# Parallel model equation ULCC cpVcp

Parallel model:equation(4)λULCC=λcpVcp+λcenoVcenoλULCC=λcpVcp+λcenoVceno

Series model:equation(5)1λULCC=Vcpλcp+Vcenoλceno

Hashin–Shtrikman (H–S) model (upper bound):equation(6)λULCC=λcp+Vceno1λceno-λcp+Vcp3λcp[48]

Hashin–Shtrikman (H–S) model (lower bound):equation(7)λULCC=λceno+Vcp1λcp-λceno+Vceno3λceno[48]

Cubic model:equation(8)λULCC=λcpVceno2/3Vceno2/3-Vceno+VcenoλcenoVceno2/3λcp+1-Vceno2/3[47]where λLLC, λcp, λceno – thermal conductivity ARRY-142886 ULCCs, cement paste, and cenospheres. Vcp and Vceno – volume ratio of cement paste and cenospheres in ULCC.

The ULCC mixtures 1, 2, and 4 and corresponding cement pastes (CP 0.35 and CP 0.45) were used for estimating the thermal conductivity of the cenospheres QK300, and results are shown in Table 7. The ULCC Mixtures 4(VMA), 7, and 8 were not used in the estimation due to possible influence of VMA, fibers, and silane on the thermal conductivity. The ULCC-3 was also not included because of different w/b. However, law of the minimum four mixtures were used to verify if the estimated thermal conductivity of the cenospheres QK300 can be used to estimate the thermal conductivity of the ULCCs.