Neutron Scattering From Colloids BY DERYCK J. CEBULA AND ROBERT K. THOMAS Physical Chemistry Laboratory South Parks Road, Oxford NICHOLAS M. HARRIS, JAMES TABONY AND JOHN W. WHITE* Institut Laue-Langevin 156X, 38042 Grenoble Cedex, France Received 15th February, 1978 This paper appraises the usefulness of neutron diffraction and small angle scattering for determin- ing the structure of dilute and concentrated sols. For monodisperse polystyrene latex, the particle size and density can be readily determined and an upper limit to density fluctuations within the colloid partide set. For the polystyrene latex peptized by the adsorption of laurate, the physical dimensions and packing density of the adsorbed phase can be determined. The effects of polydisper- sity for unpeptized and peptized graphite sols, and the effects of extreme particle anisotropy using sols of montmorillonite clay minerals have been studied.The chief advantage of neutron scattering for the study of adsorption at the solid- liquid interface, and in particular of colloidal dispersions lies in the fact that by vary- ing the hydrogen to deuterium ratio in the supporting solvent, scattering from the supporting colloid particle may be contrast-matched out of the scattering pattern, thereby leaving the information from the adsorbed layer with high signal to noise. When this is coupled with the fact that the neutron wavelength may be varied widely to avoid Bragg scattering effects inside the colloidal particles, and that the range of particle sizes readily observed by low angle neutron diffraction lies between a few Bngstrom and ~ ~ 4 0 0 0 Angstrom, we see that there may be some distinct advantages to the method.Neutron methods have now been extensively used in metallurgy and in glass and ceramics technology for the study of precipitation and defect structures,l as well as more recently in the study of biological macromolecules and assemblies.2 All of these studies have rested strongly on this phenomenon of variable contrast. Neutrons are scattered predominantly by the interaction of the neutron with the nuclei in the sample material. This interaction occurs at extremely short range (typically 10-l5m) as expressed by the delta function in the potential energy of inter- action V(r) [eqn (l)] bi 6(R - Rf). 271h V(r) = - m The intensity of the interaction is determined by the nuclear scattering length bi, and m is the neutron mass.The intensity of scattering is proportional to the square of the scattering length bl. For small angle scattering, when the momentum transfer in the scattering event is much smaller than the inverse of the particle size, an average scattering length may be used for molecular substances which is simply the sum of the * All communications should be addressed to Dr. J. W. White.D . CEBIfLA, R . K . THOMAS, N. M. HARRIS, J . TABONY, J . W. WHITE 77 scattering lengths of the separate nuclei in each molecule. From this, one can con- struct an average scattering length density knowing the number of molecules and the volume of the scattering particle. Scattering lengths and scattering length densities of the different materials making up the colloid particles in our studies are shown in table 1 as well as those for H20 and D20.If we define the object of interest in a scattering experiment in terms of its scatter- ing length density distribution, p(R) then the distribution of scattered intensity for neutrons, is directly related to the Fourier transform of this distribution: I(Q) = (IA(Q)I~> = (1 P(R)~XP(~Q- m3~i2) (2) V where Q is the momentum transfer in the scattering experiment defined by A(Q) is called the structure factor and A is the incident neutron wavelength. Eqn (2) gives the intensity distribution expected for an isolated particle surrounded by a vacuum. For the expression to be useful, in practice, the sample must be sufficiently dilute so that the observed scattering comes only from individual particles. Addi- tionally, for particles surrounded by a continuous medium, it is the difference in scattering density between the particle and the medium which determines the intensity of scattering, and so in eqn (2), we must replace p(R) by (p(R) - p,), where pb is the scattering length density of the medium.The systematic observation of I ( Q ) as a function of p, constitutes the " contrast variation " technique described later on. In general, approximations to eqn (2) are required to enable the scattering patterns to be analysed. The most widely employed is the Guinier approximation3 shown in eqn (4): I(Q) = I(0) exp -J&Q2 (4) where I(0) is the intensity at zero momentum transfer, Rg2 is the radius of gyration of the particle defined by with V the particle voIume and pm the mean scattering length density of the particle defined by (6) Pm = yl,P(R)d3R. 1 This approximation is valid at low values of the momentum transfer, Q, (QR, < 1).The Guinier approximation may apply for uniform particles of any shape, where- upon a (In I(Q), Q2) plot gives a straight line whose slope is -R:/3. For homo- geneous particles the radius of gyration is the same as the normal mechanical radius of gyration and so the particle dimensions can be calculated for particles of a given form. In cases where the density distribution has higher moments than the second, the contrast variation method can lead to further information: the method has been extensively developed by St~hrmann.~78 NEUTRON SCATTERING FROM COLLOIDS CONTRAST VARIATION METHOD For a non-homogeneous monodispersed sol at small Q, the Guinier approxima- tion applies and it can be shown that as a result of the density distribution in the particle, the radius of gyration depends upon the contrast.This is in clear distinction to the case for a uniform particle, where R,Z is independent of the contrast between the scattering particle and the surrounding medium. Eqn (5) becomes where pf(R) = p(R) - pm and p , the contrast is defined by P” Pm - ~ s - (8) R,2“ is the previously defined radius of gyration for a homogeneous particle with the mean scattering length density, and may be determined experimentally by plotting the values of R,2 obtained from Guinier plots against l/p.At l/p’ = 0 effective contrast is infinite and gives the value of RZv. Conversely, the term arising from the variation of scattering density with radius inside the particle dominates the scattering as the contrast approaches zero. To find p’ from eqn (8) we need to know pm, which is measured experimentally by observing the contrast behaviour of I(0). At zero scattering angle (Q = 0) the expo- nential in eqn (2) becomes unity, and one readily sees that I(0) = [pmV]2 = [CbiI2. (9) I(0) is thus independent of the particle geometry and density distribution, but depends upon constituent atoms forming the particle. Thus the adsorption on to a colloid particle can be readily measured by the changes in I(0). Since, in contrast variation I(0) is given by = (PmV - psQ2 (10) = (C bi - ps V)’ (1 1) then the intensity of scattering is zero when pm = ps.This immediately fixes the mean scattering length density pm, which is found by plotting m) against ps. The slope of this plot also gives the particle volume, V, if the values of intensity are normalised to absolute units (em2). This can be done by calibrating the intensities of scattering against a water standard (which scatters isotropically) or by a direct comparison with particles of known volume. When the molecular compositions of the substrate and the adsorbate are known, then the number of molecules of adsorbate per particle can be determined. Spherically symmetrical particles give rise to maxima in the scattering pattern at higher Q, which are experimentally observable for monodisperse systems.These correspond to the Bessel function maxima given by the analytical solution of eqn (2), p(R) being scalar in this case. For homogeneous spherical particles @(R) = pm), this gives In general, eqn (2) can be inverted, thereby enabling p(R) to be calculated directly from Z(Q) for monodispersed spherical systems. This technique has been used toD. CEBULA, R . I<. THOMAS, N. M. HARRIS, J. TABONY, J . W. WHITE 79 study density inhomogeneities in swelled polystyrene latex and promises to give infor- mation on the swelling process when styrene is added to preformed latex. By intro- ducing deuterated styrene monomer during swelling, a '' tracer " of high scattering length density is created (see table 1).TABLE SUR VALUES OF SCATTERING LENGTHS PER ATOM bi OR TOTAL SCATTERING LENGTHS PER MOLECULE &hi OF VARIOUS SUBSTANCES, AND THEIR CORRESPONDING SCATTERING LENGTH DENSITIES p AT (MASS) DENSITY CT b, or 0 P &bi/cm x /g ~ 1 1 - r ~ /crnc~n-~ x 10'' hydrogen deuterium H20 3 3 2 0 H-pol ystyrene D-polystyrene H-laurate D-laurate carbon montmorillonite -0.374 $0.667 -0.168 1.914 2.33 10.66 0.538 24.481 0.665 18.4 1 .oo 1.10 1.05 1.13 0.8 0.8 2.0 1.3 - 0.56 6.36 1.41 6.48 0.1 3 5.3 6.7 3.8 Suitable highly spherical monodispersed particles (e.g., latex) can also be used as a substrate for adsorption to give spherically symmetrical adsorbed layers. This enables the above technique to be used to study the density structure of these adsorbed layers. By again using hydrogen-deuterium substitution, features of the adsorbed layer can be " highlighted ".Contrast variation techniques with 2/I(O) and R,2 analysis can also be applied to these systems to yield accurate values of layer density, thickness and the surface per adsorbed molecule. I(0) can be evaluated either by Guinier extrapolation [eqn (4)] or (more accurately) by fitting the observed scattering to an equation of the form of eqn (12). The accuracy of these measurements is, however, very sensitive to sample polydispersity, as is reflected in the results of the experiment on the sodium laurate + latex system reported below. For colloidal particles which are ellipsoids, cylinders or platelets, measurements of the radius of gyration is not sufficient to describe the particle shape.For the simplest case of homogeneous particles, forms of the scattering function I@) can be derived for fitting to the observations. For the case of narrow cylinders (radius R and height H) we have: I(Q> (l/QH> ~xP(- Q2R2/4) (1 3) and for thin discs we have : I(Q) cc (1/Q2R2) exp(-Q2H2/12) (14) which are valid for QH < 1 and for QR > 1. A further approximation is valid for high Q (QH > 1 ) namely Porod's law whereupon It can be readily imagined that for non-uniform particles such as platelets with surfactants adsorbed at the interface, the scattering law would be strongly modified80 NEUTRON SCATTERING FROM COLLOIDS and that contrast variation techniques as used for the spherically symmetrical colloids above reveal many details of the texture of the adsorbed layers.A particularly interesting case is for clay platelets whose thickness may be of the order of 10 A and whose extension may be of the order of 1000 A. By adsorbing suitable partly deuter- ated molecules, the conditions under which the concept of a mean scattering length density is applicable in the direction perpendicular to the sheet can be made to break down leading, uniquely, to structural information in this direction. EXPERIMENTAL Polystyrene latices containing a single ionogenic surface species (carboxylic acid groups), and with a small coefficient of variation in the particle size (typically a few percent), have been prepared by Ottewill and his collaborator~~~~ as model colloids. Samples of this material, RB66 in stabilised dispersion at 0.19% weight per volume, and in aqueous mixtures contain- ing between 0%-60% D20 at pH 9.8 were used for the neutron scattering measurements.The mean bead diameter determined by electron microscopy was 462 A with a coefficient of variation of 19%. For these experiments the samples were contained in silica sample cells and small angle scattering was measured with 10 A neutrons at the 20 m position of the D11 small angle scattering machine in Grenoble. Acceptable statistics for high contrast samples were obtained in 2 h counting times, and spectra were taken for seven D20 concentrations and blanks. The density of the polystyrene was quoted as 1.058 g ~ r n - ~ giving a contrast matchpoint in H20 + D20 mixtures at 29% DzO: 71% H20. All measurements were made at room temperature of 25 k 1°C.The pH of the samples was maintained at pH = 9.6 to ensure the solution stability. A similar experiment was performed on samples of the latex with an adsorbed monolayer of laurate ions, following an isotherm for the laurate ion on latex determined by Ottewill et aL6 Solutions of sodium laurate (dodecanoate) were prepared from lauric acid by reaction with sodium hydroxide (AnalaR grade) for both the normal and the deuterium labelled acids. The latter was obtained from Merck, Sharpe and Dohme as lauric acid D-23 Ref. MD 1234 Lot no. B 820 of isotopic purity 98%. The protonated lauric acid was Merck Ref. 5339. Excess sodium hydroxide was added to raise the pH to 9.2 for the stock solutions of molarity 0.3. The concentration of laurate ions in the sample was 2 x 10-2mol md-2, chosen to give mono-layer adsorption and being below the critical rnicelle concentration (= 2.8 x mol- dme3).Ionic strength of solutions was raised by addition of NaCl to loe2 mol dm--3. Samples and blanks were made up at latex concentration 0.19% wt/vol. in the H20/D20 mixtures containing 0,20,29, 37, 50 and 56% D20. A sample of latex in H20 without sur- factant was also included for calibration, and direct beam attenuation measured for each sample to determine sample self-absorption. The graphite, a sample of Vulcan I11 batch no. 2A/29 surface area 71 m2 g-l, obtained from the National Physical Laboratory, Teddington, U.K. was ultrasonically dispersed in mixtures of D20 and H20. Dispersions with concentrations of 0.2 to 10% by weight carbon were sonicated for 90 s each using an ultrasonic finger in direct contact with the solution.This time was rather less than the five minutes specified by Medalia and Heckman for com- plete dispersion of the graphon aggregate^.^ To one group of samples was added 35 mg of sodium dodecyl sulphate per 100 mg of carbon, equivalent to 5 monolayers if the surfactant molecules occupy an area of 50 A2.8 This S.D.S. concentration ratio was kept constant. The peptised samples were noticeably more stable than the dispersions in water, remaining apparently dispersed for several months. Some of the unpeptised samples, particularly at high carbon concentration, were observed to have largely flocculated even during experi- mental runs (i.e. up to 3 h after dispersion).Electron micrographs of the diluted peptised suspension were taken and showed that, even in the apparently dispersed solution, clusters of graphon particles existed. Since further sonication is known to cause oxidationg this was not at tempted. For the experiments on clay platelets, the raw clay mineral used was bentonite (NumberD. CEBULA, R. K . THOMAS, N. M. HARRIS, J . TABONY, J . W. WHITE 81 1 - 26) from Clayspur, Wyoming (API Clay Minerals Standard Project 49). Standard techni- ques described elsewhere by Callaghan and Ottewill10 were used to remove residual organic compounds and traces of undersirable heavy metal cations. The clay was exchanged with lithium, sodium, potassiumA and caesium ions for the separate studies and thoroughly dialysed before use.Three separate volume fractions of clay below 2% were studied for each species. All measurements were made at a laboratory temperature of 25"C, using the D11 small angle neutron scattering camera of the Institut Laue-Langevin, Grenoble, at momentum transfers between and 10-1 A-1. The attenuation of the undeviated beamwasmeasured to enable the sample self absorption corrections to be made for all cases. a a 0 0 r J r 3 0 O El a RESULTS POLYSTYRENE LATICES Guinier plots of the small angle scattering from unpeptized polystyrene latex particles suspended in various mixtures of H20 and D20 are shown in fig. 1. Except near the contrast matching point (325% D20) good straight line portions are obtained whose slopes immediately give the radius of gyration R,v, R, = 172 & 7 A.Since, for spheres, the radius of gyration RgV2 is equal to 0.6 R2, where R is the radius of the sphere, neutron scattering measurements lead to a sphere radius of 222 & 9 A, which agrees well with the value of 231 A determined by electron microscopy? The slope of the Guinier plots is independent of the contrast within the accuracy of the measurement and, therefore, we conclude that the gradient of the scattering density within the particle is very small. At very low values of momentum transfer (Q2 < 7 .v 2 4 )-. c - 8 3 C - tAYAAAAA 2 1 A A A A82 NEUTRON SCATTERING FROM COLLOIDS 10 x A-2), slight curvature of the Guinier plots indicates presence of some large particles possibly arising from flocculation. The dependence of the extrapolated intensity at zero angle of scattering upon the scattering length density of the surrounding solvent (and hence the contrast) is shown LO 20 h 0 i t cr U c c A 0 .- w 0) CT II 4- .- 2O-20 I=" -40 FIG.2.-Square root of the intensity at zero scattering angle as a function of the scattering length density of the surrounding solvent for polystyrene latex particles. in fig. 2. length density, pm, From the contrast matching point [eqn (9) and (lo)] the mean scattcriiig pm = 1.41 & 0.05 x 1010crn-2. Since the mass density, CT, is related to the scattering length density by where M - is the molecular weight of the poystyrene subunit, (CbJ, is the total scatter- ing length of these molecules and N is Avogadro's number. This leads immediately to a mass density of 1.05 & 0.04 ~ r n - ~ , which is in good agreement with 1.057 ~ r n - ~ quoted by 0ttewill.ll SUBSTRATE WITH ADSORBED MONOLAYERS OF PROTONATED AND DEUTERATED LAURATE The same polystyrene latex as measured above and after ageing for about 4 months, was used for these measurements. The Guinier plots of the low angle neutron scat- tering intensity as a function of the squared momentum transfer are shown in fig.3(a) and (b) for adsorbed protonated lauric acid and adsorbed fully deuterated lauric acid respectively. Patterns at four different contrasts for the protonated laurate and two different contrasts for the deuterated laurate were observed; the pattern for the latexD . CEBULA, R . K. THOMAS, N. M. HARRIS, J . TABONY, J . W . WHITE 83 FIG.3.-Guinier plots of polystyrene latex particles with adsorbed protonated and deuterated sodium laurate in different contrast media. (a) Latex with an adsorbed monolayer of protonated laurate in (i) 0% D20; (ii) 37% DzO; (iii) 50% DzO; (iv) 56% D20. (b) Latex with an adsorbed monolayer of deuterated laurate in (v) 37% DzO (contrast match!); (vi) 50% DzO; (vii) 56% DzO. (c) Latex in Cviii) 0% DzO.84 NEUTRON SCATTERING FROM COLLOIDS alone supported in pure H20 was measured for comparison with the previous results Looking at the low angle scattering pattern for the latex particles alone, it is evident that some flocculation has occurred during the ageing period, leading to a considerable increase in scattering at small angles (Q2 < 0.5 x lo-' A-z); the Guinier region is thus obscured.Using the approximately linear higher momentum transfer region of this curve, the radius of gyration for the latex alone was found to be R, = 165 & 8 A in comparison with R, = 172 rt 7 A determined from the previous experiment where measurements were made at much lower angles. The relatively low accuracy of these measurements (-5%) is due to the random instrumental errors and the more systematic errors affecting the validity of the Guinier approximation, e.g., polydispersity. Both these are much reduced when one con- siders relative values obtained in experiments using the same latex sample. We thus assume a substrate particle radius of 213 A for the further analysis (= R, = 165 A). We also assume that the substrate particles have not suffered actual dimensional changes with ageing, i.e.the density is as previously measured, and pm = 1.41 x lO1O cm-2. The need for these assumptions and the high error on particle size will be eliminated in future measurements, the size of the particle being determined by observation of the full scattering curve, including several subsidiary maxima. The calculated depend- ence of scattered intensity with momentum transfer for latex with an adsorbed laurate monolayer at different values of the contrast is given in fig. 4. This clearly shows the subsidiary maxima and the effect of contrast on the scattering from such a system. The shape of the equivalent pattern given by bare latex (i.e. homogeneous particles) is contrast-invariant. [fig. 3(4i. 8 1 1 FIG.4.Variation of scattered intensity with momentum transfer (8) as calculated using relations of the form of eqn (12) for a uniform particle of radius 222 A, and of scattering length density 1.41 x 1Olo cmV2 surrounded by a layer of thickness 14 A of scattering length density 0.1 x 1O'O cm-2. 4 differ- ent values of contrast ps are shown. - ,0.5 x lolo; ---- , 1.0 x 1010; --- . , 1.5 x 1OlD; . . . . . .2.0 x 1O1O cm-2. pm = 1.16 x loio cmV2.D . CEBULA, R . K . THOMAS, N . M. HARRIS, J . TABONY, J . W . WHITE 85 The clear downward trend in the curves in fig. 3 above Q = 3 x is due to the first minimum in the diffraction curves (cf. fig. 4). Fig. 5 shows a variation in the square root of the intensity at the zero scattering angle as a function of the scattering density of the solvent for the low angle scattering patterns shown in fig.3. Since linear behaviour can be assumed [eqn (9)], the line associated with the adsorbed protonated laurate on the latex is fairly well defined by four points. The points obtained from the deuterated system must lie on a line parallel to this, as shown, even though there are only three points. The line for the latex only has been defined from the measured value of l/I(O) at zero percent D,O and x C .- Y +' -20. -30 -401 FIG. vent 5.-Dependence of the square root of the scattering intensity at zero angle scattering on the sol- scattering length density : A-latex plus deuterated laurate, B-latex plus protonated laurate, C-latex alone, by the contrast matching point assuming a particle density of 1.05 g cm3, (i.e.pm = p s = 1.41 x cm-2). In drawing the straight lines A and B of fig. 5, it has been tacitly assumed that the conformations of the adsorbed laurate ion for the deuterated and protonated molecule are the same. The ratio of the slope of the lines A and B to that of C gives the volume ratio for the adsorbed and free latex particles, leading to an average thickness for the laurate ion layer of 10 & 5 A. From the intercept on the ps axis, the mean scattering length densities for the com- posite particles and for the bare latex particle can be determined. The value pms is the volume weighted mean of the substrate and surfactant scattering densities p,' and p,"' respectively, t y / + p,"' VI" p," = V" where V" = V' + V"'. With the known volumes of the two parts of the particle, the scattering length density of the adsorbate, p,"' is immediately determined. Since the mean scattering intensity per molecule of adsorbed laurate is known, the number of laurate molecules in the adsorbed layer follows immediately and hence the surface area occupied by the laurate molecule.Using a specific surface of latex calculated from the particle geometry, the parameters determined in this way are listed in table 2.86 NEUTRON SCATTERING FROM COLLOIDS It is interesting to note that the area occupied by one laurate ion is 48 & 6 A2, which compares well with the values determined by classical adsorption isotherms.6 This number is fairly insensitive to the latex diameter, because of the relatively large volume of the adsorbate layer with respect to the bare polystyrene sphere.TABLE 2.-PmMETERS OBTAINED FROM THE VARIATION OF l/l(o) WITH CONTRAST (FIG. 5) OF LATEX WITH AN ADSORBED MONOLAYER OF LAURATE. laurate ion thickness lOA5A protonated laurate scattering density deuterated laurate scattering density no. of laurate ions adsorbed per particle surface per laurate ion density of laurate layer 0.1 & 0.1 x 1O1O cm-2 4.8 & 0.7 x lolo cm-2 1.2 & 0.2 x lo4 48 & 6 A2 0.72 & 0.1 g cm-3 Some check on the self-consistency of these analyses is given first by the inter- section of lines C and B of fig. 5, which gives the scattering length density of the deutero-laurate layer alone pm”’ = 4.4 & 1 x 1O1O cm-2. This is in agreement with the value calculated from the total mean scattering length density for the particle, pm”, calculated from the intercept of line A with the abscissa. Eqn (16) gives the density for the laurate ion in the adsorbed layer as 0.72 & 0.1 ~ m - ~ .An independent check of these values is given by the variation of R,2 with the reciprocal of the contrast. This variation for the protonated and deuterated laurate systems is shown in fig. 6 . From eqn (7) the radius of gyration of the equivalent homogeneous particle, given by the intercept is R,v = 180 & 5 A. This gives the total radius of the composite particle as R = 232 & 6 A which when compared with R = 213 & 6 A for the bare particle indicates a layer thickness of 19 & 12 A. The slope of the lines is given by the second moment of the scattering length den- 2 4 - 1.0 - 0.5 C I 0.5 (contrast)-’ / 10’0 cm* FIG.6.-Variation of the mean square radius of gyration, R,2 with inverse contrast: ( x x ) protonated laurate and (0 0) deuterated laurate adsorbed onto 222 A latex particles.D. CEBULA, R . K . THOMAS, N. M. HARRIS, J . TABONY, J . w. WHITE 87 sity distribution with respect to the mean [eqn (7)]. The observed difference in sign of the slopes is due to the deuterated and protonated laurate layer having higher and lower scattering length densities than the mean, respectively. With the available data, (4 and 3 points), these slopes cannot be evaluated to greater accuracy than -(4.2 & 1.4) x 1013 (protoiiated case), and (9.0 5 3.3) x 1013 (deuterated case), c.f. -3.2 x 1013 and 7.0 x loi3 as calculated from the layer thickness and density as measured.It should be stressed that the measurements made on these adsorbate systems were done with a few hours measuring time. It is clear that much greater precision is available, not only from a increased counting time, but also from an improvement in the design of the experiment profiting from what has been learnt during the test series. THE CARBON SOLS The effects of polydispersity on the small angle neutron scattering pattern can be readily seen in fig. 7 where the (In& Q2) plots for 2% by weight of Vulcan I11 are dis- persed in various H20 + D20 mixtures is shown. The curves do not show Guinier behaviour but it is evident that contrast matching occurs as the D20 concentration 7 6 5 0 O 0 0 0 100 200 300 400 500 (momentum transfer)' I IO-~A-* FIG.7.-Variation of the small angle scattering pattern from a 2% weight for weight colloid of Vulcan 111 graphite particles in H20 + D20 mixtures. m, 0% D20; a, 30% DzO; a, 50% D20; 0,80% DzO; A, 100% DzO; 0, background 100% HzO. varies. For the purposes of characterising the sol, and apparent radius of gyration, and an extrapolated intensity at I(0) may be obtained, using the approximately linear region above 200 + A-2. The parameters determined by this method at various contrasts are listed in table 3. In all cases the curves were corrected for sample self absorption. The square root of the intensity at zero angle is plotted as a function of the solvent scattering length density in fig. 8, where it can be seen that a reasonably good straight line is obtained leading to a mean scattering length density for the carbon particles of (6.65 & 0.7) x 1O1O cm-2.This value leads immediately to a value for the density of the carbon particles of 2.0 & 0.2 g cm3 by comparison with literature values88 NEUTRON SCATTERING FROM COLLOIDS TABLE 3.-cONTRAST VARIATION PARAMETERS FOR VULCAN III CARBON DISPERSED IN H20/D20 MIXTURES. 0 396 5.98 19.9 402 30 1 64 5.10 12.8 391 50 101 4.61 10.0 402 80 21.8 3.08 4.7 402 - 100 1.8 0.59 1.3 Intensities corrected for self absorption and normalised to 2.5 x lo5 monitor counts ~~ ~~~ ~ between 1.9 and 2.6 g cm3 for graphite and 2.2. g calculated from crystallo- graphic data on crystallite graphite. A determination of this kind can be a quick check on the microporosity and density of colloidal materials; the experiment can be done in a matter of an hour or two.When sodium dodecyl sulphonate is adsorbed on the carbon particles, a marked change in the mean scattering length density of the particles can be noted in the same way as has been demonstrated for the polystyrene latex particles. volume % D,O 2 5 -1 0 1 2 3 4 5 6 7 8 scattering length density / 10’3crn-2 FIG. 8.-Dependence of the square root of the scattering intensity at zero angle as a function of the scattering length density of the surrounding solvent for 2% weight for weight Vulcan 111 in H20 + D20. MONTMORILLONITE SOLS Because montmorillonite sols typically have a platelet thickness (H) of about 10 A and a platelet extension (3) of about 2000 A, it is possible by choosing the range of momentum transfer observed in a neutron small angle scattering experiment to study selectively adsorption and clustering phenomena on the surface of the platelets.These measurements are naturally made at much large momentum transfers than those for studying particles of diameter -2OOA. Fig. 9 shows the small angle neutron scattering for a 1 % weight for weight solutionD . CEBULA, R. K . THOMAS, N . M . HARRIS, J . TABONY, J . w. WHITE 89 of lithium montmorillonite in water corrected for background and detector efficiency. The linear section of the curve is well represented by 1 I(Q) cc p exp (-Q2H2/12) where H has the value of 10.3 A. This is a clear indication that the lithium mont- morillonite system is well dispersed.0.002 0.006 0.010 &;1-? FIG. 9.-Small angle neutron scattering from a 1% weight for weight solution of lithium montmoril- lonite in water corrected for background and detector efficiency. By contrast, as the counter ion is changed to sodium through potassium to caesium, there is a marked change in the small angle scattering pattern and, in the case of the caesium sol with the same concentration of montmorillonite, there is a marked tend- ency to follow a Q-4 law (fig. 10). Only at the lowest momentum transfers is there a tendency for the curve to turn round to follow a Q - 2 law; this sets an upper limit on the particle thickness, H, of around 40 A. The potassium montmorillonite sols can be represented in the same way as caesium, but the scattering from the sodium case is unusual and is not well represented by any of the approximate forms for I(Q) given in the Introduction.Insofar as it has been possible to detect clustering of platelets of caesium mont- morillonite, it is evident that the study of adsorption on the platelets is readily acces- sible through low angle neutron scattering; the platelet surface area is of the order of 800 m2 8-l and the contrast matching point for the montmorillonite mineral lies between 60 and 70% D20, depending on whether a full proton exchange or no proton exchange with the protons in the mineral occurs. GENERAL DISCUSSION The experiments reported here were designed to test the efficacy of neutron small angle scattering for determining the structure of the adsorbed phases on colloidal particles in liquid dispersion.For monodispersed systems like the polystyrene latex, the precision of the measurements is only limited by the measurement times, and could90 NEUTRON SCATTERING FROM COLLOIDS I 102 0 1%’ 10’ FIG. 10. Small angle scattering from a 1% weight for weight solution of caesium montmorillonite in water corrected for background and detector efficiency. The slope of the log-log plot is -4 indicating that aggregation of the particles has occurred. be improved to of the order of 1 A for the surface layer thickness, with extended measurement times on each sample to of the order of an hour or two. In the case of polydispersed articles, information on the mean particle density with and without adsorbant can be obtained readily, though further work needs to be done to set the limits on precision introduced by the effects of polydispersity. Even for such systems, the neutron small angle scattering method may be of value, in characterising the colloidal dispersion in the size range 10-500 A, so our measure- ments over a large momentum transfer range models for the particle size distribution can be fitted from the scattering curves. The measurements reported here concern only simple adsorbates. It is clear that for larger particles in using contrast matching of the adsorbent, small angle scattering patterns from adsorbed polymeric species and other stabilising agents could well be determined for dilute solutions in a manner entirely analogous to the isotropic sub- stitution method used for determining polymer concentrations in the bulk and in so1ution.12* l3 These experiments were conceived in discussions with Prof. R. Ottewill, whose help is hereby acknowledged. W. Schmatz, T. Springer, J. Schelten and K. Ibel, J. Appl. Crysf., 1974, 7, 96. B. Jacrot, Rep. Prog. Phys., 1976, 39, 911-953. A. Guinier, Ann. Phys., 1939, 12, 161-237. H. B. Stuhrmann, Actu Cryst., 1970, A26, 297.D . CEBULA, R . K . THOMAS, N. M . HARRIS, J . TABONY, J . W. WHITE 91 J. C. Brown, J. W. Goodwin, R. H. Ottewill and P. M. Pusey, Colloid and Interface Science. Hydrosols and Rheology, ed. M. Kerker (Academic Press, 1976), vol. 4. P. Connor, Ph.D. Thesis (University of Bristol, 1968). D. H. Everett, G. D. Pafit, K. S. W. Sing and R. Wilson, J. AppZ. Chem. Biotechnol., 1974, 24, 199. R. H. Ottewill, personal communication. lo I. C. Callaghan and R. H. Ottewill, Faraday Disc. Chem. SOC., 1974, no. 57. l1 R. H. Ottewill, personal communication. l2 H. Benoit, D. Decker, J. S. Higgins, C. Picot, J. P. Cotton, B. Farnoux, J. Jannink and R. Aubert, Nature, Phys. Sci., 1973, 245, 13. l3 G. D. Wignall, D. G. H. Ballard and J. Schelten, Eur. PoZymer J., 1975, 10, 861. ’ A. I. Medalia and F. A. Heckman, Carbon, 1969,7, 567.