refPotentialCathode.m

%% Reference Potential for Pos. Electrode: Unref(theta_n)
%   Created July 12, 2011 by Scott Moura

function [Uref,varargout] = refPotentialCathode(p,theta)

% % Polynomail Fit
% Uref = ppvalFast(p.Uppp,theta);

% DUALFOIL: CoO2 (Cobalt Dioxide) 0.5 < y < 0.99
Uref = 2.16216+0.07645*tanh(30.834-54.4806*theta) ...
 + 2.1581*tanh(52.294-50.294*theta) ...
 - 0.14169*tanh(11.0923-19.8543*theta) ...
 + 0.2051*tanh(1.4684-5.4888*theta) ...
 + 0.2531*tanh((-theta+0.56478)/0.1316) ...
 - 0.02167*tanh((theta-0.525)/0.006);

% Gradient of OCP wrt theta
if(nargout == 2)
    
%     % Polynomail Fit
%     dUref = ppvalFast(p.dUppp,theta);
%     varargout{1} = dUref / p.c_s_p_max;

dUref = 0.07645*(-54.4806/p.c_s_p_max)* ...
((1.0./cosh(30.834-54.4806*theta)).^2) ...
+2.1581*(-50.294/p.c_s_p_max)*((cosh(52.294-50.294*theta)).^(-2)) ...
+0.14169*(19.854/p.c_s_p_max)*((cosh(11.0923-19.8543*theta)).^(-2)) ...
-0.2051*(5.4888/p.c_s_p_max)*((cosh(1.4684-5.4888*theta)).^(-2)) ...
-0.2531/0.1316/p.c_s_p_max*((cosh((-theta+0.56478)/0.1316)).^(-2)) ...
 - 0.02167/0.006/p.c_s_p_max*((cosh((theta-0.525)/0.006)).^(-2));
varargout{1} = dUref;
    
end

% Gradient of OCP wrt temperature
if(nargout >= 3)
    
    dUdT = 0;
    varargout{2} = dUdT;
    
end