Counterion condensation and rapid transport of polyelectrolytes through aqueous polymer solutions

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ARTICLE IN PRESS Model

OLSUA-17913; No. of Pages 5

Colloids and Surfaces A: Physicochem. Eng. Aspects xxx (2012) xxx– xxx

Contents lists available at SciVerse ScienceDirect

Colloids and Surfaces A: Physicochemical andEngineering Aspects

jo ur nal homep a ge: www.elsev ier .com/ locate /co lsur fa

ounterion condensation and rapid transport of polyelectrolytes throughqueous polymer solutions

iroshi Maedaa,∗, Ken-ichi Nakamuraa, Hisayuki Yamanea, Shigeo Sasakia, Rie Kakehashib

Department of Chemistry, Faculty of Science, Kyushu University, 812-8581 Fukuoka, JapanOsaka Municipal Technical Research Institute, Morinomiya Joto-ku, 536-8553 Osaka, Japan

i g h l i g h t s

A rapid transport of polyacrylatesthrough aqueous dextran solutions isreported.The transport rate increased with thecharge density.The counterion condensation mani-fests itself in the nonlinear transportprocess.The transport rate decreased withincreasing salt concentration.

g r a p h i c a l a b s t r a c t

r t i c l e i n f o

rticle history:eceived 27 June 2012eceived in revised form 22 August 2012ccepted 24 August 2012vailable online xxx

a b s t r a c t

A rapid transport of polyacrylates through aqueous dextran solutions was reported. The transportedamount Q linearly increased with time t instead of t1/2. The rapid transport is associated with the formationof finger-like flows, a kind of dissipative structure. The transport rate V increased with the linear chargedensity of polyacrylic acid but became constant independent of the charge density if the latter exceedsa critical value. The counterion condensation was strongly suggested from this peculiar dependence

eywords:ounterion condensation

dissipative structureolyacrylateinger-like flow

on the charge density. The transport rate decreased with increasing NaCl concentration. At 0.5 M NaCl,the transport was no longer rapid but took place as a diffusion process. As another matrix–gradientsystem, transport of polyvinylpyrrolidone (PVP) through aqueous sodium polyacrylate solutions wasalso examined and rapid transport of PVP was found.

© 2012 Elsevier B.V. All rights reserved.
alt effect
. Introduction

When an aqueous solution of dextran is placed above anotherqueous solution consisting of dextran of the same concentra-ion and polyvinylpyrrolidone (PVP), the diffusion of PVP fromhe lower solution to the upper solution is expected to occur.

Please cite this article in press as: H. Maeda, et al., Counterion condensatisolutions, Colloids Surf. A: Physicochem. Eng. Aspects (2012), http://dx.doi

he situation is schematically shown in Fig. 1A where the matrixolymer is dextran and the gradient polymer is PVP. However,

rapid transport of PVP has been observed by Preston et al.

∗ Corresponding author. Tel.: +81 92 681 8080; fax: +81 92 681 8080.E-mail addresses: [email protected], [email protected]

H. Maeda).

927-7757/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.colsurfa.2012.08.072

[1,2] when both dextran and PVP concentrations exceeded respec-tive critical values. This rapid transport was found to be dueto the occurrence of a finger-like structured flow as schemat-ically shown in Fig. 1B and it was characterized by the lineardependence of the transported amount on time t rather thanon t1/2 (diffusion process). The system is called matrix–gradientsystem where PVP moves through the dextran solution matrixas a result of a given concentration gradient. We have reportedthat the PVP transport in dextran–PVP system is enhanced in thepresence of a simple salt (the same concentration in both upper

on and rapid transport of polyelectrolytes through aqueous polymer.org/10.1016/j.colsurfa.2012.08.072

and lower solutions). The extent of enhancement depends on thekind of ions and is correlated with the density of solutions [3–5].The molecular mechanism of the phenomenon is not yet fullyelucidated.

dx.doi.org/10.1016/j.colsurfa.2012.08.072


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ARTICLE IN PRESSG Model

COLSUA-17913; No. of Pages 5

2 H. Maeda et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects xxx (2012) xxx– xxx

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ig. 1. A schematic representation of the measurements with Sundelöf cells. (A)

olutions. (B) After a duration of time, finger-like flow pattern appeared in case tha

As to the effects of electric charge, a few reports on theransport of biological polyelectrolytes are found, such as chon-roitin sulfate through proteoglycan matrix [6] or hyaluronic acidatrix [7] and sodium hyaluronate through dextran matrix [8].e have examined the transport of a polyelectrolyte, polyacry-

ate, through a dextran matrix focusing on the effects of counterionpecies. The transport rates were in the following order [5]:Pr)4N+ > (Me)4N+ > Li+ > (Bu)4N+ > Na+ > NH4

+ > Cs+. The order wasinearly correlated with the partial specific volume except forBu)4N+, to which the effect of the viscosity was suggested [5]. Theffects of the charge density of polyacrylate and the salt concentra-ion will be presented in the present report. Also, some results onransport of PVP through aqueous NaPAA solutions, a new matrixNaPAA)–gradient (PVP) system, will be reported. A preliminaryxperiment using an ionic micelle as a gradient component will belso reported.

. Materials and methods

Dextran (Nacalai Tesque Inc.) was used as received. Poly-crylic acid was recovered from sodium polyacrylate (Toa Goseihemicals Co.) by repeated precipitation-dissolution by HClnd NaOH. Number-average molecular weights Mn of dextrannd PAA were 3.5 × 104 and 5.9 × 104, respectively, as deter-ined by osmotic pressure measurements (Knauer membrane

smometer) using cellulose membranes (Y1245, Knauer) ofore size 0.005 �m. Weight-average molecular weights Mw ofaPAA was 2.1 × 105 as determined by light scattering (MalvernCS100SM). Polyvinylpyrrolidone (Mn = 3.2 × 105) was the sameample as used in a previous study [5]. PAA was labeledith 9-chloromethylanthracene (Tokyo Kasei Kogyo Co. Ltd.) inimethylformamide containing tetramethyl ammonium hydrox-

de. The extent of label was about one dye molecule per 1000esidues. The transport of PAA was measured at 23 ± 1 ◦C with Sun-elöf cells. A Sundelöf cell consisted of two identical compartments.ach compartment was a cylinder of ca 1 cm long and ca. 0.2 cm2


ross section area A. At time 0 (t = 0), the upper and the lowerolutions were stratified as shown in Fig. 1A. After a time inter-al t elapsed, the two compartments were separated and broughtack to the original position and the amount of PAA in the upper

e 0, two compartments are brought into the contact position to stratify the twoonditions for the dissipative structure are satisfied.

compartment Q was determined by the absorption at 257 nm.Details of the measurement are given in the previous reports [3,4].To control pH values of the solutions proper buffer systems wereused. Finger-like flow patterns were observed using a microscopeafter an upper solution was slowly added by a pipette onto a lowersolution in a glass cell (depth 1 mm, 1 cm wide). A sharp initialboundary was obtained almost always in this way.

3. Results

3.1. Effects of the charge density of PAA on the transport rate

The transported amounts Q of PAA from the lower compart-ment to the upper compartment were measured as functions oftime t at different pH values. Identical pH values for both theupper and the lower compartments during the measurement wereexpected to be maintained by using proper buffer solutions: acetatebuffers (pH 4.2–5.5), phosphate buffers (pH 5.9–6.9) and trisHCl(pH 8.0–9.0). Buffer concentrations were 30–50 mM. The PAA con-centration present in the lower compartment C0 was 3 kg (Na saltbasis) m−3(ca 30 mM). Dextran concentration was 80 kg m−3. In allcases examined, Q increased linearly with time t indicating a non-diffusive transport. The transport rates V were evaluated accordingto Eq. (1). Also, the apparent diffusion constants Dapp were evalu-ated according to Eq. (2).

Q

AC0= Vt (1)

[Q

AC0

]2

=(

Dapp

�

)t (2)

The results are summarized in Table 1 and the transport rates Vare plotted against the degree of ionization ̨ in Fig. 2. Four solutions(open symbols in Fig. 2) were prepared by adjusting the degrees ofneutralization. For other solutions, the degrees of ionization ̨ wereapproximately evaluated from the measured pH values with the aidof a reported titration data in 20 mM and 50 mM NaCl [9].


The apparent diffusion constants Dw of NaPAA in theabsence of dextran evaluated according to Eq. (2) were0.2–0.3 ± 0.05 × 10−10 m2 s−1 at both ̨ = 0.25 and 0.64. These val-ues are smaller than Dapp values shown in Table 1, providing


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H. Maeda et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects xxx (2012) xxx– xxx 3

Table 1Transport of polyacrylic acid through aqueous dextran solutions at different pHvalues. Dextran concentration was 80 kgm−3. Initial PAA concentration in the lowercompartment was 3 kgm−3.

pH ̨ V Dapp

(±0.05) 10−7 m s−1 10−10 m2 s−1

4.1 0.1 ± 0.06 0.58 ± 0.05 4.7 ± 0.70.12 ± 0.04 0.68 ± 0.04 1.5 ± 0.4

4.8 0.2 ± 0.10 0.71 ± 0.07 5.7 ± 0.60.29 ± 0.01 1.35 ± 0.04 6.7 ± 1.7

5.2 0.3 ± 0.11 0.95 ± 0.05 4.4 ± 0.90.36 ± 0.06 1.09 ± 0.08 4.2 ± 1.50.38 ± 0.02 1.61 ± 0.08 8.1 ± 1.3

5.5 0.4 ± 0.09 1.33 ± 0.08 6.3 ± 0.65.9 0.5 ± 0.10 1.56 ± 0.11 13 ± 0.36.3 0.6 ± 0.03 1.72 ± 0.15 16 ± 1.56.6 0.7 ± 0.07 1.3 ± 0.11 9.2 ± 1.5

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Fig. 3. Transport of polyacrylate Q/(AC0) at different NaCl concentrations as func-tions of the time t after the upper and the lower solutions were stratified. Q:transported amount at time t, C0: the initial polyacrylate concentration in the lower

6.9 0.8 ± 0.03 1.52 ± 0.1 12 ± 1.58.0 0.9 ± 0.03 1.32 ± 0.13 6.8 ± 0.79.0 1 1.37 11 ± 1.3

nother indication of a non-diffusive rapid transport of NaPAA inhe present study. In Fig. 2, the transport rate increases with ̨ in theange below 0.4 indicating that electric charges enhance the trans-ort of PAA. For a range ̨ > 0.5, however, the transport rate can beegarded as constant independent of ˛, though it may go through

maximum around ̨ = 0.6. The constant transport rate is proba-ly due to the counterion condensation phenomenon. According tohe Manning–Oosawa theory [10,11], the counterion condensations predicted to take place for a range ̨ > ˛crit where ˛crit = 0.36 in thease of vinylic PAA. After the condensation takes place, the effec-ive or net charge density does not increase with ̨ but remainsonstant. It is not clear at all, however, how the counterion con-ensation, a thermodynamic concept, is related to the non-linearransport process observed in the present study. It is to be notedhat similar ˛-dependence was observed in the case of intrinsiciscosity of PAA [12].

In relation to a possible maximum in the plot of Fig. 2, it is toe stated that trisHCl buffer was used for ̨ = 0.9 and 1 whereashosphate buffer was used for ̨ = 0.5–0.8. Condensed states of Na+

nd tris+ counterions will be significantly different since differentondensed states of counterions were reported on the refractivendex [13] or density [14] of polyelectrolyte solutions.


.2. Effects of salt concentration on the transport rate of NaPAA

The transported amounts Q of NaPAA ( ̨ = 1) as functions of time are shown in Fig. 3 for different NaCl concentrations Cs. At the final

ig. 2. Dependence of the transport rate V on the degree of ionization ˛. Filled (open)ymbols refer to solutions prepared by adjusting pH (the degree of neutralization).

compartment, A: the cross sectional area of a Sundelöf cell. NaCl concentrations/Mare 0 (open circles), 0.01 (triangles), 0.05 (squares), 0.1 (diamonds), 0.2 (crosses) and0.5 (filled circles).

stage of the experiment, the polymer concentration was uniform(ca 1.5 kg m−3) throughout the upper and the lower compartments.In the case of no added salt (open circles), this state corresponds toa time domain (t > 105 s) where the ordinate values are about 3.5.As shown in Fig. 3, Q ∼ t for Cs = 0–0.2 M but Q ∼ t1/2 for Cs = 0.5 M.The apparent diffusion constants Dw of NaPAA in NaCl solutions inthe absence of dextran were measured and calculated by Eq. (2).The values of Dw/10−10 m2 s−1 (±0.01) were 0.81, 0.39, 0.30, 0.33and 0.33 for Cs = 0.01, 0.05, 0.1, 0.2 and 0.5 M, respectively. Valuesof Dapp/10−10 m2 s−1 for respective salt concentrations were 7 ± 1,6 ± 1, 4.0 ± 0.6, 0.8 ± 0.2 and 0.30 ± 0.01. When Dapp and Dw arecompared, Dapp > Dw for Cs = 0.01–0.2 M but Dw > Dapp in 0.5 M NaCl.Hence, faster transport than diffusion of PAA was supported forCs = 0.01–0.2 M but not at 0.5 M NaCl. Observations under a micro-scope showed finger-like flows for Cs = 0.01–0.2 M but no such flowfor 0.5 M NaCl. Consequently, the transport of NaPAA in 0.5 M NaClwas concluded due to ordinary diffusion in spite of the presence ofdextran solution matrix.

The dependence of the transport rate V on NaCl concentrationis shown in Fig. 4. The transport rate decreases with increasingCs except for Cs = 0. The low transport rate in salt-free solutionwas thought to be due to a high viscosity of the solution. Wemeasured relative viscosities �rel of the (NaPAA + dextran + NaCl)aqueous solutions relative to the ‘solvent’ (dextran + NaCl) aque-ous solutions. The transport rate corrected for the viscosity, V�rel,now decreases monotonously with Cs as shown by closed circles inFig. 4.

3.3. Transport of polyvinylpyrrolidone (PVP) through sodiumpolyacrylate solutions

As a new matrix–gradient system, we measured the transportof PVP through aqueous sodium polyacrylate solutions at 25 ± 1 ◦C,i.e., a matrix (Na PAA + NaCl)–gradient (PVP) system. The initial PVP


concentration in the lower compartment was 10 kg m−3. NaPAAconcentrations were 2, 10, and 20 kg m−3. Effects of NaCl concentra-tion Cs were also examined. The results are summarized in Table 2.Rapid transport of PVP was observed for all cases examined. The


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4 H. Maeda et al. / Colloids and Surfaces A: Physic

Fig. 4. Dependence of the transport rate V on the NaCl concentration Cs . Transportr�

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ates V (open circles) are given by the left-side ordinate. Corrected transport ratesrelV (filled circles) are given by the right-side ordinate.

ransport of PVP was enhanced with increasing Cs as shown inable 2. The salt effect will be explained in the similar manner asn the salt effect discussed in the preceding section in terms of theAA chain dimension. The effect of PAA concentration was inter-reted in terms of the viscosity but the highest transport rate wasbserved at the highest concentration of 20 kg m−3. In this con-ext, it is to be stated that phase separation was observed for PVP10 kg m−3)–NaPAA (20 kg m−3) mixtures when Cs was 0.16 M. Aind of instability leading to the phase separation may acceleratehe PVP transport even at Cs = 0.10 M.

.4. Transport of dodecylpyridinium chloride (DPC) throughextran solutions

As a new matrix–gradient system, we measured the transportf dodecylpyridinium chloride (DPC) through aqueous (80 kg m−3

extran + 4 M NaCl) solutions from the upper compartment towardhe lower compartment. The initial DPC concentration in the upperompartment was 70 mM. A finger-like flow was observed but itisappeared within a couple of minutes and then again the similarow pattern newly appeared and then disappeared. This character-

stic phenomenon will be due to the disintegration of DPC micelleshen they moved downward to the medium of no or low DPC con-

entrations. The transported amounts of DPC were not determinedecause measurements were often hampered by bubble forma-ion when the two solutions were stratified at time 0 by shearing.


xtension of the present study from linear polyelectrolytes to ionicicelles should be challenged in the future without using Sundelöf

ells.

able 2ransport of PVP through aqueous NaPAA + NaCl solutions at 25 ◦C.a

Matrix V Dapp

Na PAA (kg m−3) NaCl (M) 10−7 m s−1 10−10 m2 s−1

10 0 0.10 ± 0.02 0.09 ± 0.0110 0.10 0.20 ± 0.03 0.21 ± 0.0510 0.12 0.32 ± 0.03 0.56 ± 0.09

2 0.10 0.28 ± 0.06 0.08 ± 0.0120 0.10 0.32 ± 0.14 0.46 ± 0.04

a The initial PVP concentration in the lower compartment was 10 kg m−3.

PRESSochem. Eng. Aspects xxx (2012) xxx– xxx

4. Discussion

A density inversion leading to a hydrodynamic instability isone of the mechanisms for the occurrence of a macroscopic flowinstead of molecular diffusion in the case of matrix–gradient sys-tems. Development of coupled molecular diffusions of a matrixcomponent 1 (dextran) and a gradient component 2 (NaPAA) toconvective fingering can be described by coupling the pheno-menological equations for the conservation of solutes with theNavier–Stokes equation as follows [15]:

∂

∂tC1 + u · �∇C1 = D11

�∇2C1 + D12

�∇2C2 (3.1)

∂

∂tC2 + �u · �∇C2 = D21

�∇2C1 + D22

�∇2C2 (3.2)

∂

∂t�u + (�u · �∇)�u = − 1

�0

�∇p + �g�

�0+ �

�0

�∇2�u (4)

where �g, �, and u are, respectively, the gravitational acceleration,the viscosity of fluid and the local velocity of the fluid. C1, and C2 arenumber concentrations of dextran and PAA, respectively. Densitiesof the solution and the solvent (water or a salt solution) are � and�0.

When the cross diffusion coefficient D12 is significantly large,dextran molecules are effectively transported from the lower solu-tion to the upper solution in couple with the movement of Na PAAand a density inversion will result. This coupling is expected tobe enhanced when PAA chains entangle with dextran chains. Inthe present study, both effects of the charge density and the saltconcentration on the transport of PAA appear to be related to thechain dimension of PAA which is expected to increase with ̨ andto decrease with increasing Cs. When the coil dimension of PAA islarge the above mentioned entanglement with dextran chains willbe more favored.

Next, we discuss another possible mechanism accounting for thepresent results. According to a theory [16], when D22 > D11 a densityinversion can occur, which can develop the concentration fluctua-tion to the convection with the elapse of time. Small counterionsdiffuse much faster than PAA polyanion. Since small counterionsdrag a PAA, D22 becomes larger than DPAA which is the diffusioncoefficient of PAA without the dragging effect of small ions.

D22 is approximately given as follows [17]:

D22 =[

�

(1 + �)

]DPAA + DS

(1 + �), (5)

where

� = 2DS1 + Cs/(ˇNPAAC2)

ˇNPAADPAA(6)

In Eqs. (5) and (6), DS, NPAA and ˇ, respectively, are a diffusioncoefficient of a salt (for NaCl DS ∼ 16 × 10−10 m2 s−1), a degree ofpolymerization of PAA (NPAA ∼ 650) and the effective degree of ion-ization of PAA, which increases with an increase in ̨ and becomesconstant in the range ̨ > ˛crit according to the counterion conden-sation theory [10,11]. For a rough estimate of DPAA, we put D22 = Dw

in Eq. (5) and Cs = 0 in Eq. (6). Then, we get the following highlyapproximate relation

DPAA = 2DwDS

[DS(2 + ˇNPAA) − DwˇNPAA]. (7)

If we assume ̌ = 0.4 and Dw = 0.3 × 10−10 m2 s−1 (as given in Sec-tion 3.2) in addition to the given values of DS and NPAA, we have


DPAA = 2 × 10−13 m2 s−1 according to Eq. (7) as a highly approxi-mate value. Now we examine the salt effect (Section 3.2) usingthe estimated value of DPAA. For ̌ = 0.4, � = 31[1 + (Cs/M)/0.012].In the case of Cs = 0.04 M (for buffer solutions without added


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ARTICLEOLSUA-17913; No. of Pages 5

H. Maeda et al. / Colloids and Surfaces A:

aCl), Eq. (5) gives D22 ∼ DS/42 ∼ 4 × 10−11 m2 s−1, which isuch larger than D11 (assumed to be the same order as

PAA). On the contrary, D22 ∼ 0.01 × 10−10 m2 s−1 at Cs = 0.5 M and22 ∼ 0.08 × 10−10 m2 s−1 at Cs = 0.2 M. Thus, conditions of the den-ity inversion are less and less satisfied as Cs increases.

. Conclusions

A rapid transport of polyacrylates through aqueous dextranolutions was found. The transport rate increased with the degreef ionization ̨ for a range ̨ < ˛* but became approximately con-tant independent of ̨ for a range ̨ > ˛*. The present resultuggests ˛* to be about 0.4 which is close to the onset of theounterion condensation ˛crit = 0.36 for locally fully stretched PAAccording to the Manning–Oosawa theory. The counterion con-ensation manifests itself in the nonlinear transport process. Forully ionized sodium polyacrylates, the transport rate decreasedith increasing salt concentration. At 0.5 M NaCl, the trans-ort was no more enhanced by finger-like flows but becameue to diffusion process. These effects of charge density and ofhe salt concentration can be interpreted in terms of the chainimension. Entanglement of polyacrylate chains with surround-

ng dextran chains is expected when polyacrylate chains arexpanded. The entanglement induces the transport of dextranhains from the lower compartment to the upper compartmenthough dextran concentration is identical in both compartments.onsequently, a density inversion will be more effectively attainedhich in turn induces finger-like flows and results in a rapid

ransport.

cknowledgement


One of the authors (H. M.) would like to thank Professor Ger-ld S. Manning for his interest in this work and helpful commentsn the manuscript. This work was partially supported by the

[

[

PRESSochem. Eng. Aspects xxx (2012) xxx– xxx 5

Grant-in-Aid for Scientific Research (C) (No. 22500727) from theMinistry of Education, Culture, Sports, Science and Technology,Japan.

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[3] H. Maeda, T. Mashita, S. Sasaki, Enhanced polymer transport due to the presenceof salts in multicomponent convection, Chem. Lett. 20 (1991) 635–638.

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[5] H. Maeda, S. Sasaki, T. Mashita, K. Nakamura, H. Ojima, T. Gotoh, T. Fukuda,M. Yamanaka, Dissipative structure in aqueous polymer solutions, J. Mol. Liq.65/66 (1995) 341–344.

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[8] T. Gotoh, H. Maeda, Rapid transport of sodium hyaluronate in dextran solutions,Rep. Prog. Polym. Phys. Jpn. 37 (1994) 825–828.

[9] M. Nagasawa, T. Murase, K. Kondo, Potentiometric titration of stereoregularpolyelectrolytes, J. Phys. Chem. 69 (1965) 4005–4012.

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fusion, J. Fluid Mech. 126 (1983) 379–397.16] S. Sasaki, Development of coupled molecular diffusion to convective fingering,

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Counterion condensation and rapid transport of polyelectrolytes through aqueous polymer solutions