Linear Viscoelasticity and Cation Conduction in Polyurethane

Mar 23, 2018 - PEO-based polyurethane sulfonate ionomers with various PEO chain lengths and sodium counterions were synthesized and characterized by b...
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Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

Linear Viscoelasticity and Cation Conduction in Polyurethane Sulfonate Ionomers with Ions in the Soft Segment−Single Phase Systems Shih-Wa Wang† and Ralph H. Colby*,‡ †

Department of Chemical Engineering and ‡Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *

ABSTRACT: PEO-based polyurethane sulfonate ionomers with various PEO chain lengths and sodium counterions were synthesized and characterized by both linear viscoelasticity (LVE) and dielectric relaxation spectroscopy (DRS). Since pphenylene diisocyanate is a small hard segment, the ionomers were found to be single phase with only one DSC Tg which increases with both ion content and hard segment content. An electrode polarization model was used to simultaneously determine the temperature dependence of conducting ion concentration and their mobility, which show Arrhenius and Vogel−Fulcher−Tammann (VFT) temperature dependences, respectively. The polymer dipole relaxation probed by DRS was found to be between 103 and 106 times faster than the mechanical segmental relaxation observed in LVE data near Tg, suggesting that most polymer modes need to wait for the ions to rearrange. The dielectric relaxation, mechanical relaxation, and ionic conductivity all show good correlation with DSC Tg and are related to ion rearrangement. Lower ion content creates lower Tg, lower activation energy for conducting ions, and higher ion mobility, as sodium cations interact strongly with both PEO and the urethane linkage.

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INTRODUCTION Since first discovered to have outstanding cation solvation ability,1 PEO-based ion conducting materials have been widely synthesized and tested to study the mechanism of ion transport in PEO-based materials.2−4 The majority of these PEO-based ion conductors are PEO with dissolved salt which have potential issues like the following: (1) Ionic conductivity contributed more by anions because anions move faster than small cations in the PEO matrix, and the faster anions polarize at one electrode first. These polarized anions can (2) lower the field the cations see and (3) stabilize and promote the growth of dendrites which cause safety hazards and short lifetime.5,6 To avoid these problems, single-ion conductors with anionic groups attached to the polymer chain present very good potential.5 PEO has low Tg at about −60 °C, which is an advantage for ion conduction, since ion transport in a PEO matrix is strongly coupled to PEO segmental relaxation,7,8 but at the same time low Tg means low mechanical strength.9 This issue may be overcome either by cross-linking polymers (chemically10 or physically by semicrystalline PEO) or using block copolymers which contain both high Tg (mechanically strong) and low Tg (good conductivity) phases.11,12 Here, polyurethane-based single-ion conductors were chosen as our candidate for its relatively simple and inexpensive chemistry compared to block copolymers. Polyurethanes physically crosslink by hydrogen bonding between urethane linkages and naturally microphase separate into hard (high Tg) and soft (low Tg) domains, whose size can be controlled by the monomers © XXXX American Chemical Society

used. More specifically, p-phenylene diisocyanate (pPDI) was selected as the hard segment in our system because of its small symmetric chemical structure that has been observed to microphase separate cleanly, even at low hard segment content with minimum chain extension in nonionic polyurethanes.13 Strategies to prepare polyurethane ionomers can be categorized by where, how and which type of the ionic groups are attached.14,15 More specifically, there are four common routes to synthesize polyurethane anionomers: (1) Modifying the urethane linkage with an ionic group can be done by postpolymerization replacement of urethane protons with propane sultone or propiolactone. Note that this method removes some or all urethane protons and impacts microphase separation of hard and soft segments significantly.16−21 (2) Attaching an ionic group in the hard segment by using an ioncontaining chain extender (short ionic diol) such as 2,2dimethylolpropionic acid.22−33 This may be the easiest method to incorporate ions into polyurethanes since short ionic diols are commercially available that require no extra synthesis steps before or after polymerization. However, our previous study shows that placing ionic groups in the middle of the hard segment interferes with clean microphase separation and also results in ions trapped in the hard segment.24 (3) Instead of chain extending the prepolymer as in method 2, end-capping Received: November 27, 2017 Revised: February 20, 2018

A

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obtained by precipitation with excess diethyl ether and vacuum-dried at 80 °C. Excess ions and low molecular weight oligomers were removed by diafiltration. The crude products were dissolved in deionized water and injected into a Slide-A-Lyzer G2 dialysis cassette with 3500 molar mass cutoff, which was then immersed in fresh deionized water (changed every 2−8 h) until the dialysate reached a conductivity lower than 2 μS/cm. Dialysis took about a week, and the final products were vacuum-dried at 80 °C. The chemical structure is shown in Scheme 2. Experimental Methods. Differential Scanning Calorimetry (DSC). The calorimetric glass transition temperature Tg was measured using a Seiko Instruments SSC/5200. All samples were dried under vacuum at 120 °C for 2 days before measurement. All samples were first heated to 120 °C, annealed for 3 min, cooled down to −80 °C at −10 K/min, and then heated to 120 °C at 10 K/min. Tg was determined from the midpoint of the change in heat capacity during the second heating at a heating rate of 10 K/min under an ultrahigh purity nitrogen purge. Dielectric Relaxation Spectroscopy (DRS). All samples were dried at 120 °C under vacuum for 1 day to remove moisture and then sandwiched between two freshly polished brass electrodes with 100 μm Teflon spacers. The prepared cells were annealed in a vacuum oven for an additional 24 h at 120 °C before measurement. Dielectric (impedance) spectra were measured using a Novocontrol GmbH Concept 40 broadband dielectric spectrometer in the frequency range of 1 × 10−2 to 1 × 107 Hz with 0.1 V amplitude. Samples were annealed at 150 °C for 30 min in the instrument and equilibrated with temperature for 5 min before each isothermal measurement. The measurements were done from high to low temperature and then from low to high temperature to confirm no changes due to measurement history. The film thickness was double confirmed before and after DRS measurement. Linear Viscoelasticity (LVE). All samples were annealed at 120 °C under vacuum for 2 days before measurement. Note that since all samples discussed here do not microphase separate and have a Tg lower than 120 °C, they were annealed in their melt state. Linear viscoelastic response was probed in oscillatory shear using a Rheometrics RDS-II with 25 mm parallel plates for PU600s (80 to 25 °C), 7.9 mm parallel plates for PU400s (80 to 25 °C) and PU200sd400 (150 to 50 °C), and 4 mm parallel plates for PU200s (150 to 80 °C). All samples were annealed at the highest temperature studied between two parallel plates for 30 min in the instrument before measurement. All samples were allowed to equilibrate for 25 min before each isothermal measurement.

the prepolymer with a monofunctional ion-containing alcohol is a third method.34,35 This is also a very easy method to prepare PU ionomers, and since the ions are at the end of the chain, they may not interfere the microphase separation as much, although ion content will be tied to polymer molecular weight. (4) Attaching an ionic group in the soft segment by preparing ion containing polyols (long ionic diol) is a fourth method.19,36−43 In this paper, we adopted method 4 to place ions in the soft segment in order to minimize the mixing of ionic groups and hard segment.

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MATERIALS AND EXPERIMENTAL METHODS

Materials. p-Phenylene diisocyanate (pPDI), dimethyl fumarate, sodium bisulfite, tetraethylene glycol (PEG200, Mn = 194), and dibutyltin oxide were purchased from Sigma-Aldrich. Poly(ethylene glycol) (PEG, Mn = 400 and 600 with Mw/Mn < 1.2) was purchased from TCI America, Inc. Anhydrous, N,N-dimethylformamide (DMF), tetrahydrofuran (THF), toluene, and diethyl ether were purchased from EMD. All reagents were used as received without further purification, except pPDI, which was purified by sublimation at 80 °C overnight as described in the literature13 and PEGs which were dried under vacuum at 80 °C for at least 24 h to remove water (with less than 100 ppm by Karl Fischer titration). Polyurethane (PU) Ionomer Synthesis. Synthesis of Sulfonated Dimethyl Fumarate. Dimethyl fumarate (10 molar % excess) and sodium bisulfite were dissolved in methanol and distilled water, respectively, and then mixed in a round-bottom flask and stirred at 80 °C overnight.40 The solution was concentrated by rotary evaporation, and the product was crystallized in an excess of acetone at 4 °C. Crystallized product was washed with acetone and dried at 80 °C under vacuum. The chemical structure was confirmed by 1H NMR and 13 C NMR in DMSO-d6 (see Supporting Information). Synthesis of Sulfonate-Centered Diol (SC-diol). Sulfonated dimethyl fumarate and PEG (Mw = 194, 400, or 600) with a molar ratio of 1:4 and 0.5 wt % dibutyltin oxide were charged into a threeneck round-bottom flask, and oxygen was removed by 30 min of vacuum before the reaction. The reaction was carried out at 160 °C for at least 18 h with argon purge to remove methanol. Completion of the reaction was monitored by disappearance of the 13C NMR peak of the methyl group in dimethyl fumarate at 53 ppm. The product was dissolved in acetone and precipitated in toluene five times. The chemical structure was confirmed by 1H and 13C NMR (see Supporting Information). The chemical structure is shown in Scheme 1.

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RESULTS AND DISCUSSION Chemical Structures and Thermal Properties. Table 1 summarizes basic physical and thermal properties of the PU ionomers and the nonionic PUd400 studied in this paper. SCdiolXXX indicates a sulfonate-centered-diol made from PEG with molecular weight of XXX. PU indicates all the polyurethane samples, “s” indicates the use of an SC-diol as the soft segment, and the number before “s” indicates the Mn of PEG used in SC-diols. “d” and the number after are Mn of PEG diol used as a second soft nonionic segment component to dilute total ion content. Only one Tg was observed from DSC for all samples, regardless of ion content and hard segment content. No evidence of microphase separation was found by small-angle X-

Scheme 1. Chemical Structures of Three SC-diolsa

a n is 4, 9, or 13 with Mn = 572, 984, or 1384, with sample names SCdiol200, SC-diol400, or SC-diol600, respectively.

Synthesis of PU Ionomers with SC-diol. The prepared SC-diol and PEG were dried at 80 °C under vacuum overnight before use. Dried SC-diol, pPDI, and PEG (with −NCO:−OH = 1:1) were dissolved in anhydrous DMF and then reacted at 60 °C for 5−6 h until the −NCO absorption peak at ∼2270 cm−1 disappeared. Crude products were

Scheme 2. Chemical Structures of Four SC-diol-Based Polyurethane Ionomers and the Nonionic Polyurethanea

a

PU200s: n = 4, x = 1; PU200sd400: n = 4, n′ = 9, x = 0.58; PU400s: n = 9, x = 1; PU600s: n = 13, x = 1; PUd400: n′ = 9, x = 0. B

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Macromolecules Table 1. Basic Physical Properties of Sulfonate-Centered Diols and Polyurethane Ionomers Studied sample

na

SC-diol200 SC-diol400 SC-diol600 PU200s PU200sd400f PU400sf PU600s PUd400

4 9 13 4 4 9 13

n′a

9

9

xa

av no. of Kuhn monomer in soft segment, Nsoftb

ion content p0c (nm−3)

Na+/EOd

1 0.58 1 1 0

4 7 10 4 5 7 10 4

1.2 0.67 0.48 0.90 0.58 0.58 0.43 0

0.17 0.063 0.042 0.17 0.085 0.063 0.042 0

hard segment (wt %)

Tge (°C)

22 24 14 10 29

21 −16 −30g 82 53 22 −5 −1

a

n, n′, and x are number of repeating units in Schemes 1 and 2. bMolecular weight of PEO Kuhn monomer, M0 = 137.44 cAssuming all samples have the same density of 1.1 g/cm3. dNa+/EO: sodium ion to ether oxygen ratio. eDSC Tg; only one Tg was observed in DSC for all samples between −80 and 120 °C. fPU200sd400 and PU400s are designed to have the same total ion content. gSC-diol600 also shows a small melting endotherm at 15 °C.

Figure 1. (a) Relationship between DSC Tg and Na+/EO ratio of sulfonate-centered diols (crosses) and polyurethanes (filled blue circles) in this work and from the literature (filled purple diamonds: ref 45; filled red squares: ref 46; filled olive inverted triangles: ref 47; open green squares: ref 48; and open pink triangles: ref 49). Open symbols: lithium ionomers; filled symbols: sodium ionomers. (b) Comparison of the measured DSC Tg and the prediction from eq 1, shown as the dashed line. The two plots share the same legend. Note that the two highest ion content samples of ref 47 have strong nanophase separation of ions that leaves a lower ion content in the soft nanophase.

Figure 2. (a) Ionic conductivity (PUd400 is nonionic) and (b) molar conductance (conductivity normalized by theoretical ion content in Table 1) of PU ionomers as functions of Tg/T. The fact that Tg controls ion motion proves that the polymer segmental motion controls ionic conductivity.

ratio also contain higher hard segment content by experimental design (except PU200sd400) which may result in the stronger Na+/EO ratio dependence than SC-diols and other PEO-based ionomers as shown in Figure 1a. The fact that PU200sd400 and PU400s, designed to have the same ion content, show very different Tg also suggests a strong effect of urethane group/hard segment content on Tg. It was found that the Tg of SC-diols and PU samples can be described by eq 1:

ray scattering (SAXS, see Supporting Information) for these samples either, suggesting single-phase morphology, even with up to 29 wt % of hard segment. This is possibly caused by both pPDI and the PEO spacer between sulfonate groups and urethane linkage being too short, restricting formation of hard phase. The plethora of ether oxygens in the PEO chains can also serve as hydrogen bonding acceptors and compete for the proton in the urethane linkage and limit the alignment of hard segments for microphase separation. Figure 1a shows the correlation between Tg and Na+/EO ratio. Other PEO-based ionomers (polyester sodium ionomers,45,46 methacrylic random copolymer sodium ionomers,47 and polyester lithium ionomers48,49) are also included for reference. All ionomers have stronger Tg dependence on cation/EO ratio than for systems of salt dissolved in PEO50,51 since all anions are attached to the polymer chain in these ionomers. Note that the PU ionomers with higher Na+/EO

Tg (°C) = −60 + 506

pPDI Na + + 451 EO EO

(1)

where −60 °C is Tg of PEO, Na+/EO is the Na+ ion to ether oxygen molar ratio, and pPDI/EO is the molar ratio between pPDI and ether oxygen, which is half of the urethane group to ether oxygen ratio. The similarity of coefficients 506 and 451 suggests that SO3Na and pPDI have similar strong interactions with PEO, with pPDI being 11% less effective for raising Tg. C

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Figure 3 gives the temperature dependence of conducting ion concentration. Since all samples have different ion content,

Literature data on PEO-based anionomers are also included in Figure 1, and it can be seen that the polyester-based ionomers follow similar Na+/EO dependence, as expected. It is interesting that the lithium ionomers also follow the trend predicted by eq 1 (see the open symbols in Figure 1b), suggesting similar solvation interactions for Li+ with EO and Na+ with EO, although they may have different ion aggregation morphology.46 The methacrylic random copolymers (olive inverted triangles) show a weaker dependence because their ions nanophase separate strongly at the two highest ion contents, leaving the soft nanophase with significantly fewer ions.47 Ionic Conductivity. As expected, the samples with lower Tg have higher ionic conductivity, which is plotted against Tg/T for single phase PU ionomers in Figure 2a. Ionic conductivity of the nonionic PUd400 is also shown for reference. The ionic conductivity of PU ionomers below Tg was not measurable except for PU200s, for which the ionic conductivity can be measured at a temperature as low as Tg −20 °C and seems to be Arrhenius52,53 for T < Tg, although there are only two data points. Figure 2b plots the molar conductance as a function of Tg/T, and the spread of data is reduced, suggesting that these polyurethane ionomers all have continuous soft domains for cation transport, consistent with no microphase separation seen in DSC, small-angle X-ray scattering (SAXS, see Supporting Information), and linear viscoelastic properties (discussed later). Conducting Ion Concentration and Mobility. The ionic conductivity is the product of elementary charge e, simultaneously conducting ion concentration p and their mobility μ: σDC = eμp (2)

Figure 3. Temperature dependence of simultaneously conducting ion concentration divided by total cation content. The solid lines represent the best fit of eq 8 with p∞ = p0.

Figure 3 is normalized by theoretical total ion content, p0. As expected, ionomers with smaller p0 (or Na+/EO) have a larger portion of conducting ions.48,49 The conducting ion concentration exhibits an Arrhenius temperature dependence: ⎛ −E ⎞ p = p∞ exp⎜ a ⎟ ⎝ kT ⎠

where Ea is the activation energy and p∞ is the conducting ion content at infinite temperature. p∞ also gives a hint as to how many ions are available to conduct under an electric field. All data in this paper can be fit by defining p∞ equal to p0, the total cation number density, suggesting all ions are available for conduction; however, only a very small portion of these ions contribute to the conductivity at any instant. The fitting parameters are summarized in Table 2.

The conducting ion concentration and their mobility at any given instant in time can be separated by using an electrode polarization (EP) model (the Macdonald/Coelho model).54−56 For linear response of a single-ion conductor with blocking electrodes under AC electric field, the polarization can be described as tan δ =

ωτEP ε″ = ε′ 1 + ω 2τστEP

Table 2. Fitting Parameters for Temperature Dependence of Simultaneously Conducting Ion Concentration (Eq 8) and Their Mobility (Eq 9), Effectively with μ = σDC/(ep) conducting ion concentration p

(3)

where τσ and τEP represent time scales of ion conduction and full electrode polarization: εε τσ ≡ s 0 σDC (4)

τEP ≡

εEPε0 σDC

μ=

sample

log p∞a

Ea (kJ/mol)

PU200s PU200sd400 PU400s PU600s

21.0 20.8 20.8 20.6

18.9 15.1 16.6 15.2

conducting ion mobility μ log μ0

T0 (K)

D

Tg − T0 (K)

−1.41 −1.94 −1.89 −2.29

290 269 245 222

4.0 3.8 3.5 3.3

65 57 50 46

a

Without defining p∞ = p0, the p∞ is larger than p0 (within 1 order of magnitude) especially for PU200s. This can be caused by experimental error. Actually, it is more difficult to load PU200s between two electrodes because of its higher Tg, and very few small bubbles were observed in the samples after the DRS measurement, which may also affect the results. By defining p∞ = p0, the R2 values of the four samples are 0.86, 0.99, 0.92, and 0.95 from top to bottom.

(5)

where εs is the static dielectric constant of the polymer, εEP is the apparent value of the dielectric constant when electrode polarization is completed, and ε0 is the vacuum permittivity. At any given instant, conducting ion number density p and their mobility μ can be obtained, with the sample film thickness, L: p=

(8)

4σDCτEP 2kT e 2L2τσ

Figure 4 compares the activation energy of the samples in this study with other PEO-based ionomers. For PEO ionomers, no significant difference in activation energy was found between the lithium (open symbols) and sodium (filled symbols) counterions. The activation energy increases with increasing cation/EO ratio as expected, but the increment decreases with increasing cation/EO ratio. This is possibly related to the fact

(6)

eL2τσ 4τEP 2kT

(7)

In this EP model, τEP ∼ L, making p and μ interesting material properties. D

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relaxations underneath ion conduction, a derivative spectrum (eq 10) derived from the Kramers−Kronig relation was used:60 π ∂ε′(ω) (10) 2 ∂ ln ω Figure 6 shows the comparison of derivative spectra for polyurethanes with ions and without (PUd400). The ionεder(ω) = −

Figure 4. Conducting ion activation energy of PEO-based sulfonate ionomers. Filled symbols represent sodium-based ionomers, and open symbols represent lithium-based ionomers.48,49

that with increasing cation/EO ratio a higher percentage of the ions participate in aggregates.49,57,58 The temperature dependence of the mobility of the simultaneously conducting ions is displayed in Figure 5. The Figure 6. Derivative spectra of PU ionomers at Tg + 50 K (±5 K): PU200s at 130 °C, PU200sd400 at 100 °C, PU400s at 70 °C, PU600s at 50 °C, and PUd400 at 50 °C.

containing PU samples have an α relaxation before EP occurs while the neutral PUd400 appears to have a weak α′ relaxation between the α relaxation and EP. The origin of the α′ relaxation is not clear, and it might even be an artifact of the derivative calculation. The derivative spectra of Figure 6 for the polyurethane ionomers are fit to the sum of a power law (EP) and a Havriliak−Negami function for the α relaxation:60 Figure 5. Temperature dependence of conducting ion mobility. The solid lines represent the best fits to eq 9.

εder = Aω−s −

(11)

⎧ ⎫ Δε ⎬ ε′HN (ω) = Re⎨ a b ⎩ [1 + (iωτHN) ] ⎭

samples with lower Tg have higher conducting ion mobility, as shown in the inset. When normalized by Tg, the data collapse is a bit poorer than in Figure 2b. Actually, it was found that the data can be well reduced to a single curve if we set Tg of PU200sd400 and PU600s to be 333 K (7 K higher than DSC Tg) and 270 K (2 K higher than DSC Tg), respectively. The conducting ion mobility follows the Vogel−Fulcher− Tammann (VFT) equation: ⎛ −DT0 ⎞ μ = μ0 exp⎜ ⎟ ⎝ T − T0 ⎠

π ⎡ ∂ε′HN (ω) ⎤ ⎢ ⎥ 2 ⎣ ∂ ln(ω) ⎦α ⎪

⎪

⎪

⎪

(12)

The first term in eq 11 represents the EP part with constant A and s (= 1.6−1.8), and the second term represents the α relaxation. Δε is the relaxation strength (dielectric increment), a and b are shape parameters, and τHN is a characteristic relaxation time. The correlation between static dielectric constant, εs, and relaxation strength is εs ≡ lim [ε′α (ω)] + ε∞ = Δεα + ε∞ ω→0

(9)

(13)

Here, an approximate value of ε∞ = n = 2.11 was calculated from the refractive index of neat PEO.61 Figure 7 plots the α relaxation frequency as a function of Tg/T, which does not collapse the data into one curve like Figures 2b and 5. The α relaxation follows the VFT equation with fitting parameters summarized in Table 3: 2

where μ0 is the unconstrained (high T) conducting ion mobility. It was found that conducting ion mobility and α relaxation frequency (discussed later) can be fit using the same T0. The fitting parameters are summarized in Table 2. The Vogel temperature, T0, was found to be 46−65 K lower than the DSC Tg, consistent with the correlation between the glass transition temperature and the mobility of the ions shown in Figure 5. Polymer Segmental Relaxations. DRS also provides dynamic information by probing the dipole relaxations in polymers.59,60 Here, DRS was used for probing both chain and ion segmental relaxations. For ion conducting polymers, the α relaxation peak in the loss spectra (ε″) associated with the segmental motion connected to the glass transition can be easily masked by dominating ion conduction. To reveal

⎛ −DT0 ⎞ ω(T ) = ω0 exp⎜ ⎟ ⎝ T − T0 ⎠

(14)

where ω0 is the unconstrained (high T) frequency, T0 is the Vogel temperature, and D is a parameter inversely related to fragility. Although Tg normalized temperature does not superpose the ωα data into a single curve, the α relaxation shows some correlation with DSC Tg and can be fit to eq 14 using the Vogel temperature from ion mobility T0 in Table 2. E

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rearrangement (α relaxation), beyond which counterion motion becomes diffusive: D = BL D2ωα = B

ε0εskT e 2p

ωα

(16)

where B is a constant. Then the DC conductivity can be written as σDC = Bε0εsωα

Equation 17 can be further combined with eq 4 and rearranged to52,61 σDC 1 = = Bωα ε0εs τσ (18)

Figure 7. Temperature dependence of the relaxation peak frequency of the α relaxation. Solid lines represent fits to the VFT equation (eq 14) with parameters in Table 3.

making the constant B the ratio of the time scales for ion rearrangement (τα = 1/ωα) and ionic conduction (τσ). Figure 8a and b show that the data for the four polyurethane ionomers follow eq 18 with the constant B = τα/τσ decreasing with EO/Na+ ratio (i.e., increasing with ion content). That finding is opposite of what has been reported for polymerized ionic liquids, which have B decrease as ion content increases (see the inset of Figure 16 of ref 52). One possible explanation for this difference is that for the polymerized ionic liquids ion content was diluted by using longer alkyl spacers whereas the polyurethane ionomers here dilute ion content by adding more ether oxygens, which facilitate ion rearrangement. Other sulfonated styrene ionomers with EO comonomers also show B increasing with ion content until an ion-rich microphase forms, which makes B decrease as ion content is further increased.47 Linear Viscoelastic Response. Linear viscoelastic (LVE) response was probed by small-amplitude oscillatory shear, which is very useful for investigating local structure and polymer relaxations.24,66,67 Figure 9a shows the time−temperature superposition master curves of four polyurethane ionomers at reference temperature Tr = Tg + 30 K. The observation that time−temperature superposition applies to these polyurethane ionomers suggests no structural changes in the studied temperature range; the mild failure observed near Tg is common to many polymers. No evidence of microphase separation was observed, which is consistent with our DRS and SAXS results (see Supporting Information for SAXS data). The low-frequency slope of loss modulus d log G″/d log ω = 1 for all four ionomers, indicating they are viscoelastic liquids. The slope of storage modulus d log G′/d log ω in their terminal zone is smaller than 2, consistent with the polydispersity expected for polycondensation polymers68 (note that the very low molecular weight portion has been removed through

Table 3. Fitting Parameters for Temperature Dependence of α Relaxation to VFT Equation (Eq 14) α relaxation sample

log ωα0

T0 (K)

D

PU200s PU200sd400 PU400s PU600s PUd400

8.3 8.8 9.0 8.7 12.8

290 269 245 222 217

3.6 4.2 4.2 4.3 6.9

Extrapolating α relaxation frequency to 0.01 rad/s allows prediction of Tg as shown in Figure 7, which is significantly lower than the DSC Tg. Another way to correlate the α relaxation and ion conduction is using the Barton−Nakajima−Namikawa (BNN) relation. Barton, Nakajima, and Namikawa62−65 suggested that the dielectric relaxation and conduction originate from one diffusion process, and the correlation between the DC conductivity and dielectric relaxation can be derived by a simple scaling method.52,61 The DC conductivity can be rewritten using the Nernst−Einstein equation, μ = De/kT, where D is the diffusion coefficient of the charge carriers and kT is the thermal energy: σDC = eμp =

e 2Dp kT

(15)

The Debye length LD ≡ [ε0εskT/(e p)] is the length scale over which thermal fluctuations allow ions to move. Our dielectric methods directly determine the time scale of ion 2

(17)

1/2

Figure 8. (a) Correlation between the ion conduction frequency (1/τσ) and the α relaxation frequency. Solid line shows the best fit of eq 18 for PU600s, with B = 3.6. (b) B of PU ionomers in this paper and EO-based random copolymer ionomers from Wang et al.47 as a function of EO/Na+ ratio. F

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Figure 9. Time−temperature superposition master curves of (a) PU200s at Tr = 130 °C, (b) PU200sd400 at Tr = 100 °C, (c) PU400s at Tr = 70 °C, and (d) PU600s at Tr = 50 °C (G′: circles; G″: inverted triangles; tan δ: squares).

dialysis during purification). At Tr = Tg + 30 K the four master curves in Figure 9 are very similar, all showing terminal crossing of G′ and G″ near 3 rad/s and Rouse response (G′ = G″ ∼ ω1/2) for roughly 3 rad/s < ω < 100 rad/s, with no hint of entanglement, suggesting low molecular weight (M < 10 000 g/ mol). The temperature dependence of the frequency shift factor, aT, follows the Williams−Landel−Ferry (WLF) equation as shown in Figure 10: log a T = −

c1(T − Tr) c 2 + (T − Tr)

(19)

where c1 and c2 are constants. The WLF equation is mathematically equivalent to the Vogel−Fulcher−Tammann (VFT) equation (see eq 9) with Vogel temperature T0 = Tr − c2 and D ≅ 2.303c1c2/T0. The frequency scale shift factors are fit with the same T0 as conducting ion mobility and α relaxation (Tables 2 and 3), which is 46−65 K below their DSC Tg. Figure 11 compares the relaxation frequency probed by mechanical and dielectric methods. It was found that dielectric α relaxation is significantly faster than the LVE segmental relaxation (taken as the frequency at which loss modulus G″ has a maximum at high frequency, near Tg). It is not unusual that dielectric relaxation time is very different from mechanical relaxation time.69−74 However, the two relaxations show very similar temperature dependence. Note that both relaxations (and also the ion mobility) are fit with the same Vogel temperature T0 which is 46−65 K lower than the DSC Tg. The delay in polymer relaxation suggests that the mechanical

Figure 10. Temperature dependence of the frequency scale shift factor aT. Tr is selected at DSC Tg + 30 K. The solid lines are the best fits to the WLF equation (eq 19) with the fitting parameters summarized in Table 4.

Table 4. Temperature Dependence of the Frequency Scale Shift Factor aT of Figure 10 with Tr = Tg + 30 K, Fit to the WLF Equation (Eq 19) and the Corresponding VFT Equation Parameters

G

sample

c1

c2 (K)

T0 (K)

D

PU200s PU200sd400 PU400s PU600s

9.6 7.8 6.2 5.9

95 87 80 76

290 269 245 222

7.2 5.8 4.7 4.7

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DMSO-d6; 1H NMR of PUs in DMSO-d6; SAXS data of PU ionomers (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (R.H.C.). ORCID

Ralph H. Colby: 0000-0002-5492-6189 Present Address

S.-W.W.: Axalta Coating Systems, 200 Powder Mill Rd., Wilmington, DE 19308.

Figure 11. Temperature-dependent dielectric relaxation frequency (ωα, solid symbols) and mechanical segmental relaxation (ωG″max, open symbols) taken as the high frequency maximum in loss modulus near Tg. PU200s: blue circle; PU200sd400: olive diamond; PU400s: green triangle; and PU600s: red square. Solid curves represent the fit results of VFT/WLF equations.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the U.S. Army Research Office under grant No. W911NF-07-0452 Ionic Liquids in Electroactive Devices (ILEAD) MURI. SWW thanks Air Products and Chemicals for the 2008 Air Products Graduate Fellowship in Chemical Engineering at Penn State wherein she learned about polyurethane synthesis and characterization.

relaxation associated with Tg is constrained by ion associations, and most of the polymer chain modes do not relax before the ions rearrange.

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CONCLUSION PU ionomers based on sulfonate-centered PEO-based diols (SC-diols) and pPDI with different PEO spacer lengths were synthesized and characterized. All the PU ionomers studied in this paper show no evidence of microphase separation even with up to 29 wt % hard segment, likely due to the PEO spacer being too short and both ether oxygens and sulfonate competing for hydrogen bonding with urethane protons. DSC Tg increases with both increasing hard segment content and ion concentration or Na+/EO ratio. An EP model was applied to investigate the number density of simultaneously conducting Na+ ions and their mobility, which have Arrhenius and VFT temperature dependences, respectively. Only less than 2% of the ions contribute to the conductivity at any given instant but all appear to eventually contribute to conduction. This finding is in sharp contrast to our previous study that placed the ions in the hard domain, many of which never participate in conduction.24 The mobility of these conducting ions, and therefore ionic conductivity, show good correlation with DSC Tg with a Vogel temperature T0 46−65 K lower than their DSC Tg. Polymer relaxation was probed by both linear viscoelastic and dielectric responses. All relaxations show VFT temperature dependence. Time−temperature superposition can be applied to the LVE data successfully, indicating that all the PU ionomer samples have very similar single phase morphology. The dielectric α relaxation observed by DRS is a factor of 103−106 faster than the mechanical segmental relaxation. It was found that the α relaxation, the mechanical relaxation from LVE, and the ion mobility share the same Vogel temperature T0 that is 46−65 K below the DSC Tg because all three are connected with ion movement in the polymer matrix.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b02509. 1 H NMR and 13C NMR of sulfonated dimethyl fumarate in DMSO-d6; 1H NMR and 13C NMR of SC-diols in H

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