重力作用下糖分子於水溶液中之垂直方向的分布

Abstract

藉由濃度-折射率線性關係，糖水水溶液在重力以及擴散的效應下，其濃度分布圖可以被得知。糖水溶液之折射率的測量，已在此研究分析進行前，由在臺北市中小學科學展覽會中的作品，所提出之替代方式取得，而該方式所得出的結果經過文獻的參照，顯現出是可被信任的。在重量百分濃度 5% 、10% 的糖水溶液中，其濃度分布圖和著名的Perrin 分布是符合的，然而當重量百分濃度為15%、20% 和 25% 時，濃度分布趨勢呈現出和前者不同的凹向性。濃度的不同種的形式在研究分析進行之前會被探討介紹並且順帶提出一種定義稀薄溶液的方式。在研究分析中，我們考慮了溶質之熱力學性的半徑是和糖水溶液局部濃度相依的，因此傳統上之指數分布的濃度函數，在方程式的兩側都和濃度應變量有關。此種有著指數長相但是方程式兩側都為濃度相關的分布在這研究中被命名以及簡稱為DEP。當拿傳統的單純指數分布和DEP去做比較時，我們可以得出在系統內部的粒子大小分布，並且在重新檢視對於一空間中的溶質數目的計數方式後，對於不同初始濃度的糖水水溶液，此研究建立了有效粒子數對高度的分布圖。這些分布圖在所有的濃度，都呈現了凹性的一致性，並且對其做指數擬合也能得出足夠滿意的程度。

Concentration profiles of sucrose solution under the effect of gravity and diffusion are being obtained by concentration-refractive index linear relation. Refractive indices of sucrose solution are beforehand measured with an alternative way proposed by the work displayed in Taipei Primary and Secondary School Science Fair. Method and result of the work are verified to be trustworthy with supports from related literatures. Concentration profiles are found to be resembling representative Perrin’s distribution at nominal concentration 0.05, 0.10 in mass fraction while for nominal concentration 0.15, 0.20, 0.25, profiles exhibit opposite curvature compared with the two previous ones. Various expressions of concentration are introduced before analysis carried out and a criterion of dilute solution is incidentally brought. In the analysis, dependence of solute’s hydrodynamic radius on local concentration of sucrose solution is considered and subsequently classical exponential form has dependent variable on both sides of the equation. A direct comparison between classical exponential function and concentration dependence exponential function, called disguised exponential profile (DEP) in this work, enables us to produce solute size distribution within the system involved and then after reexamining how to count the number of solute in a unit of space, profiles of effective number of sucrose versus height have been built for all nominal concentrations. They are all showing the same pattern and exponential fit put on them is quite satisfying result.