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LIGHT SCATTERING INVESTIGATION OF AQUEOUS SOLUTIONS OF POLY (METHACRYLIC ACID) AND POLY (SODIUM METHACRYLATE)#
Ksenija Kogej,*abc Janez Cerkovnik,3 Hugo Berghmans,b and Sergio Paolettic
^Faculty of Chemistry and Chemical Technology, University of Ljubljana, SI-1000 Ljubljana, Slovenia b Department of Chemistry, Catholic University of Leuven, Celestijnenlaan 200F,
B-3001 Heverlee, Belgium ^Department of Biochemistry, Biophysics and Macromolecular Chemistry, University of Trieste, 1-34127
Trieste, Italy
Dedicated to Professor Davorin Dolar on the occasion of his 80th birthday. Received 21-05-2001
Abstract
Light scattering was used to study the properties of poly (methacrylic acid), PMA, and its sodium salt, NaPMA, in aqueous solutions. The polymer is an atactic one, composed of around 45% heterotactic and 55% syndiotactic triads. The weight-average molar mass of a single PMA chain (Mw,0 =131 kg/mol) was estimated from experiments with NaPMA in 0.1 M NaCl. From the scattering data at zero-angle it was concluded that PMA is inter-mo lecularly associated in 0.1 M HCl. The data were treated according to the Open Association Model of Elias, which yielded Mw for the associated PMA form equal to 188 and 170 kg/mol at 25 °C and 55 °C, respectively. Furthermore, the second virial coefficient and a relatively high value for the apparent association constant were obtained: A2 = 1.37 x 10"3 and 1.24 x 10"3 mol ml/g2 and £app = 3.4 x 105 and 2.0 x 105 at 25 °C and 55 °C, respectively. The radius of gyration of NaPMA in 0.1 M NaCl is 7?g = 47 nm, whereas for PMA in 0.1 M HCl it is equal to 20.4 nm at 25 °C. An increase in temperature from 25 °C to 55 °C brings about a decrease in Rg to 16.9 nm for PMA in 0.1 M HCl. The changes in thermodynamic functions point to a hydrophobically driven association process of PMA chains.
Introduction
Poly (methacrylic acid), PMA, is a weak polyacid with hydrophobic methyl side
chains. Their presence leads to a number of peculiarities in solution behavior of PMA, which point that some elements of structure are present in the dissolved polymer. In contrast to poly (acrylic acid), which displays a smooth transition from a more compact coil to an expanded one upon increasing its degree of ionization, PMA resists expansion before a critical charge density is attained. This transition is usually described as a cooperative change from a tightly coiled cluster of the un-ionized polyacid to an extended form of the charged polyion coil. Furthermore, PMA is known to form thermo-reversible gels in concentrated solutions that display a lower critical solution
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temperature (LCST) behavior; a gel phase is formed upon heating the solution. a From viscometric and thermodynamic studies of un-dissociated PMA it was concluded that the molecule is intramolecularly bonded in dilute solutions. These intramolecular bonds in the dilute regime eventually lead to agglomeration (e.g. gelation) in concentrated solutions caused by intermolecular association. a
The aim of this paper is preliminary studies of the association behavior of PMA in aqueous HCl solutions. Wide-angle light scattering is a very sensitive method that is able to detect even very small amounts of the associated material. Light scattering measurements will be performed in aqueous solutions of PMA at zero degree of neutralization, gin = 0, and in solutions of its sodium salt, NaPMA, at gin = 1. It has been pointed out frequently that the behavior of PMA depends considerably on the type and degree of stereo-regularity of the chain. " For example, the isotactic form of PMA displays a partly irreversible Potentiometrie behavior in aqueous solutions " in contrast to the atactic and syndiotactic ones. Binding capacity towards various counterions depends considerably on the tacticity of the polyion. In most of the investigations of PMA, however, the tacticity of the polyion is either not known or not reported. It is therefore difficult to correlate the existing data with the detailed structural features of the chain. One of the aims of our study is to also ascertain the stereo-chemical composition of the studied sample.
Experimental section Materials
Poly (methacrylic acid) was prepared by polymerization of methacrylic acid using a
standard procedure.   The tacticity of the polymer was determined from the ester form.
The   polyacid   was   dissolved   in   a   methanol/water   mixture   (2:1)   and   ethereal
diazomethane  solution was  added while  stirring to  yield the methyl  ester,  poly
(methylmethacrylate), PMMA.   The tacticity of the resulting PMMA was determined
from the signals of the a-methyl group in the proton and in the    C NMR spectrum   of
a CDCI3 solution. The polymer contains around 45% heterotactic and around 55%
syndiotactic triads. The amount of the isotactic ones is negligible.
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The stock solution of PMA for light scattering measurements was prepared by dissolving the dry acid in ultra pure water obtained with the Milli-Q-Reagent Grade Water System, Millipore. To ensure complete solubilization of the polymer, the solution was stirred overnight at room temperature. Afterwards, it was transferred quantitatively into a volumetric flask and a desired amount of 1 M HCl was added to yield the concentration of HCl equal to 0.1 M. For the preparation of NaPMA stock solution, PMA was first dissolved in water and 1 M NaOH solution was slowly added under continuous stirring and blowing through with N2 until the pH of the solution was around 8.5. The solution was then transferred into a volumetric flask and the calculated amount of 1 M NaCl was added. All light scattering experiments with NaPMA were performed in 0.1 M NaCl. Before performing light scattering measurements, all solutions were filtered directly into measuring cells through Millipore filters (type GS) with a pore size 0.22 |um using a closed circuit involving a filter holder and a peristaltic pump. The filtering time was around 5-15 minutes.
Light Scattering Measurements
The static light scattering at 25 °C and 55 °C was measured at angles between
40° and 150° using a commercial Amtec MM 100 photometer. A cylindrical cell, containing the solution, was immersed in a thermostatically controlled toluene bath. As the light source, a monochromatic and polarized beam of a He-Ne laser (Spectra Physics, Model 124) operating at 632.8 nm was used. The proper optical alignment of the instrument was checked regularly by measuring the scattering of toluene. The refractive index increment, dn/dc, for PMA and NaPMA was taken from the literature. The following variation of dn/dc with the degree of neutralization, on, is reported
-^ = 0.171 + 0.092aN(ml/g)                                                       (1)
dc
It gives dn/dc = 0.171 and 0.263 ml/g for the acid (on = 0) and for the salt (gin = 1), respectively. These values were used in elaborating the data obtained by static light
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scattering method. All light scattering experiments were performed in the concentration range of the polymer below 2 g/L.
Analysis of the Light Scattering Data
Concentration   dependence.   The   experimental   data   were   analyzed   for   the
concentration dependence according to the Open Association Model (OAM) of Elias.
For a system having a polydispersity index, PI (PI = MJMn, where the indexes w and n
denote the weight and the number averages of the molar mass, respectively), the OAM
introduces an apparent weight-average molar mass of an associating species, (Mw)ass,
as12'13
(Mw L - [K.0 Ì + /m)KmPI ¦ MwfiCp Y2                             (2)
In Eq. 2, MW;o is the weight-average molar mass of the fundamental non-associating
1 7
species (unimer ), Kass is the apparent association constant for the process, and cp is the concentration of the polymer in g/L. By substitution of Eq. 2 into the classical Zimm formula ' for the inverse of the reduced scattering intensity, Kcp/R$, at a scattering angle 6
R*
f   1                         ^
+ 2Anc„ +.
(3)
the expression for the concentration dependence of scattering at 6*—»0° takes the form
Kcp
Ro
[(MwJ+4000KassPI-M
w,0Cp
+ 2A2cp                        (4)
1/       —2~p
In Eqs. 3 and 4, K is the optical constant in the light-scattering equation, Rq is the Rayleigh ratio, A^ is the second virial coefficient, and P(Q) is the form factor of a macromolecule (note that P(Q) = 1). The PI for our sample is not known. Consequently, the product ^ass-PI was used as a single fitting parameter, Kapp = ^ass-PI,
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together with MW;o and Aj. The second virial coefficient was considered to be a constant
n   if
for each series of experiments, irrespective of the extent of association.   '    Knowing MWfi, Eq. 4 can be used as a two-parameter equation for the evaluation of Kapp and Aj.
Angular dependence. The form factor P(Q) depends on 0 and on the shape and size of the scattering particle. It can be expressed in relation to the so-called concentration-dependent static correlation length, <^(cp), by the expansion
Piß)
i-(^(cJ+A(^yy
(5)
where q is the scattering vector given by the relationship
4ft -n, sin —
À
(6)
In Eq. 6, A is the wavelength of the incident light and ns is the refractive index of the solvent (1.33 for water). P(Q) enables the evaluation of the z-average root mean square
radius of gyration, \\R2g)       , of the macromolecule. For simplicity, Rg will be used to
designate the latter quantity. The radius of gyration is obtained from the static correlation length at infinite dilution, £0> according to Eq. 7
Rg=4Z-[\ïmÇ{cp)j=S-^                                       (7)
where <^q is the result of the extrapolation of <^(cp) to cp = 0.
After substitution of P(Q) (Eq. 5) into Eq. 3, the 1/P(9) term can be approximated for small g-values by the usual linear dependence on q . One obtains then the following expression for the reduced light scattering intensity at constant cp, known as the Zimm-approximation
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Kcr
Ra
(M J    +2AlCp
V      w t ass
(l + f(c>)
(8a)
where x = q . (Although the relation between <^(cp) and R% given by Eq. 7 is strictly valid at infinite dilution only, one can operationally use a similar one
Rg«*=S'Ç{cp)
(9)
even for finite values of cp. In this notation, Eq. 8a takes the form
Kcr
Ra
(M )    +2AlCp
Vr* w ) ass
\, kppJ
(8b))
If the angular dependence of the intensity of scattered light shows a curvature when q approaches zero the linear extrapolation procedure is no longer justified. In the case of a non-linear q -dependence of the scattering function, the latter can be approximated by various relationships. A polynomial function of the second order in x
Kcr
Ra
(mw)
\      w / ass
+ 2A2c
\+<£lx+
b2x
(10)
gives a much better fit of the experimental data than the most often used linear approximation. In Eq. 10, bi is a constant resulting from the fitting procedure. Eqs. 8-10 were applied for the evaluation of the radius of gyration of PMA and NaPMA.
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Results and disccusion
1. NaPMA in 0.1 MNaCl. The completely charged sodium salt of poly (methacrylic acid) was used to estimate the weight-average molar mass of a single PMA chain under the universally accepted assumption that PMA - anions don't associate with each other. Figure 1 shows the Zimm plot15 for NaPMA in 0.1 M NaCl at 25 °C, i.e., a plot of the reduced light scattering data, KcpIRq, against sin (6/2) + kcp, where k is an arbitrary
sin (e/2) + 10c
Figure 1. The Zimm-plot of NaPMA in 0.1 MNaCl at 25 °C.
constant (k = 10 in this case). The angular dependence of scattering (at constant cp) is close to linear as it can be appreciated from the curves in Figure 1. Mw of the sample is obtained by a double extrapolation procedure, first to 6 = 0° (or q = 0, cf. Eq.6) at constant cp and then to cp = 0. The zero-angle values, Kcp/Rq, were obtained in two ways: by a linear (Eq. 8a or b) and by a second order in q polynomial fitting (Eq. 10). The difference between Kcp/Ro values obtained by both procedures is small. However, the latter one results in lower values of the sum of the squares of residuals. These Kcp/Ro results are therefore included in Figure 1 as full circles, whereas the full triangles are the result of the extrapolation at constant angle to cp = 0.
The limiting slope of the 6= 0° curve in Figure 1 is proportional to the second virial coefficient of NaPMA in 0.1 M NaCl. A value A2 = 2.64 x 10"3 mol ml g"2 is obtained.
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The extrapolation to cp = 0 was carried out by a second order polynomial fitting in cp. The resulting Mw for NaPMA is equal to (165+4) kg/mol. From this, one obtains the weight-average degree of polymerization equal to 1528. If one assumes the same degree of polymerization for the polymer also in the acid form, the resulting weight-average relative molecular mass of an isolated PMA chain is equal to 131 000 (i.e., Mw for PMA is equal to 131 kg/mol).
2. PMA in 0.1 M HCl at 25 °C and 55 °C. Scattering studies with PMA in aqueous 0.1 M HCl were performed at 25 °C and at 55 °C. Figure 2a and 2b show the resulting Zimm plots. One can clearly see that these plots are curved, markedly so at lower concentrations, whereas at higher concentrations the curvature is less pronounced. The extrapolation to 0 = 0° was carried out by the usual linear (Eq.8 a and b) and by a polynomial fitting procedure (Eq. 10). In the case of PMA, the latter one gives a much better fit of the experimental data, indicated by the lowest values of the sum of the squares of the residuals. Therefore, the polynomial fitting in q was considered for the evaluation of the Kcp/Rq values at both temperatures. These values are plotted in Figure 3. They show a pronounced deviation from linearity in the low cp range.
The upward curvature in Kcp/Ro values when cp approaches zero is diagnostic for inter-molecular association. ' Therefore, an appropriate association model has to be applied for the treatment of these data. In our case, the Open Association Model of Elias was used, in the first place as a three-parameter equation (Eq. 4: variable Mw?0, Kapp, and Ai) to evaluate Mw$. The model gives a rather good fit of the data points as can be seen from the curves reported for each temperature in Figure 3. The resulting Mwo for PMA in 0.1 M HCl is (188+4) kg/mol and (170+4) kg/mol at 25 °C and 55 °C, respectively. These values are considerably higher than the value proposed for a single un-associated PMA chain (MW;o =131 kg/mol, see above. Note that Mw obtained by a linear extrapolation ofKcp/Ro points to cp = 0 for cp >~3 x 10" g/L is even higher: Mw = 206 kg/mol and 186 kg/mol at 25 °C and 55 °C, respectively.), thus confirming the significant inter-chain association.
The values of Ai and Kapp for the isolated, non-associated chain in the acid form were obtained from the OAM by fixing in the fitting procedure Mw o to the stated value
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131 000. The resulting second virial coefficient of PMA in 0.1 M HCl is considerably lower than the one observed previously for NaPMA: A^ = 1.37 x 10 mol ml/g and 1.24x 10 mol ml/g at 25 °C and 55 °C, respectively. A lower A2 can be ascribed to an essentially
6.0
o
E
of
a)   T = 25°C
0.4            0.6           0.8
sin2(e/2) + 10c
1.2
6.5
2>  6.1 o
ir
> 5.:
5.0
b)   T	= 55°C							
						•		
¦	•		•			•	•	
>f ?¦	•	•		•	~"S"	•		
~-~A^						Y      »             T		
¦						cp103/gml_-•    0.0600	T	0.8997
	i		l		I	a    0.3000 ¦     0.6000 i	? I	1.2136 1.3564
0.0
0.2
0.4
0.6
sin2(e/2) + 10c
0.8
1.0
1.2
Figure 2. The Zimm-plots of PMA in 0.1 M HCl: a) at 25 °C andb) at 55 °C.
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uncharged  character  of PMA molecules  at  low pH  and to  the presence  of the hydrophobic methyl side-groups on the PMA main chain. In accordance with the LCST
11   17
behavior  of PMA, Aj  decreases  with increasing temperature.   '     Katchalsky and Eisenberg17 have found a value of A2 close to zero for PMA in 0.02 M HCl at 30 °C.
6.0
5.0 I 4.0 C 3.0 °    2.0
1.0
0.0
0.0000       0.0005       0.0010       0.0015
cp / g mL1
Figure 3. The dependence of the zero-angle values, Kc/Ro, on polymer concentration, cp, for PMA in 0.1 M HCl at 25 °C and at 55 °C. The lines are the results of the application of Elias Model to the treatment of the data (see text).
However, the results of Silberberg et al. show that A2 approaches the zero-value at considerably higher temperatures as reported before, i.e., at 58 °C. Temperatures around room T would then correspond to rather good solvent conditions. The same can be concluded for PMA in 0.1 M HCl in our study. The apparent association constant for PMA in 0.1 M HCl is rather high: Kapp = 3.4 x 105 and 2.0 x 105 at 25 °C and 55 °C, respectively.  These Kapp values  are  comparable to  those reported  for  a strongly
I ^
associating K-carrageenan system in aqueous salt solutions. The corresponding free enthalpy change of association is more negative at 55 °C (AG°328 = -33.3 kJ/mol) than at 25 °C (AG°298 = -31.4 kJ/mol), indicating that the increase in temperature promotes intermolecular association of PMA chains. The temperature dependence of both, AG°
II   17
and A2, is in accordance with the LCST behavior of PMA. ' From the temperature dependence of AG° one obtains an estimate for the changes in entropy AS° (= 63 J/(K
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mol)) and enthalpy AH° (= - 12.6 kJ/mol) of the association process. These values, albeit very crude, are comparable with the ones reported for the hydrophobically driven phase separation, e.g., of hydrocarbons in water.
3. Radius of Gyration. The radius of gyration was evaluated by fitting the angular dependence of the scattering data according to different formalisms of Eqs. 8-10. One first obtains for each polymer concentration a value of <^(cp) (or of the apparent radius of gyration, i?gapp, cf. Eqs. 9, 8b, 10). Rg at zero concentration is then obtained from a plot of <^(cp) vs. cp (or alternatively from a plot of i?gapp vs. cp: cf. Eq. 9) by extrapolating to cp = 0. This extrapolation was in all cases performed by using a polynomial function of the second order in cp. Both, a linear ( Eq. 8 a,b) and a second-order (Eq. 10) polynomial fittings were used, giving comparable results. The average Rg values resulting from both procedures are reported in Table 1 for NaPMA in 0.1 M NaCl and for PMA in 0.1 M HCl.
Table 1. Radius of gyration, Rg, (in nm) for NaPMA in 0.1 M NaCl at 25 °C and for PMA in 0.1 M HCl at
25°Cand55°C
system	T/°C	Rg / nm (average values)
NaPMA in 0.1 M NaCl	25	47.0 + 3.8
PMA in 0.1 M HCl	25 55	20.4 + 2.8 16.9 + 1.9
The average i?g-value for NaPMA in 0.1 M NaCl at 25 °C is 47 nm, whereas the corresponding value for PMA in 0.1 M HCl PMA is 20.4 nm. The increase of temperature to 55 °C causes a decrease of Rg for PMA in 0.1 M HCl to 16.9 nm. One can conclude that the increase of temperature leads to a more compact and concurrently more stable associated state of PMA in aqueous solutions. The length of a fully stretched, all trans, PMA chain, with a degree of polymerization equal to 1528, is around 385 nm. From the value of Rg it can be concluded that the conformation of the PMA-anion in 0.1 M NaCl is far from a fully extended one even at the highest degree of neutralization (a^ = 1). The conformation of PMA at low pH (oin = 0) is sometimes approximated by a compact sphere. A value of Rg = 20.4 nm for our sample should correspond to a sphere
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of radius R = 26 nm. This is a much higher value than the one obtained from the specific volume (= 0.68 mL/g) of PMA by proposing a spherical symmetry of the polymer in aqueous solutions. In this              sphere of radius R = 3.3 nm is obtained. One can
conclude that molecules of the "contracted" form of PMA are anyway far from being compact spheres.
References
1.     J. C. Leyte, M. Mandel, J. Polym. Sci. Part A 1964, 2, 1879-1891.
2.     a) J. Eliassaf, A. Silberberg, Polymer 1962, 3, 555-564; b) A. Silberberg, J. Eliassaf, A. Katchalsky, J. Polym. Sci. 1957, 23, 259-284.
3.     Y. Muroga, I. Noda, M. Nagasawa, Macromolecules 1985, 75,1580-1582.
4.     J. C. Leyte, H. M. R. Arbouw-van der Veen, L. H. Zuiderweg, J. Phys. Chem. 1972, 76, 2559-2561.
5.     M. Nagasawa, T. Murase, K. Kondo, J. Phys. Chem. 1965, 69, 4005-4012.
6.     K. Hatada, J. Polym. Sci. Part A, Polym. Chem. 1999, 37, 245-260.
7.     V. Creszenci, Adv. Polymer Sci. 1968, 5, 358-386, and references cited herein.
8.     J. N. Davenport, P. V. Wright, Polymer, 1980, 21, 287-292.
9.     E. Klesper, D. Strasilla, W. Regel, Makromol. Chem. 197'4,175, 523-534.
10.  A. J. Chapman, N. C. Billinghman, Eur. Polym. J. 1980,16, 21-24. U.C. Heitz, M. Rawiso, J. François, Polymer 1999, 40, 1637-1650.
12.  H.G. Elias, Association and Aggregation as Studied via Light Scattering. In Light Scattering from Polymer Solutions; Huglin, M. B., Ed.; Academic Press: London, 1972; Chapter 9, pp 397-457.
13.  K. Bongaerts, H. Reynaers, F. Zanetti, S. Paoletti, Macromolecules 1999, 32, 675-682 and references cited therein.
14.   a) B. H. J. Zimm, Chem. Phys. 1948,16, 1093; b) B. H. J. Zimm, Chem. Phys. 1948,16, 1099.
15.  P. Kratochvil, Classical Light Scattering from Polymer Solutions; Elsevier Science Publishers B. V., 1987, Amsterdam.
16.  M. B. Huglin, Light Scattering from Polymer Solutions; Academic Press Inc., 1972, London.
17.  A. Katchalsky, H. Eisenberg, J. Polym. Sci. 1951, 6, 145-154.
18.   C. Tanford, The Hydrophobic Effect: Formation of Micelles and Biological Membrane;, A Wiley-Interscience Publication, 1980, New York.
Povzetek
Sipanje svetlobe smo uporabili za študij lastnosti polimetakrilne kisline, PMA, in njene natrijeve soli, NaPMA, v vodnih raztopinah. Polimer je atakticen, sestavljen iz približno 45% heterotakticnih in 55% sindiotakticnih triad. Utežno povprecje molske mase ene same PMA verige (Mw0 =131 kg/mol) smo ocenili iz poskusov z NaPMA v 0.1 M NaCl. Iz podatkov sipanja pri kotu nic smo sklepali, daje PMA v 0.1 M HCl intermolekularno asociirana. Podatke smo obravnavali po Odprtem asociacijskem modelu po Eliasu, kije dal vrednosti za Mw za PMA 188 in 170 kg/mol pri 25 °C in pri 55 °C. Dolocili smo še drugi virialni koeficient in relativno visoko vrednost za navidezno konstanto asociacije: A2 = 1,37 x 10"3 and 1,24 x 10"3 mol ml/g2 in Km = 3,4 x 105 and 2,0 x 105 pri 25 °C in pri 55 °C. Radij giracije NaPMA v 0.1 M NaCl je Rg = 47 nm, medtem ko je za PMA v 0.1 M HCl pri 25 °C enak 20,4 nm. Dvig temperature na 55 °C vodi do zmanjšanja Rg na 16,9 nm. Spremembe v termodinamskih funkcijah kažejo, da gre za hidrofobno voden asociacij ski proces med PMA verigami.
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