Langmuir 1993,9,903-911
903
Effects of Solidification of the Oil Phase on the Structure of Colloidal Dispersions in Cyclohexane David C. Steytler and Brian H. Robinson; School of Chemical Sciences, University of East Anglia, Norwich NR4 7TJ, U.K.
Julian Eastoe and Konrad Ibel Institut Max von Laue-Paul Langevin, 156X, 38042 Grenoble Cedex, France
John C . Dore Physics Laboratory, University of Kent, Canterbury CT2 7NZ, U.K.
Isabel MacDonald Exxon Chemicals, Ltd., P.O. Box 1, Abingdon OX13 6BB, U.K. Received August 10,1992. In Final Form: December 17, 1992 The liquid-to-solid transition of the alkane-continuousphase of a dilute surfactant-stabilizedparticle or droplet dispersion can be induced in a reversible manner without destabilizing the colloid by pressure and/or temperaturechanges. The structural changes have been studied by small-angleneutron scattering (SANS)over a range of pressure (1400 bar) and temperatures (3-20"C).The SANSresults indicate that there are different levels of structure in the solidified system in which a solid alkane coexists with fluid cluster domains. The clusters show large-scale structural correlations of order 5-60 pm; within these clustersthe particlesare in close contact, so that under certain conditions,e.g. high pressure,the stabilizing surfactant layers of adjacent particles are interdigitated. The distance between particle centers, and therefore the degree of surfactant interdigitation,can be readily varied by the applicationof pressure. An interpretation of the SANS results is given in terms of the effects of temperature and pressure upon the osmotic pressure of the concentrated solution of particles/droplets. The analysis provides an estimate of the interparticle pair potential energy between adjacent particles in a cluster as a function of separation. 1. Introduction Over recent years the structure and properties of dilute colloidal particles and aggregates have been extensively investigated (e.g. refs 1-6). In these studies the continuous dispersion medium, usually water or oil (alkane),has been in the liquid state and there has been no corresponding structural examination of colloidal dispersons where the dispersion medium has been solidified. Generally colloidal dispersions fall into two categories: (1)charge-stabilizedsystems, for example solsand micelles in aqueous solution; (2) surfactant systems such as waterin-oil (w/o), or oil-in-water (o/w), microemulsions and surfactant- and polymer-stabilizedparticulate dispersions. In thisstudy we have used two different types of surfactantstabilizeddispersionsin oil-continuousmedia: (a)calcium carbonate (CaC03) particles stabilized by a calcium alkylbenzenesulfonate(Ca(ABS)2)surfactant and (b) w/o microemulsion droplets stabilized by sodium bis(2-ethylhexyl) sulfosuccinate (Aerosol-OTor AOT). The aim of this work was to characterize the structural changeswhich occur in the dispersion when the alkane solvent is selectivelysolidified by an increasein pressure or a decrease in temperature. Different structural techniques, includingSANS studies, on noninteracting, dilute dispersions of type 2 have shown that systems of colloidal particles/droplets are usually (1) Ottewill, R. H.Langmuir 1989, 5 , 4-9. (2) Chen, S.-H. Annu. Rev. Phys. Chem. 1986,37, 351-99. (3) Markovic, I.; Ottewill, R.H. Colloid Polym. Sci. 1986,264,454-62. (4) Markovic, I.; Ottewill, R. H.Colloid Polym. Sci. 1986,264,65-76. (5) Fletcher, P. D. I.; Howe, A. M.; Robinson, F. H. J. Chem. Soc., Faraday Trans. I , 1987,83,985-1006. (6)Fletcher, P. D. I.; Clarke, S.; Ye, X. Langmuir 1990, 6, 1301-09.
randomly distributed throughout the liquid dispersion medium, similar to molecules in a gas.' As the volume fraction (W occupied by the colloidal particles increases, the system becomes more ordered and attains a structure which can be described by a liquid-like structure factor.' For monodisperse particles, highly ordered "colloidal crystal" phases can also be formed at highvolumefractions. The effectof pressure (P,on aliquid of low compressibility (e.g. water) is generally negligible, and so there is little scope for pressure-induced structural changes in a liquid dispersion unless the system is close to a phase boundary or, as in the case of certain surfactants in aqueous solution, suseptible to micellar shape changes. However, for some alkane solvents, the liquid-to-solid (1-s) phase transition may be induced under near-ambient conditions of the pressure and temperature. Examples of such dispersion media are cyclic and long-chain alkanes such as cyclohexane and hexadecane. The alkane solventis of particular importance in determiningthe physical properties of these systems since surfactant-tail/organic solvent interactions are known to play an important role in controlling the stability and dynamics of the colloidal ~ y s t e m .The ~~~ present paper extends our previous investigationsof waterin-oil microemulsion droplets in the solid phase of cyclohexane.' 1.1. The Colloidal Systems. 1.1.1. The Dispersed Phase, Colloidal Carbonate Particles and Microemulsions. A schematicrepresentation of the surfactantstabilizedparticles and droplets, which definesdimensions relevant to our SANS measurements, is shown in Figure (7)Eastoe, J.; Robinson, B. H.; Steytler,D. C.;Dore, J. C.Chem. Phys. Lett. 1990, 166, 153-58.
0743-746319312409-0903$04.00/00 1993 American Chemical Society
Steytler et al.
904 Langmuir, Vol. 9, No.4, 1993
P/bar Suriactant Tall8 Haad Groups
r
Oil
Figure 1. Schematic representation of a surfactant-stabilized particle (or microemulsion droplet). rc is the particle core radius, t , is the surfactant layer thickness, and rp is the overall particle radius. (rp = r, + t s . )
1. The overall radius is given by the sum of the core radius (r,)and the thickness of the curved monolayer of surfactant Us). We have used CaC03particles similar to those described as "V-series"in a previousSANSinvestigationby Markovic and OttewilllJ4with a core radius rc= 26 A. The surfactant stabilizing the CaC03 core particles is a mixture of calcium alkylbenzenesulfonates with a distribution of different alkyl chain lengths centered on n-C248 giving a layer thickness t, of approximately 16 A.4 Under ambient conditions, dispersions of the CaC03 are thermodynamically stable in the liquid state of the solvent used in this study (cyclohexane). In the w/o microemulsions the water droplets are stabilized by the surfactant AOT which is based on two shorter alkyl chains (Zethylhexyl). The concentration of free monomeric AOT in the alkane medium is known to be small and is of the order of 1 X lV mol dm-3.9 Dilute AOT-stabilized w/o microemulsions are thermodynamically stable and may be considered to be a dispersion of essentially spherical water droplets with mean water core radius rc given by2*5v9 re (A) = 1.8~ (1) where w = [waterl/[AOTl. For small droplets, w C 25, the extent of poydispersity ~~~ studies have shown that eq 1 is is ~ m a l l .Numerous valid over a range of (i) temperature (15-100 OC6J0J1,(ii) pressure (1-1OOObar10J2),(iii) alkane chain length (ethane to dodecane5J3),and (iv) droplet volume fraction (up to @ = 0.72J4). At constant composition, AOT-stabilized w/o microemulsions have an upper and lower temperature phase boundary where the one phase (14)isotropic Lp microemulsion becomes a two-phase (24) system. The conditions that induce phase separation of the microemulsion and the processeswhich occur have been studied previously and both the thermodynamic and kinetic driving forces for phase separation have been discussed in detai1.5s6J0J1The AOT-stabilized LOsystems used in the (8)Marsh, J. F. Chem. Ind. 1987, 470-73. (9) Kotlarchyk, M.; Huang, J. S.; Chen, S.-H.J.Phys. Chem. 1985,89, 4382. (10) (a) Eastoe, J.; Robinson, B. H.; Steytler, D. C. J. Chem. Soc., Faraday Trans. 1990,86,511-17. (b) Eastoe, J.;Robinson,B. H.;Steytler, D. C.; Young, W. K. J. Chem. Soc., Faraday Trans. 1990,86, 2883-89. (11) Howe, A. M. Ph.D. thesis, Universityof Kentat Canterbury, 1986. (12) Fulton, J. L.; Smith, R. D. J. Phys. Chem. 1988,92, 2903-2907. (13) Eastoe, J.; Robinson, B. H.; Steytler, D. C.; Thorn-Leeson, C. Ado. Colloid Interface Sci., in press. (14) Kotlarchyk, M.;Chen, S. H.; Huang, J. S.; Kim, M. W. Phys. Reu Lett. 1984, 53, 941-44.
-
10
20
Figure 2. Pressure-temperature phase diagram for the 1-s transition of cyclohexane (-), 2.5% m/v dispersion of V-series particles in cyclohexane (A) and AOT-stabilized w/omicroemulsion droplets w = 10 , [AOT] = 0.1 mol dm-3 (0). Table I. Details of Colloidal Systems (All Dimensions Determined by SANS Measurements) dispersion r,(A) surfactant t,(A) alkane 25.6 Ca(ABS)Z 16.4 cyclohexane V-series CaC03 w/omicroemulsion 19.0 AOT 8.0 cyclohexane droplet w = 10
current work are known to be far from any such phase boundaries, and so complicating effeds arising from phase separation of the colloid (other than solidification of the dispersion medium) are not expected. Table I summarizes the different colloidal particles, surfactants and alkane media, used in this study. 1.1.2. The Alkane Dispersion Medium. In order to conveniently solidify the alkane dispersion medium the l-s phase boundary of the pure alkane should be at nearambient temperature. The liquid alkanes most often used as the dispersion medium for these systems are either medium length straight-chain or branched-chain hydrocarbons, for example n-heptane or isooctane. However, the normal freezing temperature of these alkanes is at around -100 "C at which the colloidaldispersionsdescribed above are unstable. However if the oil component is a cyclic (globular) alkane, for example cyclohexane (C6H12), the 1-s transition is near ambient temperature and the effects of solidifyingthe dispersion medium can be studied without destabilizing the colloid. The dispersion medium used in this study was cyclohexane with a normal freezingpoint, Tf*,of 6.6 OC. Owing to the relatively high plasticity,15the solid state of these alkanes is often referred to as a plastic crystalline phase. The entropy of fusion ASr of such phases is of order -10 J K-l mol-', which is much lower than for homologous straight-chain alkanes, where ASf is typically -100 J K-' m01-l.'~ The lower value of A& is due to the higher degree of rotational freedom in the solid phase of the cyclic alkanes. Figure 2 is a pressure/temperature phase diagram for the l-s transition of cyclohexane. At atmosphericpressure (- 1 bar) pure cyclohexane solidifies at about 6.0 OC, and at higher temperatures the solid phase is formed at proportionally higher pressures accordingto the Clapeyron equation. The onset of the l a transition for a 2.6% mass/ volume (m/v) dispersion of Ca(ABS)z-stabilizedCaC03 (15) Timmermans, J. J. Phys. Chem. Solids 1961, 18, 1-8.
Langmuir, Vol. 9, No. 4, 1993 905
Colloidal Dispersions in Cyclohexane
particlea and an AOT-stabilized water-in-cyclohexane microemulsion is ab0 shown in Figure 2. As can be seen, for these dilute dispersions, the l a transition occurs at very similar pressures and temperatures as for pure cyclohexane. For the systems examined in this work the concentration of particles, and of microemulsion droplets, in the solvent is -1 X mol dm-3 so that the mole fraction of particles XB, is 1 X lo4. The freezing point depression (Tr - Tf*) for an ideal cyclohexane solution with XB = lo4 can be calculated using eq 2
-
T - Tf* = (RTf*2/AHf)xB
(2)
TP is the freezing temperature (at 1atm) and AHf is the molar enthalpy of fusion of the pure solvent. For cyclohexane Tf* = 6.6 OC and AHf = 2.63 kJ mol-' which gives AT = 0.03 OC. The effect of the particles on the freezing point of the continuous phase should therefore be negligible. It is important to note that the transition is reversible and the values of the transition parameters are independent of pathway. With the microemulsion samples, no water separation is observed for the l-s transition; i.e. the microemulsion is thermodynamicallystable in both states of the system. Similarly no destabilization of the Ca(ABS)~-stabilizedCaC03 particles is observed on inspection of the samples after returning to the liquid state. Since the solid phases of the pure alkane and of the colloidal dispersions are both opaque, light scattering techniques are not appropriate for structural studies. However SANS is ideally suited for this purpose since the neutron refractive index in most materials is very close to unity. Furthermore different components of the sample can be easily contrasted using isotopic substitution. 2. Experimental Section 2.1. Materials. Cyclohexane (HPLC grade), deuterocyclo-
hexane, and DzO (99.8% D atom) were obtained from Aldrich. The V-series CaCOa particles were prepared by Exxon Chemicals, Ltd., as described previo~sly.~*~ Sodium bis(2-ethylhexyl) sulfosuccinate, AOT (Sigma), was used as received. 2.2. SANS Studies. SANS measurements were made on various instruments with the neutron wavelength being fixed in the range 4.5-10.0A giving a wide range of scattering vector Q
Q = (4s/h) sin(8/2)
(3)
where 8 is the scattering angle. At the Laboratoire Leon Brillouin (LLB; Saclay, France) the PACE and PAXE instruments were used to examine the Q range from 2 X 10-2to 2 X 10-IA-l (AX/X = 0.10). The high resolution D16 diffractometer (AXIX = 0.03) at the Institute Laue Langevin (ILL; Grenoble, France) was employed over the Q range 5 X to 2 X 10-lA-I to probe higher order Bragg-type reflections and to check for possible effects of instrument resolution on peak widths. In order to examine the size and morphology of particle clusters over a wide size range, SANS experiments were made on the D11 diffractometer at the ILL extending to extremely low Q values (8 X to 1 X 10-LA-1). Specific details of these instruments are given elsewhere.16 A high-pressure cell, which has been described previously,I0 was used for all measurements at elevated pressure. Modifications to the sapphire windows for SANS measurements restricted the operating pressure of the cell to 600 bar. All measurements on w/o microemulsions in the solid phase were made with systems containing D20/H-surfactant/H-alkane such that there is essentially a single contrast step at the watersurfactant interface of the droplets. Similar contrast profiles are given by the H-surfactant coated carbonate particles in (16) (a) Guide to Neutron Research Facilities; Blank, H., Maier, B.,
Eds.;ILL Grenoble, 1988. (b) Eguipments Experimentaux; LLB: Saclay, 1987. (c) Ibel, K. J. Appl. Crystallogr. 1976,9,196.
H-alkane. Measurements with these contrast profiles were also made on dispersions in the liquid phase to determine the dimensions (rc) of both the microemulsion droplet water core and the CaCOD particle core. Similar measurements using deuterated alkanes were made in the liquid phase in order to determine the overall particle dimensions (rp) and hence the surfactant layer thickness (t, = rp - rc). 2.3. Scanning Electron Microscopy (SEM). Scanning electron microscopy was used to examine the configuration adopted by the clusters of CaC03 particles in the solid phase. A liquid dispersion of the V-series colloid in cyclohexane (a = 0.10) was initially frozen by cooling to -40 O C in solid COz. The sample was then removed from the cooling bath, connected to a vacuum line, and allowed to warm. When the melting temperature is reached, liquid cyclohexane is continuously removed from the sample by a process of freeze drying leaving behind a 'skeleton" of the CaC03 colloid. A small sample of this highly porous material was carefully transferred to an SEM stub and coated with a layer of gold approximately 20 nm thick. SEM measurements were made in a Phillips 501B scanning electron microscope using an accelerating voltage of 15 kV.
3. Theory 3.1. Small-AngleNeutron Scattering (SANS). The available wavelength range (4-20 A) and low cross section for absorption of neutrons makes SANS a powerful technique for structural studies of colloidal systems with size correlations in the range 10-1OOO A. Moreover the appreciable difference in coherent scattering lengths between hydrogen (-3.74 X 10-13cm) and deuterium (6.67 X lo-" cm) introducesthe possibility of controlled contrast variation in systems containing hydrocarbons. Different parts of the system can therefore be probed by selective deuteration of the components. The total SANS scattering from a system of monodispersed particles can be expressed as
I(Q)= n$(Q)S(Q) (4) The measured scattering cross section, I(Q), contains a dimensionless intraparticle function, P(Q), characterizing the size and shape of the individual particles, and an interparticle structure factor, SCQ),which includesspatial correlationsarising from interactionsbetween the particles. The overall scattering intensity is also proportional to the number density of particles np. For a dilute system of noninteracting particles at low volume fraction (typically 0 < 0.02) S(Q) 1.0 and I(Q) is then uniquely determined by the size and shape of the particles. For monodisperse spherical particles I(Q) is given by1
-
I(Q) = n,P(Q) = n,P(Q)12
(5)
whereF(Q) = Vp(p,-pm)Etsin(QR)- (QR) cos(QR)Y(QR)31 and R = the particle radius, V, = the particle volume, and pp and pm = the mean coherent scattering length densities of the particle (p) and the surrounding medium (m). In the case of monodisperse spheres, the particle radius is easily obtained by fitting the observed I(Q) to eq 5. However,the microemulsiondroplets and CaC03particles are known to exhibit a degree of polydispersity. Various models can be adopted for the polydispersitywhich provide a mean radius R and size distribution parameter (4." Because polydispersity is low for the system we have used ( u / R = 0.20) the inclusion of a size distribution in the fitting routines yields only a marginally-improved fit to the experimentaldata. However,the mean radius obtained (17) Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys. 1983, 79, 2461.
Steytler et al.
906 Langmuir, Vol. 9, No. 4, 1993
is generally close (&5%) to that given by fitting eq 5 for a monodisperse system. The choice of polydispersity distribution function is therefore not critical for the purpose of this study. A modified Schultz model was employed to represent the size distribution of particles, f(R),in which the degree of polydispersity is represented by the RMS deviation17
f ( R )= [(Z + l)/R]Z+lRZexp(-(2
+ l)R/R)/I'(Z + 1)
P
(6)
T
where u = R/ [Z + 11lI2,2 is a width parameter and is the gamma function. For a dilute system of particles, S(Q) = 1, the observed scattering intensity is then given by
7A
X-Y
B
Figure 3. Schematic representationof the pressuretemperature
where
phase diagram and freezing process for a pure solvent. P
and
I
l = 1/[1- npC(2QR)I
(11) where C(2QR)is a function of Q, the effective hard sphere radius (rhe), and volume fraction (*hs). The equation has been successful in fitting structure factors in weaklyinteracting colloidalsystemsand has been used for avariety of sterically stabilized dispersions up to volume fractions as high as 0.57.3 3.2. Thermodynamic Functions. Figure 3 shows a schematic representation of the pressure-temperature phase diagram for the solid-liquid transition in a single component system. For a pure solvent (1) the conditions of pressure (Pf*) and temperature (Tf*) a t any point on the fusion line (X-Y) must satisfy the equality of chemical (18) Baig, M. R.; Gupta, S.; Messoloras, S.; Stewart, R. J. J . Appl. Crystallogr., 1991,24, 349. (19) Percus, J. K.; Yevick, G. J. Phys. Reo. 1958, 110, 1. (20) Ashcroft, N. W.; Lekner, J. Phys. Reo. 1966,83, 145.
By use of the fusion line for the pure solvent (1)as a reference state, the effect of temperature and pressure on the chemical potential of the pure solid can be expressed in terms of the molar entropy, SS(TP),and volume,
VWP)
The chemical potential of the solvent in the coexisting liquid phase can be similarly expressed in terms of the entropy and volume of the pure liquid statewith an osmotic pressure term accounting for the effects of changing solute concentration.
Langmuir, Vol. 9, No. 4, 1993 907
Colloidal Dispersions in Cyclohexane
Osmotic Pressure
100
3
10
5
....*.................
( n1
* .
1;
*
.............. .1 :
.01
Volume Fraction ( 0 )
G
F
H
Figure5. Schematicrepresentation of (a) the osmotic pressure volume fraction relationship for a sterically stabilized colloidal dispersion in the solid state and (b) the particle configuration in the liquid (F)and solid states (G, H).
Making the approximation that the molar entropy and volume of the pure solid and liquid phases of 1 are independent of temperature and pressure, eqs 14,15, and 16 give ?r
= (AS~AT - AVAP)/V
(17)
where ASf = Ss(Tf*,Pf*) - SL(Tf*,Pf*)
AV
= vS(Tf*,Pf*) - F(Tf*,Pf*)
AT=T-Tf*
I
'
Equation 17 represents the osmotic pressure of the solvent in the unfrozen solution within the solid phase in terms of the temperature, pressure, and accessible thermodynamic properties of the solvent. For concentrated polymer- or surfactant-stabilized colloidsit is convenientto distinguishbetween two regimes of osmotic pressure as shown in Figure 5. Firstly, at lower volume fraction, the osmotic pressure (d)increases gradually with concentration in an analogous manner to that observed for molecular solutions. This colligative effect is often accounted for using a series expansion in mass concentration (c2)
+ B3c;
...I
(18) where Bz, B3, etc. represent the second and higher virial coefficients for the particles and M2 is the molar mass of solute. As the volume fraction is increased the particles, here assumed to be spherical, eventually form an ordered structure in which the surfactant shells make contact
'
~ " ( t , ' )= -(dV/dt,')/Pfi(r, Integration of eq 19 gives
~
~
'
~
~
1
1
+ti),
V = 2 f i Jt.'r''(t,')(rc to + t,'), dt,'
(19)
(20)
The interparticle pair potential can thus be obtained from measurement of the osmotic pressure in the overlap region as a function of particle separation. Substitution for the osmotic pressure (eq 17) gives
v"(rc + t i ) , dts'
V = 2 f i Jt.'{(ASfAT- AVAP)/
AP = P - Pf*
= RT[(c,/M,)+ B,C;
~
(overlap region, G in Figure 5 b). The most probable arrangement of monodisperse, spherical particles in this "solid" phase is a hexagonal close packed configuration. When the particlesare further concentrated,the surfactant layers are forced to interdigitate (H in Figure 5 b) such that the effective thickness of the surfactant layer ( t l ) is less than the thickness of the surfactant layer in a dilute system of particles (ts). In this region the osmoticpressure (T") rises more rapidly with volume fraction. It is often referred to as an "excess osmotic pressuren21or "disjoining pressure".22 The derivative of the interparticle pairpotential energy (V) with respect to distance ( t l ) ,i.e. the interparticle force, is related to ~ ' ' ~ l
to
T'
'"'*','I
(21)
The analysispresented by equations 19-21 is essentially the same as that employed in previous studies of colligative properties of larger sterically-stabilized colloidal dispersions in apolar solvent media by vapor pressure osmometry.23*24The experimental procedures and theoretical considerations of these studies have been reviewed by Napper.,' 4. Results and Discussion The scattering intensity Z(Q) is shown in log Z(Q) vs log Q form in Figure 6 for a 5.0% (m/v) dispersion of CaCO3 particles in H-cyclohexaneat 1bar and 20 "C (liquidphase) and 500 bar and 3 "C (solid phase). The data sets were measured on two different instruments (D16 and D11) and have been superimposed to cover a wide range of Q (21) Napper, D. H.Polymeric Stabilisation of Colloidal dispersions; Academic Press: New York, 1983. ( 2 2 ) Derjaguin, B. V.; Muller, V. M. Dokl. Phys. Chem. 1967,276,738. (23) Homola, A.; Robertson, A. A. J. Colloid Interface Sci. 1976,54, 286. (24) Cairns, R. J. R.; Ottewill, R. H.;Osmond, D. W. J.; Wagstaff, I. J . Colloid Interface Sci. 1976, 54, 45.
Steytler et al.
908 Langmuir, Vol. 9, No.4, 1993 P-la bar
P-500 bar
-
\-
I I
e@
c
a.
e o e
0
1.0
I
A
A
a/k'
Figure 7. I ( Q ) SANS profiles for AOT-stabilized w/o micro-
emulsion droplets (w = 10,[AOT] = 0.10 mol dm-3) in cyclohexane. P ( Q ) was obtained at 1 bar and 20 "C in the liquid phase (A). Other profiles were obtained in the solid phase at 3 "C: 10 bar (B)and 500 bar (C).
(6.3 X 104 to 1.6 x 10-1 A-1). Above 1.6 X 10-l A-' no scattering is observed and data for this Q regime are not shown. At 1 bar cyclohexane is a liquid and the I(Q) profile shows the characteristic form of a dilute system of noninteracting spherical particles as given by eq 5. The SANS pattern from the same system in the solid phase is very different. Firstly, there is a significant S(Q) contribution at higher Q which implies that the particles are in a highly concentrated state. Secondly,there is evidence for a scattering contribution at very low Q resulting from large structures which is suggestive of large clusters of particles. Under the same physicalconditionsZ(Q)profiles for the microemulsion droplets exhibit similar features. A very reasonable explanation for the observed scattering profiles is that, in the freezing process of the organic solvent, the particles are rejected and concentrated into small liquid domains that coexist with the pure cyclohexane solid phase. A mechanism of dendritic growth of the plastic-crystallinephase has been observed previously in these systems*and it is believed that the liquid domains containing the particles arise from rejected solute/solvent that is located between the branches of the growing solid dendrites. The spatial configurationof the particle clusters is therefore determined by the specific manner in which the dendrites grow and interpenetrate in forming the solid phase.25 Similar observations have been made in SANS studies of metal lithium-aluminum alloys26although in this case the number of particles in the clusters is apparently much less than in the CaCOs system. In the analysis of the results it is convenient to separate the two regions of Q space defining the individual article size and ordering within a cluster (Q > 4 X and cluster size/shape (Q < 2 X 10-2 A-l). 4.1. High Q, Measurement of Particle Sizes and Interactions. 4.1.1. AOT-Stabilized Water-in-Oil Microemulsions. A typical set of I(Q) data is shown in Figure 7 for microemulsion droplets (w = 10) in cyclohexane. At 20 O C and 1 bar cyclohexane is in the liquid state and the scattering closely resembles that of a dilute system of spheresas has been observed previously.g.10Since the scattering-length density of H-cyclohexane closely matches that of the surfactant layer, the coherent smallangle scattering arises from the region of high contrast between the surfactant and D20 core. By fitting eq 5 to the data, the mean radius of the water core (rc)was found
1-l)
(25) Jackson,K. A.; Hunt, J. D.;Uhlmann, D. R.;Steward,T.P.Trans. Met. SOC.AIME 1966,236, 149-58. (26) Triolo, R.; Caponetti, E.; Spooner, S.Phys. Rev. B 1989,39,4588.
e
0
Q/A" Figure 8. Structure factors S(Q) obtained at 20 "C and 500 bar (a),3 "C and 10 bar (A) and 3 O C 500 bar (0) for the AOT w = 10 w/o microemulsion system.
to be 19.0 A. Similarly, using an H~O/H-AOT/C,SDI~ contrast profile, the total radius (rp) of the droplet, including the surfactant layer, was found to be 27.0 A The length of the AOT surfactant moleculeis then obtained as approximately 8.0 A and is in good agreement with previous meas~rements.~JO On cooling to 3 "C the cyclohexane freezes to a pure solid phase which is in equilibrium with a fluid phase containing a high density of droplets. The scattering is then dominated by a strong S(Q) contribution. The S(Q) peak arises from interparticle correlations in the concentrated configurationof droplets in the fluid clusterslocated within the unfrozen domains in the solid phase. On gradually increasingthe pressure up to 500bar, the position of the SCQ) peak, Qmm,moves consistently to higher Q values which indicates that the interparticle separation is decreasing according to eq 9. This systematic response is both reversible and reproducible for all the systems studied. The reversibility of the changes suggests that the system is always thermodynamically stable and no separation of the dispersed phase occurs, e.g. through irreversible coagulation of droplets. The SANS behavior of the corresponding CaC03 particle system shows essentially the same response (see section 4.1.2). No evidencefor higher order Bragg-typepeaks was found from measurements over a wider scattering angle covering a Q-range up to 2.0 A-l. This suggests that although the droplets are constrained in a concentrated configuration, the packing is probably glasslike and is not perfectly regular. This behavior is also consistent with the polydisperse condition of the dispersed water droplets. The effect of pressure and temperature on the spatial arrangement of microemulsion droplets in the solid phase can be explained in terms of changes in the surrounding solid/liquid interface. In order for more solventto solidify at this interface, as is required when, e.g. the temperature is further decreased, the liquid domains must shrink, thereby concentrating and ultimately Ycompressingnthe droplets contained within them. The response of the system to pressure (or temperature) changes is measured by the droplet separation in the liquid domains within the solid phase. S(Q) profiles for the 3 "C data, obtained by dividingthe observed scattering Z(Q) by n$'(Q) (measured at 20 "C),are shown in Figure 8. From the position of the peak the mean interparticle separation and effective surfactant layer thickness (b') can be estimated using eqs 9 and 10. A hexagonal closepacked arrangement of droplets (for which c = 1.156) has been assumed in this calculation which is in accord with previous observations on this ~ystem.~J4 At each state
.
Langmuir, Vol. 9, No.4, 1993 909
Colloidal Dispersions in Cyclohexane 4
1
I
I
I
I
I
c
3
0 1 0
I
,
5
,
I
,
15
10 D
1.1
I "' 3 j
1
0
20
5
(A)
Figure 9. Correlation of effective surfactant thickness (&') with osmotic pressure ( r )for the AOT w = 10 w/omicroemulsion at 20 OC (X), 11 O C (A),and 3 OC (+I.
point the osmotic pressure of the solution of droplets contained in the solid phase was also calculated using eq 17 with AVf = -5.1 X le3cm3 mol-', A& = -9.4 kJ K-l mol-', !P = 6.6 O C , and P = 1 bar. The dependence of A on t,' is shown in Figure 9 for the w = 10 microemulsion in cyclohexane. The data represent three different experimental isotherms and their coincidence on the plot confirm the general applicability of eq 17 in correlating the effects of temperature and pressure on the droplet configuration in the solid phase. It is clear that some energy needs to be expended before the droplets are brought into contact ( t i = t,) which arises from the increased osmotic pressure (A') of the system due to concentration effects. Measurements of freezing point depression (and freezing pressure elevation) have been made for the dilute regime of this system for which the first term of the virial expansion of eq 18 should apply. The magnitude of these colligative properties was however found to be greater than could be explained in terms of the 'molecular weight" of the droplets as determined by SANS measurements. In order to explain this discrepancy it was necessary to invoke the presence of low molecular weight components freely dissolved in the solvent. This could arise either through an impurity in the surfactant or by partitioning of a small proportion of the surfactant from the droplet surface to the surrounding solvent medium. Since meaningful interpretation of colligative effects can only be realized in dilute solutions of macromolecules that are free of extraneous low molecular weight components,a quantitative analysis of the osmotic effect was not attempted. The interdigitation of the surfactant layers is represented in Figure 9 by the region in which t,' C t,, where the curve appears to be approachinga limiting value oft,' (45.0A). The general form of the curve, and absence of a minimum, is in accord with theoretical predictions for sterically-stabilized dispersions in better than "theta" solvents for which attractive interactions are negligible compared to thermal energy. Figure 10 shows the interparticle pair-potential for the AOT-stabilized w/o system as calculated from eq 21. The energies involved are considerably less than that required to fuse the droplets (-100 kJ At high pressures the situation may be complicated by distortion of the water cores of the microemulsion droplets when tightly packed. However, the forces acting on any one droplet by its nearest neighbors will be essentially isotropic and could only distort the surface creating flat
10
15
20
(A)
1)
O
Figure 10. Interparticle potential (V)for (a) the AOT w = 10 w/o microemulsionand (b) Ca(ABS)&abilized CaC03 particles (b) in cyclohexane.
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0
0
5
10
15
20
I (A) Figure 11. Normalized force-distance curves for (a) the AOT w = 10 w/o microemulsion droplets and (b) the Ca(ABSI2stabilized CaC03 particles in cyclohexane. 1;
areas at points of contact. For a regular packing of droplets this creates polygonal symmetry for which it has been shownZ7that the overall distortion is small resulting in a reduction of interdroplet separation of approximately9 9% of the original, spherical contact diameter. 4.1.2. Carbonate Particles. Details of the particle radii and surfactant layer dimensions, obtained by fitting eq 5 to the SANS I(&) data for dilute systems, are given inTable I. The interparticle pair-potential for the V-series carbonate dispersion in cyclohexane at 3 O C is also shown in Figure 10. As for the microemulsion system, it was observed that a significant energy is initially required to overcome osmotic effects and bring the particles into contact. This is not surprising since these colloids are known to contain a minor proportion (
