  When it’s in a solution, it’s pretty much free to flop about and explore all of its different possible shapes.  But what happens when it’s near a wall?  If the wall is close enough, then the floppy molecule can only explore flattened shapes that avoid the wall.  It loses entropy near a wall, when one end is tied down, and even when it’s twined around a dense concentration of other floppy molecules (they all have to avoid one another).

Everything tends towards greater total entropy.  If there are floppy molecules around, they’ll be driven to increase their entropy (right up to the point where there’s too large an entropic cost somewhere else in they system).  If a little bead is coated with floppy molecules, all tied down at one end, the free ends of those molecules will be driven to remain as free and unfettered as possible.  When two coated beads approach one another the free ends of the floppy molecules in the coatings will want to avoid being constrained by even more floppy-molecule-ends.  The effect is a repulsion due to entropy.  This is one approach used to keep tiny particles from sticking together in processing.

If you’re looking at my “entropic repulsions” not-really-a-technical-diagram, can you find where the science is illustrated?  I will entertain and respond to both your  well-thought out analyses and your wild-ass guesses in the comments.