• Applied Chemistry for Engineering
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• v.17 no.5
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• pp.443-450
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• 2006

Micelles have been used in many applications. In these applications it is of prime importance to know how the critical micelle concentration (CMC), above which the micelles are formed, depends on temperature. Up to date polynomial functions of temperature have been used to describe temperature dependence of CMC. In this article it is shown that such polynomials are inadequate tools to express thermal behavior of CMC. Hence, new equations of CMC(T) have been derived on the basis of rigorous thermodynamic equations and experimental observations on CMCs. The new equations fit CMC data excellently, and further they lead to a power law for the CMC. The exponent of the power-law expression is 2 irrespective of surfactant systems, which points to the generality of newly found equations.

• Korean Journal of Soil Science and Fertilizer
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• v.25 no.1
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• pp.16-25
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• 1992

A pot experiment was conducted to understand effect of soil temperaute on soybean shoot and root growth, and its relations to nutrient uptake including phosporus and potassium. Pregerminated soybean seedlings, Paldal cultivar, were planted for 43 days on the pots with Ihyeon silt loam and Samgag sandy loam in the temperature controled water baths at 17, 25 and $32^{\circ}C$. Shoot and root samples were taken at four times and analyzed. Shoot and root dry matter weights were heavier as higher soil temperaure. The root dry matter increased faster than shoot at earlier period. Shoot dry matter weights grown at 17 and $25^{\circ}C$ showed little difference between two soils, however, those grown in silt loam at $32^{\circ}C$ were heavier than sandy loam. The total lengths of roots were longer as higher soil temperature, and longer in silt loam than sandy loam. The roots grown in sandy loam at low temperature were thicker than the roots grown in silt loam at high temperature. The uptakes of phosphorus and potassium were higher as higher tempeature with same trend with dry matter. The uptake rate of unit root surface area was higher in sandy loam soil than silt loam. The uptake rates showed strong dependence on soil temperature as well as dependence of water uptake rate. Based on Dalton and Gardner model, at high temperature the dependence trend of phosphorus and potassium on soil temperature showed with active uptake model, while at low temperature the dependence showed without active uptake model.