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src/sans/models/media/model_functions.rst (modified) (61 diffs)
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src/sans/models/media/model_functions.rst
r990c2eb rbf8c07b 181 181 - CoreShellEllipsoidModel_ 182 182 - CoreShellEllipsoidXTModel_ 183 - TriaxialEllipsoidModel 183 - TriaxialEllipsoidModel_ 184 184 185 185 Lamellae … … 202 202 -------------- 203 203 204 - ParallelepipedModel (including magnetic 2D version)205 - CSParallelepipedModel 204 - ParallelepipedModel_ (including magnetic 2D version) 205 - CSParallelepipedModel_ 206 206 207 207 .. _Shape-independent: … … 355 355 356 356 REFERENCE 357 357 358 A. Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955) 358 359 … … 419 420 420 421 REFERENCE 422 421 423 N. W. Ashcroft and D. C. Langreth, *Physical Review*, 156 (1967) 685-692 422 424 [Errata found in *Phys. Rev.* 166 (1968) 934] … … 481 483 482 484 REFERENCE 485 483 486 M. Stieger, J. S. Pedersen, P. Lindner, W. Richtering, *Langmuir*, 20 (2004) 7283-7292 484 487 … … 537 540 538 541 REFERENCE 542 539 543 K. Larson-Smith, A. Jackson, and D.C. Pozzo, *Small angle scattering model for Pickering emulsions and raspberry* 540 544 *particles*, *Journal of Colloid and Interface Science*, 343(1) (2010) 36-41 … … 587 591 588 592 REFERENCE 593 589 594 A. Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955) 590 595 … … 666 671 667 672 REFERENCE 668 See the CoreShell documentation. 673 674 See the CoreShellModel_ documentation. 669 675 670 676 … … 719 725 720 726 REFERENCE 727 721 728 S. King, P. Griffiths, J. Hone, and T. Cosgrove, *SANS from Adsorbed Polymer Layers*, 722 729 *Macromol. Symp.*, 190 (2002) 33-42 … … 766 773 767 774 REFERENCE 775 768 776 B. Cabane, *Small Angle Scattering Methods*, in *Surfactant Solutions: New Methods of Investigation*, Ch.2, 769 777 Surfactant Science Series Vol. 22, Ed. R. Zana and M. Dekker, New York, (1987). … … 884 892 885 893 REFERENCE 894 886 895 L. A. Feigin and D. I. Svergun, *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, 887 896 Plenum Press, New York, (1987). … … 943 952 944 953 REFERENCE 954 945 955 A. Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955) 946 956 … … 1071 1081 1072 1082 REFERENCE 1083 1073 1084 L. A. Feigin and D. I. Svergun, *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, 1074 1085 Plenum Press, New York, (1987) … … 1116 1127 1117 1128 REFERENCE 1129 1118 1130 A. V. Dobrynin, M. Rubinstein and S. P. Obukhov, *Macromol.*, 29 (1996) 2974-2979 1119 1131 … … 1180 1192 1181 1193 REFERENCE 1194 1182 1195 R. Schweins and K. Huber, *Particle Scattering Factor of Pearl Necklace Chains*, *Macromol. Symp.* 211 (2004) 25-42 2004 1183 1196 … … 1328 1341 1329 1342 REFERENCE 1343 1330 1344 L. A. Feigin and D. I. Svergun, *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, Plenum Press, 1331 1345 New York, (1987) … … 1412 1426 1413 1427 REFERENCE 1428 1414 1429 H. Kaya, *J. Appl. Cryst.*, 37 (2004) 223-230 1430 1415 1431 H. Kaya and N-R deSouza, *J. Appl. Cryst.*, 37 (2004) 508-509 (addenda and errata) 1416 1432 … … 1595 1611 1596 1612 REFERENCE 1613 1597 1614 L. A. Feigin and D. I. Svergun, *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, Plenum, 1598 1615 New York, (1987) … … 1654 1671 1655 1672 REFERENCE 1673 1656 1674 J. S. Pedersen and P. Schurtenberger. *Scattering functions of semiflexible polymers with and without excluded volume* 1657 1675 *effects*. *Macromolecules*, 29 (1996) 7602-7612 1658 1676 1659 1677 Correction of the formula can be found in 1678 1660 1679 W-R Chen, P. D. Butler and L. J. Magid, *Incorporating Intermicellar Interactions in the Fitting of SANS Data from* 1661 1680 *Cationic Wormlike Micelles*. *Langmuir*, 22(15) 2006 6539â6548 … … 1740 1759 1741 1760 REFERENCE 1761 1742 1762 J. S. Pedersen and P. Schurtenberger. *Scattering functions of semiflexible polymers with and without excluded volume* 1743 1763 *effects*. *Macromolecules*, 29 (1996) 7602-7612 1744 1764 1745 1765 Correction of the formula can be found in 1766 1746 1767 W-R Chen, P. D. Butler and L. J. Magid, *Incorporating Intermicellar Interactions in the Fitting of SANS Data from* 1747 1768 *Cationic Wormlike Micelles*. *Langmuir*, 22(15) 2006 6539â6548 … … 1801 1822 1802 1823 REFERENCE 1824 1803 1825 L. A. Feigin and D. I. Svergun, *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, Plenum Press, 1804 1826 New York, (1987) … … 1888 1910 1889 1911 REFERENCE 1912 1890 1913 H. Kaya, *J. Appl. Cryst.*, 37 (2004) 37 223-230 1914 1891 1915 H. Kaya and N-R deSouza, *J. Appl. Cryst.*, 37 (2004) 508-509 (addenda and errata) 1892 1916 … … 1973 1997 1974 1998 REFERENCE 1999 1975 2000 A. Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, 1955 2001 1976 2002 O. Kratky and G. Porod, *J. Colloid Science*, 4, (1949) 35 2003 1977 2004 J. S. Higgins and H. C. Benoit, *Polymers and Neutron Scattering*, Clarendon, Oxford, 1994 1978 2005 … … 2019 2046 2020 2047 REFERENCE 2048 2021 2049 S. Alexandru Rautu, Private Communication. 2022 2050 … … 2114 2142 2115 2143 REFERENCE 2144 2116 2145 L. A. Feigin and D. I. Svergun. *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, Plenum, 2117 2146 New York, 1987. … … 2177 2206 2178 2207 REFERENCE 2208 2179 2209 M. Kotlarchyk, S.-H. Chen, *J. Chem. Phys.*, 79 (1983) 2461 2210 2180 2211 S. J. Berr, *Phys. Chem.*, 91 (1987) 4760 2181 2212 … … 2240 2271 2241 2272 REFERENCE 2273 2242 2274 R. K. Heenan, Private communication 2243 2275 2244 2276 2245 2277 2246 .. _TriaxialEllipsoid alModel:2278 .. _TriaxialEllipsoidModel: 2247 2279 2248 2280 **2.1.28. TriaxialEllipsoidModel** … … 2314 2346 2315 2347 REFERENCE 2348 2316 2349 L. A. Feigin and D. I. Svergun, *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, Plenum, 2317 2350 New York, 1987. … … 2366 2399 REFERENCE 2367 2400 2368 Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502. 2369 2370 also in J. Phys. Chem. B, 105, (2001) 11081-11088 .2401 F. Nallet, R. Laversanne, and D. Roux, J. Phys. II France, 3, (1993) 487-502 2402 2403 also in J. Phys. Chem. B, 105, (2001) 11081-11088 2371 2404 2372 2405 … … 2423 2456 REFERENCE 2424 2457 2425 Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502. 2426 2427 also in J. Phys. Chem. B, 105, (2001) 11081-11088 .2458 F. Nallet, R. Laversanne, and D. Roux, J. Phys. II France, 3, (1993) 487-502 2459 2460 also in J. Phys. Chem. B, 105, (2001) 11081-11088 2428 2461 2429 2462 … … 2493 2526 REFERENCE 2494 2527 2495 Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502. 2496 2497 also in J. Phys. Chem. B, 105, (2001) 11081-11088 .2528 F. Nallet, R. Laversanne, and D. Roux, J. Phys. II France, 3, (1993) 487-502 2529 2530 also in J. Phys. Chem. B, 105, (2001) 11081-11088 2498 2531 2499 2532 … … 2574 2607 REFERENCE 2575 2608 2576 Nallet, Laversanne, and Roux, J. Phys. II France, 3, (1993) 487-502. 2577 2578 also in J. Phys. Chem. B, 105, (2001) 11081-11088 .2609 F. Nallet, R. Laversanne, and D. Roux, J. Phys. II France, 3, (1993) 487-502 2610 2611 also in J. Phys. Chem. B, 105, (2001) 11081-11088 2579 2612 2580 2613 … … 2643 2676 REFERENCE 2644 2677 2645 M. Bergstrom, J. S. Pedersen, P. Schurtenberger, S. U. Egelhaaf, J. 2646 Phys. Chem. B, 103 (1999) 9888-9897. 2678 M. Bergstrom, J. S. Pedersen, P. Schurtenberger, S. U. Egelhaaf, *J. Phys. Chem. B*, 103 (1999) 9888-9897 2647 2679 2648 2680 … … 2705 2737 triple integral. Very, very slow. Go get lunch. 2706 2738 2707 REFERENCE S2708 2709 Hideki Matsuoka et. al. Physical Review B, 36 (1987) 1754-1765.2739 REFERENCE 2740 2741 Hideki Matsuoka et. al. *Physical Review B*, 36 (1987) 1754-1765 2710 2742 (Original Paper) 2711 2743 2712 Hideki Matsuoka et. al. Physical Review B, 41 (1990) 3854 -3856.2744 Hideki Matsuoka et. al. *Physical Review B*, 41 (1990) 3854 -3856 2713 2745 (Corrections to FCC and BCC lattice structure calculation) 2714 2746 … … 2725 2757 ============== ======== ============= 2726 2758 2727 TEST DATASET 2759 2728 2760 2729 2761 This example dataset is produced using 200 data points, *qmin* = 0.01 … … 2815 2847 triple integral. Very, very slow. Go get lunch. 2816 2848 2817 REFERENCE S2818 2819 Hideki Matsuoka et. al. Physical Review B, 36 (1987) 1754-1765.2849 REFERENCE 2850 2851 Hideki Matsuoka et. al. *Physical Review B*, 36 (1987) 1754-1765 2820 2852 (Original Paper) 2821 2853 2822 Hideki Matsuoka et. al. Physical Review B, 41 (1990) 3854 -3856.2854 Hideki Matsuoka et. al. *Physical Review B*, 41 (1990) 3854 -3856 2823 2855 (Corrections to FCC and BCC lattice structure calculation) 2824 2856 … … 2835 2867 ============== ======== ============= 2836 2868 2837 TEST DATASET2838 2839 2869 This example dataset is produced using 200 data points, *qmin* = 0.01 2840 2870 -1, *qmax* = 0.1 -1 and the above default values. … … 2913 2943 triple integral. Very, very slow. Go get lunch. 2914 2944 2915 REFERENCE S2916 2917 Hideki Matsuoka et. al. Physical Review B, 36 (1987) 1754-1765.2945 REFERENCE 2946 2947 Hideki Matsuoka et. al. *Physical Review B*, 36 (1987) 1754-1765 2918 2948 (Original Paper) 2919 2949 2920 Hideki Matsuoka et. al. Physical Review B, 41 (1990) 3854 -3856.2950 Hideki Matsuoka et. al. *Physical Review B*, 41 (1990) 3854 -3856 2921 2951 (Corrections to FCC and BCC lattice structure calculation) 2922 2952 … … 2933 2963 ============== ======== ============= 2934 2964 2935 TEST DATASET 2965 2936 2966 2937 2967 This example dataset is produced using 200 data points, *qmin* = 0.001 … … 2968 2998 **2.1.37. ParallelepipedModel** 2969 2999 2970 This model provides the form factor, *P(q)*, for a rectangular 2971 cylinder (below) where the form factor is normalized by the volume of 2972 the cylinder. P(q) = scale*<f^2>/V+background where the volume V= ABC 2973 and the averaging < > is applied over all orientation for 1D. 3000 This model provides the form factor, *P(q)*, for a rectangular cylinder (below) where the form factor is normalized by 3001 the volume of the cylinder. 3002 3003 *P(q)* = *scale* \* <*f*\ :sup:`2`> / *V* + *background* 3004 3005 where the volume *V* = *A B C* and the averaging < > is applied over all orientations for 1D. 2974 3006 2975 3007 For information about polarised and magnetic scattering, click here_. 2976 3008 2977 2978 2979 2980 2981 The side of the solid must be satisfied the condition of A<B 2982 2983 By this definition, assuming 2984 2985 a = A/B<1; b=B/B=1; c=C/B>1, the form factor, 2986 2987 2988 2989 The contrast is defined as 2990 2991 2992 2993 The scattering intensity per unit volume is returned in the unit of 2994 |cm^-1|; I(q) = fP(q). 2995 2996 For P*S: The 2nd virial coefficient of the solid cylinder is calculate 2997 based on the averaged effective radius (= sqrt(short_a*short_b/pi)) 2998 and length( = long_c) values, and used as the effective radius toward 2999 S(Q) when P(Q)*S(Q) is applied. 3000 3001 To provide easy access to the orientation of the parallelepiped, we 3002 define the axis of the cylinder using two angles , andY. Similarly to 3003 the case of the cylinder, those angles, and , are defined on Figure 2 3004 of CylinderModel. The angle Y is the rotational angle around its own 3005 long_c axis against the q plane. For example, Y = 0 when the short_b 3006 axis is parallel to the x-axis of the detector. 3007 3008 3009 .. image:: img/image087.JPG 3010 3011 *2.1.37.1. Definition* 3012 3013 **The edge of the solid must satisfy the condition that** *A* < *B*. Then, assuming *a* = *A* / *B* < 1, 3014 *b* = *B* / *B* = 1, and *c* = *C* / *B* > 1, the form factor is 3015 3016 .. image:: img/image088.PNG 3017 3018 and the contrast is defined as 3019 3020 .. image:: img/image089.PNG 3021 3022 The scattering intensity per unit volume is returned in units of |cm^-1|; ie, *I(q)* = |phi| *P(q)*\ . 3023 3024 NB: The 2nd virial coefficient of the parallelpiped is calculated based on the the averaged effective radius 3025 (= sqrt(*short_a* \* *short_b* / |pi|)) and length(= *long_c*) values, and used as the effective radius for 3026 *S(Q)* when *P(Q)* \* *S(Q)* is applied. 3027 3028 To provide easy access to the orientation of the parallelepiped, we define the axis of the cylinder using three angles 3029 |theta|, |phi| and |bigpsi|. These angles are defined on Figure 2 of the CylinderModel_. The angle |bigpsi| is the 3030 rotational angle around the *long_c* axis against the *q* plane. For example, |bigpsi| = 0 when the *short_b* axis is 3031 parallel to the *x*-axis of the detector. 3032 3033 .. image:: img/image090.JPG 3009 3034 3010 3035 *Figure. Definition of angles for 2D*. 3011 3036 3012 3013 3014 Figure. Examples of the angles for oriented pp against the detector 3015 plane. 3037 .. image:: img/image091.JPG 3038 3039 *Figure. Examples of the angles for oriented pp against the detector plane.* 3016 3040 3017 3041 ============== ======== ============= … … 3026 3050 ============== ======== ============= 3027 3051 3028 3052 .. image:: img/image092.JPG 3029 3053 3030 3054 *Figure. 1D plot using the default values (w/1000 data point).* 3031 3055 3032 *Validation of the parallelepiped 2D model* 3033 3034 Validation of our code was done by comparing the output of the 1D 3035 calculation to the angular average of the output of 2 D calculation 3036 over all possible angles. The Figure below shows the comparison where 3037 the solid dot refers to averaged 2D while the line represents the 3038 result of 1D calculation (for the averaging, 76, 180, 76 points are 3039 taken over the angles of theta, phi, and psi respectively). 3040 3041 3056 *2.1.37.2. Validation of the parallelepiped 2D model* 3057 3058 Validation of our code was done by comparing the output of the 1D calculation to the angular average of the output of 3059 a 2D calculation over all possible angles. The Figure below shows the comparison where the solid dot refers to averaged 3060 2D while the line represents the result of the 1D calculation (for the averaging, 76, 180, 76 points are taken for the 3061 angles of |theta|, |phi|, and |psi| respectively). 3062 3063 .. image:: img/image093.GIF 3042 3064 3043 3065 *Figure. Comparison between 1D and averaged 2D.* 3044 3066 3045 Our model uses the form factor calculations implemented in a c-library 3046 provided by the NIST Center for Neutron Research (Kline, 2006): 3047 3048 REFERENCE 3049 3050 Mittelbach and Porod, Acta Physica Austriaca 14 (1961) 185-211. 3051 3067 Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research 3068 (Kline, 2006). 3069 3070 REFERENCE 3071 3072 P. Mittelbach and G. Porod, *Acta Physica Austriaca*, 14 (1961) 185-211 3052 3073 Equations (1), (13-14). (in German) 3053 3074 … … 3058 3079 **2.1.38. CSParallelepipedModel** 3059 3080 3060 Calculates the form factor for a rectangular solid with a core-shell 3061 structure. The thickness and the scattering length density of the 3062 shell or "rim" can be different on all three (pairs) of faces. The 3063 form factor is normalized by the particle volume such that P(q) = 3064 scale*<f^2>/Vol + bkg, where < > is an average over all possible 3065 orientations of the rectangular solid. An instrument resolution 3066 smeared version is also provided. 3067 3068 The function calculated is the form factor of the rectangular solid 3069 below. The core of the solid is defined by the dimensions ABC such 3070 that A < B < C. 3071 3072 3073 3074 There are rectangular "slabs" of thickness tA that add to the A 3075 dimension (on the BC faces). There are similar slabs on the AC (=tB) 3076 and AB (=tC) faces. The projection in the AB plane is then: 3077 3078 3079 3080 The volume of the solid is: 3081 3082 3083 3084 meaning that there are "gaps" at the corners of the solid. 3085 3086 The intensity calculated follows the parallelepiped model, with the 3087 core-shell intensity being calculated as the square of the sum of the 3088 amplitudes of the core and shell, in the same manner as a core-shell 3089 sphere. 3090 3091 For the calculation of the form factor to be valid, the sides of the 3092 solid MUST be chosen such that A < B < C. If this inequality in not 3093 satisfied, the model will not report an error, and the calculation 3094 will not be correct. 3095 3096 FITTING NOTES: 3097 3098 If the scale is set equal to the particle volume fraction, f, the 3099 returned value is the scattered intensity per unit volume, I(q) = 3100 f*P(q). However, no interparticle interference effects are included in 3101 this calculation. 3102 3103 There are many parameters in this model. Hold as many fixed as 3104 possible with known values, or you will certainly end up at a solution 3105 that is unphysical. 3106 3107 Constraints must be applied during fitting to ensure that the 3108 inequality A < B < C is not violated. The calculation will not report 3109 an error, but the results will not be correct. 3081 Calculates the form factor for a rectangular solid with a core-shell structure. **The thickness and the scattering** 3082 **length density of the shell or "rim" can be different on all three (pairs) of faces.** 3083 3084 The form factor is normalized by the particle volume *V* such that 3085 3086 *P(q)* = *scale* \* <*f*\ :sup:`2`> / *V* + *background* 3087 3088 where < > is an average over all possible orientations of the rectangular solid. 3089 3090 An instrument resolution smeared version of the model is also provided. 3091 3092 *2.1.38.1. Definition* 3093 3094 The function calculated is the form factor of the rectangular solid below. The core of the solid is defined by the 3095 dimensions *A*, *B*, *C* such that *A* < *B* < *C*. 3096 3097 .. image:: img/image087.JPG 3098 3099 There are rectangular "slabs" of thickness *tA* that add to the *A* dimension (on the *BC* faces). There are similar 3100 slabs on the *AC* (= *tB*) and *AB* (= *tC*) faces. The projection in the *AB* plane is then 3101 3102 .. image:: img/image094.JPG 3103 3104 The volume of the solid is 3105 3106 .. image:: img/image095.PNG 3107 3108 **meaning that there are "gaps" at the corners of the solid.** 3109 3110 The intensity calculated follows the ParallelepipedModel_, with the core-shell intensity being calculated as the 3111 square of the sum of the amplitudes of the core and shell, in the same manner as a CoreShellModel_. 3112 3113 **For the calculation of the form factor to be valid, the sides of the solid MUST be chosen such that** *A* < *B* < *C*. 3114 **If this inequality is not satisfied, the model will not report an error, and the calculation will not be correct.** 3115 3116 FITTING NOTES 3117 If the scale is set equal to the particle volume fraction, |phi|, the returned value is the scattered intensity per 3118 unit volume; ie, *I(q)* = |phi| *P(q)*\ . However, **no interparticle interference effects are included in this** 3119 **calculation.** 3120 3121 There are many parameters in this model. Hold as many fixed as possible with known values, or you will certainly end 3122 up at a solution that is unphysical. 3123 3124 Constraints must be applied during fitting to ensure that the inequality *A* < *B* < *C* is not violated. The 3125 calculation will not report an error, but the results will not be correct. 3110 3126 3111 3127 The returned value is in units of |cm^-1|, on absolute scale. 3112 3128 3113 For P*S: The 2nd virial coefficient of this CSPP is calculate based on 3114 the averaged effective radius (= 3115 sqrt((short_a+2*rim_a)*(short_b+2*rim_b)/pi)) and length( = 3116 long_c+2*rim_c) values, and used as the effective radius toward S(Q) 3117 when P(Q)*S(Q) is applied. 3118 3119 To provide easy access to the orientation of the CSparallelepiped, we 3120 define the axis of the cylinder using two angles , andY. Similarly to 3121 the case of the cylinder, those angles, and , are defined on Figure 2 3122 of CylinderModel. The angle Y is the rotational angle around its own 3123 long_c axis against the q plane. For example, Y = 0 when the short_b 3124 axis is parallel to the x-axis of the detector. 3125 3126 3129 NB: The 2nd virial coefficient of the CSParallelpiped is calculated based on the the averaged effective radius 3130 (= sqrt((*short_a* + 2 *rim_a*) \* (*short_b* + 2 *rim_b*) / |pi|)) and length(= *long_c* + 2 *rim_c*) values, and 3131 used as the effective radius for *S(Q)* when *P(Q)* \* *S(Q)* is applied. 3132 3133 To provide easy access to the orientation of the parallelepiped, we define the axis of the cylinder using three angles 3134 |theta|, |phi| and |bigpsi|. These angles are defined on Figure 2 of the CylinderModel_. The angle |bigpsi| is the 3135 rotational angle around the *long_c* axis against the *q* plane. For example, |bigpsi| = 0 when the *short_b* axis is 3136 parallel to the *x*-axis of the detector. 3137 3138 .. image:: img/image090.JPG 3127 3139 3128 3140 *Figure. Definition of angles for 2D*. 3129 3141 3130 3131 3132 Figure. Examples of the angles for oriented cspp against the detector 3133 plane. 3134 3135 TEST DATASET 3136 3137 This example dataset is produced by running the Macro 3138 Plot_CSParallelepiped(), using 100 data points, *qmin* = 0.001 |Ang^-1|, *qmax* 3139 = 0.7 -1 and the below default values. 3142 .. image:: img/image091.JPG 3143 3144 *Figure. Examples of the angles for oriented cspp against the detector plane.* 3145 3146 This example dataset was produced by running the Macro Plot_CSParallelepiped(), using 100 data points, 3147 *qmin* = 0.001 |Ang^-1|, *qmax* = 0.7 |Ang^-1| and the default values 3140 3148 3141 3149 ============== ======== ============= … … 3157 3165 ============== ======== ============= 3158 3166 3159 3167 .. image:: img/image096.JPG 3160 3168 3161 3169 *Figure. 1D plot using the default values (w/256 data points).* 3162 3170 3163 3164 3165 3166 3167 *Figure. 2D plot using the default values (w/(256X265) data 3168 points).* 3169 3170 Our model uses the form factor calculations implemented in a c-library 3171 provided by the NIST Center for Neutron Research (Kline, 2006): 3172 3173 REFERENCE 3174 3175 see: Mittelbach and Porod, Acta Physica Austriaca 14 (1961) 185-211. 3176 3177 Equations (1), (13-14). (yes, it's in German) 3171 .. image:: img/image097.JPG 3172 3173 *Figure. 2D plot using the default values (w/(256X265) data points).* 3174 3175 Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research 3176 (Kline, 2006). 3177 3178 REFERENCE 3179 3180 P. Mittelbach and G. Porod, *Acta Physica Austriaca*, 14 (1961) 185-211 3181 Equations (1), (13-14). (in German) 3178 3182 3179 3183 … … 3230 3234 3231 3235 3232 Reference: Roe, R.-J., "Methods of X-Ray and Neutron Scattering in 3233 Polymer Science", Oxford University Press, New York (2000). 3236 REFERENCE 3237 3238 R. J. Roe, *Methods of X-Ray and Neutron Scattering in Polymer Science*, Oxford University Press, New York (2000). 3234 3239 3235 3240 *3.2. BroadPeak Model* … … 3307 3312 3308 3313 3309 Reference: None. 3314 REFERENCE 3315 3316 *None* 3310 3317 3311 3318 2013/09/09 - Description reviewed by King, S. and Parker, P. … … 3380 3387 REFERENCE 3381 3388 3382 B. Hammouda, D.L. Ho and S.R. Kline, Insight into Clustering in3383 Poly(ethylene oxide) Solutions, Macromolecules 37, 6932-6937 (2004). 3389 B. Hammouda, D.L. Ho and S.R. Kline, *Insight into Clustering in Poly(ethylene oxide) Solutions*, 3390 *Macromolecules*, 37 (2004) 6932-6937 3384 3391 3385 3392 2013/09/09 - Description reviewed by King, S. and Parker, P. … … 3487 3494 REFERENCE 3488 3495 3489 Debye, Anderson, Brumberger, "Scattering by an Inhomogeneous Solid. 3490 II. The Correlation Function and its Application", J. Appl. Phys. 28 3491 (6), 679 (1957). 3492 3493 3494 3495 Debye, Bueche, "Scattering by an Inhomogeneous Solid", J. Appl. Phys. 3496 20, 518 (1949). 3496 Debye, Bueche, *Scattering by an Inhomogeneous Solid*, *J. Appl. Phys.*, 20 (1949) 518 3497 3498 Debye, Anderson, Brumberger, *Scattering by an Inhomogeneous Solid. II. The Correlation Function and its Application*, 3499 *J. Appl. Phys.*, 28(6), (1957) 679 3497 3500 3498 3501 2013/09/09 - Description reviewed by King, S. and Parker, P. … … 3593 3596 REFERENCE 3594 3597 3595 Teubner, M; Strey, R. J. Chem. Phys., 87, 3195 (1987) .3598 Teubner, M; Strey, R. J. Chem. Phys., 87, 3195 (1987) 3596 3599 3597 3600 … … 4095 4098 4096 4099 4097 REFERENCE :4100 REFERENCE 4098 4101 4099 4102 G. Evmenenko, E. Theunissen, K. Mortensen, H. Reynaers, Polymer 42 … … 4180 4183 4181 4184 Moussaid, A., Schosseler, F., Munch, J.-P., Candau, S. J. Journal de 4182 Physique II France 4183 4184 3, 573 (1993). 4185 Physique II France, 3, 573 (1993). 4185 4186 4186 4187 Raphal, E., Joanny, J.-F., Europhysics Letters 11, 179 (1990). … … 4375 4376 Parameters I0, B, qpk, and BGD can all be adjusted during fitting. 4376 4377 4377 REFERENCE: None 4378 REFERENCE 4379 4380 *None* 4378 4381 4379 4382 For 2D plot, the wave transfer is defined as . … … 4432 4435 The parameters I0, B, qpk, and BGD can all be adjusted during fitting. 4433 4436 4434 REFERENCE: None 4437 REFERENCE 4438 4439 *None* 4435 4440 4436 4441 For 2D plot, the wave transfer is defined as . … … 4498 4503 For 2D plot, the wave transfer is defined as . 4499 4504 4500 TEST DATASET 4505 4501 4506 4502 4507 This example dataset is produced by running the Poly_GaussCoil, using … … 4542 4547 4543 4548 4544 R eference:4549 REFERENCE 4545 4550 4546 4551 Glatter & Kratky - pg.404. 4547 4552 4548 J.S. Higgins, and H.C. Benoit, Polymers and Neutron Scattering, Oxford 4549 Science 4550 4551 Publications (1996). 4553 J.S. Higgins, and H.C. Benoit, Polymers and Neutron Scattering, Oxford Science Publications (1996). 4552 4554 4553 4555 *3.21. PolymerExclVolume (Model)* … … 4619 4621 Benoit, H., Comptes Rendus (1957). 245, 2244-2247. 4620 4622 4621 Hammouda, B., SANS from Homogeneous Polymer Mixtures A Unified 4622 Overview, Advances in Polym. Sci. (1993), 106, 87-133. 4623 Hammouda, B., SANS from Homogeneous Polymer Mixtures A Unified Overview, Advances in Polym. Sci. (1993), 106, 87-133. 4623 4624 4624 4625 For 2D plot, the wave transfer is defined as . 4625 4626 4626 TEST DATASET 4627 4627 4628 4628 4629 This example dataset is produced, using 200 data points, *qmin* = 0.001 … … 4884 4885 4885 4886 4886 *REFERENCE: None* 4887 REFERENCE 4888 4889 *None* 4887 4890 4888 4891 *3.24. TwoPowerLaw(Model)* … … 5258 5261 5259 5262 REFERENCE 5263 5260 5264 H. Benoit, J. Polymer Science., 11, 596-599 (1953) 5261 5265 … … 5299 5303 5300 5304 REFERENCE 5305 5301 5306 J. K. Percus, J. Yevick, *J. Phys. Rev.*, 110, (1958) 1 5302 5307 … … 5341 5346 5342 5347 REFERENCE 5348 5343 5349 R. V. Sharma, K. C. Sharma, *Physica*, 89A (1977) 213 5344 5350 … … 5381 5387 5382 5388 REFERENCE 5389 5383 5390 J. B. Hayter and J. Penfold, *Molecular Physics*, 42 (1981) 109-118 5391 5384 5392 J. P. Hansen and J. B. Hayter, *Molecular Physics*, 46 (1982) 651-656 5385 5393 … … 5436 5444 5437 5445 REFERENCE 5446 5438 5447 S. V. G. Menon, C. Manohar, and K. S. Rao, *J. Chem. Phys.*, 95(12) (1991) 9186-9190 5439 5448
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