| Abstract: | 晶種結晶技術是化學和製藥相關產業常用的方法之一，用於控制產品的晶體大小分佈並提高產品純度，一些研究皆使用了一個基於質能平衡建立的簡單經驗式來預估不同晶種大小和晶種添加量下所會獲取到的產品晶體大小。然而，該經驗式提供的假設過於理想使其無法應用於實際情況。在這篇研究中，我們希望通過考慮操作變因，如降溫範圍和晶種添加量，來修改這個經驗式，該研究還旨在提供正確的晶種結晶操作方法，其中要設計一個晶種結晶實驗有三個重要因素：（1）亞穩區寬度，（2）晶種製備方法，以及（3）晶種添加量，這三個重要因子皆會極大程度地去影響到實驗的操作方式及最終的結果。我們選擇D-甘露醇在水中的批次冷卻結晶作為我們的操作系統，並使用88至125 μm大小的晶種和自然冷卻，而冷卻溫度範圍和晶種添加量將是每組實驗中最主要的操作參數，在實驗操作期間，透過在不同時間點進行取樣，可以進一步監測晶體成核和晶體生長的行為。在這篇研究中所操作的溫度範圍為40至30 °C、45至30 °C和48至30 °C，而晶種添加量分別為1、3和5 wt%，該添加量是利用實驗所使用的主要材料D-甘露醇在水中的溶解度來去推測理論產率進而計算實際要使用的晶種重量。最終修改後的經驗方程形式會是Lp/Ls=αCs^β，其中Lp是產物晶體的大小，Ls是經種晶體的大小，Cs是晶種的添加量，α=α′exp(-Ea/RTs)，而β在目前的實驗設計中推測是隨應用系統改變的常數，α將是與溫度相關的變數，用於理解溫度對於該系統造成的效應，其中Ea是包含了所有結晶過程發生事件的活化能，R是理想氣體常數，而TS是晶種投入的溫度，在批次結晶的過程中我們使用不同時間點的取樣資料來獲取晶體成核和成長行為，從而揭示過程中發生的情況，進而協助說明實驗得到最終晶體性質。
這裡所建立的改良型晶種結晶經驗式對於實驗產生的晶體大小給予相當準確的預測，在一組使用降溫範圍43到30 °C與晶種添加量4 wt%的驗證實驗中，其結果與預測的數值只有大概0.3 %的偏差，即使是將製程進行放大也能相當準確的預測，偏差大概是4.1 %，因此由此我們可知道這篇研究所進行的實驗是可以放大並可以使用我們所建立的經驗式，只要溫度等其他條件能有良好的控制。另外我們也嘗試將實驗的數據點減少至只有4組實驗，發現了所得到的經驗式其實也可以提供相當好的預測，也表示了即使減少實驗量也能得到相當好的預測。;The seeding technique is a common method used in the chemical or pharmaceutical industry for achieving good control over the crystal size distribution of the product. Some studies are using a simple empirical equation based on mass balance to estimate the product size from different seed crystal sizes and seed loadings. However, the assumptions provided in this empirical equation makes it enable to be applied in practical situations. Here, we want to focus on modifying the empirical equation by considering the operating parameters such as temperature cooling ranges and seed loadings. This study also aims to promote the proper way to do seeding. To design a seeding crystallization experiment, three important factors would need to be determined: (1) metastable zone width, (2) seed crystal preparation method, and (3) seed loading amount. The batch cooling crystallization of D-mannitol in water was chosen as our model system, operating with 88 to 125μm size seeds and natural cooling, the cooling temperature range and seed loading amount will be the main parameters that change in each set of experiments. Crystal nucleation and crystal growth were monitored by sampling at different time points. The temperature ranges were 40° to 30 °C, 45° to 30 °C, and 48° to 30 °C, the seed loading amounts were 1, 3, and 5wt% of the theoretical yield based on the solubility. The final modified empirical equation is in the form of Lp/Ls=αCs^β, where Lp is the product size, Ls is the seed size, Cs is the seed loading, α=α′exp(-Ea/RTs) that is related to the operation temperature range and β is a constant that changes with the system applied. α will be the variant related to the temperature for understanding the temperature effect where Ea is the activation energy include all the events happened in crystallization process, R is the ideal gas constant, and TS is the seeding temperature. Furthermore, sampling data at different time points were used to get the nucleation and growth behavior shedding some lights on what happened in the process.
The modified empirical seeding equation established in this study provides a fairly accurate prediction of the crystal size produced by the experiments. In a set of verification experiments using a cooling range of 43° to 30 °C and a seed loading amount of 4 wt%, the results were consistent, with a deviation of only about 0.3 % from the predicted value. Even when the process is scaled up, the predictions remain quite accurate, with a deviation of about 4.1 %. Therefore, we can conclude that the experiments conducted in this study can be effectively scaled up using our method. The established empirical formula can predict outcomes accurately, provided that temperature and other conditions are well controlled. Additionally, we attempted to reduce the number of experimental data points to just four sets of experiments. The resulting empirical equation still provided good predictions, demonstrating that even with fewer experiments, reliable predictions can be achieved. |
