Micromeritics: N = 6 πd vn 3 ρ d vn = mean diameter based on volume-mean number (see table p. 426), cm ρ = density of the powder, g/cm 3

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1 PHCEU 55 Equaion Shee, Exam 3 C. Lim and B.Yu, Insrucors Micromeriics: N 6 πd vn 3 ρ d vn mean diameer based on volume-mean number (see able p. 46), cm ρ densiy of he powder, g/cm 3 Surface area of sphere πd Volume of sphere πd 3 /6 Surface area α s d p πd s Volume α v d 3 p πd 3 v /6 α s /α v 6 for a sphere S v surface area of paricles α s volume of paricles α v d S w surface area per uni volume S v densiy ρ ρ rue densiy α s α s d now defined as d vs for his case; ρα v d ρα v d vs d vs volume-surface diameer characerisic of specific surface For a sphere, S w 6 since α s /α v 6 ρd vs Є V bul V paricles (ofen expressed as a percen, so muliply by ) V bul V bul - V paricles void volume Bul densiy ρ bul weigh/ V bul True densiy ρ weigh/ V paricles Buliness /(bul densiy) V bul /weigh an φ µ h/r µ coefficien of fricion h heigh of powder cone r radius of powder cone

2 Rheology: Shearing sress, F: F F ηdv η viscosiy (dynes sec/cm or poise) A dr dv/dr rae of shear G (sec - ) viscosiy: η F G fluidiy: φ /η Kinemaic viscosiy η/ρ in soes where soe poise/(g/cm 3 ). η A e E v/rt η viscosiy (usually in cenipoise) A consan E v acivaion energy ruired o iniiae flow beween he molecules (cal/mol) R gas consan (.987 cal/ Kmol) T emp in Kelvins η rel η ρ η ρ ρ and ρ densiies of liquids and (g/cm 3 ) and flow imes of liquids and (sec) η and η viscosiies of liquids and (cenipoise) /η V /η + V /η V, V volume fracions of pure soluions and η, η viscosiies of soluions and U (F f) where F shearing sress, or F /A (dynes/cm ) G f yield value (dynes/cm ) G rae of shear (sec - ) (Unis of U are poise, or dynes sec/cm ) F N η G η represens a viscosiy coefficien

3 B U U ln ( / ) U and U plasic viscosiies of he down curves afer shearing a a consan rae for and, respecively. M U U ln (v /v ) Flow of a liquid: η F/G F shear sress G shear rae Elasiciy of he solid (from Hooe s Law, uaion of a spring): E elasic modulus (dyne/cm ) F sress (dyne/cm ) γ srain (dimensionless) E F/γ Coarse dispersions: G γ SL A G final G iniial γ SL (A final A iniial ) γ SL he inerfacial ension beween solid and liquid, measured in dynes/cm G surface free energy ( G) erg/cm (erg g cm /sec ) A change in surface area, cm v d (ρ s ρ o ) g 8η o v velociy of sedimenaion (cm/sec); also nown as rae of seling d diameer of paricle (cm) ρ s, ρ o densiies of dispersed phase and dispersion medium, respecively (g/cm 3 ) g acceleraion of graviy (98 cm/sec ) η o viscosiy of dispersion medium in poise v v n v rae of fall a he inerface (cm/sec) v velociy of sedimenaion from Soes Law iniial porosiy of he sysem n a measure of he hindering of he sysem (a consan for each sysem) F V u /V o V u final, or ulimae volume of sedimen 3

4 V o original volume of he suspension F V /V o β F/F V u /V β ulimae sedimen volume of flocculaed suspension ulimae sedimen volume of deflocculaed suspension F M /M o n Fracional release (F) of drug from a gel a ime : M amoun of drug released a ime (g or oher) Mo iniial amoun of drug (g or oher) rae consan (min -n ) ime (min) n diffusional exponen (uniless) Drug diffusiviy, D, in he gel marix: D o diffusiviy of solue in waer (cm /sec) H K f consan (cm /sec) H marix hydraion (uniless),. swollen gel w dry gel w. swollen gel w. Thermal degradaion wih respec o rigidiy: lnd lnd o K f ( - ) - f where f, f o rigidiy index a ime, or ime zero (g - ) f f o f rae consan (g - hr - ) heaing ime in hours f Ae -Ea/RT A Arrhenius consan Ea energy of acivaion R gas consan; T emp (K) 4

5 Kineics. The following able summarizes he resuls for, s and nd order reacions: n rae uaion / c a /.5a.a.5a lnc lna / a c ac / a 9a 9a. For pseudo zero order degradaion of suspension: S 3. Reversible reacions: K [B] [A] f r 4. The Arrhenius uaion: ( T) Aexp( Ea / RT) E a is acivaion energy (cal/mole) 5. The Q value: Q (T + ) (T) 6. Shelf life esimaion: and Q. (T ) (T ) ( T T T ) T (Q ) c( T) Ea 7. Rae consan due o caalysis exp[ ] s(t) RT 8. Specific acid-base caalysis: obs s + H [H 3 O + ] + OH [OH ] 5