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兩種半穿透型水膠之製備以及作為水泥砂漿自養護劑

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(1)國立臺灣師範大學化學系 碩士論文 指導教授:許貫中 博士. 兩種半穿透型水膠之製備以及作為水泥砂漿自養護劑. The Preparation and Application of two Semi-IPN Hydrogel as Self-Curing Agents for Cement Mortars.. 研究生:周宜婷 中 華 民 國 一百 年 七 月.

(2) 摘要 本篇論文為製備兩種半穿透式網狀水膠(semi-IPN)︰polyaspartate/polyacrylamide (Pasp/PAM) and poly(2-(3-carboxypro pan- amido) acetate)/polyacrylamide/polyethylene glycol (PPAA/PAM/ PEG)。Pasp/PAM 水膠係以 Pasp 與丙烯醯胺為反應物,Ammonium persulfate (APS) 為起始劑,N,N’ methylene bisacrylamide (MBA)為交聯劑,經由自由基 聚合反應而得;PPAA/PAM/PEG 水膠係以 PPAA、PEG 與丙烯醯胺為反應物,APS 為 起始劑 MBA 為交聯劑,經由自由基聚合反應而得。聚合得到的兩種水膠均經由量測 分析其 FTIR 光譜確認。另外,量測兩種水膠在水溶液中的吸水率。 (一) Pasp/PAM 水膠 探討不同單體配比、交聯劑和起始劑濃度,對於 Pasp/PAM 水膠在水溶液中吸水 率的影響。將水膠加入水泥漿中,探討水膠含量對於水泥漿的水泥水化程度和凝結時 間的影響;將水膠加入砂漿中,探討水膠含量對於砂漿重量損失、內部濕度、抗壓強 度、長度變化的影響。 研究結果隨著 PAM 含量的增加水膠含量的吸水率漸減;隨著 APS 或 MBA 濃度的 增加水膠含量的吸水率呈現先增加、達最大值後開始減少。當聚合時添加 0.8 mol% APS, 0.5 mol% MBA, Pasp/PAM=1/1,所得的水膠有最大的吸水率,在純水、0.1M NaCl(aq) 和 0.1M CaCl2(aq)的飽和吸水率分別為 159.7g/g, 39.2 g/g 和 32.2 g/g。 隨著水膠含量的增加,7-28 天水泥漿體中的水泥水化程度先增加、達最大值後開 始減少,水膠添加量為 0.2wt%的水泥漿體中的水泥水化程度最高。另外,隨著水膠含 量的增加,水泥漿體的初凝時間變長而終凝時間變短。 隨著水膠含量的增加,砂漿試體的重量損失、長度變化呈現先減少、達最小值後 開始增加;內部濕度、抗壓強度則先增加、達最大值後開始減少。水膠添加量為 0.2wt% 的砂漿試體有最小的重量損失和長度變化,有最高的內部濕度和抗壓強度。隨著水膠 含量的增加,水泥漿體的初凝時間變長而終凝時間變短。. i.

(3) 水膠添加量為 0.2wt%的 28 天砂漿試體的重量損失為 13.03 g,為未添加水膠砂漿 (14.46 g)的 90.1%;抗壓強度為 38.66 MPa,比未添加水膠砂漿(25.31 MPa)高;內部相 對濕度為 56.7 %,比未添加水膠砂漿(52 %)高;長度變化為為-0.19 mm,比未添加水膠 砂漿(-0.210 mm)小。. (二) PPAA/PAM/PEG 水膠 探討 PEG 含量對於 PPAA/PAM/PEG 水膠在水溶液中吸水率的影響。將 0.2wt%水 膠加入水泥漿中,探討 PEG 含量對於水泥漿的水泥水化程度和凝結時間的影響;將 0.2 wt%水膠加入砂漿中,探討水膠含量對於砂漿重量損失、內部濕度、抗壓強度、 長度變化的影響。 研究結果隨著 PEG 含量的增加水膠含量的吸水率漸減。當聚合時添加 1.0 mol% APS, 0.2 mol% MBA, PPAA/PAM=1/1,所得的水膠,在純水、0.1M NaCl(aq)和 0.1M CaCl2(aq)的飽和吸水率分別為 410.8g/g, 65 g/g 和 63 g/g。而 PEG 若接入水膠後其吸水率 會下降,例如聚合時添加 1.0 mol% APS, 0.2 mol% MBA, PPAA/PAM/PEG=1/1/0.5,所 得的水膠,在純水、0.1M NaCl(aq)和 0.1M CaCl2(aq)的飽和吸水率分別為 189.4 g/g, 32.3 g/g 和 29.8 g/g。 隨著 PEG 含量的增加,3-28 天添加 0.2 wt% 水膠的水泥漿體中的水泥水化程度先 增加、達最大值後開始減少,PEG 含量為 20 wt%的水泥漿體(水膠添加量為 0.2wt%)中 的水泥水化程度最高。另外,隨著 PEG 含量的增加,水泥漿體的初凝時間變長而終凝 時間則改變不大。 隨著 PEG 含量的增加,添加 0.2 wt% 水膠的砂漿試體的重量損失、長度變化呈現 先減少、達最小值後開始增加;內部濕度、抗壓強度則先增加、達最大值後開始減少。 PEG 添加量為 20 wt%的砂漿試體(PPAA/PAM/PEG(=1/1/0.2)水膠添加量為 0.2wt%)有 最小的重量損失和長度變化,有最高的內部濕度和抗壓強度。. ii.

(4) 關鍵字:半穿透式水膠、製備、反應物比例、吸水率、水泥漿、水化程度、砂漿、 重量損失、溼度、抗壓強度、長度變化。. iii.

(5) Abstract This thesis has prepared two semi-IPN hydrogels, i.e., polyaspartate/polyacrylamide (Pasp/PAM) and poly(2-(3-carboxypropanamido) acetate)/polyacrylamide/polyethylene glycol (PPAA/PAM/PEG). Pasp/PAM hydrogel was prepared from polyaspartate and acrylamide through free radical polymerization. PPAA/PAM/PEG hydrogel was prepared from poly(2-(3- carboxypropanamido)acetate), polyethylene glycol, and acrylamide through free radical polymerization. Ammonium persulfate (APS) and N,N’ methylene bisacrylamide (MBA) were used as an initiator and a crosslinking agent, respectively. The chemical structures of both hydrogels were verified by FTIR spectroscopy. The water absorbency of these hydrogels in aqueous solutions was measured. 1. Pasp/PAM hydrogel: The effect of reactant ratio, APS and MBA content on the water absorbency of Pasp/PAM hydrogel was studied. The hydrogel was then added in cement pastes and mortars. The effects of the hydrogels on the properties of cementitious materials were determined and discussed. The result indicates that the water absorbency of Pasp/PAM hydrogel increased with decreasing PAM content. Increase of either APS or MBA content increased the water absorbency initially, reached a maximum value, and decreased afterwards. The hydrogel showed the highest water absency when it was prepared with Pasp/PAM=1/1, using 0.8 mol% APS and 0.5 mol% MBA. The saturated water absorbency were 159.7 g/g, 39.2 g/g, and 32.2 g/g, in pure water, 0.1M NaCl(aq), and 0.1 M CaCl2(aq), respectively. At 7 and 28 days, the degree of cement hydration increased with hydrogel content first, reached a maximum value, and decreased afterwards. The cement pastes with 0.2 wt% hydrogel showed the highest degree of cement hydration. Along with increasing hydrogel iv.

(6) content, the initial setting time increased, but the final setting time decreased. Increase of hydrogel content decreased the weight loss and length change of mortars, reached minimum values, and increased subsequently. Increase of hydrogel content increased the relative humidity inside mortars and improved the compressive strength, reached maximum values, and decreased subsequently. The mortars with 0.2 wt% hydrogel showed the lowest weight loss and length change, and the highest relative humidity and compressive strength. 2. PPAA/PAM/PEG hydrogel: The effect of PEG content on the water absorbency of PPAA/PAM/PEG hydrogel was studied. The hydrogel was then added in cement pastes and mortars. The effects of the PEG content on the properties of cementitious materials with 0.2 wt% hydrogel were determined and discussed. The result indicates that the water absorbency of PPAA/PAM/PEG hydrogel decreased with increasing PEG content. The hydrogel showed the highest water absency when it was prepared with PPAA/PAM =1/1, using 1.0 mol% APS and 0.2 mol% MBA. The saturated water absorbency were 410.8 g/g, 65 g/g, and 63 g/g, in pure water, 0.1M NaCl(aq), and 0.1 M CaCl2(aq), respectively. The hydrogel showed the highest water absency when it was prepared with PPAA/PAM/PEG =1/1/0.5, using 1.0 mol% APS and 0.2 mol% MBA. The saturated water absorbency were 189.4 g/g, 32.3 g/g, and 29.8 g/g, in pure water, 0.1M NaCl(aq), and 0.1 M CaCl2(aq), respectively. At 3-28 days, the degree of cement hydration with 0.2 wt% hydrogel increased with PEG content first, reached a maximum value, and decreased afterwards. The cement pastes with 0.2 wt% hydrogel containing 20 wt% PEG showed the highest degree of cement hydration. Along with increasing PEG content, the initial setting time increased, but the final setting time did not change significantly. v.

(7) Increase of PEG content decreased the weight loss and length change of mortars with 0.2. wt% hydrogel, reached minimum values, and increased subsequently. Increase of hydrogel content increased the relative humidity inside mortars and improved the compressive strength, reached maximum values, and decreased subsequently. The mortars with 0.2 wt% hydrogel containing 20 wt% PEG (PPAA/PAM/PEG=5/5/1) showed the lowest weight loss and length change, and the highest relative humidity compressive strength.. Keywords: semi-IPN hydrogel, preparation, reactant ratio, water absorbency, cement paste, degree of cement hydration, mortar, weight loss, humidity compressive strength,length change.. vi.

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(9) 目. 錄. 摘要 ........................................................................................................................ i Abstract ................................................................................................................ iv 目. 錄 ......................................................................................................... vii. 圖. 目 錄 ......................................................................................................... xii. 表. 目 錄 ........................................................................................................ xvi. 第一章 緒論 ......................................................................................................... 1 1-1 研究背景............................................................................................. 1 1-2 研究目的............................................................................................. 3 1-3 研究內容............................................................................................. 4 第二章 文獻回顧 ................................................................................................. 5 2-1 高吸水性水膠簡介 ............................................................................ 5 2-2 水膠之吸水原理 ................................................................................ 6 2-3 影響水膠吸水能力之因素 ................................................................ 8 2-3-1 吸水官能基對水的親和力 ..................................................... 8 2-3-2 離子強度 ................................................................................. 8 2-3-3 水膠的交聯密度 ..................................................................... 9 2-3-4 水溶液的 pH 值 ...................................................................... 9 2-3-5 鹽水溶液的影響 ................................................................... 10. vii.

(10) 2-4 水膠的相關應用 .............................................................................. 11 2-4-1 應答型水膠 ........................................................................... 11 2-4-2 智慧型水膠 ........................................................................... 12 2-5 水泥................................................................................................... 13 2-5-1 波特蘭水泥之組成 ............................................................... 13 2-5-2 水泥之水化 ........................................................................... 14 2-5-3 混凝土收縮變形的種類 ....................................................... 15 2-6 混凝土的養護 .................................................................................. 16 2-6-1 外部養護(external curing) .................................................... 16 2-6-2 內部養護(internal curing) ..................................................... 17 第三章 水膠之合成與實驗流程 ....................................................................... 19 3-1 實驗流程........................................................................................... 19 3-2 實驗材料與實驗設備 ...................................................................... 20 3-2-1 藥品 ....................................................................................... 20 3-2-2 水泥 ....................................................................................... 21 3-2-3 實驗儀器 ............................................................................... 22 3-3 實驗方法........................................................................................... 23 3-3-1 Pasp 之合成........................................................................... 23 3-3-2 Pasp/PAM 水膠合成 ............................................................. 24. viii.

(11) 3-3-3 PPAA 合成 ............................................................................ 25 3-3-4 PPAA/PAM/PEG 水膠合成 .................................................. 26 3-4 聚合物結構分析與鑑定 .................................................................. 27 3-4-1 紅外線(IR)光譜分析 ............................................................ 27 3-4-2 核磁共振(NMR)光譜 ........................................................... 27 3-4-3 水膠吸水率之測量 ............................................................... 27 3-4-4 水膠釋水之測量 ................................................................... 27 3-5 聚合物 Pasp/PAM 對水泥漿之性質分析 ....................................... 28 3-5-1 水泥漿體之拌製 ................................................................... 28 3-5-2 水泥漿體內部濕度之測量 ................................................... 28 3-5-3 水泥漿凝結時間測試 ........................................................... 28 3-5-4 熱示差掃瞄卡量計(DSC)..................................................... 28 3-5-5 粉末 X 光繞射分析(Powder XRD)儀 .................................. 29 3-6 聚合物 Pasp/PAM 對水泥砂漿之性質分析 ................................... 30 3-6-1 水泥砂漿試體之拌製 ........................................................... 30 3-6-2 水泥砂漿試體重量損失量之測量 ....................................... 30 3-6-3 水泥砂漿試體抗壓強度之測量 ........................................... 30 3-6-4 水泥砂漿試體溼度之測量 ................................................... 31 3-6-5 水泥砂漿長度變化之測量 ................................................... 31. ix.

(12) 3-7 實驗配比........................................................................................... 32 第四章 結果與討論 ........................................................................................... 35 4-1 聚合物之結構鑑定 .......................................................................... 35 4-1-1 Pasp 結構鑑定....................................................................... 35 4-1-2 Pasp/PAM 結構鑑定 ............................................................. 35 4-2 反應條件對 Pasp/PAM 水膠吸水率之影響 ................................... 37 4-2-1 單體不同比例合成 Pasp/PAM 水膠對吸水率影響 ............ 37 4-2-2 交聯劑劑量合成 Pasp/PAM 水膠對吸水率影響 ................ 39 4-2-3 起始劑濃度對 Pasp/PAM 水膠吸水率之影響 .................... 40 4-2-4 反應溫度對 Pasp/PAM 水膠吸水率之影響 ........................ 42 4-3 鹽水溶液及 pH 值對於水膠吸水率之影響 ................................... 43 4-3-1 鹽水溶液濃度對水膠吸水率之影響 ................................... 44 4-3-2 pH 值對水膠吸水率之影響 ................................................. 47 4-3-3 水膠在孔隙溶液中的吸水率 ............................................... 49 4-4 水膠對水泥漿性質的影響 .............................................................. 51 4-4-1 XRD 分析(1) ......................................................................... 51 4-4-2 DSC 分析(1) .......................................................................... 56 4-4-3 水膠對水泥漿凝結時間影響 ............................................... 60 4-5 水膠對水泥砂漿性質的影響 .......................................................... 61. x.

(13) 4-5-1 水膠劑量對水泥砂漿重量損失影響 ................................... 61 4-5-2 水膠預吸水水量對水泥砂漿重量損失影響 ....................... 63 4-5-3 水膠劑量對水泥砂漿長度變化之影響 ............................... 65 4-5-4 水膠劑量對水泥砂漿抗壓強度影響 ................................... 67 4-6 PPAA/PAM 水膠添加 PEG 的影響 ............................................... 69 4-6-1 PPAA/PAM/PEG 水膠結構鑑定 .......................................... 69 4-6-2 PEG 合成比例對 PPAA/PAM 水膠吸水率之影響 ............. 71 4-6-3 PEG 比例對於 PPAA/PAM/PEG 水膠在 pore solution 中 吸水率的影響 ................................................................................. 73 4-6-4 XRD 分析(2) ...................................................................... 75 4-6-5 DSC 分析(2)....................................................................... 77 4-6-6 PPAA/PAM/PEG 水膠劑量對凝結時間之影響 ............... 80 4-6-7 PEG 添加方式對水泥砂漿重量損失的影響 ................... 81 4-6-8 PEG 添加方式對水泥砂漿長度變化的影響 ................... 84 4-6-9 PEG 添加方式對於水泥砂漿抗壓強度的影響 .................. 87 第五章 結論 ....................................................................................................... 90 第六章 參考資料 ............................................................................................... 92. xi.

(14) 圖 目 錄 圖 2-1 水膠吸水示意圖........................................................................................ 7 圖 2-2 Ca2+與水膠內-COO-官能基產生螯合 ................................................... 10 圖 2-3 水泥成分在水化過程的變化 ................................................................ 18 圖 3-1 實驗流程圖.............................................................................................. 19 圖 4- 1 Pasp 1H NMR 光譜................................................................................. 36 圖 4- 2 AM、Pasp、Pasp/PAM IR 光譜圖........................................................ 36 圖 4-3 Pasp/PAM 比例對於 Pasp/PAM 水膠在水溶液中吸水率的影響 ........ 38 圖 4-4 MBA 劑量對於 Pasp/PAM 水膠在水溶液中吸水率的影響 ................ 39 圖 4-5 APS 劑量對於 Pasp/PAM 水膠在水溶液中吸水率的影響 ................. 41 圖 4-6 反應溫度對於 Pasp/PAM 水膠在水溶液中吸水率的影響 .................. 42 圖 4-7 鹽水濃度對於 Pasp/PAM 水膠在鹽水中吸水率的影響 ...................... 45 圖 4-8 Pasp/PAM 在純水 NaOH 和 Ca(OH)2 溶液中的 IR 光譜圖 ................. 45 圖 4-9 P1222 水膠浸泡於 0.1M NaCl(aq)後的 SEM (×600)圖 ......................... 46 圖 4-10 P1222 水膠浸泡於 0.1M NaCl(aq)後的 SEM (×1200)圖..................... 46 圖 4-11 P1222 水膠浸泡於 0.1M CaCl2(aq)後的 SEM (×600)圖 ...................... 46 圖 4-12 P1222 水膠浸泡於 0.1M CaCl2(aq)後的 SEM (×1200) 圖.................. 46 圖 4-13 P1222 水膠浸泡於 water 後的 SEM (×600)圖 .................................... 46 圖 4-14 P1222 水膠浸泡於 water 後的 SEM (×1200) 圖 ................................ 46. xii.

(15) 圖 4-15 pH 值對於 Pasp/PAM 水膠在吸水率的影響 ...................................... 48 圖 4-16 Pasp 的滴定曲線圖 ............................................................................... 48 圖 4-17 浸泡時間對於 P1222 水膠吸水率的影響 ........................................... 50 圖 4-18 P1222 水膠在 pore solution 不同浸泡時間的 IR 光譜圖 ................... 50 圖 4-19 添加不同劑量 Pasp/PAM 水膠水泥漿的 XRD 圖(齡期 3 天) ........... 52 圖 4-20 添加不同劑量 Pasp/PAM 水膠水泥漿的 XRD 圖(齡期 7 天) ........... 52 圖 4-21 添加不同劑量 Pasp/PAM 水膠水泥漿的 XRD 圖(齡期 28 天) ......... 53 圖 4-22 未添加 Pasp/PAM 水膠水泥漿的 XRD 圖(齡期 3、7、28 天) ......... 53 圖 4-23 添加 0.1wt% Pasp/PAM 水膠水泥漿的 XRD 圖(齡期 3、7、28 天) 54 圖 4-24 添加 0.2wt% Pasp/PAM 水膠水泥漿的 XRD 圖(齡期 3、7、28 天) 54 圖 4-25 添加 0.4wt% Pasp/PAM 水膠水泥漿的 XRD 圖(齡期 3、7、28 天) 55 圖 4-26 未添加 Pasp/PAM 水膠水泥漿的 DSC 圖(齡期 3、7、28 天).......... 57 圖 4-27 添加 0.1wt% Pasp/PAM 水膠水泥漿的 DSC 圖(齡期 3、7、28 天) 57 圖 4-28 添加 0.2wt% Pasp/PAM 水膠水泥漿的 DSC 圖(齡期 3、7、28 天) 58 圖 4-29 添加 0.4wt% Pasp/PAM 水膠水泥漿的 DSC 圖(齡期 3、7、28 天) 58 圖 4-30 P1222 Pasp/PAM 水膠劑量對於氫氧化鈣含量的影響 ...................... 59 圖 4-31 Pasp/PAM 水膠添加量對於砂漿中內部濕度的影響 ......................... 59 圖 4-32 P1222 Pasp/PAM 水膠劑量對於水泥漿凝結時間的影響 .................. 60 圖 4-33 齡期對於砂漿重量損失的影響 ........................................................... 62. xiii.

(16) 圖 4-34 Pasp/PAM 水膠添加量對於砂漿重量損失的影響 ............................. 62 圖 4-35 齡期對於砂漿重量損失的影響 ........................................................... 64 圖 4-36 Pasp/PAM 水膠預吸水水量對於砂漿重量損失的影響 ..................... 64 圖 4-37 齡期對於砂漿乾縮量的影響 ............................................................... 66 圖 4-38 Pasp/PAM 水膠劑量對於砂漿乾縮量的影響 ..................................... 66 圖 4-39 齡期對於砂漿抗壓強度的影響 ........................................................... 68 圖 4-40 Pasp/PAM 水膠劑量對於砂漿抗壓強度的影響 ................................. 68 圖 4-41 PAM、PPAA、PEG 和 PPAA-PAM-PEG 的 IR 光譜 ........................ 70 圖 4-42 不同 PEG 比例對於 PPAA/PAM/PEG 水膠在水溶液中飽和吸水率的 影響 ..................................................................................................................... 72 圖 4-43 PEG 劑量對於 PPAA/PAM/PEG 水膠在 pore solution 中釋水率的影 響 ......................................................................................................................... 74 圖 4-44 添加不同 PEG 劑量水膠水泥漿的 XRD 圖(齡期 3 天) .................... 75 圖 4-45 添加不同 PEG 劑量水膠水泥漿的 XRD 圖(齡期 7 天) .................... 76 圖 4-46 添加不同 PEG 劑量水膠水泥漿的 XRD 圖(齡期 28 天) .................. 76 圖 4-47 添加不同 PEG 劑量水膠水泥漿的 DSC 圖 (齡期 3 天) ................... 77 圖 4-48 添加不同 PEG 劑量水膠水泥漿的 DSC 圖 (齡期 7 天) ................... 78 圖 4-49 添加不同 PEG 劑量水膠水泥漿的 DSC 圖 (齡期 28 天) ................. 78 圖 4-50 PEG 水膠劑量對於氫氧化鈣含量的影響 ........................................... 79. xiv.

(17) 圖 4-51 PEG 水膠劑量對於凝結時間的影響 ................................................... 80 圖 4-52 內添加 PPAA/PAM/PEG 的水膠之水泥砂漿在不同齡期的重量損失82 圖 4-53 內添加不同含量 PPAA/PAM/PEG 的水膠之水泥砂漿的重量損失 . 82 圖 4-54 外添加 PPAA/PAM/PEG 的水膠對水泥砂漿在不同齡期的重量損失83 圖 4-55 外添加不同含量 PPAA/PAM/PEG 的水膠之水泥砂漿的重量損失 . 83 圖 4-56 內添加 PPAA/PAM/PEG 的水膠之水泥砂漿在不同齡期的乾縮量 . 85 圖 4-57 內添加不同含量 PPAA/PAM/PEG 的水膠之水泥砂漿的乾縮量 ..... 85 圖 4-58 外添加 PPAA/PAM/PEG 的水膠之水泥砂漿在不同齡期的乾縮量 . 86 圖 4-59 外添加不同含量 PPAA/PAM/PEG 的水膠之水泥砂漿的乾縮量 ..... 86 圖 4-60 內添加 PPAA/PAM/PEG 的水膠之水泥砂漿在不同齡期的抗壓強度88 圖 4-61 內添加不同含量 PPAA/PAM/PEG 的水膠之水泥砂漿的抗壓強度 . 88 圖 4-62 外添加 PPAA/PAM/PEG 的水膠之水泥砂漿在不同齡期的抗壓強度89 圖 4-63 外添加不同含量 PPAA/PAM/PEG 的水膠之水泥砂漿的抗壓強度 . 89. xv.

(18) 表 目 錄 表 2-1 卜特蘭水泥之主要成份 ......................................................................... 13 表 2-2 水泥水化反應之方程式 ......................................................................... 14 表 3-1 水泥之組成與性質 ................................................................................. 21 表 3-2 水膠合成之條件...................................................................................... 32 表 3-3 水泥砂漿拌合之條件 ............................................................................. 33 表 3-4 水泥漿拌合之條件 ................................................................................. 34 表 3-5 水泥漿凝結時間之條件 ......................................................................... 34 表 4-1 Pore solution 之組成 .............................................................................. 49 表 4-2 水泥漿體中各成分的 XRD 數據 ........................................................... 55 表 4-3 各水化產物之吸收峰位置 ..................................................................... 56 表 4-4 添加不同 P1222 水膠劑量的氫氧化鈣積分值 ..................................... 59 表 4-5 PEG 水膠合成比例 ................................................................................. 71 表 4-6 添加不同 PEG 劑量的氫氧化鈣積分值 ................................................ 79. xvi.

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