| 摘要: | 種晶技術在批次結晶中是一種很有效的方法用來控制晶體的大小與尺寸均一性，而晶體大小的控制對於後續過濾及乾燥製程操作有很大的影響。在許多種晶技術相關的研究中，經驗方程式被用來理解晶種尺寸、晶種添加量與晶體尺寸間的關係，然而此關係式過於理想與簡略，且許多製程控制或操作參數皆被忽略。本研究的目的是透過不同參數的實驗設計來改善種晶方程式，操作溫度與過飽和度將納入考量來推導出甘露醇系統在批次冷卻結晶中種晶的方程式，用作預測不同實驗的晶體尺寸。為瞭解甘露醇在水中的結晶情形，第一部分的研究透過不同初始過飽和度: 1.45, 1.38, 1.32 與 1.25 所獲得的成核誘發時間，甘露醇的初級成核結晶動力學與熱力學參數例如:界面能、臨界Gibbs能障、成核速率、成核臨界尺寸可藉由經典成核理論來求得。第二部份的實驗中，我們調整三種種晶參數進行晶種尺寸為88 – 125 μm的批次冷卻結晶實驗：（1）冷卻溫度範圍，（2）晶種添加量，和（3）由溫度影響的過飽和度。實驗結果發現，在較低的冷卻溫度範圍30 至 15 °C以及25 至 5 °C時，晶體添加量為1, 3, 及5 重量百分比皆得到單一峰的粒徑分佈且甘露醇平均尺寸約200 μm。本研究假設出的種晶經驗方程式為: Lp/Ls =((1+Cs)/Cs )^(1/n) ，其中n=A′(C0-C* ) exp((-Ea)/kT)，由同一冷卻範圍且不同晶種添加量的實驗可得n值。實驗結果得到n值分別為5.27，7.81及11.98 當冷卻範圍為35 至 25 °C ，30 至 15 °C及25 至 5 °C。由n值可計算出甘露醇系統中二次成核的活化能Ea = 172.55×10^-22 焦耳/晶核與指數前因子A′= 1.41×10^-3 毫升溶液/毫克。甘露醇在水中的種晶經驗方程式成功地被建立，並且在後續實驗調整晶種尺寸為44 – 88 μm及125 – 177 μm的實驗中被良好地驗證。;The seeding technique is an effective method to control the size and size uniformity of crystals in the batch cooling crystallization. Crystal size has a great influence on the downstream process such as filtration and drying. In many studies related to seeding, a simple empirical equation based on mass balance is used to understand the relationship between seed crystal size, seed loading, and crystal size. However, this relationship is too ideal and simplified, and many process control or operation parameters are ignored. The purpose of this study is to modify the seeding equation by designing experiments with different operating parameters. Temperature cooling range and supersaturation will be taken into consideration to derive an equation for seeding in the D-mannitol system in batch cooling crystallization, which is used to predict the crystal size for different experiments. To understand the crystallization mechanism of D-mannitol in water, the first part of the study was conducted through the nucleation induction period obtained with different initial degrees of supersaturation of: 1.45, 1.38, 1.32 and 1.25. The kinetics and thermodynamic parameters of the primary nucleation D-mannitol system such as interface energy, critical Gibbs energy barrier, nucleation rate, and critical size of nucleation can be obtained by Classical Nucleation Theory (CNT). In the second part of the experiment, we adjusted the three seeding parameters to conduct the batch cooling crystallization experiments with seed crystal sizes ranging from 88 to 125 μm: (1) cooling temperature range, (2) seed loading, and (3) supersaturation. The experimental results found that at the lower temperature cooling ranges of 30 to 15 °C and 25 to 5 °C with seed loading of 1, 3, and 5 wt% all obtained a uni-modal size distribution of D-mannitol crystal and the mean crystal size was about 200 μm. The modified seeding empirical equation was: Lp/Ls =((1+Cs)/Cs )^(1/n), where n=A′(C0-C* ) exp((-Ea)/kT). The values of n could be obtained from experiments with the same temperature cooling range with different seed loadings. The experimental results showed that n was 5.27, 7.81, and 11.98 with the temperature cooling ranges of 35 to 25 °C, 30 to 15 °C, and 25 to 5 °C, respectively. From the value of n, the activation energy of secondary nucleation in the D-mannitol system could be calculated as Ea = 172.55 × 10-22 J·nucleus-1 and the exponential pre-factor A′ = 1.41 × 10-3 mL of solution/mg. The empirical equation for D-mannitol seeding in water was successfully established and well-validated in subsequent experiments adjusting the seed sizes to 44 – 88 μm and 125 – 177 μm. |
