Eur. P&m. J. Vol. 33, No. 10-12, pp. 1723-1730, 1997 0 1997 Elscvier Science Ltd. All rights reserved

Printed in Great Britain PIL: s0014-3057(97yJoo17-7 &W-3057/97 $17.00 + 0.00

VISCOMETRIC STUDY OF MIXTURES OF NEUTRAL AND CHARGED POLYMERS IN

AQUEOUS SOLUTION

ROSA GARC~A,CLARA M. &MEZ,IOLANDA PORCAR, JUAN E. FIGUERUELO and AGUSTiN CAMPOS

Departament de Quimica Fisica and Institut de Cikncies de Materials (ICMUV), Universitat de VaBncia, E-46100 Burjassot, Valtncia, Spain

(Received I7 June 1996; accepted in final form 22 October 1996)

Abstract-The viscosity behaviour of aqueous mixtures formed by a polyelectrolyte (A) and a neutral polymer (B) such as polystyrene sulfonate (PSS)-polyvinylpyrrolidone (PVP) and polylysine (PLL)-PVP has been studied at 25°C. The intrinsic viscosity and viscosity interaction parameter of each polymer in water have been determined and have served us to estimate the compatibility of the different mixtures according to two different methodologies: (i) mixtures of two polymers in water as solvent and (ii) mixtures of either polymer A OFB in a solvent formed by either polymer B or A in water (“polymer solvent method”). By comparing the experimental and theoretical viscosity data it is clearly seen that: mixtures of both polymers in water do not depict any kind of thermodynamic interaction; whereas mixtures formed by a polyelectrolyte in water + neutral polymer as solvent exhibit incompatibility and, on the other hand, ternary systems formed by the neutral polymer (PVP) in a polyelectrolyte solvent show compatibility. The viscosity results show that the compatibility behaviour depends on the concentration ratio of both polymers in the mixture. Finally, an attempt to establish reference systems has been made. 0 1997 Elsevier Science Ltd

INTRODUCTION

Polyelectrolyte-surfactant [l-S] or pairs of oppositely charged polyelectrolytes [6,7] complexes form spon- taneously and in a highly cooperative manner from aqueous solutions. However, when both polyions have the same charge, they exhibit electrostatic repulsion and this can lead to phase separation caused by incompatibility. The first case has been extensively investigated in the field of polyelectrolyt+ surfactant [l-S] or interpolymer complexes [8] and the second case has been given attention both from experimental and theoretical points of view [9-15).

On the other hand, ionomers are a class of ion-containing polymers that have ions in concen- trations up to IO-15 mol% distributed in non-ionic backbone chains. They tend to form aggregates in non-polar solvents depending on the solvent polarity and ion content [ 16, 171. It has been generally noticed that the aggregation is enhanced by increasing ion content.

It is very difficult to design an appropriate theoretical background to predict transport (such as viscosity) and equilibrium properties of polyelec- trolytes or ionomers mixtures since their confor- mation and solution behaviour strongly depend on the number of ionic groups. However, many experimental methods have been used to study the behaviour of these mixed polymers in solution [lo]. Among these experimental methodologies, viscome-

*To whom all correspondence should be addressed.

try has proved to be a simple and reliable technique to investigate interactions of pairs of uncharged macromolecules in solution [18-221, uncharged polymer-microemulsion mixtures [23] or mixed polyanions in pure water [2427].

The present paper, which is a continuation of our previous investigations [20,24,26,27], attempts to highlight the role of the viscometric method to determine the interactions between a polyelectrolyte (polyanion or polycation) and a neutral polymer in water. Mixtures formed by sodium polystyrene sulfonate (PSS)-polyvinylpyrrolidone (PVP) and by polylysine (PLLbPVP of various molar masses and compositions have been studied.

Consider a general ternary system polymer A/polymer B/solvent and in order to clarify the individual contribution of each polymer on their interaction two experimental strategies have been followed: (i) determination of the reduced viscosity of a system considered as a mixture of two polymers A and B as solute in a single solvent (such as water), that is: (A + B),,,,,Jsolvent (A stands for the polyelectrolyte, PSS or PLL, and B for the uncharged polymer, PVP, in this context). Moreover, the interaction parameter between both polymers, BAB, has been evaluated at several polymer weight fractions (wi; i = A, B) different from zero. (ii) determination of the reduced viscosity, according to the “polymer solvent” method [18] of a particular system in which one polymer acts as solute and the other forms part of the solvent, that is: A/ (B + solvent) or B/(A + solvent). In this case, the parameter BAB has been evaluated for w,(solute)-rO.

1723

1724 R. Garcia el al.

The formalism used to obtain the reduced viscosity in the first case is based on the theories of Krigbaum-Wall (KW) [28] and Cragg-Bigelow (CB) [12] for mixtures of neutral polymers. On the other hand, the second strategy is based on the method developed by Dondos and Benoit [ 181 that predicts the viscosity of a neutral polymer in a binary solvent formed by other neutral polymer in a single liquid.

THEORETICAL = C[q],w, + cm (. > Cbl’2W, 2. (6)

Let us first introduce the basic and general equations related to the viscosity of a simple and binary system formed by a polymer in a solvent [ 15, 19,291. In the framework of the model developed by Krigbaum-Wall [28] and Cragg-Bigelow [12], the reduced viscosity of a polymer i is defined as:

Comparison of equations (4a) and (6) gives:

hlln = ~[rll~W! = [VIAWA + [‘lie% (7)

i!bd = [Y/1, + b,,c,

d = [VI, + kH[$Ct c,

(14

(lb)

where

b,, = k,,[r?]z (2)

and

In the above equations, (qrp),, [q], , c’, , h,, and kH refer to the specific viscosity, the intrinsic viscosity, polymer concentration, viscometric interaction par- ameter between polymer chains and the Huggins constant, respectively.

1. Mixtures of uncharged polymers

This section deals with the viscosity of ternary systems formed by two polymers and a single liquid. As pointed out in the Introduction, there are two ways of considering the polymeric system, as a mixture (A + @/solvent or as an A/(B + solvent) system. Firstly, we shall start with the simplest, giving the necessary equations and stating a criterion of compatibility. Further, we will go on with ternary systems using the “polymer solvent” method to describe the compatibility of polymers in solution.

(i) Ternary system (A + &/solvent The extension of equation (1) for a mixture of

uncharged polymers leads to:

(4a)

@?!dE = hlln + kri[)11:cm, Cm

(4b)

where the subscript “m” denotes “mixture” (and the meaning of the magnitudes involved is similar to that given above).

Equation (4) can be expressed in a weight-average form as:

where w, = ci/c, is the weight fraction of polymer i (i = A, B).

Combining equations (1 b) and (5) and considering the definition of b, given in equation (2), it is deduced:

and

h, = Cb;;*w, Cl >

* = ~AAW: + bssw; + 2b~‘:b;;wAws (8)

for a mixture of two polymers A and B in a single liquid. (Subscripts AA and BB represent the interactions between chains of the same polymeric nature.)

The theoretical value of the viscometric interaction parameter between chains of different polymers, bp, is evaluated as the geometric mean value of those parameters corresponding to the interaction between like-chain polymers, i.e.

bzr = @J+;, (9)

On the other hand, the experimental value of this parameter, VLi, is given, by parallelism, as:

bZP = b*AW: + bssw:, + 26~~w*ws, (10)

where bzP is obtained from the slope of equation (4a) plots, and bAB and be, are easily obtained from solutions of A and B, respectively, through equation (la).

Then, the criterion for compatibility in polymer mixtures is based on the comparison between experimental and theoretical bA8 values [28]. Thus, !&;j > &&” represents compatibility between poly- mers, or in other words, attractive molecular interactions, whereas values of bri < bp mean incompatibility or repulsive molecular interactions. In the hypothetical case that L$‘$ = bzr it would signify that chains do not interact neither favourably nor unfavourably.

Finally, the reduced viscosity of a polymer mixture is a function of the flow times through a capillary, being also defined by:

where t,, + (A is the flow time of a solution of polymer A at cA concentration and polymer B at cn concentration in the pure solvent, and to is the flow time of the pure solvent. From equation (11) and the viscosity data of the mixture, one can obtain the flow time of the polymer B, t,,, in the mixture when cA+O,

Viscometric study of mixtures of neutral and charged polymers 1725

or the corresponding one for polymer A, t,,, when by analogy with equation (6), the reduced viscosity of c+O, which will be the purpose of the next section. a mixture of these two kinds of polymers, as:

(ii) Ternary system A/(B + solvent) (“polymer solvent” method)

Let us now consider a system in which the polymer B is dissolved in a single liquid at a given concentration CL,, originating a binary solvent. The viscosity of the polymer A (the solute) in this particular solvent can be defined as:

(&p)m _ (te, + L&/to) - 1 Cm CA + CB

= (1 + ABac:‘I)wA + ([tl]B + bBBcB)wB, (15)

(%dA,es _ (C,+,./t,,) - 1,

CA CA (12)

t,,being now the flow time of the binary solvent. By solving equation (11) for G*+~~, replacing

&)A + B/(cA + cg) by the definition given in equation (6) and finding an expression for tcB by making cA+O, and after some rearrangements, a relationship for the reduced viscosity of a polymer A in a solvent formed by a polymer B at cg dissolved in a single liquid is obtained [30, 311:

where BAA should characterize the interactions between like-chains of the polyion A. Thus, in general, Bii is equivalent in its physical meaning to the viscometric interaction parameter for neutral poly- mers, b,. Also note that, by developing equation (15) we found Bin = B b AA BB, which should have (by analogy) the same meaning as biBI that is, the interaction parameter between unlike-chains of both polymers.

bAA &)A,c. _ [VIA + 2bABcB 2 I

CA 1 + [tf]& + bssCB 1 + [q]BcB + bB&CA.

(13)

Equation (13) predicts a linear dependence of (tfsp)A,eg/~A with CA, in a similar way that equation (6) does for (q$p)A+B/(cA + cB) with the total mixture concentration, CA + cg. In addition, it is worthwhile to note that equation (13) is mainly a function of data obtained from the individual contributions of each polymer. The experimental value of b,“,P able to fit plots of equation (13) will provide us with information about compatibility between polymers A and B by means of the comparison with the theoretical value of bAB.

On the contrary, a mixture formed by a neutral polymer A and a charged one B should have a similar expression to equation (15) but with the subscripts A and B permuted. In this case, Bin = b&,&B will have a different numerical value.

Again, the comparison between theoretical and experimental BAB values will tell us about the degree of compatibility of both kinds of polymers.

Equation (15) can be solved to give t,, + eg as well as t,, and/or t,, by only making CB+O and/or cA+O, respectively. The main goal to do that will be seen in next sections.

(ii) Ternary system A/(B + solvent) (“polymer solvent” method)

The reduced viscosity of a polyelectrolyte A in a binary solvent formed by a neutral polymer A at a given cB and a single liquid is derived through the flow times from equation (15) as:

2. Mixtures of polyelectrolytes A and neutral B polymers

(&p)A,ep. _ (tc, + c./tc,) - 1

CA CA

First of all, it is important to briefly describe the viscosity behaviour of a polyelectrolyte in an aqueous solution. Due to the well-known “polyelectrolyte effect” (exponential increase on reduced viscosity as polymer concentration is decreased), the viscosity data does not obey the Huggins equation. Instead of that, Fiioss [32] found a better description given by his empirical equation:

= (1 + [t/]BcB + b$:)(I + BAAC~*) (16)

by neglecting the terms that contain DA. Two features arise from a careful inspection of

equation (16). First, at constant CR, the equation reproduces the typical polyelectrolyte functionality on CA and, secondly, in the limiting case when cB-+O it should give the viscosity of a polyion in salt-free water, that is equation (14b) as it is expected.

(iii) Ternary system B/(A + solvent) (“polymer solvent” method)

2 = D, + Ai 1 + Bit;“’ (144

where D,, A, and Bi are constants for each polyion and are obtained from viscosity measurements in salt-free water [25]. Usually, D, values are negligible compared with the other terms in equation (14a) [33]. So that [r~]; 2 Ai and hereafter Di will not be considered in the derivation of the formalism neither taken into account in future calculations. So, equation (14a) can be written in a linearized form as:

0 ij& -’ 1 Bi 112

C =-&+A,c, (14b)

(i) Ternary system (A + B)/solvent Taking in mind equation (1 a) for a neutral polymer

and equation (14) for a polyelectrolyte, we can write

The viscosity behaviour depicted in the preceding section can be completely different if the chemical nature of the polymer solution used as binary solvent is changed.

Let us now analyse and describe the viscosity of a neutral polymer B in a solvent formed by a polyelectrolyte A and a single liquid. Using the same procedure and by means of equation (15) [see section 2(i)], the reduced viscosity for this particular mixture will be given by:

1 + BAAC”* = (1 +’ BAAcA/2) ; )AAcA(h]s + bBBcB).

(17)

1726 R. Garcia et al.

An inspection of equation (17) tells us that at constant cA (polyion as solvent), the viscosity dependence on polymer B concentration, cBr is linear and shows a similar functionality as the correspond- ing one for a neutral polymer. Moreover, in the limit case, cA-+O, equation (17) will tend to equation (la) as it is expected.

Finally, in all cases described in section 2, the fitting parameter BAB (that appears in an implicit form in equations (1 S), (16) and (17) and is equal to Et = BAAbBB) is a complex interaction parameter in which hydrodynamic and thermodynamic inter- actions as well as possible associations are included. Moreover, it is a measure of the degree of compatibility between polymers. In addition, it is important to note that equations (I 5), (16) and (17) are completely different despite all of them describe the behaviour of a mixture formed by a polyion and a neutral polymer. Thus, the procedure to measure the viscosity of ternary systems (depending on their description) is crucial and attention must be paid to it.

Finally, we can say that in general, the proper combination of the formalism of KW [28] and Dondos and Benoit [18] developed for neutral polymers combined with the Fiioss [32] equation for polyelectrolytes leads to derive theoretical ex- pressions accounting for any situation or any polymer mixture that one can imagine.

EXPERIMENTAL

Chemical and reagenfs

Three different polymers have been used in this work.

one of them considered as neutral or uncharged and the other two behaving as polyelectrolytes in water. The poly(N-vinylpyrrolidone) (PVP) used were commercial samples from Fluka (Darmstadt, Germany) with nominal weight average molar masses, M,, of 52,000 and 360,000 g mol- I. Sodium poly(styrene sulfonate) (PSS) standards with narrow distributions were purchased from Pressure Chemical Co. (Pittsburgh, PA, U.S.A.) with nominal M, of 1800, 18,000, 35,000, 100,000 and 177,OOOg mol-‘. PSS behaves as a typical polyanion in salt-free aqueous solutions. The polycation here studied was the polyaminoacid poly(u, e-L-lysine) (PLL) from Sigma (St Louis, MO, U.S.A.) with nominal M, of 22,000, 38,500, 102,000 and 228,000 g mol-‘. Some features of all the polymers such as their code names used along the paper, monomer structures, molar masses and polydispersity indexes are listed in Table 1.

Pure water was used as solvent in all experiments, distilled and deionized in a Mini-Q system (Millipore, Mildford, MA, U.S.A.) The water conductivity daily tested was (2.7 &- 0.5) x 1O-6 R-’ cm-‘.

Viscometric measurements

All measurements were performed at (25.0 f O.l)“C with an AVS440 automatic Ubbelohde-type capillary viscometer from Schott GerPte (Hofheim, Germany), which allows reproduction of the flow times with an accuracy of 0.03 sec. The instrument was also equipped with a Model CT1450 thermostatted bath and with a Mode1 T80.20 piston burette, moved by a microprocessor-controlled stepping motor for sample autodilution.

The stock solution was made by dissolving the polymer samples in freshly distilled water up to concentrations of ca 0.54.7 g dL-‘. Dilutions to yield at least six lower concentrations were made by adding the appropriate aliquots of solvent. Efflux time of the solvent was always

Table I. Characterization data of the polymers used

Sample Monomer structure Nominal Nominal

PSSl

PSS2

PSS3

PSS4

PSSS

PLLl

PLL2

PLL3

M, (g mol-l) MJM,

f CH,- H-h

6

1800

18000

\

SO,Na+

?

+NH-F-- c+i (CH2)4

35000 < 1.10

1OOOOO

177000

22oocl

38500 < 1.15

102ooo

PLL4 NH3+

228ooo

PVP-K40 f CH2- yH+ 52ooo

PVP-K90 ri

‘c=o

CA

360000

PSS = sodium poly(styrene sulphonate); PLL = poly(tr,s-L-lysine); PVP = poly(N-vinyl- pyrrolidone).

Viscometric study of mixtures of neutral and charged polymers 1727

Table 2. Viscosity data for the polymers studied in salt-free water as solvent at 25°C

kL au kfII bus Sample (dL g-l) @IL g-l)l’* Sample (dL g-‘) (dL g-‘p

Psst 1.53 53.2 PVP-K40 0.22 0.0139 Pss2 4.34 42.3 PVP-K90 1.71 1.0303 pss3 9.86 38.2

E45 23.20 12.92 15.6 18.6 PLLI 1.45 4.6 PLL2 22.20 44.4 PLL3 225.30 150.4 PLL4 324.30 106.2

PSS = sodium poly(styrene sulphonate); PLL = poly(ng-L-lysine); and PVP = poly(N-vinylpyrrolidone).

above 1OOsec. For each solution, a 12mL sample, to minimize drainage errors, was loaded into the viscometer and placed in the thermostatted bath. Measurements started after an equilibration time of cu 5-10 min and were continued until several flow time readings agreed to within 0.3 sec. The elution time of each solution is then determined as the average of several readings. The dilution and measurements are stopped when v, drops below 1.10.

Kinetic energy corrections were taken into account for the evaluation of the intrinsic viscosity, [q], which was determined by extrapolation to infinite dilution (zero solute concentration) of Huggins plots, i.e. r~,,,/c vs c, in the case of PVP (uncharged polymer) and of Fiioss plots [34], namely (qlp + l)-’ vs c@, for the polyelectrolytes PSS and PLL.

The shear rate dependence of the viscosity of linear polyelectrolytes in salt-free aqueous solutions is simply neglected [35]. Thus, it is assumed that the present measurements are already very close to the zero shear limit.

C’R (g/dL)“2 0 0.2 0.4 0.6 0.8

15 . 1 . I I I I I I 0.8 a

0.6

0.4

Fig. 1. Reduced viscosity dependence on concentration (0) and Fiioss linearization given by equation (14b) (0) for polyelectrolyte samples in pure water as solvent: (a)

polyanion PSS 177000 and (b) polycation PLL 102000.

10

. 8-

6-

a

b

0

-0

0.1 0.2 0.3 0.4 0.5 0.6

cm WL)

Fig. 2. Plots of the reduced viscosity for a mixture of a polyelectrolyte and a neutral polymer in pure water as solvent as a function of the total polymer mixture concentration, c,. (a) (PSS 1OOOOO + PIP-K@) and (b) (PLL 102000 + PVP-K40). Solid lines denote the theoretical

values predicted with equation (15).

RESULTS AND DISCUSSION

Previously to the treatment of the viscosity of polymer mixtures, it is necessary to characterize the viscometric behaviour of each polymer separately in salt-free water. Measurements of the reduced viscosity of neutral and charged polymers and their respective plots fitted through equations (la) and (14b), respectively, lead to the calculation of their intrinsic viscosities as well as other viscometric parameters. These magnitudes are of great import- ance since they are the input data for theoretical predictions to be made with the proposed formalism. Their values are compiled in Table 2 for all the assayed polymers in pure water at 25°C.

The values of [q]~ and bBs for PVP have been obtained from the slope and intercept of a linear square fit of equation (la) with a regression coefficient of 0.993. The values of the Huggins constant (not shown) given by equation (1 b) for both molar masses agree fairly well with data reported by other authors [35,36]. Similarly, in the case of polyelectrolytes, PSS and PLL, a linear square fit of equation (14b) provides the values of AA (that should be identified with [VIA) and Bu from the slope and intercept, respectively. In all cases, a regression coefficient of about 0.998 was found. As an example, Fig. 1 shows the typical polyelectrolitic viscosity of PSSS (part a) and PLL3 (part b) together with the corresponding Fiioss linearization plots [equation WWI.

Next, we present the results obtained for mixtures formed by a neutral and a charged polymer in

1728 R. Gar xia et al.

accordance with the formalism developed in subsec- tion 2 of the Theory Part.

Figure 2 shows experimental and theoretical viscosity data given by equation (15) for the systems: (PSS4 + PVP-K40)/water (part a) and (PLL3 + PVP-K40)/water (part b). In general, as it can be seen, the experimental values follow the typical polyelectrolytic behaviour, i.e. a very sharp increase (near asymptotic) on the reduced viscosity as the concentration of both polymers tends to zero. Moreover, the difference in the values of the intrinsic viscosity of the mixture, [VI,,, (at c,-+O) when compared with those corresponding to each polyelec- trolyte (see Table 2) are negligible. These features would imply that the presence of the neutral PVP does not affect the overall behaviour, or in other words, that both polymers when mixed and diluted together do not interact. The same trend has been observed for the remaining systems studied (not shown here), independently of the concentration of each polymer in the mixture (at any weight fraction). From a theoretical viewpoint, equation (15) predicts the viscosity data with great accuracy in all the mixtures assayed. It is important to note that this fact would mean, on the one hand, that one can obtain the viscosity of the mixture by measuring only each polymer separately in water since equation (15) uses only parameters of individual polymers so we could say that these mixtures show an “ideal” behaviour. On the other hand, according to the KW and CB theory of mixtures, the agreement between exper-

a

imental and theoretical data would signify that the idea1 interaction parameter BAB given in equation (15) is equal to the real one (or experimental). Therefore, interactions between unlike polymer chains have the same intensity as interactions between like-chains which means that the mixture does not show neither compatibility nor incompatibility when both poly- mers are mixed together as experimentally observed.

In Fig. 3, the experimental (&A.ee/~A and theoretical viscosity data given by equation (16) according to the “polymer solvent” method have been plotted for several ternary systems. In the present case, the polyelectrolyte A (PSS in parts a and b, and PLL in parts c and d) is the dissolved compound and the solution of the neutral polymer B (PVP-40K at constant concentration, ca = 0.25 g dL_‘) is the solvent. These plots reflect changes in the molecular dimensions of the molecules of polyelec- trolyte due to the molecules of the neutral polymer and is more reliable in the determination of [q] than that obtained from measurements of a solution of a mixture of polymers at a given ratio of both components (as in Fig. 2). As it can be seen, in all cases the polyelectrolytic behaviour is maintained (it controls the viscosity), although the experimental values are always higher than those predicted by equation (16). The observed differences arise from the value of the complex viscometric interaction par- ameter BAB, which is associated with the interaction of segments of unlike polymer molecules in the field of shear forces. Moreover, the BAB parameter is

b

0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6

Fig. 3. Reduced viscosity of polyelectrolyte A (solute) in a neutral polymer B aqueous solution of PVP-K40 (CB = 0.25 g dL-‘) as solvent for different polyions: (a) PSS 1800; (b) PSS 177oo0, (c) PLL 22000 (0) and PLL 38500 (0); (d) PLL 102000 (+) and PLL 228000 (0). The solid lines correspond to the values

obtained with equation (16).

a l

l

0.24

i

l

0 ‘0 l

0

Viscometric study of mixtures of neutral and charged polymers 1729

favourable or not. In the present case, since the theoretical B,s value is higher than the experimental one a repulsive interaction and hence, incompatibility is evidenced.

On the other hand, with regard to the effect of the polyelectrolyte molecular weight not much con- clusions are clearly obtained. In general, strong or weak interactions may be connected with the influence of the molar mass of the components. Thus, the higher the molecular weight, the greater the number of interpolymer contacts and the stronger the interaction [8]. In this context, we can see in Fig. 3 that the largest relative deviations occur for the lowest molecular weights meaning higher incompati- bility. Therefore, as the molecular weight of the polyelectrolyte is raised, the interpolymer complexes are “more compatible” or less incompatible (see parts a and b of this figure).

0.1 *.--L_1 __,_____-_-______________------ The opposite case, viscosity of a solution of a

neutral polymer B in a binary solvent formed by a solution of polyelectrolyte A (CA = 0.10 g dL_‘) is depicted in Fig. 4. As an example, part a of this figure plots the experimental (~&,,~Jcs and theoretical values given by equation (17) for PVP-K40/ (PSSl + water) and PVP-K4O/(PSS3 + water); and part b for PVP-K40/(PLL3 + water) and PVP-K40/ (PLL4 + water) systems, respectively.

Fig. 4. Reduced viscosity of the neutral polymer PVP-K40 as solute in different polyelectrolyte A aqueous solutions (c~ = 0.10 g dL-‘) as solvents: (a) PSS 1800 (e) and PSS 35000 (0); (b) PLL 102000 (e) and PLL 228000 (0). Lines are the corresponding values predicted with equation (17).

originated from a superposition of several types of interactions being the hydrodynamic and the thermodynamic the most important ones. The ideal or theoretical BAB value (=B,&,s) appears on the denominator when developing equation (16) and according to the theory is calculated assuming only hydrodynamic interactions. Therefore, its difference when compared with the real or experimental BAB should be attributed to the thermodynamic inter- actions between both polymers which can be

In contrast with the preceding mixtures, in Fig. 4 the reduced viscosity-concentration relationships were always found to be linear over the entire selected concentration range of interest meaning that the viscosity behaviour of the neutral polymer follows the Huggins functionality. The comparison of (t]Sp)s,eJ~B values for PVP-K40 in these ternary systems with those obtained for the same polymer in water reflects, in general, an increase which suggests that their molecular dimensions are being affected by the presence of the polyelectrolyte.

Moreover, the experimental data are always higher than the theoretical ones predicted by means of equation (17). In terms of the interaction parameter BAB, which appears in the numerator of equation (17), the observed discrepancies would mean that the real BAB is larger than the ideal one, that is, ABAr, > 0 and according to the KW theory would evidence attractive polymer pair interactions and, hence, compatibility of the mixture. Thermodynamically speaking, the observed polymer-polyelectrolyte mis- cibility could be attributed to the intramolecular excluded volume effect resulting in an expansion of the coil. However, from a quantitative viewpoint, the slopes of these plots (a measure of BAB) are small in the ternary systems denoting weak attractive inter- actions mainly due to van der Waals forces rather than electrostatic or hydrogen binding.

Finally, and for the sake of comparison, it is important to summarize the three different viscosity trends pointed out in this paper:

Oo I. 0.1 1 * 0.2 I * 0.3 I I 0.4 I I 0 cA WdL)

Fig. 5. Reduced viscosity dependence on concentration for the mixture PSS 177OOO/(PVP-K40 + water) (a) and the mixture PSS 177OOO/(PSS 35000 + water) (0) taken as reference system. The solid line is only to guide the eye.

(i) mixtures of both polymers in a common solvent (water) with wA x wB do not show any kind of thermodynamic interaction (see Fig. 2);

(ii) systems formed by a polyelectrolyte A (PSS or PLL) in a neutral polymer B (PVP) + water solvent where the weight fractions are wA > ws exhibit incompatibility (see Fig. 3);

1730 R. Garcia et al.

(iii) ternary systems formed by the neutral polymer PVP in a polyelectrolyte (PSS or PLL) solvent for which wB > wA reflect compatibility (see Fig. 4).

5.

6.

Guillemet, F. and Piculell, L., J. Phys. Chew., 199599, 9201.

In the light of these results, it is clear that the ability of two polymers to form a complex or to strongly associate depends on the concentration ratio of both polymers in the mixture, among other factors such as solvent, chemical nature of the interacting pairs, total concentration and on molecular weight.

On the other hand, we have finally made an attempt with a different methodology in order to find other reference systems to predict the compatibility behaviour of all the above mentioned mixtures. In connection with this topic, in previous work dealing with polyanion mixtures [24,26,27] the viscosity of a polyelectrolyte in the presence of another [either itself or with different chemical nature, such as PSS/ (PSS + water) or PSS/(PGA + water)] was measured and predicted. In the light of the results there gained, we think that a valid and ideal reference system could be that one formed by a polyelectrolyte in a binary solvent constituted by the same polymer with different molar mass. Owing to the same chemical nature, one can admit that these mixtures will not present neither compatibility nor incompatibility from a thermodynamic viewpoint, that is, the intra- or inter-chain specific interactions would obey purely to hydrodynamic effects preventing the shift from ideal behaviour.

7.

8.

9. 10.

If this is so, one can choose, for example, a reference system consisting on PSS with molar mass Ml in a solvent formed by PSS with M2 to test the compatibility of the system PSS with M 1 in a solvent of neutral PVP with M3 providing that M2 and M3 are of the same magnitude. As an example, Fig. 5 shows the reduced viscosity dependence on concen- tration for the systems: PSSS/(PSS3 + water) taken as ideal and PSSS/(PVP-K40 + water) to be tested. The results are similar to those shown in Fig. 3(b) where the reference system data were obtained by means of equation (16), evidencing again compatibil- ity of the mixture.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21. 22.

23.

24.

25.

26.

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