546 DOI: 10.17344/acsi.2015.1495
Acta Chim. Slov. 2015, 62, 546-554
Scientific paper
Aggregates of Isotactic Poly(methacrylic acid) Chains in Aqueous CsCl Solutions: a Static and Dynamic
Light Scattering Study
Katarina Ho~evar, Simona Sitar and Ksenija Kogej*
Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ve~na pot 113, P.O. Box 537,
SI-1001 Ljubljana, Slovenia
* Corresponding author: E-mail: ksenija.kogej@fkkt.uni-lj.si Tel: +(386-1)-479-8538
Received: 06-03-2015
Dedicated to prof. Jože Koller on the occasion of his 70h birthday.
Abstract
Properties of isotactic polymethacrylic acid, iPMA, chains were studied at 25°C in aqueous solutions at various CsCl concentrations, cs (= 0.05-0.20 M), in dependence on degree of neutralization of the polyion's carboxyl groups, aN, using static, SLS, and dynamic light scattering, DLS, measurements. It was demonstrated that iPMA chains with aN somewhat above the solubility limit of iPMA in aqueous solutions (in the present case at aN « 0.27) are strongly aggregated. The size of the aggregates increases with increasing cs, whereas the shape parameter, p, is approximately constant (p « 0.6), irrespective of cs. The low p value suggests that the aggregates have characteristics of microgel particles with a dense core surrounded by a less dense corona. The diffusion of iPMA chains was investigated also at higher aN, up to aN = 1. The polyion slow mode arising from electrostatic interactions between charged chains was observed for aN exceeding the value 0.27 even at the highest cs (= 0.20 M). The diffusion coefficients for the show mode were nearly independent of aN and cs at the studied polymer concentration.
Keywords: isotactic poly(methacrylic acid), light scattering, hydrodynamic radius, shape parameter, aggregation, poly-electrolyte slow mode
1. Introduction
Intermolecular association and aggregate formation are important in nature and technology. Some examples from the biological field are formation of two- or three-stranded polynucleotides, supramolecular assemblies in virus shells, gelation of polysaccharides, and some from the technological field are polymer-surfactant and polymer-polymer complexation systems that are often used as materials for pharmaceutical applications.1 Very stable inter-polymer complexes are formed when a cationic and an anionic polyelectrolyte are mixed in solution; this is a result of strong electrostatic attraction between the oppositely charged polyions and of the concomitant entropy in-
crease due to the release of their counterions into the solution. Aggregates can also form between chains of the same polymer, if uncharged or weakly charged, very frequently through intermolecular H-bond formation and/or by the help of van der Waals forces and the hydrophobic effect. Hydrogen bonding is a major driving force for complexation of poly(carboxylic acids).2-5 Although a single H-bond can be rather weak (with an energy 2-167 kJ/mol),6 simultaneous formation of a large number of such bonds between two macromolecules (a cooperative phenomenon) may lead to very strong association.
In this contribution, we focus on intermolecular association between the isotactic poly(methacrylic acid), i-PMA, chains in aqueous solutions. iPMA is a highly regu-
lar form of poly(methacrylic acid), PMA, predominately composed of isotactic triads (i.e. sequences of two meso diads, denoted as mm). The other ordered isomer is the syndiotactic PMA, sPMA, made up of syndiotactic triads (the rr sequences, with r for the racemo diad), whereas the randomly substituted PMA is called the atactic or hetero-tactic PMA, aPMA, and contains, in addition to mm and rr, also the heterotactic, rm, triads. Solution properties,2-5,7-14 intermolecular association,4,5,13 and binding of species5 all depend on polymer tacticity. For example, while sPMA and aPMA dissolve in water and show similar solution behavior,8,9 in part because aPMA is normally predominately syndiotactic, iPMA is insoluble in water unless the degree of neutralization of carboxylic acid groups, aN, exceeds a value aN « 0.2.8,9,14 Insolubility of i-PMA originates from the ordered helical conformation of the chain, which is favorable for intermolecular associa-tion.3,5,13,14 It has been recently demonstrated that the regularity on the level of a single chain also leads to gelation of iPMA in concentrated solutions.13
iPMA and aPMA are both strongly associated in dilute solutions too if aN is low (aN = 0 and ~0.25 for aPMA and iPMA, respectively). This was demonstrated by light scattering, LS, studies15,16 in aqueous solutions with added alkali chlorides. However, important differences in the association mechanism exist between the two stereo-izomers. For example, the number of aPMA aggregates increases as a result of shearing the solution (a phenomenon known as negative thixotropy4,17), whereas the iPMA ones disintegrate due to shear stress and reform in solutions at rest.15 In equilibrium, the extent of aggregation is larger for iPMA than it is for aPMA. Besides, iPMA aggregates are observed at a non-zero aN value (somewhat above the solubility limit, which is at aN « 0.2), whereas the aPMA ones exist in solution only close to aN = 0. In both cases,15,16 the aggregates have characteristics of microgel particles with a core-shell structure, but the iPMA ones have a denser core.
Beside the properties of the polymer chain, intermo-lecular association depends also on the solution conditions. In the case of charged polymers (iPMA at aN « 0.27 is charged) in aqueous solutions, interactions are most frequently tuned by the addition of an inert low molecular weight salt. In our study, we have varied the concentration of CsCl in the concentration range from 0.05-0.20 M. Static, SLS, and dynamic light scattering, DLS, were used to determine the radius of gyration, Rg, and the hydrodyna-mic radius, Rh, of particles in iPMA solutions, from which the shape parameter, p (= Rg/Rh), was evaluated. The value of p is a convenient measure of the shape/architecture of particles and also of their eventual aggregated state in solution.
We have furthermore extended our LS investigations to studying diffusion of iPMA chains in solutions at higher aN values (all up to aN = 1) where inter-chain aggregates are expected to break and the dimensions of individual
iPMA chains should increase due to intramolecular repulsion between the charged carboxyl groups. Fully charged polymer chains are stiffer than the uncharged ones and their mutual interaction is strongly repulsive unless sufficient number of counterions (from the inert salt) is present in solution to screen these repulsions. Due to inter-chain repulsion, polyions move faster in solution than the corresponding neutral polymers of the same degree of polymerization; consequently, a higher value of the diffusion coefficient, D, is detected by DLS.21 Accordingly, this diffusion mode is often called the "fast mode".21 The result of inter-chain repulsion is yet another diffusive mode, so called "slow mode" that exhibits much lower D values in comparison to the fast mode. This mode originates from the formation of so called "polyion domains" in solution, within which the motion of polyion chains is correlated, i.e. affected by other chains. The attributed "apparent size" of these domains exceeds the size of individual chains and can reach values around 100 nm.21 Polyion domains are metastable but long lasting structures in solutions of polyelectrolytes. Certain physical measurements, one of them being DLS, are able to detect these "domains" as "particles" with their own value of D, and, through the Stoke-Einstein equation, the value of Rh. The slow mode is detected at high polyion concentrations, in the case of strongly charged chains, at low concentrations of the added simple salt (or in salt-free systems) and at high molecular weights of polyelectrolytes. It was demonstrated that the nature of the added salt is important as well.16 In the case of an anionic polyelectrolyte like PMA, the decisive is the added cation. Thus, it was shown that Li+ and Na+ ions better support interchain aggregation than do Cs+ ones.16 That study16 was performed at a single salt concentration, i.e. in 0.1 M CsCl, NaCl, and LiCl. In the present investigation we want to further explore the effect of decreasing/increasing the concentration of CsCl, cS, on intermolecular association and slow mode phenomenon in i-PMA solutions.
2. Experimental
2. 1. Materials
The starting iPMA was prepared by hydrolysis of the isotactic polymethylmethacrylate, iPMMA, as reported in the literature.13 Tacticity of iPMMA (93% of isotactic, 3% of syndiotactic and 4% of atactic triads) was determined from the 1H NMR spectrum in CDCl3. The weight average molecular weight, Mw (= 32 000 g/mol), and the polydispersity index, PDI (= 2.93), were obtained by size exclusion chromatography.15
Stock solutions were prepared by suspending dry i-PMA powder in triple distilled water and then slowly adding a calculated amount of 1 M CsOH in order to dissolve the polymer. The solution was stirred for ~24 hours before further handling. The exact polymer concentration,
cp, and aN value were determined by Potentiometrie titration with HCl and NaOH. aN of the stock solution was 0.53 and cp was 5.434 g/L. Higher aN values (aN > 0.53) were reached by adding 1.027 M CsOH and lower ones (aN < 0.53) by adding 1.0 M HCl. At the end, 1 M CsCl was added to all stock solutions in order to achieve the desired CsCl concentration. In this way, 20 different samples were prepared with aN = 0.27, 0.40, 0.53, 0.75 and 1.00, and with 4 different concentrations of CsCl, (cs = 0.05, 0.07, 0.10 and 0.20 M), for each aN. The final concentration of iPMA for LS studies was in all cases set to cp = 2 g/L. It has been shown previously16 that D (Rh) values of particles in iPMA solutions are affected by cp, but the shape parameter p (i.e. the nature of particles) is independent of cp. Because the aim of the present investigation was to study the nature of iPMA aggregates in depencence on cs, a constant cp value was employed.
2. 2. Light Scattering Measurements
Light scattering measurements were performed with the 3D-DLS-SLS cross-correlation spectrometer from LS Instruments GmbH (Fribourg, Switzerland). As a light source the He-Ne laser with a wavelength Xo = 632.8 nm was used. All samples were filtered through hydrophilic 0.22 |jm Millex-HV filters directly into the cylindrical measuring cell and left standing for about one hour at room temperature. LS measurements were carried in the angular range from 30° to 150° with a step of 10° after equilibrating the samples at 25 °C for 30 minutes. Constant intensity of light scattered at 90° was used as a criterion that the solution was properly equilibrated. 5 intensity correlation functions were collected at each angle and averaged. Each curve was analysed independently and compared with the averaged curve to ensure accuracy of the mathematical solution.
Detailed methodological aspects of DLS and SLS can be found elsewhere.18,19 Herein, correlation functions of the intensity of scattered light, G2(t), were recorded simultaneously with the integral time averaged intensities,
/0 = where я (= ^sm^) is the scattering vector, n0
the refractive index of the medium, and 8 the scattering angle. Intensities measured in counts of photons per second (cps) were normalized with respect to the Rayleigh ratio, R, of toluene thus converting the cps-units into the absolute intensity units given in cm-1.
The radius of gyration, Rg, of particles, was determined from the form factor, P(q) (= Iq/I0, where I0 is the scattering intensity at 8 (q) = 0), by using the following equations:22 (i) the Zimm function (Equation 1) which is valid when particle sizes fulfill the criterion qRg < 1:
(ii) the Debye function (Equation 2) used for polymer chains with a Gaussian distribution of segments:

(2)
and (iii) the Debye-Bueche scattering function (Equation 3) which applies to a spherical distribution of points around the center of gravity (such as in gels, networks, cross-linked or branched polymers), which is more random than the Gaussian distribution:
(3)
In order to determine Rh, the measured G2(t) was converted into the correlation function of the scattered electric field, g^t), by using the Siegert's relationship. For monodisperse particles, small in size compared to the wavelength of light as well as for hard spheres of any size, the g1(t) is related to the translational diffusion coefficient, D, of particles through
where т is the relaxation (or decay) time and Г (= т-1 = Dq2) is the relaxation (decay) rate. The Rh of particles is then obtained from D via the Stokes-Einstein equation
(5)
where k is the Boltzmann constant, T the absolute temperature, and n0 the solvent viscosity.
(1)
Figure 1. Comparison of the analysis of the correlation function G2(t) made by CONTIN (red) and by the bi-exponential fit (blue) for iPMA with aN = 0.27 in 0.05 M CsCl. The open black circles are the experimental data. The upper inset represents the relaxation time distributions of the corresponding g1(t) function and the lower one the residual error.
For polydisperse samples, equation 4 is written as a weighted average of all possible decays associated with several exponents (multiexponential function). For studied herein particles with moderately broad monomodal and bimodal size distributions, a bi-exponential or a multi-exponential fit to g^t) was used. The bi-exponential fit was performed with the ORIGIN 8.0 program and was used when two relaxation times of the bimodal distribution were too close to each other and the CONTIN analysis was difficult. This was the case in solutions with aN > 0.27. The multiexponential fit was based on the original inverse Laplace transform program CONTIN developed by Provencher.23 Comparison of both fits is shown in Figure 1 for the case of an iPMA solution with aN = 0.27 and cs = 0.05 M and demonstrates satisfactory agreement between both methods.
3. Results and Discussion
3. 1. Scattered Light Intensity in Dependence on aN
The result of SLS measurements is the intensity of scattered light. According to the Rayleigh equation,18,19 intensity is greater when light is scattered from a particle with a higher molar mass, provided that the conformation of the particle and the optical contrast with the medium are the same. Figure 2 shows a plot of the total LS intensity (i.e. the difference (R-Ro)0 = 0 at 8 = 0°, where Ro is the contribution of the solvent to the total LS intensity R) in dependence on aN of an iPMA solution in 0.05 M
0,0 0.2 0.4 0.6 0.8 1.0
Figure 2. Total LS intensity at 0 = 0°, (R-Ro)0=0 (black squares), the contribution of the fast (blue circles) and slow mode (red triangles), and the relaxation time distributions at 0 = 90° (see insets) for i-PMA in 0.05 M CsCl at various aN values. The distribution for aN = 0.27 was calculated by the CONTIN program and those for aN = 0.4 and 1.0 by the bi-exponential fit. The shaded area designates the aN region where iPMA is insoluble in water.
CsCl. Similar results were obtained for all cs. Clearly, the absolute LS intensity is very high at aN = 0.27, falls steeply with increasing aN and is low and approximately constant for aN > 0.40. These results suggest that large species - aggregates with high Mw are present in iPMA solution when chains are weakly charged (in the present case this is for aN below approximately 0.3) and that they disappear when aN increases to higher values. Accordingly, the distribution of relaxation times at aN = 0.27 (see the upper inset in Figure 2) shows two peaks: (i) the peak at short relaxation times corresponds to small particles (single chains) that diffuse quickly in solution, therefore the term "fast mode" is used for this diffusion, and (ii) the peak at longer relaxation times corresponds to larger particles (aggregates of several chains, i.e. particles with high molar masses) that diffuse slowly. The calculated distributions were used to split the total measured LS intensity into contributions of small (fast mode) and large particles (slow mode), which are plotted in Figure 2 together with the total LS intensity. Details of this procedure can be found in the literature.24-26 It can be seen from Figure 2 that the high LS intensity at aN = 0.27 comes predominately from the aggregates; the contribution of small particles to the total LS intensity at this aN is very small.
The calculated relaxation time distributions were bimodal also at higher aN values (see insets in Figure 2, where this is demonstrated for aN = 0.4 and 1.0; the distributions in this case were obtained by the bi-exponen-tial fit), with the peak at short times again attributed to single polyion chains ("fast mode") as in the aN = 0.27 case. The origin of the peak at longer relaxation times is different as suggested by the low scattering intensity for aN > 0.27 and by a significant drop of the contribution of the second peak to (R-Ro)0=0. This peak does not represent particles, but is due to so called polyelectrolyte "slow mode" 27,28 originating from electrostatic interactions between highly charged polyions. It is well known2-5,14,17,27,29 that this phenomenon leads to low values of the total LS intensity, in contrast to intermolecu-lar association/ aggregation, and to the apparent low diffusion coefficient value measured by DLS. Because the aggregation and the polyelectrolyte slow mode are both associated with a low value of D, a generic name "slow mode" is used for both phenomena in Figure 2. The polyelectrolyte slow mode phenomenon will be discussed in more detail in Subsection 3.3.
3. 2. iPMA Aggregates at aN = 0.27
Mean peak values of the size distributions, obtained at fixed q were used to estimate the apparent hydrodyna-mic radius, Rhapp, of particles in these solutions and the true Rh was obtained by extrapolating Rhapp to 0 = 0 for each cs. Dependencies of the corresponding relaxation rates on the square of the scattering vector, q2, were passing
through the center of coordinates, confirming the validity of the relationship Г = 1/i = Dq2, which applies to a true translational diffusion of colloidal particles in solution. Examples of the Г vs. q2 curves are shown Figure 3a for cs = 0.07 M CsCl. The slope of these curves is proportional to the diffusion coefficient of particles. The Г vs. q2 curve with a high slope corresponds to fast diffusing small particles (individual chains) and is linear. The Г vs. q2 curve for the aggregates (large particles, designated as the slow mode in Figure 2) has a considerably lower slope and shows an upward curvature (see inset in Figure 3a) at high q values as a consequence of polydispersity of the aggregates. The hydrodynamic radii of individual chains and of the aggregates, Rh 1 and Rh 2, respectively, are reported in Table 1 and plotted in Figure 4 in dependence on cs. The size of individual polyions is small at all cs (Rh x « 9-11 nm), therefore no angular dependency of the scattered light intensity was observed in this case and data reported in Table 1 are average Rh 1 values measured in the studied q range. In agreement with expectations, the aggregates are considerably larger, up to almost 20-times in comparison with small particles. Their size increases from Rh2 « 80 nm at c = 0.05 M to R , « 160 nm at c = 0.2 M. ,
Table 1. The size parameters (Rh p Rh2, Rg 2) and the shape parameter p (= Rg 2/Rh 2) in iPMA solutions with aN = 0.27 and cp = 2 gL-1 and with various CsCl concentrations, cs. The uncertainty in Rh (Rg) values is estimated to be around 10%.
cj mol L 1	Rh,1/nm	Rh, 2/nm	Rh,2/nm	P
0.05	10	79	50	0.64
0.07	9	79	48	0.61
0.10	8	88	53	0.60
0.20	11	155	93	0.60
Figure 4. The dependence of Rh p Rh2, and Rg2 on CsCl concentration, cs, in aqueous iPMA solutions with c = 2 gL-1 and aN = 0.27.
In view of the large Rh 2 value, the radius of gyration, Rg,2, could be determined for the aggregates. For this purpose, the second peak in the size distributions was treated separately for the angular dependency of the LS intensity. From Rg 2 and Rh 2, the shape parameter p (= Rg 2/Rh 2) was calculated. All these data are reported in Table 1. Rg2 increases from around 50 nm at cs = 0.05 to around 90 nm at cs = 0.2 M, whereas values of the shape parameter p (= 0.60-0.64) show no particular dependence on cs. Note that these p values are lower than the value known for a hard sphere (p = 0.78) and also considerably lower than those for a random coil.18,19 They are close to the values reported for microgel-like particles with a core-shell structure, for which p was found to be around 0.6.20,30
The increase of Rg,2 and Rh,2 with increasing cs can be explained by proposing that the extent of aggregation
Figure 3. Plots of the relaxation rate, Г, versus q2 in iPMA solutions with a) aN = 0.27 in b) aN = 1.0, both in 0.07 M CsCl. In the insets, the Г vs. q2 plot for a) aggregates or b) slow mode is enlarged.
(association) between iPMA chains increases with increasing salt concentration. This is reasonable because small counterions from the added salt (Cs+) contribute to screening of electrostatic repulsion between the negatively charged iPMA chains with aN = 0.27 and thus promote in-termolecular association. However, constant p values show that, although the aggregates grow, their fractal structure (distribution of mass within the aggregate) is not affected by cs.
In order to confirm the proposed core-shell structure, we have compared our data with the calculated scattering functions for some typical particle topologies.19 The calculated functions and the experimental data for iPMA with aN = 0.27 and cs = 0.07, 0.10, and 0.20 M are presented in the form of a Kratky plot (i.e. the dependence of (q-Rg)2P(q) on qRg) in Figure 5. It can be seen that the majority of the data points remain in the range of low q-values (qRg < 1.5) where the presented topologies are not clearly distinguishable. Only the data obtained for the highest CsCl concentration (0.20 M) extend up to around qRg « 2.5, as a consequence of the largest Rg value of the aggregates in 0.20 M CsCl (see Rg2 values in Table 1). These data points clearly fit the Debye-Bueche scattering function. Similar results were reported previously16 for the same iPMA sample in the presence of 0.1 M LiCl, NaCl and CsCl. That study was a comparative investigation of both, iPMA and aPMA. As reported there, p of the iPMA aggregates in all 0.1 M alkali chlorides was from 0.58 (0.1 M NaCl) to 0.67 (0.1 M CsCl).
The Debye-Bueche scattering function is reported in the literature for the description of hyperbranched flexible chain molecules and microgel particles from chemically cross-linked flexible chains.20,30 Therefore, iPMA aggregates in aqueous CsCl solutions can be described as sphe-
ffl D.
a:
tX
% = 0.27 cs =	0.07 M	A
	0.10 M	D
	0.20 M	□
--Zimm (£q.1)		
-Debye (Eq.2)		
-Debye-Bueche (Eq.3)		
■ -hard sphere		
		äTiJ
. —— . i		»
qR
^ 9
Figure 5. The dependence of (qRg)2P(q) on qRg for four selected particle topologies (calculated according to Equations 1-Zimm, 2-Debye, and 3-Debye-Bueche) and the experimental data (points) for large particles (i.e. aggregates) in iPMA solutions with cp = 2 g/L and aN = 0.27 and at three different CsCl concentrations: cs = 0.07, 0.10, and 0.20 M.
rical solvent draining particles with a higher polymer density in the center and a lower one towards the outer surface. On the basis of these results we believe that it is justifiable to approximate the architecture of iPMA aggregates in solutions with added CsCl with a spherical shape that has a loose corona on its surface and a denser core in the center. Such distribution of mass (with characteristic value of p«0.60) is achieved by very efficient hydrogen bonding between different chains, which is strongly coopera-tive2,3,13,15,16 and leads to some kind of segregation of pro-tonated and deprotonated carboxyl groups within the aggregate. The undissociated carboxyl groups are concentrated in the core whereas the dissociated ones constitute the corona, i.e. they are exposed to the solvent and thus provide the solubility of iPMA in water.16 It can be imagined that when starting the ionization of carboxyl groups by adding the base (CsOH), the surface carboxyl groups are ionized first. Those in the core remain uncharged and are associated through hydrogen bonding that is reinforced by the favorable presence of hydrophobic methyl groups.27 The iPMA aggregate dissolves only at some sufficiently high charge (corresponding to a, larger than ~0.2) when chain repulsion becomes strong enough to disrupt the aggregates. Another result of such association mechanism is also the observed independence of the parameter p on salt concentration. The increased salt concentration only facilitates aggregate growth by reducing electrostatic repulsion between charged portions of the chains, but has no effect on attractive interactions, i.e. hydrogen bonding and so called hydrophobic interactions.
3. 3. Slow Diffusion Due to the Polyelectrolyte Effect
As indicated above, the equation Г = Dq2 is valid for translational diffusion and predicts that Г vs. q2 curves should go through the center of coordinates. For small particles (fast mode), this is the case for all aN as demonstrated in Figure 3 for iPMA with a, = 0.27 and 1.0 in 0.07 M CsCl. On the other hand, the Г vs. q2 curves for the slow mode in iPMA solutions with a, > 0.27 do not start from the origin of the system of coordinates and therefore do not represent true translational diffusion.27 As an example, see the curve for a, = 1 in the inset of Figure 3b and note that the results were similar for all a, > 0.27. The data points for this (slow) mode are considerably more scattered and also more curved in comparison with the data points for the aggregates at a, = 0.27 (compare the insets in Figures 3a and b). Sometimes this diffusion process is called anomalous.21 The origin of the anomalous diffusion is electrostatic interactions between polyions that result in correlated motion of many charged chains, so called multimacroion or polyion domains.21 It was reported that the associated value of the diffusion coefficient of these domains is considerably lower than the diffusion coefficient of individual polyions.19,21,37
The fast and the slow mode diffusion coefficients, Df and Ds, respectively, in iPMA solutions with cp = 2 g/L are plotted in Figure 6 as a function of aN for all cs. In agreement with the above statement, the value of Ds is around one order of magnitude lower than Df. Moreover, Df and Ds are almost independent of cs and aN at the studied polymer concentration. The correlation lengths associated with the D values in Figure 6 are in the range of 7-14 nm (= Rh 1), obtained from Df, and 40-110 nm, obtained from Ds. The independence of Df and Ds on aN was recently demonstrated for both iPMA and aPMA in different alkali chloride solutions, but only for a single salt concentration cs = 0.10 M.
Other authors have previously28 determined diffusion coefficients in salt free solutions of so called conventional, i.e. atactic, PMA with a similar Mw (= 30.000 g/mol) as in the case of iPMA in this study, but with a considerably larger polymer concentration (cp = 36.6 g/L). It was demonstrated that in the aN range 0-0.4, Df of aPMA chains increases and Ds decreases with increasing aN, whereas for aN > 0.4 they are both nearly independent of aN. Taking into account that our measurements apply to the stereoregular iPMA with a non-zero degree of neutralization (aN > 0.27) and to solutions with a non-negligible amount of added CsCl (cs > 0.05 M; compare this with salt-free conditions for aPMA in ref. 28), we conclude that these results are in a reasonable agreement with each other.
Figure 6. Dependence of the fast, Df, and slow diffusion coefficient, Ds, on degree of neutralization, aN, in aqueous iPMA solutions with cp = 2 g/L and at various CsCl concentrations, cs (= 0.05-0.20 M). The shaded area designates the aN region where iPMA is insoluble in water.
It is normally expected that the slow mode phenomenon disappears when the amount added low molar mass salt is sufficient to completely screen electrostatic repulsion between the polyions. Förster et al.38 reported diffusion coefficients of quaternized poly(2-vinyl pyridi-
ne), QPVP, in aqueous solutions over a broad range of the polyion concentration (in moles of charged groups, cph) to the added salt concentration, denoted as X (= cph/cs). They demonstrated that the slow diffusive process is always observed in polyelectrolyte solutions for X larger than 1, i.e. when polyion charges are in excess with respect to the salt charges and electrostatic repulsions between polyions are not effectively screened. Solution conditions with X « 1 (equal amount of charges from the polyelectrolyte and from the slat) are described as the transition regime, where the slow mode gradually appears (or disappears) and for X < 1 (low polyion or high salt concentration) only the fast diffusion process of single chains is observed. In the case of QPVP in the presence of monovalent counterions, the slow mode disappeared for X values below ~1-5.38
With iPMA solutions investigated herein, the studied X range is somewhat below 1 (from X « 0.03 at aN = 0.27 and cs = 0.20 M to X« 0.465 at aN = 1.0 and cs = 0.05 M), which means that the number of charges from small counterions exceeds the one originating from the polyion (i.e. salt is in small excess). However, as distinguished from the QPVP case, the slow mode is still observed. This can be explained by proposing that electrostatic interactions between the iPMA polyions, as compared to the QPVP ones, are stronger. This may be a consequence of different chain rigidity and distribution of charges on i-PMA that would lead to higher polyion charge density. The data in Figure 6 suggest that in the iPMA case even 0.20 M CsCl is not sufficient to completely screen strong electrostatic forces. Further investigations are necessary to explain these findings in more detail.
4. Conclusions
We have studied dynamic behavior of isotactic poly-methacrylic acid, iPMA, chains in aqueous solutions with added CsCl at various concentrations, cs, in dependence on degree of neutralization of polyion's carboxyl groups, aN, by simultaneously performing static, SLS, and dynamic light scattering, DLS, measurements. All correlation functions measured by DLS were bimodal and revealed two diffusion modes. The fast diffusion mode was associated with individual iPMA chains whereas the slow diffusion mode either represents aggregates of several chains (the case with aN = 0.27) or so called polyion domains (higher polyion charges, aN > 0.27). The hydrodynamic radius of individual chains, Rh 1, was in the range 8-11 nm, but no dependence of Rh,1 on either aN or cs could be deduced. The hydrodynamic radius of the aggregates, Rh,2, at aN = 0.27 was found to increase with increasing cs from Rh2 « 80 nm at cs = 0.05 M to Rh2 « 160 nm at cs = 0.20 M, whereas the shape parameter, p, was found to be independent of cs. This means that the aggregates grow with increasing cs, but their nature (distribution of mass within the aggregate) remains the same. The increase in size at
higher cs is expected because the counterions from the added salt (Cs+) contribute to screening of electrostatic repulsion between iPMA chains with a relatively low charge (corresponding to aN = 0.27). As suggested by the value of p (= 0.60-0.64), the aggregates have characteristics of microgel particles with a core-shell structure. Consequently, the scattering functions for the aggregates fitted the Debye-Bueche function.
In samples with aN > 0.27, the polyelectrolyte slow mode was detected, which is due to repulsive interactions between negatively charged polyion chains and manifests itself as a correlated motion of chains. Light scattering measurements detect such motion as an additional diffusive mode, often ascribed to loose multimacroion (or pol-yion) domain formation. It has to be stressed that these polyion domains are not real particles but regions of correlated motion of polyions that are detected by DLS. The value of the diffusion coefficient of such domains can be determined from the measured correlation functions. We have determined the diffusion coefficients of individual polyions (the fast diffusion coefficient, Df) and of such polyion domains (the slow diffusion coefficient, Ds) in dependence on aN and cs. The results show that both Df and Ds are nearly independent of aN and cs at the studied polymer concentration.
5. Acknowledgment
This work was financially supported by the Slovenian Research Agency, ARRS, through the Physical Chemistry program P1-0201.
6. References
1.	V. V. Khutoryanskiy, Int. J. Pharm. 2007, 334, 15-26. http://dx.doi.org/10.1016/j.ijpharm.2007.01.037
2.	K. Kogej, H. Berghmans, H. Reynaers, S. Paoletti, J. Phys. Chem. B. 2004, 108, 18164-18173. http://dx.doi.org/10.1021/jp048657k
3.	B. Jerman, M. Breznik, K. Kogej, S. Paoletti, J. Phys. Chem. B. 2007, 111, 8435-8443. http://dx.doi.org/10.1021/jp0676080
4.	J. Eliassaf, A. Silberberg, A. Katchalsky, Nature. 1955, 176, 1119-1119. http://dx.doi.org/10.1038/1761119a0
5.	N. Vlachy, J. Dolenc, B. Jerman, K. Kogej, J. Phys. Chem. B. 2006, 110, 9061-9071. http://dx.doi.org/10.1021/jp060422g
6.	G. R. Desiraju, in J. L. Atwood, J. W. Steed (Eds.): Encyclopedia of Supramolecular Chemistry, Marcel Dekker Inc: New York, USA, 2004, pp. 658-665.
7.	E.M. Loebl, J.J. O'Neill, J. Polym. Sci. 1960, 45, 538-540. http://dx.doi.org/10.1002/pol.1960.1204514629
8.	V. Crescenzi, Adv. Polym. Sci. 1968, 5, 358-386. http://dx.doi.org/10.1007/BFb0050986
9. M. Nagasawa, T. Murase, K. Kondo, J. Phys. Chem. 1965, 69, 4005-4012. http://dx.doi.org/10.1021/j100895a060
10.	J.C. Leyte, H.M.R. Arbouw-van der Veen, L.H. Zuiderweg, J. Phys. Chem. 1972, 76, 2559-2561. http://dx.doi.org/10.1021/j100662a014
11.	J.C. Leyte, M. Mandel, J. Polym. Sci., Part A: Gen. Pap. 1964, 2, 1879-1891.
http://dx.doi.org/10.1002/pol.1964.100020429
12.	Y. Muroga, I. Nada, M. Nagasawa, Macromolecules. 1985, 18, 1580-1582. http://dx.doi.org/10.1021/ma00150a010
13.	E. van den Bosch, G. Filipcsei, H. Berghmans, H. Reynaers, Macromolecules. 2004, 37, 9673-9675. http://dx.doi.org/10.1021/ma047821z
14.	B. Jerman, K. Kogej, Acta Chim. Slov. 2006, 53, 264-273.
15.	S. Sitar, V. Aseyev, K. Kogej, Polymer. 2014, 55, 848-854. http://dx.doi.org/10.1016/j.polymer.2014.01.007
16.	S. Sitar, V. Aseyev, K. Kogej, Soft Matter. 2014, 10, 77127722. http://dx.doi.org/10.1039/C4SM01448K
17.	S. Ohoya, S. Hashiya, K. Tsubakiyama, T. Matsuo, Polym. J. 2000, 32, 133-139. http://dx.doi.org/10.1295/polymj.32.133
18.	W. Schärtl: Light Scattering from Polymer Solutions and Nanoparticle Dispersions. Springer-Verlag Berlin, Heidelberg, 2007.
19.	W. Brown, (Ed): Dynamic light scattering: the method and some applications. Clarendon Press, Oxford, 1993.
20.	W. Burchard, Macromolecules. 2004, 37, 3841-3849. http://dx.doi.org/10.1021/ma049950l
21.	M. Sedlak, Langmuir. 1999, 15, 4045-4051. http://dx.doi.org/10.1021/la981189j
22.	P. Kratochvfl, in M.B. Huglin Editor: Light Scattering from Polymer Solutions, Academic Press: London, 1972, pp. 333384.
23.	S. Provencher, Inverse Problems home page, http://s-provencher.com/index.shtml (accessed: 26 Jan, 2011).
24.	R. Klucker, J.P. Munch, F. Schosseler, Macromolecules. 1997, 30, 3839-3848. http://dx.doi.org/10.1021/ma961710l
25.	E. Raspaud, D. Lairez, M. Adam, J.-P. Carton, Macromolecules. 1994, 27, 2956-2964. http://dx.doi.org/10.1021/ma00089a011
26.	E. Tarassova, V. Aseyev, A. Filippov, H. Tenhu, Polymer. 2007, 48,4503-4510.
http://dx.doi.org/10.1016/j.polymer.2007.05.069
27.	R. Cong, E. Temyanko, P. S. Russo, N. Edwin, R. M. Uppu, Macromolecules. 2005, 39, 731-739. http://dx.doi.org/10.1021/ma051171x
28.	M. Sedlak, Č. Konakt, P. Štepanek, J. Jakes, Polymer. 1987, 28, 873-880.
http://dx.doi.org/10.1016/0032-3861(87)90156-X
29.	J. Eliassaf, A. Silberberg, Polymer. 1962, 3, 555-564. http://dx.doi.org/10.1016/0032-3861(62)90103-9
30.	G. Savin, W. Burchard, Macromolecules. 2004, 37, 30053017. http://dx.doi.org/10.1021/ma0353639
31.	S. Förster, M. Schmidt, M. Antonietti, Polymer. 1990, 31, 781-792.
http://dx.doi.org/10.1016/0032-3861(90)90036-X
Povzetek
S hkratnimi meritvami statičnega, SLS, in dinamičnega sipanja svetlobe, DLS, smo študirali dinamično obnašanje verig izotaktične polimetakrilne kisline, iPMA, v vodnih raztopinah z dodatkom CsCl v različnih koncentracijah, cs, v odvisnosti od stopnje nevtralizacije, aN, karboksilnih skupin skupin na poliionu. Vse izmerjene korelacijske funkcije z DLS so bile bimodalne in so pokazale na prisotnost dveh difuzijskih načinov (modusov). Hitri difuzijski način smo povezali z individualnimi verigami iPMA in počasnega z agregati med verigami (primer aN = 0.27) ali pa s tvorbo tako imenovanih poliionskih domen (večji naboji na poliionu, aN > 0.27). Hidrodinamski radij individualnih verig, Rh1, je bil 7-14 nm, vendar pa nismo opazili nobene posebne odvisnosti Rh 1 od aN ali cs. Hidrodinamski radij agregatov, Rh2, je naraščal od Rh2 « 80 nm pri cs = 0.05 M do Rh2 « 160 nm pri cs = 0.20 M, medtem ko je bil faktor oblike, p, neodvisen od cs. Na osnovi tega smo sklepali, da velikost agregatov sicer narašča s cs, vendar pa njihova oblika (porazdelitev mase) ostaja nespremenjena. Večja velikost pri večji cs je pričakovana, saj protiioni iz dodane soli (Cs+) prispevajo k senčenju elek-trostatskega odboja med verigami iPMA z aN = 0.27. Vrednosti parametra oblike (p = 0.61-0.67) kažejo, da imajo agregati značilnosti mikrogelov s tako imenovano »core-shell« strukturo. Sipalne krivulje za agregate so se ujemale z Debye-Buechejevo funkcijo.
V vzorcih z aN > 0.27 smo zasledili tako imenovane poliionske domene, ki so posledica elektrostatskega odboja med negativno nabitimi verigami poliiona. Meritve sipanja svetlobe tako gibanje zaznajo kot dodaten difuzijski način, ki ga pogosto pripisujejo koreliranemu gibanju večih verig. Te domene niso realni delci, ampak strukture v raztopini z dovolj dolgim življenjskim časom, da jih lahko zaznamo z DLS meritvami in določimo vrednost difuzijskega koeficienta takih domen iz izmerjenih korelacijskih funkcij. Določili smo difuzijske koeficiente za individualne verige poliionov (to smo imenovali hitra difuzija in difuzijski koeficient označili z Df) in za poliionske domene (ta difuzijski način smo imenovali počasna difuzija in difuzijski koeficient označili z Ds) v odvisnosti od aN in cs. Rezultati so pokazali, da sta tako Df kot Ds skoraj neodvisna od aN in cs za preiskovano koncentracijo iPMA.