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Table 4 Excess intermolecular free length (Lf E), excess surface tension (σE), excess molar volume (VE m) and excess of pure tributyl phosphate (TBP), toluene, and binary mixture of TBP and toluene at different mole fractions with different frequencies (1–4 MHz) for temperature 303.15 K

From: Physicochemical study of extractants for extraction of rare earth element

Mole fraction of TBP Lf E (m) × 10−7 σE (Nm−1) VE m (m3mol−1) × 10−7 ηE (Nsm−2) × 10−3
X1 1 MHz 2 MHz 3 MHz 4 MHz 1MHZ 2 MHz 3 MHz 4 MHz   
0.0000 0 0 0 0 0 0 0 0 0 0
0.0712 −5.5956 −5.4484 −6.8047 −8.1131 1917.2819 1914.73468 1317.45752 721.1185634 1.71085 −0.19532
0.1692 −9.3571 −0.1040 −0.1167 −0.1144 4205.7083 3594.97437 2985.18984 2980.563116 2.92216 −1.01283
0.2570 −0.1207 −0.1293 −0.1275 −0.1309 5041.4163 4422.12243 4416.07006 4103.943175 3.26293 −1.40152
0.4356 −0.1047 −0.1095 −0.1202 −0.1280 6332.9984 5701.36007 5070.70978 4441.054575 4.91720 −1.56675
0.5052 −0.1047 −0.1081 −0.1182 −0.1182 5918.0402 5283.47561 4649.90730 4330.474264 4.73284 −1.40087
0.5820 −9.9252 −0.1010 −0.1106 −0.1164 5365.6501 4728.40132 4092.15698 3456.922601 4.18167 −1.29212
0.7059 −7.0718 −7.6757 −8.5515 −8.9522 4634.7341 3676.19462 3036.78807 2398.401336 3.28712 −1.13512
0.7781 −5.2872 −5.7421 −6.5675 −6.8693 3956.2692 2995.21656 2354.44540 1714.698945 2.58474 −1.01863
0.8712 −4.4291 −4.0174 −4.7783 −4.9529 2193.7445 1551.11883 909.521706 268.9558308 1.09628 −0.28534
1.0000 0 0 0 0 0 0 0 0 0 0