The growth kinetics of urea monocrystals from 1-propanol-aqueous solutions

562

Journal of Crystal Growth 102 (1990) 562 565 North Holland

THE GROWTH KINETICS OF UREA MONOCRYSTALS FROM I-PROPANOL-AQUEOUS SOLUTIONS A.Z. OLECH and S.A. HODOROWICZ Faculty of chem!3try, Jag,ellonian University, M. Kara5ia 1, ~0 060 Kral.du, Poland Received 2 January ~990

The growth kinetics of urea monocrystals from

propanol aqueous solutions were studied for solvents of composition 0 25 mol~

of n-propanol. The measurements were carried out at 298 K for [0011 and [110] directions. The crystallization rate was found to he a linear function of supercooling. The influence of biuret and ammonia on the growth rate of urea crystals is defined quantitatively and the relation between soluhility and the crystallization rate is discussed.

1. Introduction The growth kinetics of urea monocrystals from aqueous [1] and 1-propanol-aqueous solutions containing above 20 mol% of propanol [2] were described a few years ago. The aim of the present work was the investigation of the urea crystallization process from 1-propanol-aqueous solutions containing below 25 mol% of propanol. This mixed solvent shows anomalous behaviour of some physico-chemical properties with changing com position [3 5]. In the paper we present and discuss the linear growth rate of urea monocrystals along the [001] and [110] directions over a small supersaturation range. The aim 0f our work was to model the crystallization conditions of industrial scale processes, therefore the measurements were done in a natural convection regime and account the influence of biuret admixture. A thermodynamic relationship between solute activity and its melting heat was used to express the crystallization driving force in terms of supercooling.

the process is often treated a priori as a unimolecular autochemisorption reaction. Hence, the ohserved growth rate V of a given crystal face can be expressed in terms of the solute activity a by the formula: V

isa

isa,

del

is ia,

(I)

where a, denotes the urea activity in a saturated solution and is is a rate constant of the crystallization reaction. When the change in ~a is small, this linear relationship is usually well confirmed experimentally. The activity of supersaturation ~a can be calculated from the urea activity a in a super saturated solution and its activity in a saturated solution a, at the same temperature T. The value of k varies slowly with temperature (at 298 K the increment is about 10% per 1 K). SO when measurements are performed at a nearly constant T, it is possible to replace is by its value iso for the temperature 1~,at which the solution under study is saturated. Thus we may write v is0 ~ (2) The rate constant is depends on the choice of the

2. Growth rate dependence on supercooling Since one cannot deduce the mechanism of crystallization solely from kinetics measurements, 0022-0248/90

$03.50

1990

standard state for the solute activity in various solutions. In order to discuss the influence of solvent composition on the value of is. it is con venient to choose the pure solute in a hypothetical

Elsevier Science Publishers B.V. (North-Holland)

AZ. Olech, S.A. Hodorow,cz

/

Growth kinetics of ureafrom 1 propanol.aqueou3 solutions

liquid state as the common standard state. For this kind of choice of the standard state the activity a5 in saturated solutions may be connected within a good approximation with the temperature T by the formula: in a5 ( T)

—

(T

Tm 1)

I

~

Hm/R

def =

A ( fl,

(3) where LXHm and Tm are solute melting heat and temperature, respectively, and R is the gas constant. If the solution composition does not change in the course of the experiment, we can, according to eq. (3), express the crystallization rate (2) as a function of temperature. For ~a from (2) we obtain: ~a(T)

— =

a(T) a5(T) a5(7~)‘y(T)/y5(T0)

—

(4)

a5(T),

where y and ‘y5 are the activity coefficients in the solution in question at temperatures T and T0, respectively. If the temperature difference z~T 7~ T is kept small enough (e.g., in the present experiment less then 1 K), it may be assumed that y(T) ~ (5) =

—

From (3), (4) and (5), we then obtain (6)

i~a(T) =exp[A(7~)1 —exp[A(T)1,

which may be cast in the form ~a(T)

—

exp[A(To)1{1

—

exp[A(T)

0)1}.

Since in the case of small supercooling the following inequality holds A(1~~)A(T) (r I T0 1) LXHm/R —

Z~(T I) Z~Hm/R<< 1,

(8)

formula (7) can be simplified to z~a(T) = ajT0) zX(T

I)

~Hm/R.

(9)

After inserting eq. (9) into (2), we obtain for the crystallization rate 1)/R V— k0a5 ~Hm ZX(T

del

As seen from eq. (10), V is a linear function of the reciprocal temperature difference ~ ( T ~). However. j.~T<
k1 Z~T/T0T—k1 ~T/T0

def = k

2 ~T.

(11)

We see that the crystallization rate treated as surface reaction in slightly supersaturated soluttons grows linearly with the supercooling ~T. 3. Experimental The measurements were performed for 1-propanol-aqueous solutions containing 0, 5, 10, 15, 20 and 25 mol% of 1-propanol in the solvent, saturated with urea at 25°C. Two series of sampies were prepared. The first one was made using urea P.A. after additional purification through crystallization. The second series, containing I mol% of biuret and ammonia, was made of the first one kept in firmly closed vessels at 900 C for 12 h. Crystallization was carried out 3 indescribed a thermoin statted cuvette of capacity 10 cm more detail in a previous paper [7]. The supersaturation was varied by lowering the temperature of a starting supersaturated solution. The temperature was measured with a copper constantan thermocouple with an accuracy of ±0.01 K. The measurements were started each time as soon as the growth rate stabilized for a given supersatura-

—A(T

(7)

=

563

k 1 Z~i(T 1),

(10)

tion and the linear rate of growth for crystallographic directions [001] and [110] was found many times using a microscope and a stopper. The crystallization was started each time on a seed crystal, with z-axis oriented vertically, glued to a glass needle. In all cases the seed crystals were obtained from the same solutions in which the measurements of kinetics were carried out. When placed in the saturated solution, the seed was at first slowly dissolved by an increase of temperature and then the actual measurement began. As the size of growing crystals was very small, the solution cornposition remained practically constant during the whole measurement (possible shift of the equilibrium state less than 0.01 K). In order to determine the saturation temperature more precisely,

A.Z. Oleh, S.A. Hodorowicz

564

Growth kinetics of urea from I propanol aqueou.i ~olutton.s

a few measurements of the dissolving rate were also carried out. 4. Results and discussion 4.1. Growth kinetics from 1 -propano/-aqueous so/utions without biuret admixture Fig. I shows the results of linear growth rate for crystallographic directions [001] and [110] as a function of supercooling. Analysis of the results obtained has shown a linear relationship between V and ~T. In all investigated cases the statistical F-test did not justify the introduction of even quadratic terms to the regression function. From the experimental data, k2 and 1’0 were calculated for each solution by the least-squares method [6]. According to (10) and (11) the soughtfor value of k0 is given by the formula 2 k RT 0 k2 . (12) a0(7~i I~Hm

The activity a,(T

00) was calculated using (3) and the following data: z.1H~1— 15.1 kJ mol °. 1~ 405.8 K and R 8.314 J mol K ~. The values of T0 and k00 obtained by the above method and . the maximum supercooling (~T)~,~5 are listed in table I for each solution. 4.2. Crystallization kinetics from solution hiuret admixture

with a

Fig. 2 shows the results of measurements in solutions containing I mol% of biuret and 1% ammonia. These compounds are products of spontaneous condensation in urea solutions Table 2 contains the data relative to the crystallization rate of urea in the presence of biuret and ammonia. A comparison of the data from tables I and 2 reveals that crystallization from a solution contaming a slight admixture of biuret and ammonia runs much slower. Also, a lower repeatability of measured growth rate values was noted in the

v/jams’ a b

V/pm ~

/0.

o~25%

Fig. 1. Growth rate of urea crystals from 1 propanal-aqueous solutions without admixtures versus supercooling: (a) for5r,[001] (1J) 15 mol%, (x)to20themol% and(c’)25 of 1-propanol. direction, (b) for [110] direction. The symbols refer following solventmol% compositions: ( ) 0 mol%, (+) 5 mol%, (•) it) mol

A. Z. Olech, S.A.

Hodorowicz / Growth kinetics of ureafrom I-propanol-aqueous solutions

565

Table I Data for kinetics of crystallization of urea from 1-propanol-aqueous solutions without admixtures; the linear crystallization rate in m was expressed in mol m 2 s using the data for urea: p 1.335 Mg m and M 60.06 g mol

Crystallo-

Content of

Number of

T

graphic

1-propanol

measurements

(K)

direction

in solvent, x (mol %)

[001]

[110]

a)

0

Maximum

k0 (mol m

supercooling

2 ~

I)

(~T)max

(K)

0.0

16

297.6

0.33

9.4 ±1.0

5.0

5

297.5

0.52

2.5 +0.6

10.0

11

298.0

0.80

2.0 +0.2

15.0 20.0 25.0

12 10 10

297.9 297.8 298.0

0.91 0.95 0.78

1.3 +0.2 1.1 +0.2 0.90+0.11

0.0 5.0 10.0 35.0 20.0 25.0

6 4 12 7 3

297.3 297.5 298.0 297.9 297.7 298.0

0.50 0.91 0.73 1.03 0.96 0.80

1.12±0.18 0.41 + 0.09 0.35+0.04 0.17+0.03 0.16+0.05 (a)

Large fluctuations of the growth rate.

second series of experiments. It should be pointed out that the presence of such slight admixtures does not practically change the urea solubility (table 3). Generally, the influence of admixtures can be taken into account, e.g., on the basis of the hy-

pothesis of growth centres. If addition of molecules to a centre is treated as a simple reaction: [(NH2)2Co1501~~0~+ centre ~

[(NH2)2Co]~5~515,+ centre,

Table 2 Data for kinetics of crystallization of urea from 1-propanol-aqueous solutions with biuret and ammonia admixtures; the linear crystallization rate in m s

expressed in mol m

2

s

using the data for urea: p

Crystallo-

Content of

Number of

T0

graphic direction

1-propanol in solvent, x (mol%)

measurements

(K)

0.0 5.0 10.0

17

15.0 20.0 25.0 0.0 5.0

[001]

[110]

—

1.335 Mg m

Maximum supercooling

and

M

—

60.06 g mol

k~a)

(mol m

2

s

(~1 )noao

(K)

10

297.5 297.5 297.9

0.39 0.60 0.75

1.32+0.16 (b) 0.86±0.20

9 10 10

297.9 297.8 298.0

1.00 0.59 0.71

0.49+0.11 0.45+0.09 0.40+0.08

4 3

297.4 297.3

1.00 0.62

0.26+0.08 0.16+0.05

10.0

8

297.9

0.80

0.14+0.03

15.0

7

20.0 25.0

3 2

295.0 297.8 298.0

1.21 0.81 0.69

0.11+0.02 0.09+0.03 0.04+0.01

~ The superscript “b” denotes the presence of biuret and ammonia. b) Large fluctuations of the growth rate.

1)

566

.4

Z Olcch. S.A. Hodorowic:

/ Growth kinetics of urea from I

propa,iol.aqueou.s solutions

— o

‘~

0

a sb

1± C

0.~~-

.8

‘aD

a

1-~

.

,-~

in C

.0 ‘U)

C

E

~

0., >

C

C

C

C

a

0..

~ CS

E C

f

0. 0

~QC

-~

\

H S~\\\\Cs~

P

H

~

~ E~ 0. >

~°

=

~ ~,

r-J

5)

~0

A.Z. Olech, S.A. Hodorowicz / Growth kinetics ofurea from I -propanol.aqueous solutions Table 3

mo[

the basis of data taken from ref. [2]) 1-propanol

297.15 K

__ 22

297.65 K

1 0

298.15 K

in 0solvent mol% Solubility of of urea 114.8 Solubility in 1-propanol-aqueous (g urea 116.1 per 100 solvents g solvent) 117.3 (evaluated on

65.11 2.98 25.33

100 50

65.85 3.03 25.66

66.61 3.08 25.98

then the rate constant k0 is given by a product ‘.,

~

‘~“ ‘

567

[centrel,

(13)

‘~o where k~’ is

the rate constant of the direct reaction relating to a single growth point on the surface of a crystal [1]. According to relation (13) the relative number of occupied growth points for a crystal growing in the solution containing biuret is equal to i~[centre] [centre]

—

k0

k~ k0

(14)

‘

As the solvent composition changes, this ratio follows the curve shown in fig. 3. Eq. (13) holds on condition that the crystaliiza. tion process is limited only by the settling of molecules on the growth centres. If the process is also diffusion-controlled, the number of occupied growth centres is actually higher than that caiculated from (14). On the other hand, the observed effect of admixtures on the value of k0 shows that the diffusion constant cannot be much less than the surface reaction rate constant k~.The values

k0 oto ~ 070

.

mat Fig. 3. Minimal proportion of growth centres occupied by

admixtures for (001) face of urea crystals growing in the particular solutions, x mol% of 1-propanol in the solvent,

Ig

00 10 2

~j~juii~j±~

x/%mo[

Fig. 4. Plot of log k0 versus solvent composition x: (a) for pure solutions (•); (b) for solutions containing biuret and ammonia (o). Additional experimental data (D) for pure solutions taken from ref. [21.

of k0 for both faces under investigation vary up to two orders of magnitude with increasing propanol concentration in the solvents. That dependence has strongly non-additive character [2]. Moreover, the presence of admixtures lowers the value of k0 several times (cf. fig. 4). The growth rate of the (0(11) face from admixtured solutions is comparable with the growth rate of the (110) face from pure solutions. This is probably caused by an increase of the mean activation energy of the process in the presence of crystallization inhibitors. 5. Conclusions A comparison of (3) and (11) shows that, as long as the changes in supercooling LIT are small, soiubility and crystallization rate are linear functions of LIT. The solubility (table 3) depends coning to (3) it is connected with the change of activity coefficient siderabiy on the kind of of thesolvent solute. used The influence and accordof solvent composition on the crystallization rate has a more complex character. If the constant k0 is taken as a surface reaction rate constant, it may depend on solvent composition only in the case when the solvent takes part in the reaction. It should be noted that an equation of the (5) type can also describe diffusion-controlled processes and those which are simultaneously diffusion and

568

A. Z. Olech, S.A. Hodoross is:

Growth kineoc.s of urea from 1 propanol aqueou solutions

surface reaction-controlled. In the two latter cases the solvent affects the crystallization rate through diffusion coefficient variation. Moreover, when natural convection occurs, the magnitude of the supercooling LIT also affects the diffusion layer thickness in a solvent-dependent way. The results obtained show that the crystallization kinetics of urea has a rather complex character. The observed admixture influence proves that the process may then be limited by surface reaction kinetics. On the other hand, notable de pendence on solvent composition can only be cxplained provided that in a certain region natural convection occurs, which has to be taken into consideration, too. The results described above are an extension of the study by Davey et a]. [8]. An estimation of the diffusion part share in the whole process requires further measurements in a broader supercooling range.

Acknowledgment This work was supported in part by the Polish Ministry of Science and Highei Education Research Project No. RP II 13.2.14.

References ]l [ S A HodorowicL

and E.B Treis us, J Crystal Gro~th 47 (1979) 573. [2] LB. Treivus, Kristallografiya 27 (1982) 165 [3] M.F. Vuks. in: Molecular Physics and Bioph’ssics of Water Systems. No. I (lzd. Leningr Urns.. Leningrad. 1973) p 7 (in Russian).

Khirn. 12 (1971) 712. [5] ME Vuks. Zh. Strukt. Khim. 14 (1973) 73() [61J.A. Irvin and TI. Quickenden. J. Chern. Fduc. 60 (1983) 711. [7] S A Hodorowics, Kristall Tech. 12 (1977) 1259 [8[ R Davey, W Fila and J Garside. J (rvstal Growth 79 [4] M.F. Vuks and L.V. Shurupova, Zh. Struki

(1986) 607.