1 | #pragma rtGlobals=1 // Use modern global access method. |
---|
2 | |
---|
3 | // calculates the scattering from a spherical particle made up of a core (aqueous) surrounded |
---|
4 | // by N spherical layers, each of which is a PAIR of shells, solvent + surfactant since there |
---|
5 | //must always be a surfactant layer on the outside |
---|
6 | // |
---|
7 | // bragg peaks arise naturally from the periodicity of the sample |
---|
8 | // resolution smeared version gives he most appropriate view of the model |
---|
9 | |
---|
10 | // |
---|
11 | // |
---|
12 | Proc PlotMultiShellSphere(num,qmin,qmax) |
---|
13 | Variable num=100,qmin=0.001,qmax=0.7 |
---|
14 | Prompt num "Enter number of data points for model: " |
---|
15 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
---|
16 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
---|
17 | |
---|
18 | make/O/D/N=(num) xwave_mss,ywave_mss |
---|
19 | xwave_mss = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
---|
20 | make/O/D coef_mss = {1.,60,10,10,6.4e-6,0.4e-6,2,0.001} |
---|
21 | make/O/T parameters_mss = {"scale","core radius (A)","shell thickness (A)","water thickness","core & solvent SLD (A-2)","Shell SLD (A-2)","number of water/shell pairs","bkg (cm-1)"} |
---|
22 | Edit/K=1 parameters_mss,coef_mss |
---|
23 | ywave_mss := MultiShellForm(coef_mss,xwave_mss) |
---|
24 | Display/K=1 ywave_mss vs xwave_mss |
---|
25 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
26 | Label bottom "q (\\S-1\\M)" |
---|
27 | Label left "Intensity (cm\\S-1\\M)" |
---|
28 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
29 | End |
---|
30 | |
---|
31 | Proc PlotSmearedMultiShell() |
---|
32 | //no input parameters necessary, it MUST use the experimental q-values |
---|
33 | // from the experimental data read in from an AVE/QSIG data file |
---|
34 | |
---|
35 | // if no gQvals wave, data must not have been loaded => abort |
---|
36 | if(Exists("gQvals") != 2) // 2 = string or numeric variable exists |
---|
37 | Abort "6-column QSIG data not loaded. Use LoadQSIGData macro" |
---|
38 | else |
---|
39 | if(WaveExists($gQvals) ==0) //wave ref does not exist |
---|
40 | Abort "6-column QSIG waves are missing. Re-load with LoadQSIGData macro" |
---|
41 | endif |
---|
42 | endif |
---|
43 | |
---|
44 | // Setup parameter table for model function |
---|
45 | make/O/D smear_coef_mss = {1.,60,10,10,6.4e-6,0.4e-6,2,0.001} |
---|
46 | make/O/T smear_parameters_mss = {"scale","core radius (A)","shell thickness (A)","water thickness","core & solvent SLD (A-2)","Shell SLD (A-2)","number of water/shell pairs","bkg (cm-1)"} |
---|
47 | Edit/K=1 smear_parameters_mss,smear_coef_mss |
---|
48 | |
---|
49 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
---|
50 | // make extra copy of experimental q-values for easy plotting |
---|
51 | Duplicate/O $gQvals smeared_mss,smeared_qvals |
---|
52 | SetScale d,0,0,"1/cm",smeared_mss |
---|
53 | |
---|
54 | smeared_mss := SmearedMultiShell(smear_coef_mss,$gQvals) |
---|
55 | Display/K=1 smeared_mss vs smeared_qvals |
---|
56 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
57 | Label bottom "q (\\S-1\\M)" |
---|
58 | Label left "Intensity (cm\\S-1\\M)" |
---|
59 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
60 | End |
---|
61 | |
---|
62 | Function MultiShellForm(w,x) :FitFunc |
---|
63 | Wave w |
---|
64 | Variable x |
---|
65 | |
---|
66 | // variables are: |
---|
67 | //[0] scale factor |
---|
68 | //[1] radius of core [] |
---|
69 | //[2] thickness of the shell [] |
---|
70 | //[3] thickness of the water layer |
---|
71 | //[4] SLD of the core = sld of the solvent[-2] |
---|
72 | //[5] SLD of the shell |
---|
73 | //[6] number of pairs (tw+tsh) |
---|
74 | //[7] background [cm-1] |
---|
75 | |
---|
76 | // All inputs are in ANGSTROMS |
---|
77 | //OUTPUT is normalized by the particle volume, and converted to [cm-1] |
---|
78 | |
---|
79 | |
---|
80 | Variable scale,rcore,tw,ts,rhocore,rhoshel,num,bkg |
---|
81 | scale = w[0] |
---|
82 | rcore = w[1] |
---|
83 | ts = w[2] |
---|
84 | tw = w[3] |
---|
85 | rhocore = w[4] |
---|
86 | rhoshel = w[5] |
---|
87 | num = w[6] |
---|
88 | bkg = w[7] |
---|
89 | |
---|
90 | //calculate with a loop, two shells at a time |
---|
91 | Variable ii=0,fval=0,voli,ri,sldi |
---|
92 | |
---|
93 | do |
---|
94 | ri = rcore + ii*ts + ii*tw |
---|
95 | voli = 4*pi/3*ri^3 |
---|
96 | sldi = rhocore-rhoshel |
---|
97 | fval += voli*sldi*F_func(ri*x) |
---|
98 | ri += ts |
---|
99 | voli = 4*pi/3*ri^3 |
---|
100 | sldi = rhoshel-rhocore |
---|
101 | fval += voli*sldi*F_func(ri*x) |
---|
102 | ii+=1 //do 2 layers at a time |
---|
103 | while(ii<=num-1) //change to make 0 < num < 2 correspond to unilamellar vesicles (C. Glinka, 11/24/03) |
---|
104 | |
---|
105 | fval *=fval //square it |
---|
106 | fval /=voli //normalize by the overall volume |
---|
107 | fval *=scale*1e8 |
---|
108 | fval += bkg |
---|
109 | |
---|
110 | return(fval) |
---|
111 | End |
---|
112 | |
---|
113 | Function F_func(qr) |
---|
114 | Variable qr |
---|
115 | |
---|
116 | Variable val=0 |
---|
117 | |
---|
118 | val = 3*(sin(qr) - qr*cos(qr))/qr^3 |
---|
119 | |
---|
120 | return(val) |
---|
121 | End |
---|
122 | |
---|
123 | |
---|
124 | // |
---|
125 | //Function Schulz_Point_ms(x,avg,zz) |
---|
126 | // |
---|
127 | // //Wave w |
---|
128 | // Variable x,avg,zz |
---|
129 | // Variable dr |
---|
130 | // |
---|
131 | // dr = zz*ln(x) - gammln(zz+1)+(zz+1)*ln((zz+1)/avg)-(x/avg*(zz+1)) |
---|
132 | // |
---|
133 | // return (exp(dr)) |
---|
134 | // |
---|
135 | //End |
---|
136 | |
---|
137 | // this is all there is to the smeared calculation! |
---|
138 | Function SmearedMultiShell(w,x) :FitFunc |
---|
139 | Wave w |
---|
140 | Variable x |
---|
141 | |
---|
142 | Variable ans |
---|
143 | SVAR sq = gSig_Q |
---|
144 | SVAR qb = gQ_bar |
---|
145 | SVAR sh = gShadow |
---|
146 | SVAR gQ = gQVals |
---|
147 | |
---|
148 | //the name of your unsmeared model is the first argument |
---|
149 | ans = Smear_Model_76(MultiShellForm,$sq,$qb,$sh,$gQ,w,x) |
---|
150 | |
---|
151 | return(ans) |
---|
152 | End |
---|