PHYSlCA[ ELSEVIER
Physica B 213&214 119951 513 514
Neutron scattering on dense solutions of tetramethylurea S. Borb61y", L. Cser a'*, T. Gr6sz a. G. J a n c s 6 b ~Research lnstitute jbr Solid State Physics, H-1525. Budapest 114, P.O.B. 49, Hungary bAtomic Energy Research Institute. H-1525, Budapest 114. P.OB. 49, Hungary
Abstract
The results of small-angle neutron scattering (SANS) carried out on aqueous and CS2 solutions of tetramethylurea (TMU) are compared. It is shown that the SANS data indicate the formation of T M U - T M U dimers in both solutions.
1. Introduction
3. Discussion
In a previous work [1] the results of a small-angle neutron scattering (SANS) study of the aqueous solution of tetramethylurea (TMU) in the low-concentration range were reported. The SANS patterns were observed at 20~C over the concentration range of 0.05 1.0 m. It was shown that the data can be successfully interpreted in terms of a model based on T M U dimer formation, i.e. T M U monomers and dimers are in statistical equilibrium. In the present work the SANS data obtained on a solution of T M U in CSz at 2 0 C over the concentration range of 0.16-2.3 m (which corresponds to the mole fraction range of 0.012 0.15) are presented, and the results are compared with those from aqueous solutions.
The basic notion of the model used is as follows: The observed scattering curves were described by the formula proposed by Guinier [-2] for the mixture of dense interacting nonuniform particles:
2. Results
A typical spectrum in the Guinier representation is shown in Fig. 1. All spectra were approximated assuming the superposition of two Guinier exponents and thus, the forward scattering intensities and the corresponding values of the radius of gyration for the monomers and dimers were estimated separately. (See Fig. 2 and Table 1). *Corresponding author.
i(q) = ion [ ~ pk(F~(q)) + ~ ~ p~pj(Fj(q)) ( F d q ) ) ~t
1f
x--
]
Akj(r)4rtr z dr ,
/)1
(1)
o
where Fk(q) denotes the structure factor of the particle of type k, Pk is the probability that one of the n particles is of type k; tq is the average volume offered to each particle, regardless of its type: sin(qr) Akj(r) = [ P k j l r ) - 1 ] qr
(2)
and Pkj(r} is a probability function which in the first approximation is expressed by the pair interaction potentials ujk(r) as Pkj(r) = e x p ( - ukj(r)].kTj
0921-4526/95/$09.50 ,c 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 1 9 6 - 4
(3)
514
S. Borbbly et al. ,' Physica B 213&214 (1995) 513 514
where Rg,k is the apparent radius of gyration of the particle of type k. It can be shown that at low concentrations and small q values the integrals containing the Pk~(r) functions (see Eq. (1)) give the second osmotic virial coefficients Bjk which describe the pair interactions between particles j and k. The probabilities Pk can be calculated through the dimerization constant (K) of the m o n o m e r dimer equilibrium
-25
"-,..
-27
--I "e 29
It--~.....
-31
33 0 (i0
0 04
0 12
00~
0 16
0 gC,
q2 A-2
Fig. 1. Scattering pattern of 0.71 m TMU solution in CS2 displayed in the Guinier coordinates.
015
•
i T l o n o I ] q e i"
•
dinae r"
0.10
///'i
II D"
11"
005
TMU + TMU~,~-[TMU-TMU],
(5)
K = nd/n2m,
(6)
where nd and nm are the concentrations of dimers and monomers in the solution respectively. It should be noted that in our model the "chemical" interaction between the monomers which leads to the formation of dimers is given by K, whereas the "physical" interaction between the monomers which are in equilibrium with the dimers is given by Bll. In our case the system consists of two types of particle: T M U monomers and T M U T M U dimers. This means that by least-squares fitting of the experimental data to Eq. (1), rewritten for the case of small q values, six parameters (i(0), R0. b Rg,2, B l l , B22 and K) can be evaluated. The values of the parameters obtained are given in Table I.
/
4. Conclusions
d( 0 O0 0 O0
0 05
, 0 10
, 0 15
Fig. 2. The forward scattering intensity of monomers and dimers as a function of the TMU concentration. X is the mole fraction. Table 1 The least-squares fit parameters for aqueous and CS2 TMU solutions Parameter
H-TMU in D 2 0 [1]
i(0) (barn) Rg. 1 (1~) o Ro. 2 (A)
114 _+ 1.7 2.81 + 0.12 4.18 + 0.15 1.96 + 0.06 -- 2.1 _+ 3 2.04 + 0.07
Bll B22
K *a
D-TMU in CS2 161 + 0.2 2.54 ___+0.04 8.24 _+ 0.1 0.15 _+ 0.01 - 3.14 + 0.26 0.63 _+ 0.02
T M U molecules forming dimers in both D 2 0 and CS2 solvents. The size of the dimers in water is much smaller than that of the dimers in CS2 which reflects the differences between the dimer structures in the two solvents. (A detailed interpretation is in progress). The smaller value of the dimerization constant in CS 2 indicates that the concentration of dimers is higher in the aqueous solutions at a given solute concentration. The values of the dimensionless second virial coefficient for monomers (see Table 1) deviates significantly from the value describing the interaction of hard spheres (B~ s = 4) in the CS2 solvent, while it is closer to the value of four in the aqueous solution. The sign and magnitude of the B22 values indicates a rather significant attractive dimer dimer interaction in both solvents. Financial support of the Hungarian Research Fund under grants OTKA-1846 and -4490 is gratefully acknowledged.
" K* is expressed as a dimensionless quantity and is equal to K/t~monomer.
References
In the low q range the Guinier approximation is valid, i.e. the structure factors in Eq. (1) can be replaced by F~(q) = exp (
1 o2
- - 3 *~'g,k, q
2,J,
(4)
[1] L. Cser, T. Grosz and Yu.M. Ostanevich, J. Phys. IV C 8 (1993) 229. [2] A. Guinier and G. Fournet, Small-Angle Scattering of Xrays (Wiley, New York; Chapman & Hall; London, 1955).