;;
;; mudcrack.nlogo, Copyright (c) 2005 by Roger E Critchlow Jr, Santa Fe, New Mexico, USA
;; This program is free software, licensed under the terms of the Gnu Public License.
;;
;; See Nature, 426: 271-274, November 20, 2003 for details
;;

globals [
  ;; coverage	     ;; cell fraction of particles, slider
  ;; eps-ll		     ;; strength of liquid-liquid attraction, slider
  ;; eps-nn      	 ;; strength of particle-particle attraction, slider
  ;; eps-nl      	 ;; strength of particle-liquid attraction, slider
  ;; mu            ;; chemical potential of liquid-vapor transition, slider
  ;; pmovement     ;; probability of diffusion step given particle patch, slider
  clock		         ;; count the iterations
  particle-color
  liquid-color
  vapor-color
  report-velocity
  velocity
  nsamples
]

patches-own [
  liquid
  particle
  nliquid
  nparticle
]

to setup
  ca
  set clock 0
  set particle-color brown + 2.5
  set liquid-color yellow - 1
  set vapor-color brown - 1
  set report-velocity true
  set velocity 0
  set nsamples 0
  ask patches [
    ifelse (random-float 1.0) < coverage [ make-particle ] [ make-liquid ]
  ]
end 

to go
  let chunk 100000
  reset-timer
  repeat chunk [
    set clock clock + 1
    ask random-one-of patches [
      ifelse is-particle? [
        if (random-float 1.0) < pmovement [ try-moving-particle ]
      ] [
        ifelse is-liquid? [ try-evaporate-liquid ] [ try-condense-vapor ]
      ]
    ]
  ]
  if report-velocity [
    set velocity (nsamples * velocity + (chunk / timer)) / (nsamples + 1)
    set nsamples nsamples + 1
    show (word (round velocity) " steps/second over " nsamples " samples")
  ]
end

to default
  set coverage 0.40
  set eps-ll 2.00
  set eps-nl 3.00
  set eps-nn 4.00
  set mu -4.50
  set pmovement 0.1
end

to sum-neighbors
  set nliquid sum values-from neighbors4 [ liquid ]
  set nparticle sum values-from neighbors4 [ particle ]
end
  
to try-moving-particle
  locals [dir]
  ;; pick a random direction
  set dir random-one-of neighbors4
  ;; see if there's liquid in that direction
  if value-from dir [ is-liquid? ] [
    sum-neighbors
    ask dir [ sum-neighbors ]
    if accept energy-of-motion dir [
      make-liquid
      ask dir [ make-particle ]
    ]
  ]
end

to try-evaporate-liquid
  sum-neighbors
  if accept energy-of-evaporation [ make-vapor ]
end

to try-condense-vapor
  sum-neighbors
  if accept energy-of-condensation [ make-liquid ]
end

to-report accept [deltaH]
  ;; compute the acceptance criterion
  report (random-float 1.0) < min (list 1 exp (- deltaH))  
end

to-report energy-as-vapor
  report 0
end

to-report energy-as-liquid
  report (- eps-ll * nliquid) - (eps-nl * nparticle) - mu
end

to-report energy-as-particle
  report (- eps-nn * nparticle) - (eps-nl * nliquid)
end

to-report energy-as-liquid-moving
  ;; this cell is a particle trying to move into an adjacent liquid cell,
  ;; so when we evaluate the energy as a liquid we assume that one of 
  ;; the neighboring liquid cells has become a particle,
  ;; hence nliquid is 1 too big, and nparticle is 1 too small
  report (- eps-ll * (nliquid - 1)) - (eps-nl * (nparticle + 1)) - mu
end

to-report energy-as-particle-moving
  ;; this cell is a liquid trying to be displaced by a particle
  ;; hence nliquid is 1 too small and nparticle is 1 too big
  report (- eps-nn * (nparticle - 1)) - (eps-nl * (nliquid + 1))
end

to-report energy-of-evaporation
  report energy-as-vapor - energy-as-vapor
end

to-report energy-of-condensation
  report energy-as-liquid - energy-as-vapor
end

to-report energy-of-motion [dir]
  report ((energy-as-liquid-moving - energy-as-particle)
             + (value-from dir [ energy-as-particle-moving - energy-as-liquid ]))
end

to make-liquid
  set liquid 1
  set particle 0
  set pcolor liquid-color
end

to-report is-liquid?
  report liquid = 1
end

to make-vapor
  set liquid 0
  set particle 0
  set pcolor vapor-color
end

to-report is-vapor?
  report (liquid = 0) and (particle = 0)
end

to make-particle 
  set liquid 0
  set particle 1
  set pcolor particle-color
end

to-report is-particle?
  report particle = 1
end
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WHAT IS IT?
-----------
This model illustrates the article "Drying-mediated self-assembly of nanoparticles" from Nature, 246, 271-274, 20 November 2003.  There is pattern formation in crystallization of nanoparticles under irreversible drying.  

HOW IT WORKS
------------
The model defines a grid of lattice points which may be occupied by liquid, vapor, or nanoparticle.  There is an energy associated with contacts between liquid occupied cells (eps-l), with contacts between solid occupied cells (eps-n), with contacts between solid and liquid occupied cells (eps-nl) and with liquid-vapor transitions (mu).

We compute the energy of a configuration surrounding a lattice point i by a formula involving sums over the four adjacent neighbors of i, lattice points j.  The formula has a term for liquid-liquid contacts, - eps-l sum(liquid(i) liquid(j)), a term for solid-solid contacts, - eps-n sum(particle(i) particle(j)), a term for solid-liquid contacts,  - eps-nl sum(particle(i) liquid(j), and a term for evaporation, - mu liquid(i).  

(Note that there is no term for a liquid center adjacent to a solid, - eps-nl sum(liquid(i) solid(j).  I don't know why it is missing, it seems it should contribute to the energy of the configuration.)

The simulation involves simulation of liquid-vapor transition and of particle diffusion.  The phase transition simply converts the  Each of these is simulated by computing a delta H for the phase transition or the particle diffusion step and accepting the 
;
; the simulation takes place on a square lattice, (i).
; each lattice cell may be occupied by solvent or vapor, l(i) = 1 or 0.
; adjacent solvent cells attract each other with strength eps(l).
; the chemical potential, mu, and temperature, T, of the surrounding
; vapor bath determine the equilibrium concentration of liquid and vapor.
; a lattice cell occupied by vapor may also be occupied by nanoparticle,
; n(i) = 1 or 0.
;
; nanoparticles are attracted to liquid with strength eps(nl) and to each
; other with strength eps(n) and form aggregates in the absence of liquid
; which may span several cells.
;
; The nanoparticles are 4x4 grid units in size.  
; eps(n) = 2eps(l).
; eps(nl) = 1.5
; 
; the dynamics of the model is stochastic: attempt to convert a randomly
; chosen cell, i, from liquid to vapor or vice versa, the perturbation accepted
; with Metropolis probability p(acc) = min(1, exp(-delta(H)/(K(b)T))), the
; delta(H) = -eps(l)sum(l(i)l(j)) - eps(n)sum(n(i)n(j)) -eps(nl)sum(n(i)l(j) - mu l(i)
;
; now I'm confused, I guess the delta(H) applies to the changed part of the
; configuration, because we're going to use the same p(acc) for the movement
; of nanoparticles, too.
;
; the lattice is three state: liquid, vapor, or nanoparticle.
;
; the dynamics has a liquid<->vapor transition, and a particle movement
; transition, depending on the state of the randomly chosen cell.
;
; the initial condition is the coverage of nanoparticles,  sum(n(i))/sum(i).
; 
; Figure 2. coverages of 5%, 30%, 40% and 60%, K(b)T = eps(l)/2, mu = -2.25eps(l),
; Figure 4. coverages of 10%, 20%, and 30%, K(b)T = eps(l)/4,



HOW TO USE IT
-------------
The first thing to try is to let liquid evaporate and see how eps-l and mu trade-off to determine the equilibrium vapor pressure.  Set the coverage to 0%, so there will be no nanoparticles at all, setup, and go.  As you increase eps-l, making liquid-liquid contact more favorable, or decrease mu, making the liquid state more favorable, the equilibrium vapor pressure will decrease as.


THINGS TO NOTICE
----------------
This section could give some ideas of things for the user to notice while running the model.


THINGS TO TRY
-------------
This section could give some ideas of things for the user to try to do (move sliders, switches, etc.) with the model.


EXTENDING THE MODEL
-------------------
This section could give some ideas of things to add or change in the procedures tab to make the model more complicated, detailed, accurate, etc.


NETLOGO FEATURES
----------------
This section could point out any especially interesting or unusual features of NetLogo that the model makes use of, particularly in the Procedures tab.  It might also point out places where workarounds were needed because of missing features.


RELATED MODELS
--------------
This section could give the names of models in the NetLogo Models Library or elsewhere which are of related interest.


CREDITS AND REFERENCES
----------------------
This section could contain a reference to the model's URL on the web if it has one, as well as any other necessary credits or references.
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NetLogo 3.0.2
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