Abstract
Through systematical experiment design, the physical blowing agent (PBA) mass loss of bio-based polyurethane rigid foam (PURF) in the foaming process was measured and calculated in this study, and different eco-friendly PBA mass losses were measured quantitatively for the first time. The core of the proposed method is to add water to replace the difference, and this method has a high fault tolerance rate for different foaming forms of foams. The method was proved to be stable and reliable through the standard deviations σ1 and σ2 for R1 (ratio of the PBA mass loss to the material total mass except the PBA) and R2 (ratio of the PBA mass loss to the PBA mass in the material total mass) in parallel experiments. It can be used to measure and calculate the actual PBA mass loss in the foaming process of both bio-based and petroleum-based PURF. The results show that the PBA mass loss in PURF with different PBA systems is controlled by its initial mass content of PBA in PU materials ω. The main way for PBA to dissipate into the air is evaporation/escape along the upper surface of foam. This study further reveals the mechanism of PBA mass loss: the evaporation/escape of PBA along the upper surface of foam is a typical diffusion behavior. Its spread power comes from the difference between the chemical potential of PBA in the interface layer and that in the outside air. For a certain PURF system, R1 has approximately linear relationship with the initial mass content of PBA in PU materials ω, which can be expressed by the functional relationship R1 = kω, where k is a variable related to PBA’s own attributes.
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Abbreviations
- a 0 :
-
The ratio of small molecule loss except PBA in PURF, wt%
- D :
-
Diffusion coefficient, m2·s−1
- k :
-
A variable related to PBA’s own characteristics
- m 0 :
-
The mass of small molecule loss except PBA in PURF, g
- m 1 :
-
The actual PBA mass loss, g
- m 2 :
-
The PBA mass in the material total mass, g
- m a :
-
The mass of adding water to the scale mark in the beaker after completion of foaming, g
- m b :
-
Material total mass for the foaming start, g
- m c :
-
Material total mass of the foaming start without PBA, g
- m f :
-
Material total mass for the foaming end, g
- m p :
-
The actual mass of air occupied by increased volume during foaming, g
- m t :
-
The mass of water added to the scale mark in the empty beaker, g
- M d :
-
The molar mass of dry air, kg·mol−1
- M v :
-
The molar mass of moist air, kg·mol−1
- N :
-
Diffusion flux, mol·cm−2·s−1
- P :
-
Total pressure, Pa
- P 0 :
-
Atmospheric pressure, kPa
- P d :
-
Pressure due to dry air, Pa
- P s :
-
The vapor saturation pressure, Pa
- P v :
-
Pressure due to water vapor, Pa
- R 1 :
-
Ratio of the PBA mass loss to the material total mass except the PBA in PURF foaming process, wt%
- R 2 :
-
Ratio of the PBA mass loss to the PBA mass in the material total mass in PURF foaming process, wt%
- R :
-
Molar gas constant, J·mol−1·K−1
- R d :
-
The specific constant of dry air, J·mol−1·K−1
- R v :
-
The specific constant of water vapor, J·mol−1·K−1
- T :
-
Moist air temperature, K
- T w :
-
Water temperature, K
- T x :
-
Given temperature, °C
- V P :
-
The volume of foam actually increased, cm3
- V c :
-
The volume of the beaker below the mark, cm3
- x v :
-
Mole fraction of water vapor
- Z :
-
Compressibility factor
- ρ m :
-
The density of polyurethane material after mixing, g·cm−3
- ρ a :
-
The density of (moist) air, kg·m−3
- ρ w :
-
The density of water, g·cm−3
- ρ da :
-
The density of dry air, kg·m−3
- ρ v :
-
The density of water vapor, kg·m−3
- φ :
-
The relative humidity, wt%
- ω :
-
The initial mass content of PBA in PU materials, wt%
- ∇c :
-
Concentration gradient, mol·cm−4
- σ :
-
Standard deviation
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Wang, H., Lin, L. & Liu, Y. Eco-friendly physical blowing agent mass loss of bio-based polyurethane rigid foam materials. Int J Miner Metall Mater 30, 782–789 (2023). https://doi.org/10.1007/s12613-022-2502-8
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DOI: https://doi.org/10.1007/s12613-022-2502-8