Nanoparticles. Educts. Nucleus formation. Nucleus. Growth. Primary particle. Agglomeration Deagglomeration. Agglomerate

Transcription

1 ucs Nucleus Nucleus omaon cal supesauaon Mng o eucs, empeaue, ec. Pmay pacle Gowh Inegaon o uson-lme pacle gowh Nanopacles Agglomeaon eagglomeaon Agglomeae Sablsaon o he nanopacles agans agglomeaon! anspo mechansm uson o convecon-conolle Pacle neacon van-e-waals aacon elecosacal / secal epulson Agglomeae sucue uklcal geomey, acals

2 Agglomeaon knecs sol nanopacles NP pacle se nm... nm agglomeaon espeson Wha s he le me o pmay nanopacles n a suspenson? specc suace aea 5 m²/g....5 m²/g sol pacle ensy ρ=. g/cm³ elecosac sablaon ea poenal ζ mv Agglomeaon knecs epens on: a anspo mechansm o NP n he meum uson Bownan moon low egme o he meum lamna, ubulen semenaon, selemen b aheson ecency slow, as coagulaon lecosac, secal epulson van-e-waals aacon LVO heoy, Fuchs sably ao

3 Agglomeaon knecs peknec as agglomeaon Smoluchowsk - uson ven Bownan moon van-e-waals oce acng only nanopacle s e abay sphee wh aus nanopacle s non-e Bownan moon uson coecen numbe concenaon sance nanopacles an wh a an ae agglomeang uson lu o -pacle acoss sphee o -pacle s Non equlbum hemoynamcs lu := popoonal aco vng oce A wh an neace aea A, hus negaon s necessay s Fck s law A n = L X wh n uson lu hough neace aea A s seay consan

4 Agglomeaon knecs peknec as agglomeaon Smoluchowsk - negaon Poblem: nanopacle s non-e now Wha s he elaon beween an? uson lu o -pacle acoss sphee o -pacle s negaon o gves bounay conons uson lu o non-e o e nanopacles chaacee by uson coecen Bownan moon an numbe concenaon anom walk n pobably p o go om o + o o - s equal hus: mean squae splacemen s p o walk y 6 o walk

5 Agglomeaon knecs peknec as agglomeaon Smoluchowsk - elaon beween an Wha s he elaon beween an? Now: uson lu o boh non-e NPs: elaon uson coecen - pacle amee anom walk o wo nanopacles - sance an mean squae splacemen s o walk el an walk nepenenly + o - hus: el wh nsen 6 k ollows 6 k nanopacle agglomeaon as a chemcal eacon k s he agglomeaon ae consan A + B chemcal eacon ae: secon oe eacon k usng uson lu 6 k k hus: k k

6 Agglomeaon knecs peknec as agglomeaon Smoluchowsk - agglomeaon ae consan nanopacle agglomeaon as a chemcal eacon A + A chemcal eacon ae: secon oe eacon k usng uson lu ollows k 6 k wh nsen k 6 ollows s he agglomeaon ae consan o a monospese nanopacle sysem k = m s - k 6 elaon uson coecen - pacle amee k k k Wha s he hal le me o hs agglomeaon? hal le me / : negaon sang wh sepaaon o vaables: / nal concenaon k k gves k k k, hus k k hal lve me / : / 8 k eample:.8 Ma-% O suspenson =.8 5 cm - hal lve me / : empeaue = 98 K vscosy wae = kg m - s - 8. cm / s. ms

7 Agglomeaon knecs Peknec slow agglomeaon Fuchs van-e-waals aacon an elecosac epulson - enegy bae see LVO heoy acs as a coune oce o vng oce concenaon gaen classcal mechancs: geneal physcs : lu: F oce = con aco velocy F v ga poenal enegy A A oce = poenal gaen v F lu = concenaon velocy A con aco o nanopacles n suspenson: k nsen k hemal enegy Sokes con oce as agglomeaon: slow agglomeaon: k nhomogeneous O o s oe: k homogeneous O o be solve: k k y y A k ep y k

8 Agglomeaon knecs Peknec slow agglomeaon Fuchs van-e-waals aacon an elecosac epulson - enegy bae see LVO heoy acs as a coune oce o vng oce concenaon gaen soluon o homogeneous O: k ep soluon o nhomogeneous O wh = : k k ep k ep ' ' k ep k ep k ep k ep bounay conons: soluon o nhomogeneous O: k ep k ep k ep k ep lu o boh NPs o slow agglomeaon: s k ep compae wh: o a as agglomeaon pocess Fuchs sably ao k ep W

9 Agglomeaon knecs ohoknec as agglomeaon Smoluchowsk - lamna shea oce, van-e-waals oce v shea gaen v sa vew numbe concenaon numbe concenaon en vew nanopacles an wh a an ae agglomeang: elave velocy o pacle o e pacle : v v, pacles wll come n conac when hey move nse a cylne wh he aus + + eenal aea s y A lu o wh A v pacles subsuon u v o n n ollows n e pacle : v ; u u u u u u