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Thermodynamic considerations on the contribution of the dissociation of silanol groups to the stability of silica sols
Volume176,number 3,4
CHEMICALPHYSICSLETTERS
18January 1991
Thermodynamic considerations on the contribution of the dissociation of silanol groups to the stability of silica sols J. Sonnefeld,
W. Vogelsberger and G. Rudakoff
Faculty ofchemistry,
Insiitute ofphysical Chemistry, Friedrich-Schiller-University, Lessingstrasse 10, O-6900 Jena, Germany
Received17September1990
4 new relationshipfor the free energy of silanol-group dissociation on silica sol particles is derived, includmg both an electrical and a chemical part. Using an equation for the calculation of the dissociation equilibrium based on the simple Gouy-Chapman model of the electrochemical double layer, we discuss the contribution of this term to stabilization of silica sol in a weak alkaline aqueous dispersion. We find minima of the Helmholtz free energy in dependence on dispersion composition. They are identified as stable states in a thermodynamic sense. Relation results between sol composition and particle size of thermodynamic stable
states.
1. Introduction The reason for the instability or the necessity for stabilization of dispersion colloids like silica sol results from the fundamental property of colloids, a considerable surface area causing a considerable surface term in thermodynamic potentials. Aggregation and Ostwald-ripening are consequences of this instability, and therefore one must distinguish between kinetic stabilization (prevention of aggregation) and a true stabilization in a thermodynamic sense. Reactions on the surface, leading to the formation of a surface charge, are frequently used for stabilization of 4s. Stabilization against aggregation of dispersion colloids described by DLVO theory [ l5 ] is based on this effect. The results are well known. They are appreciated and applied in a series of scientific considerations in this field. Different points of view exist on the general possibility of thermodynamic stabilization of dispersion colloids by simple surface reactions [ 5-7 1. Especially Yates [ 8 ] and Strehlow [9] give a thermodynamic treatment on stability of silica SOIS.Investigations of the kinetics of growth of silica spheres [ 1O] lead also to constant particle sizes at long time, and these results suggest a thermodynamic equilibrium of colloidal silica. Results of our first attempt to describe the thermodynamic properties of silica sol are published elsewhere 0009-2614/91/$
[ 111. This description includes two not-well-established points: First, the equation from Yates [ 8 ] for calculation of the free energy of silanol-group dissociation contains the chemical contribution to the charging of surface only, and, second, the two formulas [ 8,12 ] derived from experimental results for the calculation of the degree of dissociation, LY,or the acid constant of silanol groups? K,, used in ref. [ 111, differ from each other for the given parameters in some orders of magnitude. The aim of this article is to derive an expression for the free energy of silanol-group dissociation in weak alkaline aqueous solution taking into account that this is a chemical process, accompanied by the surface charge formation. This expression is combined with a relationship for calculating the free energy of formation of a system of monodisperse spherical uncharged silica sol particles, as derived in ref. [ 111, to discuss the thermodynamic stability of silica sol. Thereby, we used an expression for the acidity constant, KS, of silanol groups [ 13 1, which is based on a site dissociation model in connection with the simple Gouy-Chapman model for an electrochemical double layer. It agrees well with the experimental results of Schindler and Kamber [ 121. In a recent paper, Strehlow [9] calculated conditions for thermodynamic stability of silica sol in ethanolic solutions. He used for the electrochemical
03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland)
309
Volume 176, number3,4
double layer the low,potential approximation for spherical particles and characterized the surface dissociation by a constant value of charge per particle over some orders of magnitude of particle size. Both approaches are not applicable to weak alkaline aqueous dispersions (see e.g. ref. [ 141). The following constants are applied: T=298 K (temperature); cr= 50 mN/m (surface tension of the sol particle/water interface) [ 151; Vs=27.2 cm3/mol (molar volume of silica in sol particles) [ 161; C”=2~10-3 mol/P (solubility of silica) [ 17-191; PsioH= 1.3 X 1O-’ mol/m* (surface density of silanol groups; we use a maximum value given by Iler [ 161. pKi =6.8 1 (p&-value limit for a zero degree of dissociation ( CX=0) ). We use a value calculated by Schindler and Kamber [ 13 ] from experimental results. e,=78.5 (relative permittivity of water at 298 K)
1201.
2. Helmholtz free energy of silanol group dissociation We consider the surface charge formation of silica sol in alkaline aqueous dispersion as site dissociation of acid sites =SiOH@=SiO-tH+
,
(1)
where the equilibrium degree of dissociation for a given silica sample is determined by the ratio of interface area to dispersion volume and the dispersion composition. Furthermore, we restrict ourselves to sols without foreign salts and to sodium hydroxide as stabilizing agent. Then, the sol composition is primarily characterized by the total supersaturation Y and the molar SiO,/Na,O ratio X Y2&
18January 1991
CHEMICAL PHYSICS LETTERS
+, WJ+
(2)
where up is the total amount of silica in the sol, v the volume of sol and C,,+ the sodium ion concentration. The equilibrium, eq. ( 1 ), is described by a “classical” acid constant,
lution volume. Since the silanol-group dissociation is connected with a charge separation, the acid constant, KS, cannot be constant, but depends on the degree of dissociation. Therefore, we define an intrinsic acid constant, g, which is identical with the limit at zero degree of dissociation, Kg= limK,(a),
(4)
a-0
and characterize deviations from ps by a function f(Q)> &(a)=Gexp[-f(a)].
(5)
The calculation of the Helmholtz free energy of silanol-group dissociation, A& is done by integrating overtheelectrochemicalpotentials,Fj,ofthereactants
I
&f=nT 1 (/Z~i)da
5
(6)
where nr is the total amount of silanol groups, v, are the stoichiometric numbers and the integration limits are the zero degree of dissociation (cw=O), on the one hand, and the dissociation equilibrium (a), on the other hand. Changes in the solution due to surface dissociation are expressed in the change of H+ ion concentration from C”,+ to c’d+ The electrochemical potential is the sum of a chemical, ,u, and an electrical, be’, part. We assume ideal behaviour and use the concentrations, C, of species in bulk phases, instead of using activities, and the amount of substance, n, in the case of surface species, respectively. This yields CAY,=
C
(Pi+P?)
(7) where R is the gas constant. With the well-known relation C ,u:Y,= - RTln Ki,
(8)
it follows that c _&v,= -RTln
Kg
+RTln I&= -%,+ 1-a
, In the equilibrium state, we have from eqs. (9) and
where Cn+ is the H+ ion concentration 310
in the so-
(3L
Volume 176, number 3,4
CHEMICAL PHYSICS LETTERS
Cp,v~‘=RT[lnK~-lnK,(a)],
(10)
Inserting eq. ( 16) into eq. (5) and then into eq. ( 14) yields
(11)
(18)
(12)
Using the numerical results of the exact equation for charge balance including the dissociation of dissolved manosilicic acid, as discussed in ref. [ 13 1, we can now calculate ADF.
and inserting eq. ( 5) into eq. ( 10) yields ~$vi=RTf((a)
18 January 1991
or 1 P,v;=Rf-hK$+h
(z)+f(a)],
respectively Now we may integrate eq. (6). For this purpose, we relate the extensive free energy of silanol-group dissociation, A& to the total amount of silica, np, and express this quantity in units of RT, ADF= ST. g
(13)
Furthermore, we introduce the abbreviation Z, (14) where the integration limits are the same as discussed above. Then, we have with A,F= s
cw+ln( 1-a)+Z
( )I
3. Results and discussion The stability behaviour of silica sols in diluted aqueous solution of NaOH in the thermodynamic sense can be described by the Helmholtz free energy, AF, being the sum of the Helmholtz free energy of the formation of an uncharged sol and of the surface dissociation of the silanol groups: AF=AsF*+ADF.
(19)
For the first term on the right-hand side of eq. ( 19), we use an expression derived in ref. [ 121 for metastable states of a system of monodisperse spherical sol particles,
+2co”-cw + -CNa+ln gi ___ CT
c,
cg’
’
a suitable equation for calculating the free energy of silanol-group dissociation. Here, C, is the volume concentration of the total amount of surface groups or the total amount of surface groups per volume of dispersion. For calculation, it is necessary to have an expression for Ks( a) or f(cr), respectively. We use a recently derived equation [ 131 which agrees well with the experimental results of Schindler and Kamber [ 121, &(a)=
G 1+(2Ear/C,,+)(Ecrt,/w)’ (16)
where E is defined, with the Debye-Hiickel parameter, K, as E=%
PSiOH
4Jc,,,’
(17)
where the abbreviation H= oV,/RT is used and Yis the radius of the sol particles. Notice that the limit of A$‘* for infinite particle radius, which is designated Asp,, corresponds to equilibrium of the bulk phases. Fig. 1 shows, for a supersaturation of Y= 100, that the amount of Helmholtz free energy of silanol-group dissociation of monodisperse silica sol decreases continously with increasing particle radius. This agrees with the general experience that the influence of surface effects in colloidal systems decreases with the decreasing degree of disperson. A$ decreases with increasing SiOJNaOH ratio (i.e. decreasing concentration of stabilizing agent). This corresponds to expectation. We find, for suitable sol compositions (see fig. 2., e.g. Y= 100 and X+ 50) and for particles larger than a determined radius, that the values of AF become 311
Volume 176,number 3,4
CHEMICALPHYSICSLETTERS
I8 January 199I
AnF
Fig. I. Helmboltz free energy of silanol-group dissociation A& of a system of monodisperse spherical particles in metastable state in dependence on particle radius r for a supersaturation I’= 100. (I) X= 50; (II) X= 100; (III ) X= 200; (IV) X= 300.
Fig. 2. Helmholtz free energy AFin dependence on particle radius rof metastable states in comparison with AsF’(---) and A& (-,-); Y= 100:(I) x=50; (II) x=100; (III)X=200.
more negative than A$‘,, the value for the equilibrium of bulk phases. Therefore, our calculationssupport the thesis of the possibility of thermodynamic stabilization of silica ~01s.We find minima of AF which are interpreted as a thermodynamically stable particle size. Fig. 3 shows the influence of supersaturation on the radius of stable particles for a constant value of X. Radii of stable particles decrease with increasing 312
Y,caused by increasingNaOH concentration at constant Z. This is in agreement with the decreasingof stable particle size with the increasingof concentration of stabilizing agent. Furthermore, it can be shown that the concentration of NaOH has an important influence on the stability behaviour if the amount of substance of SiOz within the silica sol is kept constant. This influence is not observed for high values of X (see figs. 4 and 2, e.g. Y= 100 and
Volume176,number 3,4
I8 January I99 I
CHEMICALPHYSICSLETTERS
0
lo
20
30
40
r/nm
50
Fig. 3. Dependence of radius r of thermodynamically stable sol particles on supersaturation Y for a fixed Si02/Na20-ratio (X= 100).
150
X
104
50
0 0
I
I
I
I
0
20
30
40
r Inm
I
50
Fig. 4. Dependence of radius r of thermodynamically stable sol particles on Si02/Na20-ratio for a fired supersaturation ( Y= 100).
Xk 130) where minima do not exist and the graphs of AsF* and L\Fboth approach the graph AsF2, from the same direction. This agreeswith the thesis of Stol and de Bruyn [7] which postulated only a limited range of concentration of stabilization agent where thermodynamic stabilization is possible.This region is limited, on the one hand, by molecular resolution and, on the other hand, by the equilibrium of bulk phases. Iler [ 161 gives a summary of many commercial
stable silica soIs. Most of the sols contain particles of 5-25 nm in radius and values of X between 50 and 300. They are always smaller than predicted by our results. Bryant [2 I] investigated particle size of silica sols prepared by peptisation of freshly prepared gels. Here, an influence of the molar SiOz/NazO ratio, X, to the particle size is found, which tends to agreewith our results.But this influence is very small. An explanation of the divergence between the observation described above and our predictions is 313
Volume 176, number 3,4
CHEMICAL PHYSICS LETTERS
given in ref. [ 16 1. Investigations of the kinetics of Ostwald-ripening of silica sols shows that this is a very slow process at room temperature and for sols with narrow size distribution and particles greater than 10 nm in diameter. It is reported that Ostwaldripening is observed over a few months and a small increasing of particle size occurs over 20 years. Thus, it seems that the abovedescribed sols are not equilibrated. But two interesting results on silica-sol particle growth have been published. Alexander and Iler [ 221 observed the particle growth of a primarily sol by adding a supersaturated silica solution. The final result of these experiments is a sol with a particle radius of 33 nm and a value of X=85. Since the kinetics of Ostwald-ripening is influenced by temperature, Iler [ 161 gives a summary of experiments on particle growth at high temperatures under superatmospheric pressure. Here, a final value of particle diameter of 64 nm is given for a sol which is prepared at 568 Kand has a composition of X= 85. Both particle sizes agree well with the results in fig. 4.
References [l] B.V. Derjaguin: Kolloid Z. 69
314
( 1934) 155.
I8 January 1991
[ 21 B.V. Derjaguin and L. Landau, Acta Phaysicochim. USSR 14 (1941) 633. [ 31 B.V. Derjagum, Trans. Faraday Sot. 36 (1940) 203. [41 E.J.W. Verwey, Trans. Faraday Sot. 36 (1940) 192. [ 51 E.J.W. Verwey and J. Th. G. Overbeek, Theory of the stability of lyophobic colloids (Elsevier, Amsterdam, 1948). [61 J. Th. G. Overbeek, Advan. Colloid Interface Sci. 15 ( 1982) 251. [7] R.J. Stol and P.L. de Bruyn, J. Colloid Interface Sci. 75 (1980) 251.
[81 P.C. Yates, Abstr. Div. Colloid Chem. Symp. on Colloidal Silicaand Silicates, 137 th. Meeting Am.Chem. Sot. (1960). [9] P. Strehlow, J. Non.-Cryst. Solids 107 (1988) 55, [IO] A.P. Philipse, Colloid Polym. Sci. 266 (1988) 1174. [ I 11J. Sonnefeld, W. Vogelsberger and G. Rudakoff, Z. Physik. Chem. (Leipzig) 266 (1985) 449. [ 121 P. Schindlerand H.R. Kamber, Helv. Chim. Acta 51 ( 1988) 1781. [ 131 G. Rudakoff, J. Sonnefeld and W. Vogelsberger, Z. Physik. Chem. (Leipzig) 269 (1988) 441. [ 141 H. Sonntag, Lehrbuch der Kolloidwissenschaft (Deutscher Verlag der Wissenschaften, Berlin, 1977). [ 151 G.B. Alexander, J. Phys. Chem. 61 (1957) 1563. [ 161 R.K. Iler, The chemistry of silica (Wiley, New York, 1979). [ 171G.B. Alexander, W.M. Heston and R.K. Iler, J. Phys. Chem. 58 (1954) 453. [IS] H. Bilinski andN. Ingri, ActaChem. Stand. 21 (1967) 2503. [ 191 K.R. Anderson, L.N. Dent Glaser and D.N. Smith, ACS Symp. Ser. 194 (1982) 115. [ 201 K. Schwabe, pH-Messung, WTB Bd. 247 (Akademie-Verlag, Berlin, 1980). [?l] K.C. Bryant, I. Chem. Sot. (1952) 3017. [22] G.B. Alexander and R.K. Iler, J. Phys. Chem. 57 ( 1953) 932.
CHEMICALPHYSICSLETTERS
18January 1991
Thermodynamic considerations on the contribution of the dissociation of silanol groups to the stability of silica sols J. Sonnefeld,
W. Vogelsberger and G. Rudakoff
Faculty ofchemistry,
Insiitute ofphysical Chemistry, Friedrich-Schiller-University, Lessingstrasse 10, O-6900 Jena, Germany
Received17September1990
4 new relationshipfor the free energy of silanol-group dissociation on silica sol particles is derived, includmg both an electrical and a chemical part. Using an equation for the calculation of the dissociation equilibrium based on the simple Gouy-Chapman model of the electrochemical double layer, we discuss the contribution of this term to stabilization of silica sol in a weak alkaline aqueous dispersion. We find minima of the Helmholtz free energy in dependence on dispersion composition. They are identified as stable states in a thermodynamic sense. Relation results between sol composition and particle size of thermodynamic stable
states.
1. Introduction The reason for the instability or the necessity for stabilization of dispersion colloids like silica sol results from the fundamental property of colloids, a considerable surface area causing a considerable surface term in thermodynamic potentials. Aggregation and Ostwald-ripening are consequences of this instability, and therefore one must distinguish between kinetic stabilization (prevention of aggregation) and a true stabilization in a thermodynamic sense. Reactions on the surface, leading to the formation of a surface charge, are frequently used for stabilization of 4s. Stabilization against aggregation of dispersion colloids described by DLVO theory [ l5 ] is based on this effect. The results are well known. They are appreciated and applied in a series of scientific considerations in this field. Different points of view exist on the general possibility of thermodynamic stabilization of dispersion colloids by simple surface reactions [ 5-7 1. Especially Yates [ 8 ] and Strehlow [9] give a thermodynamic treatment on stability of silica SOIS.Investigations of the kinetics of growth of silica spheres [ 1O] lead also to constant particle sizes at long time, and these results suggest a thermodynamic equilibrium of colloidal silica. Results of our first attempt to describe the thermodynamic properties of silica sol are published elsewhere 0009-2614/91/$
[ 111. This description includes two not-well-established points: First, the equation from Yates [ 8 ] for calculation of the free energy of silanol-group dissociation contains the chemical contribution to the charging of surface only, and, second, the two formulas [ 8,12 ] derived from experimental results for the calculation of the degree of dissociation, LY,or the acid constant of silanol groups? K,, used in ref. [ 111, differ from each other for the given parameters in some orders of magnitude. The aim of this article is to derive an expression for the free energy of silanol-group dissociation in weak alkaline aqueous solution taking into account that this is a chemical process, accompanied by the surface charge formation. This expression is combined with a relationship for calculating the free energy of formation of a system of monodisperse spherical uncharged silica sol particles, as derived in ref. [ 111, to discuss the thermodynamic stability of silica sol. Thereby, we used an expression for the acidity constant, KS, of silanol groups [ 13 1, which is based on a site dissociation model in connection with the simple Gouy-Chapman model for an electrochemical double layer. It agrees well with the experimental results of Schindler and Kamber [ 121. In a recent paper, Strehlow [9] calculated conditions for thermodynamic stability of silica sol in ethanolic solutions. He used for the electrochemical
03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland)
309
Volume 176, number3,4
double layer the low,potential approximation for spherical particles and characterized the surface dissociation by a constant value of charge per particle over some orders of magnitude of particle size. Both approaches are not applicable to weak alkaline aqueous dispersions (see e.g. ref. [ 141). The following constants are applied: T=298 K (temperature); cr= 50 mN/m (surface tension of the sol particle/water interface) [ 151; Vs=27.2 cm3/mol (molar volume of silica in sol particles) [ 161; C”=2~10-3 mol/P (solubility of silica) [ 17-191; PsioH= 1.3 X 1O-’ mol/m* (surface density of silanol groups; we use a maximum value given by Iler [ 161. pKi =6.8 1 (p&-value limit for a zero degree of dissociation ( CX=0) ). We use a value calculated by Schindler and Kamber [ 13 ] from experimental results. e,=78.5 (relative permittivity of water at 298 K)
1201.
2. Helmholtz free energy of silanol group dissociation We consider the surface charge formation of silica sol in alkaline aqueous dispersion as site dissociation of acid sites =SiOH@=SiO-tH+
,
(1)
where the equilibrium degree of dissociation for a given silica sample is determined by the ratio of interface area to dispersion volume and the dispersion composition. Furthermore, we restrict ourselves to sols without foreign salts and to sodium hydroxide as stabilizing agent. Then, the sol composition is primarily characterized by the total supersaturation Y and the molar SiO,/Na,O ratio X Y2&
18January 1991
CHEMICAL PHYSICS LETTERS
+, WJ+
(2)
where up is the total amount of silica in the sol, v the volume of sol and C,,+ the sodium ion concentration. The equilibrium, eq. ( 1 ), is described by a “classical” acid constant,
lution volume. Since the silanol-group dissociation is connected with a charge separation, the acid constant, KS, cannot be constant, but depends on the degree of dissociation. Therefore, we define an intrinsic acid constant, g, which is identical with the limit at zero degree of dissociation, Kg= limK,(a),
(4)
a-0
and characterize deviations from ps by a function f(Q)> &(a)=Gexp[-f(a)].
(5)
The calculation of the Helmholtz free energy of silanol-group dissociation, A& is done by integrating overtheelectrochemicalpotentials,Fj,ofthereactants
I
&f=nT 1 (/Z~i)da
5
(6)
where nr is the total amount of silanol groups, v, are the stoichiometric numbers and the integration limits are the zero degree of dissociation (cw=O), on the one hand, and the dissociation equilibrium (a), on the other hand. Changes in the solution due to surface dissociation are expressed in the change of H+ ion concentration from C”,+ to c’d+ The electrochemical potential is the sum of a chemical, ,u, and an electrical, be’, part. We assume ideal behaviour and use the concentrations, C, of species in bulk phases, instead of using activities, and the amount of substance, n, in the case of surface species, respectively. This yields CAY,=
C
(Pi+P?)
(7) where R is the gas constant. With the well-known relation C ,u:Y,= - RTln Ki,
(8)
it follows that c _&v,= -RTln
Kg
+RTln I&= -%,+ 1-a
, In the equilibrium state, we have from eqs. (9) and
where Cn+ is the H+ ion concentration 310
in the so-
(3L
Volume 176, number 3,4
CHEMICAL PHYSICS LETTERS
Cp,v~‘=RT[lnK~-lnK,(a)],
(10)
Inserting eq. ( 16) into eq. (5) and then into eq. ( 14) yields
(11)
(18)
(12)
Using the numerical results of the exact equation for charge balance including the dissociation of dissolved manosilicic acid, as discussed in ref. [ 13 1, we can now calculate ADF.
and inserting eq. ( 5) into eq. ( 10) yields ~$vi=RTf((a)
18 January 1991
or 1 P,v;=Rf-hK$+h
(z)+f(a)],
respectively Now we may integrate eq. (6). For this purpose, we relate the extensive free energy of silanol-group dissociation, A& to the total amount of silica, np, and express this quantity in units of RT, ADF= ST. g
(13)
Furthermore, we introduce the abbreviation Z, (14) where the integration limits are the same as discussed above. Then, we have with A,F= s
cw+ln( 1-a)+Z
( )I
3. Results and discussion The stability behaviour of silica sols in diluted aqueous solution of NaOH in the thermodynamic sense can be described by the Helmholtz free energy, AF, being the sum of the Helmholtz free energy of the formation of an uncharged sol and of the surface dissociation of the silanol groups: AF=AsF*+ADF.
(19)
For the first term on the right-hand side of eq. ( 19), we use an expression derived in ref. [ 121 for metastable states of a system of monodisperse spherical sol particles,
+2co”-cw + -CNa+ln gi ___ CT
c,
cg’
’
a suitable equation for calculating the free energy of silanol-group dissociation. Here, C, is the volume concentration of the total amount of surface groups or the total amount of surface groups per volume of dispersion. For calculation, it is necessary to have an expression for Ks( a) or f(cr), respectively. We use a recently derived equation [ 131 which agrees well with the experimental results of Schindler and Kamber [ 121, &(a)=
G 1+(2Ear/C,,+)(Ecrt,/w)’ (16)
where E is defined, with the Debye-Hiickel parameter, K, as E=%
PSiOH
4Jc,,,’
(17)
where the abbreviation H= oV,/RT is used and Yis the radius of the sol particles. Notice that the limit of A$‘* for infinite particle radius, which is designated Asp,, corresponds to equilibrium of the bulk phases. Fig. 1 shows, for a supersaturation of Y= 100, that the amount of Helmholtz free energy of silanol-group dissociation of monodisperse silica sol decreases continously with increasing particle radius. This agrees with the general experience that the influence of surface effects in colloidal systems decreases with the decreasing degree of disperson. A$ decreases with increasing SiOJNaOH ratio (i.e. decreasing concentration of stabilizing agent). This corresponds to expectation. We find, for suitable sol compositions (see fig. 2., e.g. Y= 100 and X+ 50) and for particles larger than a determined radius, that the values of AF become 311
Volume 176,number 3,4
CHEMICALPHYSICSLETTERS
I8 January 199I
AnF
Fig. I. Helmboltz free energy of silanol-group dissociation A& of a system of monodisperse spherical particles in metastable state in dependence on particle radius r for a supersaturation I’= 100. (I) X= 50; (II) X= 100; (III ) X= 200; (IV) X= 300.
Fig. 2. Helmholtz free energy AFin dependence on particle radius rof metastable states in comparison with AsF’(---) and A& (-,-); Y= 100:(I) x=50; (II) x=100; (III)X=200.
more negative than A$‘,, the value for the equilibrium of bulk phases. Therefore, our calculationssupport the thesis of the possibility of thermodynamic stabilization of silica ~01s.We find minima of AF which are interpreted as a thermodynamically stable particle size. Fig. 3 shows the influence of supersaturation on the radius of stable particles for a constant value of X. Radii of stable particles decrease with increasing 312
Y,caused by increasingNaOH concentration at constant Z. This is in agreement with the decreasingof stable particle size with the increasingof concentration of stabilizing agent. Furthermore, it can be shown that the concentration of NaOH has an important influence on the stability behaviour if the amount of substance of SiOz within the silica sol is kept constant. This influence is not observed for high values of X (see figs. 4 and 2, e.g. Y= 100 and
Volume176,number 3,4
I8 January I99 I
CHEMICALPHYSICSLETTERS
0
lo
20
30
40
r/nm
50
Fig. 3. Dependence of radius r of thermodynamically stable sol particles on supersaturation Y for a fixed Si02/Na20-ratio (X= 100).
150
X
104
50
0 0
I
I
I
I
0
20
30
40
r Inm
I
50
Fig. 4. Dependence of radius r of thermodynamically stable sol particles on Si02/Na20-ratio for a fired supersaturation ( Y= 100).
Xk 130) where minima do not exist and the graphs of AsF* and L\Fboth approach the graph AsF2, from the same direction. This agreeswith the thesis of Stol and de Bruyn [7] which postulated only a limited range of concentration of stabilization agent where thermodynamic stabilization is possible.This region is limited, on the one hand, by molecular resolution and, on the other hand, by the equilibrium of bulk phases. Iler [ 161 gives a summary of many commercial
stable silica soIs. Most of the sols contain particles of 5-25 nm in radius and values of X between 50 and 300. They are always smaller than predicted by our results. Bryant [2 I] investigated particle size of silica sols prepared by peptisation of freshly prepared gels. Here, an influence of the molar SiOz/NazO ratio, X, to the particle size is found, which tends to agreewith our results.But this influence is very small. An explanation of the divergence between the observation described above and our predictions is 313
Volume 176, number 3,4
CHEMICAL PHYSICS LETTERS
given in ref. [ 16 1. Investigations of the kinetics of Ostwald-ripening of silica sols shows that this is a very slow process at room temperature and for sols with narrow size distribution and particles greater than 10 nm in diameter. It is reported that Ostwaldripening is observed over a few months and a small increasing of particle size occurs over 20 years. Thus, it seems that the abovedescribed sols are not equilibrated. But two interesting results on silica-sol particle growth have been published. Alexander and Iler [ 221 observed the particle growth of a primarily sol by adding a supersaturated silica solution. The final result of these experiments is a sol with a particle radius of 33 nm and a value of X=85. Since the kinetics of Ostwald-ripening is influenced by temperature, Iler [ 161 gives a summary of experiments on particle growth at high temperatures under superatmospheric pressure. Here, a final value of particle diameter of 64 nm is given for a sol which is prepared at 568 Kand has a composition of X= 85. Both particle sizes agree well with the results in fig. 4.
References [l] B.V. Derjaguin: Kolloid Z. 69
314
( 1934) 155.
I8 January 1991
[ 21 B.V. Derjaguin and L. Landau, Acta Phaysicochim. USSR 14 (1941) 633. [ 31 B.V. Derjagum, Trans. Faraday Sot. 36 (1940) 203. [41 E.J.W. Verwey, Trans. Faraday Sot. 36 (1940) 192. [ 51 E.J.W. Verwey and J. Th. G. Overbeek, Theory of the stability of lyophobic colloids (Elsevier, Amsterdam, 1948). [61 J. Th. G. Overbeek, Advan. Colloid Interface Sci. 15 ( 1982) 251. [7] R.J. Stol and P.L. de Bruyn, J. Colloid Interface Sci. 75 (1980) 251.
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