L a f a y e tte C ollege, E a sto n , P a.
A
P H Y S IC A L (diffusional) process is m ost frequently implied in describing th e course of crystallization of sucrose from necessarily viscous solutions; however, it has been frequently suggested (7, 16, 21, 22, 27) t h a t such previous tran sp o rt of sucrose across th e crystal-solution boundary m ay n o t necessarily control th e ra te of to ta l grow th u n d er ordinary operating conditions. I n th is situ atio n it m ay be, ra th e r, th e proper fitting an d orienting of th e individual m olecules in to th e crystal lattice which is th e slower and, therefore, rate-controlling step in th e crystal
lization process. T h e present p ap er reports a n analysis an d some experim ents favoring th e la tte r in terp retatio n .
> T he first tw o papers in th is aeries appeared in N ovem ber, 1944, pages 1042 and 1048.
* Present address, U n iv ersity of W yom ing, Laram ie, W yo.
T h e m echanism of heterogeneous reaction in general a n d crys
tallizatio n in p a rtic u la r is discussed by m any au th o rs (10, 12, 19, 28, 25, 26). T h e consensus of conclusions is t h a t th e N oyes- W hitn ey -N ern st-B ru n n er hypothesis of a diffusion-controlling ste p is n o t ad eq u ate for all crystallization, n o t solution (11), processes. T h e usual considerations leading to th is decision are:
ra te s of solution an d deposition of different crystalline faces;
ra te s of diffusion a n d viscosity vs. reaction velocity; effects of stirrin g ; an d effects of a d d ed colloids. T hese item s are discussed below in connection w ith th e cry stallizatio n of sucrose from p u re aqueous solution.
R A T E S O F D E P O S I T I O N O F C R Y S T A L L I N E F A C E S A ny sim ple diffusion th eo ry of heterogeneous reactio n rates- w ould dem and t h a t th e ra te s of th e reciprocal processes of
solu-August, 194S I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y tio n a n d crystallization be th e sam e a t equal displacem ents from
s a tu ra tio n an d also identical over all th e surfaces of individual growing crystals. T he form er specification has been shown to be untenable in th e case of sucrose crystals (IS) even a fte r allowing liberally for an y change in available surface by etching. In the la tte r connection i t is well known th a t sucrose crystals are fre
q u en tly elongated an d otherw ise d isto rted (2, 16, 20, S I, SO), an indication of unequal ra te of grow th, an d solution (2), of different faces. Such form s ap p ear upon grow th from pure solutions and are exaggerated upon grow th from im pure sirups. A lthough this inequality of ra te of grow th (and solution) of different faces seems to be th e norm al situ atio n , th ere is a practical working rule (due to KuCharenko, 16) th a t “un d er equal conditions of crystallization, there se ttle on a u n itj' of surface (average surface, IS) of a crys
tal, equal q u an tities of su b stan ce” .
D I F F U S I O N A N D V IS C O S IT Y v s . R E A C T IO N V E L O C IT Y I n th e form al N oyes-W hitney-N ernst-B runner theory th e unim olecular velocity co n stan t, in th e ra te expression
- ( d c /d t ) - fc (C - C„w.) is comprised of several com ponents as follows:
ifc = O D /V s
where C, C„td. = concentration of sucrose in actu al an d sa tu rated sirups, respectively
D = diffusion coefficient 0 — area c f reaction
7i = viscosity V = volum e of solution
S = thickness of adhering sa tu rate d fluid film T he dimensions of C are m ost accurately defined as activities (27). However, over n o t too g reat a spread in concentration,
Frequently it is assumed th a t a physical process (diffusion or viscosity) is th e rate-determ ining step in the crystalli
zation of sucrose from ordinary sirups. Several workers have indicated th a t th is is not necessarily so, b u t th a t a homogeneous and interfacial (chemical) reaction may be th e prim ary kinetic step. These works are reviewed, and are supplemented with stirring and colloid addition experi
m ents. The conclusion is confirmed th a t a homogeneous surface reaction is the rate-determ ining one.
molalities or sucrose-w ater ratios are appropriate, and even o rdinary degrees of supersaturations,
g _ % sucrose in sirup__
% sucrose in satd. sirup are approxim ately valid a t low concentrations.
T he facts expressing th e behavior of pure sucrose solutions are t h a t values of k (16, 27) increase and values of D decrease (29) w ith increasing concentration under conditions equivalent to co n stan t 0 an d V. D ecreasing diffusivities are also expressed by th e transposition (29)
D - f ( l /v )
According to th e preceding expression, this com bination of be
haviors dem ands a diminishing fluid-film thickness as concen
tratio n is increased. Since this behavior is exactly contrary to th e accepted expectation, i t throw s considerable question on th e validity of th e original expression an d its physical interpretation, as applied to th e p articu lar case of growing sucrose crystals.
Absolute values of <5 have been com puted (6) for some reactions for which complete d a ta are available, w ith th e general conclu
sion th a t unreasonably large values are realized. As suggested above, th e discrepancy would undoubtedly be fu rth er exaggerated in th e case of sucrose solutions. Since incom pletely known hydrodynam ic factors seriously affect th e significance of such com putations of absolute values, it is preferred to compare the possibility of a tru ly heterogeneous or homogeneously controlled reaction on th e basis of th eir tem perature coefficients; by this m eans th e uncertain fluid-film thickness is elim inated from
con-O S iru p S700 a S iru p 5702
I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 37, No. 8
o
D iffe r e n t s p e e d s o n s p in d le□ S p in d le s o f d iffe r e n t d ia m e t e r s , r o t a t e d a t s a m e s p e ed
sideration. T his com parison has already been perform ed in a prelim inary w ay (27); b u t w ith d a ta w hich have since become available (29), it is possible to im prove, extend, an d confirm th e form er presentation which indicated th e predom inance of a homo
geneous reaction.
T he tem p eratu re dependence of th e ra te s of th e factors in
volved in such a comparison— diffusion (or th e reciprocally re
lated viscosity) a n d crystallization velocity—is b est expressed in th e usual exponential form,
k = t o e ' W
w here k = diffusivity, viscosity, or specific reaction ra te constant E — a co n stan t designated as activ atio n energy of cor
responding process R = gas constant
T = absolute tem p eratu re
E is determ ined from th e slope of a p lo t of log K vs. l / T p lo t;
it is obviously definitive of th e tem perature-velocity relation and m ay be considered as an energy barrier to be surm ounted for the ensuing action. I n a n y sequence of reactions, th e larger activation energy will d ictate th e controlling course of th e reaction.
T able I an d Figure 1 represent schem atically th e activation energies of th e processes of crystallization, diffusion, an d vis
cosity of sucrose solutions. T he values are com puted from th e d a ta of K ucharenko (2,16), V an H ook (27, 28, 29), L..'.gham and Jackson (4), an d L a n d t (2, 17). (T aim ni’s viscosity d a ta and equations seem to be som ew hat irregular a t higher concentra
tions, 24.) T he values realized for diffusion an d viscosity are w ithin th e range usually allotted to “physical” processes (9), while th e consistently higher values for th e grow th process are of th e order usually assigned to purely “ chem ical” reactions. T his
T a b l e I . A c t i v a t i o n E n e r g i e s o f C r y s t a l l i z a t i o n , D i f f u s i o n , a n d V i s c o s i t y o f S u c r o s e S o l u t i o n s a t a
C o n s t a n t S u p e r s a t u r a t i o n o f 1.05
Growth (1 S - 1 6. t 7 , 1 8 , B9) Diffusion Q89) V iscosity (g, 4 , 1 7 ) T em p.,
°c.
E , kg.- ca l./m o le
D , sq. E , kg.- c m ./ c a l./
day mole V
E, kg.- ca l./m o le
10 0 .0 2 5 2 4 .4 0 .0 6 5 8 .0 940 8 .0
20 0 .3 6 2 0 .0 0 .0 6 0 4 .7
402 & 7 . 0
40 1 .9 0 1 1 .7 0 .0 5 0 2 .0 4.5
60 6 . 0 1 0 .0 - 0 . 0 0 7 ° 0 . 5(?) 222 3 . 0
80 1 2 .6 7 .4 — 0.013® 4 .7 (? ) 214 2 .0
w ould seem to indicate t h a t diffusion (or vis
cosity) is n o t th e rate-controlling ste p in th e crystal-grow ing process. S im ilar co m p u ta
tions a t o th er co n stan t su p ersatu ratio n s give th e sam e relativ e results.
E F F E C T S O F S T I R R I N G
I t is generally recognized (12) t h a t th e reac
tio n ra te co n stan t is a pow er fu n ctio n of th e ra te of stirrin g :
K = a(N)P w here K — velocity co n stan t
N = ra te of stirrin g a, f) = constants
W hen th e reaction is diffusion-controlled, /S as
sum es th e value of 1 or n early 1; its value approaches zero for reactio n s controlled by a n in terfacial reaction. W hen b o th actions are significant, it is usually found t h a t /S will ru n th ro u g h th e com plete range of values if a sufficiently wide range of s tirre r speeds is observed.
In some grow th experim ents in w hich an abu n d an ce of sucrose crystals were suspended in th e growing m edium , it w as observed (27) t h a t th e m easured velocity c o n stan t w as e rratic a t low rates of stirrin g (below a b o u t 100 revolutions p er m in u te in th e ap
p a ra tu s used), b u t becam e linear a t speeds betw een 100 a n d 300 r.p.m . an d th e n slackened off to a c o n stan t value beyond 350- 400 r.p.m . T h is linear section is also rep o rte d b y A m agasa (1), b u t only for th ree different stirrin g ra te s; th e sam e leveling off is observed by o thers (8, S I) a t speeds depending on th e dimensions of th e a p p ara tu s used. I f th e curves are appraised according to th e above logarithm ic suggestion, exponents of less th a n 0.4 are realized in all cases; th is suggests t h a t diffusion is n o t th e con
trolling step in this reaction, alth o u g h th e w riter (27) believes th a t th e effects of false graining obscure th e issue in th is ty p e of experim ent. I n fact, i t has been suggested (27) th a t th e linear p ortio n of th e curve m ay be largely th e re su lt of a ttritio n of th e larger size crystals for, w ith an equal w eight of v ery finely powdered seeds, th ere is no appreciable difference in th e ra te of
“Extrapolated. b A t 30° C
I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 785 velocity of th e grow th was com puted from microscopic m easure
m ents of th e lateral a an d c axes (2, 15). In th e second series, am ount of solution used, suggests th a t th e deviation from linearity displayed in Figure 4 m ay be due to this behavior. Em pirically effects of false graining. D uring th e sequence of exposures, a few nodules developed and grew on th e p a ren t crystal, b u t n o t to the extent of interfering w ith th e m easurem ents of th e size of th e m ajor crystal. T he corresponding decrease in sirup concentra
tion during th e tim e of m easurem ent could n o t be d etected re-
m endously, y et has little effect on th e crystallization velocity.
As specific examples, different am ounts of gum acacia were
dis-persed by steeping in h ot sirup equivalent to a supersaturation of 1.08 a t 30° C. Two clear filtered sirups displayed rising bubble viscosities four an d tw enty-five tim es as g reat as th e pure sirup, y e t th e velocities of crystallization from such sirups were only 98 and 99% of th e original velocity, respectively. T he to ta l reduc
tion in refractive indices in all th ree cases was approxim ately the same, suggesting (1) th a t th e solubility of sucrose was not changed by th e presence of these colloids.
I M P U R E S I R U P S
T he only evidence indicating th a t an interfacial ra th e r th an a tran sp o rt action controls in th e crystallization of sucrose from actual sirups is th e fact th a t a high-tem perature index of reaction velocity (a t least 2 per 10° C. rise or an activation energy of the
term ined prim arily by some interfacial (homogeneous) reaction ra th e r th a n an interboundary (heterogeneous) reaction.
A CK NO W L E D G M E N T