Viscoelastic and Orientational Relaxation of Linear and Ring Rouse Chains Undergoing Reversible End-Association and Dissociation

For dilute telechelic linear and ring Rouse chains undergoing reversible end-association and dissociation, the time (<i>t</i>) evolution equation was analytically formulated for the bond vector of the subchain (or segment), <b>u</b>^[c](<i>n</i>,<i>t</i>) with <i>n</i> being the subchain index and the superscript c specifying the chain (c = L and R for the linear and ring chains). The end-association of the linear chain (i.e., ring formation) occurs only when the ends of the linear chain come into close proximity. Because of this constraint for the ring formation, the time evolution equation for <b>u</b>^[L](<i>n</i>,<i>t</i>) of the linear chain was formulated with a conceptually new, two-step expansion method: <b>u</b>^[L](<i>n</i>,<i>t</i>) was first expanded with respect to its sinusoidal Rouse eigenfunction, sin­(<i>p</i>π<i>n</i>/<i>N</i>) with <i>p</i> = integer and <i>N</i> being the number of subchains <i>per</i> chain, and then the series of odd sine modes is re-expanded with respect to cosine eigenfunctions of the ring chain, cos­(2απ<i>n</i>/<i>N</i>) with α = integer, so as to account for that constraint. This formulation allowed analytical calculation of the orientational correlation function, <i>S</i>^[c](<i>n</i>,<i>m</i>,<i>t</i>) = <i>b</i>^–2⟨<i>u</i>_<i>x</i>^[c](<i>n</i>,<i>t</i>)<i>u</i>_<i>y</i>^[c](<i>m</i>,<i>t</i>)⟩ (c = L, R) with <i>b</i> being the subchain step length, and the viscoelastic relaxation function, <i>g</i>^[c](<i>t</i>) ∝ ∫₀^<i>N</i><i>S</i>^[c](<i>n</i>,<i>n</i>,<i>t</i>) d<i>n</i>. It turned out that the terminal relaxation of <i>g</i>^[R](<i>t</i>) and <i>g</i>^[L](<i>t</i>) of the ring and linear chains is retarded and accelerated, respectively, due to the motional coupling of those chains occurring through the reaction. This coupling breaks the ring symmetry (equivalence of all subchains of the ring chain in the absence of reaction), thereby leading to oscillation of the orientational anisotropy <i>S</i>^[R](<i>n</i>,<i>n</i>,<i>t</i>) of the ring chain at long <i>t</i> with the subchain index <i>n</i>. The coupling also reduces a difference of the anisotropy <i>S</i>^[L](<i>n</i>,<i>n</i>,<i>t</i>) of the linear chain at the middle (<i>n</i> ∼ <i>N</i>/2) and end (<i>n</i> ∼ 0)

Copper Shell Networks in Polymer Composites for Efficient Thermal Conduction

Thermal management of polymeric composites is a crucial issue to determine the performance and reliability of the devices. Here, we report a straightforward route to prepare polymeric composites with Cu thin film networks. Taking advantage of the fluidity of polymer melt and the ductile properties of Cu films, the polymeric composites were created by the Cu metallization of PS bead and the hot press molding of Cu-plated PS beads. The unique three-dimensional Cu shell-networks in the PS matrix demonstrated isotropic and ideal conductive performance at even extremely low Cu contents. In contrast to the conventional simple melt-mixed Cu beads/PS composites at the same concentration of 23.0 vol %, the PS composites with Cu shell networks indeed revealed 60 times larger thermal conductivity and 8 orders of magnitude larger electrical conductivity. Our strategy offers a straightforward and high-throughput route for the isotropic thermal and electrical conductive composites