Changes in / [59994557:ec8b9a3] in sasmodels
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- sasmodels/models
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- 2 edited
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sasmodels/models/polymer_micelle.py
rbba9361 ra807206 11 11 12 12 The 1D scattering intensity for this model is calculated according to 13 the equations given by Pedersen (Pedersen, 2000), summarised briefly here. 14 15 The micelle core is imagined as $N\_aggreg$ polymer heads, each of volume $v\_core$, 16 which then defines a micelle core of $radius\_core$, which is a separate parameter 17 even though it could be directly determined. 18 The Gaussian random coil tails, of gyration radius $rg$, are imagined uniformly 19 distributed around the spherical core, centred at a distance $radius\_core + d\_penetration.rg$ 20 from the micelle centre, where $d\_penetration$ is of order unity. 21 A volume $v\_corona$ is defined for each coil. 22 The model in detail seems to separately parametrise the terms for the shape of I(Q) and the 23 relative intensity of each term, so use with caution and check parameters for consistency. 24 The spherical core is monodisperse, so it's intensity and the cross terms may have sharp 25 oscillations (use q resolution smearing if needs be to help remove them). 26 27 .. math:: 28 P(q) = N^2\beta^2_s\Phi(qR)^2+N\beta^2_cP_c(q)+2N^2\beta_s\beta_cS_{sc}s_c(q)+N(N-1)\beta_c^2S_{cc}(q) 29 30 \beta_s = v\_core(sld\_core - sld\_solvent) 31 32 \beta_c = v\_corona(sld\_corona - sld\_solvent) 33 34 where $N = n\_aggreg$, and for the spherical core of radius $R$ 35 36 .. math:: 37 \Phi(qR)= \frac{\sin(qr) - qr\cos(qr)}{(qr)^3} 38 39 whilst for the Gaussian coils 40 41 .. math:: 42 43 P_c(q) &= 2 [\exp(-Z) + Z - 1] / Z^2 44 45 Z &= (q R_g)^2 46 47 The sphere to coil ( core to corona) and coil to coil (corona to corona) cross terms are 48 approximated by: 49 50 .. math:: 51 52 S_{sc}(q)=\Phi(qR)\psi(Z)\frac{sin(q(R+d.R_g))}{q(R+d.R_g)} 53 54 S_{cc}(q)=\psi(Z)^2\left[\frac{sin(q(R+d.R_g))}{q(R+d.R_g)} \right ]^2 55 56 \psi(Z)=\frac{[1-exp^{-Z}]}{Z} 13 the equations given by Pedersen (Pedersen, 2000). 57 14 58 15 Validation 59 16 ---------- 60 17 61 $P(q)$ above is multiplied by $ndensity$, and a units conversion of 10^{-13}, so $scale$ 62 is likely 1.0 if the scattering data is in absolute units. This model has not yet been 63 independently validated. 18 This model has not yet been validated. Feb2015 64 19 65 20 … … 76 31 title = "Polymer micelle model" 77 32 description = """ 78 This model provides the form factor, $P(q)$, for a micelle with a spherical 79 core and Gaussian polymer chains attached to the surface, thus may be applied 80 to block copolymer micelles. To work well the Gaussian chains must be much 81 smaller than the core, which is often not the case. Please study the 82 reference to Pedersen and full documentation carefully. 33 This model provides an approximate form factor, P(q), for a micelle with 34 a spherical core with Gaussian polymer chains attached to the surface. 83 35 """ 84 85 86 36 category = "shape:sphere" 87 37 -
sasmodels/models/spinodal.py
rbba9361 r43fe34b 5 5 This model calculates the SAS signal of a phase separating solution under spinodal decomposition. 6 6 The scattering intensity $I(q)$ is calculated as 7 8 .. math:: 9 I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B 10 11 where $x=q/q_0$ and $B$ is a flat background. The characteristic structure length 12 scales with the correlation peak at $q_0$. The exponent $\gamma$ is equal to 7 .. math:: I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B 8 where $x=q/q_0$ and $B$ is a flat background. The characteristic structure length 9 scales with the correlation peak at $q_0$. The exponent $\gamma$ is equal to 13 10 $d+1$ with d the dimensionality of the off-critical concentration mixtures. 14 A transition to $\gamma=2 d$ is seen near the percolation threshold into the11 A transition to $\gamma=2 d$is seen near the percolation treshold into the 15 12 critical concentration regime. 16 13 … … 46 43 # pylint: disable=bad-whitespace, line-too-long 47 44 # ["name", "units", default, [lower, upper], "type", "description"], 48 parameters = [["scale", "", 49 ["gamma", "", 3.0, [-inf, inf], "", "Exponent"],45 parameters = [["scale", "", 1.0, [-inf, inf], "", "Scale factor"], 46 ["gamma", "", 3.0, [-inf, inf], "", "Exponent"], 50 47 ["q_0", "1/Ang", 0.1, [-inf, inf], "", "Correlation peak position"] 51 48 ]
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