Thermal Conductivity of Cellulose Fibers in Different Size Scales and Densities

Abstract

Considering the growing use of cellulose in various applications, knowledge and understanding of its physical properties become increasingly important. Thermal conductivity is a key property, but its variation with porosity and density is unknown, and it is not known if such a variation is affected by fiber size and temperature. Here, we determine the relationships by measurements of the thermal conductivity of cellulose fibers (CFs) and cellulose nanofibers (CNFs) derived from commercial birch pulp as a function of pressure and temperature. The results show that the thermal conductivity varies relatively weakly with density (ρ sample = 1340–1560 kg m –3 ) and that its temperature dependence is independent of density, porosity, and fiber size for temperatures in the range 80–380 K. The universal temperature and density dependencies of the thermal conductivity of a random network of CNFs are described by a third-order polynomial function (SI-units): κ CNF = (0.0787 + 2.73 × 10 –3 · T – 7.6749 × 10 –6 · T 2 + 8.4637 × 10 –9 · T 3 )·(ρ sample /ρ 0 ) 2 , where ρ 0 = 1340 kg m –3 and κ CF = 1.065·κ CNF . Despite a relatively high degree of crystallinity, both CF and CNF samples show amorphous-like thermal conductivity, that is, it increases with increasing temperature. This appears to be due to the nano-sized elementary fibrils of cellulose, which explains that the thermal conductivity of CNFs and CFs shows identical behavior and differs by only ca. 6%. The nano-sized fibrils effectively limit the phonon mean free path to a few nanometers for heat conduction across fibers, and it is only significantly longer for highly directed heat conduction along fibers. This feature of cellulose makes it easier to apply in applications that require low thermal conductivity combined with high strength; the weak density dependence of the thermal conductivity is a particularly useful property when the material is subjected to high loads. The results for thermal conductivity also suggest that the crystalline structures of cellulose remain stable up to at least 0.7 GPa.

Thermal Conductivity of Porous and Dense Networks of Cellulose Nanocrystals

“…Such scaling, with ρ 0 = 1340 kg m −3 , is shown in Figure 6 together with corresponding scaling for CF and CNF. 7 The scaled results, κ 0 (T), of CNC not only reveal a slight variation for the three isobars but also that the temperature dependence is strikingly similar to κ 0 (T) of CF and CNF. The results for CF and CNF show virtually identical variation, and the data sets for κ 0 (T) of CF and CNF can be described by the same third-order polynomial with a κ 0 shift of the function by about 6%.…”

“…Therefore, the sample was initially pressurized up to 0.06 GPa, which produces a well compacted but still porous sample. 7 Thereafter, it was temperature cycled isobarically down to ca. 100 K to study the temperature dependence of κ of porous CNC (the pressure of 0.06 GPa is typically the minimum pressure required to ensure good thermal contact between a soft solid sample and the wire probe, and it was the pressure used in the previous study of CNF and CF samples 7 ).…”

“…7 Thereafter, it was temperature cycled isobarically down to ca. 100 K to study the temperature dependence of κ of porous CNC (the pressure of 0.06 GPa is typically the minimum pressure required to ensure good thermal contact between a soft solid sample and the wire probe, and it was the pressure used in the previous study of CNF and CF samples 7 ). Subsequently, the sample was pressure cycled to 0.7 GPa, with an intermediate temperature cycle at 0.5 GPa, to form and study the κ behavior of nonporous CNC.…”

“…5,9 The previously measured results for κ(T) of CNF and CF under high-pressure conditions led us to the same conclusion. 7 That is, the amorphous-like κ(T) of CNF and CF is due to the nano-sized building blocks of the fibers, which limits the phonon mean free path to a few nanometers; it can only be significantly longer for heat flow along the fibers.…”

“…Previous studies also show that κ of CF and CNF increases with increasing temperature. 7,9 This behavior is normally associated with amorphous polymers, whereas κ of crystalline and semicrystalline polymers commonly decreases with temperature at room temperatures. 10 More specifically, at temperatures above the low-temperature range where crystal sizes limit phonon (heat quanta) propagation (above ∼100 K).…”