1186
Langmuir 1989,5, 1186-1190
monolayers. Because the computer program used had a standard value for xsc of 0.288, we have done the calculations with xsPO parameters based on this value instead of 0.2. Therefore, the xsvalues in the last line of table V were incremented by 0.1. Figure 4 shows four isotherms. For the curves labeled 1and 3, we have taken xsPO values from Table V determined for nonathermal solvent mixtures. The isotherms 2 and 4 are calculated with xsPO values, based on athermal behavior of the solvent mixtures. Displacement isotherms 1and 2 are the results of computer calculations done with literature values for x, given in Table IV. For the curves 3 and 4, we have taken all x parameters equal to zero (athermal). The experimental critical point is also indicated in the figure. Only the critical points of the calculated curves 1 (completely nonathermal) and 4 (completely athermal) correspond with each other and with the experimental value. Curves 2 and 3, where solvent effects were either omitted from the theory or from the experimentally obtained value of xBW, show deviating critical points. This implies that the simplified model of Cohen Stuart et al. and the solvent concept of Snyder are consistent with the extended model of Scheutjens and Fleer, as long as a consistent procedure for the determination of xsW is used. The influence of the solvent-polymer, displacer-polymer, and displacer-solvent interactions on the critical point is shown by the shifted isotherms 2 and 3. Clearly, solvency effects have to be (27) The factor 2.303 arises because Snyder uses decimal rather than natural logarithms.
taken into account for the determination of the segmental energy.
Conclusions Adsorption thin-layer chromatographyis a very sensitive technique for determining the critical point in polymer adsorption experiments. The chromatographic solvent strength concept of Snyder is very useful in polymer adsorption studies. The segmental adsorption energy can be easily determined with the help of the well-known eluotropic series. The determination of this energy is more complicated when strongly adsorbing componentsare used, because the substrate may be heterogeneous with respect to these components. A consequence of this is that the adsorption energy of strongly adsorbing components is not a well-defined parameter on heterogeneous surfaces. Specific interactions between polymer and displacer do not play a significant role in the displacement of polystyrene from silica by chloroform. The effective adsorption energy for PS on silica is l.OkT in carbon tetrachloride and 1.9kT in cyclohexane. These values correspond, within experimental error, to the difference in adsorption energy between cyclohexane and carbon tetrachloride. Acknowledgment. This work was supported by a grant from the ministry of Economic Affairs of The Netherlands under program 1OP.PCBP nr. 3. Registry No. PS, 9003-53-6;silica, 7631-86-9; carbon tetrachloride, 56-23-5; cyclohexane, 110-82-7; methylene chloride, 75-09-2; benzene, 71-43-2; toluene, 108-88-3;chloroform,67-66-3.
Small-Angle X-ray Scattering Investigation of the Silica/Water Interface: Evolution of the Structure with P H M. A. V. Axelos,+ D.Tchoubar,' and J. Y. Bottero*vg I.N.R.A. Laboratoire d'gtude des macromolgcules, Nantes 44000, France, Laboratoire de Cristallographie, UA810 CNRS Universitg d'orleans, 45067 Orlgans Cedex, France, and Equipe de recherche sur la coagulation-floculation, UA235 CNRS, CRVM BP40, Vandoeuvre 54501, France Received April 7, 1988. In Final Form: April 27, 1989 Precipitated silica colloids in suspension in water (Ludox HS) were studied by using small-angle X-ray scattering (SAXS) in order to evaluate the modifications of the interface (roughness, gel-like structure, ...) with pH variations. The electrokinetic data show that for pH 28 the surface charge increases sharply. SAXS yields two pieces of information about silica particles: (1)when pH increases from 7 to 10 the volume and the radius decrease from 2.5 X 103to 1.9 X 103nm3and from 7.4 to 7.15 nm, respectively; (2) the structure of the colloid/solvent interface is predicted by the Porod law. At pH 7, the two phases are separated by a sharp density transition. A t pH 10, a transition region appears, modeled by convoluting the ideal sharp density distribution with a smoothing distribution which is assumed to be Gaussian. The thickness of the perturbated region is about 1.1nm, and the radius of the resulting dense core particle is 5.6 nm instead of the 6.7 nm calculated from a log normal size distribution. The stability of colloidal sols depends on the surface properties. In the case of oxides, it is well-known that the surface sites undergo amphoteric dissociation. In some cases, metallic oxides show very different behavior compared to silver iodide or mercury electrode.'p2 For oxides like precipitated silica from an acidic or basic method, the I.N.R.A. Laboratoire d'etude des macromol6cules. Laboratoire de Cristallographie, Universit6 $Orleans.
* * Equipe de recherche sur la coagulation-floculation.
0743-7463/89/2405-ll86$01.50/0
number of silanol groups determined from potentiometric titration can be 25.5 OH/nm2.3 This value is much higher than can be assumed considering a surface area of 0.1-0.12 nm2/0H group. Correlatively, the surface charge can be very high and also exceeds what would be obtained from (1) Lyklema, J. Croat. Chem. Acta 1971,43, 249. (2) Lyklema, J. Interactions in colloidal systems. Ecole des Houches
du CNRS,1985. (3) Yates, D. E.; Healy, T. W. J . Colloid Interface Sci. 1976, 55, 9.
0 1989 American Chemical Society
Langmuir, Vol. 5, No. 5, 1989 1187
SAXS Investigation of SilicalWater Interface
-I
m -2oc -20G
$ -300
a c.
2
-40-
-50-
$* Figure 1. {potential of Ludox HS silica in 10-' and 10-2 M NaC1. the total theoretical dissociation of surface groups ( - 5 OH/nm2)? Very recently, it has been shown that the silica surface perturbated the structuration of water occurring beyond -6 nm from the ~ u r f a c e . ~Generally, on other oxides or aluminosilicates the perturbation is limited to two or three water To explain the very high surface charge, the existence of a porous surface layer permeable to protons and counterions has been earlier propo~ed.'~~ Surface roughness can be postulated to explain such behavior. This discussion remains open if no physical evidence is given. The aim of this paper is to bring a physical meaning to the variation of the interfacial or surface structure with pH through small-angle X-ray scattering technique. Experimental Section Sample. The colloidswere silica Ludox HS which was recently studied by scattering technique^.'^-'^ From TEM image analysis, the mean diameter was found to be 16 nm. By use of small-angle X-ray scattering, the mean diameter was found to be 13 nm on the basis of a log normal size distribution.13J4 Potentiometric titration and electrophoretic mobility techniques with nonpyrogenic silica showed that the point of zero charge (PZC) equaled the isoelectric point (IEP) -2-3 in NaCl electrolyte. If ApH = pH - p H p S~ 6, the surface charge uois low. It increases for ApH > 6 to -100 pCcm-2in KCl or NaCl at M and pH 10. The density site number (NJ is currently of the order of 8-10 OHmf2 as determinedwith IR spectroscopy,water adsorption, or chemical reaction^.'^ A t large pH values, direct calculations from potentiometric titration yield very large N, values of 25 OH.nm-2? The electrokinetic potential of Ludox HS silica (0.1% w/w) in NaCl of and lo-' M determined with a laser Zee Meter (Pen Kem Inc.) apparatus shows two distinctive parts (Figure 1). For pH 58,the curves are very similar to those previously publi~hed.'"'~ For pH >8,the sharp increase of { corresponds to
-
an increase of oelek = q associated with a large increase of the surface charge bo. This qualitative result is consistent with a surface charge increase due to the formation of an intermediate region named "gel" l s 3 between solid surface and liquid bulk. Small-Angle X-ray Scattering Data Recordings. SAXS measurements were carried out on 1w t % suspensions at pH 7 and pH 10with HCl as pH regulator. The synchrotron radiation of the D.C.I. storage ring of L.U.R.E.(Universitg de Paris Sud) was used to benefit from the very intense X-ray beam and ita point collimation. The Q range of collected data varied from 2.5 X lo4 to lo-' A-l. Q = 47r sin B / X is the scattering vector amplitude, where 6 and X are half the scattering angle and the wavelength (1.6 A), respectively. As point collimation was very sharp, the only corrections concern the absorption by the sample and the solvent. The scattering due to the solvent was subtracted from the total scattering. Results Small-Angle X-ray Scattering, The theory of SAXS by suspensions of particles predicts some characteristic behaviors of the scattering functions which can be related to size, shape, and external surface features of particles. For suspensions of noninteracting monodisperse particles (large dilution), Guinier's law19predicts that for small wave vector Q the scattering intensity I(&) can be approximated by I(Q) = I(0)exp(-Q2R:/3) (1) where R, is the radius of gyration of a particle. Therefore, log I(Q) - Q2has to display a linear portion in the range of the smallest Q values. The slope of this relation allows one to calculate R,. By extrapolation of this linear part to Q = 0, the intensity I(0) is related to the volume Vo of a particle Vo = IN@) and IN(Q) = I(Q)/P (2) where P is the total scattering power of the sample
P = (1/2r2)1Q21(Q) dQ Moreover, irrelative to the dilution conditions, Porod's law predicts the behavior of the scattering curve at the largest Q values. If the surface is smooth, the density of the medium varies as a step function at the particle-solvent interface, and I(Q) falls off as g.lso that @I(Q) is constant at large Q values. The asymptotic limit Q41~(Q)/4r= 2/L = s/2 (3) where L is the average intercept segment or average chord of a particle and S is its surface area. In the last 5 years Porod's law was generalized to the case of fractal surfaces. In such cases, Porod's lawz0Vz1is expressed as
-
I(Q) ~
~~
~~
(4) Zhuravlev, L. T . Langmuir 1987,3, 316. (5)Ramsay, J. D.F.; Poinsignon, C. Langmuir 1987,3,320. (6)Partyka, S.;Rouquerol, F.; Rouquerol, 3. J.Colloid Interface Sci. 1979,68, 21. (7) Pons, C. H.; Tchoubar, C.; Tchoubar, D. Bull. Miner. 1980,103, 452. (8) Pons, C. H.; Roumeaux, F.; Tchoubax, D. Clay Miner. 1981,16,23. (9)Fripiat, J. J.; Cases, J. M.; Francois, M.; Letellier, M. J. Colloid Interface Sci. 1982,89,378. (10)Cases, J. M.;Francois, M. Agronomie 1982,20, 931. (11)Ramsav, J. D.F.: Booth, B. 0. J. Chem. SOC.,Faraday. Tram. 1 1983, 79, 173. (12)Ramsav. J. D. F.: Averv, _ .R. G.: Benest. L. Faradav Discuss. Chem. SOC. llS, 73,53.' (13)Axelos, M. A. V. These 3O Cycle, 1985, Universitg d'Orl6ans. (14)Walter, G.; Kranold, R.; Gerber, T. H. J . Appl. Crystallogr. 1985, 18. 205. (15)James, R. 0.; Parke, G. A. In Surface and Colloid Science; Matijevic, E.; Ed.; Plenum: New York, London, 1982;Vol. 12. (16)Bolt, G. H.J.Phys. Chem. 1957,61,1166. (17)Allen, L.H.;Matijevic, E. J. Colloid Interface Sei. 1969,31,287. (18)Capelle, P. Ph.D. Thesis, UniversiU Catholique de Louvain-Laneuve, 1987,p 230.
Q-(D-Zd)
where D is the fractal dimension of the surface (2 I D I 3) and d the Euclidian dimension (d = 3). Recently, the scattering asymptotic limitation was discussed for rough surfaces by analogy with random-field Ising systems.22 The asymptotic form is predicted as I(Q) AQ-(d+x)+ BQb4+ ... (4) where x is the exponent which defines the root mean square fluctuation w of the roughness over a distance r by w--rx In the w e where the conventional g.l asymptotic behavior
-
(19)Guinier, A.; Foumet, F. Small-Angle Scattering of X-Rays;Wiley New York, 1955. (20)Bale, H.D.;Schmidt, P. W. Phys. Reu. Lett. 1984,596-599. (21)Kjems, J. In abstracts of papers presented at the symposium on Small Angle Scattering and related methods, Hamburg, West Germany, 1984. (22)Po-Zen, W.Phys. Reu. B 1985,32, 7417.
1188 Langmuir, Vol. 5, No. 5, 1989
Arelos et al.
I
0
0.004
0.008 Q2
0.012
k 2)
Figure 2. Guinier plot of Ludox silica at pH 7. 4.1
is observed, it is easy to give a simple meaning of the Fourier transform of I(Q) through the radial distance distribution P(r). It must be recalled that in the case of an isotropic medium Fourier’s integral has the form P(r) = (r2/2r2)$Q21dQ)(sin Qr/Qr) dQ
(5)
As previously the profile and the intensity of P(r) distribution characterize the volume of the particle. Another interesting distribution is the chord distribution @(L),which is very sensitive to the particle surface shape.% I t can be calculated by using the following equation: @(r)= 1 / 2 r $ [ 2
- L@IN(Q)/4r][-4(sin Qr/Qr)”] dQ
The condition @(O) = 0 is observed for a rounded surface particle,24whereas @(O) # 0 means that the surface contains some point angularities or sharp facet edges. Ludox HS Samples: Size and Shape. In silica suspensions, the condition of high dilution is valid because the large extent of the Guinier plot (Figure 2) means that no interparticle interactions are detectable. Nevertheless, there is a size polydispersity. In such a case, the experimental parameters are averaged values: (R,), ( Vo), and ( L ) . These parameters correspond to various ways of averaging the size of the particle population. Let N(R) be the number of particles with a *radius” R and (R”)the nth moment of N(R),then ( ~ n =)
~ R ~ N (d~ R )
with the condition of normalization
SN(R) d~ = 1
and the mean “radius”
R=
SRN(R)
As already lirgely dis~ussed,’~ the parameters are related to the ratios of various moments (R”)without any as(23)Glatter, 0.; Kratky, 0.Small Angle X-ray Scattering; Academic: New York, 1982. (24) Mering, J.; Tchoubar, D.J. Appl. Crystallogr. 1968, I, 153.
6
4
8
ki
Figure 3. Calculation of the average and standard deviation of the size distribution. sumption on the form of N(R): (R;) is related to ( R 8 ) / ( R 6(Vo) ) , is related to ( P ) / ( R 3 )and , ( L )is related to ( R 3 ) / ( R 2 )One . can also use the “length correlation”
(L,) = 1/2*$QIdQ)
dQ
where (L,) is related to ( R 4 ) / ( R 3and ) the “surface correlation” (f) = l / r l I d Q )dQ
(6)
where (sin x / x ) ” is the second derivative of the Fourier kernel versus x . An important feature is the value of @(O):
2
0
where ( f ) is related to ( R5)/ (R3). The assumption of spherical particles is a good approximation according to the transmission electron microscopy results. Therefore, five averaged radii Ri associated with the parameters given above can be defined:
R1 = (5/3)1/2(R,2) R2 = [(3/4) ( V O ) I ~ ’ ~ R3
= [(5/4)(f)11’2
Rr, = (4/3)(L) R5 = (4/3)(~5) If N(R) is a log normal di~tribution,’~ its geometric mean and its standard deviation u are related to Ri by
p
In Ri = ki ln2 u + In p
(7)
The ki are tabulated constants for each Ri. Sample at pH 7. Figure 3 displays the variation of In Ri versus ki. It shows that the experimental values R1,R2, R , and R4 are conveniently related by eq 7. Thus it justifies the choice of a log normal distribution ( p = R = 6.7 nm and a = 1.25 nm) to represent the polydispersity of silica particles. Such a radius distribution is shown in Figure 4. In Figure 5a, the experimental P(r) is well fitted by a theoretical curve, which is computed from the scattering intensity (Z(Q)) by using
U(QH
= J N ( R ) R ~ M Qd~ )
(8)
where IR(Q) is the scattering by a sphere of radius R. Table I displays the values of (R,) and ( Vo)which are obtained from the Guinier plot (Figure 2) and eq 1 and 2. It can
Langmuir, Vol. 5, No. 5, 1989 1189
SAXS Investigation of SilicalWater Interface -Gaussian
law
normal law
----Log
0
2000
-
1600-
A
-
I
I
0.004
0.008
0.016
0.012
Q2
--- log-normal law ~
Ibl
~ 6 . 7
- Experimental P (r)= 1.25 (I
-0
14001200
0
-
~
0.004
0.008
0.012
Q2 ( A e 2 )
(a)
L
n 1000800
Figure 6. Asymptotic behavior of the scattering curve at pH 7 (curve a) and pH 10 (curve b).
-
-0
4
8
12
16
20
24
28
32
36
r (nm)
0
r (nm)
Figure 5. (a) Experimental and calculated distance distribution: dashed line corresponds to spherical particles with log normal size distribution; solid line is the experimental curve. (b) Distance distribution function P(r) versus r (nm) for Ludox silica at pH 7 and pH 10.
Table I. Calculated Parameters from SAXS Technique parameter
R nm
6 nm3
PH 7 7.4 2.5 x 103
pH 10 7.15 1.9 x 103
be seen that the statistical weight of the largest particles is enhanced in comparison with the numerical averages ( R = 5.2 nm and V , = 1.26 X lo3 nm3), which are deduced from R = 6.7 nm (Figure 5). Sample at pH 10. Lower (R,) and (V,) are observed compared to results at pH 7 as well as a decrease in the
5
10
15 20 r (nml
25
30
35
Figure 7. Chord distribution function @(r)versus r (nm) at pH 7. The dashed line corresponds to the experiment and the solid line to a calculated curve relative to spherical particles with a log normal size distribution. intensity of P(r) (Figure 5b), meaning a decrease of the average volume of matter.
Surface Roughness Sample at pH 7. The asymptotic behavior in Q4 observed at pH 7 (Figure 6a) confirms that for this pH the particle-solvent interface is characterized by a sharp drop of the electron density from the solid surface to the liquid bulk. It is also observed (Figure 3) that R5,which is specifically related to the surface area of the particles, does not fit eq 7, contrary to the other R j . This expresses the volume effect to the scattering. This discrepancy between
1190 Langmuir, Vol. 5, No. 5, 1989
Axelos et al.
surface and volume effect is particularly enhanced in the profile of the chord distribution @(r).Figure 7 shows the comparison between the experimental @(r)and the theoretical one computed from the log normal distribution of spheres. The discrepancy affecting the range of the smallest r values is characteristic of the presence of some point angularities on the surface or a polyhedral shape of the particles with sharp facet edges.24 Sample at pH 10. The asymptotic behavior (Figure 6b) is quite different of that at pH 7. The curve @1(Q) linearly decreases with Q2. At first sight, such behavior recalls the recent theoritical predictions concerning the surface roughness of self-similar or self-affinity fractal Such surface structures could logically result from an interfacial dissolution process when the pH increases from 7 to 10. The power law which could be deduced from Figure 6b would take the form 1(Q)
-
Q-a with a = 5.2
Recently, values of 4.21-4.95 have been obtained from reversed phase silica.25 This result was interpreted according to recent theoretical predictions26as due to the existence of a “fuzzy” surface. In our case, the interpretation is similar. The decay is due to a density transition with a finite widthn of the interfacial region perpendicular to the interface. This transition zone can be conveniently represented by the convolution product of the ideal step function and of a smoothing distribution h(r) as the density distribution p ( r ) becomes = P(r)theorh(r)
In this case, the intensity 1(Q) = [H(Q)]21th,r(Q) for large Q values, where H(Q) is the Fourier transform of h(r). Let u2 be the variance of the smoothing distribution h(r) perpendicular to the interface. If H(Q) is assumed to be Gaussian, then H(Q) = exp(-Q2u2) and eq 7 becomes Q41N(Q)/47r= 2/[L exp(-2Q2u2)]
(9)
Therefore In [Q41N(Q)/47r]= -2Q2u2 + In (2/L) By this method u2 can be calculated as well as the width of the h ( r ) distribution, which is u = 0.55 nm. Discussion The physical characterization of the interfacial structure of solids (surface charge, charge at the beginning of the diffuse layer) can be achieved by using modeling of the surface charge from potentiometry and electrophoresis. But the main problem could be the self-consistency of the calculations. It seems interesting to combine such elecK.
(25) Schmidt, P. W. In Characterization of Porous Solids; Unger, K. e t al., Eds.; Elsevier Science Publishers: Amsterdam, 1988. (26) Auvray, L.; de Gennes, P.-G. Europhys. Lett. 1986,2,647-650. (27) Ruland, W. J. Appl. Crystallogr. 1971, 4, 70.
r
Smoothing function‘
Electron density profile
Figure 8. Simulation of the electron profile density interface: the dashed line is relative to pH 7 and the solid line is relative to pH 10.
trochemical data with methods such as SAXS, SANS, or ‘H NMR. This second approach would allow one to prove that the first approach was not only sef-consistent. In this study, SAXS allowed one to evaluate the shape and size of particles and the structure of the interfacial region of Ludox silica. At pH 7, SAXS technique showed that the surface is not smooth at the scale of the X-ray wavelength. The surface presents local discontinuities, as shown by the value of @(O) # 0 (Figure 7). To understand the interfacial structure of the sample at pH 10, it is necessary to recall the physical meaning of P(r). The intensity of the P(r) distribution depends directly on the volume of matter within particles. The conditions of normalization in eq 14 yield 47r
SP(r)dr = V ,
where V , is the volume of matter within particles. Therefore, the decrease of the P(r) surface area at pH 10 can be interpreted as a decrease of V , due to a dissolution process. The hatched area in Figure 5b represents the volume of dissolved matter which corresponds to a “porosity” of 13%. The distribution of residual matter in the new interfacial region at pH 10 has a profile shown in Figure 8. The resulting particle can be schematized as a porous surface about 1nm thick and with a dense core of 5.6-nm radius. In the outer part of the interface, a gel-like phase is constituted by the fraction of the dissolved silica surface. These results are in good agreement with those of Yates and Healy,’O who calculated a gel-like surface with a thickness a t pH -10 of 1.15 nm. The gel-like region can be compared with the “long-range” perturbated water structure at the Ludox solution interface as determined by neutron scattering4 at the same pH. Moreover, these results confirm the existence of surface roughness at pH
