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Small angle neutron scattering study of steroidal gels
P. Terech, F. Volino, R. Ramasseul
To cite this version:
P. Terech, F. Volino, R. Ramasseul. Small angle neutron scattering study of steroidal gels. Journal de Physique, 1985, 46 (6), pp.895-903. �10.1051/jphys:01985004606089500�. �jpa-00210035�
Small Angle Neutron Scattering study of steroidal gels
P. Terech (*), F. Volino (*) and R. Ramasseul (**)
Département de Recherche Fondamentale, Centre d’Etudes Nucléaires de Grenoble, 85X, F-38041 Grenoble Cedex, France
(Reçu le 1 er octobre 1984, accepté le 5 février 1985)
Résumé. 2014 Des gels formés à partir de solutions diluées dans le cyclohexane de stéroïdes modifiés, sont étudiés par diffusion de neutrons aux petits angles. La présence d’objets très longs associés avec le réseau du gel est mise claire- ment en évidence. Des experiences de variation de contraste montrent que ces objets sont essentiellement composés
par des molécules stéroïdes. Des mesures d’intensités absolues et l’ajustement des courbes de diffusion à des modèles
simples suggèrent que ces objets sont chiraux, probablement des doubles hélices symétriques de diamètre d’environ
100 Å. On suggère que les « points de contacts » entre objets sont formés en torsadant deux ou plusieurs de ces longs objets sur des distances relativement grandes par rapport au diamètre. L’influence de ce recouvrement des
objets sur la forme des courbes de diffusion est discutée.
Abstract. 2014 Gels formed by a dilute solution of modified steroids in cyclohexane have been studied by Small Angle Neutron Scattering. The presence of very long objects associated with the gel network is clearly demonstrat- ed. Contrast variation experiments show that these objects are essentially composed of steroid molecules. Absolute intensity measurements, and fits of the full scattering curves using models, suggest that these objects are chiral, possibly symmetrical double helices of diameter ca. 100 Å. It is suggested that the « contact points » in the network of the gel are achieved by coiling together two or more long objects over distances rather large compared to the
diameter. The influence of the existence of such overlapping on the shape of the experimental scattering curves is
discussed.
Classification
Physics Abstracts
61.12F
1. Introduction.
A relatively large number of organic, low molecular
weight molecules form gels upon recrystallization from
suitable solvents instead of depositing crystals [1-6].
We have previously presented preliminary results concerning rheology [7], the phase diagram [8], kine-
tics of formation and structure [9] of a gel formed by a
dilute solution (- 1 wt % solution) of a paramagnetic
modified steroid, 3 fl-hydroxy-17,17-dipropyl-17a-aza- D-homoandrostanyl-17a-oxy (molecule 2b in Fig. 1)
in cyclohexane. Electron spin resonance (ESR)
demonstrated that the gelation phenomenon was governed by supersaturation effects [8]. Small Angle
Neutron Scattering (SANS) showed that the gel net-
work consisted of very long objects (length > 5 000 A)
with a radius of gyration of the section of about
40 A [7]. Kinetic measurements performed by ESR supported this linear character of the objects [9].
(*) Groupe de Physico-Chimie Moleculaire, Section de Physique du Solide.
(**) Laboratoires de Chimie (LA CNRS 321).
In this paper, we present a detailed SANS study of
this gel, in order to gain information about the actual geometry and composition of these long objects, as a
function of the nature of steroidal molecules (mole-
cules 2a, 1 band 2b of Fig. 1 were used), of the initial steroid concentration in the solution, and of the tem- perature. The data will be first analysed in terms of
the radius of gyration Rg of the section and absolute intensities. Contrast variation measurements are des-
Fig. 1. - Chemical formulae of the steroidal molecules used in this study.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01985004606089500
896
cribed and show that the long objects are essentially composed of steroidal molecules.
This information is used to estimate the number of steroids per unit length of objects. The full scatter- ing laws are then compared with simple models : homogeneous cylinder, homogeneous hollow cylin- der, homogeneous double helix. The best fit is obtained with this last model and independent arguments are
given which support the chiral character of the objects.
The nature of the « contact points >> between objects in
the gels and their influence on the shape of the expe- rimental scattering curves are discussed.
2. Methods.
2. 1 MATERIAL. - The modified steroids were pre-
pared as previously described [ 10] and dissolved in hot reagent grade cyclohexane, perdeuterated cyclohexane
or mixtures of both, at concentrations ranging from
0.5 to 6 x 10- 2 M (- 0.25 to 3 wt %).
2.2 EXPERIMENTAL. - Samples were held in 1 mm- path QS quartz cells which are standard in SANS.
Experiments were performed on spectrometers D11 and D17 of the Institute Lafe-Langevin with the
neutron momentum transfer Q ranging between 10- 3
and 2 x 10 - I A - 1. Typical counting times varied
from a few minutes for concentrated gels to about one
hour for the most dilute gels. Absolute intensity
measurements were performed by comparison with
a 1 mm thick water sample. Corrections for detector
efficiency, sample holder scattering and background
were performed.
2.3 SCATTERING DATA EVALUATION. - Since in all
cases the scattering appeared to be essentially isotropic,
the intensities were averaged over all possible orienta-
tions of the scattering plane for a given value of the momentum transfer modulus Q. Defining J(Q) as the
ratio of intensities scattered by the gel and by the water samples, respectively, corrected for transmission and relative thickness of sample, the absolute differential
cross section £ of the sample is finally given by
[11, 12] : drg2 ) p Y g Y
where dw and T,, are the thickness and transmission coefficients of the water sample, and where g(Â) is a
known correction factor depending on the neutron wavelength it, which takes into account inelastic effects for water.
For infinitely long objects, J(Q) diverges as Q -1
at low Q. The mass ML per unit length of objects is
related to the cross section at Q = 0 by [11, 12] :
where c is the massic concentration of the objects (g/cml) and ab is the specific contrast defined as
in which b2 is the specific scattering length of the objects (cm/g), v2 is the specific volume of the objects (cm3 jg) and p. the scattering length per unit volume of solvent (cm/cml). Ob can be varied by changing the
relative fractions p’ and 1 - p’ of deuterated and pro- tonated solvent (contrast variation method). Deter-
mination of the zero contrast point yields important
information on the composition of the objects.
Absolute intensity measurements provide additional
information concerning the concentration and mass
of these objects.
Further information is contained in the behaviour of the scattering curve at low Q. For sufficiently low Q,
we have for infinitely long objects [13,14] :
where Rg is the radius of gyration of the section of these objects. J A Guinier plot p i.e. Ln dE Q Ug-2 versus Q 2, yields both R and g the extrapolated intensity Q
B
dEdO 0’Finally, the full scattering curve contains informa- tion about the details of the shape of the objects.
Extraction of this information is generally achieved by comparison with theoretical scattering laws of objects of known shape and composition.
3. Results.
Data were taken for a large number of samples by varying the nature of the steroid, the initial steroid
concentration, temperature and partial deuteration of the solvent, in a wide Q range, from 10- 3 to 2 x 10-1 A-1. Figure 2 shows QI(Q) against Q in a log-log representation, for three gels made with molecule 2b
in C6D 12’ using three different initial concentration co. These data, taken at very low Q with the Dll instrument, clearly demonstrate the Q-’ divergence
which is characteristic of the scattering by very (infi- nitely) long objects [14, 15]. Note that the low Q pla-
teau extends over more than one decade in Q. Decrease
of the curve at higher Q is indicative of the finite dimen- sion of the section of these objects. Figure 3 shows
normalized scattering curves taken at higher Q with
the spectrometer D 17 using the same log-log repre- sentation. One can guess the plateau at very low Q by comparison with figure 2, but the shape at higher Q is
more instructive. We note the presence of one or two
more or less defined shoulders around Q - 0.1 A -1.
Fig. 2. - Scattering curves for three gel samples of diffe-
rent initial concentrations at room temperature. The specific log-log representation QI(Q) versus Q is used. Each curve is obtained by four different experiments in different ranges of momentum transfer. The ordinates are in arbitrary units but
are proportional to the concentration of long objets. Q is expressed in A-1. (0) co = 1 x 10-2 M; (0) co = 2 x.
10-2 M; (+) co = 3 x 10-2 M.
Fig. 3. - Typical normalized scattering curves in the high Q range : (0) compound 2b, co = 1.2 x 10- 2 M; (+)
compound 2b, co = 4 x 10-zM; (0) compound 1 b, co = 2.5 x 10- 2 M. Temperature : 19 OC. Q is expressed in A-1.
We note also that all curves are very close to one
another. As a general trend, it is observed that the shoulders are better defined for low concentrated
gels and they tend to smear out for higher concentrated
gels.
4. Analysis.
4.1 RADIUS OF GYRATION OF THE CROSS SECTION OF THE OBJECTS : I GUINIER PLOTS. - Figure 4 shows typical Guinier plots for several gels from which both
[QI(Q)]o and Rg are deduced. Tables I and II collect the results obtained with gels made using molecule 2b
Fig. 4. - Guinier plots of Log [QI(Q)] against Q 2 for
different gel samples : (0) compound 2a, co = 2 x 10 - 2 M,
T = 19 °C ; (0) compound 2b, co = 1.2 x 10- 2 M, T = 15 °C ; (*) compound 1 b, co = 3 x 10-2 M, T = 19 °C ; (+) compound 2b, co = 1.2 x 10 - 2 M, T = 19 °C. Q is expressed in A-’.
and molecule 1b respectively, for various initial con-
centrations and temperatures. It is observed that while
Q
T7))
(proportional to [QI(Q)]o) varies consi- B O)oderably from sample to sample, on the contrary, Rg is
found to be rather constant. A common value of
Rg = 41 ± 3 A can be retained for all samples studied.
This result is a first indication that all gels contains
the same kind of long objects.
4.2 COMPOSITION OF THE OBJECTS : CONTRAST VARIA- TION METHOD [16, 17]. - This experiment was performed on the spectrometer D 17 with gels stabi-
lized at 20 °C, made with molecule 2b at a concentra-
tion of co = 2 x 10- 2 M in mixtures of perdeuterated
and normal cyclohexane. Calling ps 6012 and ps 6H12 the
scattering lengths per unit volume of C6D 12 and C6Hl2 at 20 °C, respectively, and p’ and 1 - p’ the relative fractions of C6D12 and C6H12 in the mixtures,
the scattering length per unit volume of the solvent of
composition p’ is given by
Combining equations (2), (3) and (5) shows that the [ d z 1 /2
quantity dQ is ultimately a linear function of//.
L "J
The experiment was performed for seven solvent compositions. The extrapolated intensity value was
deduced for each experiment from Guinier plots as previously.
Figure 5 shows the results in a representation
, drB 1 /2
LBQ dQ
versus p’. It is seen that the plot is prac-- Q 0
tically linear for p’ 0.8 and zero contrast is obtained
for a composition /po 0.117. According to equa-
898
Fig. 5. - Variation of the quantity (QI)112, representative
of the total scattering per unit length of the object relative to
its solvent, with percentage p’ of C6D12 in the solvent. The
matching point is obtained for p’ = U.117. The arrow indi-
cates the theoretical value for the solid steroid (see Sect. 4b
for details).
tion (3) for this composition we have
In the following, we show that this result means that the long objects are practically composed of steroid
molecules only, as suggested by the ESR study [8].
For this purpose, it is necessary to calculate the
scattering length per unit volume ps b = b22-b/v2-b of a
compact solid composed of molecules 2b. From the chemical formula of 2b and tables of neutron scatter-
ing lengths, we calculate b2 = 0.349 x 101 ° cm/g. To
calculate v2b, it is necessary to know the density of the objects. Preliminary X-ray diffraction data on the solid phase of molecule 2b shows that the structure is monoclinic with 4 molecules per unit cell, correspond- ing to a density of d2b = 1.0996 g/cm3 [18]. Assuming
that the density of the objects is the same as in the solid, and using the fact that v2 = 1jd2b, we finally
obtain
Equating the second members of (5) and (7), one can
deduce for which composition p", zero contrast would
be obtained. For this purpose knowledge of ps for pure
C6Dl2 and C6Hl2 are required. From the chemical formulae, we deduce b26°12 = 7.522 x 101 ° cm/g and
b26H12 = _ 0.358 x 101° cm/g. With tfC6D12=0.897
9/CM3 and tJC6H12=0.78 g/cm3, we deduce pC6DI2s
6.748 x 1010 cm/cm3 and pg 6H12 = _ 0.279 x 1010 cm/
cm3. From these numbers, we finally obtain p" = 0.096.
This value is shown by an arrow in figure 5. Although p" is found to be slightly smaller than po, both values
can be considered to be the same within experimental uncertainty, showing that the objects are essentially composed of steroid molecules with a compacity comparable to that of the solid.
This result, together with the finding that Rg is
constant (cf Tables I, II and III) show that the com- position and geometry of the long objects, to be asso-
ciated with the gel network, are essentially the same
for all the gels studied. Using these results and abso- lute intensity values, it is now possible to estimate
the mass per unit length of these long objects.
4.3 MASS PER UNIT LENGTH : I ABSOLUTE INTENSITY MEASUREMENTS. - Absolute intensity values have been deduced from Guinier plots and the results for all
gels studied are collected in tables I, II and III. Combin- ing equations (2), (3) and (6), we obtain :
Table I. - SANS results for gels formed with the nitroxide steroid compound 2b.
From this equation, it is possible to estimate the
mass per unit length of objects ML. For this purpose, it is necessary to know ps(p’), ps(po), v2 and c. Since all the experiments were performed in pure C6D12, equation (5) with p’ = 1 yields ps( 1 ) pC6DI2 s =
6.748 x 1010 cm/cm3. From the contrast variation experiment, we obtain ps( po) = 0.543 x 1010 cm/
cm 3 Since this last value is much smaller than p. (I),
the uncertainty on po plays a small role in this calcu- lation. To determine v2l an assumption should be made
concerning the composition of the objects. Assuming,
as suggested by the preceding section, that the objects
are composed of the steroid molecules only, with a density equal to that of the solid, we obtain v2 = v2b = I/dib- = 0.909 cm3/g.
The massic concentration of the objects c is related
to the initial concentration of steroid in the solution co by the relation
Table II. - SANS results for gels formed with the
amine steroid compound lb.
Table III. - SANS results for gel samples (compound 2b, co = 2 x 10- 2 M, T = 19 °C) with different solvent
compositions : contrast variation method.
-
where p is the fraction of steroid molecules taking part in the long objects. Finally the mass per unit length
of objects ML is related to the number of steroid molecules per unit length of objects nL by the relation :
where M is the molecular mass of the steroid and N the Avogadro number. Combining equations (8), (9), (10), it is seen that the quantity pnL can finally be
extracted from these experiments. The corresponding
numbers are collected in tables I, II and III.
To determine nL, it is necessary to know p. From the ESR study [8], we have shown that for the normal
cyclohexane/molecule 2b system, p is such that the concentration of steroid in the liquid part of the gel,
namely co( 1 - p), is just the saturation concentration
cs(T). The value of p can be estimated from the ESR spectra in the gel phase, by separating two components in the spectra corresponding to steroid molecules in the network and steroid molecules in solution [8]. This separation was performed on the ESR spectra of gels prepared from the same parent solution and in the
same conditions as in the SANS experiments, at least
for the runs quoted in table I. The values of p estimated
in this way are given in this table, as well as the deduced values of nL. For molecule I b which is not parama-
gnetic, this procedure is not possible. However, it
appears from experiment that, at room temperature, the solubility of this molecule is about twice as large as
that of molecule 2b. From this observation, a value of p
can be estimated and the corresponding values of nL
900
can be deduced and are given in table II. Finally, for
the contrast variation experiment, performed at
constant co and constant temperature, a mean value of
p - 0.5 ± 0.1 is retained for all solvent compositions.
The corresponding values of nL are given in table III.
It is observed that, despite the uncertainties, nL is found to be relatively constant for all experiments,
except for p’ = 1 in table III. The common value
retained from the whole set of data, and which is
expected to be valid for all the gels studied is
nL = 7 + 2 steroid molecules per A.
4.4 MODELIZATION OF THE CROSS SECTION. - To
summarize, from the asymptotic behaviour of the
scattering curves and from absolute intensity measu-
rements, it has been established in all gels studied and whatever the initial concentration, temperature or
nature of the steroid molecules (experiments were
also performed with molecule 1 b which gave essen-
tially the same results) the presence of very long objects
made up of steroid molecules, with a density close
to that of the solid, containing - 7 steroid molecules
per A of object, and whose radius of gyration of the
cross section is - 40 A. More information about the actual shape of the cross section can now be obtained from a detailed analysis of the scattering curves at larger Q values. The simplest model is to assume that
the objects are homogeneous cylinders of radius R (Fig. 6a). The scattering law for such isolated infinite
cylinders is well known and is given by, after averaging
over all orientations [15] :
where J1 is the Bessel function of order 1. The radius of gyration is Rg = R/fi. Assuming Rg = 40 A, we
obtain R = 56.6 A. The theoretical scattering curve
is shown in figure 7a together with the experimental
curve for one typical gel. It is seen that the general shape is reproduced, but the second and third minima
are considerably smeared out in the experiment. This
effect is not due to instrumental resolution. Improve-
ment of the fit can be achieved by assuming a distribu-
tion of radii around R. Assuming a normalized Gaus-
Fig. 6. - Definition of the geometrical parameters of the three models considered in this work : a) cylinder, b) hollow cylinder, c) double helix.
Fig. 7. - a) Comparison between experimental and theo-
retical scattering curves for cylinders (Fig. 6a). The points
are experimental (compound 1 b, co = 2 x 10- 2 M, T =
19 °C) ; the full line is the best fit of equation [11] obtained
for R = 56 A.
b) Theoretical scattering curves showing the influence of a
distribution of radii : (-) e = 0 ; (---) s = 0.16 best fit; (-.-)
E = 0.25.
sian distribution centred around Ro of the form
where AR,/2 is the full width at half maximum of this
distribution, and putting
comparison between figures 7a, 7b and 3 shows that with values of 8 ranging between 0.16 and 0.25, it is possible to reproduce all the experimental shapes.
Although reasonable fits are obtained, the homo-
geneous cylinder is probably not the correct model.
Indeed, the volume of a section of such a cylinder of height 1 A is 10 029 A3. With a density of 1.0996 g/cm3 corresponding to v = 1.69 x 10- 3 molecules/A3, we
obtain nL ’" 17 steroid molecules per A of cylinder,
