J. Phys. Chem. 1993,97, 9825-9830
9825
Calcium-Induced Shrinking of Polyacrylate Chains in Aqueous Solution Klaus Huber Ciba- Geigy AG, Chemicals Division. K-420.205, CH-4002 Basel, Switzerland Received: March 31, 1993; In Final Form: July 7, 19936
Conformational changes of polyacrylate chains induced by Ca2+ions have been studied by means of static light scattering and viscosity measurements with two different sodium polyacrylate samples. The reference system was sodium polyacrylate in an aqueous solution of 0.1 N NaCl at a pH of 9. Replacement of different amounts of the Na+ ions from the added NaCl by Ca2+ ions led to different Ca2+ fractions at constant ionic strength of the low molecular weight salt. At each Ca2+ion fraction, the size of the polyelectrolyte coils was recorded as a function of polyacrylate concentration. The results were discussed in terms of a coil collapse which precedes precipitation of the calcium polyacrylate when lowering the polyacrylate concentration. The polyacrylate concentration where this coil collapse occurs correlates with the content of calcium ions in solution.
Introduction Neutralized carboxylic acids have a high tendency to interact with calcium ions. This characteristic feature is of utmost importance, both in the chemistry of living systems and in industrial processes. Often COO- groups of proteins and polysaccharides form complex bonds to calciumions, leadingto distinct conformational changes or intermolecular bridges among the biopolymeric molecules. This in turn modifies the biological activity of the polymers involved in such complex reactions as blood clotting and muscular contraction. Many processes in the household and industry like washing or heat exchange are disturbed by calcium ions which in water precipitate with several anions. This problem is usually countered by using complexing agents and/or dispersants. Whereas complexing agents have to be used at least in equimolar amounts, a stable dispersion of insoluble calcium salts might already be achieved with substoichiometricportions of a dispersant. Since the late 70s polyacrylates have found increasing application in this field.192 In polyacrylates a COO- group is attached to every other carbon atom of the backbone chain. The wide range of applications of polyacrylates made it one of the most extensively investigated polyelectrolytes. Lightscattering studies of polyacrylate were published as early as 1951 by Wall et al., followed by the pioneering work of Flory et al.4.5 Further workdealt with the dilute solutionbehavior of polyacrylate in the presence of added salt: Kitano et a1.6 and Hara and Nakajima’ used static light scattering (SLS) experiments to characterize the conformational behavior of polyacrylate. Simultaneously several papers on the intrinsic viscosity of polyacrylatein aqueoussolution were published by Nagasawa et al.899 and Kay and Treloar.*o Their results can be summarized as follows: Adding neutral low molecular weight electrolyte to polyelectrolyte solutions lowers electrostatic repulsions between COOgroups, belonging to either the same or different polyelectrolyte chains. This leads to a decreaseof the coil dimensions, the second osmotic virial coefficient, and the intrinsic viscosity. Thus, the role of the added salt in polyelectrolyte solution behavior in many respects resembles the solvent quality in classical polymer solution theory. The results on polyacrylate are consistent with findings on other polyelectrolytes. Unlike alkali metal cations of most neutral salts, Ca2+ions bind to the carboxylate groups of dissociated polyacrylates in aqueous solution. If the binding capacity is exceeded, polyacryAbstract published in Advance ACS Absfracfs.September 1, 1993.
lates form an insoluble calcium salt. In the presence of carbonate anions, polyacrylate acts as dispersant and fojmation of macroscopic CaCO3 precipitation is inhibited. Simultaneously, precipitation of calcium polyacrylateis shifted to Ca2+concentrations much higher than thosewithout carbonate.11 This effect, often denoted as threshold, is widely exploited in washing processes. As early as 1951, Wall and Drenan12 investigated the precipitation of polyacrylatewith Ca2+,Ba2+, and Sr2+ions. They interpreted their results as gelation induced by bond formation between cationsand the polyelectrolyte chains. Three years later, Flory and Osterheld4 pointed out that adding Ca2+ to partly neutralized polyacrylatescauses a much stronger coil contraction than an equivalent amount of Na+ ions would. Contrary to Wall and Drenan, Flory and Osterheld explained this as a mere osmotic effect, the origin of which lays in an increased electrostatic interaction with counterions if Na+ is substituted by Ca2+. These findings, together with the biological and industrial aspects of Ca2+binding to polymers, inspired us to look in more detail at the conformationof polyacrylatein the presence of Ca2+ ions. SLS and viscosity experimentson aqueous solutions of the polyacrylate at 0.1 N NaCl as neutral salt were carried out. Hereby, the influence of Ca2+ions was investigated by recording the coil radius and the intrinsic viscosity as a function of partial replacement of Na+ by an equivalent amount of Ca2+ ions. Experiments were performed at pH = 9, where polyacrylate is the completely dissociated sodium polyacrylate denoted as NaPAA. Special care had to be taken that all relevant experimentsweredonebelow the critical Ca2+concentration which leads to aggregation and precipitation of calcium polyacrylates.
Experimental Section Materials. Experiments were carried out with two different polyacrylic acid samples. Both samples were synthesized by radical polymerization using potassium persulfate as initiator. From each sample an aqueous solution with a polymer content of 5% was prepared. The pH of the solution was adjusted to pH = 9 with aqueous sodium hydroxide solution. All solutions were dialyzed for at least 3 days against water which was adjusted to the respective pH value. To this end dialyzing hoses filled with the polymer solutions were immersed into vessels with 10 times more of the solvent. The solvent, which was water at pH = 9, was exchanged three times a day. Freeze drying of the dialyzed solutions then yielded NaPAA from each sample. No fractionation of the polymer samples was carried out, and the molecular weight distribution of all samples was assumed to be polydisperse. Preparation of Solutions. All experimentswith NaPAA were carried out in an aqueous solution of low molecular weight salt
0022-365419312097-9825%04.00/0 0 1993 American Chemical Society
9826
Huber
The Journal of Physical Chemistry, Vol. 97, No. 38, 1993
which corresponds to a mixed solvent. The mixed solvent was prepared with bidistilled water and 0.1 M sodium chloride as the added low molecular weight salt (pa grade, Merck). Finally, the solvent was set to pH = 9. Polymer concentrations were chosen to lie between 10-4 and 10-3 g/L and are always expressed in terms of the free polyacrylic acid. In order to investigate Ca2+-induced changes in the coil conformation of NaPAA polyions, up to 10% of the Na+ ions from the added electrolytewere replaced by an equivalent amount of Ca2+ ions (CaC1~2H20,pa grade, Fluka). The content of Ca2+ ions in solution was expressed by the ratio r,
rCa= 2[Ca2+]/([Na']
+ 2[Ca2+])
(1)
where [Ca2+] and [Na+] represent the molar concentration of Ca2+ and Na+, respectively. The denominator of eq 1 has a constant value of 0.1 M. According to Takahashi et al.13 1.5 N NaBr solution at T = 15 OC is a @-solvent for NaPAA. In order to estimate the unperturbed dimensionsof both NaPAA samples,additional SLS experiments were carried out at 1.5 N NaCl and T = 15 OC. Light Scattering. All scattering experiments were done with a Model 1800static light scattering instrument from ALV-Laser Vertriebsgesellsohaft (FRG). A krypton ion laser Model 2016 STABILITE from Spectra Physics, operating at a wavelength X = 647.1 nm, was used as a light source. The primary beam was focused into the center of a goniometer which contained an index matching bath. Toluene was applied as a bath liquid. A sample holder placed the scattering cells in the center of the index matching bath. Cylindrical quartz cells with a diameter for 20 mm served as scattering cells. The scattering intensity was observed under 19different anglessimultaneouslyby using optical fibers. A prototype of this light-scattering instrument, which differs only slightly from the one used in the present work, was described recently by Becker and Schmidt.14 All solutions and solvents were purified from dust by filtering them with Millipore filters directly into the scattering cells before the actual measurements. Solvents were passed through MILLEX-GV filters with a pore width of 0.22 pm. The NaPAA solutions of sample PA3K2 were cleaned with MILLEX-HV (0.45 Nm) filters. For r, 1 0.06, additional solutionswere purified with MILLEX-AA (0.8 Nm) filters. No difference in scattering intensities between solutions purified with filters of pore width 0.45 and 0.8 Nm were observed. Solutions of the sample PA4Sl were always passed through MILLEX-AA (0.8 pm) filters. Refractive Index Increments. Refractive index increments dn/ dc are required to calculate the contrast factor K used in SLS
K = 4~n~(dn/dc)~/(A~N,)
(2) where n is the refractive index of the solvent, X is the laser wavelength in vacuo (647.1 nm), and NAis Avogadro's number. Measurements were carried out with an interferometric refractometer OPTILAB B 903 from Wyatt operating at the He-Ne laser wavelength of 647.1 nm. Refractive index increments dn/ dc were calculated on the basis of at least five different concentrations. For NaPAA in 0.1 N NaCl at pH = 9, a value of dn/dc = 0.20 cm3/g was determined, independent of molecular weight. Viscosity Measurements. Viscositiesof NaPAA solutions were determined by an Ubbelohde viscometer using capillary Oa with an inner tube cross section of 0.53 mm. Efflux time of the 0.1 N NaCl solution was 178.4 s. Hagenbach corrections were subtracted from all efflux times. Reduced viscosities qsp/cwere then calculated according to eq 3 TSP/C = ( t - t,)/t,c (3) without further corrections. In eq 3, to and t are the corrected efflux times of the solvent and the polymer solution with concentration c, respectively.
TABLE k Dilute Solution Parameters of Polyacrylate Samples at pH = 9 Determined by SLS Measurements mnc of Mv A2 sample NaCP (M) (lo3g/mol) (10-4mol om3 g2) ( 9 ) o (nm2) PA3K2 PA4Sl PA3K2 PA4S 1 a
0.1 0.1 1.5 1.5
193 1250
8.5 3.8 1.1 1.1
10800 2 1400 6230 9880
Temperature is 25 OC at 0.1 M and 15 O C at 1.5 M.
Evaluation of SLS Data Light-scattering experiments were interpreted according to the following approximation
KC/AR= I/M,(I
+ 2 ~ d , c+ .., (s2),,/3q2 + ...)
(4a)
with the weight average molecular weight, (S2)othe z-averaged mean-square radius of gyration, and A2 the second osmotic virial coefficient. The scattering intensity of the dissolved polymer chains, expressed in terms of the Rayleigh factor AR,is measured as a function of the polymer concentration c and the scattering vector q. Within the range 0 C q 2 C 4 X 1Olocm-2, Kc/AR was always linear in q2. Fitting the data yielded a slope and a cutoff corresponding to an apparent square radius of gyration and a reciprocal apparent molecular weight KC/AROat zero angle, respectively. In the calcium-free cases, extrapolation of Kc/ARo and of the apparent square radius of gyration to infinite dilution could be used to characterize the polymers in terms of M,, (S2)0,and A2. Each polymer characterization was based on five different polymer concentrations. The results are summarized in Table I. All molecular weight data are expressed in grams of free polyacrylic acid. As already mentioned, both NaPAA samples were also characterized in 1.5 N NaCl solution at T = 15 OC, which can be expected to be close to a 8-solvent for NaPAA.13 In each case measurements were carried out at five different NaPAA concentrations. Indeed, A2 for both samples was considerablysmaller than at 0.1 N NaCl, and the apparent square radius of gyration was almost independent of the NaPAA concentration. Polyelectrolytes in solution with low molecular weight salt preferentially adsorb or desorb the added salt ions. This affects the interpretation of SLS data with increasing concentration of the low molecular weight salt.15 Such effects can be taken into account by carrying out SLS and refractive index experiments at constant chemical potential of the added salt, which can be achieved by dialysis of each polyelectrolyte solution against the respective solution of the added salt. Fortunately, practice has shown that light scattering, carried out at constant concentration of the added salt, also yields reliable results as long as the evaluationof the SLS data is based on a refractive index increment at constant chemical potential of the added salt. Measuremens of dn/dc at constant chemical potential lead to values which are 5% lower for half neutralized polymethacrylic acid in 0.1 N NaC116 or 13% lower for NaPAA in 0.3 N NaCl solution15 compared to the respective results at constant concentration of the added salt. In the present work, the determination of dn/dc like the SLSexperimentsis carried out at constant concentration of the added salt. Therefore the M, values given in Table I should be regarded as a relative measure only of the polyelectrolyte molecular weight. However, precise values for molecular weights are not essential here because we focus on the change in geometric dimensions of the polyelectrolytechains in the presence of Ca2+ ions. Here, the added low molecular weight electrolyte mostly consisted of Na+ and Ca2+ cations, and dialysis of the polyelectrolyte solution against mixed Na+/Ca2+solutions would have caused preferential
The Journal of Physical Chemistry, Vol. 97, No. 38, 1993 9821
Calcium-Induced Shrinking of Polyacrylate Chains
07
3
0 w
/ l I
n
E c
.
u z n
\ A
Y
1.5
(u
v)
V
u
'50
2
4
6
n
0
4
q2 / 10"cm' Figure 1. Angular dependence of SLS data at r, = 0.0 (l), 0.02 (2), 0.04 (3), 0.06 (4), and 0.08 (S), normalized with the respective Kc/& from eq 4b. Polyacrylate concentrations are within 0.2 < c < 0.28 g/L.
adsorptionof Ca2+to polyacrylate anions and finally precipitation of CaPAA in the dialysis hose. Thus, contrary to earlier work,6v7 dialysis of NaPAA solutions prior to measurement becomes invalid. Concentration-dependent interactions between Ca2+ ions and the polyelectrolytechains render a classical Zimm analysis of the concentration-dependent SLS data uncertain. Therefore,in Ca2+containing solutions, the only measure of the geometric size of PAA chains at finite concentrations of NaPAA and Ca2+which is accessible to SLS is an apparent mean-square radius of gyration (S2). Values for ( S 2 )were calculated according to
K c / A R = Kc/ARo(l
--E
8
+ (S2)/3q2 + ...)
M
\
0
\
4
.OZ
Ob
.04
.06
.08 11
F
rca Figure 2. Apparent mean-square radius of gyration (a) and reduced viscosity (b) as a function of Ca2+content at pH = 9. The concentration of sample PA3K2 is 0.24 g/L or close to 0.24 g/L. 10
1
A
\
A
(4b)
Fortunately, repulsive forces between polyelectrolyte chains decrease with increasing r,, and for r, > 0.06 the concentration dependence of Kc/ARo is getting small compared to the A2 value at r, = 0. Examples are given in Figures 7b and 8b for r, = 0.08. A pronounced shrinking of the polyelectrolyte coils was observed if Na+ ions of the added salt were partially replaced by CaZ+ ions. This is illustrated in Figure 1 for sample PA3K2 at polymer concentrations of 0.2 g/L < c < 0.28 g/L by plotting the normalized reciprocal intensities l / P ( q ) = ( K c / A R ) / (Kc(AR0)as a function of 42. Cutoff values which were used as normalizationfactors were found to lie between the corresponding Kc/AZ?o values for r, = 0 and r, = 0.8, Le. between 1.26 X 1O-a mol/g and 1.67 X IW mol/g at c = 0.2 g/L. The onset of the shrinking is significant already at a Ca2+ content corresponding to r, = 0.02, i.e. a replacement of 2% of the added 0.1 N NaCl by CaC12. This geometric shrinking will be investigated in more detail in the following paragraphs.
Calcium-Induced Coil Shrinking At a given NaPAA concentration and ionic strength, an increasing amount of Ca*+ ions leads to a decreasing radius of gyration of NaPAA chains (Figures 1 and 2a). As expected, the extent of the geometric shrinking depends on the polyacrylate concentration. This is demonstrated in Figure 3, where (s?)is measured as a function of the NaPAA concentration at five different amounts of added CaZ+ions. However, one has to bear in mind that a change in (Sz) with concentration may stem from two different origins. First, the intramolecular scattering pattern is modified by spatial correlations between different polymer chains, which is a characteristic feature for polymers in good solvent or charged polymers in solution and renders (S2) an apparent quantity. Second, with decreasing polymer concentration the ratio of Ca2+ ions to carboxylate groups increases, which may have an impact on the actual chain conformation. At very low Ca2+ contents the apparent radius of gyration increases with decreasing polymer concentration. With growing Ca2+ concentration intra- and intermolecular repulsions are increasingly balanced by Ca2+ions, and in the regime 0.02 < r,
" V
c / g1-' Figure 3. Apparent mean-square radius of gyration as a function of PA3K2 concentration at pH = 9: (A)r, = 0.0;(A)r, = 0.02; (0)r, = 0.04;(m) r, = 0.06;(0) r, = 0.08;( 0 )r, = 0.1. Data of PA3K2 at 0-conditions,denoted by connectinglines, are included for comparison. m
0 4 Ly
E d
\ A N v)V
00
.2
.4
.6
.8
1
c / gl-' Figure 4. Apparent mean-square radius of gyration as a function of polymer concentration for sample PA3K2 at pH = 9: (0)r, = 0.07;(m) r, = 0.08;(0) r, = 0.09;( 0 )r, = 0.1.
< 0.04 a transitionoccurs. For r, t0.04, (s2)graduallydecreases with decreasing NaPAA concentration. Here it is worth taking a look at the radii determined at 1.5 N NaCl and T = 15 "C. For sample PA3K2, the respective results are included in Figure 3 as points connected by solid lines. It is interesting to note that the values are comparable to those in the r, regime where the above-mentioned transition of the concentration dependence of (Sz)occurs, i.e. in 0.02 < r, < 0.04. As is shown in Table I, the unperturbed radii of both samples are well above the coil radii determined at r, > 0.06. In order to gain a deeper insight into the Ca2+-inducedcoil shrinking, SLS experiments were focused on the Ca2+ concentration range corresponding to 0.07 Ir, I 0.1. Figure 4 shows (S2)data for sample PA3K2 as a function of NaPAA concentration at four different Ca2+ contents, Le. r, equals 0.07,0.08, 0.09, and 0.1. All four sets of data exhibit a strong downward
9828
The Journal of Physical Chemistry, Vol. 97, No. 38, 1993
Huber
m 0 '21
I
,M 120
E
90
\
c / gl-' Figure 5. Apparent mean-square radius of gyration as a function of polymer concentration for sample PA4Sl at pH = 9: ( 0 )r, = 0.07; (m) r, = 0.08; ( 0 )r, = 0.09;( 0 )r, = 0.1.
bending of the (S2)plots, suggesting an extrapolation of the polymer concentration to lim( (s1)-4). The extrapolatedvalues indicate threshold concentrations where the coils collapse and beyond which precipitation occurs. A similar trend is observed with polyacrylate sample PA4S1, the results of which are represented in Figure 5 . To confirm the presented SLS results, complementaryviscosity measurements were carried out. Experimental data are interpreted in terms of the reduced viscosity qlp/c. Extrapolation of qlp/ctoinfinite dilution yields theintrinsicviscosity [ q ] . Referring to Einstein's law," [ q ] in g/ 100 mL can be related to the equivalent hydrodynamic sphere volume V, of a polymer chain. In solutions containing Ca2+ ions the actual coil radius is a function of polymer concentration and qap/chas to be discussed at the respective concentrations. In Figure 2b, the decreasein the reduced viscosity q8p/c is shown as a function of the Ca2+ content r,, which is consistent with the behavior of (9). At a polymer concentration of 2.8 X 10.4 M the hydrodynamicallyeffectivevolume expressed in terms of qIP/cshrinks by a factor of 0.076 if the Ca2+ content isincreasedfromr, = 0.0t00.08. At thesametime, thegeometric volume shrinks by a factor of 0.033. However,one has to consider that the values of qV/c like (S2) may be influenced by intermolecular interactions. Similar results were published by Flory and O~terheld.~ They investigatedpolyacrylates at two different CaCl2 contents (0.005 and 0.0025 M ionic strength), which was the only salt being added. Extrapolation of the resulting data to infinite dilution led to the well-known Staudinger index. Finally results at both ionic strengths were compared with the respective data from sodium salts, indicating that Ca2+ ions lead to a much stronger shrinking of polyacrylates than Na+ ions do. However, unlike the case of the present work, the polyacrylates of Flory and Osterheld had a degree of neutralization of only 0.1. In order to give further evidence for the influence of the ratio of Ca2+ions to carboxylate groups on the shrinkingof polyacrylate coils, viscosity measurements were carried out with sample PA4S 1, analogous to the SLS experiments represented in Figure 5. As is shown in Figure 6, the reduced viscosity decreases with decreasing NaPAA concentration, confirming that the coils drastically decrease their size while lowering their concentration at a constant Ca2+content. As already indicated by the SLS data, this shrinking of the polyelectrolytecoil is shifted to higher NaPAA concentrations if r, is increased.
Discussion
Coil SMnkiag and Precipitation. If r, is larger than 0.06, the concentration dependence of Kc/& exhibits a sharp decrease, induced by a sudden increase of the scattering intensity. Examples of this behavior are shown in Figures 7b and 8b at r, = 0.08.
m 0
c
u 0
0
gm1-'
Figure 6. Reduced viscosity as a function of concentration at pH = 9 for sample PA4S1. Symbols have the same meaning as in Figure 5 .
2 n
E
m
3..
A
m
A
A A
a
c/
g1-'
Figure 7. Apparent mean-square radius of gyration (a) and Kc/& (b) as a function of polymer concentration at r, = 0.08 for sample PA3K2. The samples are purified with filters of two different pore sizes: ( 0 )0.8 pm; (A)0.45 pm.
c / gl-' Figure 8. Apparent mean-square radius of gyration (a) and Kc/& (b) as a function of polymer concentration at r, = 0.08 for sample PA4Sl. The samples are purified with filters of a pore size of 0.8 pm.
Further dilution of the polyelectrolyte at a constant concentration of the added salt lead to turbid solutions. The sharp drop of Kc/& is usually accompanied by an increase of (S2) (Figure 7a), although a distinct minimum in (s2)is not always detectable (Figure 8a). Obviously, interparticular interactions induced by Ca2+ ions lead to aggregation and finally precipitation as the polymer concentration is decreased. The sharp decrease of Kc/ A& indicates the onset of this aggregation. It is interesting to note that the sharp drop observed with the concentration dependencesof Kc/ is preceded by a maximum. Three reasons may serve as possible explanations: (i) A decrease in may be caused by filtration of aggregated/precipitated polyacrylateprior to light scattering. However, as shown in Figure
Calcium-Induced Shrinking of Polyacrylate Chains
5
;P
81
.
I
. O
The Journal of Physical Chemistry, Vol. 97, No. 38, 1993 9829
q
12,
I
i
2E
-
\ N +
(11
"0
.2
.4
.6
.8
[COO'], / mmol/l
c / gl-' Figure 9. Extrapolation of (Sz)2 versus polymer concentration c to lim((sZ)--O)resulting in collapse concentrations C, for sample PA3K2.
The symbols have the same meaning as in Figure 4.
-
-
Figure 11. CaZ+content as a function of the collapse concentration for polyacrylate in 0.1 N C1-: (0)PA3K2;( 0 )PA4Sl. The straight linw indicate fits according to eq 6,which yield ro = 0.55and m = 6.8 mM for sample PA3K2 and ro = 0.54and m = 6.23mM for sample PA4Sl.
1
100,
U
oy cu
0
801
I
As is shown in Figure 11, both sets of data imply an approximation by the following empirical relation
2[ca2+] = COO-], + m
c / gl-' Figure 10. Extrapolation of (S2)2versus polymer concentration c to lim( (P)--O) resulting in collapse concentrations C, for sample PA4S1. The symbols have the same meaning as in Figure 5.
7, SLS experiments prepared by filters of different pore size (0.45 or 0.8 pm) basically yielded the same results. (ii) Polyacrylate molecules which become saturated with Ca2+may have a refractive index increment lower than the respective polyanion. This is supported by the fact that protonation of the polyanion also leads to a drastic decrease of the dn/dc value. Unfortunately, dn/dc values in such low concentration ranges are difficult to measure. (iii) Decreasing the NaPAA concentration at a constant Ca2+ content may lead to an oversaturation of the polyanion with Ca2+ which in turn is responsible for intermolecular repulsions and a modified second virial coefficient. Interestinglyenough, the excess of Ca2+relative to COO- groups in the experiments with sample PA3K2 in Figure 7 is larger and the maximum in Kc/ARo is more pronounced than with sample PA4S1 in Figure 8. However, results from SLS measurements below the concentration where K,/ARo steeply descends suffer from low reproducibility and will not be further used. Limit of Maximum Coil Shrinking. As already mentioned, the strong dependence of (S2)on polymer concentration suggests an extrapolation of c to l i m ( ( S 2 ) 4 ) which corresponds to a concentration limit where the extent of coil shrinking is largest. In order to better extrapolate the strongly bent curves in Figures 4 and 5, (S2)2instead of (S2)is plotted as a function of polymer concentration. For each Ca2+content, a linear regression of those four or five (S2) values was carried out, the concentrations of which border the onset of aggregation, indicated by a drop of Kc/ARo. The values of the threshold concentrations so obtained are denoted as C,. Details of the procedure are shown in Figures 9 and 10 for both NaPAA samples. The small values for (Sz)measured close to C,, as well as the steep descend of the (S2) plots, indicate an intramolecular coil collapse. This collapse depends on the Ca2+ content. Such dependences are represented as plots of the Ca2+ concentration versus the collapse concentration of carboxylate groups in Figure 11. To this end, the quantities r, and C, have to be transformed into molar concentrations of calcium ions [Ca2+] and of carboxylate groups from the polymer chains [COO-], in solution, respectively.
(6)
which is determined by two parameters, a finite slope ro and a cutoff m. Values for theslope roareclose to 0.5 for both NaPAA samples. This implies that the coil collapse concentration [COO-], will be shifted by an increment which is 4 times as large as the corresponding increase in the Ca2+ concentration. The proportionality points to a stoichiometricnature of the type of interaction between Ca2+ions and COO- groups of the polymer backbone. The second parameter m occurring in eq 6 corresponds to the amount of Ca2+required to induce a coil collapse with infinitely diluted polyacrylate. Whereas sample PA3K2 is characterized by m = 0.0068 M, the data of sample PA4S1 lead to a value of 0.0063 M. Contrary to ro, this parameter differs slightly for the two molecular weights of the polyacrylate samples, which is noticeable as a shift of the data in Figure 11. The results clearly show that Ca2+ ions experience a much stronger interaction with polyacrylate than Na+ ions do. This was visualized by a strong coil contraction which leads to CaPAA precipitation while decreasing NaPAA concentration at constant [Ca2+]. Still, precipitation only takes place above a critical Ca2+ concentration. The strong interaction may be explained by complex bonding of neighboring COO- groups to Ca2+ which makes the molecule less hydrophilic. Due to the high degree of neutralization ( loo%), additional intramolecular COO-CaZ+--OOC bridges are very likely to occur, which amplifies the tendency to collapse. Type of Precipitation. According to Ikegami and Imai,l* two types of polyacrylate precipitation exist, depending on the counterion and the degree of ionization of the polyelectrolyte. In the first type, denoted as H-type, the critical cation concentration where precipitation takes place is high and independent of polyelectrolyte concentration. In the second type, called L-type, the critical cation concentration is generally low and proportional to the polyelectrolyte concentration. In a recent publication, Narh and Keller19 also discussed two modes of polyelectrolyte precipitation when adding selectedmetal cations to polystyrenesulfonate. In mode 1, the polystyrenesulfonate concentration at the precipitation threshold increased with decreasing cation content, which is consistent with the law of mass action for salt precipitation processes. The authors could show that interactions between the ionic groups are responsible for the precipitation of the polyelectrolyte. Depending on the type of the added metal cation, a completely different type of precipitation was observed: Now, the cation concentration, required to induce precipitation, increases linearly with the polyelectrolyteconcentration at the threshold. According to Narh and Keller, precipitation in mode 2 is due to hydrophobic intramolecular interactionswhich in turn are triggered by bridging N
Huber
9830 The Journal of Physical Chemistry, Vol. 97, No. 38, 199.3 through certain metal cations. Clearly mode 2 corresponds to the L-type precipitation in the publication of Ikegami and Imai.ls Although the concentration C,, where (Sz) is at its minimum, is not necessarily identical to the concentration where the solution gets turbid, C, can as well be assumed to indicate the onset of precipitation within experimentalerror. Under this consideration, the results in Figure 11 are consistent with the corresponding plots in Ikegami and Imai’s work as well as in Narh and Keller’s communication. In other words, the Ca2+-inducedcoil collapse of NaPAA preceds an L-type or mode 2 precipitation of CaPAA. However, one has to keep in mind that Ikegami and Imai**like Narh and Kellerlo varied the amount of the precipitating cation without adding other low molecular weight electrolytes. Contrary to this, a constant overall concentration of the low molecular weight salt was used in the present work, Le. CaZ+ was added by replacing Na+ ions. The precipitation process for CaPAA can be treated as a “twostep reaction”. First, the polyelectrolyte becomes hydrophobic by interactions with Ca2+ cations. Relationships of the type of eq 6 are characteristic for this step. Being less hydrophilic, the polymer chains can readily interact and, in a second step, shrink and form large aggregates. It is this step which reflects the polymeric nature of the precipitating polyelectrolyte.
Summary The present work shows that CaZ+-inducedcoil shrinking of polyacrylate chains can be investigated close to the precipitation limit of calcium polyacrylate. For completely dissociated polyacrylate in 0.1 N NaC1, this was achieved by replacing a few percent of the Na+ ions by CaZ+ions. As is shown by viscosity and SLS experiments, the squared coil radius shrinks by an order of magnitude. Close to the precipitation limit, values for (S2) are much lower than for those of NaPAA even under 0-conditions. Such a shrinking behavior is comparable to a coil collapse which was observed in classical polymer science by several research groups.20 Whereas this coil collapse led to densely packed spheres, a detailed picture of the shrunken polyacrylate chains cannot yet be offered. Further experiments on this aspect are in progress.
The polymer concentration where the polyacrylate chains are assumed to collapse and which borders on precipitation is low (- lCP g/mL) and increases with increasing concentration of Ca2+ ions. We observed 4 d[COO-1, = d[Ca2+]
(7)
independent of moleclar weight.
Acknowledgment. The author is indebted to N. Fritz and E. Bouynet for their assistance in performing the experimental work and to W. Schreiber and R. Kuratli for preparing the polymers used in this study. Stimulating discussions with Dr. A. HBhener, Dr. R. Scartazzini and Professor M. Schmidt are greatly acknowledged. The author thanks CIBA GEIGY AG for permission to publish this paper. References and Notes (1) Zini, P. Seifen, &le, Fette, Wachse 1987, 113, 45, 187. (2) Perner, J.; Neumann, H.-W. Tenside, Surfactants, Deter. 1987,24, 334. (3) Wall, F. T.; Drenan, J. W.; Hatfield, M. R.; Painter, C. L. J. Chem. Phys. 1951, 19, 585. (4) Flory, P. J.; Osterheld, J. E. J. Phys. Chem. 1954, 58, 653. ( 5 ) Orofino, T. A.; Flory, P. J. J . Phys. Chem. 1959, 63, 283. (6) Kitano, T.; Taguchi, A.; Ncda, I.; Nagasawa, M. Macromolecules 1980, 13, 57. (7) Hara, M.; Nakajima, A. Polym. J . 1980, 12, 701. (8) Takahashi, A.; Nagasawa, M. J. Am. Chem. Soc. 1964.86, 543. (9) Ncda, I.; Tsuge, T.; Nagasawa, M. J . Phys. Chem. 1970, 74, 710. (IO) Kay, P. J.; Treloar, F. E. Makromol. Chem. 1974, 175, 3207. (1 1) Richter, F.; Winkler, E.W. Tenride, Surfactants, Deterg. 1987, 24, 213. (12) Wall, F. T.; Drenan, J. W. J. Polym. Sci. 1951, 7, 83. (1 3) Takahashi, A.; Yamori, S.; Kagawa, I. Kogyo Kaguku Zasshi 1962, 83, 11. (14) Becker, A.;Schmidt, M. Makromol. Chem.,Macromol. Symp. 1991, 50, 249. (15) Briisau, R.;Goetz,N.; Michtle, W.;Stblting, J. Tenside,Surfactants, Deterg. 1991, 28, 396. (16) Vrij, A.; Overbeek, J. Th. G. J . Colloid Sci. 1962, 17, 570. (17) Einstein, A. Ann. Phys. (Leipzig) 1910, 33, 1275. (18) Ikegami, A.; Imai, N. J . Polym. Sci. 1962, 56, 133. (19) Narh, K. A.; Keller, A. J. Polym. Sci., Part B Polym. Phys. 1993, 31, 231. (20) Fujita, H. Polymer Solutions; Elsevier: Amsterdam, Oxford, New York, Tokyo, 1990; Chapter 4.2 and references therein.
