globals [ tick-length ;; clock variables max-tick-length ;; the largest a tick length is allowed to be box-edge ;; distance of box edge from axes avg-energy ;; keeps track of average kinetic energy of gas molecules fast medium slow ;; current counts percent-slow percent-medium percent-fast ;; percentage of current counts max-energy ;; maximum kinetic energy of a particle particle-size activation-energy ;; total kinetic energy of gas molecule involved in collision required for chemical reaction to occur total-oxygen-molecules ;; keeps track of total molecules total-nitrogen-molecules ;; keeps track of total molecules total-carbondioxide-molecules ;; keeps track of total molecules total-carboncharcoal-atoms ;; keeps track of total molecules ] breed [ gas-molecules gas-molecule ] breed [ carbons carbon ] gas-molecules-own [energy speed mass last-collision] carbons-own [energy] ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; SETUP PROCEDURES ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to setup clear-all set particle-size 1.5 set activation-energy 1000 set max-tick-length 0.01 set max-energy 10000 set box-edge (round (max-pxcor )) make-box make-charcoal make-gas-molecules update-variables reset-ticks end to make-box ask patches with [ ((abs pxcor = box-edge) and (abs pycor <= box-edge)) or ((abs pycor = box-edge) and (abs pxcor <= box-edge)) ] [ set pcolor gray ] end to make-charcoal set-default-shape carbons "carbon" if charcoal-geometry = "6 x 6" [ ask patches with [ pxcor <= 3 and abs pycor <= 3 and pxcor >= -2 and pycor >= -2] [ sprout-carbons 1 [set color yellow set size particle-size]] ] if charcoal-geometry = "4 x 9" [ ask patches with [ pxcor <= 2 and abs pycor <= 4 and pxcor >= -1 and pycor >= -4] [ sprout-carbons 1 [set color yellow set size particle-size]] ] if charcoal-geometry = "3 x 12" [ ask patches with [ pxcor <= 1 and abs pycor <= 6 and pxcor >= -1 and pycor >= -5] [ sprout-carbons 1 [set color yellow set size particle-size]] ] if charcoal-geometry = "2 x 18" [ ask patches with [ pxcor <= 1 and abs pycor <= 9 and pxcor >= 0 and pycor >= -8] [ sprout-carbons 1 [set color yellow set size particle-size]] ] end to make-gas-molecules create-gas-molecules initial-O2-molecules [ setup-oxygen-molecules random-position ] create-gas-molecules initial-N2-molecules [ setup-nitrogen-molecules random-position ] end to setup-oxygen-molecules ;; gas-molecules procedure set shape "oxygen" set size particle-size set energy initial-gas-temp set mass (8 + 8) ;; atomic masses of oxygen atoms set speed speed-from-energy set last-collision nobody end to setup-nitrogen-molecules ;; gas-molecules procedure set shape "nitrogen" set size particle-size set energy initial-gas-temp set mass (7 + 7) ;; atomic masses of oxygen atoms set speed speed-from-energy set last-collision nobody end ;; Place gas-molecules at random, but they must not be placed on top of carbon atoms. ;; This procedure takes into account the fact that carbon molecules could have two possible arrangements, ;; i.e. high-surface area to low-surface area. to random-position ;; gas-molecules procedure let open-patches nobody let open-patch nobody set open-patches patches with [not any? turtles-here and pxcor != max-pxcor and pxcor != min-pxcor and pycor != min-pycor and pycor != max-pycor] set open-patch one-of open-patches move-to open-patch set heading random-float 360 end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; RUNTIME PROCEDURES ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to go ask gas-molecules [ bounce move check-for-collision] ask gas-molecules with [any? carbons-here] [remove-from-matrix] visualize-vibrational-energy ask gas-molecules with [shape = "oxygen"] [ check-for-reaction ] calculate-tick-length update-variables tick-advance tick-length update-plots display end to update-variables set avg-energy mean [energy ] of gas-molecules set total-oxygen-molecules count gas-molecules with [shape = "oxygen"] set total-nitrogen-molecules count gas-molecules with [shape = "nitrogen"] set total-carbondioxide-molecules count gas-molecules with [shape = "co2"] set total-carboncharcoal-atoms count carbons end to visualize-vibrational-energy ask carbons [ ;; visualize energy as a vibration in charcoal setxy pxcor + (5 * (1 - random-float 2)) / 100 pycor + (5 * (1 - random-float 2)) / 100 ] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; CHEMICAL REACTION PROCEDURES ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to check-for-reaction let hit-carbon one-of carbons in-cone 1 180 let speed-loss 0 if hit-carbon != nobody [ let hit-angle towards hit-carbon ifelse (hit-angle < 135 and hit-angle > 45) or (hit-angle < 315 and hit-angle > 225) [set heading (- heading)] [set heading (180 - heading)] ;; oxygen has enough energy itself or oxygen has enough energy with carbon's energy to initiate the reaction if (shape != "co2") and ((energy > activation-energy) or [shape] of hit-carbon = "carbon-activated") [ ask hit-carbon [die] set shape "co2" set mass (6 + 8 + 8) ;; atomic masses of carbon, oxygen, and oxygen set energy energy + energy-released set speed sqrt (energy * 2 / mass) ] ] end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;GAS MOLECULES MOVEMENT;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to bounce ;; gas-molecules procedure ;; get the coordinates of the patch we'll be on if we go forward 1 let new-patch patch-ahead 1 let new-px [pxcor] of new-patch let new-py [pycor] of new-patch ;; if we're not about to hit a wall, we don't need to do any further checks if not shade-of? gray [pcolor] of new-patch [ stop ] ;; if hitting left or right wall, reflect heading around x axis if (abs new-px = box-edge) [ set heading (- heading) ] ;; if hitting top or bottom wall, reflect heading around y axis if (abs new-py = box-edge) [ set heading (180 - heading)] end to move ;; gas-molecules procedure if patch-ahead (speed * tick-length) != patch-here [ set last-collision nobody ] jump (speed * tick-length) end to remove-from-matrix let available-patches patches with [not any? carbons-here] let closest-patch nobody if (any? available-patches) [ set closest-patch min-one-of available-patches [distance myself] set heading towards closest-patch move-to closest-patch ] end to speed-up-one-molecule clear-drawing ask gas-molecules [penup] ask one-of gas-molecules [ set energy (max-energy / 2) set speed speed-from-energy pendown ] calculate-tick-length end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;GAS MOLECULES COLLISIONS;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;from GasLab to calculate-tick-length ;; tick-length is calculated in such way that even the fastest ;; gas-molecules will jump at most 1 patch length in a clock tick. As ;; gas-molecules jump (speed * tick-length) at every clock tick, making ;; tick length the inverse of the speed of the fastest gas-molecules ;; (1/max speed) assures that. Having each gas-molecules advance at most ; one patch-length is necessary for it not to "jump over" a wall ; or another gas-molecules. ifelse any? gas-molecules with [speed > 0] [ set tick-length min list (1 / (ceiling max [speed] of gas-molecules)) max-tick-length ] [ set tick-length max-tick-length ] end to check-for-collision ;; gas-molecules procedure if count other gas-molecules-here in-radius 1 = 1 [ ;; the following conditions are imposed on collision candidates: ;; 1. they must have a lower who number than my own, because collision ;; code is asymmetrical: it must always happen from the point of view ;; of just one gas-molecules. ;; 2. they must not be the same gas-molecules that we last collided with on ;; this patch, so that we have a chance to leave the patch after we've ;; collided with someone. let candidate one-of other gas-molecules-here with [self < myself and myself != last-collision] ;; we also only collide if one of us has non-zero speed. It's useless ;; (and incorrect, actually) for two gas-molecules with zero speed to collide. if (candidate != nobody) and (speed > 0 or [speed] of candidate > 0) [ collide-with candidate set last-collision candidate let this-candidate self ask candidate [set last-collision this-candidate] ] ] end ;; implements a collision with another gas-molecule. ;; ;; The two gas-molecules colliding are self and other-gas-molecules, and while the ;; collision is performed from the point of view of self, both gas-molecules are ;; modified to reflect its effects. This is somewhat complicated, so I'll ;; give a general outline here: ;; 1. Do initial setup, and determine the heading between gas-molecules centers ;; (call it theta). ;; 2. Convert the representation of the velocity of each gas-molecule from ;; speed/heading to a theta-based vector whose first component is the ;; gas-molecule's speed along theta, and whose second component is the speed ;; perpendicular to theta. ;; 3. Modify the velocity vectors to reflect the effects of the collision. ;; This involves: ;; a. computing the velocity of the center of mass of the whole system ;; along direction theta ;; b. updating the along-theta components of the two velocity vectors. ;; 4. Convert from the theta-based vector representation of velocity back to ;; the usual speed/heading representation for each gas-molecules. ;; 5. Perform final cleanup and update derived quantities. to collide-with [ other-gas-molecules ] ;; gas-molecules procedure ;;; PHASE 1: initial setup ;; for convenience, grab some quantities from other-gas-molecules let mass2 [mass] of other-gas-molecules let speed2 [speed] of other-gas-molecules let heading2 [heading] of other-gas-molecules ;; since gas-molecules are modeled as zero-size points, theta isn't meaningfully ;; defined. we can assign it randomly without affecting the model's outcome. let theta (random-float 360) ;;; PHASE 2: convert velocities to theta-based vector representation ;; now convert my velocity from speed/heading representation to components ;; along theta and perpendicular to theta let v1t (speed * cos (theta - heading)) let v1l (speed * sin (theta - heading)) ;; do the same for other-gas-molecules let v2t (speed2 * cos (theta - heading2)) let v2l (speed2 * sin (theta - heading2)) ;;; PHASE 3: manipulate vectors to implement collision ;; compute the velocity of the system's center of mass along theta let vcm (((mass * v1t) + (mass2 * v2t)) / (mass + mass2) ) ;; now compute the new velocity for each gas-molecules along direction theta. ;; velocity perpendicular to theta is unaffected by a collision along theta, ;; so the next two lines actually implement the collision itself, in the ;; sense that the effects of the collision are exactly the following changes ;; in gas-molecules velocity. set v1t (2 * vcm - v1t) set v2t (2 * vcm - v2t) ;;; PHASE 4: convert back to normal speed/heading ;; now convert my velocity vector into my new speed and heading set speed sqrt ((v1t ^ 2) + (v1l ^ 2)) set energy (0.5 * mass * speed ^ 2) ;; if the magnitude of the velocity vector is 0, atan is undefined. but ;; speed will be 0, so heading is irrelevant anyway. therefore, in that ;; case we'll just leave it unmodified. if v1l != 0 or v1t != 0 [ set heading (theta - (atan v1l v1t)) ] ;; and do the same for other-gas-molecules ask other-gas-molecules [ set speed sqrt ((v2t ^ 2) + (v2l ^ 2)) set energy (0.5 * mass * (speed ^ 2)) if v2l != 0 or v2t != 0 [ set heading (theta - (atan v2l v2t)) ] ] penup end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;REPORTERS;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to-report speed-from-energy report sqrt (2 * energy / mass) end to-report energy-from-speed report (mass * speed * speed / 2) end to-report last-n [n the-list] ifelse n >= length the-list [ report the-list ] [ report last-n n butfirst the-list ] end ; Copyright 2007 Uri Wilensky. ; See Info tab for full copyright and license. @#$#@#$#@ GRAPHICS-WINDOW 305 10 665 391 12 12 14.0 1 10 1 1 1 0 0 0 1 -12 12 -12 12 1 1 1 ticks 30.0 BUTTON 90 10 180 43 go/stop go T 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 5 10 91 43 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 5 80 155 113 initial-O2-molecules initial-O2-molecules 1 100 22 1 1 NIL HORIZONTAL PLOT 4 149 304 269 Number of Molecules time count 0.0 10.0 0.0 100.0 true true "" "" PENS "Oxygen" 1.0 0 -13345367 true "" "plotxy ticks total-oxygen-molecules" "Carbon Dioxide" 1.0 0 -4539718 true "" "plotxy ticks total-carbondioxide-molecules" "Charcoal" 1.0 0 -955883 true "" "plotxy ticks total-carboncharcoal-atoms" "Nitrogen" 1.0 0 -6565750 true "" "plotxy ticks total-nitrogen-molecules" SLIDER 5 115 155 148 initial-gas-temp initial-gas-temp 10 500 300 10 1 NIL HORIZONTAL SLIDER 155 115 305 148 energy-released energy-released 0 5000 1000 100 1 NIL HORIZONTAL CHOOSER 185 10 305 55 charcoal-geometry charcoal-geometry "6 x 6" "4 x 9" "3 x 12" "2 x 18" 0 PLOT 5 270 305 390 Temperature of gas time temp 0.0 10.0 0.0 200.0 true false "" "" PENS "Gas" 1.0 0 -13345367 true "" "plotxy ticks (avg-energy)" SLIDER 155 80 305 113 initial-N2-molecules initial-N2-molecules 0 100 76 1 1 NIL HORIZONTAL BUTTON 5 45 180 78 speed up & trace a molecule speed-up-one-molecule NIL 1 T OBSERVER NIL NIL NIL NIL 1 @#$#@#$#@ ## WHAT IS IT? This model shows the chemical kinetics of the combustion reaction for burning charcoal. The chemical reaction that charcoal undergoes in combustion releases energy (exothermic reaction) when the carbon (C) atoms that make up the charcoal react with the oxygen found in air (O2). This reaction produces carbon dioxide CO2. This chemical reaction is represented as follows: C + O2 -> CO2 C and O are called the reactants and CO2 is the product of the reaction. In this model, charcoal is modeled as a block o pure solid of 100% carbon. The surrounding gas is modeled as oxygen and nitrogen. Nitrogen is treated as an inert gas in this model that neither reacts with the oxygen nor the carbon. In reality, at high temperatures, molecular nitrogen and oxygen can combine to form nitric oxide. And at high temperatures and pressures two N2 molecules can react to become N4, which is called nitrogen diamond. Neither of these reactions are represented in this model. ## HOW IT WORKS For a reaction to occur, oxygen (O2) and carbon (C) must have enough energy to break the atomic bond in oxygen and allow the atoms to rearrange to make CO2. This bond breaking energy threshold is called the activation energy. When both the oxygen molecule and the carbon atom have a net amount of molecular kinetic energy (thermal energy) greater than or equal to the activation energy, the reaction occurs. This tends to occur more often at higher temperatures, where molecules have higher amounts of kinetic energy. At higher temperatures it is more likely that any set of reactants will have enough energy to break the bonds of oxygen and causing a rearrangement of the atoms from the reactants. This bond breakage and rearrangement converts chemical potential energy of the reactants into molecular kinetic energy of the products. This is due to the fact that the the atomic bonds of CO2 store less potential energy than those of O2. This excess energy is called the BOND-ENERGY. When the bond energy is increased the products heat up due to an increased transfer of bond-energy to kinetic energy in the chemical reaction. ## HOW TO USE IT Press SETUP and then GO/STOP to run the model. SPEED UP & TRACE A MOLECULE gives a speed boost to a single gas molecule and traces its path until the first collision it encounters. This additional kinetic energy added to this molecule may be enough to cause a chain reaction that leads to the burning of the charcoal. Pressing it also increases the temperature of the gas because temperature is a measure of the average kinetic energy of the molecules. CHARCOAL-GEOMETRY determines the shape of the cluster of carbon atoms (this is referred to as the solid matrix in the procedures). INITIAL-O2-MOLECULES determines the number of initial oxygen (O2) molecules the simulation starts with. INITIAL-N2-MOLECULES determines the number of initial oxygen (N2) molecules the simulation starts with. (The composition of the atmosphere has approximately 78% nitrogen and 21% oxygen). INITIAL-GAS-TEMP sets the initial temperature of the gases. Charcoal will not burn if the total kinetic energy of the carbon atom and oxygen molecule that are set to react is lower than the activation energy ENERGY-RELEASED is the amount of potential chemical energy released in the burning reaction. This energy is converted and transferred into the kinetic energy of the products. ## THINGS TO NOTICE Why does the average speed of the molecules speed up after a few chemical reactions, continue speeding up more quickly, then start to speed up less quickly as the time progresses? How many molecules of oxygen are needed to completely react with the 6 x 6 charcoal solid? Why do different geometries of carbon atoms in the charcoal solid react more or less quickly, even if the number of carbon atoms is the same? ## THINGS TO TRY Try Different ENERGY-RELEASED levels INITIAL-GAS-TEMP values to make the chemical reaction occur at different rates (or not at all). Compare the rate of the reaction with different charcoal solid shapes. Try adjusting the amount of oxygen to make the carbon burn faster. Try adjusting the amount of oxygen and nitrogen to give highest final gas temperature. Try adjusting the amount of oxygen to use up all the oxygen and charcoal in the reaction. ## EXTENDING THE MODEL Energy is transfer to the carbon atoms in collision with gas molecules. This energy is transferred in one discrete chunk (activation-energy). Model the energy transfer in the solid so that different values of energy can be transferred to and from the solid in collisions. Then add diffusion of vibrational energy through the solid (heat transfer) Change the gas to be a mixture of molecules like in the atmosphere. Add a pathway for incomplete combustion: 2C + 02 --> 2CO and the conditions it occurs under. Add a pathway for generating nitrous oxide: 2C + 02 --> 2NO and the conditions it occurs under. ## NETLOGO FEATURES Uses GasLab particle collision code. ## CREDITS AND REFERENCES This model is part of the Connected Chemistry curriculum. See http://ccl.northwestern.edu/curriculum/chemistry. We would like to thank Sharona Levy and Michael Novak for their substantial contributions to this model. ## HOW TO CITE If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software: * Novak, M. and Wilensky, U. (2007). NetLogo Connected Chemistry Solid Combustion model. http://ccl.northwestern.edu/netlogo/models/ConnectedChemistrySolidCombustion. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. * Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. To cite the Connected Chemistry curriculum as a whole, please use: Wilensky, U., Levy, S. T., & Novak, M. (2004). Connected Chemistry curriculum. http://ccl.northwestern.edu/curriculum/chemistry. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. ## COPYRIGHT AND LICENSE Copyright 2007 Uri Wilensky. ![CC BY-NC-SA 3.0](http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png) This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 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