Colloids and Surfaces, 23 (1987) 313-343 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

Adsorption and Desorption of Hydrolyzed Ions. III. Scandium and Chromium

BARRY GRAY* and EGON MATIJEVIC

313

Metal

Department of Chemistry and Institute of Colloid and Surface Science, Clarkson University, Potsdam, NY 13676 (U.S.A.)

(Received 23 March 1986; accepted in final form 23 September 1986)

ABSTRACT

Adsorption of scandium( III) and chromium (III) species on a PVC latex was measured using radioactive isotopes; the uptake increased with increasing pH. The data were interpreted by com- bining aspects of the models of James and Healy and also of Anderson and Bockris. The experi- mental and calculated results agree quite well for scandium, but not for chromium. The deviation in the latter case is believed to be due to polymerization of the hydrolyzed chromium cations and to the interaction of chromium with the anionic surface groups of the latex. Neither of these interactions occur with scandium. Hydrolyzed scandium species adsorbed on the latex were removed by acidifying the dispersion, while chromium complexes were not, substantiating the proposed difference in the chemical nature of chromium and scandium species at the solid/solution interface.

INTRODUCTION

The adsorption phenomena of metal ions on various surfaces has been extensively studied. The major observations can be summarized as follows: (1) the unhydrolyzed (hydrated) cations do not adsorb on hydrophobic surfaces unless they form chemical bonds with constituent ions of the solid of opposite charge; the exception seems to be adsorbents of high dielectric constants such as TiO,; (2) hydrolyzed ions are specifically adsorbed onto hydrophobic sub- strates and can cause surface charge reversal; consequently, the uptake of hydrolyzable ions is strongly pH dependent; and (3) hydrolyzable cations adsorb onto many different substrates of widely varying surface properties including glass, metal oxides, polymer latexes, and silver halides. Conversely, desorption of hydroxylated ions can take place if these are dehydrolyzed by protonation in acidic solutions. The reversibility of the adsorption process depends on the nature of the complexes at the surface. If no bonds are formed between the adsorbed species and the constituent ions of the solid, and if no

*Present address: Eastman Kodak Company, Rochester, NY, U.S.A.

0166-6622/87/$03.50 0 1987 Elsevier Science Publishers B.V.

314

further polymerization of the hydrolyzed ions takes place after adsorption onto the solid surfaces, the removal on acidification can be quite rapid. Otherwise, desorption is slow and incomplete.

While considerable experimental information on these problems has been reported in the literature, the theoretical interpretation of the results has been lagging. An important step forward in the development of an understanding of the mechanism of metal ion adsorption was made with the model by James and Healy [ l] and the model by Anderson and Bockris [ 21. By stressing the importance of the hydration energy, in addition to other obvious contributions (coulombic and chemical), they have been able to account for certain aspects of the observed phenomena.

In previous papers [ 3,4] we reported adsorption and desorption data of alu- minum, cobalt, and thorium ions using latexes and silver halide colloids as substrates. This work represents an analogous study using a PVC latex in the presence of scandium (III) and chromium (III) ions. The chosen cations have the same charge and readily hydrolyze. However, hydrolyzed chromium ions tend to polymerize on aging and also strongly bind certain anions, such as sulfate and phosphate; scandium forms well defined mononuclear and poly- nuclear hydrolysis products and does not complex with the same anions. Thus, the surface chemical reactions of these two ions should cause different adsorp- tion/desorption phenomena.

In the interpretation of the results the Anderson and Bockris model has been slightly modified but their definition of specific adsorption has been retained: the ion is assumed to form a direct bond with the substrate without an inter- vening water layer. This is accomplished by a partial dehydration involving the removal of some of the ion’s inner sphere water molecules. In the case of scandium (III) the calculated adsorption densities were in good agreement with the experimental values.

EXPERIMENTAL

Materials

Chromium (III) nitrate (Fisher Certified Reagent) and scandium (III) nitrate, 99.9% pure (“K and K” Laboratories), were not further purified before use. The stock solutions made from these chemicals were passed through Nuclepore polycarbonate filters to remove any suspended contaminants. To prevent metal ion hydrolysis, the stock solutions of both salts were acidified with nitric acid to pH 1.5. No aging was noticed during the storage of the stock solutions for one month at 25°C. The concentrations of the dissolved chro- mium and scandium salts were determined by gravimetric analysis.

The polyvinyl chloride (PVC) latex was the same as used in the previous study [ 31 and it was purfied as described earlier.

315

The radioactive isotopes 46Sc3+ and 51Cr3+, employed in this work, were obtained from New England Nuclear as chloride salts dissolved in 0.5 mol dmp3 HCl.

Metal ion adsorption by gamma ray spectrometry

The metal ion adsorption onto the PVC latex was determined by the radio- tracer technique using a Packard Auto-Gamma Spectrometer, Model No. 5022. To a series of test tubes, each containing constant amounts of the latex and of NaNO,, were added varying quantities of either nitric acid or sodium hydrox- ide to adjust the pH. The metal salt solution with the corresponding radiotra- cer cation was introduced last, and the final volume in each system was brought to 20 cm3 with doubly distilled water. After vigorous shaking, a 5 cm3 aliquot was removed to determine the total activity of the metal ion present in the latex dispersion. The remaining sample was aged for 24 h, filtered through a Nuclepore membrane (pore diameter 0.1 pm), and then the filter with the collected dry PVC particles was counted. A series of blanks containing no latex but identical concentrations of all other components was treated in an analo- gous way. Any metal ion removed from the reference solution was in the form of precipitated metal hydroxide. At any pH, the fraction of the metal ion adsorbed was determined by subtracting the amount removed in the reference solution from that removed in the systems with latex. The loss of metal ions to the walls was negligible since the latex in each sample had a surface area - 10,000 times larger than that of the glass tube.

Electrophoresis

Electrophoretic mobilities were measured at room temperature in the Rank Brothers Mark II microelectrophoresis apparatus using a cylindrical thin walled cell. The mobilities were ascertained at different pH values 24 h after mixing the reacting components. To keep the ionic strength constant, all determina- tions were made at 1 x lo-’ mol dmp3 NaNO,.

Coagulation

In a series of test tubes the concentrations of the latex and of the electrolyte (1 x lo-’ mol dme3 NaNO,) were held constant whereas the pH was changed systematically. Light scattering measurements were made with a Brice-Phoe- nix light scattering photometer using the 436 nm mercury line. The data were plotted as relative scattering intensities (at 45 ’ to that at 0 o ) as a function of pH. Stable sols showed high scattering intensities, whereas coagulated sols settled out and scattered little light.

316

PVC LATEX: 0.25% l ,= NO PVC NaNO,: 1~10-~IcI

6.0

Fig. 1. Fraction of SC (III) removed as a function of pH from solution of 2 x 10 -4 mol dm-” ( 0, 0 ) and 2 x 10e5 mol dm-” ( 0, n ) SC (NO,) R 24 h after mixing the reacting components. The open symbols give data in the presence of the PVC latex (0.25% by weight) and the darkened symbols are for systems in the absence of PVC.

RESULTS

Adsorption

The percent SC (III) removed as a function of pH, in the presence and in the absence of PVC latex, in systems containing either 2 x 10e4 mol dm-” or 2 x 10W5 mol dme3 SC ( N03)3 is shown in Fig. 1. An analogous plot for 2 x 1O-4 mol dmp3 Cr (NO,) 3 is given in Fig. 2. Based on the procedure described above, the percentage of chromium adsorbed, as a function of pH, on a latex that was 2~10~~moldm~~inCr(NO,),isshowninFig. 3.

The adsorption envelopes for latex containing 2 x lo-* mol dm-” and 2 x 10m5 mol dmp3 of Sc( NO,), are shown in Fig. 4 and the envelopes for latex with Cr (NO,) 3 at the same concentrations are shown in Fig. 5. The arrows indicate the pH values at which 5% of scandium or chromium precipitated as hydrox- ides. All adsorption density values are well below that of a monolayer coverage of hydrated cations. The relevant adsorption data for these systems are sum- marized in Table 1.

317

100

NaNO,: 0.01 M 0 PVC: 0.25 % 0 NO PVC

60 -24 hr

60

2 3 4 5 6 7

PH Fig. 2. The same plot as in Fig. 1 in the presence of 2 x 10m4 mol dmm3 Cr (NO,),.

Electrokinetic and coagulation measurements

Figure 6 gives the electrokinetic and light scattering data as a function of pH for the PVC latex in the presence of two different concentrations of SC (NO,) 3. At sufficiently high pH ( - 4) scandium ion reverses the charge of the polymer particles from negative to positive. At still higher pH values ( > 7) the latex again becomes negatively charged.

The corresponding light scattering data show that the stability of the latex depends both on the pH and on the concentration of SC ( N03) 3. In the presence of 2 x lop4 mol dme3 SC (NO,) 3, which is close to the expected critical coagu- lation concentration of Sc3+ ion for negatively charged sols [ 561, there is a stability maximum over the pH range corresponding to the highest mobility of particles of reversed (positive) charge. When 2 x lop5 mol dmw3 SC (NO,) 3 is added, PVC latex remains stable at pH sufficiently low to prevent hydrolysis. At somewhat higher pH the sols are destabilized by charge neutralization due to adsorption of hydrolyzed scandium complexes. Finally, at pH >, 5.5 latex is restabilized due to charge reversal.

Analogous phenomena are observed on addition of Cr (NO,) 3 as shown in Fig. 7. The pH regions of unstable or stable latex are somewhat different than

318

PVC: 0.25 % _ Cr(NOJ,: 2x10-‘M

NaNO,: 1x10-*/w 24 hr

t

p’ 1 4 5

PH Fig. 3. Fraction of Cr (III) adsorbed onto a PVC latex (0.25% by weight) from a 2 X 10 -5 mol dmm3 solution of Cr (NO,), as a function of pH, 24 h after mixing the reacting components.

those systems containing SC (NO,) 3 which is to be expected in view of the different hydrolysis characteristics of the metal ions.

Desorption

Acidification of the sols consisting of particles with adsorbed hydrolyzed metal species can bring about desorption of these complexes and, conse- quently, a change in the surface charge to less positive or even negative. Figure 8 shows that on addition of HNO, to yield a pH of -3, only two hours were needed to sufficiently desorb scandium species from the PVC latex particles to reverse the charge back to negative. These data were obtained by allowing a sol of pH 4.5 and a SC (NO,) 3 concentration of 2 x 10s4 mol dmp3 to equili- brate for 24 h after which time the latex was acidified by adding microliter amounts of concentrated HN03. The mobilities were then measured after the indicated times.

319

a Io-l3l I 4.0 4.5 5.0 5.5 6.0

PH

Fig. 4. Adsorption density as a function of pH for PVC latex (0.25% by weight) in 2 x 10m4 mol drnm3 (0 1 and 2 X 10m5 mol dme3 ( 0 ) SC (NO,),. Dashed lines and full symbols give values calculated using Eqn (3 ) .

Chromium (III) ions show no propensity to desorb after acidification. A PVC latex in the presence of 2~ lop4 mol dme3 Cr( NO,), at pH 4.3 was equili- brated for 24 h and then acidified to pH 2.1. The mobility did not change even after eight days.

ADSORPTION MODEL

James and Healy [ 1 ] have proposed a thermodynamic model for the adsorp- tion of hydrolyzable metal ions at an oxide-water interface, according to which the standard free energy of adsorption of a species i is

A&s, = AGiL, + AG:~I,, fAGkern, (1)

where the subscripts denote the coulombic, solvation, and chemical contribu- tions. Even though the expression was derived for adsorption at an oxide-water interface, it should be applicable to the hydrophobic latex-water system used in the present study.

While this model has greatly contributed to a better understanding of adsorption phenomena of complex ions from aqueous solutions, it still cannot explain some experimental observations. Complexes different than those hav-

320

Fig. 5. The same plot as in Fig. 4 in the presence of 2 x 10m4 mol dmm3 ( 0 ) and 2 x 10e5 mol dme3

(0) CrtNO,),.

ing the hydroxyl ligand do not follow the expected adsorption behavior. For example, no uptake of A1FA3-“’ or AlSO,+ species is detected on the same surfaces on which aluminum hydrolysis products are strongly adsorbed and no charge reversal by these complexes could be observed [ 7,8].

A refined approach, based mainly on the Anderson-Bockris model [ 21, is introduced here and tested against the experimental results described earlier. The number of physical processes for ion adsorption that must be quantified

TABLE I

Adsorption density data at the adsorption maximum

Concentration Adsorption density, Area per adsorbed Average number of adsorbed

(mol dmm3) r mar (mol cm-*) metal ion metal ions per surface (P, sulfonate group

Sc(NO,)s 2x10-4 2x lo-”

Cr(NO,), 2x10-* 2x10m”

1.0x 1ow’o 170 1.8 1.2x 10m” 1370 0.2

1.4x lo-lo 120 2.5 2.5~10~” 670 0.4

321

3:

k -2

I

G

p -4

’ PVC: 3x10-3% \

NaNO,: 0.01 M

SctNO,),

0 zxlo-‘M

0 2x10-sM

24 hr

PVC ONLY

2 4 6 8

PH

Fig. 6. Relative light scattering intensities (upper) and electrophoretic mobilities (lower) of PVC latex (3 X 10m3 wt% ) as a function of pH in the presence of 2 x 10e4 mol dm-” ( 0 ) and 2 x 1O-5 mol dmm3 ( 0 ) SC (NO,) 3, 24 h after mixing the reacting components.

to successfully explain the phenomena is appreciable, and the Ander- son-Bockris model accounts for a number of these processes. They studied the adsorption of group I and II cations; hydrolyzable metal ions are even more involved and our modification considers the effects of the resulting solutes. In view of the complexity of the system the employed treatment should be inter- preted as a first order approximation only.

The free energy of adsorption, once estimated, can then be used to calculate the adsorption density of species i of bulk concentration Ci by means of Gra- hame’s expression [ 91

Ti = 2rhyd, Ciexp ( - AGz,,,/RT) (2)

where ri_.d, is the radius of the hydrated species i.

322

2 4 6 8

2 4 6

PH

8

Fig.7.ThesameplotasinFig.6for2X10~4moldm-” (0) and2XlO~“moldn+ (0) Cr(NO,,),.

Before presenting the details of the Anderson-Bockris model, a discussion and calculation of some of the more important energy terms will be presented.

Coulombic energy

The coulombic adsorption energy, as by James and Healy, is based on the Gouy-Chapman model of the electrical double layer:

AGZL, =ziFy/x (3)

where potential ry, is evaluated at the distance x= I-~+ 2r, from the particle surface:

323

PH

Fig. 8. Electrophoretic mobilities of a PVC latex (3 x 10e3 wt% ) in the presence of 2 x 10e4 mol drnm3 SC (NO,) 3 as a function of pH. The initial dispersion of pH 4.5 was allowed to equilibrate for 24 h and then acidified with concentrated HNO, and the mobilities were determined 2 h ( 0 ) , 1 day ( A ) , and 7 days ( 0 ) after acidification.

2kT cy, =- In

gevo/2kT + 1) + ( ezeVo/2kT _ 1) e-K%

1 (Volt) ze ( eze&2kT +I) _ (ezeVo/2kT_l) e_KX (4)

where ri and rw are the radii of the adsorbing ion and of the water molecule, respectively, z the charge of the adsorbing ion including the sign, cy, the surface potential, while other symbols have the usual meaning.

The James and Healy coulombic energy calculation assumes that the elec- trostatic potential, (I/~, remains constant throughout the adsorption process, but this is clearly not so. At sufficiently high pH the hydrolyzed cationic spe- cies will adsorb and cause a decrease in the negative charge of the particles. The electrostatic potential y, evaluated at the distance x will, therefore, decrease as more cations are adsorbed. At the isoelectric point of the dispersion the potential ly,, calculated from the Gouy-Chapman model of the double layer, will be zero and so will be the coulombic adsorption energy. Any further cation adsorption will only make both the electrostatic potential and the coulombic adsorption energy positive, thus inhibiting further uptake of cationic species. Clearly, the James and Healy model overestimates the coulombic energy term and, if evaluated correctly, would predict adsorption tending to the isoelectric point only.

Adsorption to nearly monolayer coverage of hydrolyzed neutral Hf (OH) 4 species on glass was established earlier [lo], although there could be no con- tribution of coulombic energy in this case. The same conclusion was reached for other systems [ 111. For the above reasons, the electrostatic interaction is

324

assumed to be of negligible importance and will not be included in the calculations.

Born energy

When an ion of radius ri moves from a medium of continuous dielectric ei, to another medium of dielectric tF, then the change in the enthalpy is given by

[21:

AH,,,, = HF-Hi=~ (ze)2 7 j 7 !$f(;_t)~&j’&$ 32x2 q,

@=Ot'=OR=r,

(5)

where R, 8, and $ are the polar coordinates and e. is the electric permittivity of the free space. This equation indicates that the free energy increases on moving an ion from a particular medium to one of a lower dielectric constant.

To calculate the Born energy of adsorption of metal ions onto the PVC latex, the dielectric constant of the interfacial water must be kown as function of the distance x from the latex surface. As discussed in Appendix I, the interfacial water is assumed to have a dielectric constant equal to that of bulk water.

The Born energy of adsorption can thus be calculated by considering only two regions of differing dielectric constant: bulk water and the solid PVC. The metal ion species is assumed to adsorb directly onto the PVC surface without an intervening water layer [ 121, as illustrated in this drawing:

325

For the systems investigated in this work the following quantities apply: x distance from the PVC latex surface: ( ri+ 2~~) m

00 surface charge density: 5.4 ,~coul cm-’

ri ionic crystal radius 0.73 X 10-‘” m for Sc3+ 0.63 x lo-” m for Cr3+

Ebulk dielectric constant of bulk water: 78.5

Esolid dielectric constant of solid PVC: 3

1/(47rco) 9xlO’J m coul-2

rW radius of a water molecule in solution: 1.38 x 10WIO m e 1.6~10-‘~ coul

Equation (5) applied to the present case reads:

which on integration and substitution of known quantities yields

AH&,,i=5.5.10-6 C (J mol-‘) ri

(7)

The solvation energy term in the James and Healy model is simply the Born energy for the configuration where a layer of water molecules exists between the metal ion and the particle surface. For this configuration, the Born or sol- vation energy is as follows [ l] :

2 e2N AC,,, = -& -!---

0 ri + 2r, ri 21 (;-T&J 2(ri+2rW)

+Ex&) (&A) C8) London dispersion energy of attraction between the adsorbed metal ion and the latex surface

The latex surface can be approximated as a flat plane in relation to the metal

ion. The dispersion energy, AH,, between an atom or a molecule and the flat substrate is given by [ 131:

dH = - 1.082pN: np

d 2Md3(4ne,)’ (9)

where p is the density of PVC ( lo6 g rn-” ) , M is the molecular weight of the monomer unit of PVC (75 g mol-‘) , d is the separation distance between the atom on the surface ( = ri for specific adsorption), and

with Y,, v, associated with the electron orbital frequency in the polymer PVC and the SC or Cr ion, respectively, h is Planck’s constant (6.63 x 1O-34 J s), and ayl, az are the polarizabilities of the monomer vinyl chloride and the SC (III) or Cr (III) ion, respectively. Equation (9) is valid for very small separations d.

The polarizabilities of the polymer cyl and the metal ion cy, are approximated by [14]:

a2 -4ntorf

=4.33x10e41 coul* m* JJ1 for Sc3+

= 2.78~ 10e41 cou12 m2 JJ’ for Cr3+

(11)

Ck’,-“3E,, M

-= 3.3 x 10p3' coul* m* JJ1 for PVC PNL3

(12)

The characteristic frequency of PVC, v,, will be taken the same as that of polystyrene [ 151 which is 2.62 X 1015 s’.

The quantity hv is often approximated as the ionization potential and thus hv, can be assumed equal to the fourth ionization potential of SC (III) and Cr(II1).

hvZ=74eV=1.2x10-i7 JforSc3+

=50 eV=8.0x10-‘s J for Cr3+

With these approximations, /3 becomes

/3=3.24~10-‘~ cou14 m4 J-’ for Sc3+

=1.96X 10pg7 cou14 m4 J-l for Cr3+

The adsorption model will now be presented in detail.

327

The heat changes accompanying specific adsorption

The Anderson-Bockris model [ 21 will be used to calculate the heat changes accompanying specific adsorption. Since the description of their model is too lengthy to be summarized here, the reader is referred to the original article for any clarification. The details of the calculation are given in the Appendix II. The main components of the enthalpy changes of adsorption are the Born repulsion energy and the London dispersion energy of attraction, all of which were discussed in detail earlier.

Entropy changes accompanying specific adsorption

Along with an enthalpy change for the adsorption process there is an entropy change the calculations of which are shown in Appendix IV.

PREDICTIONS OF THE ADSORPTION MODEL

Hydrolysis of chromium and scandium ions

Several studies on the hydrolysis of Sc( III) and Cr( III) ions have been reported and later reviewed by Baes and Mesmer [ 161. The hydrolysis species along with their measured hydrolysis constants are given in Table 2.

Species distribution diagrams were computed for constant scandium (III) and constant chromium (III) concentrations of 2 x 10 -* mol dmp3 and 2 x 1O-5 mol dmp3 for the pH range of 2-8, but are not reproduced here.

To calculate the total adsorption density for a metal ion, it is necessary to evaluate the fraction adsorbed of each ionic species. Thus, for the case of scan- dium ion:

.;:,““a’ = r SC3f +rscoI++ +&on&+ +r SC(OH)~

f2f Scp(OH)j+ +3rS~3(0H)$+

and an analogous equation can be written for the chromium ion.

(13)

Born energy

The Born energy, which is simply the electrostatic energy required to move an ion from bulk water (t=78.5) to the interface between solid PVC (e=3) and water, is always positive for all hydrolyzed metal ion species and, therefore, inhibits adsorption and enhances desorption. This energy increases as the die- lectric constant of the solid decreases and is close to its maximum for a very low dielectric such as PVC; it also increases as the square of the valency Zi of

328

TABLE 2

Hydrolysis species and constants of SC (III) and Cr (III)

Sc(II1) 1. ScOH”

SC”+ +H20 / - &OH’+ f N+ 2. Sc(OH);

SC”’ + 2H20 ti Sc(OH): +2H+

3. Sc(OH),(aq) Sc3+ +3H 0 -

4. Sc,(OH):+ 2 - Sc(OH),+3H+

logK,,= -4.3~0.1

log K,,= -9.7

logK1s= -16.1

2ScR + + 2H,O ti Sc,(OH);* +2H+ log K** = - 6.0 + 0.1

5. Sc3(OH);+

3Sc3+ +5Hz0 ti Sc,(OH)$+ +5H+

6. Sc(OH);

Sc3+ + 4H,O e Sc(OH); +4H+

Cr(II1)

log&,=-16.3kO.l

log K,, = - 59

1.

2.

3.

4.

5.

6.

CrOH2+ Cr3++Hz0 ---- - CrOH2’+H’

Cr(OH)L:

Cr3+ + 2H,O c__ Cr(OH)$ +2H+

Cr(OH),(aq) Cr” + + 3H20 -

Cr,(OH)z+ - Cr(OH),+3H+

log&,,= -4.Of0.3

log K,,= -9.7

log K,, = - 18.0

2Cr”’ + 2H,O a Cr,(OH)i+ i-2H’

Cr,(OH)i+

3Cr3 + + 4H,O 6 Cr,(OH)t+ +4H+

Cr(OH);

Cr3+ +4HZ0 w Cr(OH), +4H+

log x;, = - 5.0 t 0.1

log&= -8.2fO.l

log K,, = - 27.4

the absorbing species; thus, highly charged species face a considerable energy barrier to adsorption.

The dimers Sc<$$>Sc’+ and Cr<$& Cr*+ have planar configurations [ 161; the radius of the former will approximately be 2ri+ $_rW = 2 (0.73) + f (1.38) = 2.15 A and of the latter 2 (0.63) + j(l.38) = 1.95 A. The hydrolyzed chro- mium and scandium trimers have “cage like” configurations [ 161, so that the radius can be approximated by _( 3rW+2r,) which for SC, (OH);+ equals 2.15 A and for Cr, ( OH ) 2’ to 1.95 A. The calculated Born energies are given in Table 3.

Dispersion energy between the adsorbed metal ion and the latex surface

It will be assumed that the dimers of Cr3+ and Sc3+ adsorb with their planes parallel to the latex surface; thus, both metal atoms in each species will touch

329

0

r~

+

+ + + + ; ;

+ + + + + +

I , f I i i t I , , 7 7

4-- 4 - 4 - 4 -

4 ~ ÷ + ~-

~ o ~ o ~ ~+ ~ o O O - - 5 - - 5 ~ ~+ "~'S~ ~ + ~ o o ~

r~ r.~ r~ r.~ oO ~ r..p (.3 r~ r...) r.3 r.p

330

the latex surface. The dimers will therefore have twice the dispersion energy of the mononuclear species. A similar situation will hold for the trimers. The dispersion energies are also listed in Table 3.

The entropy of adsorption

Mononuclear species have a cross-sectional area of n ( ri + 2r,) ’ or 38 A” for SC (III) and 36 A” for Cr (III). Therefore, upon adsorption the number of inter- facial water molecules (equals n” in the notation of Appendix IV) displaced from the latex by chromium and scandium mononuclear species can be roughly estimated to be n( ri+ 2r,) 2/n ?w~ 6. In addition, [ Sc.GH,O] 3+ is an extremely labile complex having a characteristic rate constant for the substitution of inner sphere water molecules of x 6 x lo7 s-l [ 171. Therefore, water ligands [equal to ( nl - n ; ) , see Appendix IV] of the inner coordination sphere can be displaced as the scandium ion adsorbs on the PVC latex surface, liberating roughly one additional water molecule.

The unhydrolyzed chromium (III) species [ Cr (H,O) 6] 3+ is quite inert to the substiution of the inner sphere water ligands. The rate constant for the exchange of water molecules in the first coordination sphere in aqueous solu- tion is k= lop6 s-’ [ 181. This small rate constant suggests that water mole- cules will always exist between the chromium atom and the PVC surface for the species [ Cr*GH,O] 3+. Consequently, this unhydrolyzed cation cannot be specifically adsorbed and will not cause charge reversal, as indeed confirmed at low pH values where only the unhydrolyzed ion exists.

Baes and Mesmer [ 161, Eigen and Wilkins [ 191 and Langford and Gray [ 201 have proposed models that predict extreme efficiency of the OH- ligand in promoting the substitution of inner sphere water molecules by other ligands. Espenson [ 211 has experimentally measured the rate constant for the substi- tution of inner sphere water molecules of Cr (III) species as a function of many different ligands and has found that even the first hydrolysis product [ Cr (H,O) 50H] 2+ has a rate constant, depending on the entering ligand, three to four orders of magnitude larger than that of the unhydrolyzed cation. Baes and Mesmer’s model predicts that the substitution rate constant will increase rapidly as the number of inner sphere OH- ligands increases. Finally, the very formation of the dimer and trimer complexes from the mononuclear hydrolysis species, which involves the loss of inner sphere water molecules, attests to considerable lability of the hydrolyzed species. Mononuclear chromium hydrolysis products will consequently be assumed to be as labile as the scan- dium species and to liberate an equal number (seven) of water molecules upon adsorption.

If the dimers of both Cr (III) and SC (III) adsorb with their planes parallel to the latex surface, they will each present a cross-sectional area approximately twice that of the mononuclear species. Assuming also the losses of one inner

331

sphere water ligandper metal atom on direct approach to the surface, the dimers of both chromium and scandium will each liberate 14 water molecules on con- tact with the latex. In view of the “cage like” configuration of the trimers, each face, having two metal atoms, will have approximately the same area as the dimers; therefore, they should also liberate 14 water molecules upon adsorption.

The terms that constitute the entropy of adsorption are listed in Table 4.

The enthalpy of adsorption

The number of water molecules n, and n; liberated upon metal ion adsorp- tion (see Appendix II for a definition of these quantities) was estimated in a manner similar to that discussed in the preceding section. The main three terms in the enthalpy of adsorption as listed in Table 3 are: (1) the Born energy of repulsion, (2) the London dispersion energy of attraction between the metal ions of the complex in contact with the latex surface and the latex itself, and (3) the energy required to desorb inner sphere water molecules in the complex to effect specific adsorption. The last term manifests as a repulsive force.

Free energy of adsorption

The free energy of adsorption AG,,, is described by

AG,d, = AH,,, - TAs,d, (14)

The free energies for all hydroiysis species of Cr3+ and Sc3+ are listed in Table 5. The entropic component of the free energy of adsorption is very small in comparison to the enthalpic energy.

Total adsorption densities

With the adsorption free energy now developed, the adsorption density of each species can be calculated using the Grahame expression [ Eqn ( 2 ) 1. The concentration Ci of each species as a function of pH must be evaluated and the corresponding hydrated radius estimated from its configuration [ 161. An equi- librium constant for the adsorption can be defined as follows:

Ki = exp (AGz,,/RT) (15)

Using data in Tables 3 and 4 and Eqns (14 ) and (15 ) calculated values of A@&, and of Ki are also given in Table 5. The orders of magnitude of Ki indi- cate that there is essentially no uptake of Sc3+, SC, (OH):+, and ScOH’+ spe- cies, but complexes SC ( OH),+, SC (OH) 3 and SC, (OH) i’ quantitatively adsorb.

Analogous data for the Cr ( NO,) ,-PVC system are also included in Table 5. The adsorption densities calculated using Grahame’s expression, Eqn ( 2))

332

~3

I

0

0

4 - ~

0

o

~s 0

o

~s

0 . ~

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

q q q q q q q q q q q q 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

~o ~; o~ ~ ~ ~o~o~ O 0 0 0 ...~. ~

r.~ r..;3 r.~ r_.~ r.f3 0Q ~..) r..) r._) c.p r..p {..~

T A B L E 5

T h e r m o d y n a m i c a d s o r p t i o n p a r a m e t e r s for t h e s y s t e m s Sc (II I ) - P V C a n d Cr ( I I I ) - P V C

333

Species , i rhzd, AI-~ AS °e~ AG~ K~ (A) ( k J m o 1 - 1 ) ( k J m o l 1 K 1) ( k J m o l - 1 )

[Sc(NOD3] Sc 3+ 3.5 756 0.255 680 ~ 0 S c O H 2+ 3.5 206 0.256 130 1.6 × 10 -2 Sc ( O H ) ~ 3.5 - 162 0.256 - 238 5.2 × 104' Sc { O H ) 3 3.5 - 357 0.255 - 433 7.9 × 1075

S c 2 ( O H ) ~ + 4.9 + 2 2 1 0.551 57 1 . 0 × 1 0 - ' ° S c 3 ( 0 H ) ~ + 4.9 + 5 8 0.552 - 1 0 6 3.8><10 TM

[ C r ( N 0 3 ) ~ ] Cr 3 3.4 + 1044 0.256 968 ~ 0 C r O H 2+ 3.4 423 0.255 347 1.5 × 10 61 C r ( O H ) ~ 3.4 - 2 6 0.255 - 102 7 . 6 × 1017 Cr ( O H ) 3 3.4 - 257 0.255 - 333 2.3 × 105s C r 2 ( O H ) ~ + 4.7 + 5 9 5 0.551 430 4 . 2 × 1 0 -76 C r 3 ( O H ) ~ + 4.7 + 6 7 1 0.552 506 2 . 0 × 1 0 -s9

are given in Table 6 and are plotted as dotted curves in Figs 4 and 5. The agreement between the measured and calculated adsorption densities for Sc (III) is reasonable, although it may be somewhat fortuitous considering the rough nature of the model. The absence of strong, specific bonding between the adsorbed scandium species and the PVC latex, as demonstrated by the desorption experiments, suggest that the Sc(III) -PVC system fits the assumptions for the adsorption model fairly well. The main adsorbing species is Sc (OH) ~- at both scandium nitrate concentrations.

This adsorption model is completely independent of the intrinsic particle surface charge. The only substrate characteristics involved are the dielectric constant and the Hamaker constant of the solids. Most substrates have much lower dielectric constants than water and thus will have large Born energies. Titanium dioxide is an exception with a dielectric constant of 78.5 and, indeed, James and Healy [ 22 ] have found charge reversal for the TiO2-Co (II) system at a low pH value where only the unhydrolyzed cobalt ion exists.

The Born energy of repulsion for other dispersions cannot be much greater than that of the PVC latex. Polymers have relatively low Hamaker constants when compared to other solids; thus, their London dispersion energy of attrac- tion will probably be at least as large as for the PVC latex studied here. Hence, this model is relatively independent of the substrate.

Figure 5 shows that data calculated for the Cr (NO3)3-PVC system do not fit the experimental results. There are several possible reasons for this dis- crepancy. It is well known that Cr(III) tends to polymerize on hydrolysis

TA

BL

E

6

Cal

cula

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adso

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den

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Tot

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9.

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4.4

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1.1

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4.5

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1.2X

10~

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[Sc(

NO

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z] =

2x10

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oldm

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4.0

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7.4x

lo

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9.6x

10

m’R

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1.3x

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7

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”

2.9x

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5.7x

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lo

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1.5x

lo

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2.8x

lo

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9.1x

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2.7x

lo

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4.6x

1O

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2.9x

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14

2.2x

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3

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335

TABLE I

Calculated adsorption parameters using the James and Healy model

Species Z0 sob, dGO ZX”l, 2%’ sd* K ads, (kJ mol-‘) (kJ mol-‘) (kJ mol-‘)

SC?+ 143 -27 116 5x10-= ScOH2+ 63 -18 45 1x10-8 Sc(OH): 16 -9 I 6~10~

Sc(OH), 0 0 0 0 Sc,(OH);+ 254 -36 218 6~10~~~~ Sc,(OH);+ 254 -36 218 6x10-=

Cr3+ 147 -27 120 CrOH2+ 65 -18 47 Cr(OH): 16 -9 7

Cr(OH), 0 0 0 Cr,(OH):+ 261 -36 225 Cr,(OH)i+ 409 -45 364

9x10mzz 5x 10-9 5x10-2 0 4x10-40 2x10me4

[ 23,241; consequently, the complexes listed in Table 2 do not properly repre- sent the composition at the interface, which is substantiated by the failure of hydrolyzed chromium products to desorb on acidification. Also, the existence of chemical bonds between the chromium species and the sulfate groups on the PVC latex is strongly indicated, as discussed in the section on ion desorption. Such bonding is ignored in these calculations.

The thermodynamic parameters based on the model of James and Healy are summarized in Table 7, in which the prime is used to indicate the neglect of the AGzh,,i term in the evaluation of AGz++, . No measurable adsorption is pre- dicted for any of the SC (III) or Cr (III) species even though the coulombic attractive energy is greatly overestimated. The James and Healy model is also very dependent on the adsorbent’s surface properties through its surface charge density in the coulombic energy term. As stated earlier the experimental evi- dence tends to suggest otherwise.

DISCUSSION

Electrokinetic arcd coagulation measurements

A quantitative comparison between the electrokinetic or coagulation data and adsorption densities is not possible because different latex concentrations had to be used. Qualitatively, charge reversal is seen to occur over approxi- mately the same pH range as the incipient adsorption.

The first charge reversal is noted at pH -4 for the PVC latex containing

336

2 x lo-4 mol dmp3 and 2 x lop5 mol dm-3 SC ( N03) 3 and corresponds to the onset of formation of the SC ( OH ) 2’ complex. The proposed adsorption model does indeed predict this to be the main adsorbing species. The mobility changes very little over the pH range of 2.5-3.5, for both scandium nitrate concentra- tions, indicating little SC (III) adsorption. Over this pH range the distribution diagrams reveal the main species to be Sc3+ and ScOH’+; again, the adsorption model correctly predicts that these ions will not adsorb to any significant amount.

The first charge reversal in the system PVC-Cr( NO,), containing 2 x lop4 mol dm-3 of the electrolyte takes place at pH - 2.5 which is the same pH value of the incipient formation of the CrOH’+ complex. Thus, CrOH*+ is apparently the main adsorbing cation.

In both instances the second charge reversal from positive to negative at pH - 8 is probably caused by the adsorption of the neutral species Cr (OH) 3 and SC ( OH) 3 which can be shown to exist in significant amounts under these con- ditions. The intrinsic negative charge of the latex would manifest itself even though neutral species adsorb.

Desorption

The desorption experiments demonstrate that the interactions of scandium species with latex are reversible indicating that strong chemical bonds are not formed. The formation of scandium hydrolysis products in solution is rapid and reversible [ 161. Acidification causes dehydrolyzation (protonation) and consequent diffusion away of the adsorbates from the surface.

The lack of any desorption of chromium, even at very low pH values, sug- gests that the adsorbed chromium species may form strong, specific chemical bonds with the PVC surface, most likely with the surface sulfonate groups. Chromium ( III) hydrolysis species have been shown to bind sulfate groups on dextran sulfate polymers [ 251. The adsorbed hydrolyzed complexes should also polymerize on the surface as they tend to do so in solution [ 23,241. These polymers may be difficult to break up on acidification; as a result desorption would not take place. Polynuclear chromium hydrolysis species show a pro- pensity to oxolate, i.e., to replace hydroxide bridges by oxide bridges which are much more resistant to protonation [ 231. The surface sulfonate and sulfate groups may catalyze this “deolation” reaction. Indeed, it has been shown that the presence of the sulfate ion greatly enhances the precipitation of chromium hydroxide from aqueous chromium salt solutions [ 26,271.

Concluding remarks

The work presented here suggests that the adsorption of hydrolyzed metal ions can be interpreted by a combination of a modified James and Healy model

337

along with a modified Anderson and Bockris model in which the entropic effects are also taken into consideration. As expected a favorable comparison between the calculated and experimental data is possible as long as the adsorbing spe- cies are well defined and no chemical reactions take place between the sub- strate and the solutes. This is apparently the case in the PVC-SC (NO,) 3 system. The absence of any bond formation is substantiated by the desorption effects and by the coagulation reported earlier [ 51, albeit with a different sol.

In contrast, data with Cr ( NO3) 3 could not be matched with the calculated values. There is considerable experimental evidence that the chromium hydrolysis process is more complicated than that of scandium, and that the complex species change on aging. Furthermore, the tendency of chromium to bind a number of anions is also well established. Again coagulation studies using negative colloids with chromium as counterion have reflected the com- plexity of chromium solution chemistry [ 281. Thus, there is no surprise that the model could not explain the adsorption results.

APPENDIX I

The dielectric constant of surface water

Beyond a radius of - 3 A from an ion, the dielectric constant of water is essentially equal to the bulk value ( - 80) [ 291. Inside this radius, the dielec- tric constant is as low as 6. The PVC latex has an area per surface charge of 300 A”. The ratio of the latter to the area around each surface charge contain- ing water with reduced dielectric coonstant is - 10. Consequently, a better part of the latex surface is in contact with water of a bulk dielectric constant of 80.

The dielectric constant of water is low near ions because the strength of ion-water bonds is significant as compared to the strength of water-water bonds; thus, the water structure is altered near an ion, changing the dielectric constant of the local water. Since the interaction of water with very hydropho- bic molecules is weak compared to the interaction of water with itself, the dielectric constant of water adsorbed to the PVC surface but far from the latex’s surface charges should not be significantly altered and will also be assumed to be 80.

The Born energy of repulsion for ion adsorption is much less near areas where the interfacial water has a high dielectric constant; thus, ion adsorption is assumed to occur on areas away from the latex surface charges.

James and Healy’s model assumes the metal oxide interface has a continu- ous as opposed to a discrete surface charge. Applying such a model to the PVC latex surface to calculate the dielectric constant E, of the interfacial water as a function of the distance x from the latex surface, gives:

338

E bulk - 6 t, = 2 +6

r

The electric field strength x at a distance x from X

the Gouy-Chapman model of the electric double layer:

dW 2kT~ sinh -=- dx ze

The surface electrostatic potential cy, is

(Al)

the surface is given by

(AZ)

(A3)

where ~=0.328~10’~ 11’2 rn-‘, with Ithe ionic strength (=O.Ol mol dme3). The PVC latex used has a small surface charge density of o. = 5.4 pcoul cme2

producing an interfacial electrostatic field of only 5.0x lo7 V m-l. Conse- quently, the calculated dielectric constant of the interfacial water at a distance of x= 3.49 A is eX= 76.4, which again is essentially the same as for bulk water.

APPENDIX II

The heat changes accompanying specific adsorption

A calculation similar to that involved in the Born-Haber cycle will be per- formed to estimate all the enthalpy changes that occur upon specific metal ion adsorption. The Anderson-Bockris model will be used with appropriate mod- ifications. For the case of mononuclear hydrolysis species of Cr3+ and Sc3+, one water molecule (n= 1 using the Anderson-Bockris notation) will desorb from the latex surface into the electrolyte solution upon the specific adsorption of a metal ion since only one water molecule must be removed to make space for a partially dehydrated Cr3+ or Sc3+ ion. To simplify the calculation, this water molecule will be considered to be first removed into the gas phase and then condensed into the liquid. The heat changes for this process are: loss of interaction of the water molecule with the latex surface (AH,_ 1), loss of hydrogen bonding with second layer water molecules ( d&_bond), and the gain of interaction between the n (n= 1) water molecules and the bulk ( - nAH,,,,) , where dHcond is the heat of condensation. The total enthalpy change H, for this water desorption is:

339

AH1 = n ( A& ~ 1 + AH, ~ bond - A&d 1 (A2-1)

with dHW_bond= 18.8 kJ mall’ and dHC,,d=43.9 kJ mall’. The energy of interaction of a water molecule with a polymer surface, AH,_ 1,

is unknown. This will be estimated by using the heat of interaction of water molecules on a Hg surface, AHw_Hg, and adjusting it by the ratio of the work of adhesion of water on mercury and hydrocarbon.

AH,_, EAH,_~, E-H/w-Hg (A2-2)

where AH, _ Hg = + 73.6 kJ mall’ [ 21; WrPH = work of adhesion of water and hexadecane = 46.4 mJ me2; WzeHg = work of adhesion of water on Hg= 131 mJ mP2.

These values yield for AH,- 1 ‘Y 25.9 kJ mall’ and, consequently, AH, = n 0.8 kJ mol-l=0.8 kJ mol-l.

Next, the ion is considered to be totally dehydrated and moved to its adsorbed position where it is again hydrated. The enthalpy change (AH,) associated with this process is the sum of the enthalpies of several steps: (i) the gain of both the London dispersion attraction energy, AH,, and the Born repulsion

energy, A&,,, (both discussed in the main body of this paper) between the ion species and the latex surface, (ii) the loss of interaction with n, primary water molecules in the bulk and the gain of interaction with n; water molecules at the latex surface [ - (n, -n; )AHi,,.,] , and (iii) the energy gain from a hole, left by the ion in solution, filling with water [ -n, dH,_,,& ] and the energy loss from forming a hole in the solution, by removal of the n; water molecules, at the latex surface [ + n; AH,_,,,,/2] where: n, = the total num- ber of inner sphere water molecules associated with the ion or the hydrolyzed species and n; = the total number of inner sphere water molecules associated with the ion or hydrolyzed species after specific adsorption. Hence AH, is given

by

AH, = AH, + AH,,,, - (nl -n;) AHim-,- (n,-n;) ~HH-I,,,,/~

= AH, + AH,,,, - (n,-n;) AHi,,~,-(n,-rz;) 9.4kJmoll’ (A2-3)

The calculation of the bond energy, AHion_,, between the ion and the inner sphere water molecules in the hydrolysis species is discussed in Appendix III.

The total enthalpy change of specific adsorption is then

AH,,, = AH, + AH, (A2-4)

APPENDIX III

Enthalpy of ion solvation

The interaction energy, AHiOn_w, between an ion and its primary water mol- ecules is most accurately modeled as consisting of four separate terms: (i) the

340

coulombic energy between the ion and the permanent dipole moment of the water molecule; (ii) the coulombic energy between the ion and the quadrupole moment of the water molecule; (iii) the coulombic energy between the ion and the induced dipole of the water molecules that arises from the polarizability of water molecules in an electric field; and (iv) the crystal field stabilization energy associated with the hydrated ion [29-31] . The first three terms are derived in Ref. [ 29 ] and are listed below:

AHion_w (ion-permanent water dipole) - - 1 ZeffeflwN a 4~eo ( r i+rw) 2 (A3-1)

where ze, is the effective valency of the metal ion in the hydrolyzed species, ttw the permanent dipole moment of water ( = 1.87 debyes = 6.28 × 10 -30 coul m ).

ZeffePwNa AHi . . . . ( ion-quadrupole) = + (A3-2)

(47~0) 2 (riWrw) ~

where Pw is the quadrupole moment of water ( - -3 .9×10-26 esu cm2= 1.3× 10 -39 coul m 2)

--1 ol w (zeffe)2Na JHi . . . . ( ion-induced dipole) - (47~eo)2 2(ri +rw) 4 (A3-3)

where a~ is the polarizability of water [ = 1 . 4 4 × 1 0 -24 cm 3 (cgs units) or 1.6× 10 -4° couF m 2 j - 1 (S.I. units) ].

Scandium (III) does not have any d electrons and so the crystal field stabi- lization is zero. This should ensure that the first three coulombic energy terms acurately describe the ion-water interaction energy.

Chromium (III) has three d electrons to produce an extra attactive energy of 37 kJ mol - 1 per inner sphere water molecule [ 29-31 ].

The bonds between the metal ions and the O H - ligand are neither com- pletely ionic nor covalent and, thus, the negative charge on the O H - ligand is partially shared between the metal ion and the ligand [ 16 ]. It will be assumed that the charge is shared equally and so the effective charge, zeff, on the metal ion is not 3 + , but is decreased by one half of an electronic charge for each OH ligand. For instance, the species Sc (OH)4÷ has one O H - ligand per Sc atom, so zeff= + 3 - ½ (1) = + 2.5. Table 8 lists JHion_ ~ and its component energy terms for the hydrolysis species of Cr (III) and Sc (III ).

APPENDIX IV

Entropy changes accompanying specific adsorption

The approach presented here for the entropy changes accompanying ion adsorption is based on a simplified version of the Anderson and Bockris model in which the vibrational terms are ignored since they are very small [ 2 ].

(i) Upon ion adsorption, ( nl - n~ ) inner sphere water molecules are desorbed

341

TABLE 8

AH,,,-, for the hydrolysis species of SC ( III ) and Cr ( III )

Species, i Z eff Ion-dipole Ion- Ion-induced Crystal-field AH,,,_, term quadrupole dipole stabilization (kJ molF ’ ) (kJ mol-‘) (kJ molt’) (kJ molt’) energy

(kJ molt’)

sc”+ 3.0 -366 +179 - 452 0 - 639 &OH’+ 2.5 -305 +150 -314 0 - 469

Sc(OH); 2.0 - 244 + 120 -201 0 -325

Sc(OH),, 1.5 -183 +90 -113 0 -206

Sc,(OH):+ 2.5 - 305 +150 -314 0 - 469

Sc,(OH):+ 2.2 -268 +132 -252 0 -388

Cr3 3.0 -403 +207 -548 -37 - 781

CrOH*+ 2.5 -356 +173 -381 -37 -601

Cr(OH)$ 2.0 -269 + 138 - 244 -37 -412

Cr(OH), 1.5 -201 + 104 - 137 -37 -271

Cr,(OH:+ 2.5 -356 +173 -381 -37 -601

Cr,(OH);+ 2.3 -308 +159 -323 -37 -509

from the ion. The entropy changes that are associated with the modification in the translational-librational movements of each of these liberated water molecules are dS &,,, and dS iii, , respectively.

(ii) The ion and its n, inner sphere water molecules, have three transla- tional degrees of freedom in the “free” volume of the solution, but only two translational degrees of freedom on the “free” area of the surface. The total entropy difference is [ 21:

s:fa”d”s” + s;gf; (AIV-1)

where

Cp”“” L,soin = i In Mi + 17.76

s;;a”d”s” = RlnM: + 9.86

Mi = Mien Mw/(Mw + n;Mion) (AIV-2)

Mi,, being the molecular weight of Cr (III) or SC (III) and Mw the molecular weight of water.

(iii) In order to make room on the latex surface for the adsorbing ionic species, 72” water molecules must be desorbed from the latex. The entropy change of this desorption process is [ 21

ASdes,w = 0.043 kJ K-’ mol-’

342

The total entropy change accompanying specific adsorption is

ASads = ( n, - n; ) ( AS;ib + AS;,,,, ) + S:fa”d”s” - S:fs”o;: + n” ASdes,w

The value of IZ” was estimated in the text.

(AIV-3)

The translational and librational entropy changes (AS&,, and AS’,ib) a water molecule undergoes after detachment from a Cr3+ or Sc3+ ion has not been experimentally determined. Theory [ 321, though, suggests that these quan- tities are mainly a function of the charge and the size of the ion. Hence, values for Fe3+ [ 231 should be a good approximation:

AS;,,,, = 0.012 kJ KP’molP’

AS& = -0.023 kJ K-’ mall’

ACKNOWLEDGEMENT

Supported by the NSF Grant CHE-83 18196.

REFERENCES

1

2

3

4

5

6

7

8

9

19

11

12

13

14

15

16

17

18

19

20 21

22

23 24

R.O. James and T.W. Healy, J. Colloid Interface Sci., 40 (1972) 65.

T.N. Anderson and J.O.M. Bockris, Electrochim. Acta, 9 (1964) 347.

L. Ericksson, E. MatijeviC and S. Friberg, J. Colloid Interface Sci., 43 (1973) 591.

E. MatijeviC and D. White, Colloids Surfaces, 9 (1984) 355.

E. Matijevid, A.B. Levit and G.E. Janauer, J. Colloid Interface Sci., 28 (1968) 10.

E. Matijevic, J. Colloid Interface Sci., 43 (1973) 217.

E. MatijeviC, S. Kratohvil and J. Stickels, J. Phys. Chem., 73 (1969) 564.

L.J. Stryker and E. MatijeviE, J. Phys. Chem., 73 (1969) 1484. D.C. Grahame, Chem. Rev., 41 (1947) 441.

L.J. Stryker and E. Matijevic, Adv. Chem. Ser., 79 (1968) 44.

C.P. Huang and Y.T. Lin, in P.H. Tewari (Ed.), Adsorption from Aqueous Solutions, Plenum

Press, New York, 1981, p. 61ff. W. Stumm and C.R. O’Melia, J. Am. Water Works Assoc., 60 (1968) 514.

P.C. Himenz, Principles of Colloid and Surfaces Chemistry, Marcel Dekker, New York, 1977.

J.N. Israelachvili, Contemp. Phys., 15 (1974) 159.

J. Gregory, Adv. Colloid Interface Sci., 2 (1969) 396.

C. Baes and R. Mesmer, The Hydrolysis of Cations, Wiley-Interscience, New York, 1976.

CM. Frey and J. Stuehr, in H. Sigel (Ed.), Metal Ions in Biological Systems, Vol. 1, Marcel

Dekker, New York, 1974.

R.G. Pearson and P.C. Ellgen, in H. Eyring (Ed.), Physical Chemistry, An Advanced Trea-

tise, Vol. VII, Academic Press, New York, 1975.

M. Eigen and R.G. Wilkins, Adv. Chem. Ser., 49 (1965).

C.H. Langford and H.B. Gray, Ligand Substitution Process, Benjamin, New York, 1966.

H.H. Espenson, Inorg. Chem., 8 (1969) 1554.

R.O. James and T.W. Healy, J. Colloid Interface Sci., 40 (1972) 42.

H.T. Hall and H. Eyring, J. Am. Chem. Sot., 72 (1960) 782.

A. Bell and E. Matijevid, J. Inorg. Nucl. Chem., 37 (1975) 567.

343

25 M. Onofusa and E. Matijevic’, J. Colloid Interface Sci., 71 (1979) 167. 26 R. Demchak and E. MatijeviC, J. Colloid Interface Sci., 31 (1969) 257. 27 A. Bell and E. MatijeviC, J. Phys. Chem., 78 (1974) 2621. 28 S. Kratohvil and E. Matijevic, J. Colloid Interface Sci., 24 (1967) 47. 29 J.O’M. Bockris and A.K.N. Reddy, Modern Electrochemistry, Vol. 2, Plenum Press, New

York, 1977. 30 O.G. Holmes and D.S. McClure, J. Chem. Pys., 26 (1957) 1686. 31 L.E. Orgel, Transition Metal Chemistry, Wiley, New York, 1960. 32 D.P. Eley and M.G. Evans, Trans. Faraday Sot., 34 (1938) 1093.