¡Ò÷ӤÇÒÁà¢éÒ㨠dynamical system ¢Í§»¯Ô¡ÔÃÔÂÒ BZ  ¨Óà»ç¹µéͧà¢éÒ㨷ÕèÁҢͧÊÁ¡Ò÷Õè¡Ó˹´ reaction kinetic ¢Í§»¯Ô¡ÔÃÔÂÒÍѹ¡Ó˹´â´Â mechanism ¢Í§ overall BZ reaction «Öè§à»ç¹¾×é¹°Ò¹·ÕèÊӤѭ â´Â mechanism ¢Í§»¯Ô¡ÔÃÔÂÒ BZ ¹Õé¾Ñ²¹Òâ´Â Field-Koros-Noyes(FKN) ·ÕèÁËÒÇÔ·ÂÒÅÑ Oregon àÃÒ¨Ö§àÃÕ¡ mechanism ¢Í§ BZ ¹ÕéÇèÒ Oregonator model ËÃ×Í FKN model â´Â¨Ð¹ÔÂÁ Oregonator ÁÒ¡¡ÇèÒ à¾ÃÒÐÁÕÃٻẺ·ÕèàËÁÒÐÊÁ¡ÇèÒ â´Âã¹»¯Ô¡ÔÃÔÂÒÃÇÁ¨Ð¾ºÇèÒÁÕ species µèÒ§æ ¹éÍÂÁÒ¡ áµè㹤ÇÒÁà»ç¹¨ÃÔ§áÅéÇÁÕ species áÅÐ intermediate ÁÒ¡ÁÒÂËÅÒµÑÇ ËÒ¡µéͧ¡ÒÃÈÖ¡ÉÒÅÐàÍÕ´àªÔ­ÍèÒ¹ä´é·Õè J. Am. Chem. Soc., 94, 1972, 8649 ¨ÐäÁè¼Ô´ËÇѧ áµèã¹ homepage ¹Õé¨Ð͸ԺÒÂã¹ÀÒ¾ÃÇÁ·Õè¨ÐàËç¹ÀÒ¾ä´éªÑ´´éÇ FKN model  áÅШÐáÊ´§ mathematical derived ´éÇ Oregonator ·ÕèÊдǡ㹷ҧ¤³ÔµÈÒʵÃìÁÒ¡¡ÇèÒ
                        ¨Ò¡ FKN model ·ÕèµÑ´àÍÒ»¯Ô¡ÔÃÔÂÒÂèÍ·ÕèäÁèÁռŵèÍ»¯Ô¡ÔÃÔÂÒÃÇÁÍÍ¡ä» àËÅ×Íáµè»¯Ô¡ÔÃÔÂÒ·ÕèÊӤѭà·èÒ¹Ñé¹â´Âáºè§à»ç¹ Process µèÒ§ æ 3 ¢Ñé¹´éÇ¡ѹ ¤×Í Process A ·ÕèÁÕ¡ÒáӨѴ [Br^-] ÍÍ¡, Process B ·ÕèÁÕ Autocatalysis ¢Í§ HBrO₂ à¡Ô´¢Öé¹  áÅÐã¹ Process C ·ÕèÁÕ¡ÒÃÊÃéÒ§ [Br^-] ¡ÅѺÁÒÍÕ¡¤ÃÑé§ ä´é´Ñ§¹Õé
                        ¢Ñé¹ÊӤѭ㹠Process A
(FKN3)  BrO₃^- + Br^- + 2H⁺ --> HBrO₂ + HOBr  â´ÂÁÕ rate = k₃[BrO₃^-][Br^-][H⁺]²
(FKN2) HBrO₂ + Br^- + H⁺ -->  HOBr                 â´ÂÁÕ rate = k₂[HBrO₂][Br^-][H⁺]
Process A :   BrO₃^- + 2Br^- + 3H⁺ -->   3HOBr
                        ¨Ò¡»¯Ô¡ÔÃÔÂÒ¢éÒ§º¹ã¹ process A ¾ºÇèÒ bromide ion ¨Ð¶Ù¡¡Ó¨Ñ´ÍÂèÒ§ÃÇ´àÃçÇä»à»ç¹ HOBr «Ö觨ÐÁÕ¼Åâ´ÂµÃ§µèÍ process C àÁ×èÍ bromide ion Ŵŧ¶Ö§¨Ø´Ë¹Öè§áÅéÇ»¯Ô¡ÔÃÔÂҨРshift ä»ÂѧÍÕ¡ species ¹Ñ蹤×Í HBrO₂ ·Õè¨Ðà»ÅÕè¹ä»à»ç¹ HOBr ´éÇ FKN2 «Ö觨ش¹Õè¨Ðà»ç¹¨Ø´àÃÔèÁ Process B ·Õèà»ç¹
                        Process B
(FKN5)   BrO₃^- + HBrO₂  + H⁺ <--> 2BrO₂í + H₂ â´ÂÁÕ rate = k₅[BrO₃^-][HBrO₂ ][H⁺] - k₅[HBrO_2í]
(FKN6)  BrO₂í + M_red + H⁺  -->  HBrO₂ + M_ox     â´ÂÁÕ rate = k₆[BrO₂í ][M_red][H⁺]
Process B :  BrO₃^- + HBrO₂  + 2M_red + 3H⁺ -->  2HBrO₂ + 2M_ox + H₂O
                        â´ÂàÁ×è;ԨÒóһ¯Ô¡ÔÃÔÂÒ FKN-5(»¯Ô¡ÔÃÔÂÒÂé͹¡ÅѺ¢Í§ FKN5) áÅéÇá·º¨ÐäÁèà¡Ô´¢Öé¹ ·ÓãËéä´é BrO₂í à¡Ô´¢Öé¹à»ç¹  balance ÃÐËÇèÒ§ FKN5 áÅÐ FKN6 àÁ×è;ԨÒÃ³Ò Process B ÃÇÁ ¨Ðà»ç¹¡ÒÃà¾ÔèÁ»ÃÔÁÒ³µÑÇàͧ¢Í§HBrO₂ ·ÕèàÃÕ¡ÇèÒ Autocatalysis ¢Í§ HBrO₂  «Ö觡ÒÃà¡Ô´ HBrO₂ ¢Ö鹡Ѻ FKN5 «Öè§à»ç¹¼ÅãËéÁÕ [HBrO₂] à¾ÔèÁ¢Öé¹  áµèÍÂèÒ§äáç´Õ¡ÒÃà¾ÔèÁ¢Í§ HBrO₂ ¶Ù¡¤Çº¤ØÁâ´Â self-disproportionation reaction ¢Í§ HBrO₂ ¹Ñè¹àͧ
                (FKN4)  2HBrO₂  -->  BrO₃^- + HOBr + H⁺             â´ÂÁÕ rate = k₄[HBrO₂]²
«Ö觡ÒÃà»ÅÕè¹ Process ¨Ò¡ A ä» B à¡Ô´¢Öé¹àÁ×èÍ rate ã¹ FKN5 à¡×ͺà·èҡѹ¡Ñº FKN2 áÅéÇËÒ [Br^-] ·ÕèàÃÔèÁà¡Ô´ Autocatalysis ã¹ process B  ´Ñ§¹Ñé¹ HBrO₂ áÊ´§µÑÇà»ç¹ inhibitor ¢Í§ Br^- ¹Ñè¹àͧ   áÅÐã¹ FKN4 ·Õè·ÓãËé [Br^-] Ŵŧä»ÍÕ¡àÁ×èÍà¡Ô´ autocatalysis à¾ÃÒÐÁÕ¡ÒÃÊѧà¤ÃÒÐËì BrO₃^- ¢Öé¹ áÅÐàÁ×èÍ [Br^-] ŴŧÁÒ¨¹¶Ö§ critical bromide ion concentration «Öè§à·èҡѺ
               k₂[HBrO₂][Br^-][H⁺]       =     k₅[BrO₃^-][HBrO₂ ][H⁺]
                                      [Br^-]_cr     =  (k₅/k₂)[BrO₃^-]  = 1.4 x 10^-5[BrO₃^-]
                        àÁ×èͶ֧ [Br^-]_cr  áÅéǨÐÁÕ¡ÒüèÒ¹¢Ñ鹵͹ Process B ä» C·ÕèÁÕ¡ÒÃà¡Ô´ autocatalytic acceleratory oxidation of metal ion catalyst ä´éá¡è
Process C :  2M_ox + MA + BrMA --> fBr^- + 2M_red + other product ·ÕèÁÕ rate = k_c[Org][M_ox]
àÁ×è;ԨÒÃ³Ò Process C  BrMA( Bromomalonic acid ) ¹Ñé¹à¡Ô´¨Ò¡ HOBr ·Õèà¾ÔèÁ¢Ö鹨ҡ process A áÅÐ M_ox ·Õèä´é¨Ò¡ process B
â´Â·Ñé§ MA (malonic acid) áÅÐ BrMA (bromomalonic acid) ÅéǹáÅéÇáµè¨Ð·Ó»¯Ô¡ÔÃÔÂҡѺ M_ox ·Ñ駤Ùè áÅéÇä´é Bromide ion ¡ÅѺ¤×¹
áµè¤èÒ stoichiometric factor f ¢Í§ bromide ion à»ç¹ parameter ·Õè adjust ¤èÒä´é ¶éÒ M_ox ·Ó»¯Ô¡ÔÃÔÂÒ੾ÒСѺ BrMA áÅéÇ f = 2, ËÒ¡ f > 2/3 áÅéÇ net concentration ¢Í§ Br^- ¨Ðà¾ÔèÁ¢Öé¹·Ø¡Ãͺ¢Í§¡Òà oscillate   ¹Í¡¨Ò¡¹Õé f  ÂѧÁÕ¤èÒä´éËÅÒ¤èÒµÒÁ MA , BrMA, HOBr áÅÐÍÕ¡ËÅÒ æ intermediate species áµèÍÂèÒ§äáçµÒÁ rate ¢Í§ process C ¡ç¢Ö鹡Ѻ¤ÇÒÁà¢éÁ¢é¹¢Í§ Org species ¡çä´é «Ö觻ÃÐÁÒ³ä´éà·èҡѺ¤ÇÒÁà¢éÁ¢é¹àÃÔèÁµé¹¢Í§ MA ¹Ñè¹àͧ