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Weakly charged polyelectrolyte gels : temperature and salt effects on the statics and the dynamics
F. Schosseler, A. Moussaid, J. Munch, S. Candau
To cite this version:
F. Schosseler, A. Moussaid, J. Munch, S. Candau. Weakly charged polyelectrolyte gels : temperature and salt effects on the statics and the dynamics. Journal de Physique II, EDP Sciences, 1991, 1 (10), pp.1197-1219. �10.1051/jp2:1991128�. �jpa-00247584�
J. Phys. II France 1 (1991) l197-1219 OCTOBRE 1991, PAGE l197
Classificafion Physics Abstracts
61.25H 82.70 05.90
Weakly charged polyelectrolyte gels : temperature and salt effects on the statics and the dynamics
F. Schosseler (I), A. Moussaid ~2), J. P. Munch (2) and S. J. Candau ~2)
(1) Institut Charles Sadron, C-R-M--E-A-H-P-, 6 rue Boussingault, 67083 Strasbourg Cedex, France
f) Laboratoire d'Ultrasons et de Dynarnique des Fluides Complexes (*) Universitd Louis Pasteur, 4 rue Blaise Pascal, 67070 Strasbourg Cedex, France (Received 30 April 1991, accepted l7July 1991)
Rksumk.-Nous mesurons le facteur de structure statique S(q) et le coeffident de diffusion coop6ratif D~ pour des gels d'adde polyacrylique partiellement ionisds, m fonction de la
tempkrature et de la concentration saline. L'influence de ces paramdtres sur S(q) est en accord serni.quantitatif avec les prkdictions d'un moddle rkcent qui prkvoit l'apparition de mdsophases dans des systdmes similaires. Nous calculons D~ en utilisant ce facteur de structure thkorique dans
une approche sirnplifike. L'expression obtenue dkcrit de manidre satisfaisante le comportement observk dons les expkriences.
Abswact, We measure the static structure factor S(q) and the cooperative diffusion coefficient D~ of weakly charged poly(acrylic acid) gels as a function of temperature and salt concentration.
The variations of S(q) with these parameters agree senfi-quantitatively with a recent model that
predicts the occurrence of mesophases in similar systems. We use the theoretical S(q) to derive D~ in a simplified approach. The obtained expression describes satisfactorily the experimental
behaviour of D~.
Inwoduction.
Partially charged polyelectrolyte systems have received much attention from both experimen-
talists [1-8] and theoreticians [9-11]. This is partly due to their numerous applications in food and cosmectics industries, metal solution recovery and petroleum enhanced recovery. Also
they are thoujht to provide simple models for complicated biological systems,
However the physics of those systems is far from being completely understood. Contrary to the case of neutral polymer systems whose properties are controlled by short range Van der Waals interactions, in a fully charged polyelectrolyte system, the physics is dominated by long
range electrostatic forces. Thus the properties of these systems are qualitatively difserent and
one obtains difserent regimes by switching on and increasing continuously the electrostatic interactions in an originally neutral polymer system.
(*) Unitk de Recherche Associde au C-N-R-S- n 851.
l198 JOURNAL DE PHYSIQUE II bt lo
Weakly charged polyelectrolytes in poor solveljt constitute
a good example of this feature.
Recent theoretical considerations have predicted that these systems should be able to undergo
a microscopic phase transition upon cooling and form mesophases [9-10], These predictions
have obtained partial support from experimental results obtained on weakly charged
poly(acrylic acid) ~I~AA) gels. A peak wis observed in the structure factor measured by small angle neutron scattering (SANS) technique for gels with difserent iod2ation degrees and
polymer concentrations [5, 6]. The position of this peak varies with the ionization degree as expected from the theory. However, the concentration dependence of the position of the maximum was at variance with the predicted- one and this discordance was tentatively interpreted as an efsect of the presence of crosslinks in the gels. Nevertheless the validity of the model may still be questioned. A decisive breakthrough would consist in testing the
evolution of the structure factor with the salt concentration and the temperature.
In this paper we report on light and neutron scattering experiments varying these
parameters. The obtained results support further the theoretical model. Moreover the numerical coefficients obtained from the data evaluation together with simple arguments allow us to describe in a semi-quantitative way the dynamic properties of these gels when the polymer concentration, the ionization degree, the salt concentration and the temperature are
varied.
Theoretical background,
The detailed theoretical analysis of weakly charged polyelectrolyte systems is possible in poor solvent conditions. In this case the po1ynler chain conformation remains nearly gaussian and the RPA formalism can be used safely. This feature was reccgn~ed only recently and led to a
renewed interest in those systems.
The recent models [9, 10] consider semi-dilute solutions of partially ionized polymer chains slightly below the Flory compensation temperature @. Typical examples are water solutions of
weak polyacids (Poly(acrylic acid) or Poly(methacrylic acid)) that have a hydrophobic
backbone. Without the presence of electrical interactions, such systems would undergo a
macroscopic phase separation but the small fraction of ionized monomers ensure their solubilization. If the quality of the solvent is further decreased, the phase separation of such systems is predicted to occur now on a microscopic scale and to lead to mesophase formation.
The presence of small ions is responsible for this new feature. Due to overall electroneutrality requirement, a macroscopic phase separation would compell the counterions to follow the
polymer chains in the polymer rich phase. This would lead to a dramatic loss of entropy for the ccunterions. It is much more favorable for the system to undergo a nficroscopic phase separation into oppositely charged polymer rich and polymer poor domains. The free-energy
increase due to the local violation of the electroneutrality condition is compensated by the
gain of entropy for the counterions. Assunfing the polymer chains to remain nearly gaussian
in the vicinity of the transition, the structure factor of the polymer solution can be calculated.
In terms of reduced variables it reads :
~ ~~~
4
i~
r( a
~ (x~ +
i~~~~
t) + ~~~
Here itt is the BjermJn length, a the fraction of ionized monomers and ro is a typical
distance given by :
~~2 =
48j~» ~>~ a ~ i/~ ~~~
M 10 WEAKLY CHARGED GELS : TEMPERATURE AND SALT EFFECTS l199
where a is the length of the monomer unit and p the polymer concentration, The reduced wavevector x is defined as the product of the length ro by the usual wavevector transfer defined in a scattering experiment q =4 «IA sin (@'/2), where A is the wavelength of incident particles and @' the scattering angle. Similarly s is a reduced ionic strength defined as
s= «~r(, where «~~ is the usual Debye Hfickel screening length and t is a reduced temperature given by t = 12 r(hp la~, where h
= (2 vr + 3 wp )is the usual virial term in
a solvent, v being the excluded volume, r
= (T- >16 the reduced temperature and
w the third virial coefficient.
In a finfited range of polymer concentration p, ionization degree a and salt concentration
p~, the structure factor (Eq.(I)) exhibits a maxhnum for a non-zero value q* of the
wavevector transfer, given by :
q*~ + « ~
= ri ~ (3)
This corresponds to cases where the system would undergo upon cooling a microphase separation transition with a domain periodicity given by 2 w/q*. The observed peak reflects that concentration fluctuations with wavelength 2 w/q* are favored above the microphase separation transition. At the transition, the maximum increases vithout changing its position
and becomes a Bragg peak, revealing the onset of an ordering in the system. Upon increasing
salt concentration or decreasing polymer concentration and/or ionization degree, equation (3) shows that the maximum shifts to smaller q values. Vn1en the condition « ~
~ rp~ is no longer fulfilled, the maximum is pinned at zero q value and upon cooling, the system undergoes an usual macroscopic phase separation. The description of the phase diagram has been given in reference [9]. The agreement of the above theoretical picture with experimental results is
rather satisfactory.
Dynamic properties of weak polyelectrolytes in poor solvent are a priori more difficult to understand. A possible approach consists in using Kubo formulation to calculate the dynamics of such systems [12]. Assunfing that concentration and velocity fluctuations are statistically independent and using a preaveraged Oseen tensor for hydrodynamic interactions, this
approach relates dynamic properties to the static correlation function of monomer concen- tration g(r) :
d~re'~~ g (r) kT/6 w qr
~~~~
dr e'~~ g(r)
~~~
where q is the solvent viscosity and k the Boltzmann constant. In the limiting case
q = 0, D(q) corresponds to the cooperative difsusion coefficient D~ that is measured in a
dynamic light scattering experiment. The integration of equation (4) in tiffs limit is performed
in the Appendix and leads to the final result :
Of course this approach is only a rough approximation because polyelectrolyte systems are
multicomponent systems. A rigorous description of their dynamics requires the contributions of all components to the relaxation process to be taken into account. The expressions of tl~e
corresponding difsusion coefficients are then much heavier to handle. For the purpose of this
JOURNAL DE PHY~QUE JJ T i,M lo. OCTOBRE 1991 52
1200 JOURNAL DE PHYSIQUE II bt 10 paper, equation (5) is suffcient since it gives a qualitative behavior of D~ in agreement with the experimental trends. More rigorous expressions are found in reference [13].
Expedmental section.
For the sample preparation we have followed the procedure already described in a preceding
paper [5]. Gels are prepared by radical copolymerization in an aqueous solution of acrylic acid and N-N~-methylenebis(acrylamide). The gelation reaction is initiated by ammonium
peroxydisulfate. The ionization degree, a, is defined as the ratio of the number of carboxylate
groups to the total number of monomers. Since poly(acrylic acid) is a weak acid,
a can be varied over a wide range by changing the pH of the medium. In aqueous solution,
a has a nonzero value due to the acido-basic equilibrium :
x~
-CIf~CH(COOH~ + H ~O# -CH~CH(COO ~ + H~O+ (6)
The ionization degree is a decreasing function of the polymer concentration. For the concentrations used in this study (0.416 M
< C~ ~ l.44 M ) the dissociation of the polyacid is very low. Thus, we have approximated the dissociation constant to that of the monomeric acrylic acid: K~ = 5.6 x10~~ T%s leads to values for
a decreasing from I.I x10~~ to
5 x 10~~ when the polymer concentration increases from 0.416 M to 1.44 M.
Higher ionization degrees (a ~ 10- ~) are obtained by partial neutralization of the polyacid with NaOH to a given stoichiometric ionization degree according to :
-CH~CH(COOH~ + Na + OH
~ -CH~CH(COO ) + H~O + Na+ (7)
Very low ionization degrees (a < 5 x 10~~) are obtained by addition of HCI to the solution to shift the dissociation equilibrium of the weak acid towards the acidic form :
K~
-CIf~CH(COO ~ + H~O+ + Cl~ m -CIf~CH(COOH~ + H ~O + Cl (8)
After the mixing of the components, the solutions are futered with 0.2 ~m futers to get rid of dust particles. Gelification is carried out at 70 °C for 12 h directly in the scattering cell after
nitrogen has been bubbled in the solution to remove the dissolved oxygen tht would inhibit the radical reaction. Samples for SANS experiments are prepared along the same lines but
vith replacement of H~O by D~O to obtain a good contrast. The samples prepared at the lowest polymer concentration, I-e-, C~ = 0.42 M, are not macroscopic gels but solutions of
branched polymers.
SANS experiments were performed on spectrometer PACE in Laboratoire Lkon Brillouin
(Laboratoire commun CEA-CNRS). The two sets of experiments were performed under
nearly the same conditions ;
= 8 A for the wavelength of the incident neutrons and
a
sample detector distance equal to 1.50 m. More precisely A was 8.051during the study of salt efsects and 8.161i for the investigation of temperature efsects. These apparatus
configurations allow one to obtain q value in the range (1.5 x 10~ ~
< q (1- ~)
< l.7 x 10~ ').
All data were treated according to standard procedures for small-angle isotropic scattering.
The spectra were corrected for transmission, sample thickness, and electronic noise.
Monomer solutions with the same compositions as those used to prepare gels were taken as
background samples. This choice gives background samples very similar to the samples as far
bt 10 WEAKLY CHARGED GELS : TEMPERATURE AND SALT EFFECTS 1201
as incoherent scattering is concemed. In particular their transmissions differ generally less than I fb. Normalization to the unit incident flux, geometrical factors, and detector cell
efficiency corrections were performed by using the incoherent scattering of H~O, corrected for the scattering of the empty cell. The data were put on an absolute scale by introducing the
value d3/dJ2
= 0.92 cm- for the difserential incoherent cross section per unit volume of
H~O at 25 °C. This absolute scattering intensity I(q) is directly proportional to the structure factor S(q) (G(x) in dimensionless variables) that is calculated theoretically (Eq.(I)).
Unfortunately we have no measurements of the proportionality constant which is the contrast between the polymer and the solvent. In principle this contrast can be calculated if we know the partial molar volume of the scattering centers. In the case of polyelectrolytes this parameter is difficult to evaluate and usually only orders of magnitude can be obtained for the contrast factor. Note that here again we neglect the intensity scattered by small components
as well as the intensity arising from crosscorrelations between them and the polyions. This simplification is justified here because we keep small ionization degrees as well as low salt
concentrations [5].
The optical source on the light-scattering apparatus is a Spectra-Physics argon ion laser operating at A
o = 4 880 A. The time-dependent correlation function of the scattered intensity
is obtained by using a 64-channel digital correlator (Brookhaven BI 2030). The scattering angle could be varied between 10° and 160°.
For all the gels investigated in this study the intensity correlation data were processed by using the method of cunlulants to obtain tl~e average decay rate, (r), and the variance,
v = ( (r~) (r)~)/(r~)). In these gels we do not observe intensity correlation functions vith two distinct decay rates, as has been reported for polyelectrolyte solutions, but rather a
moderate distribution of exponential decays (v « 0.I ).
For neutral networks the intensity scattered from longitudinal fluctuations of swollen networks is generally heterodyned to some extent by the quasi-static component due to
nonrandom, long-range, stationary concentration fluctuations [14]. In fact, detailed compari-
sons of the intensity correlation functions measured in homodyne and heterodyne detection
geometries showed that the presence of electric interactions leads to a pure homodyne detection mode for the gels with ionization degree larger than 0.05 [8]. In this case,
(r) is found to be proportional to K~, contrary to what was stated in the study of
reference [3] (last entry) where experiments performed in too small cells showed deviations from the K~ dependence in the small K range. Therefore these gels can be considered as homogeneous at the length scale probed by lijht scattering experiments. For the gels with the lowest ionization degrees, the rate of signal heterodyning by quasi-static concentration
inhomogeneities increases as the scattering angle is decreased. The cooperative difsusion
constant measured for the larger scattering angles can however be assigned to a pure
homodyne detection mode.
The scattered intensity data were treated according to standard procedures [5]. The static structure factor in the limit q
~ 0 was obtained from the excess intensity scattered from concentration fluctuations using the relationship':
6l (q
~ 0)
= A dn 2
~ ~~24
° dC ~'m m S(0)
A
(9)
where Ao is an apparatus constants, that is determined by using the benzene as a reference
sample [5], M~ is the molar mass of acrylic acid and NA Avogadro number. For
(dn/dC) we used the values obtained by Kitano et al. [15] for dilute solutions of PAR in
water.
1202 JOURNAL DE PHYSIQUE II M lo
Resultso
1. SCATTERED INTENSITY. As a general trend, the intensity scattered from the gels
increases when the temperature is decreased.
In the range of small q values, this is illustrated by the data in figures I and 2, obtained from light scattering experiments. For gels with ionization degrees larger than a
= 0.05, the
intensity does not depend on the value of the momentum transfer at room temperature and tills feature is not altered upon varying the temperature between 288 K and 318 K (Fig. I).
Cs(n1M) T(°C)
~
0 15
.
0 45
~ o 75 15
. 75 45
~
i
q~ / 0~~i ~~
Fig. I. Structure factor as obtained by light scattering for gels at C~ = 0.707 M and a
= 0.05 for two
temperatures and two salt contents. Lines are guides for the eye.
The intensity is only slightly dependent on the temperature (Fig. 2). Lowering the temperature from 333 K to 283 K results in an increase of about 30 9b in the scattering intensity for a gel with a
= 0.I.
When the ionization degree decreases, the effect of the temperature becomes more
important (Fig. 2a). If a strong acid @ICl) is added into the reaction bath to further,reduce the ionization degree, this efsect is still more pronounced : for q = 2.42 x 10-~ l~~, the
increase in the scattering intensity is about 200 fb when the temperature is decreased from 323 K to 283 K (Fig. 2a).
For an ionization degree a =0.051, the same trend is observed if the ionic strength is increased through the addition of salt. As the salt concentration increases, the gels become more and more sensitive to the temperature, especially at low q values (Figs. I and 2b).
In the
~q range investigated by SANS experiments, the intensity of the maximum increases when the temperature decreases. The position of the maximum appears to remain unchanged
for the gel with
a = 0.10 (Fig. 3a). For the gel vith a
= 0.05 (Fig. 3b), the peak seems to shift slightly to smaller q values as T is decreased. The effect of temperature on the peak position is shown in figure 4.
M 10 WEAKLY CHARGED GELS : TEMPERATURE AND SALT EFFECTS 1203
2.5
~
2.O . pHo
D PHI
o 0.009 m
/~f~
~/~
oo.5
O
T a)
1204 JOURNAL DE PHYSIQUE II bt 10 o.zo
~i~ o
15°C
~a°Oo zooc
a~~no ~ ~ooc
n n +
~+~ i~ ~ 40°C
O.12 '**',~~
-~ ~+~ o
tJM #~
~_ te
+~ e
0.08 "a
., .a
.o .a'I,
~~~ ~~~~'iv,
o.oo
a) q/A~'
oio
o 15~C
o_08 b 20~C
o°(iO + 30~C
on~ a2
~
40°C oR~++z$~tRg
0.06 ]~+$~~ ~ t+I
~s +$* ~t~fi
tJ~
~- ~~
~M '
0.04 'lo
+O+O
#j~~
002 ~~~i
) oo
b) q/A~'
Fig. 3. -Variation of the SANS intensities vith the temperature. The polpner concentration, C~ =
0.707 M, is the same for both figures. a) a = 0.051; b) a = 0.101.
The addition of a salt induces
an increase of the intensity scattered by the gels. In the small q range investigated in light scattering experiments, the intensity is independent of the
wavevector momentum and is given by I~
~
(l /4 aria) (« la)~ as soon as the ionization degree
is larger than a few per cent. This result can be obtained readily from equation (I) and is well verified by experiments. This can be seen in figure 5 where the ligl~t scattering intensity values
obtained in reference [5] are plotted as a function of xl a )~. Thus at the length scale probed by light scattering experiments the amplitude of the fluctuations of polymer concentration is
related to the ratio of the mean distance between charges along the chains (~ a ~) to the
Debye-Hfickel screening length « For small values of this ratio, the electric interactions
