source: sans/Analysis/trunk/Put in User Procedures/SANS_Models_v3.00/BE_Polyelectrolyte.ipf @ 42

#pragma rtGlobals=1             // Use modern global access method.

////////////////////////////////////////////////
// Template: 
// 06 NOV 98 SRK
////////////////////////////////////////////////
// Giovanni Nisato 30 Nov 1998
// Borue-Erukhimovich RPA for linear polyelectrolytes
// references:  Borue, V. Y.; Erukhimovich, I. Y. Macromolecules 1988, 21, 3240.
//                      Joanny, J.-F.; Leibler, L. Journal de Physique 1990, 51, 545.
//                      Moussaid, A.; Schosseler, F.; Munch, J.-P.; Candau, S. J. Journal de Physique II France 1993, 3, 573.
////////////////////////////////////////////////

Proc PlotBE_Polyelectrolyte(num,qmin,qmax)
        Variable num=512,qmin=0.001,qmax=0.2
        Prompt num "Enter number of data points for model: "
        Prompt qmin "Enter minimum q-value (^-1) for model: "
        Prompt qmax "Enter maximum q-value (^-1) for model: "  

        make/o/n=(num) xwave_BE,ywave_BE
        xwave_BE =  alog(log(qmin) + x*((log(qmax)-log(qmin))/num))     
        make/o coef_BE = {10,7.1,12,10,0.00,0.05,0.7,0.001}
        make/o/t parameters_BE = {"K (barns)","Lb ()","h (-3)","b ()","Cs (mol/L)","alpha","C (mol/L)","Background"} 
        Edit parameters_BE,coef_BE
        ywave_BE := BEPolyelectrolyte(coef_BE,xwave_BE)
        Display ywave_BE vs xwave_BE
        ModifyGraph log=0,marker=29,msize=2,mode=4                      //**** log=0 if linear scale desired
        Label bottom "q (\\S-1\\M)"
        Label left "S(q) BE , cm\\S-1\\M"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
End

///////////////////////////////////////////////////////////

Proc PlotSmearedBE_Polyelectrolyte()                                                            //**** name of your function
        //no input parameters necessary, it MUST use the experimental q-values
        // from the experimental data read in from an AVE/QSIG data file
        // if no gQvals wave, data must not have been loaded => abort
        if(ResolutionWavesMissing())
                Abort
        endif
        
        // Setup parameter table for model function
        make/o smear_coef_BE = {10,7.1,12,10,0.00,0.05,0.7,0.001}                                       //**** mod, coef values to match unsmeared model above
        make/o/t smear_parameters_BE= {"K (barns)","Lb ()","h (-3)","b ()","Cs (mol/L)","alpha","C (mol/L)","Background"}    
        Edit smear_parameters_BE,smear_coef_BE                                  //**** mod
        
        // output smeared intensity wave, dimensions are identical to experimental QSIG values
        // make extra copy of experimental q-values for easy plotting
        Duplicate/O $gQvals smeared_BE,smeared_qvals                            //**** mod
        SetScale d,0,0,"1/cm",smeared_BE                                                //**** mod

        smeared_BE := SmearedBEPolyelec(smear_coef_BE,$gQvals)          //**** mod, your SMEARED function name
        Display smeared_BE vs smeared_qvals                                                                     //**** mod
        ModifyGraph log=0,marker=29,msize=2,mode=4
        Label bottom "q (\\S-1\\M)"
        Label left "I  sBE (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
End

///////////////////////////////////////////////////////////////
// unsmeared model calculation
///////////////////////////
// Borue-Erukhimovich RPA model for linear polyelectrolytes
///////////////////////////


Function BEPolyelectrolyte(w,q) : FitFunc
        Wave w
        Variable q
// Input (fitting) variables are:
        //[0] K  = contrast factor  (barns = 10-24 cm^2=10-4 ^2)
        //[1] Lb = Bjerrum length ; this parameter needs to be kept constant for a given solvent and temperature!  ()
        //[2]  h = virial parameter (3)
        //[3]  b = monomer length  ()
        //[4]  Cs = concentration of monovalent salt (mol/L)
        //[5]  alpha = ionization degree : ratio of charged monomers  to total number of monomers
        //[6]  C  = polymer molar concentration (mol/L)
        //[7]  Bkd = Background 
//  local variables
        Variable K,Lb,h,b,alpha,C,Ca,Cs,Csa,r02,K2,q2,Sq,Bkd
        K = w[0]  
        Lb = w[1]
        h = w[2]  
        b = w[3]
        Cs = w[4]
        alpha = w[5]
        C  = w[6]
        Bkd =w[7]
       
        Ca = C *6.022136e-4                     //   polymer number concentration in angstroms-3
        Csa = Cs * 6.022136e-4          //  1:1 salt concentration, angstroms-3
        k2= 4*Pi*Lb*(2*Cs+alpha*Ca)     //    inverse Debye length, squared; classical definition

// alternative definitionfor ANNEALED (weak) polyelectrolytes (e.g. : polyacrylic acid): 
// k2= 4*Pi*Lb*(2*Cs+2*alpha*Ca)        
// reference:  Rapha‘l, E.; Joanny, J.-F. Europhysics Letters 1990, 11, 179.                                                                                                    
                                                                
        r02 = 1./alpha / Ca^0.5*( b / (48*Pi*Lb) ^0.5 )
        q2 = q^2        
        

//   K = a^2  with:  a = (bp - vp/vsolvent * bsolvent)
// where : b = Sum(batom) ; batom = scattering length in cm-12 
//              vp = partial molar volume of the polymer ; vsolvent= partial molar volume of the solvent
// NB :K in  Barns = 10^-24 cm2 ; the rest of the expression is in -3 = 10^24 cm3
//  -> there is no multiplication factor to get the result in cm-1 . 
// Returns S(q) in cm-1

        Sq = K*1./(4*Pi*Lb*alpha^2)  * (q2 + k2)  /  (1+(r02^2) * (q2+k2) * (q2- (12*h*Ca/b^2)) ) + Bkd
        
        Return (Sq)
End
//End of function BE()
///////////////////////////////////////////////////////////////



///////////////////////////////////////////////////////////////
// smeared model calculation
///////////////////////////

        // this is all there is to the smeared calculation!
Function SmearedBEPolyelec(w,x) :FitFunc
        Wave w
        Variable x
        
        Variable ans
        SVAR sq = gSig_Q
        SVAR qb = gQ_bar
        SVAR sh = gShadow
        SVAR gQ = gQVals
        
        //the name of your unsmeared model is the first argument
        ans = Smear_Model_20(BEPolyelectrolyte,$sq,$qb,$sh,$gQ,w,x)

        return(ans)
End