Changeset cb97bff in sasmodels for sasmodels/models/mono_gauss_coil.py
- Timestamp:
- Mar 16, 2016 4:59:52 PM (8 years ago)
- Branches:
- master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
- Children:
- 310ddcb, bf227cd
- Parents:
- 38d2c97 (diff), 5be92e8 (diff)
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sasmodels/models/mono_gauss_coil.py
r38d2c97 rcb97bff 6 6 7 7 r""" 8 This model strictly describes the scattering from *monodisperse* polymer chains in theta solvents or polymer melts, conditions under which the distances between segments follow a Gaussian distribution. Provided the number of segments is large (ie, high molecular weight polymers) the single-chain Form Factor P(Q) is that described by Debye (1947).8 This model strictly describes the scattering from *monodisperse* polymer chains in theta solvents or polymer melts, conditions under which the distances between segments follow a Gaussian distribution. Provided the number of segments is large (ie, high molecular weight polymers) the single-chain form factor P(Q) is that described by Debye (1947). 9 9 10 10 To describe the scattering from *polydisperse* polymer chains, see the poly_gauss_coil model. … … 13 13 ---------- 14 14 15 *I(q)* = *scale* x*P(q)* + *background*15 *I(q)* = *scale* |cdot| *P(q)* + *background* 16 16 17 17 where 18 18 19 *scale* = |phi|\ :sub:`poly` x *V* x (|rho|\ :sub:`poly` - |rho|\ :sub:`solv`)\ :sup:'2'19 *scale* = |phi|\ :sub:`poly` |cdot| *V* |cdot| (|rho|\ :sub:`poly` - |rho|\ :sub:`solv`)\ :sup:`2` 20 20 21 *P(q)* = 2 [exp(-Z) + Z - 1] / Z \ :sup:'2'21 *P(q)* = 2 [exp(-Z) + Z - 1] / Z \ :sup:`2` 22 22 23 *Z* = (*q R* \ :sub:'g')\ :sup:'2'23 *Z* = (*q R* \ :sub:`g`)\ :sup:`2` 24 24 25 25 and 26 26 27 *V* = *M* / (*N*\ :sub: 'A'|delta|)27 *V* = *M* / (*N*\ :sub:`A` |delta|) 28 28 29 Here, |phi|\ :sub:`poly` , is the volume fraction of polymer, *V* is the volume of a polymer coil, *M* is the molecular weight of the polymer, *N*\ :sub:'A' is Avogadro's Number, |delta| is the bulk density of the polymer, |rho|\ :sub:`poly` is the sld of the polymer, |rho|\ :sub:`solv` is the sld of the solvent, and *R*\ :sub:'g'is the radius of gyration of the polymer coil.29 Here, |phi|\ :sub:`poly` is the volume fraction of polymer, *V* is the volume of a polymer coil, *M* is the molecular weight of the polymer, *N*\ :sub:`A` is Avogadro's Number, |delta| is the bulk density of the polymer, |rho|\ :sub:`poly` is the sld of the polymer, |rho|\ :sub:`solv` is the sld of the solvent, and *R*\ :sub:`g` is the radius of gyration of the polymer coil. 30 30 31 31 .. figure:: img/mono_gauss_coil_1d.jpg
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