teubner_strey

Teubner-Strey model of microemulsions

Parameter Description Units Default value
scale Scale factor or Volume fraction None 1
background Source background cm-1 0.001
volfraction_a Volume fraction of phase a None 0.5
sld_a SLD of phase a 10-6-2 0.3
sld_b SLD of phase b 10-6-2 6.3
d Domain size (periodicity) 100
xi Correlation length 30

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

Definition

This model calculates the scattered intensity of a two-component system using the Teubner-Strey model. Unlike dab this function generates a peak. A two-phase material can be characterised by two length scales - a correlation length and a domain size (periodicity).

The original paper by Teubner and Strey defined the function as:

I(q)1a2+c1q2+c2q4+background

where the parameters a2, c1 and c2 are defined in terms of the periodicity, d, and correlation length ξ as:

a2=[1+(2πξd)2]2c1=2ξ2(2πξd)2+2ξ2c2=ξ4

and thus, the periodicity, d is given by

d=2π[12(a2c2)1/214c1c2]1/2

and the correlation length, ξ, is given by

ξ=[12(a2c2)1/2+14c1c2]1/2

Here the model is parameterised in terms of d and ξ and with an explicit volume fraction for one phase, ϕa, and contrast, δρ2=(ρaρb)2 :

I(q)=8πϕa(1ϕa)(Δρ)2c2/ξa2+c1q2+c2q4

where 8πϕa(1ϕa)(Δρ)2c2/ξ is the constant of proportionality from the first equation above.

In the case of a microemulsion, a2>0, c1<0, and c2>0.

For 2D data, scattering intensity is calculated in the same way as 1D, where the q vector is defined as

q=q2x+q2y
../../_images/teubner_strey_autogenfig.png

Fig. 119 1D plot corresponding to the default parameters of the model.

Source

teubner_strey.py

References

  1. M Teubner, R Strey, J. Chem. Phys., 87 (1987) 3195
  2. K V Schubert, R Strey, S R Kline and E W Kaler, J. Chem. Phys., 101 (1994) 5343
  3. H Endo, M Mihailescu, M. Monkenbusch, J Allgaier, G Gompper, D Richter, B Jakobs, T Sottmann, R Strey, and I Grillo, J. Chem. Phys., 115 (2001), 580

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