Supersaturated solutions and NetLogo - Soluzioni supersature e NetLogo
In a site with movies of basic chemical experiments I have found this page about crystallization of supersaturated solutions, the Explanation part is expecially interesting:
http://chemed.chem.purdue.edu/demos/main_pages/15.2.html
15.2 Supersaturated Solutions
Chemical Concept Demonstrated: Supersaturation
Demonstration:
A small NaOAc crystal is added to a supersaturated solution of NaOAc. (Non ricordo cosa sia il NaOAc).
Also, the supersaturated solution could have been slowly poured over a NaOAc crystal in a dish.
Observations:
All of the NaOAc comes crashing out of solution, creating a solid mass where the liquid once was.
Getman and Daniels offered the following explanation of supersaturation in Outlines of Theoretical Chemistry, 6th Edition, Wiley and Sons, 1937:
When a saturated solution is cooled, every trace of solid solute being excluded, the excess of dissolved solid may not separate. Such a solution is said to be supersaturated. The explanation of supersaturation is probably to be found in the fact that the submicroscopic crystals that would normally be the first to deposit have a higher solubility and the crystallization process cannot get started. When an ordinary crystal of the solute with a normal solubility is introduced, however, the extra dissolved material crystallizes out immediately. The greater solubility of the very small crystals may, perhaps, be attributed to the existence of more isolated atoms or groups of molecules which can break away from the crystal more easily. This view is strengthened by the fact that if a mixture of large crystals and very small ones is allowed to stand the small ones disappear and the larger ones grow larger — a procedure which is followed in the digesting of precipitates in quantitative analysis to render them better suited for filtration.
This reaction gives off so much heat that it has been used as the basis of a commercial hot-pack produced by Prism Technologies, which is distributed by Buckeye Heat-Pack [(800) 395-6382].
It reminds me of the classic Termites simulation:
http://ccl.northwestern.edu/netlogo/models/Termites
http://education.mit.edu/starlogo/samples/termites.htm
The sourcecode of one of those little simulations:
http://ccl.northwestern.edu/netlogo/models/models/Sample%20Models/Biology/Termites.nlogo
That Termites simulation starts with a random initial state, and after some minutes it (often?) ends with a single blob more or less round with somewhat smooth borders (this means a fractal dimension close to 2).
On a first sight the situation with termites that carry units around can look quite different from the situation of a liquid with atoms/molecules/ions of a salt that move around autonomously, but after thinking a moment about it I think termites can be thought just as a formal way to simulate the movement of the matter particles itself :-)
But there are some important differences between the termites simulation and that crystallization experience, that liquid has some extra complexities not present in the termites simulation. I think some of those things can be added to a simulation.
In the termite simulation it never happens that a "big" piece of material detaches itself, I don't know how much important this can be. In the termites simulation the "balance" is quite shifted toward the ever increasing aggregation, but that texts says that in that supersaturated solution if there aren't seed(s) big enough, then the tiny aggregates (very small crystals) keep their number and size roughly constant (dynamically speaking this surely means they grow and shrink, create and destroy at the same rate). Only when a sizable enough crystalline seed is introduced in the supersaturated solution, then the equilibrium shifts toward an aggregation of particles on it, that makes it grow. Seeing the crystallization speed from the movie, I think such equilibrium shift is very strong!
It may be interesting to see if the termite simulation can be modified to emulate some of those crystallization characteristics.
A problem is that those real solutions are 3D, so a crystalline plane can form, as in the movie, in the 3D bulk of water. In a 2D simulation to form a continuous crystalline plane all the cells have to be full from the start, and this is silly :-)
This little problem can be solved in various ways, like making the solution create a fractal with fractal dimension less than 2, with many holes. Or doing a 2 1/2 D simulation, this means with many planes, filled with "water" and "matter", where particles can freely jump between such planes, and they can form a continuos (without hole) 2D crystal in one of such planes...
As usual comments and ideas are appreciated.
-------------------
Leggendo pagine su un interessante sito che mostra filmati e spiega vari esperimenti/esperienze chimici classici, ho trovato questa che parla di cristallizzazione e soluzionu supersature:
http://chemed.chem.purdue.edu/demos/main_pages/15.2.html
15.2 Supersaturated Solutions
Chemical Concept Demonstrated: Supersaturation
Demonstration:
A small NaOAc crystal is added to a supersaturated solution of NaOAc. (Non ricordo cosa sia il NaOAc).
Also, the supersaturated solution could have been slowly poured over a NaOAc crystal in a dish.
Observations:
All of the NaOAc comes crashing out of solution, creating a solid mass where the liquid once was.
Explanation:
Getman and Daniels offered the following explanation of supersaturation in Outlines of Theoretical Chemistry, 6th Edition, Wiley and Sons, 1937:
When a saturated solution is cooled, every trace of solid solute being excluded, the excess of dissolved solid may not separate. Such a solution is said to be supersaturated. The explanation of supersaturation is probably to be found in the fact that the submicroscopic crystals that would normally be the first to deposit have a higher solubility and the crystallization process cannot get started. When an ordinary crystal of the solute with a normal solubility is introduced, however, the extra dissolved material crystallizes out immediately. The greater solubility of the very small crystals may, perhaps, be attributed to the existence of more isolated atoms or groups of molecules which can break away from the crystal more easily. This view is strengthened by the fact that if a mixture of large crystals and very small ones is allowed to stand the small ones disappear and the larger ones grow larger — a procedure which is followed in the digesting of precipitates in quantitative analysis to render them better suited for filtration.
This reaction gives off so much heat that it has been used as the basis of a commercial hot-pack produced by Prism Technologies, which is distributed by Buckeye Heat-Pack [(800) 395-6382].
Questo mi ha ricordato molto la classica simulazione "Termiti":
http://ccl.northwestern.edu/netlogo/models/Termites
http://education.mit.edu/starlogo/samples/termites.htm
Possono essere fatte funzionare da chi ha Java.
Il sorgente di una di tali piccole simulazioni:
http://ccl.northwestern.edu/netlogo/models/models/Sample%20Models/Biology/Termites.nlogo
Il codice in Star/Parallel Logo e' piuttosto semplice anche per chi non conosce tale linguaggio (copyright 1998 by Uri Wilensky):
to setup
ca
ask patches [ ;;randomly distributes wood chips
if random-float 100 < density
[set pcolor yellow ]
]
create-turtles number ;;randomly distributes termites
ask turtles [
set color white
setxy random-float screen-size-x
random-float screen-size-y
]
end
to go ; turtle procedure
search-for-chip
find-new-pile
put-down-chip
end
to search-for-chip ; turtle procedure -- "picks up chip" by turning orange
ifelse pcolor = yellow
[ set pcolor black
set color orange
fd 20 ]
[ wiggle
search-for-chip ]
end
to find-new-pile ; turtle procedure -- look for yellow patches
if pcolor != yellow
[wiggle
find-new-pile]
end
to put-down-chip ; turtle procedure -- finds empty spot & drops chip
ifelse pcolor = black
[set pcolor yellow
set color white
get-away]
[rt random-float 360
fd 1
put-down-chip]
end
to get-away ; turtle procedure -- escape from yello piles
rt random-float 360
fd 20
if pcolor != black
[get-away]
end
to wiggle ; turtle procedure
fd 1
rt random-float 50 - random-float 50
end
La simulazione e' semplice:
>This project is inspired by the behavior of termites gathering wood chips into piles. The termites follow a set of simple rules. Each termite starts wandering randomly. If it bumps into a wood chip, it picks the chip up, and continues to wander randomly. When it bumps into another wood chip, it finds a nearby empty space and puts its wood chip down. With these simple rules, the wood chips eventually end up in a single pile.<
Partendo da uno stato iniziale del tutto casuale, lo stato finale che si raggiunge dopo alcuni minuti e' un singolo blob piu' o meno rotondo dai bordi poco frastagliati (significa una dimensione frattale molto vicina a 2).
La situazione di termiti che portano in giro unita' puo' sembrare molto diversa dalla situazione di un liquido con atomi (ioni) di un sale che vanno in giro autonomamente, ma se ci si pensa un momento, si vede che le termiti potrebbero essere pensate come un modo formalizzato per simulare lo spostamento delle particelle solide stesse.
Pero' tra la situazione del liquido supersaturo e la simulazione delle termiti ha delle differenze. Direi che la situazione del liquido ha delle complessita' extra, non considerate nella simulazione delle termiti. Ma credo che almeno alcune di tali complessita' vi potrebbero essere aggiunge :-)
Nella simulazione selle termiti non capita mai che un pezzetto di varie unita' si stacchi, inoltre l'equilibrio della simulazione e' abbastanza spostato verso l'aggregazione, mentre nelle soluzioni sovrasature se non ci sono corpuscoli (cristalli) abbastanza grandi i minuscoli cristallini esistono ma rimangono piu' o meno stabili come numero e dimensione (cioe' presumo si creino e si distruggano, perdano e aquistino atomi piu' o meno in quantiata' uguale). Solo quando viene introdotto un seme cristallino abbastanza grande allora l'equilibrio si sposta verso un ulteriore accumulo di atomi su tale seme, che cresce. Vista la velocita' anche molto alta di crescita di tale seme, direi che a quel punto l'equilibrio viene spostato di molto :-)
Sarebbe interessante vedere se si puo' modificare la simulazione delle termiti a sufficienza per simulare questi fenomeni di cristallizzazione di soluzioni supersature (un problema e' che tali soluzioni sono 3D, per cui si puo' formare un "piano" cristallino. In una soluzione 2D perche' si formi un piano continuo tutte le celle dovrebbero gia' essere piene di una particella, il che e' impossibile/inutile. Questo problema credo si possa risolvere in vari modi, o facendo creare un frattale 2D, che quindi e' zeppo di buchi, o ad esempio facendo una similazione in 2 1/2 D, cioe' con vari piani affiancati, dove le particelle possono saltare da un piano all'altro a piacimento).
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leonardo_m) wrote,
