Thermal Imaging of Block Copolymers with Sub-10 nm Resolution

Abstract

Thermal silicon probes have demonstrated their potential to investigate the thermal properties of various materials at high resolution. However, a thorough assessment of the achievable resolution is missing. Here, we present a probe-based thermal-imaging technique capable of providing sub-10 nm lateral resolution at a sub-10 ms pixel rate. We demonstrate the resolution by resolving microphase-separated PS-b-PMMA block copolymers that self-assemble in 11 to 19 nm half-period lamellar structures. We resolve an asymmetry in the heat flux signal at submolecular dimensions and assess the ratio of heat flux into both polymers in various geometries. These observations are quantitatively compared with coarse-grained molecular simulations of energy transport that reveal an enhancement of transport along the macromolecular backbone and a Kapitza resistance at the internal interfaces of the self-assembled structure. This comparison discloses a tip–sample contact radius of a ≈ 4 nm and identifies combinations of enhanced intramolecular transport and Kapitza resistance.

Microscopic Model to Quantify the Difference of Energy-Transfer Rates between Bonded and Nonbonded Monomers in Polymers

“…In the opposite limit, G b < N 2 nG nb , we obtain and κ∼ , i.e., the Gaussian single-chain structure results in a subdiffusive, spatial energy transport for c / G b < Δ t ≲ c /( nG nb ) and reduces the second term in eq . The subdiffusive scaling was also explicitly found in the numerical simulation of eq for a melt of Gaussian polymers …”

“…Such an assignment of a temperature to a thermodynamically small group of atoms is also employed in eDPD − or eMC , models. We start from a general, energy-transport equation where Greek indices, 0 ≤ α,β < n poly , and Roman indices, 0 ≤ i , j < N , enumerate polymers and monomers, respectively. The prime indicates that the monomer α, i is excluded from the sum over β, j .…”

“…Establishing a link between molecular structure and physical properties is the key for the design of functional materials with tunable behavior. − Here, one of the most important material properties is the ability to conduct heat. , Therefore, the thermal conductivity coefficient, κ, often dictates the use of materials under various environmental conditions, such as electronic packaging, , heat sinks, , interfacial composites, optoelectronics, , and thermoelectric devices. , Traditionally, significant effort has been devoted to study the heat flow in conventional crystalline and amorphous materials, where the typical examples include carbon- or silicon-based bulk materials, inorganic alloys, and quasi-one-dimensional materials. − Recent efforts have also been directed toward solvent-free solid polymeric materials, such as systems consisting of linear (co)­polymers, ,, polymer blends, , cross-linked polymers, , and/or chain-oriented configurations. − …”

“…Because of this stark contrast in the relative strengths between the bonded and the nonbonded interactions, there is also a significant difference between their relative stiffness and concomitant frequencies, i.e., covalent bonds are over 100 times stiffer than vdW contacts . Therefore, the energy-transfer rate between two bonded monomers is expected to be significantly faster than the transport between two nonbonded neighbors. ,,− , Furthermore, κ is directly related to the macroscopic elastic moduli of a material, , and thus the precise information of the component-wise heat flow between different molecular constituents can provide a control strategy for thermal transport behavior.…”

“…12,13 Traditionally, significant effort has been devoted to study the heat flow in conventional crystalline and amorphous materials, where the typical examples include carbon-or silicon-based bulk materials, inorganic alloys, and quasi-one-dimensional materials. 14−16 Recent efforts have also been directed toward solvent-free solid polymeric materials, such as systems consisting of linear (co)polymers, 7,17,18 polymer blends, 6,19 cross-linked polymers, 20,21 and/or chain-oriented configurations. 22−24 Polymers are of particular interest because they provide a flexible molecular architecture that can be used to design lightweight, high-performance materials with extraordinary and unexpected mechanical 25−27 and thermal behavior.…”