J. Phys. Chem. B 2000, 104, 6963-6972
6963
Influence of Ionic Content in Polyurethane Ionomer Solutions Srinivas Nomula† and Stuart L. Cooper*,‡ Department of Chemical Engineering, UniVersity of Delaware, Newark, Delaware 19716 ReceiVed: March 13, 2000; In Final Form: May 18, 2000
Model polyurethane ionomers were synthesized with regularly spaced ionic groups along the polymeric backbone. Viscometry and static and dynamic light scattering applied to these ionomer solutions in a polar solvent, N-methylformamide, revealed characteristic polyelectrolyte behavior. An upturn is seen in reduced viscosity measurements, an abnormal Zimm plot is obtained from static light scattering (SLS) measurements, and two diffusive modes are seen in dynamic light scattering (DLS) measurements. A combined analysis of SLS and DLS data indicated the presence of single polyions, as well as loose aggregates in solution. Loose aggregates are domains consisting of polyions held together by electrostatic interactions. The results show that, even when the solvent is a poor solvent for the ionomer backbone, sufficiently high ionic content can cause dissolution of the ionomer without any backbone aggregation. The ionic content of an ionomer is identified as a critical parameter in determining ionomer solution behavior.
Introduction Ionomers are polymers that have a small fraction of ionic groups (usually less than 15 mol %) covalently bound to a polymeric backbone. Ionomer solutions are of great practical importance as stabilizers for paint suspensions and as coating materials and, hence, have been the subject of a number of investigations in recent years. Traditionally, ionomer solution behavior has been classified on the basis of the polarity of the solvent.1 In low-polarity solvents, association of ionic groups takes place because of dipolar interactions. In high-polarity solvents, counterions are solvated, and electrostatic interactions in solution result in behavior characteristic of polyelectrolyte solutions. The association of ionomer molecules in low-polarity solvents results from strong dipole-dipole interactions among the ionic groups. Evidence of intermolecular association in ionomer solutions in low-polarity solvents has been most dramatically demonstrated by a significant enhancement in the viscosity of the ionomer in solution compared to that of solutions of the parent polymer.1-5 Light and neutron scattering data obtained from these solutions indicated the formation of multimers and also showed that the extent and average size of the multimers increases with concentration.6,7 In highly polar solvents, ionomers behave identically to aqueous polyelectrolyte solutions8-10 and exhibit a dramatic increase in reduced viscosity with decreasing polymer concentration. This is quite surprising, as ionomers contain a relatively low ionic content whereas polyelectrolytes contain a very high ionic content, usually one ionic group per repeat unit. The identification of polyelectrolyte behavior in high-polarity ionomer solutions has also been supported by static and dynamic light scattering6,9-11 and smallangle neutron scattering (SANS)7,12 experiments that show features that are characteristic of polyelectrolyte solutions. The influence of solvent characteristics, other than polarity, on the ionomer solution behavior has received serious consid* Author to whom correspondence should be addressed. † Present address: Symyx Technologies, 3100 Central Expressway, Santa Clara, CA 95051. ‡ Present address: Illinois Institute of Technology, 10 West 33rd Street, Chicago, IL 60616.
eration only recently. Polymer-solvent interactions (interactions between the solvent and the ionomer backbone) were found to play an important role in the solution behavior of ionomers. Studies with model polyurethane ionomers13 and perfluorosulfonated ionomers14 in N-methylformamide (NMF) showed that colloidal nanoparticles are formed in solution. Consequently ionomer solution behavior in polar solvents was further classified as follows:14 (i) ionomer solutions in polar solvents that are able to dissolve the polymer backbone demonstrate characteristic polyelectrolyte behavior, and (ii) ionomer solutions in polar solvents in which the analogous neutral polymer is not soluble are characterized by polymer-solvent phase separation, leading to a colloidal dispersion. The behavior of polyelectrolytes with added salt is well understood in terms of the screening, by simple ions, of electrostatic interactions among fixed ions and can be described by the scaling theory developed for neutral polymer solutions.15 The structure and dynamics of polyelectrolyte solutions with low salt concentrations, although extensively studied, is currently not well understood. This is because of the many difficulties involved in theoretical treatments and experimental research due to the complexity of a system consisting of several components, including polyions, counterions, co-ions, and solvent. Because of its multicomponent nature, there are several interactions in a polyelectrolyte solution: intramolecular interactions between segments of the same macromolecule, intermolecular interactions between different macromolecules, interactions between polyions and counterions, electrostatic screening by the lowmolecular-weight salt, polymer-solvent interactions, and entropic forces (mainly due to the presence of counterions). The ionic strength dependence of the dimensions of polyelectrolytes is still a subject of controversial theoretical arguments and experimental results.16 Despite a number of studies on salt-free polyelectrolyte solutions, the origin of polyelectrolyte behavior and the nature of the solution structure are currently controversial. The experimental data can often be interpreted in different ways. The solution structure must be consistent with the observed upturn in reduced viscosity at low concentrations, a broad single peak in the scattered intensity profile in small-angle X-ray scattering
10.1021/jp0009397 CCC: $19.00 © 2000 American Chemical Society Published on Web 06/30/2000
6964 J. Phys. Chem. B, Vol. 104, No. 29, 2000 (SAXS) and small-angle neutron scattering (SANS) experiments, abnormal Zimm plots in static light scattering experiments, and two modes in dynamic light scattering measurements. Hara recently reviewed the behavior of polyelectrolytes and ionomers in nonaqueous solution and demonstrated that ionomers offer good model systems for investigating the characteristic behavior of salt-free polyelectrolyte solutions.17 There are other advantages in studying ionomers. Because condensed counterions make dipoles on the polyion that can conceivably attract one another (ionic aggregation), it is useful to study polyions with low charge intensities, for which no counterion condensation will occur. Effects of charge density and solvent dielectric constant on the solution properties of polyelectrolytes can be investigated. Another advantage is that ionomers have solvent-compatible backbones. Ionomers, because of their low ionic content, can dissolve in organic solvents, and many times the amount of the un-ionized polymer can be dissolved in a given solvent. Thus, the effect of ionic interactions can be explicitly studied. This, in addition to the feature that a wide variety of architectures (in terms of the placement of ionic groups) can be synthesized, allows one to get a better understanding of the interactions in solutions of ionic polymers. Previous studies on the solution properties of ionomers have focused primarily on random copolymer ionomers and model telechelic ionomers. Because of the imposition of ionic interactions over polymer-solvent interactions, a model ionomer system would be preferable for these studies. Model telechelic ionomers have ionic groups located at the ends of the polymer chains and are typically of low molecular weight in order to achieve a sufficiently high ionic content. Also, the influence of chain length and ionic content on the morphology of ionomers cannot be studied independently using these systems. Model polyurethane ionomers, developed using polyurethane chemistry, have regularly spaced ionic groups along the polymer backbone and allow a direct correlation of ionomer structure and properties.18 Slow relaxation of the concentration fluctuations that are observed in salt-free aqueous polyelectrolyte solutions has been reported for a wide variety of polymer systems in the past,19-25 and several theoretical models have been proposed to explain these modes.26-30 To distinguish their physical origin, it is necessary to determine how they contribute to the scattering intensity and whether their characteristic time is linked to an intrinsic characteristic time of the system (structure relaxation) or to a characteristic length probed in the measurement (diffusive process). For this purpose, the scattering wave vector dependencies for the scattering intensity and for the amplitudes and characteristic times associated with the relaxation modes must be carefully characterized. This can be achieved by a combination of the static and dynamic light scattering techniques, which provide a powerful tool for better understanding the physical mechanisms that are at the origin of the interesting rheological behavior of these systems. Dynamic light scattering is not only sensitive in detecting aggregates, it is also one of the few techniques that is able to resolve a possible coexistence between large aggregates and single polymers. Previously, we discovered that, if the solvent is a poor solvent for the ionomer backbone, backbone aggregation takes place, resulting in the formation of colloidal nanoparticles.13 In this paper, the effect of an increase in the ionic content of the ionomer is explored. In previous studies of similar systems,14,31 higher ionic content ionomers were found to form smaller particles. In this study, it was found that sufficiently high ionic content can cause dissolution of the ionomer as a whole,
Nomula and Cooper
Figure 1. Structure of model polyurethane ionomer.
TABLE 1: Molecular Characteristics of Polymers
a
PU sample
Mwa
ion content (wt %)
PU-1000 PU-4500 PU1 PU4
62500 56500 77000 60000
0.0 0.0 6.5 2.0
Mw is the weight-average molecular weight.
resulting in a different kind of solution behavior. Combined static and dynamic light scattering experiments have been applied to model ionomers to better understand the solution structure that results in characteristic polyelectrolyte behavior. Experimental Section Materials. The synthesis of model sulfonated polyurethane ionomers is described in detail elsewhere.18 Poly(tetramethylene oxide) (PTMO) of molecular weights 1000 and 4500 au were used, and the ionomers are designated PU1 and PU4, respectively. The corresponding unsulfonated polyurethanes are denoted by PU-1000 and PU-4500, respectively. The molecular architecture of the model polyurethane ionomer is shown in Figure 1. The precursor polymer has been characterized by gel permeation chromatography (GPC).18 The values for the ionomer are based on calculations assuming that the sulfonation reaction does not alter the polyurethane backbone. The GPC results based on polystyrene standards are shown in Table 1. Polymer solutions were prepared by dissolving the ionomer samples in N-methylformamide (Aldrich, spectrophotometric grade) with stirring for 1 day at room temperature. Measurements. Viscometric experiments were conducted with an automated AVS 300 Schott-Gerate viscometer measuring station with an automatic dilution control unit, a piston buret, and basic unit with computer output. The kinematic viscosity was measured using KPG-Ubbelohde capillary viscometers (Schott-Gerate), whose size was selected to be appropriate to the viscosity range of the sample under study. In all cases, the flow time was more than 200 s. Kinematic corrections were applied, depending on the specific viscometer used. The polymers were dissolved in N-methylformamide (NMF), and measurements were made at concentrations ranging from 0.01 to 0.5 g/dL. The temperature was maintained at 35 ( 0.1 °C in a thermostated bath. Samples were stirred and thermally equilibrated for at least 30 min between dilutions. The measurements were repeated until the difference between subsequent measurements was less than 1%. Between samples, the viscometer was cleaned with Chromerge, rinsed with deionized water and then with acetone, and finally dried for at least 12 h at 120 °C. Static and dynamic light scattering measurements were conducted with a BI-200SM goniometer (Brookhaven) and a BI-9000AT digital correlator (Brookhaven) at a wavelength of 488 nm from a 300-mW Ar Lexel laser. Measurements were made at 35 ( 0.1 °C. The temperature of the sample was kept constant through the external circulation of water around the sample holder. Angular measurements were made using a goniometer in the range of scattering angles from 30° to 150°. Solutions were filtered using 0.45-µm syringe filters (Gelman Sciences, Ann Arbor, MI). The Rayleigh ratio for toluene, taken
Ionic Content in Polyurethane Ionomer Solutions
J. Phys. Chem. B, Vol. 104, No. 29, 2000 6965 where the line width Γ (or decay rate or relaxation rate) is related to the particle diffusion coefficient D by Γ ) Dq2; q is the amplitude of the scattering wave vector defined as q ) 4πn/λ sin(θ/2); and G(Γ) is the normalized distribution function of the line widths, which contains detailed information on the distribution of diffusivity, particle size, or relaxation times.32 In terms of the relaxation time (τ ) 1/Γ, where Γ is the decay rate), the above equation can be written as
∫0∞ A(q, τ) exp(-t/τ) dτ
g(1)(q, t) )
Figure 2. Viscosity measurements: ([) PU1 in DMAc, (2) PU1 in NMF, and (b) PU4 in NMF.
as the reference solvent, was obtained for unpolarized detected light as 39.6 × 10-6 cm-1 at 25 °C and 488 nm. In dynamic light scattering measurements, the channel numbers were 256, of which 6 data channels were used to determine the baseline. To eliminate dust effects, the data were discarded whenever the difference between measured and calculated baselines was greater than 0.1%. The scattered data from the correlator were transferred to a computer for analysis. Sample times from 0.1 µsec to 1 s were used. Results Viscometry. The results of viscometric measurements are presented in the form of reduced viscosity vs concentration diagrams. Figure 2 contains the data obtained for the sulfonated polyurethanes PU1 and PU4 in N-methylformamide (NMF) and PU1 in dimethylacetamide (DMAc). The data for PU1 in NMF and DMAc exhibit an upturn in reduced viscosity at low concentrations, representative of polyelectrolyte behavior. PU4 in NMF does not show polyelectrolyte behavior and has very low values of viscosity. For a neutral polymer, the reduced viscosity increases linearly with polymer concentration as suggested by the Huggins equation
ηred ) [η] + k′[η] c 2
(1)
where [η] is the intrinsic viscosity and k′ is the Huggins constant. Dynamic Light Scattering. In a dynamic light scattering experiment, the measured intensity correlation function G(2)(t) is related to the first-order (or field) correlation function g(1)(t) by the Siegert relation
G (q, t) ) B[1 + β|g (q, t)| ] (2)
(1)
2
(2)
where B is the experimentally determined baseline [B ) G(2)(∞)] and the parameter β, 0 < β < 1, is due to experimental variables. β is used as a parameter either in the fitting procedure or in normalizing G(2)(t). The background count B (count rate at very long times) is directly measured by the correlator. In general, the source of light scattering in a polymer solution is the existence of concentration fluctuations, which give rise to fluctuations in the refractive index of the scattering medium. Therefore, the scattered electric field time autocorrelation function is proportional to the time autocorrelation function of the fluctuations in refractive index. The electric field correlation function g(1)(q, t) is written as
g(1)(q, t) )
∫0
∞
G(Γ, q) exp(-Γt) dΓ
(3)
(4)
Here, A(q, τ) is the distribution function of relaxation times. The spectrum of relaxation times obtained from correlation functions by inverse Laplace transform is frequently a multimodal distribution in which separate peaks can be ascribed to different modes. The position of the peak on the time axis corresponds to the relaxation time of the particular mode, and the peak area corresponds to the portion of scattering intensity due to this mode. The total scattering intensity, as measured in a static light scattering experiment, is given by
I(q) )
∫0∞ A(q, τ) dτ
(5)
The mutual diffusion coefficient for nonaggregating polymers (systems with weak interactions) is given by the generalized Stokes-Einstein equation as
D)
M(1 - υc) ∂∏ NAf(c) ∂c
( )
(6)
where M is the molecular weight, υ is the partial specific volume, f(c) is the frictional coefficient, c is the concentration of the polymer, ∂∏/∂c is the inverse osmotic compressibility, and NA is the Avogadro’s number. For strongly interacting systems, by using Zernicke-Prins equation for light scattering analysis with the Born-Green approximation, it can be shown33 that
Kc N ∝ 1 + m0 R0 V
(
)
(7)
where Kc/R0 is the reduced scattered intensity at zero angle, N/V is the number of particles per unit volume, and m0 is the intermolecular excluded volume. From fluctuation theory, it is shown34 that
1 ∂∏ Kc ∝ R0 RT ∂c
(
)
(8)
The reduced scattered intensity at zero angle, Kc/R0, is a function of concentration and is a measure of intermolecular excluded volume as well as inverse osmotic compressibility. For strongly interacting systems, the inverse osmotic compressibility term in eq 6 dominates,35 and
D∝
(∂∏ ∂c )
(9)
From the above three equations,
D∝
N ∂∏ ∝ 1 + m0 ∂c V
(
)
Also, for the inverse osmotic compressibility
(10)
6966 J. Phys. Chem. B, Vol. 104, No. 29, 2000
∂∏ RT ) (1 + 2A2c + ...) ∂c M
Nomula and Cooper
(11)
where A2 is the second virial coefficient. An effective hydrodynamic radius, Rh, can be evaluated using the Stokes-Einstein relation
Deff ) (kBT/6πη)(1/Rh)
(12)
where kB is the Boltzmann constant, η is the solvent viscosity, and T is the absolute temperature of the solution. The analysis of the experimental data from DLS experiments is, in general, a mathematically ill-posed problem.36 The data analysis was performed using CONTIN, a robust algorithm developed by Provencher.37,38 Data analysis with CONTIN provides information on the moments of the relaxation time distribution from which the z-average diffusion coefficient can be evaluated. The diffusion coefficient is defined in the limit of small scattering vector q as Dz ) limqf0 Γ/q2. If only translational motion is present, the relaxation time decreases with scattering angle, and the diffusion coefficient D is independent of q, or similarly, Γ varies as q-squared. In addition, D varies linearly with concentration in the dilute solution regime, and therefore, the diffusion coefficient is defined as the value at the limit of zero concentration. In the analysis that follows in this paper, the data are presented in terms of an effective diffusion coefficient, Deff(q, c) ) Γ(q, c)/q2, which is a function of both scattering angle and concentration. There are two distributions of effective diffusion coefficients corresponding to the two relaxation modes identified. The weighted average decay rate is calculated as the first moment of G(Γ, q), divided by the zeroth moment of G(Γ, q). The average effective diffusion coefficient is defined by /q2 ) Deff, where is the average value of Γ. Dynamic light scattering (DLS) was applied to the ionomer solutions to characterize the solution structure. Figure 3 shows the average effective diffusion coefficients corresponding to the two modes of PU1 as a function of q2. A straight line is drawn through the diffusion coefficients corresponding to each mode by the method of least squares. The two modes differ by more than an order of magnitude, with both the fast mode (∼10-7 cm2/s) and the slow mode (∼10-8 cm2/s) showing a small negative q2 dependence. A relaxation mode in which D is independent of q is an indication of a translational diffusion mode. The q-squared dependence of the diffusion coefficients, which contains the effect of polydispersity, internal motions (chain flexibility/rotational diffusion coefficient), and electrostatic interactions, will not be analyzed because it is very difficult to decompose it into its various components. The effect of concentration on the effective diffusion coefficients that are evaluated from the two relaxation modes observed in the ionomer solutions of PU1 is shown in Figure 4. The concentration dependence can be analyzed at each value of q. The effective diffusion coefficients extrapolated to zero q, to eliminate effects associated with the q2 dependence, are plotted against concentration. From the figure, we can see that the fast mode increases slightly with concentration. In polyelectrolyte solutions, a significant increase in the fast mode with polymer concentration was reported.23,39 The slow mode is seen to remain constant within statistical error and so is independent of concentration. The slow mode was found to have significant concentration dependence in salt-free polyelectrolyte solutions. From the slow-mode diffusion coefficient extrapolated to zero concentration (2.32 × 10-8 cm2/s), the corresponding hydro-
Figure 3. Diffusion coefficients (in cm2/s) for PU1 in NMF at a concentration of 0.5 g/dL: ([) fast mode and (9) slow mode.
Figure 4. Diffusion coefficients (in cm2/s) as a function of concentration for PU1 in NMF: ([) fast mode and (9) slow mode.
dynamic radius can be calculated using the Stokes-Einstein relation (eq 12) as 70 nm. Additional information about the solution strucuture can be obtained from the amplitudes of the two relaxational processes. The contributions of the fast and the slow modes are denoted by Af and As, repectively (see eq 4). Ar, a ratio of Af and As, is plotted as a function of q2 and concentration in Figures 5 and 6, respectively. Static Light Scattering. In a static light scattering experiment, the intensity of the scattered light is measured as a function of the angle. This is converted to the Rayleigh ratio, Rθ, which is then used in the equation
Kc 1 1 ) 1 + q2Rg2 + 2A2c Rθ M 3
(
)
(13)
where K is the optical constant, defined by 4π2n02(dn/dc)2/NAλ04 for a polarized incident beam; n0 is the refractive index of the solvent; dn/dc is the refractive index increment; NA is Avogadro’s number; and λ0 is the wavelength of the incident light in a vacuum. M is the molecular weight. This representation of scattering data is called a Zimm plot. The different curves are then extrapolated to zero scattering angle and, for each scattering angle, to concentration c ) 0. This procedure leads to two
Ionic Content in Polyurethane Ionomer Solutions
J. Phys. Chem. B, Vol. 104, No. 29, 2000 6967
Figure 7. Angular dependence of c/Rθ: ([) 0.01 g/dL, (9) 0.02 g/dL, (2) 0.05 g/dL, (×) 0.1 g/dL, (4) 0.2 g/dL, (b) 0.3 g/dL, (+) 0.4 g/dL, and (O) 0.5 g/dL.
Figure 5. Ar as a function of q2 at a concentration of 0.1 g/dL.
true radius of gyration of the scattering particles, RG, and the radius of gyration of the excluded volume surrounding the particles, ξ. An apparent radius of gyration can be determined as
(
R0 R2G,app a1 R2G ξ2 ) ) 13 a0 3 6 MKc
Figure 6. Ar as a function of concentration at 60°.
limiting curves: (i) the angular dependence at c ) 0 results from the scattering behavior of individual chains with no intermolecular interactions, and (ii) the other, at q ) 0, represents the intermolecular interactions that are not influenced by interference effects resulting from the size of the particles. Both of the limiting curves can be conclusively interpreted.40 This approach is valid only for systems with weak interactions and at dilute concentrations. In systems that show intermolecular interactions, the scattering data can be described in power series of q2 as
Kc ) a0 + a1q2 + a2q4 Rθ
(14)
where the coefficients a0, a1, and a2 are defined according to the specific intermolecular interaction potential.41 a0 is the reciprocal scattered intensity at zero angle, defined as
a0 )
( )
Kc 1 Kc ) ) Mw,app R0 Rθ
θf0
)
(
)
1 N 1 + m0 M V
(15)
Here, Mw,app is an apparent weight-average molecular weight that contains contributions from the true molecular weight of the polymer and thermodynamic interactions in solution. N is the number of particles in volume V, and m0 is the intermolecular excluded volume. In a similar way, a1 is related to the size of particles in solution and contains contributions from both the
)
(16)
Figure 7 shows c/Rθ plotted as a function of q2 at each concentration for the polyurethane ionomer PU1 in NMF. The apparent molecular weight and radius of gyration appear to be sensitive to polymer concentrations, a behavior that is strongly dominated by the ionic interactions. Abnormal Zimm plots with negative angular dependencies have been obtained for polymer solutions with dominant electrostatic interactions.33 The q2 dependence of c/Rθ gives the apparent radius of gyration of particles in solution. The data are fit as a quadratic equation in q2 according to eq 14, and apparent radius of gyration values are calculated using eq 16. The reduced scattered intensity has a negative q2 dependency at lower concentrations (0.01, 0.02, and 0.05 g/dL). This is because of the high intermolecular excluded volume at low concentrations. Higher concentrations have an apparent radius of gyration of 20-50 nm. As the ionomer concentration is increased, the apparent size increases. This may be due to the decrease in intermolecular excluded volume with increasing concentration. The intercepts from Figure 7 (c/Rθ as q2 f 0) are plotted as a function of concentration in Figure 8. The reciprocal reduced scattered intensity at zero angle, c/R0, rises steeply from the intercept, bends over, and becomes nearly horizontal at higher polymer concentrations. The slope is a measure of the value of the second virial coefficient. It has been shown that the emergence of nonlinear terms in the expansion {Kc/R0} vs c, for some ionic strengths, does not affect substantially the determination of A2, if the analysis is limited to low-c intervals.42 The second virial coefficient is positive, indicating that there are repulsive interactions in the solution and that NMF is a good solvent for the polyurethane ionomer. The slope decreases with increasing concentration, indicating reduced repulsive interactions and, consequently, reduced intermolecular excluded volume. This observation is consistent with that made from the apparent radius of gyration values. Af and As are the amplitudes of the fast and slow relaxations, respectively. These amplitudes constitute relative contributions
6968 J. Phys. Chem. B, Vol. 104, No. 29, 2000
Nomula and Cooper
Figure 8. Concentration dependence of c/R0.
Figure 10. Angular dependence of the intensity corresponding to the slow mode: ([) 0.01 g/dL, (9) 0.02 g/dL, (2) 0.05 g/dL, (×) 0.1 g/dL, (4) 0.2 g/dL, (b) 0.3 g/dL, (+) 0.4 g/dL, and (O) 0.5 g/dL.
Figure 9. Angular dependence of the intensity corresponding to the fast mode at a concentration of 0.01 g/dL.
of each process to a given correlation function, which can be combined with the absolute scattering intensities to give the absolute scattering intensity of each dynamic mode. These absolute intensities, If and Is, are calculated as follows:
If(q) ) Af(q) I(q)
(17)
Is(q) ) As(q) I(q)
(18)
The fraction of the total scattering intensity due to each mode, given by the above equations, can be independently analyzed. Figure 9 shows a plot of If(0)/If(q) vs q2. [If(q)]-1 has a negative q2 dependency and can be interpreted in terms of eq 16. The lines in Figure 10, a plot of Is(0)/Is(q) vs q2, can be analyzed as static intensity data at fixed polymer concentration, except that the “concentration” of the slow mode may not be the same as the polymer concentration; it is difficult to attribute a dn/dc to the domain. However, the radius of gyration can be calculated, and values of 50-100 nm are obtained. Discussion Viscometry and static and dynamic light scattering data for PU1 solutions in NMF indicated characteristic polyelectrolyte behavior. Viscometric measurements showed an upturn in reduced viscosity at low concentrations, representative of polyelectrolyte behavior. Two decay modes have been identified in dynamic light scattering measurements. In static light
scattering measurements, the reciprocal reduced scattered intensity at zero angle, Kc/R0, rises steeply from the intercept, bends over, and becomes nearly horizontal at higher polymer concentrations. During the last twenty years, numerous speculations on the nature of the two relaxations in low-salt polyelectrolyte solutions observed in DLS measurements arose considering effects such as coil-to-rod transitions, two state structures, cage effects, aggregation, coupled diffusion, nondraining-draining transitions, or polyion-specific effects. The two modes are not the result of different correlation lengths arising out of isotropic solutions, as a number of studies mentioned later in the paper have confirmed. The two modes are q2-dependent, showing that they are diffusive processes. The fast relaxation corresponds to polyion diffusion and can be qualitatively described by two theoretical concepts. The fast mode can be explained using the concept of interacting Brownian particles.43,44 The Brownian motion is accelerated because of interparticle interactions. The diffusion coefficient is derived from the first cumulant as
D)Do/S(q)
(19)
where Do stands for free particle diffusion coefficient (infinite dilution) and S(q) is the static structure factor reflecting the interactions involved. Low values of S(q) (yielding high values of D) due to low osmotic compressibility are typical for polyelectrolyte solutions at low ionic strength. This is because the inverse osmotic compressibility is very large for polyion solutions because of repulsive interactions, which lead to large intermolecular excluded volume. At relatively low polymer concentrations (0.01-0.1 g/L) and low added-salt concentrations, the polyion diffusion coefficient exhibits angular minima corresponding to angular maxima in S(q).45 The fast mode can also be explained in terms of what can be called polyion-counterion coupling. The coupled-mode theories explain the high diffusion rate of polyions as a consequence of the coupling of the polyion motion with the dynamics of small and much faster counterions. Both polyions and counterions are charged species, creating a common electrostatic field, which fluctuates because of their motion and reversibly influences their dynamics. Under salt-free conditions, the diffusion coefficient can be shown to approach that of the small ions,46 and so the
Ionic Content in Polyurethane Ionomer Solutions significant increase in the diffusion coefficient of single ionomer chains as compared to that of the underivatized polyurethane is not unreasonable. Slow relaxation of polymer concentration fluctuations is not an uncommon feature for polymer solutions in the semidilute or concentrated regimes. It has been observed in a number of different systems, including linear neutral polymers in good20 or theta21 solvents, branched polydisperse polymers in a good solvent,19 polyelectrolyte solutions in the presence22 or in the absence of added salt,22,23 and associating polymer solutions.24,25 Although the generic name of slow-mode relaxation is widely used, its physical origin may differ according to the system considered. In particular, dynamic coupling of elementary processes,47 coupling of stress and polymer concentration fluctuations,26-30 or diffusion of large particle aggregates20,23 are possible mechanisms that might be responsible for a slow component in the decay of the intensity-intensity correlation function, apart from a fast component that is, in general, more easily understood. The variations in the relative amplitudes of the two modes, in the associated scattered intensities, and in the rates of relaxation as a function of scattering wave vector and polymer concentration can be considered in determining the mechanism suitable for a given system. The interpretation of the slow-mode diffusion coefficient observed in low-salt polyelectrolyte solutions has been controversial. The slow mode has been attributed to the translational diffusion of (temporal) clusters (temporal-aggregate model) by Schmitz,48 multi-chain domains (clusters) by Sedlak,23,49,50 localized ordered structures (two-state model) by Ise,51,52 and filterable aggregates (filterable-aggregate model).53-55 Temporal domains39 and the correlation-hole concept56 have also been used to interpret the data. Viscometric and DLS measurements of model polyurethane ionomers in DMAc, which is a polar solvent, revealed characteristic polyelectrolyte behavior.18 The slow mode is shown to not be attributable to the presence of hydrophobic aggregates or filterable aggregates. DMAc is a good solvent for the unsulfonated polyurethane, and hence, the slow mode is not due to aggregates arising out of poor backbone solvation. The slow mode is unaffected by filtering with filters whose pore size is smaller than the calculated aggregate size. This suggests that the domains that give rise to the slow mode are formed by dynamic interactions in solution. The study also showed no time dependencies, and so, the two modes are due to equilibrium structures. On the basis of these results, it was concluded that both free polyions and some kind of aggregates coexist in dilute solutions of PU ionomers. Extrapolation to zero concentration of the D ) f(c) curve for the slow mode gives a hydrodynamic radius of 70 nm, indicating that this mode can be attributed to polymer clusters/aggregates. Because of the dissociation of counterions, ionomer solutions in polar solvents contain polyions and counterions. Hence, the aggregates correspond to domains consisting of polyions and counterions loosely held together by electrostatic interactions. In other words, the structures giving rise to the slow mode are loose aggregates. The region around a macroion corresponds to a highly concentrated simple ionic solution: for vinylic polymers the distance between ionized groups would be on the order of 2.5 Å, whereas the average interionic distance in 10 M 1:1 electrolyte solutions is about 4 Å.57 Small numbers of ionic aggregates, similar to those found in ionomer solutions in lowpolarity solvents, therefore can be expected to form in polyelectrolyte solutions. These kind of aggregates are not formed
J. Phys. Chem. B, Vol. 104, No. 29, 2000 6969 in the present system because of the regular positioning of ionic groups and the low ionic content. The loose aggregate is structurally similar to the domains proposed by Ise and Schmitz and consists of polyions and counterions in a small region of solution. The formation of the loose aggregates is attributed to electrostatic interactions between polyions and counterions inside the aggregate. The loose aggregate, as the name suggests, has polyions loosely held together, and hence, it can be disrupted by very weak external/ shear forces. No mechanism is proposed for the formation of such structures. In the two-state model by Ise,51 the formation of domains is explained in terms of attractive interactions between different polyions through intermediary counterions. There exist free (single polyions and counterions) and lattice domains. The lattice structures are stabilized by direct electrostatic interactions between small ions and polyions whose positions are affixed to particular locations within the lattice such that the energy is minimized. According to the temporalaggregate model by Schmitz et al.,58 the aggregates are formed because of dipole-dipole type attractions through the distortion of counterion clouds. Counterions screen direct repulsive interaction between the polyions and provide a “fluctuating dipole” interaction. Thus, there exist free and temporal aggregate domains. The critical size, and hence stability, of these aggregates is proposed to result from a balance between attractive forces arising from fluctuations in the small ion and polyion distributions and the disruptive Brownian forces. The temporalaggregate model stresses the dynamic character of counterions and is the electrodynamic analogue of the electrostatic twostate model. Electrodynamic refers to the fluctuating electrical forces arising from asymmetric distributions of interacting small ions and polyions. The relative viscosity measurements do not reflect large structural changes in solution that should occur in the formation or dissolution of lattice domains. Nevertheless, it is possible that the lattice domains may be disrupted by very weak external forces. A major hurdle in the acceptance of the domain/loose aggregate concept is the lack of a theoretical explanation for the presence of similarly charged polymer ions in a small region. Several attempts have been made recently, in both the colloid and the polyelectrolyte communities, to explain a possible attractive interaction between like-charged particles. The system of equations describing interactions among the spheres, solvent, and simple ions is so highly nonlinear that it resists analytical treatment to this day. The DLVO formulation avoids this complexity by linearizing the equations and averaging out ionic fluctuations. Despite these simplifying approximations, the DLVO theory serves as the standard model for colloidal electrostatic interactions, because it accounts very well for the stability and properties of charge-stabilized colloidal suspensions. Recent measurements indicate that, although isolated pairs of like-charged spheres are found to repel each other, as predicted by the DLVO theory, spheres confined by glass walls or by a concentration of other spheres develop long-range attractions, which is inconsistent with DLVO theory.59 Attractions are favored by highly charged spheres in very low salt concentrations, circumstances under which the DLVO approximations might be expected to fail. The apparent breakdown of linear superposition (pairs repel but groups cohere) implicates nonlinearity as the culprit, and a recent numerical study by Bowen and Sharif60 demonstrates that nonlinearity can indeed explain the observed attractions. A number of alternative explanations have been proposed, including the inherently linear Sogami-Ise theory and mechanisms involving fluctuations in
6970 J. Phys. Chem. B, Vol. 104, No. 29, 2000 the simple-ion distributions. Differences between these theories hinge on the experimentally invisible simple ions. The simpleion distribution around an isolated pair of spheres mediates repulsive interactions, even in the nonlinear calculations. Confining walls, however, redistribute the simple ions so as to mediate a long-range attraction. (Under DLVO approximations, the comparable redistributions turn out to be too subtle to induce attraction.) Thus, both nonlinearity and confinement are needed to yield attractions between spheres. Temporal fluctuations are not considered in these calculations and, therefore, are not necessary. It is still not understood how nonlinearity and geometric confinement conspire to produce simple-ion distributions conducive to long-range cohesion between neighboring spheres. Experimental data56,61,62 on polyelectrolyte solutions suggest the presence of an attractive component in the effective potential interaction. Several theoretical attempts63-66 have been made to derive such an attractive component, some of which are controversial.67 The usual short-range excluded-volume interaction and the electrostatically screened Coulomb interaction in polyelectrolyte solutions are further screened by the presence of polyelectrolyte chains at nonzero concentrations.68 This excluded-volume screening arises from the entropy and connectivity of the chains. One of the consequences of the excludedvolume screening is the emergence of an attractive component in the effective interaction between segments with charges of same sign. The strength and range of this attractive component are critically determined by the concentration of the polyelectrolyte and salt ions. There can also be more than one attractive minimum in the effective potential. An analysis of the amplitudes of the fast and slow modes presents further evidence for the presence of domains. Ar, a ratio of the amplitude of the fast mode (Af) to the amplitude of the slow mode (As), increases with increasing q2. Af can be expected to be independent of q2, as the single polyions are much smaller than the resolution length, but Af shows a positive q2 dependency because of strong intermolecular interactions. As has a negative q2 dependency, which arises from the size of the aggregates. Consequently, Ar has a positive q2 dependency, as shown in Figure 5. The fast-mode diffusion coefficient increases with concentration (indicating a positive virial coefficient), whereas the slowmode diffusion coefficient is more or less independent of concentration (indicating very weak interactions). With increasing concentration, Af increases, and As decreases (resulting in an increase in Ar, as shown in Figure 6). This cannot be conclusively interpreted and can be due to any or a combination of several reasons, including: (1) the number of single polyions increases, and the number of domains decreases; (2) the size of domains in solution decreases, although the number ratio of single polyions to domains remains the same; and (3) the scattering contrast of the domains in solution increases/decreases because of a different order (arrangement) of polyions inside the domain, higher or lower polyion concentration inside the domain, or voids (polymer-free regions in solution), although the number ratio of single polyions to domains and the size of the domains remain the same. There are several corroborations for the presence of domains in ionic polymer solutions. In the solutions in which ultraslow modes were observed by DLS, what appear to be loose aggregates of DNA globules were observed in the electron micrographs obtained using cryo-electron microscopy.62 Numerous arguments can also be found in a recent book by K. S. Schmitz.67 Viscometric measurements are also consistent with domains. Polyelectrolyte behavior has been attributed to a globular-to-
Nomula and Cooper extended state transition of free polyelectrolyte chains in solution.69 The ionomer solutions are placed in an ultrasonic cleaner for 1h. Immediately after sonication, the reduced viscosities at low concentrations are higher than those of the unsonicated solutions. If the sonicated solutions sit undisturbed overnight, the reduced viscosities return to their presonication (lower) values. These data suggest that free polyelectrolyte chains exist in equilibrium with many-chain particles. Furthermore, ultrasonication causes fragmentation of some of the particles, thus increasing the concentration of free chains. This process is reversible, and with time, the fragmented particles coalesce. This also presents evidence of a shear-dependent structure. It has been suggested that domains are mechanically disrupted when the samples are filtered through routinely used membrane filters with pores smaller than their natural dimensions.18,70 The fact that domains can be disrupted upon mechanical distortion is interpreted in terms of the domains being metastable (nonequilibrium structures) with rather long lifetimes.71 It is proposed that these nonequilibrium structures can escape spontaneously from the metastable state. Time-dependent scattering studies4 and the reversibility of domain formation argue against such conclusions. There seems to be a consensus evolving in the polyelectrolyte community that there can be an attractive interaction between similarly charged polyions because of the counterion distribution. The key issue that remains to be resolved is whether this attractive potential is just enough for the formation of loose aggregates or strong enough to form stable macroscopically ordered structures. Recently, the conductivity of a salt-free polyelectrolyte solution72 was explained in terms of aggregation of polyions, which is consistent with the loose aggregate picture depicted in this paper. The light scattering intensities from the polyurethane ionomer solutions are very small. The small amount of scattering is representative of ionic interactions. The decrease in scattering intensity is caused mainly by the decrease in the osmotic compressibility of the solution due to the presence of charge interactions. Figure 7 shows that the reduced scattered intensity has a negative q2 dependency at lower concentrations (0.01, 0.02, and 0.05 g/dL). This is because of the high intermolecular excluded volume at low concentrations. Higher concentrations have an apparent radius of gyration of 20-50 nm. As the ionomer concentration is increased, the apparent size increases. This is due to the decrease in intermolecular excluded volume with increasing concentration. With an increase in the ionic content of an ionomer in a solvent that is a good solvent for the backbone, the number of counterions in solution increases, resulting in enhanced screening and reduced intermolecular electrostatic interactions. A similar effect is observed as the dielectric constant of a solvent is increased for an ionic polymer in the condensation regime. The change in hydrodynamic volume is not significant. For these reasons, the intermolecular excluded volume is higher for ionomers in solution than for a polyelectrolyte. Consequently, the negative values of the apparent radius of gyration observed in ionomer solutions are not typically seen in polyelectrolyte solutions. For the same reason, negative q2 dependencies were observed for both modes in the DLS measurements in this study, where, as usual, a negative slope for the fast mode and a positive slope for the slow mode are reported for salt-free polyelectrolyte solutions.23,39 Importance of Ionic Content. Static and dynamic light scattering results can be used to deduce the solution structure in NMF. Single polyions as well as loose aggregates are present
Ionic Content in Polyurethane Ionomer Solutions in the solution. An analysis of the thermodynamic interactions in the system can be done through the second virial coefficient. For a good solvent, the second virial coefficient is positive. Both the static and dynamic light scattering measurements show a positive virial coefficient. This implies that NMF is a good solvent for the polyurethane ionomer PU1. Figure 2 shows that PU4 in NMF does not exhibit polyelectrolyte behavior. In ionomer solutions (both PU1 and PU4), counterions are completely dissociated in all high-polarity solvents. The unsulfonated polyurethanes does not dissove in NMF; i.e., NMF is a poor solvent for the sulfonated polyurethane backbone. Thus, polymer chain aggregation can be expected to occur to minimize interfacial energy. Spherical particles are formed because they have maximum area per ionic group. The effective hydrodynamic volume in these solutions is small because of the formation of compact structures. Because viscosity depends directly on hydrodynamic volume, these solutions have a low reduced viscosity. It was shown that both the absence of polyelectrolyte behavior and the low values of reduced viscosity are a result of solution structure driven by hydrophobic interactions.13 PU1 in NMF shows all of the signature features of polyelectrolyte behavior. The results indicate that an increase in ionic content leads to solubility of PU1 in NMF, demonstrating the importance of the ionic content of the ionomer when the solvent is a poor solvent for the backbone. Fluorescence measurements show an insignificant amount of hydrophobic aggregation.73 The second virial coefficient is positive, indicating repulsive interactions and ionomer solubility. Another indication of ionomer solubility is the high hydrodynamic volume, as can been seen from the large viscosity values. The results clearly show that there is a dramatic difference in the thermodynamic interactions between the two systems. NMF solutions of PU1 provide evidence of a good polymer/solvent system, in contrast to PU4 solutions in NMF. Polyelectrolyte behavior for PU1 in DMAc has been demonstrated by viscometric and dynamic light scattering measurements.18 DMAc is a good solvent for the ionomer backbone, whereas NMF is a poor solvent for the backbone. Because the polymer backbone is compatible with DMAc, there is no particle formation in solutions of PU1 in DMAc, because of aggregation of hydrophobic regions, i.e., because of poor backbone solvation. This shows that strong correlations promoted by electrostatic interactions dominate the physics of polyelectrolyte solutions and that the influences of poor backbone solvation are not necessary for explaining the primary characteristics of polyelectrolyte scattering. For quite some time, the concept of hydrophobic aggregation has been used as an argument against the presence of domains/loose aggregates in aqueous polyelectrolyte solutions, as water is often a poor solvent for the polyelectrolyte backbone. The results here show that electrostatic interactions cause polyelectrolyte behavior even in the presence of hydrophobic interactions. Implications to Viscosity. The viscosity values for PU1 solutions in NMF are lower than those for PU1 in DMAc. This is counterintuitive, because the polyelectrolyte effect can be expected to increase as the range of electrostatic interactions increases with increasing dielectric constant of the solvent. The slope of the diffusion coefficient vs concentration curve is smaller in NMF than in DMAc, indicating weaker interactions.18 That there are weaker interactions in solution can also be seen from the lower apparent molecular weight in NMF. Reduced viscosities are also correspondingly smaller in NMF. This shows that electrostatic interactions contribute significantly to the reduced viscosity of solutions of ionic polymers.
J. Phys. Chem. B, Vol. 104, No. 29, 2000 6971 Conclusions The polyurethane ionomers studied have regularly spaced ionic groups, which allow a direct correlation of observed properties and solution structure. They form a good model system for studying the effect of ionic interactions and also for understanding the behavior of salt-free polyelectrolyte solutions, which suffer from the disadvantages of weak scattering and difficulty in filtration and purification. In addition to the polarity of the solvent and the polymersolvent interactions, the ionic content of the ionomer also plays a critical role in determining the solution behavior of ionomers. Previously, it was accepted that, if the polar solvent could not dissolve the ionomer backbone, then colloidal nanoparticles were formed in solution. This study shows that, at sufficiently high ionic content of the ionomer, electrostatic interactions dominate, irrespective of the nature of the ionomer backbone-solvent interactions, resulting in polyelectrolyte behavior. An increase in the ionic content increases the solubility and leads to the elimination of hydrophobic aggregation. The change in interactions can be seen from the change in the second virial coefficient. Consequently, electrostatic interactions dominate the solution behavior. Both loose aggregates and single polyions are present in the solution. Model polyurethane ionomers allow systematic studies of the effect of ionic content on the solution behavior of ionomers. Acknowledgment. We thank Dr. Chang Zheng Yang of Nanjing University for synthesizing the polyurethane ionomers used in this work. We are grateful to National Science Foundation for financial support through Grant DMR 9531069. References and Notes (1) Lundberg, R. D.; Phillips, R. R. J. Polym. Sci., Polym. Phys. Ed. 1982, 20, 1143. (2) Tant, M. R.; Wilkes, G. L. J. Macromol. Sci., ReV. Macromol. Chem. Phys. 1988, C28 (1), 1. (3) Fitzgerald, J. J.; Weiss, R. A. J. Macromol. Sci., ReV. Macromol. Chem. Phys. 1988, C28, 99. (4) Lantman, C. W.; MacKnight, W. J. Annu. ReV. Mater. Sci. 1989, 19, 295. (5) Lundberg, R. D. In Structure and Properties of Ionomers; Pineri, M., Eisenberg, A., Eds.; D. Reidel Publishing Company: Dordrecht, The Netherlands, 1986; Vol. 198, p 387. (6) Lantman, C. W.; MacKnight, W. J.; Sinha, S. K.; Peiffer, D. G.; Lundberg, R. D. Macromolecules 1987, 20, 1096. (7) Lantman, C. W.; MacKnight, W. J.; Sinha, S. K.; Peiffer, D. G.; Lundberg, R. D.; Wignall, G. D. Macromolecules 1988, 21, 1339. (8) Rochas, C.; Domard, A.; Rinuado, M. Polymer 1979, 20, 76. (9) Peiffer, D. G.; Lundberg, R. D. J. Polym. Sci., Polym. Chem. Ed. 1984, 22, 1757. (10) Hara, M.; Wu, J. L. Macromolecules 1988, 21, 402. (11) Hara, M.; Wu, J. L. In Multiphase Polymers: Blends and Ionomers; Utracki, L. A., Weiss, R. A., Eds.; American Chemical Society: Washington, D.C.: 1989; Vol. 395, p 446. (12) MacKnight, J.; Lantman, C. W.; Lundberg, R. D.; Sinha, S. K.; Peiffer, D. G. Polym. Prep. 1986, 27, 327. (13) Nomula, S.; Cooper, S. L. J. Colloid Interface Sci. 1998, 205, 331339. (14) Gebel, G.; Loppinet, B.; Hara, H.; Hirasawa, E. J. Phys. Chem. B 1997, 101, 3980. (15) Mandel, M. In Polyelectrolytes: Science and Technology; Hara, M., Ed.; Marcel Dekker: New York, 1993; p 1. (16) Beer, M.; Schmidt, M.; Muthukumar, M. Macromolecules 1997, 30, 8375-8385. (17) Hara, M. Polyelectrolytes in Nonaqueous Solution. In Polyelectrolytes: Science and Technology; Hara, M., Ed.; Marcel Dekker: New York, 1993; p 193. (18) Nomula, S.; Cooper, S. L. Macromolecules 1997, 30, 1355-1362. (19) Delsanti, M.; Munch, J. P. J. Phys. II 1994, 4, 265. (20) Mathiez, P.; Mouttet, C.; Weisbuch, G. J. Phys. (Orsay, Fr.) 1980, 41, 519. (21) Adam, M.; Delsanti, M. Macromolecules 1985, 18, 1760.
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