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Copy pathMF_pl.cpp
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MF_pl.cpp
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#include <iostream>
#include <cmath>
#include <vector>
#include "tclap/CmdLine.h"
using namespace std;
using namespace TCLAP;
enum Species {Vacancy, Charge, Exciton};
enum Rates {kr, kEEA, k_EEA, kECA, k_ECA, kRec, k_Rec, ki, k_i, K_Rec, K_EEA, K_ECA, K_i, kDC, k_DC, kDE, k_DE, NUMBER_OF_RATES};
void getConc(vector<double> &OnSiteAvg, vector<double> BathAvg, vector<double> BathRatesAvg, vector<double> rates ) {
int NN = 4;
// calculate D*x_i from rate equations
OnSiteAvg[Vacancy] = NN * rates[kRec] * rates[kECA] * BathAvg[Charge] * BathAvg[Charge] + (BathRatesAvg[Charge] + rates[kDC] * BathAvg[Vacancy]) * (rates[k_i] + rates[kr] + NN * rates[kEEA] * BathAvg[Exciton] + NN * (rates[k_Rec] + rates[kDE]) * BathAvg[Vacancy]) + (rates[k_i] * rates[kRec] + rates[kr] * rates[kRec] + NN * (rates[kEEA] * rates[kRec] * BathAvg[Exciton] + rates[kECA] * BathRatesAvg[Charge] + rates[kDC] * rates[kECA] * BathAvg[Vacancy] + rates[kDE] * rates[kRec] * BathAvg[Vacancy])) * BathAvg[Charge];
// OnSiteAvg[Vacancy] = (rates[k_i] + NN * BathRatesAvg[Charge] + NN * rates[kDC] * BathAvg[Vacancy]) * (rates[kr] + NN * rates[k_Rec] * BathAvg[Vacancy] + NN * rates[kEEA] * BathAvg[Exciton] + NN * rates[kECA] * BathAvg[Charge] + NN * rates[kDE] * BathAvg[Vacancy]) + NN * rates[kRec] * BathAvg[Charge] * (rates[kr] + NN * rates[kEEA] * BathAvg[Exciton] + NN * rates[kECA] * BathAvg[Charge] + NN * rates[kDE] * BathAvg[Vacancy]);
OnSiteAvg[Charge] = (rates[k_DC] * BathAvg[Charge] + BathRatesAvg[Exciton]) * (rates[k_i] + rates[kr] + NN * rates[kECA] * BathAvg[Charge] + NN * rates[kEEA] * BathAvg[Exciton]) + ((rates[k_DC] * BathAvg[Charge] + BathRatesAvg[Exciton]) * rates[kDE] * NN + rates[k_Rec] * (rates[ki] + NN * ((rates[k_DC] + rates[k_ECA]) * BathAvg[Charge] + (rates[k_DE] + rates[k_EEA]) * BathAvg[Exciton] + BathRatesAvg[Exciton]))) * BathAvg[Vacancy];
// OnSiteAvg[Charge] = (rates[ki] + NN * BathRatesAvg[Exciton] + NN * rates[k_DC] * BathAvg[Charge]) *(rates[kr] + NN * rates[k_Rec] * BathAvg[Vacancy] + NN * rates[kEEA] * BathAvg[Exciton] + NN * rates[kECA] * BathAvg[Charge] + NN * rates[kDE] * BathAvg[Vacancy]) + (NN * rates[k_EEA] * BathAvg[Exciton] + NN * rates[k_ECA] * BathAvg[Charge] + NN * rates[k_DE] * BathAvg[Exciton]) * NN * rates[k_Rec] * BathAvg[Vacancy];
OnSiteAvg[Exciton] = NN * (rates[k_DC] + rates[k_ECA]) * rates[kRec] * BathAvg[Charge] * BathAvg[Charge] + (rates[ki] + NN * (rates[k_DE] + rates[k_EEA]) * BathAvg[Exciton]) * (BathRatesAvg[Charge] + rates[kDC] * BathAvg[Vacancy]) + (rates[ki] * rates[kRec] + NN * (((rates[k_DE] + rates[k_EEA]) * BathAvg[Exciton] + BathRatesAvg[Exciton]) * rates[kRec] + rates[k_ECA] * (BathRatesAvg[Charge] + rates[kDC] * BathAvg[Vacancy]))) * BathAvg[Charge];
// OnSiteAvg[Exciton] = NN * rates[kRec] * BathAvg[Charge] * (rates[ki] + NN * BathRatesAvg[Exciton] + NN * rates[k_DC] * BathAvg[Charge]) + (NN * rates[k_EEA] * BathAvg[Exciton] + NN * rates[k_ECA] * BathAvg[Charge] + NN * rates[k_DE] * BathAvg[Exciton]) * (rates[k_i] + NN * rates[kRec] * BathAvg[Charge] + NN * BathRatesAvg[Charge] + NN * rates[kDC] * BathAvg[Vacancy]);
// calculate D
double denom = OnSiteAvg[Vacancy] + OnSiteAvg[Charge] + OnSiteAvg[Exciton];
// returns x_i at a given site
OnSiteAvg[Vacancy] /= denom;
OnSiteAvg[Charge] /= denom;
OnSiteAvg[Exciton] /= denom;
}
int main(int argc, char** argv) {
double xAvg;
double yAvg;
int N = 50;
double sigmaX;
double sigmaY;
// vector<double> VacI(2*N);
// vector<double> ChargeI(2*N);
// vector<double> ExcitonI(2*N);
vector<double> OnSiteAvg(3);
vector<double> BathAvg(3);
vector<double> BathRatesAvg(3);
vector<double> rates(NUMBER_OF_RATES);
int disorderedRate;
try {
CmdLine cmd("Enter rates and stuff");
ValueArg<double> krArg("r", "kr", "Exciton radiative rate", true,0.1,"double");
cmd.add(krArg);
ValueArg<double> kEEAArg("a", "eea", "Exciton exciton annhilation rate", true,0.1,"double");
cmd.add(kEEAArg);
ValueArg<double> kECAArg("d", "eca", "Exicton charge annihlation rate", true,0.1,"double");
cmd.add(kECAArg);
ValueArg<double> k_ECAArg("", "beca", "Exicton charge annihlation backward rate", true,0.1,"double"); // set to 0
cmd.add(k_ECAArg);
ValueArg<double> kRecArg("e", "rec", "Charge charge recombination rate", true,0.1,"double");
cmd.add(kRecArg);
ValueArg<double> k_RecArg("b", "brec", "Charge charge recombination backward rate", true,0.1,"double"); // constant
cmd.add(k_RecArg);
ValueArg<double> kiArg("", "ki", "Charge injection rate", true,0.1,"double"); // constant
cmd.add(kiArg);
ValueArg<double> k_iArg("i", "kbi", "Charge injection backward rate", true,50,"double");
cmd.add(k_iArg);
ValueArg<double> meanXArg("", "meanX", "bimolecular reaction rate mean", true, -6 ,"double");
cmd.add(meanXArg);
ValueArg<double> sigmaXArg("", "sigmaX", "bi molecular reaction rate sigma", true,0,"double");
cmd.add(sigmaXArg);
ValueArg<double> meanYArg("", "meanY", "injection reaction rate mean", true, -6 ,"double"); // ki (controls current)
cmd.add(meanYArg);
ValueArg<double> sigmaYArg("", "sigmaY", "injection reaction rate sigma", true,0,"double"); // set to 0
cmd.add(sigmaYArg);
ValueArg<double> k_EEAArg("z", "beea", "Exciton exciton annhilation backward rate", true,0,"double"); // set to 0
cmd.add(k_EEAArg);
ValueArg<double> kDCArg("p", "dc", "Charge Diffusion rate", true,0,"double"); // constant
cmd.add(kDCArg);
ValueArg<double> k_DCArg("x", "bdc", "Charge Diffusion backward rate", true,0,"double"); // constant, = dc
cmd.add(k_DCArg);
ValueArg<double> kDEArg("y", "de", "Exciton Diffusion rate", true,0,"double"); // constant, = dc
cmd.add(kDEArg);
ValueArg<double> k_DEArg("q", "bde", "Exciton Diffusion backward rate", true,0,"double"); //constant, = dc
cmd.add(k_DEArg);
ValueArg<int> DisArg("", "disr", "Bimolecular rate to disorder", true,1,"int"); // index of the rate w disorder
cmd.add(DisArg);
ValueArg<double> initVac("v","vac", "initial Vacancy pop", false, 0.45,"double");
cmd.add(initVac);
ValueArg<double> initC("C","cpop", "initial charge pop", false, 0.45,"double");
cmd.add(initC);
cmd.parse(argc, argv);
//enum Rates {kr, kEEA, k_EEA, kECA, k_ECA, kRec, k_Rec, ki, k_i, K_Rec, K_EEA, K_ECA, K_i, kDC, k_DC, kDE, k_DE};
disorderedRate = DisArg.getValue();
// rates = list of rate constants
rates[kr] = krArg.getValue();
rates[kEEA] = kEEAArg.getValue();
rates[k_EEA] = k_EEAArg.getValue();
rates[kECA] = kECAArg.getValue();
rates[k_ECA] = k_ECAArg.getValue();
rates[kRec] = kRecArg.getValue();
rates[k_Rec] = k_RecArg.getValue();
rates[ki] = kiArg.getValue();
rates[k_i] = k_iArg.getValue();
//equilibrium constants at end of rates vector
if (rates[k_Rec] == 0) rates[k_Rec] = 0.00000001;
if (rates[k_EEA] == 0) rates[k_EEA] = 0.00000001;
if (rates[k_ECA] == 0) rates[k_ECA] = 0.00000001;
if (rates[k_i] == 0) rates[k_i] = 0.00000001;
//if (rates[k_DC] == 0) rates[k_DC] = 0.00000001;
//if (rates[k_DE] == 0) rates[k_DE] = 0.00000001;
//equilibrium constants
rates[K_i] = rates[ki] / rates[k_i];
rates[K_EEA] = rates[kEEA] / rates[k_EEA];
rates[K_ECA] = rates[kECA] / rates[k_ECA];
rates[K_Rec] = rates[kRec] / rates[k_Rec];
//diffusion constants
rates[kDC] = kDCArg.getValue();
rates[k_DC] = k_DCArg.getValue();
rates[kDE] = kDEArg.getValue();
rates[k_DE] = k_DEArg.getValue();
xAvg = meanXArg.getValue();
sigmaX = sigmaXArg.getValue();
yAvg = meanYArg.getValue();
sigmaY = sigmaYArg.getValue();
BathAvg[Vacancy] = initVac.getValue();
BathAvg[Charge] = initC.getValue();
BathAvg[Exciton] = 1 - BathAvg[Charge] - BathAvg[Vacancy];
} catch (ArgException &e) {
cerr << "error: " << e.error() << " for arg " << e.argId() << endl;
return 1;
}
cout.precision(17);
// for (double sigma = 100*exp(-15); sigma < 1; sigma++) {
// VacB = 0.45;
// HB = VacB;
BathRatesAvg[Charge] = BathAvg[Charge] * rates[kRec];
BathRatesAvg[Exciton] = BathAvg[Exciton] * rates[k_Rec];
if (sigmaX == 0) sigmaX = 0.0000001;
if (sigmaY == 0) sigmaY = 0.0000000000000001;
double dx = 0.15 * sqrt(sigmaX);
double dy = 0.15 * sqrt(sigmaY);
double Px;
double Py;
// BEGIN SCF: res = 0 when converged
double res = 1;
while (res > pow(10,-8)) {
vector<double> Accum(3, 0);
vector<double> RatesAccum(3, 0);
double Norm = 0;
for (int j = -0; j <= 0; j++){
double y = yAvg + j*dy;
Py = 1;
dy = 1;
//Py = exp(-(y-yAvg)*(y-yAvg)/(2*sigmaY)) / sqrt(2*sigmaY*3.1415926536);
// First disorderd rate
rates[ki] = rates[k_i]*exp(-y);
// rates[ki] = exp(-y);
// integrates over distribution of disordered rate
for (int i = -N; i <= N; i++){
double x = xAvg + i*dx;
Px = exp(-(x-xAvg)*(x-xAvg)/(2*sigmaX)) / sqrt(2*sigmaX*3.1415926536);
// disorderd rate here
rates[disorderedRate] = exp(-x);
if (disorderedRate == kRec) rates[k_Rec] = rates[kRec] * rates[K_Rec];
// get concentrations of each species
vector<double> OnSite(3);
getConc(OnSite, BathAvg, BathRatesAvg, rates);
// weighted avg over dist. to get new averages (eventually)
// if i = N or -N, only 2 nearest neighbors (???)
if ((i == -N) || (i == N)) {
Accum[Vacancy] += OnSite[Vacancy] * Px * Py * 0.5;
Accum[Charge] += OnSite[Charge] * Px * Py * 0.5;
Accum[Exciton] += OnSite[Exciton] * Px * Py * 0.5;
RatesAccum[Vacancy] += OnSite[Vacancy] * Px * Py * rates[k_Rec] * 0.5;
RatesAccum[Charge] += OnSite[Charge] * Px * Py * rates[kRec] * 0.5;
RatesAccum[Exciton] += OnSite[Exciton] * Px * Py * rates[k_Rec] * 0.5;
Norm += Px * Py * 0.5;
}
else {
Accum[Vacancy] += OnSite[Vacancy] * Px * Py;
Accum[Charge] += OnSite[Charge] * Px * Py;
Accum[Exciton] += OnSite[Exciton] * Px * Py;
RatesAccum[Vacancy] += OnSite[Vacancy] * Px * Py * rates[k_Rec];
RatesAccum[Charge] += OnSite[Charge] * Px * Py * rates[kRec];
RatesAccum[Exciton] += OnSite[Exciton] * Px * Py * rates[k_Rec];
Norm += Px * Py;
}
// cout << ki << endl;
}
}
// new averages!
Accum[Vacancy] *= dx * dy;
Accum[Charge] *= dx * dy;
Accum[Exciton] *= dx * dy;
// new average rates (avg(krec*x))
RatesAccum[Vacancy] *= dx * dy;
RatesAccum[Charge] *= dx * dy;
RatesAccum[Exciton] *= dx * dy;
Norm *= dx * dy;
// calc difference for scf convergence
res = abs(Accum[Vacancy] - BathAvg[Vacancy]) + abs(Accum[Charge] - BathAvg[Charge]) + abs(Accum[Exciton] - BathAvg[Exciton]);
// update with new avg's
BathAvg[Vacancy] = Accum[Vacancy];
BathAvg[Charge] = Accum[Charge];
BathAvg[Exciton] = Accum[Exciton];
BathRatesAvg[Vacancy] = RatesAccum[Vacancy];
BathRatesAvg[Charge] = RatesAccum[Charge];
BathRatesAvg[Exciton] = RatesAccum[Exciton];
}
// for (int i= 0; i < 2*N + 1;i++) {
// cout << xAvg + (i - N) * dx << "\t " << VacI[i] << "\t " << HI[i] << "\t " << H2I[i]<< endl;
// }
// if converged, return avg phi, c, e
cout << BathAvg[Vacancy] << " " << BathAvg[Charge] << " " << BathAvg[Exciton] << endl;
// }
return 0;
}