This unusually long answer -- a mini-tutorial really -- is an development on his answer. I"ve included a long background ar that supplies informal, quickly visualized analogies to define a number of related concepts, yet the piece is quiet intended as a straight answer come the question that was asked. The extra background material hopefully makes the answer more memorable, and also makes it possible for me to attend to some much more subtle facets of the differences in between periodicity and also randomness.
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A dance of Molecules
The Random texting Dance
Imagine if you deserve to a crowd of people in some city plaza who are walking rapidly and constantly text massage or twitting. (Any same of this to actual life is completely coincidental.) They are all so engaged in what they room typing the for the most component they are blissfully unaware of each other"s existence, other than when they sometimes bump harmlessly right into each other.
Let"s speak to this case the random texting dance, due to the fact that all that activity makes the a little bit like a dance, however one with no details pattern come it.
Next, let’s additional assume the it"s the Chinese new Year, and that come celebrate the occasion the city has listed both a number of Dragon Dancers -- a dozen or so world under a lengthy Chinese Dragon costume -- and also a few very well trained Chinese Elephants, people trained to give way even to extremely distracted human being texters. (They go in large for Chinese brand-new Year in this city!)
Now this is a basic question: What will occur when these large and oddly-shaped participants go right right into the center of the random texting dance?
Well, because everyone is in motions and has room to navigate, the an easy answer is the both the Dragons and also the Elephants will be accommodated without lot trouble. The texters relocate out of their way and allow them to become parts that the as whole random text massage dance.
Now in that is simplest feasible form, the case I just explained can additionally be thought of in molecular terms. The arbitrarily dance the the texters plays the role of a solvent, when the two big participants are examples of bigger molecules that are deserve to slip right into the crowd and also become part of the as whole dance, also if in ~ a somewhat slower pace.
The arbitrarily Square Dance
Now let"s look at a 2nd version the the exact same crowd, one that I"ll speak to the arbitrarily square dance. In this old-fashioned crowd, nobody is texting. In fact, by the rules of this crowd, nobody is even allowed to move forward unless they deserve to find and also grasp the hand of another dancer, even if only for a couple of moments. As soon as they uncover such a help hand, both that the dancers have the right to move and readjust positions within the crowd. That part is prefer a actual square dance, yet unlike a real square run there"s no pattern in the overall motion that the crowd.
In part ways, the random text massage dance and also the random square dance room not all the different. In both cases, individual dancers can move about pretty lot at random with the crowd. A video of their motions likely would present rather comparable results, with perhaps much more turns and pivots in the random square dance.
Some Dances are a real Gas
However, if you look an ext closely in ~ the two cases, you uncover out something a little surprising: the random texting dance behaves a lot choose a gas, while the arbitrarily square run looks a lot an ext like a liquid. To see this difference, friend only must look in ~ what happens when the 2 dances encounter a huge empty space.
In the random text massage dance, nobody is linked to anyone else. That means that every time among the dancers encounters the sheet of an empty space, she or the will just drift off randomly right into it. That"s a nice close tantamount to a gas widening out right into an open container.
In the arbitrarily square dancing, something starkly different happens. These dancers have the right to only move forward when here are hands because that them to grasp, and there space no hands in the large empty space!
The an outcome of this lack of a route forward conveniently results in a well-defined boundary at i beg your pardon the dancers can travel no farther. Dancers at this border are also pulled a bit much more tightly in the direction of the crowd, because they have actually hands pulling lock inward, but no hand pulling castle out. That"s a different instance from the interior where hands pull equally in all directions. The traction at the boundary also tends come smooth out any kind of bumps, since any person sticking far out will be pulled only ago towards the crowd, without any canceling traction from any type of other direction.
Put the all together and you have pretty much exactly what happens at the surface ar of a true liquid: The molecule are required to "lock hands" with various other molecules to relocate forward, for this reason they finish up forming a flat, dense, and elastic (bumps and also dimples gain flattened out) boundary. If you identify that bonds space bonds no issue what the scale is, the chathamtownfc.net of the arbitrarily square dance crowd really is no different from the of the molecules in a liquid. The existence of together a border is the literal definition of the difference between a gas and a liquid, and is why the random text massage crowd qualifies no as a liquid, yet as a gas.
Chances the Precipitation
Now it’s necessary to point out the you can dissolve building materials in gases simply as you deserve to in liquids, and also the instances are comparable in numerous ways. However, the terminology transforms a little when friend do. Because that example, water liquified in air is called "water vapor" rather of "an air solution of water." The amount of water dissolved in waiting is referred to as the "humidity" that the air, v high humidity just an interpretation you have more water dissolved in it. And also just as liquid water have the right to only host so lot salt prior to the salt starts precipitating out as crystals, air have the right to only organize so lot water before he water starts precipitating the end of the as, well... Precipitation. (There are many, many details I"m leaving out in the last one. Rainfall is actually a very complex phenomenon, with many components that room still not well understood.)
Time for a Mashup
Now the trouble with straightforward models is the they usually revolve out to be too... Well... simple.
For example, I"ve been talking around random texting and random square dancing is if each to be a separate and unique case. As with real people and real texters and also real dancers, the physical human being is rarely that simple. So, what if for grins we ago off a little from the strict "hands only" ascendancy in arbitrarily square dancing, and instead permit your dancers to mix in a bit of random texting dances? because that example, they might be allowed to send very quick tweets together they are traveling between the hands of various other dancers.
What that does is develop a kind of spectrum of habits that can selection between the 2 extremes of arbitrarily texting and also random square dancing. If only really brief episodes of tweeting are ever permitted, the design looks an extremely much favor random square dancing, therefore you have actually a liquid. If the require to master hands prior to moving is mostly eliminated, dancers will finish up type of shaking hands sometimes as they happen by, however for the most part they will exhibit the type of volume-filling habits seen in the random text massage dance. In in between those 2 extremes space the far an ext interesting and curious situations that come closer to what we see in real liquids and also real gases.
The an excellent Escape
For example, if some level of text massage is allowed, what wake up at the boundary between a random square dance and also some big open area?
Well, because that the most component you will certainly still get the development of a boundary or surface ar where anyone is pulled earlier by the require to organize hands together they move. However, occasionally among the faster-moving members of the dance will decide come tweet while right at the sheet of the surface, and because castle are relocating fast, they will be out in the open before they can uncover a brand-new hand to organize onto.
They have escaped! even though the crowd continues to be a fluid, enabling short tweets enables some members the the group to cost-free themselves and behave favor a gas.
That"s much more commonly recognized as evaporation. Because that molecules, together for people, it"s an event that is more likely to occur to those that are moving faster and also so are able to gain farther conscious before bonds deserve to pull lock back. Notice also the the average speed that the crowd will sluggish down if you lose a many those much faster members in this fashion. That"s dubbed evaporative cooling, and you only have to stand in prior of a fan after an unanticipated rain shower captures you outside to feel the influence of the molecular version of that an excellent escape.
Righty Tighty, Lefty Loosey
Now it"s time to introduce one more complication: What if you add the rule that dancers have the right to only master left hands to right hands? Let"s contact the left hand a "+" and also the right hand a "-" for short. (And why no the other way around? Well, while appropriate handed myself, I"ve noticed end the years the left-handed folks it seems ~ to get snubbed an horrible lot in language, literature, manufacturing, and also various other subtle and also not-so-subtle ways. So, I just think they worthy a "+" for "left" for a change.)
In electrical tools the assignment that $+$ and $-$ is called the polarity that the device, for this reason it’s not too lot of a large to call dancers with specific roles for their $+$ left and also $-$ appropriate hands polar dancers... At least as lengthy as you realize it has actually nothing to execute with just how cold it is outside!
I should cite in advancement that these arbitrarily polar dancers have a many of features in usual with water, the most typical of all solvents. The is why i’m bothering through these odd complications. Water molecules are close to being best molecular polar dancers, in fact, because they are hard to break and also have a quite solid difference in real electric charge in between the two hydrogen atoms ($+$) and also the oxygen atom ($-$). The fact that they have two hydrogen atom -- about the tantamount of having an extra left arm -- also permits water molecule to "network" far better with each other as castle dance. You could stare at a three-handed dance companion a bit, but those extra hands do for a tighter overall dance!
Red States and Blue States?
With this new and an ext detailed version of a solvent, it"s time come go earlier to mine original example of "dissolving" both Elephants and also Dragons right into a randomly moving crowd that people.
Originally, I dissolved the Elephants and also Dragons right into what amounted to a basic non-polar gas, as stood for by a random text massage crowd. Therefore what wake up if you shot to dissolve the same Elephants and Dragons right into a group of random polar dancers with their more complicated mixing rules?
First it’s crucial to clarify 2 points. The first is that Elephants have no hands. The 2nd point is that due to the fact that the Dragons are actually a bunch of humans holding increase a costume, they have lots and lots that hands. We"re going come assume the their specific dragon costumes enables them to make full use the those hands, and that their hands monitor the same $+$ left and $-$ rules as the polar dancers. Therefore what happens in both cases?
The first sharp distinction is that the elephants room now actively repelled through the crowd! because Elephants have no hands through which to bond to members that the random polar dance, the run crowd reacts to them simply as they would an open up space: They type a surface at i beg your pardon they host hands with each other, however not with the elephant... Which has none. The result is that the polar dancers end up pushing back against the Elephants and also trying to store them the end of the dance. (Some advice if you need to ever find yourself in this case in real life: Do not press on the elephant.)
The situation I just described is remarkably similar to what wake up if friend drop oil into water. One oil molecule has actually no "polar hands," which because that areal molecule way no molecular-scale excesses that $+$ and $-$ electrical charge on different parts that its surface. The in turn way it doesn"t have any kind of easy handles because that the dancing water molecule to grab hold of. The extremely polar water molecule thus finish up joining hands with each other and resisting the intrusion that the "elephantine" oil molecules. It"s no that girlfriend can"t force an elephant into the group -- or an oil molecule into water. It"s simply that the oil molecule will never be accepted really well, and also so will constantly be subjected to forces of molecular-scale surface tension that will shot constantly to press it earlier out to other oil molecule or any nearby surface.
Peas and also Carrots
So, what about the other situation of the Dragon? What happens to dragon in random polar dances?
Just opposing of the Elephant! A Dragon is welcomed right into the run easily, because its plenty of human hand beneath the costume make it resemble an expanded, chain-like variation of a water molecule.
You have the right to see this impact whenever you dissolve sugar in water. Ironically, street is internally comparable to oil, because both generally have huge chains the carbon atoms because that backbones. However, in the instance of sugar, each carbon is "decorated" with the two components of a water molecule. One component is a hydrogen atom, and also the various other is an oxygen-hydrogen item (called a hydroxyl radical). This similarity to water is why sugar is referred to as a "carbo" (carbon backbone) "hydrate" (decorated with water, as in "fully hydrated").
Annie gain Your Cat
All the this is fine, however what around salt? Wasn"t the original question around salt, no oil or sugar? Yes, and that require a pair new characters to hand over to the random polar dance. What is needed is this: One-handed robots!
Each of this one-handed robots has only $+$ left hand or $-$ best hand. Because they are manufactured by a tiny company called Ion Technologies, we"ll just contact these robots "ions" because that short. The agency has a sense of humor, incidentally, so it puts photos of the firm cat (named Cat) ~ above its $+$ left-handed robots, and pictures of their founder, Annie, ~ above its $-$ right-handed robots. That brought about the lefties being called "Cat Ions" (or "cations" for short), and the righties being referred to as “Annie Ions” (or “anions” for short). So, if I happen to speak cation I just mean a $+$ or left-handed robot, and if ns say anion I just mean a $-$ or right-handed robot.
Breaking increase is hard To Do... Sometimes
So, if a arbitrarily polar run crowd bumps right into a squadron of same numbers of cations and also anions, what will happen? will certainly they be permitted to sign up with the dance, as the Dragon was?
Sure! At the very least in most cases, that is.
The first problem is the if you have lot the cations and anions together, they will unavoidably lock hands with each other, and also likely tightly. However, because the polar dancers have solid polarity themselves and are relocating bout pretty quickly, lock can quickly have enough pull and energy rest up also quite chop grips in between the cations and anions. As soon as that happens, the cations and anions have the right to be pulled in to the exact same wild dance as the polar dancers, and in general, a good time will be had by all.
This case is of course the one that is analogous come salt dissolving right into water. And not just the sort of salt we placed on tables, however "salt" in the more comprehensive meaning of any kind of compound composed of small, positively fee (usually metal) and also negatively fee components, or ions. One of the reasons why water is such a great solvent is that its extremely polar molecules deserve to break up almost any type of salt or ionic solid right into individual ions that then deserve to joint into their dance.
And finally, at last, it"s time to go back to the initial question: Why is that that once a systems of salt (or other substances) in water (or various other solvents) is cooled down enough, the salt begins to different out? and also why does the water form crystals that, if the cooling is done progressively enough, contain little or no salt? Or more informally, why does the previously close friendship between water and also salt additionally seem come cool down dramatically as the temperature drops?
The price boils under to this: The random dancers aren"t always random. The is, if lock start relocating ever an ext slowly and ever more cautiously -- the crowd tantamount of dropping the temperature -- you will certainly sooner or later on reach a allude when a great handshake dominates end a great dance, and the dancers no longer have enough power to break the handshake.
The factor that happens is that as soon as random motion departs, geometry takes over as king. In this case, geometry dictates that at cold enough temperatures, repetition and also monotony will always win out over randomness and also diversity. Cold likes to leveling things.
To describe why this is it"s necessary to explain why crystals form in the an initial place. In the case of the two-handed polar dancers the easiest form of decision to make is as long chain. However, due to the fact that chains aren"t very an excellent at pushing and also the goal here is to show how crystals can push points around, I’ll make one much more addition come the rule of the polar dancers.
The dominion is this: The dancers every have huge sheets that Velcro on your backs. So, as soon as things start gaining slow and also chilly, the very first thing that happens come the dancers is they start obtaining stuck to each various other in back-to- ago pairs. The outcomes is bag of dancers with alternating $+$ and also $-$ hands sticking out choose the 4 direction ~ above a map. I need to emphasize that this is not what happens v water, back you can construct compounds that behave prefer this. Mine goal right here is simply to offer a version of the polar dancers that likes to take up a most dance floor space when they acquire together.
So the very first step is the development of these four-handed dance pairs. Then, as temperatures drop still further and the stuck-together dancers thrive even more lethargic, the pairs start to lock hands with adjacent pairs because that longer and longer durations of time. The case finally get a suggest where if one pair grasps the hand of another pair, the shortcut is likely to last for a really long time indeed. That is just what happens to molecules in plenty of of the more remote parts of our people (or universe) in which cold dominates and also is i can not qualify to turning back anytime soon.
Now if friend imagine this four-handed bag linking up through each other, it’s essential to notification that due to the fact that they are formed from dancers who space all the same size, the distances between their staying hands becomes both exact and also repetitious. Because that example, if you had two long east-west chains of these dancer pairs, then every one of their north-facing and also south-facing hands will be precisely lined up and perfectly spaced to enable strong grips. That’s an extremely different from what happens if the spacings space variable or random, due to the fact that in that situation it becomes anyone’s guess even if it is a pair that hands across two parallel chain will complement up or not.
This means that repetition because of identical geometry has actually a dramatically more powerful at low temperatures than you can expect. Random space chains would certainly for instance bond only really weakly, if in ~ all. In sharp contrast, repetition of the same units multiplies the all at once strength that the bond in between the two chains, so that every unit adds yet an additional "reason" because that the chains to shortcut together. This multiplication method that comparable geometry thus begins to arise a dominant impact when temperatures room no much longer high sufficient to save pieces moving about randomly.
Now v that point around the power of repetition in mind, what happens if objects like Dragons or ion that have the best bonds, but not the ideal shapes or distances in between their bonds?
Simple: The non-standard devices start getting pushed out. that is, as soon as stronger bonding with repetition begins to take over as temperatures drop, segregation by kind starts to end up being a universal rule for just how to accomplish the best feasible bonding. That"s why if you execute it carefully enough and also slowly enough, it"s feasible to crystallize really nearly any kind that uniform molecule in existence, also huge, cumbersome proteins. (X-ray diffraction crystallographers often spend far an ext of your time make such complicated crystals 보다 they execute making X-rays of them when they have them!)
All fall Down
Now if friend think about it a bit, the preeminence of repetition helps describe both why water molecules have tendency to exclude other molecules, and why salt crystals begin to form even before the ice crystals form.
In both cases, better overall bonding with long-range repeat of identical units starts as well look more attractive 보다 the weakening power of the random dance. The salt cations and anions, for example, start to get bored through the ever-slower pace of the polar dance, and also no longer discover its tenderness movements solid enough to store them far from the more powerful attraction of your own straight handshakes. Together they brush by an existing decision of cations and also anions, the attraction of that crystal now overcomes the weaker bumps and also motions the the polar dance, and also they decision to drop out. The decision grows even prior to the ice cream begins. Part crystals may add a bit of diversity by combine different species of molecules right into a solitary crystal, yet even then there will certainly be repetition in the way the different molecules alternating and repeat in ~ the crystal.
And soon, together cooling proceeds even further, the dancers themselves prosper weary and ready come rest. Repetition again rules, and also like the anions and also cations the polar dancers begin to look because that the boring but an effective patterns of repetition that permit them to bond firmly and also strongly to those about them. The last crystals form, and the period of remainder begins. That rest may variety from very short to very long indeed.
And to End, Something really Cool
But i can’t finish a piece like this on such a note! if the cosmos as a entirety tends either towards very hot and also random (e.g., the facility of a star) or really cold and also regular (e.g., the cold clouds that interstellar space), there room a very small number of places where a molecule can wind up cycling rapidly in between such extremes, experience both random dances and the simplicity the cold over again and again. One example of together a an extremely special and remarkable region of the universes is miscellaneous we contact "the surface of Earth." there in this distinctive environment, a molecule can experience in rapid sequence the freeze of water or the flowing of liquids. Molecules of flow water might themselves go into into the exalted run of being dissolved into the air, permitting it to flowing to great heights and touch space itself before coming back again in cooler and much more orderly creates as water or ice.
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And a very couple of of this molecules will certainly sometimes find themselves entering right into systems wherein the both the randomness of the warmth dance and the cold regime of regularity it seems to be ~ to have been rotate topsy-turvy. For those few molecules the usual rules the simplicity are somehow changed by sharply defined complexity and also the development of new molecules that are magnificent both in scale and also in the specificity of your functions. The arbitrarily dance goes below too, however in means that room controlled and also customized towards startlingly particular and extremely unlikely outcomes. The is the dream holidays for any type of molecule, the chance to be a part of a human being that seems to defy every odds. That destination is of food you, and me, and also every other living organism approximately us. Life is the can be fried gem in the setting of the entire universe.