Temperature dependence of crystal melt coexistence for supported polyethylene filaments

An interface or surface may be considered as a planar perturbation reflected by changes in molecular properties in the direction perpendicular to the interface or surface. As a consequence, predicted by theory and shown by experiments, crystals are often covered by a thin liquid layer of their own melt. Such crystal-melt coexistence can be related to phenomena of surface premelting, secondary nucleation and melting point depression, particularly important for small systems. Here, we employed intermittent-contact mode atomic force microscopy imaging on nanoscopic semi-cylindrical filaments of polyethylene on a substrate to observe that these filaments contained a crystalline core bounded by molten regions of rather uniform width, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow> <mml:mrow><mml:mi>soft</mml:mi></mml:mrow> </mml:msub> <mml:mo>=</mml:mo></mml:math> (9 ± 2) nm at room temperature, which increased reversibly with temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi> <mml:mo>.</mml:mo></mml:math> Filaments smaller than ca. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mn>2</mml:mn> <mml:mo>⋅</mml:mo> <mml:mi>W</mml:mi></mml:mrow> <mml:mrow><mml:mi>soft</mml:mi></mml:mrow> </mml:msub> <mml:mfenced><mml:mrow><mml:mi>T</mml:mi></mml:mrow> </mml:mfenced> </mml:math> were completely molten. The values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>W</mml:mi></mml:mrow> <mml:mrow><mml:mi>soft</mml:mi></mml:mrow> </mml:msub> <mml:mfenced><mml:mrow><mml:mi>T</mml:mi></mml:mrow> </mml:mfenced> </mml:math> compared favorably with theoretically predicted characteristic length scales in the context of nucleation, surface premelting and the melting point depression of finite size crystals. Altogether, we propose that these three phenomena are related and dominated by the intermolecular forces acting at crystal surfaces.