Letter pubs.acs.org/macroletters
Thermal Conductivity in the Radial Direction of Deformed Polymer Fibers Yanfu Lu,† Jun Liu,*,†,‡ Xu Xie,† and David G. Cahill† †
Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States ‡ Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695, United States S Supporting Information *
ABSTRACT: Thermal conductivity of polymer fibers in the axial direction has been extensively studied while thermal conductivity in the radial direction Λ remains unknown. In this work, polymer fibers with different molecular arrangements (crystalline, liquid crystalline, and amorphous) were plastically deformed. Λ was measured at engineering strains ε = 0.2−2.3 using time-domain thermoreflectance. Λ decreases with increasing strains for polyethylene (PE) and poly(p-phenylene-2,6-benzobisoxazole) (PBO) fibers and is independent of strain for poly(methyl methacrylate) (PMMA) fibers. The extrapolated thermal conductivity at zero strain is Λ0 ≈ 0.27 Wm−1 K−1 for crystalline PE, Λ0 ≈ 0.29 Wm−1 K−1 for liquid crystalline PBO, and Λ0 ≈ 0.18 Wm−1 K−1 for amorphous PMMA. Λ of PE drops to Λ ≈ 0.14 Wm−1 K−1 at ε = 1.9; Λ of PBO drops to Λ ≈ 0.12 Wm−1 K−1 at ε = 2.1. We attribute the decrease of Λ with ε in crystalline and liquid crystalline fibers to structural disorder induced by plastic deformation. The combination of structural disorder and phonon focusing effects produces a thermal conductivity in deformed PE and PBO fibers that is lower than amorphous PMMA. olymer fibers can have a variety of molecular arrangements, e.g., crystalline, liquid crystalline, or amorphous. Crystalline fibers are usually processed by drawing to obtain aligned molecular chains along the backbones.1 Polyethylene (PE) fibers, as an example, consist of aligned aliphatic carbon backbones. The strength of the covalent bonds in the chain backbone is much stronger than the van der Waals interactions between chains in fibers. Chain alignment creates anisotropic thermal conductivity and tensile strength in crystalline fibers.2−4 In liquid crystalline polymer fibers, rigid molecular structures align in the axial direction. Amorphous fibers have randomly packed molecular chains and thus have isotropic mechanical and thermal properties. Exploring the upper and lower limit of thermal conductivity of polymeric materials is an active area of research.5,6 Polymers with ultrahigh thermal conductivity could potentially be used as thermal management materials, for example, thermal interface materials or lightweight heat spreaders. Recently, Wang et al. measured the thermal conductivities along the axial direction of individual high modulus fibers with ≈20 μm diameters using time-domain thermoreflectance (TDTR).5 The thermal conductivity of fibers along the axial direction is Λx ≈ 2−25 Wm−1 K−1, 1−2 orders of magnitude higher than the thermal conductivity of typical amorphous polymers. To the best of our knowledge, thermal conductivity in the radial direction of polymer fibers, Λ, has not been systematically measured. The typical assumption in prior work is that the thermal conductivity in the radial direction of fibers is the same as in bulk amorphous polymers.7 In amorphous polymers, the
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© XXXX American Chemical Society
random-walk of vibration energy is governed by the van der Waals interactions among chains, which can be described well by the conventional minimum thermal conductivity model (Cahill and Pohl8) and is not directly connected to the details of the molecular structure.4,7,9−11 Due to the highly anisotropic structure of crystalline and liquid crystalline fibers, the conventional minimum thermal conductivity model might not be valid due to phonon focusing effects. Phonon focusing refers to the suppression of the average phonon group velocity in one direction because of the relatively high group velocity in an orthogonal direction and resulting suppression of phonon density of states due to the truncation of the first Brilliouin zone. Recently, Zhen and Dames12 proposed a modified minimum thermal conductivity model that includes the consideration of phonon focusing effects. They found that a significantly suppressed thermal conductivity can be achieved in highly anisotropic materials. We cannot directly measure Λ of polymer fibers using TDTR due to the curved surface of the fiber. In this work, we describe an indention method which flattens the surface and satisfies the measurement requirement of low surface roughness (
