200938294 六、發明說明： 【發明所屬之技術領域】 本發明係指製造膠態金屬氧化物粒子之方法。 【先前技術】 在所屬領域中持續努力以高效能方式來形成膠態金屬氧 化物粒子。 在所屬領域中，具有在最佳化裝置利用時以高效能方式 改良來形成膠態金屬氧化物粒子之方法的需求。 ’【發明內容】 本發明提供形成膠態金屬氧化物粒子之新方法。所揭露 形成膠態金屬氧化物粒子之方法，在接近最適方法條件 下，能使膠態金屬氧化物粒子形成，以便以非常有效率的 方式形成膠態金屬氧化物粒子。再者，所揭露的形成膠態 金屬氧化物粒子之方法，由於能夠減少形成膠態金屬氧化 物粒子所需之反應週期，而能使反應槽最適利用。 p 所揭露形成膠態金屬氧化物粒子之方法，其包括添加一 種或多種反應物至反應槽的步驟，其中該添加一種或多種 反應物之步驟考慮不同的原位反應條件，其包括但不受限 於（i)反應槽中粒子成核速率，（ii)存在的金屬氧化物粒子之 上的金屬氧化物沉積速率（例如：晶種金屬氧化物粒子及/ 或成核金靥氧化物粒子，及/或（Hi)反應槽中金屬氧化物粒 子的生長（例如：晶種金屬氧化物粒子及/或成核金屬氧化物 粒子）中的至少一個。 在一個範例的具體實施例中，製造膠態金屬氧化物粒子 200938294 之方法包括以金屬氧化物質量添加速率將反應性金屬氧化 物添加至反應槽的步驟，該金屬氧化物質量添加速率係基 於數學模式，該數學模式考慮至少一個的（i)粒子成核速 率，（ii)存在的金屬氧化物之上的金屬氧化物粒子沉積速 率，及/或（iii)反應槽中金屬氧化物粒子的生長，其中增加 該金屬氧化物質量添加速率作爲反應時間的函數。另一個 具體實施例中，在至少一部分的該反應週期期間，該添加 速率每小時每1 000平方公尺（m2)之總粒子表面積的反應性 金屬氧化物係大於10.0克（g/l〇〇〇m2-hr)。在甚至另一個範 例性具體實施例中，根據本發明之製造膠態金屬氧化物粒 子之方法’，其包括以根據數學模式之金屬氧化物質量添加 速率將反應性金屬氧化物添加至反應槽的步驟，該數學模 式提供最適金屬氧化物質量添加速率，q由下式表示： q = (3 m 〇 G r / D p 〇3) ( D p 〇 + G r t)2 其中： Q (a) m。代表在反應槽中金屬氧化物粒子的質量，其量測. 以克（g)計； (b) 代表在反應槽中金屬氧化物粒子之金屬氧化物粒 子生長速率，其係藉由增加粒徑來求出並且以每小 時奈米（nm/hr)量測； (c) Dp。代表以奈米（nm)量測之平均金屬氧化物粒徑；以 及 (d) t代表以小時計之時間（hr)。 200938294 揭露製造膠態金屬氧化物粒子之方法可包括形成成核金 屬氧化物粒子之步驟及/或使金屬氧化物晶種粒子成長之 步驟。在一個範例性具體實施例中，製造膠態金屬氧化物 粒子之方法包括添加一種或多種反應物至（i)含有水且（ii) 實質上無任何晶種金屬氧化物粒子之反應槽的步驟，其中 該一種或多種反應物可以形成成核金屬氧化物粒子；在反 應槽中形成成核金屬氧化物粒子；以及在反應槽中使成核 _ 金屬氧化物粒子成長，以便形成膠態金屬氧化物粒子，'其 中成長步驟包括在反應週期期間，增加一種或多種反應物 之進料速率。 1 揭露製造膠態金屬氧化物粒子之方法，爲了形成膠態金 屬氧化物粒子，而以具有反應週期遠低於傳統反應週期之 能量效率方式可能產生膠態金屬氧化物粒子。在一個範例 性具體實施例中，係製造膠態金屬氧化物粒子之方法，其 包括在超過反應週期期間、以金屬氧化物質量添加速率將 Φ 反應性金屬氧化物添加至反應槽中的步驟，以便形成具有 範圍爲約10nm至約200nm平均最終粒徑之膠態金屬氧化物 粒子，其中該反應週期係與低於50%的使用傳統技術（例如： 恆定之反應性金屬氧化物進料速率）之相似反應週期一 樣。例如：當形成相似大小膠態金屬氧化物粒子的傳統方 法需要至少30分鐘的反應週期，典型上爲約31至40分鐘 時，使用本方法可在約21-28分鐘之反應週期形成具有範 圍爲約20_ 30n m平均粒徑之膠態金屬氧化物粒子。 200938294 在另一範例性具體實施例中，係製造膠態金屬氧化物粒 子之方法，其包括在超過反應週期期間、以金屬氧化物質 量添加速率將反應性金屬氧化物添加至反應槽中的步驟， 以便形成具有範圍爲約20nm至約200nm平均最終粒徑之膠 態金屬氧化物粒子，該金屬氧化物質量添加速率在反應週 期期間至少增加一次。該金屬氧化物質量添加速率的增加 (例如）可爲單一步驟增加或多步驟增加。 本發明進一步指的是使用膠態金屬氧化物粒子之方法。 ❹ 在一個使用膠態金屬氧化物粒子之範例方法中，該方法包 括在基材上施用膠態金屬氧化物粒子組成物，並乾燥該膠 態金屬氧化物粒子組成物，以便在基材上形成塗層。 本發明的這些和其他特徵以及優點在看過下列所揭露之 具體實施例和所附之申請專利範圍的詳細敘述後將變得清 楚。 【實施方式】 φ 爲促進對本發明原理的理解，本發明遵循特定具體實施 例的描述並採用特定的語言描述特定具體實施例。然而， 應理解的是並不打算利用特定語言對於本發明範圍進行限 制。如本發明所屬技術領域中具有通常知識者通常所爲， 預期將對前面討論過之本發明原理，進行改變、進一步修 飾和進一步應用。 必須要注意在本發明及所附的申請專利範圍中使用之單 數形式「一」、「及」和「該」除本文清楚地不同指定外， 200938294 否則包括複數指示對象。因此，（例如）提及「氧化物」包 括複數的該氧化物，以及提及「氧化物」包括提及一種或 一種以上之氧化物和本技術領域中嫻熟技藝者所知之其相 等物等等。 「約」使用於揭露具體實施例的描述之組成物、濃度、 體積、程序溫度、程序時間、回收率或產率、流率、和類 似値、和其範圍中修飾（例如）組分的數量，其指的是（例如） Ο 可經典型量測和處理程序；經在這些程序中不注意的犯 錯；經不同的使用於進行本方法之組分；以及類似的原因 發生的數値量的變化。術語「約」亦包含因具特定初始濃 度之調配物或混合物的老化之不同量，以及因具特定初始 濃度的調配物或混合物之混合和處理之不同量。不管是藉 由術語「約」修飾，申請專利範圍關於這個附加，包含相 同的這些量。 使用於本文之「金屬氧化物」係定義爲二元氧化合物 〇 (binary oxygen compound)，其中該金屬爲陽離子，該氧化 物爲陰離子。該金屬亦可包含準金屬（metalloid)。金屬包含 在周期表上由硼至釙所劃斜線的左邊那些元素。準金屬或 半金屬（semi-metal)包含在此線上那些元素。金屬氧化物的 例子包含二氧化矽、氧化鋁、二氧化鈦、二氧化鍩等及其 混合物。 本發明係指製造膠態金屬氧化物粒子之方法。本發明進 一步指的是膠態金屬氧化物粒子、包括膠態金屬氧化物粒 200938294 子之組成物以及使用膠態金屬氧化物粒子之方法。以下提 供膠態金屬氧化物粒子、製造膠態金屬氧化物粒子之方 法、以及使用膠態金屬氧化物粒子之方法之範例的敘述。 I. 製造膠態金屬氧化物粒子之方法 本發明係指製造膠態金屬氧化物粒子之方法。以下詳述 用來形成本發明膠態金屬氧化物粒子之原料，以及形成本 發明膠態金屬氧化物粒子之方法步驟。 A.原料 揭露製造膠態金屬氧化物粒子之方法，其可利用一種或 多種下列原料以製造膠態二氧化矽粒子，但替代的原料可 被利用於形成其他種類的膠態金屬氧化物&料，像是膠態 氧化鋁粒子、膠態二氧化鈦粒子、膠態二氧化鉻粒子等等、 以及其組合。 1. 砍酸鹽 製造膠態二氧化矽粒子之方法，其可利用一種或多種之 φ 含矽原料。合適的含矽原料包括但不受限於矽酸鹽，如鹼 金屬矽酸鹽。合意地，使用一種或多種鹼金屬矽酸鹽以形 成膠態二氧化矽粒子。合適的鹼金屬矽酸鹽包括但不受限 於矽酸鈉鹽、矽酸鉀鹽、矽酸鈣鹽、矽酸鋰鹽、矽酸鎂鹽 及其組合。 合適的商業獲得矽酸鹽包括但不受限於由包含PQ股份 有限公司（Valley Forge, PA)和 Zaclon 公司（Cleveland, OH) 之數個來源之商購取得的矽酸鈉鹽以及矽酸鉀鹽。 200938294 2. 離子交換樹脂 在所揭露之方法中，任何單一矽酸鹽或矽酸鹽之組合可 與一種或多種陽離子交換樹脂反應以形成膠態二氧化矽粒 子。本發明所使用的合適的陽離子交換樹脂包含但不受限 於強酸陽離子（SAC)樹脂、弱酸陽離子（WAC)樹脂、以及其 組合。 合適的商業獲得陽離子交換樹脂包含，但不受限於，由 數種來源之商業獲得陽離子交換樹脂，該來源包含Purolite 〇 有限公司（Bala Cynwyd，PA)，像是以PUROLITE®商品設計 所販賣的；以及陶氏化學（Dow Chemical)(Midland, MI)，像 是以D0WEX®商品設計所販1賣的。 典型上，以樹脂添加速率，將一種或多種陽粒子交換樹 脂添加至反應槽，以便保持反應槽的pH在約8.0和約10.0 之間，期望在約9.2和約9.6之間。 3. 晶種金屬氧化物粒子 Q 在本發明之一些具體實施例中，晶種金屬氧化物粒子被 用作爲開始原料。在這些具體實施例中，可使用數個提供 者之晶種膠態金屬氧化物粒子。使用於本發明之合適的晶 種膠態金屬氧化物粒子包含但不受限於晶種膠態金屬氧化 物粒子，像是由Nissan化學美國公司（Houston，TX)和Eka 化學有限公司（Marietta，GA)商業獲得之膠態二氧化矽粒 子。 B.方法步驟 200938294 揭露製造膠態金屬氧化物粒子之方法，其包括數個如下 詳述之步驟。 1. 反應槽的製備 揭露製造膠態金屬氧化物粒子之方法，爲了形成膠態金 屬氧化物粒子而可能產生具有反應週期遠低於傳統反應週 期之能量效率方式使膠態金屬氧化物粒子。在一個範例實 施例中，製造膠態金屬氧化物粒子之方法，其包括添加一 ^ 種或多種反應物至⑴含有水且（ii)實質上無任何晶種金屬 Ο 氧化物粒子之反應槽的步驟，其中該一種或多種反應物可 以形成成核金屬氧化物粒子。在此具體實施例中，製備反 應槽的步驟_單包括添加預定量去離子（DI)水至反應槽。 在另一具體實施例中，製造膠態金屬氧化物粒子之方 法，其包括添加一種或多種反應物至含⑴去離子（DI)水和 (ii)實質上無任何晶種金屬氧化物粒子之反應槽的步驟，其 中該一種或多種反應物能形成成核金屬氧化物粒子及/或 φ 使晶種金屬氧化物粒子生長。在此具體實施例中，製備反 應槽的步驟包括將⑴去離子（DI)水之期望量和（Π)晶種金 屬氧化物粒子添加至反應槽之期望量。在利用晶種金屬氧 化物粒子的時候，該晶種金屬氧化物粒子典型上具有範圍 爲約5nm至約15nm的初始平均粒子大小（亦即最大尺寸）。 2. 添加反應性金屬氧化物 揭露形成膠態金屬氧化物粒子之方法，其包括將一種或 多種上述反應物添加至反應槽的步驟，其中添加一種或多 -10- 200938294 種反應物的步驟考慮不同的原位反應條件，該反應條件包 含但不受限於至少一個的⑴反應槽中粒子成核速率、（ϋ) 反應槽中，存在的金屬氧化物粒子（例如：晶種金屬氧化物 粒子及/或成核金屬氧化物粒子）之上的金屬氧化物沉積速 率、及/或（iii)反應槽中金屬氧化物粒子（例如：晶種金屬氧 化物粒子及/或成核金屬氧化物粒子）的生長。揭露平衡反 應物進料速率抑制存在的金屬氧化物粒子之上的反應性金 _ 屬氧化物沉積速率所形成的膠態金屬化物粒子之方法，以 便於溶液相中控制反應性金屬氧化物的過飽和程度。 在一個範例性具體實施例中，製造膠態金屬氧化物粒子 ' 之方法，其包括以金屬氧化物質量添加速率將反應性金屬 氧化物添加至反應槽的步驟，在基於數學模式之金屬氧化 物質量添加速率下，將反應性金屬氧化物添加至反應槽， 該金靥氧化物質量添加速率係基於考慮至少一個之（i)粒子 成核速率，（ii)存在的金屬氧化物粒子之上的金屬氧化物沉 〇 積速率，及/或（iii)反應槽中金屬氧化物粒子的生長之數學 模式，其中該金屬氧化物質量添加速率隨著反應時間函數 增加。在另一具體實施例中，在至少一部分的反應週期期 間，該添加速率每小時每1000平方公尺（m2)總粒子表面積 的反應性金屬氧化物係大於10.0克（g/1000m2-hr)。在更進 一步的具體實施例中，根據本發明所製造的膠態金屬氧化 物粒子之方法，其包括以根據數學模式之金屬氧化物質量 添加速率，將反應性金屬氧化物添加至反應槽的步驟，該 -11- 200938294 數學模式提供最適金屬氧化物質量添加速率，q由下式表 不：q = (3 m。G r / D p。3) (D p。+ G r t)2 其中： (a) nu代表在反應槽中金屬氧化物粒子的質量，其量測 以克（g)計； (b) Gr代表在反應槽中金屬氧化物粒子之金屬氧化物粒 子生長速率，其係藉由增加粒徑來求出並且以每小 ^ 時奈米（nm/hr)來量測； 〇 (c) Dp。代表以奈米（nm)來量測之平均金屬氧化物粒徑； 以及 (d) t代表以小時計之時間（hr)。 某些具體實施例中，在至少一部分的反應週期期間，Gr 範圍爲約 10至約 50nm/hr，以及 q範圍爲約 10.6至約 52.8g/1000m\hr。在其他具體實施例中，在至少一部分的 反應週期期間，Gr範圍爲約20至約40nm/hr，以及q範圍 〇 爲約 21.1 至約 42.3g/1000m2-hr » 第1圖爲以圖表描述隨著反應性金屬氧化物濃度的改變 之⑴反應性金屬氧化物之成核速率（Rn)以及（ii)在存在的 粒子上之反應性金屬氧化物的沉積速率（DR)的曲線圖。如 第1圖所示，直到（i)反應性金屬氧化物濃度超過飽和濃度 (Cs)，以及（ii)達到以Cc識別之過飽和臨界程度才發生成核 作用。在此時點，當沉積速率隨著反應性金屬氧化物濃度 增加而持續沿著線性路徑時，成核作用以指數速率進行。 -12- 200938294 第2圖爲以圖表描述方法條件，該方法條件有利於（i)在 存在的粒子之上的反應性金屬氧化物沉積速率（即在反應 性金屬氧化物濃度低於Cc時），（ii)新膠態金屬氧化物粒子 的成核作用（即在反應性金屬氧化物濃度在Cc以上時），以 及（iii)(i)和（ii)兩者（即反應性金屬氧化物濃度高於C。或低 於第2圖所示之濃度Cn)隨著反應性金屬氧化物濃度而增 加。當反應性金屬氧化物的濃度增加在第2圖所示之Cn以 A 上時，方法條件顯著地有利於在存在的粒子上之金屬氧化 物的沉積期間，新金屬氧化物粒子的成核作用。 3. 粒子成形步驟的完成 一旦達到預定的金屬氧化物粒子尺寸，停止反應物添加 至反應槽，以及爲了淬火該反應而添加一定量去離子水至 反應槽中。 4. 過濾步驟 淬火步驟之後係過濾步驟（例如：超過濾步驟）可用於移除 φ 由一種或多種陽離子交換樹脂與一種或多種金屬氧化物原 料所產生之多餘的鹽類。 C.方法之優勢 揭露製造膠態金屬氧化物粒子之方法，在使反應器時間 及能量的利用最適化的同時，能夠生產膠態金屬氧化物粒 子。在某些範例性的具體實施例中，製造膠態金屬氧化物 粒子之方法，在反應週期中，使能生產具有範圍爲約30至 約200nm最終粒徑之膠態金屬氧化物粒子，該反應週期代 -13- 200938294 表使用傳統方法製造相同的膠態金屬氧化物粒子所需之反 應週期減少50%。 第3圖爲以圖表描述使用（i)本發明之最適反應性二氧化 矽進料速率和（ii)傳統方法使用不變的反應性二氧化矽進 料速率，而減少形成具有22nm平均粒徑之膠態二氧化矽粒 子所需的反應時間。 第4圖爲以圖表描述使用本發明之最適方法逐步地添加 _ 反應性二氧化矽，以便接近緊接的最適進料速率。如第4 圖所示，揭露製造膠態二氧化矽粒子之方法可包括在所給 予之反應週期期間，一次或多次逐步地增加反應性二氧化 矽進料速率。雖然第4圖已顯示只有兩階段i三階段之方 法，但任何次數階段增加反應性二氧化矽進料速率，該反 應速率係爲使用於本發明以緊隨著藉由第4圖所示之「最 適的」線描述之最適進料速率。 II.產生膠態金屬氧化物粒子 φ 在上述本發明方法中形成的膠態金屬氧化物粒子，其具 有相似如下所述之形成膠態金屬氧化物粒子之傳統方法中 所形成的膠態金屬氧化物粒子之物理結構和性質。 A.金屬氧化物粒子之尺寸 本發明之膠態金屬氧化物粒子具有平均最大粒子尺寸 (即最大直徑尺寸）之球型粒子形狀。典型上，本發明之膠 態金屬氧化物粒子具有低於約700μιη的平均最大粒子尺 寸，更典型爲低於約100 μπι。在本發明之一個期望的具體 -14- 200938294 實施例中，膠態金屬氧化物粒子具有約10.0至約100 μιη的 平均最大粒子尺寸，更期望爲約10.0至約30μιη。 本發明之膠態金屬氧化物粒子典型上具有低於約1.4的 縱橫比，其係（例如）使用透射式電子顯微鏡（ΤΕΜ)技術來量 測。本文所使用術語「縱橫比」用來描述（i)膠態金屬氧化 物粒子之平均最大粒子尺寸以及（ii)膠態金屬氧化物粒子 之平均最大截面粒子尺寸之間的比，其中截面粒子尺寸實 ^ 質上垂直膠態金屬氧化物粒子之最大粒子尺寸。在本發明 ❹ 的一些具體實施例中，膠態金屬氧化物粒子具有低於約 1. 3 (或低於約1.2、或低於約1.1、或低於約1.0 5)的縱橫比。 典型上，膠態金屬氧化物粒子真有約1.0至約1.2的縱橫比。 B.金屬氧化物粒子之表面積 本發明之膠態金屬氧化物粒子具有相似傳統方法形成之 膠態金屬氧化物粒子的平均表面積。典型上，本發明之膠 態金屬氧化物粒子具有範圍爲約90m2/g至約180m2/g的平 φ 均表面積。期望地，本發明之膠態金屬氧化物粒子具有範 圍爲約100m2/g至約160m2/g的平均表面積，更期望爲約 1 10m2/g 至約 150m2/g。 第5圖藉由圖表來比較由本發明最適方法所形成的膠態 金屬氧化物粒子（在此情況爲膠態二氧化矽粒子）與由傳統 方法（即非最適方法，亦即不變的金屬氧化物原料進料速率） 所形成的膠態二氧化矽粒子。如第5圖所示，傳統方法所 形成的膠態二氧化矽粒子具有約27.6nm的平均粒子大小以 -15- 200938294 及約136m2/g的平均粒子表面積，然而本發明最適方法所 形成的膠態二氧化矽粒子具有約28.7nm的平均粒子大小以 及約142m2/g的平均粒子表面積。 如第5圖所示，本發明最適方法所形成的膠態金屬氧化 物（例如：二氧化矽）粒子實質上可生產類似由傳統方法所形 成的膠態金屬氧化物粒子。然而，如上所述，藉由本發明 之最適方法所形成的膠態金屬氧化物粒子可利用高達50% I 之更少的反應器時間和方法能量之更有效方式生產。 ❹ III.使用金屬氧化物粒子之方法 本發明進一步指以上述方法形成之膠態金屬氧化物粒子 的使用方法。¥—個使用膠態金屬氧化物粒子的示範性方 法中，該方法包括在基材上施用膠態金屬氧化物粒子組成 物，並乾燥該膠態金屬氧化物粒子組成物，以便在基材上 形成塗層。合適的基材包含但不受限於紙、聚合物的薄膜、 聚合物的泡沬材料、玻璃、金屬、陶瓷、及織物。 φ 在一個示範性具體實施例中，使用膠態金屬氧化物粒子 之方法包括利用膠態金屬氧化物粒子作爲用於微電子或其 他物件之硏磨/磨光組成物。在其他示範性具體實施例中， 使用膠態金屬氧化物粒子的方法包括利用膠態金屬氧化物 粒子作爲塗料之添加劑以改良乾塗膜之機械性質。 實施例 本發明進一步藉由下列實施例說明，但不以任何形式構 成對本發明範圍之限制。相反地，可清楚了解，在閱讀過 -16- 200938294 本文之敘述後，技術領域中嫻熟此技藝者，將在不脫離本 發明精神及/或所附申請專利範圍之範圍的情況下，根據本 發明方法得到各種實施例、改變及其等價物。 窗施例1 使用晶種二氧化矽粒子和最適二氧化矽添加速率來製備 膠態二氧化矽粒子 將28.4公斤（kg)(62,6磅（lb))去離子(DI)水添加至113.5 A 升（1)(30加侖（gal))的加熱攪拌槽，該槽已加入4.9kg( 10.91b) 的12nm膠態二氧化矽材料的40重量％固體懸浮液作爲晶 種材料。在攪拌的時候，加熱該混合物並保持溫度在90~96 °(：範圍之間。接著以等同 167.8 克（g)Si〇2/min(0.371bSiO” min)之初始矽酸鹽添加速率同時將矽酸鈉鹽（29重量％ Si〇2 ，9重量％Na2〇)和強酸離子交換樹脂加入該槽。10分鐘後， 將矽酸鹽添加速率增加至317.5g Si〇2/min(0.701bSi〇2/min) ，並在另外的11分鐘維持在此較高的速率。 〇 整個方法中，控制樹脂添加速率來維持該槽之pH在9.2 及9.6之間。在矽酸鹽添加21分鐘後，兩者的添加皆停止 並藉由DI水的添加來淬火該反應。 所產生之產物被量測爲具有22 + 2nm的粒子大小，與小粒 子之額外成核作用的最細微讀數。 比較實施例丄 使用晶種二氧化矽粒子和矽酸鹽進料速率維持恆定來製 備膠態二氧化矽粒子 -17- 200938294 除了整個方法維持等同167.8克（g)Si〇2/min(0.3 71bSi〇2/ min)之矽酸鹽添加速率外，重複實施例1之程序。控制樹 脂添加速率維持該槽之pH在9.2及9.6之間。在停止添加 矽酸鹽和離子交換樹脂以及藉由添加DI水以淬火該生長 反應之後，此方法持續31分鐘。 所產生之產物被量測爲具有22 + 2nm的粒子大小。 雖然本發明已描述有限數量的具體實施例，但這些具體 的實施例並不會像本文其他地方所描述或主張被認爲限制 本發明之範圍。在所屬技術領域中具有通常知識者，重新 檢視本發明之範例性具體實施例如此可進一步地修改、相 等物以及變化應爲顯而易見的。在實施例中之全部與百分 比以及說明書中剩餘物，除了明確說明以外，係根據重量。 此外，在本說明書或申請專利範圍中詳述之任何數字的範 圍，像是代表特定組的性質、測量單位、條件、物理狀態 或百分比，係被認爲清楚地完全倂入本文做爲參考或其反 i 面，任何落在該範圍間的數字係包括在所描述的任何範圍 中數字的任何子集。例如：無論何時揭露具有下限Rt以及 上限Ru之數値範圍，落入該範圍中被具體地揭露的任何數 字 R。特別是，在該範圍中之下列數字被具體揭露： R = RL + k(Ru-Ri·)，其中k爲在具有1%增加量之1%至100%的 範圍變化，例如：k 爲 1 %、2 %、3 %、4 %、5 % ... 5 0 %、5 1 %、 52%...95 %、96%、97% ' 98%、99 % 或 100%。此外，亦具體 揭露如上述被計算之R的任何兩個値來表示任何數値範 圍。除本文已顯示及已敘述的之外，由前面的敘述及所附 -18- 200938294 圖式，本發明的任何改變對於技術領域中熟知此技藝者將 變得更顯而易見的。此種改變被認爲落入所附申請專利範 圍的範圍中。所有在本文被引用之公開案，將其全文倂入 做爲參考。 【圖式簡單說明】 第1圖爲以圖表描述隨著反應性金屬氧化物濃度的改變 之⑴反應性金屬氧化物之成核速率以及（ii)反應性金，屬氧 化物在存在的粒子上的沉積速率； 第2圖爲圖表描述有利於（i)在存在的粒子之上的反應性 金屬氧化物沉積速率，（ii)新膠態金屬氧化物粒子的成核以 及（iii)(i)和（ii)兩者隨著反應性金屬氧化物濃度的改變； 第3圖爲圖表描述使用（i)本發明之最適反應性金屬氧化 物進料速率和（ii)傳統方法所使用之維持反應性金屬氧化 物粒子進料速率恆定，而減少形成具有22nm平均粒徑之膠 態金屬氧化物粒子所需的反應時間； 第4圖爲圖表描述使用本發明之最適方法逐步地添加反 應性金屬氧化物，以便緊隨著最適進料速率；以及 第5圖爲圖表描述粒子大小和表面積且以經本發明最適 方法形成之膠態二氧化矽粒子對上經由傳統方法形成的膠 態二氧化矽粒子（亦即維持反應性二氧化矽進料速率恆 定）。 【主要元件符號說明】 無。 -19-200938294 VI. Description of the Invention: [Technical Field to Which the Invention Is Ascribed] The present invention refers to a method of producing colloidal metal oxide particles. [Prior Art] Efforts have been made in the art to form colloidal metal oxide particles in a highly efficient manner. There is a need in the art for a method of forming colloidal metal oxide particles in a high performance manner when optimized for use. SUMMARY OF THE INVENTION The present invention provides a novel method of forming colloidal metal oxide particles. It is disclosed that a method of forming colloidal metal oxide particles can form colloidal metal oxide particles under conditions close to the optimum method to form colloidal metal oxide particles in a very efficient manner. Further, the disclosed method of forming colloidal metal oxide particles enables the reaction tank to be optimally utilized because it can reduce the reaction cycle required to form colloidal metal oxide particles. p discloses a method of forming colloidal metal oxide particles comprising the step of adding one or more reactants to a reaction tank, wherein the step of adding one or more reactants takes into account different in situ reaction conditions, including but not Limited to (i) particle nucleation rate in the reaction tank, (ii) metal oxide deposition rate over the metal oxide particles present (eg, seed metal oxide particles and/or nucleated gold ruthenium oxide particles, And/or at least one of (Hi) the growth of metal oxide particles (eg, seed metal oxide particles and/or nucleating metal oxide particles) in the reaction tank. In an exemplary embodiment, the glue is produced. The method of the metal oxide particles 200938294 includes the step of adding a reactive metal oxide to the reaction vessel at a metal oxide mass addition rate, the metal oxide mass addition rate being based on a mathematical mode that considers at least one of ) particle nucleation rate, (ii) metal oxide particle deposition rate over the metal oxide present, and/or (iii) metal oxygen in the reaction cell Growth of the chemical particles, wherein the metal oxide mass addition rate is increased as a function of reaction time. In another embodiment, the addition rate is every 1 000 square meters (m2) per hour during at least a portion of the reaction cycle. The total particle surface area of the reactive metal oxide system is greater than 10.0 grams (g/l 2- m2-hr). In even another exemplary embodiment, the method of making colloidal metal oxide particles in accordance with the present invention ', which includes the step of adding a reactive metal oxide to the reaction tank at a metal oxide mass addition rate according to a mathematical mode, the mathematical mode providing an optimum metal oxide mass addition rate, q being represented by the following formula: q = (3 m 〇G r / D p 〇3) ( D p 〇+ G rt ) 2 where: Q (a) m represents the mass of the metal oxide particles in the reaction bath, measured in grams (g); (b) represents the growth rate of metal oxide particles of metal oxide particles in the reaction tank, which is determined by increasing the particle diameter and measured in nanometers per hour (nm/hr); (c) Dp. Measured in nanometer (nm) The average metal oxide particle size; and (d) t represents the time in hours (hr). 200938294 discloses that the method of making the colloidal metal oxide particles can include the steps of forming nucleating metal oxide particles and/or oxidizing the metal. Step of growing seed particles. In an exemplary embodiment, the method of making colloidal metal oxide particles includes adding one or more reactants to (i) containing water and (ii) substantially free of any seed metal a step of a reaction vessel of oxide particles, wherein the one or more reactants can form nucleating metal oxide particles; forming nucleation metal oxide particles in the reaction tank; and nucleating the metal oxide particles in the reaction tank Grow to form colloidal metal oxide particles, 'where the growth step involves increasing the feed rate of one or more reactants during the reaction cycle. 1 Disclosure of a method for producing colloidal metal oxide particles, in order to form colloidal metal oxide particles, may result in colloidal metal oxide particles in an energy efficient manner having a reaction period much lower than the conventional reaction period. In an exemplary embodiment, a method of producing colloidal metal oxide particles, the method comprising the step of adding a Φ reactive metal oxide to a reaction vessel at a metal oxide mass addition rate during a reaction period, To form colloidal metal oxide particles having an average final particle size ranging from about 10 nm to about 200 nm, wherein the reaction cycle is less than 50% using conventional techniques (eg, a constant reactive metal oxide feed rate) The similar reaction cycle is the same. For example, when conventional methods of forming colloidal metal oxide particles of similar size require a reaction cycle of at least 30 minutes, typically about 31 to 40 minutes, the process can be formed in a reaction cycle of about 21-28 minutes using the process. Colloidal metal oxide particles having an average particle size of about 20-30 nm. 200938294 In another exemplary embodiment, a method of making colloidal metal oxide particles comprising the step of adding a reactive metal oxide to a reaction tank at a metal oxide mass addition rate during a reaction period in excess of the reaction period To form colloidal metal oxide particles having an average final particle size ranging from about 20 nm to about 200 nm, the metal oxide mass addition rate being increased at least once during the reaction cycle. The increase in the rate of mass addition of the metal oxide, for example, can be a single step increase or a multi-step increase. The invention further refers to a method of using colloidal metal oxide particles. ❹ In an exemplary method of using colloidal metal oxide particles, the method comprises applying a colloidal metal oxide particle composition on a substrate and drying the colloidal metal oxide particle composition to form on a substrate coating. These and other features and advantages of the present invention will become apparent from the Detailed Description of the appended claims. [Embodiment] φ is intended to facilitate an understanding of the principles of the invention. The invention is described in the specific embodiments. However, it should be understood that the scope of the invention is not intended to be limited by the specific language. Modifications, further modifications, and further applications of the principles of the invention discussed above are contemplated as would be apparent to those of ordinary skill in the art. It must be noted that the singular forms "a", "and" and "the" are used in the meaning of the invention and the appended claims. Thus, for example, reference to "an oxide" includes a plurality of such oxides, and reference to "oxide" includes reference to one or more oxides and equivalents known to those skilled in the art. Wait. "About" is used to disclose the composition, concentration, volume, program temperature, program time, recovery or yield, flow rate, and similar enthalpy of the description of the specific embodiments, and the number of modified (for example) components in the range thereof. , which refers to, for example, 经典 classic type measurement and processing procedures; mistakes that are not noticed in these procedures; components that are used differently for the method; and numbers that occur for similar reasons Variety. The term "about" also encompasses different amounts of aging due to a particular initial concentration of the formulation or mixture, as well as different amounts of mixing and handling of the formulation or mixture with a particular initial concentration. Whether modified by the term "about", the scope of the patent application relates to this addition and includes the same quantities. As used herein, "metal oxide" is defined as a binary oxygen compound wherein the metal is a cation and the oxide is an anion. The metal may also comprise a metalloid. The metal contains those elements on the left side of the periodic table that are diagonally drawn from boron to germanium. The quasi-metal or semi-metal contains those elements on this line. Examples of the metal oxide include cerium oxide, aluminum oxide, titanium oxide, cerium oxide, and the like, and a mixture thereof. The present invention is directed to a method of making colloidal metal oxide particles. The invention further refers to colloidal metal oxide particles, compositions comprising colloidal metal oxide particles 200938294, and methods of using colloidal metal oxide particles. The following description provides examples of colloidal metal oxide particles, methods for producing colloidal metal oxide particles, and methods for using colloidal metal oxide particles. I. Method of Making Colloidal Metal Oxide Particles The present invention is directed to a method of making colloidal metal oxide particles. The materials used to form the colloidal metal oxide particles of the present invention, as well as the method steps for forming the colloidal metal oxide particles of the present invention, are detailed below. A. Starting Material A method of making colloidal metal oxide particles that utilizes one or more of the following materials to produce colloidal ceria particles, but alternative materials can be utilized to form other types of colloidal metal oxides & Materials such as colloidal alumina particles, colloidal titanium dioxide particles, colloidal chromium dioxide particles, and the like, and combinations thereof. 1. Citrate A method of producing colloidal cerium oxide particles which utilizes one or more of the φ cerium-containing materials. Suitable rhodium-containing materials include, but are not limited to, niobates such as alkali metal niobates. Desirably, one or more alkali metal silicates are used to form colloidal cerium oxide particles. Suitable alkali metal silicates include, but are not limited to, sodium citrate, potassium citrate, calcium citrate, lithium niobate, magnesium citrate, and combinations thereof. Suitable commercially available phthalates include, but are not limited to, commercially available sodium citrate salts and potassium citrate from several sources including PQ Corporation (Valley Forge, PA) and Zaclon Corporation (Cleveland, OH). salt. 200938294 2. Ion Exchange Resin In the disclosed method, any single citrate or citrate combination can be reacted with one or more cation exchange resins to form colloidal cerium oxide particles. Suitable cation exchange resins for use in the present invention include, but are not limited to, strong acid cation (SAC) resins, weak acid cation (WAC) resins, and combinations thereof. Suitable commercially available cation exchange resins include, but are not limited to, commercially available cation exchange resins from several sources, including Purolite Co., Ltd. (Bala Cynwyd, PA), as sold under the PUROLITE® product design. And Dow Chemical (Midland, MI), as sold by the D0WEX® product design. Typically, one or more cation exchange resin resins are added to the reaction tank at a resin addition rate to maintain the pH of the reaction tank between about 8.0 and about 10.0, desirably between about 9.2 and about 9.6. 3. Seed Metal Oxide Particles Q In some embodiments of the invention, seed metal oxide particles are used as starting materials. In these embodiments, a plurality of donor seed colloidal metal oxide particles can be used. Suitable seed colloidal metal oxide particles for use in the present invention include, but are not limited to, seed colloidal metal oxide particles, such as by Nissan Chemicals, Inc. (Houston, TX) and Eka Chemical Co., Ltd. (Marietta, GA) Commercially obtained colloidal cerium oxide particles. B. Method Steps 200938294 discloses a method of making colloidal metal oxide particles comprising a number of steps as detailed below. 1. Preparation of Reaction Celles The method of producing colloidal metal oxide particles is disclosed. In order to form colloidal metal oxide particles, colloidal metal oxide particles may be produced in an energy efficient manner having a reaction period much lower than the conventional reaction period. In an exemplary embodiment, a method of making colloidal metal oxide particles includes adding one or more reactants to (1) a reaction vessel containing water and (ii) substantially free of any seed metal cerium oxide particles. a step wherein the one or more reactants can form nucleating metal oxide particles. In this particular embodiment, the step of preparing the reaction vessel - single comprises adding a predetermined amount of deionized (DI) water to the reaction vessel. In another embodiment, a method of making colloidal metal oxide particles comprising adding one or more reactants to (1) deionized (DI) water and (ii) substantially free of any seed metal oxide particles A step of a reaction tank in which the one or more reactants are capable of forming nucleating metal oxide particles and/or φ to grow the seed metal oxide particles. In this embodiment, the step of preparing the reaction vessel comprises adding (1) a desired amount of deionized (DI) water and a desired amount of (Π) seed metal oxide particles to the reaction vessel. When seeding metal oxide particles are utilized, the seed metal oxide particles typically have an initial average particle size (i.e., maximum dimension) ranging from about 5 nm to about 15 nm. 2. The addition of a reactive metal oxide reveals a method of forming colloidal metal oxide particles comprising the step of adding one or more of the above reactants to a reaction tank, wherein the step of adding one or more of -10, 2009,294,294 reactants is considered Different in-situ reaction conditions, including but not limited to at least one (1) particle nucleation rate in the reaction tank, (ϋ) in the reaction tank, presence of metal oxide particles (eg, seed metal oxide particles) And/or nucleation metal oxide particles) metal oxide deposition rate, and/or (iii) metal oxide particles in the reaction bath (eg, seed metal oxide particles and/or nucleating metal oxide particles) ) growth. A method of balancing the reactant feed rate to inhibit colloidal metallization particles formed by reactive gold oxide deposition rates over metal oxide particles present to facilitate supersaturation of the reactive metal oxide in the solution phase degree. In an exemplary embodiment, a method of making colloidal metal oxide particles' includes the step of adding a reactive metal oxide to a reaction vessel at a metal oxide mass addition rate, in a mathematical mode based metal oxide species At a rate of addition, a reactive metal oxide is added to the reaction tank based on the rate of nucleation of at least one of (i) particles, (ii) above the metal oxide particles present. A mathematical mode of metal oxide deposition rate, and/or (iii) growth of metal oxide particles in the reaction tank, wherein the metal oxide mass addition rate increases as a function of reaction time. In another embodiment, the rate of addition of the reactive metal oxide system per 1000 square meters (m2) of total particle surface area per hour is greater than 10.0 grams (g/1000 m2-hr) during at least a portion of the reaction cycle. In a still further embodiment, the method of colloidal metal oxide particles produced in accordance with the present invention comprises the step of adding a reactive metal oxide to the reaction vessel at a metal oxide mass addition rate according to a mathematical model , The -11-200938294 mathematical model provides the optimum rate of metal oxide mass addition, q is given by: q = (3 m. G r / D p. 3) (D p. + G rt) 2 where: ( a) nu represents the mass of the metal oxide particles in the reaction tank, and the measurement is in grams (g); (b) Gr represents the growth rate of the metal oxide particles of the metal oxide particles in the reaction tank by Increasing the particle size to determine and measure in nanometers per hour (nm/hr); 〇(c) Dp. Represents the average metal oxide particle size measured in nanometers (nm); and (d) t represents time in hours (hr). In certain embodiments, Gr ranges from about 10 to about 50 nm/hr during at least a portion of the reaction cycle, and q ranges from about 10.6 to about 52.8 g/1000 m\hr. In other embodiments, during at least a portion of the reaction cycle, Gr ranges from about 20 to about 40 nm/hr, and the q range 〇 is from about 21.1 to about 42.3 g/1000 m2-hr. A plot of the change in reactive metal oxide concentration (1) the nucleation rate (Rn) of the reactive metal oxide and (ii) the rate of deposition (DR) of the reactive metal oxide on the particles present. As shown in Fig. 1, nucleation occurs until (i) the concentration of the reactive metal oxide exceeds the saturation concentration (Cs), and (ii) reaches the critical degree of supersaturation identified by Cc. At this point, nucleation proceeds at an exponential rate as the deposition rate continues along the linear path as the concentration of reactive metal oxide increases. -12- 200938294 Figure 2 is a graphical representation of the process conditions that favor (i) the rate of reactive metal oxide deposition over the particles present (ie, when the reactive metal oxide concentration is below Cc) (ii) nucleation of new colloidal metal oxide particles (ie, when the reactive metal oxide concentration is above Cc), and (iii) both (i) and (ii) (ie, reactive metal oxides) The concentration is higher than C. or lower than the concentration Cn shown in Fig. 2 as the concentration of the reactive metal oxide increases. When the concentration of the reactive metal oxide is increased by Cn as shown in Figure 2, the process conditions are significantly advantageous for the nucleation of the new metal oxide particles during the deposition of the metal oxide on the existing particles. . 3. Completion of the particle forming step Once the predetermined metal oxide particle size is reached, the reactants are stopped from being added to the reaction tank, and a certain amount of deionized water is added to the reaction tank in order to quench the reaction. 4. Filtration Steps After the quenching step, a filtration step (e.g., an ultrafiltration step) can be used to remove φ excess salts from one or more cation exchange resins and one or more metal oxide materials. C. Advantages of the Method The method of producing colloidal metal oxide particles is disclosed to produce colloidal metal oxide particles while optimizing reactor time and energy utilization. In certain exemplary embodiments, the method of making colloidal metal oxide particles enables the production of colloidal metal oxide particles having a final particle size ranging from about 30 to about 200 nm during the reaction cycle. Cycle Generation-13- 200938294 The reaction cycle required to produce the same colloidal metal oxide particles using conventional methods is reduced by 50%. Figure 3 is a graphical depiction of the use of (i) the optimum reactive ceria feed rate of the present invention and (ii) the conventional method using a constant reactive ceria feed rate to reduce the formation of an average particle size of 22 nm. The reaction time required for the colloidal ceria particles. Figure 4 is a graphical representation of the stepwise addition of _ reactive cerium oxide using the optimum method of the present invention to approximate the immediate optimum feed rate. As shown in Figure 4, a method of making colloidal ceria particles can be disclosed that includes increasing the reactive ceria feed rate one or more times during the given reaction cycle. Although Figure 4 has shown that there is only a two-stage i three-stage process, the reactive ceria feed rate is increased for any number of stages, which is used in the present invention to follow the Figure 4 The "Optimum" line describes the optimum feed rate. II. Production of Colloidal Metal Oxide Particles φ Colloidal metal oxide particles formed in the above method of the present invention having colloidal metal oxidation formed in a conventional method similar to the formation of colloidal metal oxide particles as described below The physical structure and properties of the particles. A. Size of Metal Oxide Particles The colloidal metal oxide particles of the present invention have a spherical particle shape having an average maximum particle size (i.e., a maximum diameter size). Typically, the colloidal metal oxide particles of the present invention have an average maximum particle size of less than about 700 μηη, more typically less than about 100 μπι. In a preferred embodiment of the invention, the colloidal metal oxide particles have an average maximum particle size of from about 10.0 to about 100 μηη, more desirably from about 10.0 to about 30 μm. The colloidal metal oxide particles of the present invention typically have an aspect ratio of less than about 1.4, which is measured, for example, using transmission electron microscopy (ΤΕΜ) techniques. The term "aspect ratio" as used herein is used to describe the ratio between (i) the average maximum particle size of the colloidal metal oxide particles and (ii) the average maximum cross-sectional particle size of the colloidal metal oxide particles, wherein the cross-sectional particle size The maximum particle size of the vertically colloidal metal oxide particles. In some embodiments of the invention, the colloidal metal oxide particles have an aspect ratio of less than about 1.3 (or less than about 1.2, or less than about 1.1, or less than about 1.05). Typically, the colloidal metal oxide particles have an aspect ratio of from about 1.0 to about 1.2. B. Surface Area of Metal Oxide Particles The colloidal metal oxide particles of the present invention have an average surface area of colloidal metal oxide particles formed by a similar conventional method. Typically, the colloidal metal oxide particles of the present invention have a flat φ uniform surface area ranging from about 90 m2/g to about 180 m2/g. Desirably, the colloidal metal oxide particles of the present invention have an average surface area in the range of from about 100 m2/g to about 160 m2/g, more desirably from about 1 10 m2/g to about 150 m2/g. Figure 5 is a graph comparing the colloidal metal oxide particles (in this case colloidal ceria particles) formed by the optimum method of the present invention with conventional methods (i.e., non-optimal methods, i.e., constant metal oxidation). Material feed rate) The formed colloidal cerium oxide particles. As shown in Fig. 5, the colloidal ceria particles formed by the conventional method have an average particle size of about 27.6 nm and an average particle surface area of -15-200938294 and about 136 m2/g, whereas the gel formed by the optimum method of the present invention The cerium oxide particles have an average particle size of about 28.7 nm and an average particle surface area of about 142 m 2 /g. As shown in Fig. 5, the colloidal metal oxide (e.g., cerium oxide) particles formed by the optimum method of the present invention can substantially produce colloidal metal oxide particles similar to those formed by conventional methods. However, as noted above, the colloidal metal oxide particles formed by the optimum method of the present invention can be produced in a more efficient manner with less reactor time and process energy of up to 50% I. ❹ III. Method of using metal oxide particles The present invention further relates to a method of using colloidal metal oxide particles formed by the above method. In an exemplary method of using colloidal metal oxide particles, the method comprises applying a colloidal metal oxide particle composition on a substrate and drying the colloidal metal oxide particle composition to be on a substrate A coating is formed. Suitable substrates include, but are not limited to, paper, polymeric films, polymeric foam materials, glass, metals, ceramics, and fabrics. φ In an exemplary embodiment, the method of using colloidal metal oxide particles includes the use of colloidal metal oxide particles as a honing/polishing composition for microelectronics or other articles. In other exemplary embodiments, the method of using colloidal metal oxide particles includes the use of colloidal metal oxide particles as an additive to the coating to improve the mechanical properties of the dry coating film. The invention is further illustrated by the following examples, which are not to be construed as limiting the scope of the invention. On the contrary, it will be apparent that, after reading the description of the present invention, the skilled person in the art will be able to devise the scope of the present invention and/or the scope of the appended claims. The invention is susceptible to various embodiments, modifications, and equivalents. Window Example 1 Preparation of colloidal cerium oxide particles using seed cerium oxide particles and optimum cerium oxide addition rate. Add 28.4 kg (kg, 62 lbs) of deionized (DI) water to 113.5. A liter (1) (30 gallon (gal)) heated stirred tank to which 4.9 kg (10.91 b) of a 40 wt% solid suspension of 12 nm colloidal ceria material has been added as a seed material. While stirring, heat the mixture and maintain the temperature between 90 and 96 ° (: range. Then the equivalent citrate addition rate of 167.8 g (g) Si 〇 2 / min (0.371 b SiO" min) will be Sodium citrate salt (29% by weight of Si〇2, 9% by weight of Na2〇) and a strong acid ion exchange resin were added to the tank. After 10 minutes, the citrate addition rate was increased to 317.5 g Si〇2/min (0.701 bSi〇). 2/min) and maintained at this higher rate for another 11 minutes. 〇In the whole method, the resin addition rate was controlled to maintain the pH of the tank between 9.2 and 9.6. After 21 minutes of citrate addition, Both additions were stopped and the reaction was quenched by the addition of DI water. The resulting product was measured to have a particle size of 22 + 2 nm, the finest reading with additional nucleation of small particles.制备Preparation of colloidal cerium oxide particles using seed cerium oxide particles and citrate feed rate is maintained constant-17- 200938294 In addition to the overall method, the equivalent of 167.8 g (g) Si 〇 2 / min (0.3 71 bSi 〇 2 / The procedure of Example 1 was repeated except for the rate of citrate addition of min). The fat addition rate maintains the pH of the tank between 9.2 and 9.6. This method lasts for 31 minutes after the addition of the citrate and ion exchange resin is stopped and the growth reaction is quenched by the addition of DI water. It is measured to have a particle size of 22 + 2 nm. Although a limited number of specific embodiments have been described in the present invention, these specific embodiments are not to be construed as limiting or limiting the scope of the invention. It is obvious that the exemplary embodiments of the present invention may be further modified, equivalents, and variations, as will be apparent to those of ordinary skill in the art. In addition, the range of any number detailed in this specification or the scope of the patent application, as if it represents a particular group of properties, units of measurement, condition, physical state or percentage, is considered to be completely clear. In this document, as a reference or its inverse, any number falling within the range is included in the description. Any subset of numbers in the range. For example, whenever the range of the number R 以及 having the lower limit Rt and the upper limit Ru is revealed, any number R that is specifically disclosed in the range is specifically disclosed. In particular, the following numbers in the range are Specifically disclosed: R = RL + k(Ru-Ri·), where k is a range of 1% to 100% with a 1% increase, for example: k is 1%, 2%, 3%, 4%, 5 % ... 5 0 %, 5 1 %, 52%...95 %, 96%, 97% ' 98%, 99 % or 100%. In addition, any two ranges of R calculated as described above are also specifically disclosed to represent any range of numbers. Other variations of the invention will become apparent to those skilled in the art in the <RTIgt;the</RTI> <RTIgt; </ RTI> <RTIgt; </ RTI> <RTIgt; Such changes are considered to fall within the scope of the appended patent application. All publications cited herein are incorporated by reference in their entirety. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a graph depicting (1) the nucleation rate of a reactive metal oxide and (ii) a reactive gold as a function of the concentration of a reactive metal oxide, which is an oxide present on the particles. The deposition rate; Figure 2 is a diagram depicting the benefits of (i) the rate of reactive metal oxide deposition over the particles present, (ii) the nucleation of the new colloidal metal oxide particles, and (iii) (i) And (ii) both with changes in the concentration of reactive metal oxides; Figure 3 is a graph depicting the use of (i) the optimum reactive metal oxide feed rate of the present invention and (ii) the maintenance reaction used in conventional methods. The metal oxide particle feed rate is constant, and the reaction time required to form colloidal metal oxide particles having an average particle diameter of 22 nm is reduced; FIG. 4 is a graph depicting the stepwise addition of reactive metal oxidation using the optimum method of the present invention. In order to follow the optimum feed rate; and Figure 5 is a diagram depicting particle size and surface area and formed by colloidal cerium oxide particles formed by the optimum method of the present invention. The colloidal ceria particles (i.e., maintaining a reactive ceria feed rate constant). [Main component symbol description] None. -19-