ddG

ddGCALC(xB,T,I0AB,I1AB,I2AB,I3AB,I4AB,I5AB) is for calculating the second derivative Gibbs of binary single solution system.

%% Information 

%ddGCALC(xB,T,I0AB,I1AB,I2AB,I3AB,I4AB,I5AB) is for calculating the second derivative Gibbs of binary single solution system.. 

% I0AB,I1AB,I2AB,I3AB,I4AB,I5AB are parameters of Redlich-Kister binary excess model (Redlich & Kister, 1948)

%Contact: x.chen@mpie.de

function[ddG]= ddGCALC(varargin)

narginchk(3,8)

R=8.314;

if nargin==3

    xB=varargin{1};

    xA=1-xB;

    T=varargin{2};

    IAB=varargin{3};

switch xB

    case {0,1}

        ddG=R*T*(1/xB+1/(xA))-2*IAB; %+0.00001 for preventing Inf cases

    otherwise

        ddG=R*T*(1/xB+1/(xA))-2*IAB;

end

end

if nargin==4

    xB=varargin{1};

    xA=1-xB;

    T=varargin{2};

    IAB=varargin{3}+varargin{4}*(1-2*xB);%???????

    dIAB=varargin{4}*(-2);

switch xB

    case {0,1}

       ddG=R*T*(1/(xB+0.00001)+1/(xA+0.00001))-2*IAB+(1-2*xB)*dIAB+(1-2*xB)*dIAB;

    otherwise

       ddG=R*T*(1/xB+1/(xA))-2*IAB+(1-2*xB)*dIAB+(1-2*xB)*dIAB;

end

end

if nargin==5

    xB=varargin{1};

    xA=1-xB;

    T=varargin{2};

    IAB=varargin{3}+varargin{4}*(1-2*xB)+varargin{5}*(1-2*xB)^2;%???????

    dIAB=varargin{4}*(-2)+varargin{5}*(8*xB-4);%???????

    ddIAB=varargin{5}*8;

switch xB

    case {0,1}

       ddG=R*T*(1/(xB+0.00001)+1/(xA+0.00001))-2*IAB+(1-2*xB)*dIAB+(1-2*xB)*dIAB+ xA*xB*ddIAB;

    otherwise

       ddG=R*T*(1/xB+1/(xA))-2*IAB+(1-2*xB)*dIAB+(1-2*xB)*dIAB+ xA*xB*ddIAB;

end

end

if nargin==6

    xB=varargin{1};

    xA=1-xB;

    T=varargin{2};

    IAB=varargin{3}+varargin{4}*(1-2*xB)+varargin{5}*(1-2*xB)^2+varargin{6}*(1-2*xB)^3;%???????

    dIAB=varargin{4}*(-2)+varargin{5}*(8*xB-4)+varargin{6}*(-6*(2*xB-1)^2);%???????

    ddIAB=varargin{5}*8+varargin{6}*(24 - 48*xB);

switch xB

    case {0,1}

       ddG=R*T*(1/(xB+0.00001)+1/(xA+0.00001))-2*IAB+(1-2*xB)*dIAB+(1-2*xB)*dIAB+ xA*xB*ddIAB;

    otherwise

       ddG=R*T*(1/xB+1/(xA))-2*IAB+(1-2*xB)*dIAB+(1-2*xB)*dIAB+ xA*xB*ddIAB;

end

end

if nargin==7

    xB=varargin{1};

    xA=1-xB;

    T=varargin{2};

    IAB=varargin{3}+varargin{4}*(1-2*xB)+varargin{5}*(1-2*xB)^2+varargin{6}*(1-2*xB)^3+varargin{7}*(1-2*xB)^4;%???????

    dIAB=varargin{4}*(-2)+varargin{5}*(8*xB-4)+varargin{6}*(-6*(2*xB-1)^2)+varargin{7}*(8*(2*xB-1)^3);%???????

    ddIAB=varargin{5}*8+varargin{6}*(24 - 48*xB)+varargin{7}*(48*(2*xB-1)^2);

switch xB

    case {0,1}

       ddG=R*T*(1/(xB+0.00001)+1/(xA+0.00001))-2*IAB+(1-2*xB)*dIAB+(1-2*xB)*dIAB+ xA*xB*ddIAB;

    otherwise

       ddG=R*T*(1/xB+1/(xA))-2*IAB+(1-2*xB)*dIAB+(1-2*xB)*dIAB+ xA*xB*ddIAB;

end

end

if nargin==8

    xB=varargin{1};

    xA=1-xB;

    T=varargin{2};

    IAB=varargin{3}+varargin{4}*(1-2*xB)+varargin{5}*(1-2*xB)^2+varargin{6}*(1-2*xB)^3+varargin{7}*(1-2*xB)^4+varargin{8}*(1-2*xB)^5;%???????

    dIAB=varargin{4}*(-2)+varargin{5}*(8*xB-4)+varargin{6}*(-6*(2*xB-1)^2)+varargin{7}*(8*(2*xB-1)^3)+varargin{8}*(-10*(2*xB - 1)^4);%???????

    ddIAB=varargin{5}*8+varargin{6}*(24 - 48*xB)+varargin{7}*(48*(2*xB-1)^2)+varargin{8}*(-80*(2*xB-1)^3);

switch xB

    case {0,1}

       ddG=R*T*(1/(xB+0.00001)+1/(xA+0.00001))-2*IAB+(1-2*xB)*dIAB+(1-2*xB)*dIAB+ xA*xB*ddIAB;

    otherwise

       ddG=R*T*(1/xB+1/(xA))-2*IAB+(1-2*xB)*dIAB+(1-2*xB)*dIAB+ xA*xB*ddIAB;

end

end

end