Indian Journal of ChemistryVol. 21A, August 1982, pp. 808-810

Diffusion of Cadmium Acetate &Self-diffusion of Cadmium Ions in

Cadmium Acetate in Agar Gel Medium+

SF PATIL* & N G ADHYAPAK

Department of Chemistry, University of Poona, Pune 411 007

Received 19 December 1981; revised 24 March 1982; re-reoised andaccepted 10 May 1982

Concentration dependence of DCct' + (over the concentrationrange of 5 x 10-5 to 10 ·3 M) in agar gel medium at 25T has beenstudied and an apparent agreement is observed betweenexperimental and theoretical diffusion coefficients in thisconcentration range. The observed dependence of activation energyand Do on gel concentration is consistent with transition state theoryof diffusion.

Numerous studies have been made on the self-diffusion of different ions in order to verify the validityof Onsager theory! for self-diffusion for both diluteand concentrated solutions. It was observed that thistheory failed as the electrolyte concentrationincreased. The present work has been undertaken tosee the applicability of Onsager's equation for thediffusion of Cd2 + ions in the gel medium. Thedependence of activation energy on gel concentrationover the temperature range of 25-4S'C for thediffusion of Cd(CH3COOh and Cd2 + 10

Cd(CH3COO)z, has also been investigated.Radioactive 115mCd2+ (t 1/2 = 45 days), was obtained

from the Bhabha Atomic Research Centre, Bombay,in the form of Cd(N03h and was converted intoCd(CH3COO)z.

The self-diffusion coefficients of Cd2+ ions atvarious concentrations in I% agar gel medium weredetermined at 25°C using zone-diffusion .technique.The influence of agar gel concentration on theactivation energy for the diffusion of Cd2+ ions andCd(CH3COO)z was examined by varying the gelpercentage between 1.0 and 2.5% at varioustemperatures, keeping the electrolyte concentrationconstant. The experimental set up and the calculationsinvolved in obtaining diffusion coefficient weredescribed earlier".

Concentration dependence of DCct2+-Substitution ofthe different parameters for the self-diffusion of Cd2 +in Cd(CH3COO)z in the theoretical equation ofOnsager-Gosting-Harned 1.3 results in the followinglimiting expressionDcct'+ x 10°cm -2S1 = 7.184-10.490JC ... (I)

t Dedicated to Dr. H.J. Arnikar, Professor Emeritus, University ofPoona, Pune, on his 70th Birthday.

808

while extended limiting law" for the self-diffusion ofCd2+ takes the following form

DCct'+ X 10° em "2S1

=7184-10490----~ JC _. . (I +3.6437 )<=)(1 +3.6437 JCI J2

... (2)

The data on the variation of theoretical Dcct' + (Eqs 1and 2) and the experimental Dcct'- with concentrationof cadmium acetate, presented in Table I, show adecrease in DCd' - with increasing concentration of theelectrolyte as predicted by the theory, and at very lowconcentrations, it approaches the Nernst ' limitingvalue (7.184 x 10 -6 em 2s -I ). Further, the deviationsof D:xp values from D(heorare only 0.2 to 1.3% over theconcentration range studied, indicating quantitativeagreement between the experiment and theory.

The observed agreement with the theory in thepresent system is somewhat surprising because a largedeviation from the theory observed earlier69 wasattributed to different types of interactions occurringin the ion-gel-water system. As described earlier, theagar macromolecules reduce the rate of diffusion byobstruction I0.11 and adsorption 12effects while water-gel interaction enhances the diffusion rate. The presentresults for the Cd2 + ion indicate that these interactionsare also taking place in gel medium, but the magnitudeof opposing interactions gets cancelled resulting in anapparent agreement with theory.

Effect of gel concentration on the activation energyfor the diffusion of Cd2+ ion and of Cd(CH3COO)zelectrolyte-- The Arrhenius plots for the self-diffusionof cadmium ion and electrolyte-diffusion of cadmiumacetate respectively for different gel percentages (1.0 to--~-------'--"'-----'-'-"------'---

Table I-Variation of Self-Diffusion Coefficient ofCadmium Ion with Concentration of Cd(CH3COO)2 in I~<)

Agar Gel at 2ST

Cone.(M)

Theoretical Experimental

Equation I Equation 2

0 7.1845 x 10-5 7.109 7.113 7.165I x 10 -4 7.079 7.085 7.0952.5 x 10-4 7.018 7.033 7.0545 x 10-4 6.949 6.978 7.0007.5 x 10.4 6.896 6.940 6.985I x 10-3 6.852 6.908 6.920

2.5~/~)are linear (Fig. I). The energies of activation e,required for the process of diffusion and Do values forboth the systems studied are obtained using the usualequation

... (3)

- 5.2

~-----~J.'J----~~~~J.43.2

\' / T I K x '03

Fig. 1·-- Activation energy for self-diffusion of Cd' + ---·--andelectrolyte-diffusion of Cd(CHJCOO)r-----for different gel

concentrations at 5 x 105M [Cd(CHJCOO),J

Wl/)

NOTES

The values of E, and Do with standard deviationsobtained by the method of least squares, presented inTable 2, reveal that E, and Do decrease with increasinggel concentration for both self- and electrolyte-diffusion. Similar results were reported by us forchromate", chloride 7 and zincl ' ions. This decrease inDo and E; can be accounted for on the basis of thetransition state theory of diffusion as was done by Fujiiand Thomas 14 for the diffusion of Na + in agar gelmedium.

As reported earlier": 13, by solving the Eyring's 15

expression for the diffusion, expression for Do comesout to be

D ·zkT "'S' Ro = e/. Ii-e + ... (4)

where ~st is the entropy change and i. is the averageelementary displacement in the direction of diffusion.Assuming the entropy of activation to be independentof the agar content, the decrease in Do implies that )"should decrease with increasing gel concentration. Ifwe assume cubical packing in the liquid, this geometrypredicts each molecule to be at a distance Vl/3 from theorigin, where V is the volume. It means that thecomponent i. in the direction of diffusion, varies withVI/3 and hence with W -1/3 where W is the weightpercentage of agar and as Do is proportional to A.2 (Eq.

1.0

-w

1.41.0 1.1 1.2 I.) 1.4

A

4.0lb)

21 9·0

(0)

'tII).0 20 'tII 7-0-;-

NE ~NE

uu ~N 2.0 19 ~

'0 5-0'~ '"~ ~.0 w ,00 0

1.0 18 )·0

1.0

1.)

B

11

10~oE

()'6 0·7 0.8 Q.9 1.0 0.6

w-2/)

Fig. 2-- Variation of (a) Do with w -, J and (b) E with W' , for (A) self-diffusion[Cd(CH,COO),] at 5 x 10 -5 M

0·7 0.8 0·9 1.0

w-2/)

of Cd2+ ion and (B) electrolyte-diffusion as

Table 2-- Variation of Do and E, for Self-Diffusion of Cd2 + Ion and Electrolyte-Diffusion of Cd(CH3COOh with GelPercentage at 5 x 105M Concentration

Gel Self-diffusion of Cd' + ion in Cd(CH,COO),----------_.- ---_._-- .._." "

1.0

L52.02.5

D~(I0-'cm's -I)

3.8±0.322 ±0.5LI ±0.2O.6±0.2

E(kJrnol-')

21.4±0.320.0±0.818.4 ± 0.617.2± 1.0

Electrolyte-diffusion of Cd(CH ,COO),

Do(104crn's ')

9.1 ± 1.44.7±1.03.0±0.31.6±0.3

E(kJ mol ')

11.6±0.510.1 +0.79.0±0.37.6±0.5

809

INDIAN 1. CHEM., VOL. 21A, AUGUST 1982

100

80

60

40;!

20

00

a

16 24 328

Polymeorizatlon time Itv

Fig. I-·Conversion as a function or the polymerization time for thepolymerization or L-IeucineNCA in acetonitrile at 30''C initiated by:(a) hexamethylenediamine, (b) ethylenediamine and (c) bis(4-aminophenyl) ether; monomer concentration = 0.434 mol/drn ';

mole ratio or monomer to initiator.= 400

appeared after 30 see, suggesting that during the veryearly stages of polymerization, soluble oligo-L-leucineswere formed, which on attaining a certain degree ofpolymerization, started precipitating at the cloudpoint 1. The results also showed that the polymeri-zation rate was dependent on the kind of the initiatorused and the rates followed the order: HM > ED> AP (Fig. I). This might be due to high basicity ofaliphatic diamines as compared to the aromatic one.Also the basicity of an aliphatic diarnine increases withincreasing its carbon chain",

The high conversion observed at a relatively shorttime for HM-initiated polymerization in comparisonto butylamine-initiated polymerization previouslyreported", indicated that the two amino groups of HMcan initiate the polymerization process simultaneouslyas a result of its flexible chain. However, a lowconversion obtained when AP was used as an initiator(59% after 6 days) suggested that the two amino groupsof such initiator could not initiate polymerizationsimultaneously as in the case of HM. This means thatthe polyu-leucines) formed, in the system initiated byAP, contain different molecular chain lengths incomparison with ED or HM-initiated polymerization.

812

The IR absorption spectra of the resultant poly (L-leucine) initiated by HM, ED or AP exhibited amide-Iband at 1650, the amide-Il band at 1540 and threeamide-V bands at 694, 657 and 614 em -I,

respectively 7, suggesting that the polymer samples

could be assigend the ex-form. The formation of the ex-helix suggested the formation of extended chaincrystals of polyu-leucine) during polymerization of theNCA3.

The X-ray diffraction patterns of polymer samplesobtained using the initiator HM, ED or AP showed astrong reflection at 28 = 7.7" which is characteristic forthe ex-helical structure of polyu-leucine):'. This is ingood agreement with the IR analysis.

The crystals of polyu-leucine) formed at the laterstages of polymerization showed under electronmicroscope a mixture of fibre and lamellae. In the caseof AP-initiated polymerization, the crystals formedduring polymerization of the NCA at the initial stages,were in the form of thin fibres. Thereafter, the fibrouscrystals just like super-helices were formed in the laterstages of polymerization.

The author wishes to express his deep thanks toProf. T. Kawai and Dr. T. Komoto of the Departmentof Polymer Technology, Tokyo Institute ofTechnology, Japan, for their help during this work.

References

I Komoto T, Akaishi T, Oya M & Kawai T, Makromo{ Chem, 154(1972) 151.

2 Komoto T, Kim K Y, Minoshima Y, Oya M & Kawai T,Makromol Chem, 168 (1973) 261.

3 Komoto T, Kim K Y, Oya M & Kawai T. Makromol Chem, 175(1974) 283.

4 Komoto T, Abo EI-Khair B M, Maeda K, Oya M & Kawai T.Makromol Chem, 177 (1976) 2491.

5 Abo,EI-Khair B M, Komoto T & Kawai T, Makromol Chem, 177(1976) 2481.

6 Lange N A, Handbook of chemistry, 11th Edn (McGraw-Hill,New York), 1973.

7 Itoh K, Shimanouchi T & Oya M, Biopolymers, 7 (1969) 649.