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Brillouin scattering from cross-linked gels
Francesco Mallamace, Norberto Micali, Cirino Vasi, Rama Bansil, Sinisa Pajevic, Francesco Sciortino
To cite this version:
Francesco Mallamace, Norberto Micali, Cirino Vasi, Rama Bansil, Sinisa Pajevic, et al.. Brillouin scattering from cross-linked gels. Journal de Physique II, EDP Sciences, 1992, 2 (12), pp.2081-2088.
�10.1051/jp2:1992253�. �jpa-00247790�
Classification Physics Abstracts
82.70G 62.60 43.20
Short Communication
Brillouin scattering from cross-linked gels
Francesco Mallamace(~), Norberto Micali(~), Cirino Vasi(~), Rama Bansil(~), Sinisa
Pajevic(~) and Francesco Sciortino(~)
(~) Dipartimento di Fisica, Universita'di Messina, 98166 Villagio S. Agata, C-P. 55, Messina, Italy
(~) Istituto Tecniche Spettroscopiche del C-N-R-, 98166 Messina, Italy
(~) Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, U-S-A-
(Received 12 August 1992, accepted in final form 12 October1992)
Abstract In this letter
we report Brillouin scattering measurements on methyl-methacrylate (MMA) gels crosslinked with varying amounts of ethylene-dimethacrylate (EDMA). We find
that the k dependence of the phase velocity changes on increasing the cross-link content. For
higher concentrations of crosslink we observe maxima and minima in the k dependence of the phase velocity. We associate these minima and maxima With spatial inhomogeneities in the gel, with the formation of regions of low and high cross-link density, respectively. This micro-phase separation is frozen in by the presence of the already existing spanning network.
AS is well known a gel is a jellylike binary material composed of a cross-linked polymer
network and a solvent occupying the pores in the network. Considerable attention is presently
devoted to the characterization of the structure and dynamics of cross-linked gels because of their fundamental and technological importance in many fields of physics, chemistry and
biology. Quasi-elastic light scattering studies have established the existence of a collective diffusion mode with
a diffusion constant inversely proportional to the hydrodynamic correlation
length in the network [Ii. Several investigators have studied the dependence of this mode
on the concentration, extent of crosslinking and temperature of the gel [2]. The sol-gel (SG)
transition is usually interpreted in terms of percolation models [3]. A critical line, characterized
by the divergence of the pair connectedness function, separates the polymer concentration
versus crosslinker concentration phase diagram into a sol and a gel phase. At a fixed total
monomer concentration, the SG transition can be triggered by increasing the concentration of
the crosslinking molecules. The structure of the system at this critical point can be described
by a power-low distribution of clusters with no characteristic length. At this critical point the viscosity of the solution diverges. Beyond this SG threshold, the gel displays elastic behavior.
Several studies of the scaling behavior at the sol-gel transition have been reported [4].
2082 JOURNAL DE PHYSIQUE II N°12
Much less is known about the scaling behavior at high cross-link concentration because of complications due to heterogeneities in the gel. In fact, even in very good solvent, the branched
polymers generated in the cross-linking process will tend to segregate as the number of cross- links goes beyond the critical percolation point [5]. However, macroscopic phase segregation is
prevented by the existence of the spanning network. As a result, only a microscopic segregation
takes place, leading to localized heterogeneities in the gel structure. This phenomenon, known
as micro-synerisis or microphase separation, is also a major problem in making homogeneous interpenetrating networks. For example, it is well known that polyacrylamide gels become turbid at high crosslink content, and their swelling capacity and pore size distributions are non-monotonic functions of crosslink content [6, 7]. Raman spectra of these gels show that the distribution of the cross-links is non-uniform, and that clusters of the crosslinking monomer
appear to form at high crosslink content [7]. Computer simulations also show the existence of
spatial correlations [8] in the distribution of crosslinking monomers.
Similarly, linear polystyrene incorporated in a styrene-divinyl benzene gel exhibits phase separation behavior as a function of crosslink content, even though the monomers involved are compatible and miscible [9]. Recent theoretical work supports the hypothesis that segregation phenomena may occur at high cross-link concentration [10]. Such phase separation would takes
place on microscopic scales ("micro-phase separation") because the pre-existing crosslinking
network hinders macroscopic segregation. At present not much is known about the structure of such microphase-separated gels.
Here we show that Brillouin scattering can be used to probe the dynamics of microphase separated gels, and is also sensitive to the viscoelastic changes at the sol-gel transition. Hyper-
sound experiments performed with Brillouin light scattering give information on the collective oscillations of the system. This technique represents a powerful experimental method for the study of complex systems such as polymeric solutions [IIi, gels [12], dense or supercooled flu- ids [13], and dense supramolecular aggregates as micelles [14] or microemulsions [15], I-e- the class of systems characterized by strong viscoelastic behavior. In such systems, there exists a
crossover frequency (or wavevector k) such that the behavior of the system can be interpreted
as mainly an elastic material for short times and large k and as a viscous fluid for long times and small k. Since the structure and dynamics of the gel is determined by the crosslink con- tent, a question of particular interest is the dependence of the cross-over frequency and the
cross-over wavevector on the cross-link concentration.
The Brillouin scattering measurements reported here were made for several different scatter-
ing vectors in order to analyze the spatial dependence of the elastic properties of the system.
We show that a new length scale, different from the hydrodynamic one, appears in the struc- ture of the gel for high cross-link concentration. We associate this new length scale to the
microscopic segregation process. It should be emphasized that the samples were optically clear
implying that the phase separation process occurs on length scales much smaller than light.
The experiments were performed on methyl-methacrylate (MMA) gels crosslinked with ethylene-dimethacrylate (EDMA). The gels were made by free radical copolymerization of
MMA and EDMA in dioxane with ABIN as the initiator. Sealed vials containing 12 ill
MMA+EDMA in dioxane were polymerized for 80 hours in a 50 °C bath. The fraction of EDMA in the total monomer mixture of MMA+EDMA was varied from 0 to 6 ill. The sample with 0 ill EDMA corresponds to a linear polymer solution. All other samples were gels, in the
phase region beyond the (SG) threshold.
The investigated samples cover a range of crosslink content, defined as fEDMA the ratio of the volume fraction of EDMA to that of the total monomer (EDMA + MMA). We have studied for comparison also the pure solvent (dioxane) and a solution of MMA. The refractive index n of the different compounds are respectively lA165 for dioxane, 1.4549 for EDMA and lA140
for MMA. The respective densities are d
= 1.032, 1.051 and 0.936. All the data for n and d refer to T = 20 °C.
Figure I shows the total scattered intensity at 90° as a function of the crosslink content. The increase in scattered intensity with increasing crosslink content could arise from the presence of heterogeneities in the gel.
] 1400 fl
~ 1000
I
C
(W
0 2 4 6
f [%]
EDMA
Fig. 1. Scattered intensity at 90 degrees as a function of crosslink content.
Quasielastic light scattering (QELS) measurements of the scattered light intensity auto- correlation function, g2(t), at a constant temperature of 20 °C and scattering angle of 90° were
performed using a standard laser light multi-angle spectrometer with a argon-ion laser and a Brookhaven Instruments (Model BI-2030AT) 256-channel digital correlator. The data shows the presence of only one diflusional mode, D, corresponding to the collective diflusional mode of the gel network. The value of D obtained by assuming homodyne detection shows a decrease by approximately a factor of two as the crosslink content increases above 4 ill. However, since
the increase of total scattered intensity implies the presence of heterogeneities, it is possible
that the measured correlation function exhibits partial hetrodyning at higher crosslink content.
If we had assumed a completely heterodyne mode of detection for the higher crosslink content
samples then the factor of two would be accounted for by homodyne to heterodyne detection and D would be practically independent of crosslink content. Complications arising from non-
ergodicity might also be expected to change the apparent diffusion coefficient [16]. A detailed study of these effects using different schemes for ensemble averaging in MMA + EDMA gels
will be discussed separately.
We study the elastic properties of the system by measuring the k dependence of the Brillouin
frequency shift. To maximize the stray-light rejection, we have performed the measurements
with a double pass double monochromator (DMDP 2000) SOPRA spectrometer using the
5145 I line from
a Ar+ laser (Spectra-physics 2020) operating at 0.5 watt. The experiments
were made at four scattering angles, namely 90, 1IS, 135 and 150 degree using a computer controlled goniometer corresponding to k at 24.6, 29.5, 32.I and 33.6 pm~~ respectively. All
the mea~urements are performed at constant temperature T = 17 + 0.02 °C, using a fluid
filled thermostatted scattering optical cell. The matching fluid (water/dibutylphtalate) has the same refractive index of the scattering cell in order to avoid unwanted stray-light effects.
At all the angles studied, the Brillouin peaks are well resolved from the quasi-elastic zero
frequency contribution.
2084 JOURNAL DE PHYSIQUE II N°12
We performed the data analysis using a well established procedure [17]. In particular,
we used a convolution method between the hydrodynamic triplet [18] and the instrumental response to obtain the frequency shift value. The high quality of the obtained fit does not give
the possibility to consider other central (w = 0) components due to relaxation modes [19].
Figure 2 shows the Brillouin frequency shift Aw as a function of the scattered wavevector k for samples with different crosslink concentrations; in the same figure are also shown the
corresponding data for pure dioxane and for pure MMA (unpolymeriZed) in dioxane. All the data are in the frequency range of 5.I to 7.8 GHz.
As can be seen from figure 2 Aw increases linearly with increasing wavevector for the linear
polymer solution (IEDMA " 0) as well as for the gels with cross-link concentration less than I ill. For higher concentrations of crosslink we observe two opposite k behavior; (I) for gels
with IEDMA " 1.5 ill and 2 ill we find a positive curvature in Aw vs. k; (it) for gels with fEDMA " 4 ill and 6 ill the curvature is negative.
This result can be rationalized by examining the k-dependence of the calculated phase velocity (V(k)) shown in figure 3. In this figure the data that present different behavior in the dispersion curves are grouped separately. Figure 3a shows the case of linear dispersion in sound velocity vs. k for dioxane (dashed line), and dioxane-MMA and for samples with crosslink
concentration less than I ill; figure 3b shows similar data for gel samples with dispersion curves
Aw vs. k with positive curvature IEDMA " 1.5 ill, 2 ill) and figure 3c shows the velocity data for gels with higher crosslinking content (negative curvature in the dispersion curves). The sound velocity for dioxane (V = 1370 m/s) agrees, within the experimental error, with the data obtained from ultrasonic experiments at 2 MHZ [20].
Linear polymer solution of MMA and the gel with the lower content of crosslink show linear
dependence of V vs. k. The comparison of the sound velocities of the low concentration samples
with the velocity value of dioxane indicates coupling between the elastic waves propagating in the polymer network with those propagating in the solvent [21]. Since the density of the different materials in these samples is nearly the same, we can also consider the velocity data
as a measure of the real part of the longitudinal modulus [22]; therefore in the length scale
observable in this experiment we find that the longitudinal modulus of low crosslink content
samples are comparable with the bulk modulus of the solvent. The elastic properties of the medium are characterized in terms of the complex longitudinal modulus M = M'+ I M"
directly connected with the experimentally measured quantities, I-e- the velocity V and the
absorption coefficient a. In particular, the velocity is associated to the real part of M by V~
= M'/p (p is the average density). Furthermore, since M is related to the compressional
modulus It and the shear modulus G(M
= It + 4G/3), the Brillouin data are also sensitive to the shear rigidity of the system, although only longitudinal properties are probed directly.
Therefore, we can associate higher sound velocity with a solid-like behavior, and slower sound
velocity to a liquid-like behavior [14].
The behavior of the velocity data and therefore of the longitudinal modulus for the gels with
intermediate crosslink content IEDMA " 1.5 ill,2 ill) is quite different to that of low crosslink content samples and in this case Aw vs. k (see Fig. 2) shows a positive curvature. As can be easily observed in figure 3b, the sound velocity shows a slow decrease up to a minimum that is located at about 29 pm~~ for the I-S ill gel and 28 pm~~ for the 2 ill gel. For samples with
higher contents of crosslinker (Fig. 3c) instead of minima we observe maxima that are located at about 28 pm~~ for gel with 4 ill of crosslink and 31 pm~~ for gel with 6 ill crosslink.
We interpret the k dependence of the extrema in figure 3 IEDMA > 1.5 ill) by associating
the position of the minimum with the characteristic size of the less dense regions and the
position of the maxima with the characteristic size of the highly cross-linked regions. This
interpretation is based on the expectation of a higher (solid-like) sound velocity in the highly
026 26
u dioxane o Pure mma
021 21
(a) (b)
o
A o % o .o %
021 021
j (c) (d)
~ °
0 26
o26
$~ A 1.5 %
a 2.O%a
~l
021
021
(e) (f)
0 16
° 4.O % cJ 6.O%
021 021
(9) (~)
016
24 26 28 30 32 34 24 26 28 3D 32 34
k(~m'~)
Fig. 2. The Brillouin frequency shift &(w) as a function of the scattered wavevector k for samples
with different crosslink concentrations, fEDMA. The frequency shift for dioxane and unpolimerized MMA solution is also shown for comparison.
2086 JOURNAL DE PHYSIQUE II N°12
1450
1400
1350 . 6.0 %a (C)
1300
24 26 28 30 32 34
isoo
11 1.5%a (b)
- 1450 O 2 %a
)
# ~~~~
> 350
;300
24 26 28 30 32 34
O 0 % (a)
j450 11 Pure mma
h 0%a
'400
1350
1300
24 26 28 30 32 34
~~~ ~-i~
Fig. 3. Phase velocity V as a function of scattered wavevector: (a) for dioxane (dashed line), dioxane-unpolymerized MMA (square), and for samples with crosslink concentration fEDMA
" 0 %
(circle) and % (triangle); (b) for fEDMA
" I-s % (square) and 2 % (circle); (c) for fEDMA
" 4 %
(filled circle) and 6 $i (filled square).
cross-linked regions and a slower (liquid-like) sound velocity in the less cross-linked regions.
Although the data do not extend over a large k-range, the trend in the position of the minimum as a function of k suggests that the size of the less dense regions increases on in-
creasing the crosslink content. Correspondingly the characteristic size of the high crosslink
regions seems to decrease on increasing the cross-link content. This is consistent with the pos- sibility that increasing the cross-link concentration favors a further clustering of the polymers [5]. Since a spanning network is already present in the gel, distribution of additional crosslink
clusters can only be accomplished by an exclusion of the solvent from the already existing clusters, with a corresponding reduction of the cluster sizes and an increased size of the low density "liquid like" islands in the gel. The difference in concentration between the high and
low cross-linked regions increases on increasing of the cross-link content, in agreement with the observed increase of scattered intensity.
Further support to this interpretation is offered by a recent Study of depolarized Rayleigh scattering on the same samples [23]. In the same concentration range where we observe this solvent-exclusion phenomenon, we measure a change in the number of freely rotating terminal groups of the MMA polymer.
This interpretation is also confirmed by computer simulations using the kinetic gelation
model where we found that at higher crosslink content the distribution of the crosslinking
monomers became non-uniform and indicated the presence of correlations. In polyacrylamide
gels(which are prepared by similar methods of free-radical polymerization as used in this study)
Raman spectra showed the presence of clusters of cross-linking monomers. The decreased swelling capacity of highly crosslinked gelsis also well known and consistent with our suggestion
that solvent is excluded from regions of high crosslink content.
In summary, our results are consistent with the possibility that at high crosslink concentra- tion the gel undergoes a micro-phase separation triggered by increased cross-link content, as predicted by de Gennes [5]. This phase separation is frozen in by the presence of the already existing spanning network, explaining the observed microscopic k scale. Brillouin scattering
can successfully be used to detect such microscopic inhomogeneity.
Acknowledgements.
We wish to thank Mr. Chien Shiu Kuo for help with preparing samples and C. Konak and H-E- Stanley for helpful discussions. The research at Boston University was supported by grants from NSF and British Petroleum. The research of F.M. was supported by MURST.
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