Direct determination of the SANS contrast factor by neutron interferometry
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Letters to the Editor
DIRECT DETERMINATION OF THE SANS CONTRAST
FACTOR BY NEUTRON INTERFEROMETRY
P. Luke, 3. Kulda, P. Mikula
Nuclear Physics Institute, CzechosL Acad. Sci.,
250 68 Re~ near Prague, Czechoslovakia
Institute of Macroraolecular Chemistry, Czechosl. Acad. Sci.,
16~ 06 Prague 6, Czechoslovakia
Received 26March 1990
An important application of neutron interferometric methods is a precise measurement of the neutron refractive index which is connected with the scattering length density of a sample. The experiment of such type can be easily modified for the SANS (small-angle neutron scattering) contrast factor measurement. For a two-component solution the contrast factor Ab (the excess scattering length) may be written as
Ab = b - V~o (1)
where b, ~r and ~o axe scattering length, paxtial volume of the dissolved compound and scattering density of the solvent, respectively. The value of the excess scattering length is a useful parameter for SANS data evaluation, especially for the molecular weight determi- nation [1-3]. If the quantities b, ~r and #0 are known, Ab can be calculated from eq. (1). However, this way fails if, for example, the chemical composition of the dissolved compound is not known. In such a case a direct method should be employed. Recently, it has been shown that the contrast factor may be determined from the concentration dependence of the SANS intensity , . An alternative way, analogous to light optics, represents the use of the neutron interferometry .
The present contribution demonstrates the measurement of the scattering length den- sity of polymer solutions (enabling one to estimate excess scattering length) using neutron intederometry. The principle of the experimental technique consists in the measurement of the mutual phase shift of two coherent neutron beams produced and recombined in the interferometer. The relative phase shift Ar is introduced by passing one neutron beam through the sample and may be described by
A~ = ~te~ (2)
Czech. J. Phys. 40 (1990) 697
Le~cr$ ~o ~he Editor
where ~ is the average scattering density of the Sample, k is neutron wavelength and ~ef is effective sample thickness given by tel = t/cos0. Then, because of Ab = a~/Oc , the excess scattering length can be expressed as
1 aZ~@ ~b= At~ Oc (3)
and determined experimentally fxom a set of phase shift values observed with samples of different concentration.
The experiment was performed on the DIFRAN diffractometer at the IBR-2 rea~tor at JINR Dubna (USSR). The Si interferometer (conventional LLL type) having the interference contrast of 30% was operated at the neutron wavelength ~ = 1.085 ]k ; detailed description of the present experimental setup will be given elsewhere . The set of samples comprised four solutions of polymethacrylic acid (PMA) in D20 (0.009 < c < 0.035 g cm -3) and pure (99.6 %) D20 was used as the solvent. The samples were put into precise plane-parallel quarz container with inner thickness 2 ram.
In the course of the experiment we simultaneously measured three interference patterns corresponding to the sample position in either of the coherent beams and outside the in- terfer0meter. In this way we excluded errors in the determination of tel due to nonparallel position of the sample with respect to the intetferometer wafers . The phase shifts were then determined (modulo 2~) by fitting the usual theoretical formula to the data. Figure 1 displays the measured values of the phase shift A@ plotted against the PMA concentration. From the slope of this dependence we obtained the following experimental value of the excess scattering length of PMA in D20
~b -- -3.33(6) 10 l~ cm g- i .
2 , I t I .... I I I
0.1 0.2 02 C [gcm -~]
Fig. 1. Concentration dependence of measured phase shift.
The same quantity can be calculated using definition (1). From the structure of the repeat unit
698 Czech. J. Phys. 40 (1990)
Letters ~o ~he Bdi~or
I I - - C C - -
I I H COOH
the scattering length of PMA was evaluated as b : 1.10 101~ cm g-1. The scattering length
density of the solvent (D20 + 0.4 vol % H20) is ~0 : 6.34 10 l~ cm 2. Then with the partial
specific volume of PMA in water, ~" = 0.69 cm 3 g-1 , we obtained from eq. (1) the
Ab : -3.27 10 l~ cm g-1
which agrees well with our experimental result.
It should be stressed that the above given values of Ab cannot be used for the calculation
of molecular weight or other contrast dependent quantities for PMA. The reason is that the
procedure used here is strictly valid only for a two-component system. It is known, however, that protons of carboxyl groups of PMA are exchangable in D20 solution. The excess scattering length is very sensitive to the H-D exchange while the mean scattering density of
solution is not influenced by this effect. It means that the interferometric method, which is based on the measurement of the mean scattering length, does not provide the correct
SANS contrast factor in this case. To obtain the true value of the excess scattering length
one has to perform experiments with the solutions in dialysis with the solvent.
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