Article pubs.acs.org/Macromolecules
Thermal Conductivity, Heat Capacity, and Elastic Constants of WaterSoluble Polymers and Polymer Blends Xu Xie,*,† Dongyao Li,†,‡ Tsung-Han Tsai,† Jun Liu,† Paul V. Braun,† and David G. Cahill*,†,‡ †
Department of Materials Science and Engineering and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States ‡ International Institute for Carbon Neutral Energy Research, Kyushu University, Fukuoka 819-0395, Japan S Supporting Information *
ABSTRACT: We use time-domain thermoreflectance (TDTR), and the generation and detection of longitudinal and surface acoustic waves, to study the thermal conductivity, heat capacity, and elastic properties of thin films of poly(vinyl alcohol) (PVA), poly(acrylic acid) (PAA), polyacrylamide (PAM), poly(vinylpyrrolidone) (PVP), methyl cellulose (MC), poly(4-styrenesulfonic acid) (PSS), poly(N-acryloylpiperidine) (PAP), poly(methyl methacrylate) (PMMA), and a polymer blend of PVA/PAA. The thermal conductivity of six water-soluble polymers in the dry state varies by a factor of ≈2, from 0.21 to 0.38 W m−1 K−1, where the largest values appear among polymers with a high concentration of hydrogen bonding (PAA, PAM, PSS). The longitudinal elastic constants range from 7.4 to 24.5 GPa and scale linearly with the shear elastic constants, suggesting a narrow distribution of Possion’s ratio 0.35 < ν < 0.40. The thermal conductivity increases with the average sound velocity, as expected based on the model of the minimum thermal conductivity. The thermal conductivity of polymer blends of PVA (0.31 W m−1 K−1) and PAA (0.37 W m−1 K−1) is in agreement with a simple rule of mixtures.
1. INTRODUCTION The thermal and elastic properties of polymers are critical engineering considerations for the design of flexible substrate,1,2 interfacial binders,1,3 and encapsulation layers4,5 for electronics. While high thermal conductivity is favorable for thermal management,1,6 thermal transport in polymers is generally limited by structural disorder and weak interactions between chains. Typical glassy polymers have a low thermal conductivity of Λ ≈ 0.2 W m−1 K−1. Recently, Kim et al. reported an improvement of thermal conductivity of amorphous polymers by a factor of ≈7 (from ≈0.2 to >1.5 W m−1 K−1), in blends of poly(N-acryloyl piperidine) (PAP) and poly(acrylic acid) (PAA).7 A more modest enhancement of a factor of ≈2 was observed in blends of PAP and poly(vinyl alcohol) (PVA). The authors of ref 7 attributed the enhancement to the creation of a homogeneously distributed thermal network, in which the intermolecular hydrogen bonds replace the weak van der Waals interactions to improve the interchain thermal transport. The significant enhancement in thermal conductivity reported in ref 7 and attributed to an increased strength of intermolecular interactions stands in contrast to the relatively modest pressure dependence of the thermal conductivity of poly(methyl methacrylate) (PMMA).8 A pressure of 10 GPa is required to increase the thermal conductivity of PMMA by a factor of ≈2.5. Because of the anharmonicity of the © XXXX American Chemical Society
intermolecular interactions, the longitudinal modulus of PMMA increases to ≈80 GPa at a pressure of 10 GPa, a factor of ≈3 higher than the longitudinal modulus of any of the polymers studied here and comparable to the modulus of aligned fibers of Kevlar. We have not been able to reproduce the large enhancement of thermal conductivity in PAP/PAA blends reported in ref 7. We find that thin films of PAP/PAA blends near the mixing ratio where significant increase of thermal conductivity was reported7 are phase separated. In the present work, we apply a laser-based pump−probe technique, time-domain thermoreflectance (TDTR), to measure the thermal conductivity and heat capacity of several common water-soluble polymers and one of their blends. Water-soluble polymers generally have a high concentration of hydrophilic groups (e.g., alcohol or carboxylic acid groups)9 that enable the formation of hydrogen bonds. We use measurements of longitudinal and surface acoustic waves to determine the elastic constants and compare the changes in elastic constants to the changes in thermal conductivity. The thermal conductivity of six water-soluble polymers ranges from 0.21 to 0.38 W m−1 K−1, where the highest values appear Received: November 15, 2015 Revised: January 13, 2016
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DOI: 10.1021/acs.macromol.5b02477 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
(Na2SO4, Fisher Scientific), the residue is purified by column chromatography (hexane:ethyl acetate ≈1:1, Fisher Scientific) to yield clear colorless or light yellow oil. Gel permeation chromatography (GPC) relies on a system composed of a Waters 515 HPLC pump, an autosampler (Thermoseparations Trace series AS100), a series of three Waters HR Styragel columns (7.8 ft, 300 mm, HR3, HR4, and HR5), and a Viscotek TDA Model 300 triple detector array, in HPLC grade THF (flow rate = 1.0 mL min−1) at 30 °C. We use NMR spectroscopy (Varian 400 MHz) to verify the composition of AP. The spectra contain H NMR (400 MHz, CDCl3): δ 6.49 (dd, 1H, CHCH2), 6.13 (d, 1H, CHCHtrans), 5.52 (d, 1H, CHCHcis), 3.53−3.50 (m, 4H, CH2−N), 1.59−1.53 (m, 4H, CH2), 1.49−1.43 (m, 2H, CH2). 13C NMR (400 MHz, CDCl3): 165.05, 127.92, 126.79, 46.73, 42.84, 26.44, 25.35, 24.38. To synthesize the polymer PAP from the monomer AP, AP (10 mml) and 2,2′-azobis(2-methylpropionitrile) (AIBN, 0.06 mmol, Sigma-Aldrich) are dissolved in anisole (7 mL, Sigma-Aldrich), followed by purging with N2 for 30 min. The polymerization is carried out at 65 °C for 24 h. The PAP polymer (Mw = 49 kg mol−1) is precipitated in diethyl ether and dried under vacuum. 2.2. Fabrication of Polymer Thin Films. We spin-cast thin films of polymers on Si substrates followed by solvent evaporation. We adjust the polymer concentration, solvent, and spin-coating speeds to optimize the morphology and thickness for different measurements. Dispersion of each water-soluble polymer (PVA 5 wt %, PAA 3 wt %, PAM 3 wt %, PVP 6 wt %, MC ≈2 wt %, PSS 6 wt %) in DI water followed by stirring at ≈60 °C for several hours ensures full dissolution. PAP (3 wt %) is dissolved in toluene at ≈80 °C. To form polymer blends of PAP and PAA, and blends of PVA and PAA, we first prepare polymer solutions of the individual polymers by dissolving the polymer in dimethylformamide (DMF) at ≈150 °C for 10 min while stirring, followed by cooling to room temperature. We prepare solutions for spin-coating by mixing PAP (1 wt %) with PAA (1 wt %) or PVA (3 wt %) with PAA (3 wt %) at different ratios. The blends are then heated to ≈150 °C for 5 min. Prior to spin-coating, we prepare the Si substrates by rinsing sequentially with acetone (sonication for 5 min), IPA (sonication for 5 min), water, and IPA, followed by drying with nitrogen gas. Finally, the Si substrates are exposed to a UV ozone treatment for 20 min that produces a hydrophilic surface. Spin-coating with speeds ranging from 3000 to 5000 rpm for 60 s results in polymer films with thicknesses between 80 and 150 nm. The thin films are initially annealed in air at 90 °C (for polymers dissolved in water and toluene) or 110 °C (for PVA/PAA blends dissolved in DMF) for 30 min and then baked at 60 °C in a vacuum chamber at a pressure of 16 h. To obtain cross-linked PAA, the spin-coated PAA film is baked at 200 °C (30 min) followed by the same vacuum annealing. The cross-linked film becomes insoluble in water due to anhydride formation.14−16 Thin films of PAA, PVP, PAM, PSS, MC, PMMA, and PAP prepared by spin-casting and annealing are generally considered amorphous, and PVA film is partially crystalline.17,18 We do not attempt to determine the crystallinity of the thin films of polymers here and assume all polymer layers are isotropic for all the measurements. The surface roughness of the as-prepared polymers is 25 μm2.
among polymers that form intra- and interchain hydrogen bonds (PAA, PAM, PSS). The elastic constants suggest a narrow distribution of Possion’s ratio from 0.35 to 0.4. We also study miscible blends of PAA and PVA.10−12 Within the measurement uncertainties, the thermal conductivity of PAA/ PVA blends follows a simple rule of mixtures.
2. SAMPLE PREPARATION AND CHARACTERIZATION 2.1. Polymer Synthesis and Preparation. Figure 1 presents the chemical structures of the six water-soluble polymers we investigated:
Figure 1. Chemical structures of the six water-soluble polymers (PVA, PAA, PAM, PVP, MC, PSS) and two non-water-soluble polymers (PMMA, PAP) investigated for their thermal conductivity, heat capacity, and elastic constants. poly(vinyl alcohol) (PVA, 80% hydrolyzed, Mw = 10 kg mol−1, SigmaAldrich); poly(acrylic acid) (PAA, Mv = 450 kg mol−1, Sigma-Aldrich); polyacrylamide (PAM, Mn = 40 kg mol−1, Sigma-Aldrich); poly(vinylpyrrolidone) (PVP, Mw = 25 kg mol−1, Sigma-Aldrich); methyl cellulose (MC, viscosity: 4000 cP, Sigma-Aldrich); and poly(4styrenesulfonic acid) (PSS, Mw = 75 kg mol−1, Sigma-Aldrich). These polymers are either synthetic (PVA, PAA, PAM, PVP, PSS) or derived from natural sources (MC). We also include two waterinsoluble polymers, poly(methyl methacrylate) (PMMA 950K A2, MicroChem) and poly(N-acryloylpiperidine) (PAP, laboratory synthesis) (Figure 1), in the measurements for comparisons. We synthesize PAP to make comparisons with ref 7. Our approach starts with the synthesis of N-acryloylpiperidine (AP) monomers using a modification of procedures described previously.13 A solution of acryloyl chloride (0.24 mol, Sigma-Aldrich) in anhydrous dichloromethane (DCM) (100 mL, Sigma-Aldrich) is added to a solution of piperidine (0.22 mol, Sigma-Aldrich) and triethylamine (0.24 mol, Sigma-Aldrich) in anhydrous DCM (150 mL) at 0 °C. After 30 min, the solution is warmed to room temperature and stirred for 4 h. The resulting solution is filtered to remove the precipitate. A rotary evaporator subsequently removes the solvent in the solution. The residue is dissolved in 100 mL of ethyl acetate (Fisher Scientific) followed by sequentially washing with 5% hydrogen chloride (HCl) solution (3 times of 100 mL, Fisher Scientific), saturated sodium bicarbonate (NaHCO3) solution (100 mL, Fisher Scientific), and brine (100 mL, Fisher Scientific). After drying over sodium carbonate
3. MEASUREMENTS AND ERROR ANALYSIS 3.1. Thermal Conductivity and Heat Capacity. Thermal conductivity (Λ) and volumetric heat capacity (C) of polymer thin films are derived from TDTR data acquired at multiple modulation frequencies.19−22 We use spectroscopic ellipsometry (J.A. Woollam VASE) to measure the thickness (≈100 nm) of the polymer films with an uncertainty
