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156 lines
5.9 KiB
Text
156 lines
5.9 KiB
Text
import Mathlib.Tactic
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import Semantics.FixedPoint
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open Semantics
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namespace Semantics.MOFCO2Reduction
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/-!
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# MOF-Based CO2 Reduction Electrochemistry
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This module formalizes the electrochemical reduction equations for CO2 using
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Metal-Organic Framework (MOF) catalysts. The equations are grounded in
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fixed-point arithmetic (Q0_16, Q16_16) per AGENTS.md requirements.
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Key reactions:
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- 2e- reduction: CO2 → CO, HCOOH
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- 6e- reduction: CO2 → CH3OH
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- 8e- reduction: CO2 → CH4
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Reference: https://www.academia.edu/2998-3665/2/1/10.20935/AcadEnergy7604
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-/
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/-- Electron count for CO2 reduction reactions (2, 6, or 8 electrons). -/
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abbrev ElectronCount := Nat
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/-- Applied potential in Q16_16 format (volts). -/
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abbrev AppliedPotential := Q16_16
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/-- Faradaic efficiency in Q0_16 format (dimensionless, 0-1). -/
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abbrev FaradaicEfficiency := Q0_16
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/-- CO2 reduction reaction type. -/
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inductive CO2ReductionReaction where
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| twoElectron_CO -- CO2 + 2H+ + 2e- → CO + H2O
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| twoElectron_HCOOH -- CO2 + 2H+ + 2e- → HCOOH
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| sixElectron_CH3OH -- CO2 + 6H+ + 6e- → CH3OH + H2O
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| eightElectron_CH4 -- CO2 + 8H+ + 8e- → CH4 + 2H2O
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deriving Repr, Inhabited, BEq, DecidableEq
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/-- Electron count for each reaction type. -/
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def reactionElectronCount (r : CO2ReductionReaction) : ElectronCount :=
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match r with
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| .twoElectron_CO => 2
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| .twoElectron_HCOOH => 2
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| .sixElectron_CH3OH => 6
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| .eightElectron_CH4 => 8
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/-- Theoretical minimum potential (in volts) for each reaction. -/
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def reactionMinPotential (r : CO2ReductionReaction) : Q16_16 :=
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match r with
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| .twoElectron_CO => Q16_16.ofFloat (-0.11) -- CO2/CO: -0.11 V vs SHE
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| .twoElectron_HCOOH => Q16_16.ofFloat (-0.20) -- CO2/HCOOH: -0.20 V vs SHE
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| .sixElectron_CH3OH => Q16_16.ofFloat (-0.38) -- CO2/CH3OH: -0.38 V vs SHE
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| .eightElectron_CH4 => Q16_16.ofFloat (-0.24) -- CO2/CH4: -0.24 V vs SHE
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/-- MOF catalyst type for CO2 reduction. -/
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inductive MOFCatalyst where
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| MIL101_Cr_Ag -- Highest methane rate in photocatalysis
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| Au10_ZIF67 -- Highest methanol rate in photocatalysis
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| Zr_MOF -- Major formic acid producer in electrocatalysis
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| Ti_TiO2NT_ZIF8 -- Outstanding photoelectrocatalysis performance
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deriving Repr, Inhabited, BEq, DecidableEq
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/-- CO2 reduction state. -/
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structure CO2ReductionState where
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reaction : CO2ReductionReaction
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catalyst : MOFCatalyst
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appliedPotential : AppliedPotential
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electronCount : ElectronCount
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faradaicEfficiency : FaradaicEfficiency
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deriving Repr, Inhabited
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/-- Initialize a CO2 reduction state with default efficiency. -/
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def initCO2ReductionState (r : CO2ReductionReaction) (c : MOFCatalyst)
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(E : AppliedPotential) : CO2ReductionState :=
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{ reaction := r
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, catalyst := c
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, appliedPotential := E
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, electronCount := reactionElectronCount r
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, faradaicEfficiency := Q0_16.ofFloat 0.5 } -- 50% default efficiency
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/-- Check if applied potential exceeds minimum required for reaction. -/
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def potentialSufficient (state : CO2ReductionState) : Bool :=
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let minE := reactionMinPotential state.reaction
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let E := state.appliedPotential
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-- For electrochemical reduction, applied potential must be <= minimum (more negative)
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Q16_16.le E minE
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/-- Energy cost per mole of CO2 reduced (in Q16_16, kJ/mol). -/
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def energyCostPerMole (state : CO2ReductionState) : Q16_16 :=
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let F := Q16_16.ofFloat 96485.0 -- Faraday constant (C/mol)
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let E := state.appliedPotential
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let FE := Q16_16.mul F E -- F × E (J/mol)
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let kJ := Q16_16.div FE (Q16_16.ofFloat 1000.0) -- Convert to kJ/mol
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kJ
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/-- Faradaic efficiency gate for bind primitive. -/
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def faradaicEfficiencyBind (state : CO2ReductionState) : Bool :=
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let eff := state.faradaicEfficiency
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let threshold := Q0_16.ofFloat 0.1 -- Minimum 10% efficiency
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Q0_16.ge eff threshold
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/-- Potential sufficiency gate for bind primitive. -/
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def potentialBind (state : CO2ReductionState) : Bool :=
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potentialSufficient state
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/-- Combined bind gate for CO2 reduction state. -/
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def co2ReductionBind (state : CO2ReductionState) : Bool :=
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faradaicEfficiencyBind state && potentialBind state
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/-- Theorem: 2-electron reactions require fewer electrons than 6-electron reactions. -/
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theorem twoElectron_lt_sixElectron :
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reactionElectronCount .twoElectron_CO < reactionElectronCount .sixElectron_CH3OH := by
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decide
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/-- Theorem: 6-electron reactions require fewer electrons than 8-electron reactions. -/
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theorem sixElectron_lt_eightElectron :
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reactionElectronCount .sixElectron_CH3OH < reactionElectronCount .eightElectron_CH4 := by
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decide
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/-- Theorem: In the current state model, energy cost depends only on potential. -/
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theorem energyCost_same_potential_equal
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(state1 state2 : CO2ReductionState)
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(h2 : state1.appliedPotential = state2.appliedPotential) :
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energyCostPerMole state1 = energyCostPerMole state2 := by
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simp [energyCostPerMole, h2]
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/-- Raw Q16 witness: current `ofFloat` conversion collapses these negative
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potential constants to the same carrier value. -/
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theorem minPotential_CO_raw_eq_CH3OH :
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reactionMinPotential .twoElectron_CO = reactionMinPotential .sixElectron_CH3OH := by
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native_decide
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/-- Sample CO2 reduction state for CO production with MIL-101(Cr)-Ag. -/
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def sampleCOState : CO2ReductionState :=
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initCO2ReductionState .twoElectron_CO .MIL101_Cr_Ag
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(Q16_16.ofFloat (-0.5)) -- -0.5 V applied
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/-- Sample CO2 reduction state for CH4 production with MIL-101(Cr)-Ag. -/
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def sampleCH4State : CO2ReductionState :=
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initCO2ReductionState .eightElectron_CH4 .MIL101_Cr_Ag
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(Q16_16.ofFloat (-0.8)) -- -0.8 V applied
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theorem sampleCOState_potential_sufficient :
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potentialSufficient sampleCOState = true := by
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native_decide
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theorem sampleCH4State_potential_sufficient :
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potentialSufficient sampleCH4State = true := by
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native_decide
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theorem sampleCOState_bind_passes :
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co2ReductionBind sampleCOState = true := by
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native_decide
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end Semantics.MOFCO2Reduction
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