Changeset adc753d in sasmodels
 Timestamp:
 Oct 6, 2016 6:12:24 PM (5 years ago)
 Branches:
 master, core_shell_microgels, costrafo411, magnetic_model, ticket1257vesicleproduct, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
 Children:
 b3f2a24
 Parents:
 a86b9f4
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 1 edited
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sasmodels/models/core_shell_bicelle.py
ra0fee3b radc753d 2 2 Definition 3 3  4 4 5 This model provides the form factor for a circular cylinder with a 5 6 coreshell scattering length density profile. Thus this is a variation … … 8 9 factor is normalized by the particle volume. 9 10 10 .. _coreshellbicellegeometry:11 11 12 12 .. figure:: img/core_shell_bicelle_geometry.png … … 21 21 and core regions in order to estimate appropriate starting parameters. 22 22 23 Given the scattering length densities (sld) $\rho_c$, the core sld, $\rho_f$, 24 the face sld, $\rho_r$, the rim sld and $\rho_s$ the solvent sld, the 25 scattering length density variation along the cylinder axis is: 26 27 .. math:: 28 29 \rho(r) = 30 \begin{cases} 31 &\rho_c \text{ for } 0 \lt r \lt R; L \lt z\lt L \\[1.5ex] 32 &\rho_f \text{ for } 0 \lt r \lt R; (L+2t) \lt z\lt L; 33 L \lt z\lt (L+2t) \\[1.5ex] 34 &\rho_r\text{ for } 0 \lt r \lt R; (L+2t) \lt z\lt L; L \lt z\lt (L+2t) 35 \end{cases} 36 37 The form factor for the bicelle is calculated in cylindrical coordinates, where 38 $\alpha$ is the angle between the $Q$ vector and the cylinder axis, to give: 39 40 .. math:: 41 42 I(Q,\alpha) = \frac{\text{scale}}{V} \cdot 43 F(Q,\alpha)^2 + \text{background} 44 where 45 46 .. math:: 47 48 \begin{align} 49 F(Q,\alpha) = &\frac{1}{V_t} \bigg[ 50 (\rho_c  \rho_f) V_c \frac{J_1(QRsin \alpha)}{QRsin\alpha}\frac{2 \cdot QLcos\alpha}{QLcos\alpha} \\ 51 &+(\rho_f  \rho_r) V_{c+f} \frac{J_1(QRsin\alpha)}{QRsin\alpha}\frac{2 \cdot Q(L+t_f)cos\alpha}{Q(L+t_f)cos\alpha} \\ 52 &+(\rho_r  \rho_s) V_t \frac{J_1(Q(R+t_r)sin\alpha)}{Q(R+t_r)sin\alpha}\frac{2 \cdot Q(L+t_f)cos\alpha}{Q(L+t_f)cos\alpha} 53 \bigg] 54 \end{align} 55 56 where $V_t$ is the total volume of the bicelle, $V_c$ the volume of the core, 57 $V_{c+f}$ the volume of the core plus the volume of the faces, $R$ is the radius 58 of the core, $L$ the length of the core, $t_f$ the thickness of the face, $t_r$ 59 the thickness of the rim and $J_1$ the usual first order bessel function. 60 23 61 The output of the 1D scattering intensity function for randomly oriented 24 cylinders is then given by the equation above.62 cylinders is then given by integrating over all possible $\theta$ and $\phi$. 25 63 26 64 The *theta* and *phi* parameters are not used for the 1D output. … … 40 78  41 79 42 .. [# Matusmori] `N Matsumori and M Murata <http://dx.doi.org/10.1039/C0NP000043 2G>`_, *Nat. Prod. Rep.* 27 (2010) 1480149244 .. [#] L A Feigin and D I Svergun, *Structure Analysis by SmallAngle XRay and45 Neutron Scattering,* Plenum Press, New York, (1987)80 .. [#] D Singh (2009). *Small angle scattering studies of self assembly in 81 lipid mixtures*, John's Hopkins University Thesis (2009) 223225. `Available 82 from Proquest <http://search.proquest.com/docview/304915826?accountid 83 =26379>`_ 46 84 47 85 Authorship and Verification … … 49 87 50 88 * **Author:** NIST IGOR/DANSE **Date:** pre 2010 51 * **Last Modified by:** Paul Butler **Date:** Septmber 30, 2016 52 * **Last Reviewed by:** Under Review **Date:** October 5, 2016 53 89 * **Last Modified by:** Paul Butler **Date:** September 30, 2016 90 * **Last Reviewed by:** Richard Heenan **Date:** October 5, 2016 54 91 """ 55 92
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