Segmental Dynamics and Dielectric Constant of Polysiloxane Polar

Research Article www.acsami.org

Segmental Dynamics and Dielectric Constant of Polysiloxane Polar Copolymers as Plasticizers for Polymer Electrolytes U Hyeok Choi,†,‡ Siwei Liang,†,§ Quan Chen,†,∥ James Runt,† and Ralph H. Colby*,† †

Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, United States Functional Composites Department, Korea Institute of Materials Science, Changwon 642-831, Korea § Joint Center for Artificial Photosynthesis, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, California 94720, United States ∥ State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China

ACS Appl. Mater. Interfaces 2016.8:3215-3225. Downloaded from pubs.acs.org by UNIV OF SUNDERLAND on 10/12/18. For personal use only.

‡

ABSTRACT: Dielectric relaxation spectroscopy was used to investigate the segmental dynamics of a series of siloxane-based polar copolymers combining pendant cyclic carbonates and short poly(ethylene oxide) (PEO) chains. The homopolymer with cyclic carbonate as the only side chain exhibits higher glass transition temperature Tg and dielectric constant εs than the one with only PEO side chains. For their copolymers the observed Tg (agreeing well with the predicted values from the Fox equation) and εs decrease with increasing PEO side chain content. These polar polymers exhibit a glassy β relaxation with Arrhenius character, attributed to local chain motions of side groups attached to the main chain, and a segmental α relaxation, associated with the glass transition with a Vogel temperature dependence. As PEO side chain content increases, narrowing of the local glassy β relaxation was observed in the copolymers. The segmental α dynamics were observed to be faster, with an increase in breadth and decrease in strength with increasing PEO side chain content. Owing to the trade-off between Tg and εs, copolymers of intermediate composition result in the highest ionic conductivity when these copolymers are used to plasticize Li single-ion conducting ionomers. KEYWORDS: polymer electrolyte, plasticizer, dielectric constant, glass transition temperature, siloxane-based polar copolymer, lithium ion battery

1. INTRODUCTION Polymer electrolytes are of great interest as materials in energy storage (lithium ion batteries and supercapacitors), energy conversion (fuel cells and solar cells), and electromechanical transduction devices1−5 (actuators and sensors) because low Tg ion conducting polymers offer high ionic conductivity, good adherence to electrodes, and excellent processability for thin films.6,7 Poly(ethylene oxide) (PEO) with lithium salts is one candidate for a solid-state polymer electrolyte and has been widely studied.8−12 However, PEO/salt electrolytes suffer from low ionic conductivity at room temperature, due to high crystallinity of PEO restricting polymer segmental motion, and have cation transference number less than 0.5,13,14 limiting power density and recharging rates due to anion concentration polarization.15,16 In an effort to overcome these issues, of particular interest are polysiloxane-based single-ion conductors in which anions are covalently bonded to a highly flexible siloxane backbone (imparting low glass transition temperature and elimination of crystallization), thereby only having mobile cations (near unity Li+ transference number). Previously, polysiloxane single-ion conductors containing polar cyclic carbonates and weak© 2016 American Chemical Society

binding tetraphenyl borate anions with lithium counterions as randomly placed side chains were synthesized.17 These singleion conductors exhibited low lithium ion activation energy (∼9 kJ/mol), but their ionic conductivities were low due to microphase separation of carbonates from the large borate anions, effectively aggregating ions and restricting segmental motion (raising Tg).17 To improve ionic conductivity, several methods have been proposed, such as using anion receptors18−21 (not covalently attached to the polymer, thus avoiding the devastating effect of anion attachment on the overall chain dynamics), adding inorganic particles or ceramic fillers,22−27 and introducing various plasticizers (such as ionic liquids, carbonate solvents, and oligoether solvents).28−33 We conducted an investigation of the effect of a low molecular weight, low Tg solvating plasticizer on the conductometric/dielectric properties of polysiloxane single-ion conductors.32 Poly(ethylene glycol) with Mn = 600 g/mol (PEG13) was used as the plasticizer, Received: November 9, 2015 Accepted: January 6, 2016 Published: January 6, 2016 3215

DOI: 10.1021/acsami.5b10797 ACS Appl. Mater. Interfaces 2016, 8, 3215−3225

Research Article

ACS Applied Materials & Interfaces

dielectric constants (εs = 60−95) and dipole moments (μ ∼ 4.9 D), but high viscosity (η = 1.5−2.5 cP) (raising Tg) and overlap of polarizability volume (Vp/Vm > 1 meaning that dipoles strongly interact), while acyclic oligoether molecules have low viscosity (η = 0.1−0.5 cP) (lower Tg) and no overlap of polarizability volume (Vp/Vm < 1), but moderate dielectric constants (εs = 2−7) and dipole moments (μ ∼ 1.5 D).35 As a result, the dielectric constant and molecular mobility of the siloxane polar copolymers strongly depend on the composition of the more polar cyclic carbonate and the more flexible oligomeric PEO side groups. In our copolymers each side group has four oxygens. In the present paper, the segmental dynamics of a series of the siloxane-based polar copolymers, where the concentrations of cyclic carbonate and oligomeric PEO units are varied, are reported using dielectric relaxation spectroscopy (DRS). DRS is a particularly powerful technique for the investigation of relatively polar copolymers, facilitating investigation of the dynamics over a very broad range of frequencies in both glassy and liquid states. The influences of the chemical linkage between two side chain species on local and segmental dynamics are demonstrated by comparing the relaxation spectra of a copolymer series (Figure 1a) and a blend series (Figure 1b). This provides useful insights for understanding the relationship between chemistry and molecular dynamics to tailor material performance, evaluated in the end by using these plasticizers to blend with a single-ion conducting ionomer.

and its ether oxygens dissolved ion aggregates by coordinating strongly with cations and hence lowering Tg, leading to an increase of the conductivity by as much as 3 orders of magnitude compared to that of the host single-ion conductor.32 When more than ∼50 wt % PEG13 was added, however, the conductivity significantly decreases below 15 °C from PEG13 crystallization. Also, the hydroxyl end groups of PEG13 can react with a lithium metal electrode34 so such a plasticizer would not be suitable for a high energy-density battery. Herein, siloxane-based polar copolymer plasticizers are synthesized with cyclic carbonate and oligomeric PEO units as randomly placed side chains (see Figure 1a). These low

2. EXPERIMENTAL SECTION Figure 1a shows the molecular structures of polysiloxane polar homopolymers with either cyclic carbonate (CECA) side chains (m = 52 or 100 mol % of CECA; referred to as C100P0) or oligomeric poly(ethylene oxide) (PEO3) side chains (n = 52 or 100 mol % of PEO3; referred to as C0P100) and their random copolymers (CmPn, m:n = 80:20, 57:43, 31:69, and 19:81, where m and n were determined by the integrated areas of 1H NMR peaks). The homopolymers and copolymers were synthesized by hydrosilylation as described earlier.17,45−48 Unfortunately, our usual exhaustive aqueous dialysis purification cannot be applied to these plasticizers because the cyclic carbonate ring would hydrolyze, so the siloxane plasticizers were instead washed by toluene multiple times to remove unreacted monomers and other impurities.46 Figure 1b shows the blend system under investigation, where different ratios of CECA homopolymer (C100P0) and poly(ethylene glycol) with Mn = 600 g/mol (PEG13) (8, 13, and 32 wt % PEG13) were weighed into 10 mL vials. The mixtures were dissolved in acetone to form a fully homogeneous solution, the acetone was removed by rotary evaporation, and the transparent residue was dried in a vacuum oven overnight at 100 °C before evaluation. 2.A. Thermal Characterization. Glass transition temperature (Tg) was determined using a TA Q100 differential scanning calorimeter (DSC) using 10 K/min heating and cooling rates on ∼10 mg samples. Tg is taken as the midpoint of the heat capacity change in the second heating. 2.B. Dielectric Relaxation Spectroscopy (DRS). Dielectric spectroscopy measurements were conducted on samples that were prepared by allowing them to flow to cover a 30 mm diameter freshly polished brass electrode at 100 °C in vacuo. To control the sample thickness at 50 μm, silica spacers were placed on top of the sample after it flowed to cover the electrode. Then, a 15 mm diameter freshly polished brass electrode was placed on top to create a parallel plate capacitor cell which was squeezed to a gap of 50 μm in the instrument (with precise thickness verified after dielectric measurements were complete). The samples were positioned in a Novocontrol GmbH Concept 40 broadband dielectric spectrometer, after being in a vacuum oven at 100 °C for 24 h. Each sample was then annealed in the

Figure 1. Chemical structures of (a) polysiloxane-based homopolymers having either cyclic carbonate (CECA) (100 mol %, C100P0) or oligomeric poly(ethylene oxide) (PEO3) (100 mol %, C0P100) and their random copolymers (CmPn, m:n = 80:20, 57:43, 31:69, and 19:81) and (b) the components [C100P0 and poly(ethylene glycol) with Mn = 600 g/mol (PEG13)] of the blends under consideration. All siloxanes in this paper were made from the same parent polydisperse siloxane with DPn = m + n = 52.

volatility copolymers (Mn > 10 000 g/mol) eliminate the possibility of solvent evaporation. Since siloxanes are known for their low dielectric constants and hence limited solvation toward Li+,21 in order to make feasible plasticizers, functional moieties capable of solvating lithium cations, breaking ion aggregates, and lowering Tg must be attached to them. Carbonyl oxygens of the cyclic carbonates and ether oxygens of the oligomeric PEO are the preferred members of the primary solvation shell of Li+ because their lone-pair electrons are most effective in solvating the small lithium cation.21 As seen in Table 1, the cyclic carbonate molecules have high 3216


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Table 1. Physical Properties of Cyclic Carbonate and Acyclic Ether Molecules at 298 K:35−41 Static Dielectric Constant εs, Viscosity η, Dipole Moment μ, Kirkwood Correlation Factor g, Melting Temperature Tm, Refractive Index n, Density ρ, Polarizability Volume Vp, and Overlap of Polarizability Volume Vp/Vm sample

εs

η (cP)

μ (D)

ga

Tm (K)

n

ρ (g/cm3)

Vpb (nm3)

Vp/Vmc

ethylene carbonate (EC) propylene carbonate (PC) dimethyoxy ethane (DMOE) dimethyl ether (DME)

95.3 64.96 7.03 5

1.9d 2.5 0.46 0.13

4.87 4.90 1.70 1.30

1.62 1.37 1.34 1.15

310 224 215 132

1.42 1.42 1.38 1.30e

1.32 1.2 0.87 0.66

0.19 0.20 0.02 0.01

1.74 1.37 0.14 0.12

a

Kirkwood correlation factor g determined from eq 3. bPolarizability volume Vp determined from Vp = (1/4πε0)(μ2/3kT).42 cOverlap of polarizability volume Vp/Vm; Vm is the molecule volume.36,43 dη of EC was reported at 313 K.35 en of DME was determined from the group contribution method based on the molecular structure.44

Table 2. Values for DSC and DRS Glass Transition Temperature Tg, Number-Average Molecular Weight Mn, Number Density of Dipole ν, Overlap of Polarizability Volume Vp/Vm, and Dipole Correlation g Factor of the Siloxane Homopolymers and Their Copolymers sample

DSCa Tg ± 2 (K)

DRSb Tg ± 5 (K)

Mnc (g/mol)

d νCECA (nm−3) PC

d νCECA (nm−3) EO

C100P0 C80P20 C57P43 C31P69 C19P81 C0P100

248 229 218 202 194 187

244 225 216 200 193 184

11 100 11 400 11 800 12 200 12 400 12 700

5.5 4.1 2.7 1.4 0.8

5.5 4.1 2.7 1.4 0.8

d νPEO3 (nm−3) EO

Vp/Vme (T = 303 K)

gf (T = 303 K)

4.1 8.2 12.1 13.7 16.0

1.1 0.9 0.6 0.4 0.3 0.1

1.3 1.2 1.2 1.0 1.0 1.1

Tg measured by DSC with 10 K/min heating and cooling rates. bTg determined from dielectric relaxation spectroscopy [ωα(T) is fit to VFT eq 10 and extrapolated to ωα(Tg) = 10−2 rad/s]. cNumber-average molecular weight Mn, calculated from the integrated areas of 1H NMR peaks, assuming number-average DPn = 52.47 dNumber density of three dipoles in polar side chains ν estimated from group contribution method based on molecular structure.44 eVp/Vm determined from eq 4. fg determined from eq 3. a

Novocontrol sample chamber at 120 °C in a heated stream of nitrogen for 1 h prior to measurements to remove water acquired during sample loading. The dielectric permittivity was measured using a sinusoidal voltage with amplitude 0.1 V and 10−1−107 Hz frequency range for all experiments. Data were collected in isothermal frequency sweeps every 5 °C, from 120 to −100 °C.

3. RESULTS AND DISCUSSION 3.A. Glass Transition Temperature. The siloxane homopolymers (C100P0 and C0P100) and their copolymers (C80P20, C57P43, C31P69, and C19P81) each have a single glass transition, as reported in Table 2. The polymers do not display crystallization or melting in the temperature range −100 to 200 °C by DSC, indicating that these amorphous plasticizers can be used over a wide temperature range for applications. The siloxane homopolymer with cyclic carbonate side chains (C100P0) exhibits ∼60 K higher Tg than that with PEO3 side chains (C0P100). After hydrosilylation, presumably the cyclic carbonate side group (having higher viscosity) leads to a significant decrease of siloxane backbone flexibility, compared to the linear oligoether PEO3 side chain (having lower viscosity).47 For their random copolymers, an increase of the PEO3 content lowers the observed DSC glass transition and the dynamic glass transition discussed in detail in section 3C (see Table 2). As seen in Table 2, the molecular weights of these homopolymers and copolymers are slightly larger than 10 000 g/mol, imparting very low volatility that can eliminate the safety issue of organic carbonate solvents used in the lithium ion battery industry because combustion occurs in the vapor phase. 3.B. Static Dielectric Constant. Figure 2 shows the frequency dependence of the dielectric permittivity spectra ε′(ω) at 303 K, which were horizontally shifted to display the static dielectric constant εs difference among the siloxane homopolymers and their copolymers. The static dielectric

Figure 2. Dielectric permittivity spectra ε′ at 303 K shifted by horizontal shift factor, X [C100P0 (X = 46.2); C80P20 (X = 3.2); C57P43 (X = 1.9); C31P69 (X = 3.0); C19P81 (X = 0.4); C0P100 (X = 1.0)], to superimpose in the range 102 < ε′ < 103 and hence compare the static dielectric constants, defined as the low frequency plateau of ε′(ω) before the onset of electrode polarization, of the siloxane homopolymers and their copolymers [and of the cyclic carbonate monomer (CECA, Y = 1.0), propylene carbonate (PC, Y = 0.2), and PEG13 (Y = 12.4) in the inset].

constant εs is defined as the low frequency plateau of ε′(ω) before the onset of electrode polarization. For the two homopolymers, C100P0 with CECA side chain C P (εs 100 0 = 50) has 8 times higher εs than C0P100 with PEO3 side CP chain (εs 0 100 = 6) at 303 K. This can be explained by the comparison of their corresponding side groups before hydrosilylation in the inset of Figure 2, where the cyclic carbonate (CECA, having four oxygens) monomer exhibits slightly higher εs than propylene carbonate (PC, having three oxygens) and much higher εs than oligomeric PEG13.49−51 For the siloxane 3217


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temperature increases. This is usual for amorphous polymers and non-hydrogen bonding polar liquids due to thermal dipole randomization (Figure 3a). The siloxane copolymers with higher PEO3 content exhibit static dielectric constants that obey the Onsager52 prediction, but εs exhibits a stronger temperature dependence for the siloxane polymers with higher CECA content. For the PEO3 homopolymer C0P100, its experimental εs agrees well with the Onsager prediction across the entire temperature range, while the CECA homopolymer C100P0 exhibits εs that is further above the Onsager prediction (eq 2) as temperature is lowered. It is therefore interesting to consider local directional correlations between neighboring dipoles. The Kirkwood−Frö hlich equation introduces a dipole correlation g factor into the Onsager equation (eq 2) and is given by60−64

copolymers, incorporating more of the PEO3 side chain lowers the static dielectric constant εs (see Figure 2) and the glass transition temperature Tg (see Table 2). We then consider the temperature dependence of εs for the siloxane polymers by utilizing the Onsager equation52−54 (εs − ε∞)(2εs + ε∞) εs(ε∞ + 2)2

=

∑ i

2 νμ i i

9ε0kT

(1)

wherein νi, listed in Table 2, is the number density of dipoles, μi is their dipole moment, ε0 is the vacuum permittivity, k is the Boltzmann constant, T is absolute temperature, and ε∞ is the high frequency limit of the dielectric constant [here taken to be ε∞ = n2, where n = 1.40 is the refractive index of polydimethylsiloxane (PDMS)55]. For the homopolymers and copolymers, the Onsager equation can be considered as a sum of two dipoles of each side group, the CECA contribution (assuming CECA has two independent dipoles of the EO connector, μEO = 1.04 D,56 and the cyclic carbonate as propylene carbonate, μPC = 4.9 D) 57 and the PEO3 contribution (using dipole of a single EO, μEO = 1.04 D, and its number density νPEO3 EO , listed in Table 2, determined from the PEO3 monomer density multiplied by four EO’s per monomer unit):53,54,58,59

g= =

+

9ε0kT CECA νEO μEO2

+

⎡ (ε − ε )(2ε + ε ) ⎤ ∞ ∞ s ⎢ s ⎥ εs(ε∞ + 2)2 ⎦

PEO3 νEO μEO2 ⎣

The Kirkwood−Fröhlich g factor is a measure of the effect of dipole interactions on the experimental dielectric constant. Dipole correlation factors shown in Figure 3b were calculated from eq 3 using the number densities of side groups νi listed in Table 2, and dipole moments of μPC = 4.9 D and μEO = 1.04 D. The g factor of C100P0 with CECA side chains is g ∼ 1.0−1.6 (depending on temperature), indicating that all the dipoles in this homopolymer contribute to the dielectric constant, with orienting surrounding dipoles having preferential alignment in the same direction (g > 1) at low temperature, but the thermal energy kT seems to break the parallel dipolar correlation, eventually approaching no correlation (g ∼ 1) at high temperature. The cyclic carbonates EC and PC also exhibit g > 1 (see Table 1).65−69 On the other hand, C0P100 with PEO3 side chain exhibits g ∼ 1 over the whole temperature range studied, meaning that, on average, there is no dipolar correlation between neighboring dipolar side groups. The observed g value of C0P100 with the oligomeric EO side chains is slightly lower than that of the acyclic oligoether molecules (see Table 1). This is likely due to the siloxane backbone restricting dipole motion. The steric effect of the backbone seems to be more sensitive to the weaker dipoles of EO than the stronger dipoles of CECA since the latter are further away from the backbone. For the copolymers C80P20, C57P43, C31P69, and C19P81, the higher CECA content copolymers exhibit 1 < g < 1.5, which are higher than those of the higher PEO3 content copolymers (0.8 < g < 1.2). The dielectric constant for these siloxane polar polymers can be further understood through overlap of the polarizability volumes of dipoles, which is a ratio of polarizability volume Vp to molecular volume Vm

εs(ε∞ + 2)2 CECA CECA PEO3 νPC μPC 2 + νEO μEO2 + νEO μEO2

9ε0kT

CECA νPC μPC 2

(3)

(εs − ε∞)(2εs + ε∞)

=

9ε0kT ⎡ (εs − ε∞)(2εs + ε∞) ⎤ ⎢ ⎥ 2 ∑i νμ εs(ε∞ + 2)2 ⎦ i i ⎣

(2)

The solid lines in Figure 3a are the Onsager predictions of eq 2 for the homopolymers and their copolymers, assuming the contribution from siloxane segments is negligible and all CECA and PEO3 dipoles are free and noninteracting. The Onsager equation predicts that the static dielectric constant decreases as

Vp/Vm =

∑ i

Figure 3. Temperature dependence of (a) the static dielectric constant εs and (b) the Kirkwood g correlation factor estimated from the measured static dielectric constant via eq 3 for the siloxane homopolymers and their copolymers. The solid lines are predictions of the Onsager equation (eq 2) with fixed concentration and strength of dipoles, assuming the Kirkwood correlation factor g = 1.

=

2 νμ i i

12πε0kT

CECA νPC μPC 2

CECA PEO3 + νEO μEO2 + νEO μEO2

12πε0kT

(4)

wherein Vp = (1/4πε0)(μ2i /3kT),42 defined by Debye,70 and Vm = 1/ν. Vp/Vm > 1 pushes the dipoles to interact strongly.36,43 3218


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which is longer than the PEO3 side chain of C0P100 and has two −OH end groups (see Figure 5a). The blend containing 32 wt

We have recently shown that the polarizability volume overlap parameter Vp/Vm controls the εs in a class of ionomers having ion pair dipoles.36 For Vp/Vm > 3.5, strongly overlapping ion pairs leads to the lowest εs because of hindered rotation of dipoles, whereas for 1 < Vp/Vm < 3.5, εs increases with decreasing Vp/Vm because less overlapping of ion pair polarizability volumes allows these dipoles to align under an applied field. In the current study, the siloxane homopolymers and copolymers have 0 < Vp/Vm < 1 (listed in Table 2), indicating no overlapping of dipole polarizability volumes, where the dipoles do not interact with neighboring ones: consequently, g ∼ 1. This Vp/Vm probably tells us why the PEO3 homopolymer C0P100 having Vp/Vm ∼ 0.1, rarely interacting, has much lower Tg than the CECA homopolymer C100P0 having Vp/Vm ∼ 1.1. The Vp/Vm dependence of static dielectric constant shown in Figure 4 can be evaluated by combining the Onsager eq (eq 1) and the overlap of the polarizability volume (eq 4):36 (εs − ε∞)(2εs + ε∞) 2

εs(ε∞ + 2)

=

∑ i

2 νμ i i

9ε0kT

=

4π Vp 3 Vm

(5)

Figure 5. (a) Temperature dependence of the static dielectric constant εs for C100P0 blends with PEG13. (b) Compositional variation in εs for copolymers (filled symbols) and blends (open symbols) at 303 K, where ΦC0P100 and ΦPEG13 are the weight fraction of side chains that are PEO3 and PEG13, respectively.

% PEG13 shows that static dielectric constant suddenly decreases below 288 K due to PEG crystallization, which is also observed in the neat semicrystalline PEG13 at the same temperature. As expected, when PEG13 having lower dielectric constant (εs = 11 at 303 K) is added to C100P0 (εs = 50 at 303 K), the dielectric constant of the blends gradually decreases with PEG13 content owing to dilution with lower dielectric constant PEG13. As shown in Figure 5b, the dilution effect on εs is observed in both copolymers and blends. 3.C. Dielectric Relaxations. Figure 6 displays two isochronal representative examples of the dielectric loss spectrum ε″ as a function of temperature at various frequencies for the siloxane copolymer C57P43 and homopolymer C100P0 blend with 32 wt % PEG13. All siloxane polymers under investigation here exhibit a single secondary β relaxation at lower temperatures and a single segmental α relaxation at higher temperatures. The dipolar relaxations were analyzed by fitting the isothermal dielectric loss spectra as functions of frequency using the appropriate form of the Havriliak−Negami equation for each relaxation process71

Figure 4. Correlation between the static dielectric constant εs and the polarizability volume overlap parameter Vp/Vm at 303 K for PC and DME (black filled symbols), siloxane homopolymers and copolymers (colored filled symbols), and siloxane homopolymer C100P0 blends with PEG13 (colored open symbols). Dashed and solid lines are fits of the Onsager equation of eqs 5 and 6, respectively.

In the high polarity limit, the Onsager equation becomes36 εs ≈

Vp 2π (ε∞ + 2)2 3 Vm

(6)

The dashed and solid lines shown in Figure 4 are a fit to eqs 5 and 6 with a single fitting parameter (ε∞ = 2.6), respectively, and the two only differ for εs < 7. The high frequency dielectric constant value is similar to what is used in the Onsager analysis (ε∞ = 2.0). Incorporating more PEO3 allows the dipolar side groups to form more isolated dipoles, which do not show a preference for correlation with neighboring ones (g ∼ 1), and this is why εs of the siloxane polymers decreases with decreasing Vp/Vm as expected by Onsager dilution (eq 6). For comparison, we also investigate εs of the siloxane homopolymer C100P0 blends containing 8, 13, and 34 wt % poly(ethylene glycol) oligomer with Mn = 600 g/mol (PEG13),

* (ω) = εHN

Δε [1 + (iω/ωHN)a ]b

(7)

wherein Δε is the relaxation strength, a and b are shape parameters, and ωHN is a characteristic frequency related to the frequency of maximal loss ωmax by72 3219


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Figure 7. (a) Frequency dependence of dielectric loss ε″ of the siloxane copolymers in the glassy state (178 K) where the β process is clearly observed and (b) temperature dependence of relaxation frequency maxima ωmax of the β process: dashed lines are fits of the Arrhenius equation (eq 9).

Figure 6. Representative dielectric loss spectra ε″ as a function of temperature at selected frequencies for (a) siloxane copolymer C57P43 and (b) homopolymer C100P0 blend with 32 wt % PEG13. −1/ a 1/ a ⎛ aπ ⎞ ⎛ abπ ⎞ ⎟ ⎜sin ⎟ ωmax = ωHN⎜sin ⎝ 2 + 2b ⎠ ⎝ 2 + 2b ⎠

(8)

transition (see Table 2). As the PEO3 content increases, the α loss peak tends to broaden, and its intensity indeed decreases. The HN shape parameter a (from eq 7) decreases from 0.77 to 0.52 with increasing PEO3 content. The relaxation strength Δεα of the segmental α process decreases with increasing PEO3 content and with increasing temperature (see Figure 8b), consistent with the decrease of εs (Figure 3a). For the siloxane polymers with higher PEO3 content, Δεα has the weak temperature dependence expected by Onsager52 (eq 1), whereas Δεα exhibits a stronger temperature dependence for the siloxane polymers with higher CECA content. The peak relaxation frequency ωmax of the α process of these copolymers follows the Vogel−Fulcher−Tammann (VFT) equation

Copolymer Dynamics. Figure 7a shows dielectric loss spectra of the siloxane copolymers at 178 K. The siloxane homopolymer C100P0 exhibits a single, broad β process around 104 rad/s, associated with local chain motions of cyclic carbonate side chains. For the copolymers having two side groups, a single local β process is still observed. The β peak gradually narrows and shifts to higher frequency as the PEO3 side chain content increases (see Figure 7a). The peak relaxation frequencies (ωmax) of the β process of the siloxane copolymers are plotted as a function of inverse temperature in Figure 7b. Their temperature dependence was fit using the Arrhenius equation (see dashed lines in Figure 7b) ⎛ E ⎞ ωmax = ω∞exp⎜ − a ⎟ ⎝ RT ⎠

⎛ DT0 ⎞ ωmax = ω∞ exp⎜ − ⎟ ⎝ T − T0 ⎠

(9)

wherein ω∞ and Ea, listed in Table 3, are the high temperature limiting frequency and the activation energy for the β process, respectively, and R is the gas constant. Although higher PEO3 content in the copolymers makes the β process faster at the temperature studied, the PEO3 content has no effect on the activation energy; i.e., all copolymers have a similar activation energy of ∼33 kJ/mol (see Table 3). Such an Arrhenius temperature dependence below Tg with an activation energy of ∼30 kJ/mol has been observed in the amorphous polymers with pendant structures, of which typical values for Ea are 20−50 kJ/mol.72 Figure 8a displays the dielectric loss ε″ normalized by the peak frequency maxima ωmax of the α process at Tg + 20 K. The siloxane copolymers each exhibit a single α relaxation process, corresponding to the segmental motion of the polymer and hence exhibiting the typical dynamic characteristics of the glass

(10)

The solid curves in Figure 8c are fits to eq 10 with the high temperature limiting frequency ω∞, strength parameter D (reciprocally related to fragility m), and Vogel temperature T0, listed in Table 3. The temperature at which the VFT extrapolated relaxation time is τα(=1/ωα) = 100 s (denoted DRS Tg) is in good agreement with the calorimetric glass transition temperature (denoted DSC Tg) within experimental uncertainty (see Table 2 and Figure 8d). The homopolymer C100P0 (with cyclic carbonate side chains) having higher Tg and T0 exhibits a slower α process than the homopolymer C0P100 (with PEO3 side chains) having lower Tg and T0. For their copolymers, as the PEO3 content increases, the α process becomes gradually faster due to a decrease of Tg (see Figure 8c). The characteristic decrease in Tg of the copolymers with increasing PEO3 content can be predicted by the Fox equation 3220


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Table 3. Fitting Parameters of the Arrhenius Temperature Dependences (Equation 9) of the β Process and the VFT Temperature Dependence (Equation 10) of the α Process, DRS Glass Transition Temperature Tg, and Fragility m Arrhenius β process

VFT α process

sample

log(ω∞) (rad/s)

Ea (kJ/mol)

log(ω∞) (rad/s)

D

T0 (K)

DRS Tga ± 5 (K)

mb ± 10

C100P0 C80P20 C57P43 C31P69 C19P81 C0P100 32%_PEG13 PEG13

13.8 14.2 14.5 14.9 15.8

33 33 32 31 34

14.2 15.7

34 40

12.4 12.2 12.1 12.1 12.4 14.8 13.1 12.0

4.0 5.1 5.3 6.0 6.7 7.1 5.0 6.7

217 195 185 169 160 156 210 169

244 225 216 200 193 184 240 204

132 105 99 91 85 108 121 80

Tg determined from dielectric relaxation spectroscopy (defined at ωα(Tg) = 10−2 rad/s). bm determined from eq 13 using the VFT fit parameters for the segmental (α) peak frequencies based on the DRS Tg.

a

Figure 8. (a) Dielectric loss ε″ of the siloxane polymers vs ω/ωmax in the region of the α process (Tg + 20 K). Temperature dependence of (b) the relaxation strength Δε and (c) the relaxation frequency maxima ωmax of the α process: solid curves are fits of the VFT equation (eq 10). (d) Compositional variation in the glass transition temperature Tg, where ΦC0P100 is the weight fraction of side chains that are PEO3: DRS Tg (filled symbols), DSC Tg (open symbols), and Fox predictions from eqs 11 (dashed line) and 12 (solid line).

1 T gCmPn

=

1 − ΦC0P100 T gC100P0

+

TPEO3 are the three component glass transition temperatures as g adjustable parameters. The solid line in Figure 8d is the prediction from eq 12 using Tsiloxanebackbone = 149 K, TCECA = g g PEO3 322 K, and Tg = 200 K, showing that the Tsiloxanebackbone and g TPEO3 are very close to the expected Tg values of the PDMS g (TPDMS = 145 K) and PEO (TPEO = 206 K), respectively. The g g increase of PEO3 content also changes the strength parameter D of the copolymers from 5.1 to 6.7 (see Table 3), indicating that the fragility of these copolymers decreases as more PEO3 side groups are incorporated. This is consistent with the quantitative analysis of the fragility m described in a later section. Blend Dynamics. Figure 9a displays dielectric loss spectra of the siloxane homopolymer C100P0, PEG13, and their blend with 32 wt % PEG13 in the glassy state (193 K). Like the homopolymer C100P0, PEG13 displays a single β process

ΦC0P100 T gC0P100

(11)

wherein ΦC0P100 is the weight fraction of side chains that are PEO3, TCg 100P0 = 244 K, and TCg 0P100 = 184 K, shown as the dashed line in Figure 8d. The Tg−composition dependence of the copolymers is also well-described by the three-component Fox equation 1 TgCmPn

=

Φsiloxanebackbone Tgsiloxanebackbone

+

ΦCECA TgCECA

+

ΦPEO3 TgPEO3

(12)

wherein Φsiloxanebackbone, ΦCECA, and ΦPEO3 = 0.78ΦC0P100 are the weight fractions of siloxane backbone, CECA side chain, and PEO3 side chain, respectively, and Tsiloxanebackbone , TCECA , and g g 3221


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Figure 9. Frequency dependence of dielectric loss ε″ of siloxane homopolymer C100P0, PEG13, and their blend with 32 wt % PEG13 (a) in the glassy state (193 K) where the β process is clearly observed (Δεβ vs ΦPEG13, where ΦPEG13 is the weight fraction of PEG13, in the inset) and (b) in the region of the α process at Tg + 20 K. (c) Temperature dependence of relaxation frequency maxima ωmax of the β (ωβ, open symbols) and α (ωα, filled symbols) processes and (d) ωα vs Tg/T using the DRS Tg (listed in Table 3) of all polymers studied: solid curves are fits of the VFT equation (eq 10).

around 105 rad/s, associated with local chain twisting of amorphous PEG segments.73 However, the β loss peak of PEG13 is much narrower than that of the homopolymer C100P0. Blending C100P0 with PEG13 results in a narrowing of the observed single β relaxation, and no new local processes appear in the blend with 32 wt % PEG13 (see Figure 9a). The narrowing of the local β relaxation, upon addition of PEG13, is also observed in the copolymer systems, where the β loss peak becomes progressively narrower as PEO3 content increases (see Figure 7a). The relaxation strength (inset of Figure 9a) of the β process decreases with increasing PEG13 content and varies in rough proportion to the weight fraction of C100P0 and PEG13 in the blend. The host polymers C100P0 and PEG13 exhibit almost identical peak relaxation frequency ωmax of the β process. As a result, the β process in the blend with 32 wt % PEG13 also has an Arrhenius temperature dependence (eq 9) with an activation energy of 34 kJ/mol, identical to that observed in the siloxane copolymers (see Table 3). Figure 9b displays dielectric loss spectra ε″ of the neat C100P0 and PEG13 and their blend with 32 wt % PEG13 above the glass transition temperature (Tg + 20 K), where all the polymers studied herein exhibit a single α process. For neat PEG13 the loss α peak is broader and has much lower strength, compared to that for neat C100P0. Blending C100P0 with PEG13 leads to a broad α process and a decrease in its strength. As observed in the local β relaxation, for both blend and copolymer systems, their loss α peaks exhibit the same PEG or PEO3 concentration dependence. The α peak relaxation frequencies ωmax of the blend system also follow the same VFT temperature dependence as the copolymers. The PEG13 having lower Tg exhibits faster α process than the homopolymer

C100P0 having higher Tg. In weakly interacting miscible blends, the dynamics of the two components are often observed to be decoupled, resulting in two segmental relaxations in their blend.74−76 For the blend with 32 wt % PEG13, however, a single segmental relaxation is observed, and its peak frequencies and Tg are almost identical to those observed in the neat polymer C100P0. This reflects that the segment dynamics of the blend is primarily due to the mobility of the more polar CECA side groups of the C100P0 component (see Table 1). The temperature dependence of the α relaxation frequencies is well-described by the VFT equation (eq 10, solid curves in Figure 9c) as shown in the copolymers (Figure 8c). The VFT fit also makes it possible to calculate the fragility m77 m=−

dlog(ω) d(Tg /T )

= T = Tg

DT0 Tg(ln 10)(1 − T0/Tg)2

(13)

wherein D and the Vogel temperature T0 (listed in Table 3) are VFT fitting parameters for ωα (filled symbols in Figures 8c and 9c). The estimated fragility m values of the polymers under investigation here are given in Table 3. In Figure 9d, ωα was plotted in the Tg-normalized VFT form, showing the steepness of the slope of ωα dependence on Tg/T near Tg. A stronger deviation from Arrhenius behavior (more bending in Figure 9d) corresponds to a more fragile system. Polydimethylsiloxane, having a very flexible backbone and extremely low Tg ∼ 145 K, is known to have similar fragility m ∼ 80−100.78 For the copolymer and blend systems, addition of either PEO3 (as side groups of copolymers) or PEG13 (as a component of blends) to C100P0 leads to a decrease of fragility. Both homopolymers (C100P0 and C0P100) exhibit similar high fragility, but their 3222


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ACS Applied Materials & Interfaces copolymers (C80P20, C57P43, C31P69, and C19P81) are far less fragile. This is presumably owing to the chain packing efficiency,78−80 and suggests that blending rules for fragility will be complicated. The siloxane-based CECA homopolymer (C100P0) naturally has a packing crisis owing to the cyclic carbonates. This gives C100P0 the largest fragility (see Table 3) and presumably makes all the copolymers have lower fragility (weaker temperature dependence of the segmental dynamics), because PEO3 side chains are flexible and can alleviate the packing crisis somewhat.

4. CONCLUSIONS The segmental dynamics of siloxane-based polar copolymers containing cyclic carbonate (CECA) and short PEO3 side chains are reported from dielectric relaxation spectroscopy. The copolymerization with the two pendent groups in the resulting copolymers suppresses crystallization. The effect of concentration of the side chains is clearly observed in the glass transition temperature Tg and dielectric constant εs: the CECArich polymers have higher Tg and εs than the PEO3-rich polymers. The composition dependence of Tg for the polar copolymers is well-described by the Fox equation. Furthermore, the measured εs for the copolymers and blends decreases with increasing PEO3 and PEG13 content, respectively. From the analysis of the static dielectric constants using the Kirkwood− Fröhlich dipole correlation g factor, the CECA homopolymer exhibits g ≥ 1 because overlapping of dipole polarizability volume (Vp/Vm ≥ 1) allows dipoles to show a preference for correlation with neighboring ones. For the PEO3 homopolymer with Vp/Vm ∼ 0.1, however, the dipoles do not overlap, thereby forming more isolated dipoles which interact less with their neighbors (g ∼ 1). Their copolymers (having two different dipole groups around each other and 0.3 ≤ Vp/Vm ≤ 0.9) exhibit εs that decreases with decreasing Vp/Vm as predicted by Onsager. All the copolymers and the blend with PEG13 exhibit a single glassy (β) relaxation process, associated with local chain motions of side chains. The local relaxation is affected by changing side chain content: the relaxation broadens considerably and slows down with increasing CECA side chain fraction, indicating an increasingly heterogeneous environment. All of the homopolymers and copolymers display a single DSC Tg and correspondingly a single α process in DRS, whose extrapolated relaxation time to τα(=1/ωα) = 100 s is in good agreement with the DSC Tg. The α relaxation of the CECA-rich polymers is much narrower than that of the PEO3rich polymer, with its strength increasing systematically with CECA content. The same dynamics are also observed in the CECA homopolymer blend with PEG13. An important question is whether substantial improvement in ionic conductivity can be induced on the utilization of these polar copolymers as plasticizers. Figure 10 displays the conductivities of blends of polysiloxane single-ion Li + conductors17 with the copolymer plasticizers, demonstrating the conductivity was boosted by ∼105 (from 10−11 S/cm to 10−6 S/cm at 303 K). This remarkably enhanced conductivity is due to a combination of glass transition temperature and dielectric constant of the copolymer plasticizers. In contrast, the best oligomers in ref 47 (PEO oligomers with cyclic carbonate end groups) have σDC = 2 × 10−5 S/cm, and a 50:50 mixture of ethylene carbonate and propylene carbonate yielded σDC = 4 × 10−4 S/cm when mixed with a structurally similar 20 wt % ionomer at 303 K. The mixture of small cyclic carbonates has

Figure 10. Ionic conductivity at 303 K for a neat polysiloxane-based single-ion conductor having lithium tetraphenyl borate (14 mol %) and cyclic carbonate (86 mol %) as randomly placed side chains (P14),17 indicated by the dashed horizontal line, and its blends with polar copolymers (80 wt % copolymer plasticizer/20 wt % ionomer),47 indicated by the filled symbols. The best conductivity is at intermediate copolymer composition, owing to the trade-off between PEO3 side chains lowering Tg and CECA side chains raising the dielectric constant.

far superior conductivity because those molecules are likely small enough to travel with Li+, greatly boosting mobility. Therefore, by mixing with these low volatility polar copolymer plasticizers, the single-ion conductors are potential candidates to make safer gel polymer electrolyte with high enough ionic conductivities for lithium ion rechargeable battery separators because the plasticizers can solvate and transport Li+ cations more efficiently.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Department of Energy under Grant BES-DE-FG02-07ER46409. Karen I. Winey (at UPenn), Janna K. Maranas, and Karl T. Mueller (both at Penn State) are thanked for helpful discussions.

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REFERENCES

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Segmental Dynamics and Dielectric Constant of Polysiloxane Polar

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