# gel_fit

Fitting using fine-scale polymer distribution in a gel.

Parameter | Description | Units | Default value |
---|---|---|---|

scale | Source intensity | None | 1 |

background | Source background | cm^{-1} |
0.001 |

guinier_scale | Guinier length scale | cm^-1 | 1.7 |

lorentz_scale | Lorentzian length scale | cm^-1 | 3.5 |

rg | Radius of gyration | Å | 104 |

fractal_dim | Fractal exponent | None | 2 |

cor_length | Correlation length | Å | 16 |

The returned value is scaled to units of cm^{-1} sr^{-1}, absolute scale.

*This model was implemented by an interested user!*

Unlike a concentrated polymer solution, the fine-scale polymer distribution in a gel involves at least two characteristic length scales, a shorter correlation length ( \(a1\) ) to describe the rapid fluctuations in the position of the polymer chains that ensure thermodynamic equilibrium, and a longer distance (denoted here as \(a2\) ) needed to account for the static accumulations of polymer pinned down by junction points or clusters of such points. The latter is derived from a simple Guinier function. Compare also the gauss_lorentz_gel model.

**Definition**

The scattered intensity \(I(q)\) is calculated as

where

Note that the first term reduces to the Ornstein-Zernicke equation when \(D = 2\); ie, when the Flory exponent is 0.5 (theta conditions). In gels with significant hydrogen bonding \(D\) has been reported to be ~2.6 to 2.8.

**References**

Mitsuhiro Shibayama, Toyoichi Tanaka, Charles C Han,
*J. Chem. Phys.* 1992, 97 (9), 6829-6841

Simon Mallam, Ferenc Horkay, Anne-Marie Hecht, Adrian R Rennie, Erik Geissler,
*Macromolecules* 1991, 24, 543-548