Effect of Molecular Architecture on the Polyelectrolyte Structuring

Article pubs.acs.org/Macromolecules

Effect of Molecular Architecture on the Polyelectrolyte Structuring under Confinement Cagri Ü züm,† Ricardas Makuska,‡ and Regine von Klitzing*,† †

Stranski-Laboratorium, Institut für Chemie, Technische Universität Berlin, Strasse des 17. Juni 124, D-10623 Berlin, Germany Department of Polymer Chemistry, Vilnius University, LT-03225 Vilnius, Lithuania

‡

ABSTRACT: The paper addresses the structuring and rheology of semidilute polyelectrolyte solutions with varied concentration and degree of polymer branching. The used polymer is constituted of the units of sodium 2-acrylamido-2-methylpropanesulfonate (NaPAMPS) with the branching inserts of 2-(2-bromopropionyloxy)ethyl acrylate (BPEA). The content of the branching units of BPEA in the polyelectrolytes was 6, 17, and 24%. Comparison of data obtained by small-angle X-ray scattering (SAXS) and colloidal probe atomic force microscope (CP-AFM) was used to study the effects of a solid−solid confinement on the structuring. Scattering peaks from SAXS and oscillatory force curves from CP-AFM indicate a transient network of polyelectrolyte chains with structural parameters such as interchain distance, correlation length, and interaction strength. The interchain distance and the correlation length obtained by SAXS (bulk) and CP-AFM (confinement) are in the same range, suggesting no compression of the network in the confined geometry. The interchain distance is not affected by the degree of branching at a fixed monomeric unit concentration. The correlation length (the range of ordering), the strength of the interchain interactions, and the solution viscosity, on the other hand, depend slightly on the degree of branching. The electrostatic correlation length and the interaction strength are smaller for 17% and 24% branched chains, reflecting a more disordered network.

1. INTRODUCTION Polyelectrolytes are defined as polymers with ionizable groups.1 In contrast to neutral polymers, small-angle scattering techniques (SAXS or SANS) give structural peaks of dilute or semidilute polyelectrolyte solutions.2 The peak position, qmax, can be used to determine the interchain distance d in bulk, using the Bragg equation d = 2π/qmax. Under confinement, structural forces arise in polyelectrolyte systems which are strongly related to the structuring in bulk.3−6 Force vs confinement thickness profile shows oscillatory behavior as the confinement interfaces come as close as a few times of the interchain distance, which is interpreted as a mesh-by-mesh expulsion of the polyelectrolytes from the slit pore, i.e., the film. The oscillation period gives therefore the interchain distance under confinement. Depending on this fact, structuring, i.e., ordering, under confinement can be studied by surface force apparatus (SFA), 7 total internal reflection microscopy (TIRM),7,8 optical tweezers,7 thin film pressure balance (TFPB),3,9−14 or atomic force microscopy (AFM).4−6,14−21 There are several reviews discussing the determination of structural forces.7,22−24 An outstanding observation in the past 10 years is that the bulk and the thin-film structuring differ only slightly in polyelectrolyte systems, restricted that there is no surface adsorption.4,5,12,17 As an exception, a 20% compression of the interchain distance in confined geometry was reported for dilute and semidilute NaPSS solutions.25 © 2012 American Chemical Society

Analyzing small-angle scattering patterns or structural forces, the scaling of interchain distance with the concentration can be gathered. This scaling gives information about the structuring in a polyelectrolyte solution, since the conformation of polyelectrolyte chains in the solution depends mainly on their concentration.2,26−29 At low polyelectrolyte concentrations, i.e., in the dilute regime, the chains form coils and the interchain distance in dilute regime scales with the concentration as c−1/3 as was reported for spherical hard particles.30−34 The mean intercoil distance can be approximated from particle number density.25 At the overlap concentration c*, polyelectrolyte chains can no longer exist as individual coils and they start to overlap. Overlapping leads to a transient network in the unentangled-semidilute regime.26,29 Milling and Kendall,16 Thedoly et al.,17 and Jönsson et al.35 proposed a parallel aligned lateral layers instead of a network structure. Rapoport et al. recently reported that a transition may occur between a lateral layer structure and a network structure.36 In both cases, the interchain distance in semidilute regime (c > c*) scales with the concentration2,26,27,29,37−41 as c−1/2, and it corresponds to the mesh size of the transient network. Briefly, a transition from semidilute to dilute regime causes a change in the scaling law4,42,43 from c−1/2 to c−1/3. Besides Received: December 21, 2011 Revised: February 28, 2012 Published: March 23, 2012 3168

dx.doi.org/10.1021/ma202763m | Macromolecules 2012, 45, 3168−3176

Macromolecules

Article

decreasing the concentration, this transition can be induced by charge reduction and increasing the chain hydrophobicity.4,42 Still, it was reported that there is a charge fraction above which Manning condensation occurs, and the polyelectrolyte structuring becomes independent of the charge fraction.5 If a hydrophilic neutral monomer is chosen, the scaling law remains as c−1/2 even for lower charge fractions,5,44 and the network structure is preserved. In addition to the charge fraction, polyelectrolyte chain length and molecular architecture play an important role for the structuring of polyelectrolytes. Previously, the impacts of chain length on the structuring under confinement was discussed in detail.3,16,19,20,25,45,46 It was shown that the interchain distance scaling changes from c−1/3 to c−1/2 with increasing chain length at a fixed monomer concentration range. As for the effects of architecture, the structure of the (mostly individual) branched or star-shaped polymers have been studied recently by experiments, simulations, or theory in bulk47−53 and in confined geometry.54−63 Because of the very different nature of the studied chains, different types of structuring were observed. For example, the interchain distance d was shown to scale as c−1/3 for confined PEI (38% secondary N atoms) dendrimers, and d increased with increasing molecular weight at a fixed concentration, indicating a spherelike ordering.54 Starshaped NaPSS, on the other hand, has a scaling of d ∼ c−1/2 above the overlap concentration and resembles the linear chains at even higher concentrations.64 It was found that the viscosity of randomly branched polymers is smaller compared to linear ones with the same molecular weight.65 The viscosity depends also less on the molecular weight for branched polymers.66 Despite the number of studies focusing on the effects of confinement on branched polyelectrolytes, most of these studies involve isolated, individual, and highly branched dendrimers or star-shaped chains. A systematic investigation of the polyelectrolyte structuring under confinement as a function of (relatively low) degree of molecular branching is not reported yet. In the current study, the degree of branching of a hydrophilic polyelectrolyte PAMPS was tuned by using 6, 17, and 24% branching monomer-initiator BPEA, as it was previously characterized and studied in the dilute regime.67 The impacts of the architectural change on the interchain distance, correlation length, and interaction strength were studied in semidilute regime. CP-AFM and SAXS were used to study the structuring in thin-film (confinement) and bulk, respectively. The dependence of conductivity and viscosity on the monomeric unit concentration is discussed in order to correlate the microscopic structuring to macroscopic solution properties.

Table 1. Characteristic Properties of Studied Branched PAMPS Samples Taken from Ref 67 sample

BPEA content, mol %

Mw

Mw/Mn

LPAMPS BPAMPS-6 BPAMPS-17 BPAMPS-24

0 6 17 24

858 000 112 000 95 000 119 000

2.07 1.99 1.98 2.47

degree of BPAMPS-24 was obviously much higher than that of BPAMPS-6. Chemical structures of LPAMPS and branched BPAMPS are presented in Figure 1. The solutions were prepared in Milli-Q (Millipore) water without any further purification or additives. 2.2. Colloidal Probe Atomic Force Microscopy (CP-AFM). The colloidal probe technique developed by Ducker et al.68 was used to study the effect of confinement on the polyelectrolyte structuring. A silica particle was glued with epoxy to a tipless cantilever with a given spring constant of 0.03−0.08 N/m (Ultrasharp Contact Silicon Cantilevers, CSC12, Micromasch). Silica particles with a radius R of about 3.35 μm were purchased from Bangs Laboratories, Inc. The cantilevers carrying the colloidal probes were exposed to air plasma cleaning for 20 min to remove all organic components on their surface. The substrate was a silicon wafer with a native SiO2 top layer, cleaned with the RCA method,69 and stored in Milli-Q water. Just before each experiment, the substrate was taken out of the water and dried in a nitrogen stream. Then a drop of the polyelectrolyte solution was put onto the substrate, and the probing head is fully immersed in the solution. Force−separation curves were collected via a commercial atomic force microscope MFP3D (Asylum Research, Inc.). The forces between the silica probe and the substrate were assumed to occur between two flat surfaces, considering that the separation between the probe and the substrate is much smaller than the size of the probe (Derjaguin approximation). No adsorption of the PAMPS is expected as both the polymer chains and the SiO2 surfaces are negatively charged in the experimental conditions. 15 to 25 force−distance curves were taken at different positions on the same substrate as well as on different substrates with different cantilevers for better statistics. For the analysis, the oscillatory force−separation curves obtained by colloidal probe AFM were fitted with the formula4−6

F(x)/2πR = A−λx cos[2π(x /d) + φ] + offset

(1)

Here, F(x) is the force as a function of the separation between the two confining walls x. R is the radius of the colloidal probe, A is the amplitude, and λ is the decay length of the oscillation. d corresponds to the period of the oscillation while φ and offset are nonessential correction parameters. It should be noted that while fitting the force data, the region very close to hard contact (x < 10 nm) should not be included due to additional contribution of the nonstructural forces. 2.3. Small-Angle X-ray Scattering (SAXS). The SAXS measurements were performed using a SAXSess mc2 system (Anton Paar KG, Graz, Austria) equipped with a sealed tube microsource and a line collimation. Cu Kα radiation having a wavelength of 0.154 nm was produced at 40 kV and 50 mA. Data analysis was done using SAXSquant 3.5 (Anton Paar, Austria) and Igor Pro (Wavemetrics) software packages, for q < 4 nm−1. The background subtracted data were desmeared against the beam length profile of the source. All measurements were performed in a 1 mm quartz capillary at 25 °C. 2.4. Conductivity and Viscosity Measurements. The conductivity of the solutions was measured at ambient conditions by a InoLab Cond 720 instrument (WTW GmbH, Weilheim, Germany). The viscosity of the solutions were measured at 25 °C by a commercial Processor Viscosity System PVS1 (Lauda, Germany) using a micro-Ubbelohde glass capillary viscometer (Schott, Germany) with a viscometer constant of 0.010 05 mm2 s2. The flow time was detected by two infrared sensors, and the analysis was made by the relevant Lauda software.

2. EXPERIMENTAL SECTION 2.1. Materials. Randomly branched poly(sodium 2-acrylamido-2methylpropanesulfonates) (NaPAMPS) were synthesized via selfcondensing AGET ATRP of sodium 2-acrylamido-2-methylpropanesulfonate (NaAMPS) in the presence of 2-(2-bromopropionyloxy)ethyl acrylate (BPEA) as a branching monomer-initiator (inimer), as the details are given somewhere else.67 The average fractal dimension is 1.43. Linear LPAMPS was synthesized by homopolymerization of NaAMPS under the same conditions. Composition of the branched NaPAMPS (BPEA content), molecular weight Mw, and polydispersity index Mw/Mn of the branched polymers are presented in Table 1. According to the data of 1H NMR spectroscopy, the content of BPEA units in the branched PAMPS varied as 6, 17, and 24 mol %, namely BPAMPS-6, BPAMPS-17, and BPAMPS-24. The content of branching units (branching degree) in the copolymers was expected to be somewhat less since a part of BPEA units were terminal. Branching 3169


Macromolecules

Article

Figure 1. Chemical structures of (a) LPAMPS and (b) BPAMPS.

3. RESULTS AND DISCUSSION Understanding the structuring is the first step to clarify the chain conformation and ion distribution in a branched polymer system. In this study, the chain architecture (degree of branching) was systematically changed for a better understanding of its effects in a confined geometry. Four P(AMPS) derivatives with different degrees of branching, namely from the linear to the most densely branched:67 LPAMPS, BPAMPS-6, BPAMPS-17, and BPAMPS-24 were compared in terms of their conductivity, viscosity, and structuring (via CP-AFM and SAXS). The samples have a fractal dimension of 1.43, so the chain architecture is between rod-like and arborescent.67 The corresponding charge fractions were calculated as LPAMPS = 100%, BPAMPS-6 = 94%, BPAMPS-17 = 83%, and BPAMPS24 = 76%. Considering the Manning condensation concept,5,70 the effective charge fraction is expected to be the same for all four samples at around 45%.5,71 Figure 2 confirms this

0.1 M, respectively, are shown in Figure 3. Oscillatory force curves from CP-AFM indicate the existence of structural forces,

Figure 2. Concentration dependence of the conductivity for P(AMPS) derivatives with different density of branching. The lines present the linear fits. The exact agreement of the conductivities suggest same amount of charge on the chains regardless of the architecture.

Figure 3. (a) CP-AFM force-separation curves (shifted in y-axis for better visualization) and (b) SAXS patterns for LPAMPS, BPAMPS-6, BPAMPS-17, and BPAMPS-24 at a fixed polymer concentration of 0.04 and 0.1 M, respectively. The solid lines correspond to (a) the extrapolated fits with eq 1 and (b) the Lorentzian fits around the peak.

assumption by showing the same conductivity values for all samples at a same polymer concentration (expressed in concentration of monomeric units: mol monomer/L or monoM). Keeping in mind that the nominal degree of charge is the same for all systems at a fixed monomeric unit concentration, and assuming that the branched chains in this study have similar molecular weights, any difference in the structuring can be attributed to the different degrees of branching. CP-AFM force−distance curves and SAXS spectra for all samples at a fixed monomeric unit concentration of 0.04 and

i.e., some layering of the polyelectrolyte chains. The broad peaks in SAXS also indicate at least a near range structuring. The solid lines in the CP-AFM graph are the fits of the force− separation curves according to eq 1, and the ones on the SAXS spectra are the Lorentzian fits.5,72 Equation 1 defines the asymptotic pair correlation function in bulk, for infinite 3170


Macromolecules

Article

Figure 4. (a) CP-AFM force−separation curves (shifted in y-axis for better visualization) and (b) SAXS patterns for BPAMPS-6 at different polymer concentrations. The solid lines show (a) the extrapolated fits of the force data according to eq 1 and on (b) the Lorentzian fits.

Figure 5. Concentration dependence of (a) CP-AFM periods d obtained from oscillatory force−distance curves by eq 1 and (b) 2π/qmax obtained from SAXS. Samples with different degrees of branching were considered. Both parameters correspond to the interchain distance (mesh size) in the semidilute network. Lines show the linear fits in the log scale. (c) A comparison of all the d and 2π/qmax values. The solid line is the 2π/qmax = d reference, and the dashed line is the actual linear fit of the data showing 2π/qmax = 1.03d.

distance.31,73 However, it was found to be valid in nanoparticle systems under confinement as well.30,31 At a fixed c, CP-AFM oscillatory forces become more pronounced and SAXS maximum scattering intensity increases with decreasing degree of branching. The period of the oscillatory forces and the position of the maximum scattering in SAXS seem to be unaffected by the branching. This observation is valid for all studied concentrations. Figure 4 presents the same plots for various c at a fixed degree of branching (BPAMPS-6). CP-AFM force curves become more pronounced, and they oscillate with a smaller period with increasing concentration. In SAXS spectra scattering intensity of the maximum increases, and its position is shifted to higher q (momentum transfer) values with

increasing polymer concentration. This behavior applies to all studied degrees of branching. Interchain distance, correlation length, and interaction strength as measured by CP-AFM and SAXS are discussed in the following sections. 3.1. Interchain Distance: CP-AFM Period d vs SAXS 2π/qmax. The concentration dependence of the period of the oscillatory CP-AFM force−distance curves is shown in Figure 5a. The period d is nearly the same for all the samples at a fixed c, and it decreases with increasing c. A concentration regime at which the size of a star-shaped polyelectrolyte is equal to the size of a linear polyelectrolyte was already reported.52 Apparently, this behavior applies also to the branched BPAMPS at the studied concentration range. 3171


Macromolecules

Article

Table 2. α and β Values in the Relations d or 2π/qmax ∼ cα and λ or 1/Δq ∼ cβ As Obtained by CP-AFM and SAXS Measurements on Polyelectrolytes with Different Degrees of Branching sample

degree of branching

LPAMPS BPAMPS-6 BPAMPS-17 BPAMPS-24

0 6 17 24

αAFM −0.43 −0.42 −0.42 −0.41

± ± ± ±

αSAXS −0.42 −0.45 −0.41 −0.39

0.02 0.02 0.03 0.01

± ± ± ±

βAFM 0.02 0.02 0.02 0.02

−0.66 −0.54 −0.35 −0.31

± ± ± ±

βAFM 0.07 0.04 0.04 0.06

−0.64 −0.44 −0.38 −0.34

± ± ± ±

0.08 0.06 0.06 0.04

Figure 6. Concentration dependence of (a) CP-AFM decay length λ obtained from oscillatory force−distance curves by eq 1 and (b) reciprocal peak width 1/Δq obtained from SAXS for samples with different degrees of branching. Both parameters give the range of ordering in the semidilute network. The lines present the linear fits in the log scale. The calculated Debye lengths are shown as a thick solid line. (c) A comparison of λ vs 1/ Δq. The solid line is the 1/Δq = λ reference, and the dashed line is the actual linear fit with 1/Δq = 0.92λ.

qmax, where qmax is the momentum transfer at the position of maximum scattering intensity. The 2π/qmax−c dependence for all four degrees of branching is shown in Figure 5b. As in the case of CP-AFM d, 2π/qmax is also unchanged for all degrees of branching at a fixed concentration. 2π/qmax decreases with increasing c as 2π/qmax ∼ cαSAXS. αSAXS values for all four samples were calculated from a linear fit of the 2π/qmax vs c data in the log scale (shown as various lines in Figure 5b). αSAXS = −0.41 ± 0.04 for all degrees of branching, indicating a network-like structuring in the semidilute regime. Table 2 shows the scaling exponent α in the relations d ∼ cαAFM and 2π/qmax ∼ cαSAXS for CP-AFM and SAXS, respectively. The two scaling exponents coincide well within the error range. A similar scaling law of 2π/qmax ∼ c−1/2 was previously reported64 for star-shaped NaPSS above c*. On the other hand, branched PEI (38% secondary N atoms) was reported to have a particle-like scaling of d ∼ c−1/3, and d increased with increasing molecular weight.54 In order to compare the absolute interchain distances in bulk and in thin film, CP-AFM d is plotted against SAXS 2π/qmax Figure in 5c. The solid line is the reference 2π/qmax = d line, and the dashed line is the actual fit showing that 2π/qmax = 1.03d. It should be noted again that these branched chains were

For all four samples, the concentration dependence of the period d was defined as d ∼ cαAFM, where αAFM is the scaling exponent. αAFM = −0.42 ± 0.03 was found independent of the degree of branching, which lies between the theoretical values −0.5 (transient network) or −0.33 (coils). Noting that the typical experimental scaling exponent for a semidilute polyelectrolyte system is not exactly −0.5 but ≈−0.45, αAFM = −0.42 indicates a network structuring rather than layering of individual coils.5,25 If the chains are long enough, roughly saying when they are made of more than 300 monomeric units, the solution already passes the overlap concentration c* in the studied concentration regime (>0.005 M) as has been proposed by theory2,29 and observed experimentally by small-angle scattering techniques (SAXS and SANS),3−5,17,25,43,44,74,75 dynamic light scattering (DLS),76−79 thin film pressure balance (TFPB),3,9−14 and colloidal probe AFM.4−6,14,18−21,25 Once c* is reached, only the total number of charged groups determines the interchain distance in the salt-free solutions of linear polyelectrolytes. This behavior was reported previously for different charge fractions5 and different chain lengths.25 In order to compare the thin film (confined) structuring with the bulk one, interchain distance in the solution bulk was determined by SAXS. The interchain distance is given as 2π/ 3172


Macromolecules

Article

Figure 7. Concentration dependence of (a) CP-AFM amplitude A obtained from fitting the oscillatory force data with eq 1 and (b) maximum SAXS intensity Imax for the linear and the branched polyelectrolytes. The lines present the linear fits.

arms as well as the distance from the core of the star.64 Moreover, simulations suggested two types of counterion capturing between the brushes of the star-shaped polyelectrolytes: A strong Manning condensation and a weak trapping which allows the counterions to move within the arms but restrict them from leaving the brush interior.62 It should be noted that different backbone25,54 or branch64 lengths can also result in slightly different correlation lengths, which might explain the difference of BPAMPS-6, BPAMPS-17, and BPAMPS-24 in the current study. Some studies4,5 correlated λ with the theoretical Debye length λD; therefore, also for the studied branched systems, the experimental λ values were compared to the theoretical Debye length (λD = 1/(4πlb feffc)1/2, where feff is the effective charge fraction under the assumption that Manning condensation takes place and lb = 7.1 Å is the Bjerrum length4,5). This equation suggests that λD scales as λD ∼ c−0.5, which is not valid for λ of the studied polymers (see Table 2). The calculated λD is shown in Figure 6a (thick line) for comparison with the experimental λ. In analogy with the literature,4,5,43 λ is much larger than λD. Of course, the calculation of λD is based on many assumptions which might explain the deviation; however, there are strong indications that not only electrostatics but also entropy (steric interactions) determine the correlation length.4−6,25 The reciprocal width at half-maximum of a SAXS pattern 1/ Δq is a bulk property and gives also information about the correlation length of the system.4,5,72 Figure 6b shows 1/Δq as a function of c for all degrees of branching. Determining Δq is not as straightforward as determining qmax due to the low contrast of the SAXS data, and the possible errors are larger, up to ±15%. But 1/Δq clearly decreases with c with a dependence of [1/Δq] ∼ cβSAXS where βSAXS is in the same range as βAFM. To summarize, although the correlation length or the counterion distribution within the network depends slightly on the degree of branching, no quantitative trend could be obtained. The agreement between λ and 1/Δq as well as between βAFM and βSAXS suggests that ion distribution around the chains or the range of ordering in the network system does not depend on the existence of a confinement, in agreement with previous reports.4,5,43 3.3. CP-AFM Amplitude A and SAXS Intensity Imax. Figure 7a shows how the CP-AFM oscillatory force amplitude A depends on the concentration and on the degree of branching. A increases with increasing polymer concentration for all the linear and the branched polyelectrolytes. This behavior was observed in other studies for several polyelec-

reported to be in the intermediate region between rod-like and arborescent structure.67 The results above suggest that, first, the rod-like character dominates the interchain distance, at least for c > c*. This is the only explanation for the fact that the more branched samples have similar interchain distance as their lessbranched and even linear equivalents. Second, confinement leads to stratification for all degrees of branching and changes the bulk interchain distance only slightly if none, in analogy with the previous reports.4,5,43 However, NaPSS systems were reported to show a 20% compression under confinement.25 Note that simulations also predicted a slight compression of star-shaped polyelectrolytes near the walls.62,63 3.2. Correlation Length: CP-AFM Decay Length λ vs SAXS 1/Δq. The decay length of the oscillatory force−distance curves is a measure of the correlation length, i.e., the range of ordering in a system, and it can be extracted from eq 1.4,5 The dependence of the CP-AFM decay length (correlation length) λ on c is presented in Figure 6a for the branched BPAMPS-6, BPAMPS-17, and BPAMPS-24 and the linear LPAMPS. λ decreases with increasing c for all four degrees of branching as in the case of d. Since LPAMPS has a much higher molecular weight than the branched BPAMPS (Table 1), no direct comparison of its decay length with that of branched ones was performed as the molecular weight might affect this parameter.25 Figure 6 shows that the more branched samples BPAMPS-17 and BPAMPS-24 have smaller decay lengths than the less branched BPAMPS-6. Under the assumption that the decay length is correlated to the distribution of counterions, it is concluded that the two more branched chains (BPAMPS-17 and BPAMPS-24) have a higher counterion density within the network than the less branched BPAMPS-6. At this point, it is worth recalling the results from the previous part that the interchain distance d remains the same at a fixed monomeric unit concentration irrespective of the degree of branching. A similar behavior was obtained for other branched or linear chains so that the increase in the charge fraction5,6 or in the ionic strength3,54 resulted in a decrease in the correlation length while the interchain distance remained the same. BPAMPS-17 and BPAMPS-24, however, have very close correlation lengths which make a quantitative conclusion about degree of branching dependence of λ impossible. Although the polyelectrolytes addressed in the current study are far from being star-shaped, they are also not purely rod-like. As a comparison, for the star-shaped NaPSS (d ∼ c−1/2) it was reported that the counterion distribution between the arms has a complex nature and depends on the length and density of the 3173


Macromolecules

Article

trolyte systems,3−6,15,16,18,25,45,80 and it is an outcome of the increasing total chain charge in the system and decreasing translational entropy of a single chain. The chains therefore repel each other more strongly before one of the layers is pressed out of the confinement. However, in force measurements, a high solution viscosity was observed to affect the amplitude of the oscillatory curves as well, suppressing the oscillation peaks and giving a significant increase in the hydrodynamic drag force. The dramatic effect of the confinement velocity has been already reported for CP-AFM and thin film pressure balance (TFPB) techniques.7 According to that, a sufficient relaxation time has to be provided for the ordered layers to rebuild their formation. In the case of TFPB measurements, this can be achieved by increasing the viscosity of the system so that the thinning of the film is slower. In CPAFM force measurements, the velocity of the piezo extension can be easily lowered to an optimum value. In the current study, a measurement velocity of 20−100 nm/s was used, and it was observed that within this velocity range the peaks are more pronounced. For lower velocities (1000 nm/s), the soft cantilever is exposed to a strong hydrodynamic drag and the force curves do not give any detectable oscillations. An important parameter that was observed to affect the oscillation amplitude in force measurements is the polymer chain length. Longer chains give more pronounced oscillatory force profiles16,25 and scattering peaks25,81 due to an entropy penalty. The studied branched samples have comparable chain lengths, but it should be noted that the linear sample LPAMPS has a larger contour length compared to the branched ones, which might explain its larger A shown in Figure 7a. Figure 7a also shows that the least branched BPAMPS-6 presents higher A as compared to BPAMPS-17 and BPAMPS24. This trend is the same as for the correlation lengths λ and 1/Δq discussed in the previous section. This similarity is not surprising considering that a smaller correlation length means a more disordered structure in which the translational entropy of a single chain is increased. Therefore, less work is required in branched systems to exclude the chains out of the confinement, resulting in a decrease in the amplitude A of the structural forces. The SAXS maximum scattering intensity Imax is a measure of the interchain interaction strength and the translational entropy of a single chain in the polyelectrolyte solution bulk. Imax as a function of polymer concentration is presented in Figure 7b. The trend under confinement and in solution bulk is the same: A and Imax increase with increasing concentration for a fixed degree of branching and decrease with increasing density of branching at a fixed concentration. It is not possible to quantitatively compare A (CP-AFM) and Imax (SAXS) and to reveal the effect of confinement on the interaction strength; however, simulations for star-branched polymers show that their mobility decreases with increasing degree of confinement,58,59 which in turn should result in enhanced interactions in the confined geometry due to entropic reasons explained above. 3.4. Viscosity. Rheological properties of polyelectrolyte solutions are determined by their configuration relative to each other82 and are highly concentration dependent. It was suggested that the overlap concentration, c*, is reached when η ≈ 2ηs, i.e., (η − ηs)/ηs = 1, where η is the measured viscosity and ηs is the solvent viscosity.82,83 Figure 8 shows the

Figure 8. Specific viscosities of PAMPS with different degrees of branching. The dashed line corresponds to the estimated viscosity where concentration regime changes from dilute to semidilute. Error bars are smaller than ±5% and not shown.

concentration dependence of the specific viscosity for all four degrees of branching. The horizontal dashed line represents the dilute−semidilute transition viscosity. As it was found in section 3.1 from interchain distance vs concentration scaling, viscosity measurements also indicate a semidilute structuring for all the samples, except for very low concentrations of the three branched samples. There is no systematic increase/decrease in the viscosity with respect to the degree of branching. The viscosity increases with increasing concentration and in the order BPAMPS-17 < BPAMPS-24 < BPAMPS-6 < LPAMPS at a fixed monomeric unit concentration. This order is different than that of the microscopic parameters discussed in the sections above. It has been already reported that viscosity of linear polyelectrolytes increases with increasing chain length.25,29,82,83 This fact explains the much higher viscosity of LPAMPS compared to the BPAMPS samples (see Table 1). The slightly lower viscosity of BPAMPS-17 can be also explained by its ≈10% lower Mw compared to BPAMPS-6 and BPAMPS-24, in agreement with previous reports discussing the viscosity of branched polymers.84,85 For the linear sample, LPAMPS, the dependence of the viscosity is ∼ c0.5 for c < 0.1 M and ∼ c0.84 for c > 0.1 M. The scaling of specific viscosity with ∼c0.5 up to a polymer concentration of 0.1 M is predicted by theory29,83 and shown experimentally25,82,86 for various linear polyelectrolytes. The theoretical scaling for c > 0.1 M is predicted as 3/2,29,83 not explaining the scaling exponent of 0.84 found in this study for LPAMPS. Nevertheless, a scaling lower than 3/2 in this regime was observed previously.25,82,83 Presumably, the scaling between the unentangled- and entangled-semidilute regimes is not sharp and around the transition concentration, it starts to increase starting from 1/2 and reaches to 3/2 at a higher concentration.25 An interesting result for the branched samples is that the concentration dependence of the specific viscosity is the same for BPAMPS-6, BPAMPS-17, and BPAMPS-24: (η − ηs)/ηs ∼ c0.65 for c < 0.1 M and ∼ c0.95 for c > 0.1 M. The lower scaling exponent compared to linear polymers can be explained by the effect of branching66 so that interdigitation of neighboring chains is less probable for branched polymer chains, but more theoretical effort is needed to clarify why samples with different degrees of branching would have the same viscosity− concentration dependence. 3174


Macromolecules

Article

(2) Dobrynin, A.; Rubinstein, M. Prog. Polym. Sci. 2005, 30, 1049− 1118. (3) von Klitzing, R.; Kolaric, B.; Jaeger, W.; Brandt, A. Phys. Chem. Chem. Phys. 2002, 4, 1907−1914. (4) Qu, D.; Baigl, D.; Williams, C.; Mohwald, H.; Fery, A. Macromolecules 2003, 36, 6878−6883. (5) Qu, D.; Pedersen, J. S.; Garnier, S.; Laschewsky, A.; Moehwald, H.; von Klitzing, R. Macromolecules 2006, 39, 7364−7371. (6) Qu, D.; Brotons, G.; Bosio, V.; Fery, A.; Salditt, T.; Langevin, D.; von Klitzing, R. Colloids Surf., A 2007, 303, 97−109. (7) Kleshchanok, D.; Tuinier, R.; Lang, P. R. J. Phys.: Condens. Matter 2008, 20, 073101. (8) Biggs, S.; Prieve, D.; Dagastine, R. Langmuir 2005, 21, 5421− 5428. (9) Asnacios, A.; Espert, A.; Colin, A.; Langevin, D. Phys. Rev. Lett. 1997, 78, 4974−4977. (10) Kolaric, B.; Jaeger, W.; von Klitzing, R. J. Phys. Chem. B 2000, 104, 5096−5101. (11) von Klitzing, R.; Espert, A.; Asnacios, A.; Hellweg, T.; Colin, A.; Langevin, D. Colloids Surf., A 1999, 149, 131−140. (12) von Klitzing, R.; Espert, A.; Colin, A.; Langevin, D. Colloids Surf., A 2001, 176, 109−116. (13) Langevin, D. Eur. Phys. J. E 2001, 5, 81−85. (14) Kleinschmidt, F.; Stubenrauch, C.; Delacotte, J.; von Klitzing, R.; Langevin, D. J. Phys. Chem. B 2009, 113, 3972−3980. (15) Milling, A. J. Phys. Chem. 1996, 100, 8986−8993. (16) Milling, A.; Kendall, K. Langmuir 2000, 16, 5106−5115. (17) Theodoly, O.; Tan, J.; Ober, R.; Williams, C.; Bergeron, V. Langmuir 2001, 17, 4910−4918. (18) Biggs, S.; Dagastine, R.; Prieve, D. J. Phys. Chem. B 2002, 106, 11557−11564. (19) Knoben, W.; Besseling, N. A. M.; Stuart, M. A. C. Phys. Rev. Lett. 2006, 97, 068301. (20) Knoben, W.; Besseling, N. A. M.; Stuart, M. A. C. Langmuir 2007, 23, 6095−6105. (21) Ribeiro, W.; Orfao, M.; Mata, J. L.; Saramago, B. J. Colloid Interface Sci. 2008, 317, 536−543. (22) Stubenrauch, C.; von Klitzing, R. J. Phys.: Condens. Matter 2003, 15, R1197−R1232. (23) Bonaccurso, E.; Kappl, M.; Butt, H.-J. Curr. Opin. Colloid Interface Sci. 2008, 13, 107−119. (24) Ü züm, C.; Kristen, N.; von Klitzing, R. Curr. Opin. Colloid Interface Sci. 2010, 15, 303−314. (25) Ü züm, C.; Christau, S.; von Klitzing, R. Macromolecules 2011, 44, 7782−7791. (26) Degennes, P.; Pincus, P.; Velasco, R.; Brochard, F. J. Phys. (Paris) 1976, 37, 1461−1473. (27) Odijk, T. Macromolecules 1979, 12, 688−693. (28) Barrat, J.; Joanny, J. Europhys. Lett. 1993, 24, 333−338. (29) Dobrynin, A.; Colby, R.; Rubinstein, M. Macromolecules 1995, 28, 1859−1871. (30) Klapp, S. H. L.; Zeng, Y.; Qu, D.; von Klitzing, R. Phys. Rev. Lett. 2008, 100, 118303. (31) Klapp, S. H. L.; Grandner, S.; Zeng, Y.; von Klitzing, R. J. Phys.: Condens. Matter 2008, 20, 494232. (32) Grandner, S.; Zeng, Y.; von Klitzing, R.; Klapp, S. H. L. J. Chem. Phys. 2009, 131, 154702. (33) Klapp, S. H. L.; Grandner, S.; Zeng, Y.; von Klitzing, R. Soft Matter 2010, 6, 2330−2336. (34) Zeng, Y.; von Klitzing, R. Soft Matter 2011, 7, 5329−5338. (35) Jonsson, B.; Broukhno, A.; Forsman, J.; Akesson, T. Langmuir 2003, 19, 9914−9922. (36) Rapoport, D. H.; Anghel, D. F.; Hedicke, G.; Moehwald, H.; von Klitzing, R. J. Phys. Chem. C 2007, 111, 5726−5734. (37) Degennes, P. Macromolecules 1981, 14, 1637−1644. (38) Khokhlov, A.; Khachaturian, K. Polymer 1982, 23, 1742−1750. (39) Yethiraj, A.; Shew, C. Phys. Rev. Lett. 1996, 77, 3937−3940. (40) Yethiraj, A. J. Chem. Phys. 1999, 111, 1797−1800. (41) Netz, R.; Andelman, D. Phys. Rep. 2003, 380, 1−95.

Finally, it should be noted that viscosity measurements suggest a dilute structuring of BPAMPS samples for c ≤ 0.02 M which could not be observed with CP-AFM or SAXS measurements (d ≈ 2π/qmax ∼ c−1/2 was observed instead of ∼c−1/3). This difference can be attributed to the narrow concentration range (0.01−0.02 M) measured in this region, which is not enough to show a distinguishable dilute solution trend. It should also be reminded that the dilute−semidilute transition line in Figure 8 is only a rough estimation.

4. CONCLUSION The effect of degree of branching (chain architecture) on polyelectrolyte structuring in salt-free aqueous solutions was studied. In order to better understand the effects of physical confinement, structural parameters such as the interchain distance, the correlation length, and the interchain interaction strength were extracted from CP-AFM (in confined geometry) and SAXS (in bulk). Randomly branched polyelectrolyte chains (with a structure between rod-like and arborescent67), with a similar molecular weight but different degrees of branching were compared. CP-AFM, SAXS, and viscosity measurements indicate that the solutions are in the semidilute regime and consist of transient networks. The interchain distance of the polyelectrolyte network is insensitive to the degree of branching, suggesting that it is dominated by chain’s rod-like character. The electrostatic correlation length of the least branched chain is, however, larger than that of the other two, indicating a longer range of ordering. Interaction strength between the polyelectrolyte chains depends slightly on the degree of branching by similar means as the correlation length. A direct comparison of the experimental interaction strength under confinement and in bulk is not possible, but theory suggests a decrease in entropy and in turn an increase in the interaction strength under confinement. The interchain distance and correlation length in the thin film (confinement) and bulk are the same regardless of the degree of branching, showing that there is no compression of the chains or counterions even under strong confinement. All branched samples have the same specific viscosity−concentration scaling, which is lower compared to linear polymers. The independence of this scaling from the degree of branching is still to be clarified by theory.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Ph: +49 (30) 314 23476; Fax: +49 (30) 314 26602. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank Stephanie Christau for her valuable help with the viscosity measurements (financing: DFG IGRTG 1524). Technical University of Berlin, Research Council of Lithuania (Contract MIP-50/2010), and European Union Marie Curie Network SOCON (MCRTN-CT-2004-512331) are acknowledged for the financial support.

■

REFERENCES

(1) Liao, Q.; Dobrynin, A. V.; Rubinstein, M. Macromolecules 2003, 36, 3386−3398. 3175


Macromolecules

Article

(42) Limbach, H.; Holm, C.; Kremer, K. Europhys. Lett. 2002, 60, 566−572. (43) Baigl, D.; Ober, R.; Qu, D.; Fery, A.; Williams, C. Europhys. Lett. 2003, 62, 588−594. (44) Nishida, K.; Kaji, K.; Kanaya, T. Macromolecules 1995, 28, 2472−2475. (45) Biggs, S.; Burns, J.; Yan, Y.; Jameson, G.; Jenkins, P. Langmuir 2000, 16, 9242−9248. (46) Biggs, S. Phys. Chem. Chem. Phys. 2010, 12, 4172−4177. (47) Charmuszko, K.; Sikorski, A. J. Non-Cryst. Solids 2009, 355, 1408−1413. (48) Gray-Weale, A.; Gilbert, R. G. J. Polym. Sci., Part A1 2009, 47, 3914−3930. (49) Moeller, D.; Munstedt, H.; Kaspar, H. Rheol. Acta 2009, 48, 509−516. (50) Bosko, J. T.; Prakash, J. R. Macromolecules 2011, 44, 660−670. (51) Knaapila, M.; Stepanyan, R.; Torkkeli, M.; Lyons, B.; Ikonen, T.; Almasy, L.; Foreman, J.; Serimaa, R.; Guntner, R.; Scherf, U.; Monkman, A. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2005, 71, 041802. (52) Shusharina, N. P.; Rubinstein, M. Macromolecules 2008, 41, 203−217. (53) Jusufi, A.; Likos, C. N. Rev. Mod. Phys. 2009, 81, 1753−1772. (54) von Klitzing, R.; Kolaric, B. Aqueous Polym.-Cosolute Syst. 2003, 122, 122−129. (55) Knaapila, M.; Stepanyan, R.; Lyons, B.; Torkkeli, M.; Hase, T.; Serimaa, R.; Guntner, R.; Seeck, O.; Scherf, U.; Monkman, A. Macromolecules 2005, 38, 2744−2753. (56) Cordeiro, C.; Molisana, M.; Thirumalai, D. J. Phys. II 1997, 7, 433−447. (57) Chen, Z.; Escobedo, F. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2004, 69, 021802. (58) Sikorski, A.; Romiszowski, P. J. Chem. Phys. 2004, 120, 7206− 7211. (59) Romiszowski, P.; Sikorski, A. J. Chem. Phys. 2002, 116, 1731− 1736. (60) Romiszowski, P.; Sikorski, A. J. Chem. Phys. 2005, 123, 104905. (61) Romiszowski, P.; Sikorski, A. Monatsh. Chem. 2006, 137, 969− 976. (62) Konieczny, M.; Likos, C. N. Macromol. Symp. 2006, 245, 276− 286. (63) Konieczny, M.; Likos, C. N. J. Chem. Phys. 2006, 124, 214904. (64) Heinrich, M.; Rawiso, M.; Zilliox, J.; Lesieur, P.; Simon, J. Eur. Phys. J. E 2001, 4, 131−142. (65) Graessle, W.; Mittelha, H. J. Polym. Sci. 1967, 5, 431. (66) Valles, E.; Macosko, C. Macromolecules 1979, 12, 521−526. (67) Gromadzki, D.; Tereshchenko, A.; Makuska, R. Polymer 2010, 51, 5680−5687. (68) Ducker, W.; Senden, T.; Pashley, R. Nature 1991, 353, 239− 241. (69) Riegler, H.; Engel, M. Ber. Bunsen. Phys. Chem. 1991, 95, 1424− 1430. (70) Manning, G. J. Chem. Phys. 1969, 51, 924−933. (71) Essafi, W. Structure des polyelectrolytes fortement charges. Ph.D. Thesis, University of Paris VI, 1996. (72) Helm, C. A.; Möhwald, H.; Kjaer, K.; Als-Nielsen, J. Biophys. J. 1987, 52, 381−390. (73) Evans, R.; Henderson, J.; Hoyle, D.; Parry, A.; Sabeur, Z. Mol. Phys. 1993, 80, 755−775. (74) Nierlich, M.; Williams, C.; Boue, F.; Cotton, J.; Daoud, M.; Farnoux, B.; Jannink, G.; Picot, C.; Moan, M.; Wolff, C.; Rinaudo, M.; Gennes, P. J. Phys. (Paris) 1979, 40, 701−704. (75) Nierlich, M.; Boue, F.; Lapp, A.; Oberthur, R. J. Phys. (Paris) 1985, 46, 649−655. (76) Koene, R.; Mandel, M. Macromolecules 1983, 16, 220−227. (77) Drifford, M.; Dalbiez, J. J. Phys. Chem. 1984, 88, 5368−5375. (78) Sedlak, M.; Amis, E. J. Chem. Phys. 1992, 96, 826−834. (79) Sedlak, M.; Amis, E. J. Chem. Phys. 1992, 96, 817−825.

(80) Milling, A.; Vincent, B. J. Chem. Soc., Faraday Trans. 1997, 93, 3179−3183. (81) Kaji, K.; Urakawa, H.; Kanaya, T.; Kitamiru, R. J. Phys. (Paris) 1988, 49, 993−1000. (82) Boris, D.; Colby, R. Macromolecules 1998, 31, 5746−5755. (83) Colby, R. H. Rheol. Acta 2010, 49, 425−442. (84) Graessle, W.; Prentice, J. J. Polym. Sci. 1968, 6, 1887. (85) Claesson, H.; Malmstrom, E.; Johansson, M.; Hult, A. Polymer 2002, 43, 3511−3518. (86) Prini, R.; Lagos, A. J. Polym. Sci., Part A 1964, 2, 2917.

3176


Effect of Molecular Architecture on the Polyelectrolyte Structuring

Recommend Documents