Indian Journal of Chemistry Vol. 38A, March 1999, pp. 244-248

Nucleation studies in supersaturated aqueous solutions of (NH

4)H

2P0

4 doped with NaCl and NaH

2P0

4.2H

20

C Mahadevan* Department of Phys ics, S T Hindu College, Nagercoi l 629 002, Tamilnadu , India

and T K Jeya Sobha & V Umayorubhagan

Department of Chemistry, S T Hindu College , Nagercoil 629002, Tamilnadu , India

Received 10 September 1997; revised 10 December 1998

Induction periods have been measured for va rious supersatu rated aq ueous solutions of ammonium dihydrogen orthophosphate doped with sodi um chl oride and sodium dihydrogen orthophosphate dihydrate by the direct vis ion method. Various cri tical nucleation parameters have been calcu lated based on classical theory for homogeneous nucleation and the results are discussed. The critical nucleation parameters increase with the increase in concentrati on of doping in the (N H) HlO. solutions for both the dopants.

Nucleation process is the first and most important phe­nomenon in liquid- solid phase transition . The induction period ('t) can be measured 1.2 and used to calculate cer­

tain critical nuc leati on parameters like inte rfacial ten­s ion (cr) of the solid re lative to its solution, energy of fo rmation (~G) of a critical nucleus, and radius of the nuclcus( r) in equilibrium with its so luti on, based on the classical theory of homogenous nucleation. During the study of nucleati on, both theore tical and experimental difficulties are encountered . The major theore tical diffi­culty ari ses from the fact that the size of the nucleus is too sma ll to be treated by the thermodynami c theories and too large to be dealt with the atomi sti c concepts. Since the c ritical nuc lei a re so small , accurate measure­ments are not reall y feasible and calculated values de­pend very much on assumptions made, many of whic h cannot as yet be independentl y tested. The inferences drawn from observations are therefore indirec t.

Ammon ium dih ydrogen orthophosphate (A DP), (NH) Hl0

4, is an inte res ting material widely used in

industri es. It is iso morph ous with KDP (po tass ium dihydrogen orthophosphate) and has te tragonal structure very simil a r to that of zircon. The dimens ions of the tetramolecular unit celP are a=b=7 .5 lo A and c=7.564A.. The so lubility of ADP in water at 20, 40, 60 and 80llC is 37.4, 56.7 , 82.5 and 11 8.0 parts by weight per 100 parts by we ight of water respec ti ve ly4. Nucleation studies on

aqueous ADP solutions with and without some added impurities (doping concentration 100 ppm) have already been reported by Nagalingam et aI'J,. In the present study we atte mpt to investi gate the effect of the impurities like NaCI and (NH

4)H

2P0

4.2H

20 on the nuc leation param­

eters of ADP. The cri t ica l nucleati on parameters have been calculated and the e ffect of supersaturati on and con­centrati on of doping on them is a lso repo rted and di s­cussed.

Materials and Methods Analytical reagent grade samples of (NH

4)H

2P0

4,

NaCi and(NH4)H2P04.2HP and doubl y distilled water were used in the present study. Aqueous so lu tions of various supersaturated concentrat ions were prepared by dissolving the required amoun t of ADP and dopant (rang­ing from 2000 ppm to 10000 ppm) in doubl y distilled water, at te mperatures sl ightl y hi gher than the satura­ti on te mperature . Supersaturation was attai ned by natu­ra l cooling.

Induction peri ods(L) have been measured by the di­rect vision method2 .. '.-7 . The experimental set up for in­duction period measurement consisted of two identical nucleation cells ( I OOml corning g lass beakers) kept at a constant temperature o f 33 11C (controlled to an accuracy of ± O.IIIC) . One of the ce ll s was used as dummy (as inserti on of thermometer in the experi men tal cell may

MAHADEVAN el al.: NUCLEATION STUDIES IN SUPERSATURATED SOLUTIONS 245

disturb the system). The cell s could be illuminated us­ing a powerful lamp. Supersaturated (saturated at a re­quired higher temperature) aqueous solutions of equal volume were taken in the cells. A sensitive thermom­eter (accuracy is 0.1 0c) was placed in the dummy cell. As the temperature of the cell reached the experimental temperature, the time was noted . Once the nucleation occurred, it grew quickly and a bright sparking particle was seen. The time of observation of the sparkling par­ticle in the undi sturbed nucleation cell from the time at which the solution reached the experimental tempera­ture gave the induction peri od.

Experiments were performed at fi ve selected degrees of supersaturations (xl xl)) , viz ., 1.200, 1.225, 1.250, 1.275 and 1.300 at 331)C, where x is the mole frac­tion of the solute in the supersaturated salt solution at the experimental temperature and xI) is the mole fraction of solute in the salt solution saturated at the experimen­tal temperature. XII was found to be 2.734 M. The vol­ume of the solution taken in the nucleation cell s was maintained at 20m I in all the experiments. Several nucle­ation mns were carried out under contro lled and unstirred conditions. Reproducible results within an accuracy of ±2% were obtained in the present study.

The direct vision method is not very accurate and does not in volve ri gorous methodology to study nucleation. The nuclei are not visible even by micro­scopes and at the observable level, they are already at the growth stage. It is assumed that the time required fo r the critical nucleus to grow to an observable level is very small and negligible compared to the inducti on pe­riod. Despite all these problems, this method was con­sidered fo r the reason that no other better method is avail­ab le to study nucleation in supersaturated so lutions of highl y soluble substances. To reduce the inaccuracy, care was taken so that the supersaturated concentrati on con­sidered prov ided an inducti on peri od of at least 50 sec. The effect of heterogeneous nucleation due to dust par­ticles fro m air was reduced by carrying out the ex peri­ment in a re lati vely dust-free space. Also, the effect of heterogeneous nucleat ion due to scratchings on the in­ner wa ll of the nucleati on cell (glass beaker) was re­duced by choos ing a glass beaker without sc ratches (tested with a microscope).

Results and Discussion The measured inducti on peri ods are presented

in Table I. For both the dopants considered in the present study, the va lue of 't decreases and hence the nuclea ti on rate increases as the supersaturat ion and concent ration of doping of the aqueous so lution increase. This is simi-

Table 1- Resul ts of induction period measurements

Doping ratio x/x() t (5) for

NaCI doped NaHl O4·2Hp ADP doped ADP

Pure ADP 1.200 15480 15480 1.225 8280 8280 1.250 3480 3480 1.275 2 160 2 160 1.300 1020 1020

1:0.002 1.200 13200 4380 1.225 7300 2340 1.250 3060 960 1.275 1860 600 1.300 900 290

1:0.004 1.200 10920 3660 1.225 5760 1980 1.250 2430 840 1.275 1380 5 10 1.300 720 240

1:0.006 1.200 8640 3060 1.225 4620 1620 1.250 1920 660 1.275 960 420 1.300 570 200

1:0.008 1.200 6660 1860 1.225 3 120 960 1.250 1320 420 1.275 720 240 1.300 390 120

1:0.0 10 1.200 4440 900 1.225 1920 480 1.250 780 2 10 1.275 420 120 1.300 240 57

lar to the results observed fo r KDP doped (in the same rati o considered in the present study) with KBr, K

2Cr0

4

and K2Cr

20/ref. 8-1 0) .

As per the c lass ica l theo ry of ho mogeneous nucleati on, we expect a linear relati onshi p between 1111 and I IIn2 (xix). However, we observed small dev iat ions from lineari ty at lower supersaturation levels (Figs I and 2) of 1111 versus I IIn2 (xlxl))' Such dev iati ons from I inear­ity have been reported earlier also 25 .7- JI) and expla ined by considering the heterogeneous nucleation caused by the unwanted impurity particles present in the aqueous solution. Nagalingam el af5 observed thi s lineari ty fo r pure ADP at temperatures higher than 251)C. However,

246 INDIAN J CHEM, SEC. A, MARCH 1999

.. .5

.. .E

" "0 e

10

9.

8

7

6

5

14

10

9

8

6

5

4

3

14

17 20 23

Il1n'(IIIo)

26

1 _ 1'0000 I 1 --1;0:002

--1:0.004 ---1:0.006 -x-I :O.OO8 -<>-1:0.010

29

Fig. 1 - Plots of In~ against Il1n'iIl~) fOT N.CI doped ADP

17 20 23 26 29

1I1n'(IIIo)

Fig. 2· Plots of Int .gainst l/In'i!I~) for NaH,PO,.2H,O doped ADI'

11~----------------------------------~

14 --1 :0.000 -1:O.OOl --1 :0.004 --1:0.006

~ 11 ..... 1:0.008 -1:0.010

t5 <l

..

8

s~------__ ~------~--------~------~ U S 1.2 1.25

II""

1.3

13

Fig. 3 • Dependence of energy of formation of critical nucleus on supersaturation for NaCI doped ADP

--1:0.000 l -1:0.002

-1:0.006 -X-I :O.OOS

"0 10.5 .e

-1:0.004 1

-1:0.010 I

:;) t5 <l

5.5 "---------'---------_------__ ~------~

l.l5 1.2 1.25

II ..

\.3 1.35

Fig .... Depcodeoce of energy of !ormation of critical DuciclU OD

lupersaturation for Nall,I'O,.2ll,O doped ADP

a !!, ...

a !!,

1.25 r-------------------.

1.15

1.05

0.95

0.85

0.75

US 1.2 1.25

II ..

--1:0.000 -<>-1:0.002 -1:0.004 -1:0.006 --1:0.008 -1:0.010

1.35

Fig. 5· Dependence of ra.dius of critical nucleus On supenaturation for NBCI doped ADI'

1.15

1.05

r --1:0.000 --J :0.002 --1:0.004 -1:0.006 '""'-1:0.008 -1:0.010

... 0.9.5

0.85

0.75 +---------;.-------+_---------"'-----...J 1.15 1.2 1.25

IIx.

1.3

Fig. 6· Dependence of .. ad ius of critical nucleus on supersaturation for NaB,PO,.2H,O doped ADI'

1.35

linear relationship has been observed fi at 300C for ADP

doped with NH4CI, (NH4)2S04' NH4I, NH~NO}' KDP and NaH

2P0

4 (doping concentration is· 100 ppm). Thi s dis­

crepancy could be because the doping concentrati on in the present study ranges from 2000 to 10000 ppm (more­over the dopants are different) and also til e temperature is higher (33°C) . This non-linearity is al so ex plained by considering the heterogeneou s nucleation caused by the unwanted impurity particles present in the aqueous so­lution .

Although the ex periments were conducted at controlled conditions, the practical difficulties (such as hav ing the solvent free from natural impuri ties) in main­taining the nucleation strictly homogeneous led to de­viations from the class ical theory for homogeneous nucle­ation especially at lower supersaturations . For higher supersaturated solutions, the effect of the unwanted im­purity particles present in the solvent is dominated by the presence of greater amount of solute . Hence, we ex­pect a linear relationship at higher supersaturation s. Also, the linear dependence is greater when the solubility of

MAH ADEVAN et al.: NUCLEATION ST UDI ES IN SUPERSATURATED SOLUTIONS 247

Table 2-Nucleation parameters

Doping ratio For NaCI doped ADP For NaHl04.2Hp doped ADP

cr (mlm·2) *""G (klmol") *r (nm) cr (mlm·2) *""G (klmol" ) *r (nm)

PureADP 3.985 5.9 17 0.767 3.985 5.9 17 0.767

1:0.002 4.098 6.434 0.789 4.083 6.368 0.786

1:0.004 4 .163 6.603 0.80 1 4.094 6.41 9 0 .788

1:0.006 4.279 7.329 0.827 4. 10 1 6.449 0.793

1:0.008 4 .326 7.573 0.833 4. 128 6.578 0 .795

1:0.0 10 4.38 1 7.865 0.843 4 .203 6.944 0.809

*""G and r values are calcul ated at the maximum supersaturati on.

the substance is greater. The higher solubility compo­nent may dominate over the unwanted impurities present in the sol vent more effecti ve ly than a substance with lower solubility as it was observed with FeS0

4.7Hp

(lowe r solubility and lowe r linear depende nce) and ZnS0

4.7Hp (hi gher solubility and greater lineardepen­

dence)1.

Considering the principles of homogeneous and het­erogeneous nucleati on, the free energy of formati on of a nucleus under heterogeneous nuc leation is less than that under homogeneous conditi on2

.

The effect of solvent impuri ties cannot be reduced by increasing the supersaturati on because the max imum prac tical limit for the measurement of inducti on period does not a ll ow the supersaturation to exceed 1.300. If the supersaturation is beyond thi s practical limi t, then nucleation occurs before the attainment of supersatura­ti on (that is before cooling to the experimental tempera­ture). Hence, in order to reduce the effect of these prac­tical di ffi culties on the nucleation parameters, the re­sults were obtained in the present study using the slopes determined in the I inear region of the pl ots of 1m aga inst I/ln2(x/x).

Vari ous critical nucleati on parameters have been ca l­culated using the express ions2

:

r = 2cr V 1 [RT In(x/x)] where V,N, R, T and 117 are the molar vo lume of crystal, Avagadro's number, gas constant , temperature and slope

of the line plot of In1 aga inst Illn2(x/xo) respecti vely. The results are presented in Table 2. The values of f,.C and r at vari ous supersaturations have also been calcu­lated for a ll the crystals and the results are presented in F igs 3-6 .

In the present study, it was observed that for both the dopants, the va lues of f,.C and r decrease with increase in supersaturated concentration which is similar to the results observed fo r pure and doped ADps.6 , pure and doped KDp2.X, IO and FeSO .7H 0 a nd ZnSO 7H 0

4 2 4 ' ?

(ref.7). -

It was seen that the values of cr, f,.C and r increased with the increase in concentration of doping in the ADP solution (Table 2 and F igs 3-6). Similar results have been observed for the dopants KBr, K CrO and K Cr 0 in

2 4 2 2 7 the case of KDpx, '1I

Thus the present study indicates that the induction period decreases with increase in doping concentration in the aqueous solution of ADP. The nuc leation param­eters calculated based on the class ical theory fo r homo­geneous crystal nuc leation increase with increase in dop­ing concentration. The class ical theory for homogeneous crystal nucleation is well ex pl ai ned by the experi men­tally observed linear re lationship between 1m and I/ In2

(x/x) .

References

Mu ll in J W, Crystallizatioll (B utterworth-Heinemann, Oxford), 1993.

2 Shanmugham M, Gnan am F D & Ramasamy r J Matcr Sri 19 ( 1984) 2837. ' , ,

248 INDIAN 1 CHEM , SEC. A, MARCH 1999

3 WyekoffR W G, Crystal structllres. Vol 3, 2nd Edn (Interseienee, New York), 1960.

4 10hn A Dean, Lange 's handbook of chemist!)'; 12th Edn (Me Graw-Hill Book Company, New York), 1979.

5 Nagalingam S, Vasudevan S, Ramasamy P & Laddha G S, Kristall und Technik. 15 (1 980) 1151.

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7 Baekiyam M, Anitha R Nair & Mahadevan C, Indian J Pllre &

Appl Phys. 29 (1 99 1) 455.

8 1aniland Angel G, Mahadevan C & Umayorubhagan V, Paper presented in VI/national seminar on Clystal growth , Al agappa University, Karaikudi, 1997.

9 1agadeesan C S & Mahadevan C, Paper presented in VII na­tional seminar 0 11 c rystal growth. Alaga ppa Uni vers it y, Karaikudi , 1997.

10 Anton Sophana V, Mahadevan C & Umaryorubhagan V. Paper presented ill VI/national seminar on crystal growth. Al agappa University. Karaikudi 1997.