Study of emulsions of pharmaceutical interest by light scattering

Study of emulsions of pharmaceutical interest by light scattering

Colloids Elsevier and Surfaces, 14 (1985) Science Publishers B.V.. STUDY OF EMULSIONS LIGHT SCATTERING A. CAO, E. HANTZ 217-229 Amsterdam 6 Octo...

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Colloids Elsevier

and Surfaces, 14 (1985) Science Publishers B.V..

STUDY OF EMULSIONS LIGHT SCATTERING

A. CAO,

E. HANTZ

217-229 Amsterdam

6 October

INTEREST

BY

and E. TAILLANDIER

U.E.R. de Mkdecine (France)

- Universitk

Paris

and M. SEILLER

Laboratoire de Pharmacie 14032 Caen (France) (Received

in The Netherlands

OF PHARMACEUTICAL

Laboratoire de Spectroscopic Biomolhculaire, XIII, 74, rue Marcel Cachin, 93000 Bobigny P. DEPRAETERE

217 -Printed

Gale’nique,

1983;

accepted

Universitk

de Caen, 1, rue Vaubenard,

in final form

25 July

1984)

ABSTRACT Emulsions of light liquid paraffin oil in water have been studied by a light-scattering technique. These emulsions were stabilized with a mixture of simulsol 92 and simulsol 96 as surfactants in the critical HLB range. The influence of the dilution and of the physical parameters of the continuous phase on the translational-diffusion coefficient D, and that of the surfactant HLB, as a function of pH, salinity and temperature, have been established. The extrapolation to infinite dilution of D, leads to an accurate determination of the hydrodynamic radius of the droplets which is in the submicrometre range. On the other hand, the intensity data permitted an estimation of the gyration radius and provided insights into the surfactant layer thickness of the particles. The stability of the emulsions has been discussed in terms of the interaction potential barrier.

INTRODUCTION

Although emulsions of oil in water are thermodynamically unstable, they are widely used in the pharmaceutical domain in the form of parenteral dosage or in contrast radiography, and they have attracted much interest. The size and the granulometric distribution of the dispersed phase are particularly important factors, therefore much effort has been devoted to producing fine stabilized droplets [l-5]. The advantage of using a mixture of nonionic surfactants over single emulsifiers has been shown [4, 51. The ratio of constituents in the mixture, characterized by the hydrophile-lipophile balance (HLB), seems to play a very important role in the stabilization. Many authors have found a critical range of HLB values over which the emulsions exhibit a maximum stability, expressed as the maximum of the zeta potential [4] or as the greatest resistance to the effect of added electrolytes. Emulsions of light liquid paraffin in water stabilized with a mixture of dioxyethylene oleyl and decaoxyethylene oleyl ethers have been known for 0166-6622/85/$03.30

o 1985

Elsevier

Science

Publishers

B.V.

218

a long time to be very stable [3]. In the critical range (HLB - 8.50) the minimum mean size is about 0.1 pm. Many studies have included an investigation of the physical properties of these emulsions [3, 61, but few workers have paid attention to the diffusion process which is related simultaneously to the size of the droplets and to the viscosity of the dispersing medium, i.e. to the homogeneity of the system and to the motion of the droplets. Moreover, in the submicrometre range, size determination by practical methods such as photomicroscopy, Coulter counter or Coulter nanosizer apparatus is insufficiently accurate. The technique used in the present work to investigate these O/W (oil/ water) emulsions is quasi-elastic light scattering (QLS). This technique has been used successfully in the study of emulsions [5, 7-91 or micellar media [lo, 111. QLS provides direct information on the translational motion of the droplets via the measurement of the diffusion coefficient D. The size of the droplets can then be determined accurately, either from the Stokes-Einstein relation [12] or from a scattered intensity study [13, 141. A combination of two measurements can lead to the determination of droplet shape [14]. In the following section are reported the results of QLS measurements of the diffusion coefficient and its variations versus the HLB of the surfactant mixture and the variation of physical parameters of the dispersing phase. Later, the size of the droplets is discussed. MATERIALS

AND METHODS

Pi-epara tion 0 f emulsions The dispersed phase is a light liquid paraffin oil up to the standard of the Pharmacopee Francaise. The surfactants used were dioxyethylene oleyl ether (simulsol 92, with a lipophilic tendency) and decaoxyethylene oleyl ether (simulsol 96, with a hydrophylic tendency). At 25”C, the oil has a density of 0.869, a viscosity of 122 mPa, a dielectric constant of 2.7, and a refractive index n, at 20°C of 1.4765. The surfactant characteristics for dioxyethylene oleyl ether are: density 0.896, dielectric constant 4.58 at 4O”C, HLB 4.9, cloud point at 61- 63” and for decaoxyethylene oleyl ether: density 1.0090, dielectric constant 5.81, HLB 12.4 and cloud point at 5759°C. All the studied emulsions were prepared from the same lot of oil and the same lot of each emulsifier. The dispersing phase was bidistilled water prepared from an apparatus in neutral glass. The ionic strength of the water was controlled by electrical specific conductivity measurement and the resistivity had a minimum value of 2 X lo6 R cm. The general formula for an emulsion with a fixed ratio of surfactant is as follows: Light liquid Dioxyethylene

paraffin oleyl

oil ether

100 g (a)

xg

219

Decaoxyethylene Bidistilled water

oleyl ether (b)

The HLB of the mixture and b according to HLB = (HLB),x

QS was calculated

+ (HLB)b(S S

- x)

50;;

from the HLB of the constituents

a

(1)

where S is the total mass of the surfactant mixture. The primary emulsions studied have 5% of surfactants with S = 25 g. After introducing the two surfactants into the oil phase, the emulsions were prepared at 70°C by phase inversion using a blade stirrer at 200 rpm and operating it for 30 min. The emulsions obtained were stored in sealed ampoules at room temperature. Some emulsions were autoclaved or frozen in order to study the influence of these treatments on their stability and storage, especially with reference to their pharmaceutical use. Sample preparation The primary emulsions have a volume fraction @0- 0.27, as determined from density measurements (Sodev 02D densimeter). It is observed that only those emulsions obtained by dilution (by at least 20 times) were sufficiently dilute to be measured by the QLS method. The dilutions were made with fresh bidistilled water filtered through Millex 0.22~pm Millipore filters. As has been mentioned above, the results obtained by Depraetere et al. [6] and preliminary measurements by the present authors showed that the particle sizes were about 0.1 I.tm, but fluctuations in the scattering power, caused by the biggest particles passing throughout the scattering volume, were observed. Fluctuations of this type are usually even more important when most of the particles are very small. Therefore, to eliminate dust and unwanted aggregates, the emulsions were filtered through 0.22~pm or 0.45pm Millex filters directly to the cell for QLS measurements. The effect of filtration was controlled by the conservative absorption of light and also by the scattered intensity. The results obtained after filtrations were the same when using either 0.45~pm or 0.22~pm membranes. Therefore, it is thought that the biggest particles (aggregates or dust) are larger than 400 nm. Furthermore, supposing that these largest particles were pure aggregates, the present intensity measurements showed that they would represent less than 1% of the total weight of the emulsion droplets. Also note that, for pharmaceutical usage, filtration is sometimes required for sterilization purposes. The pH of the emulsions was adjusted with 0.1 M solutions of HCl or NaOH and controlled with a GR 80 pH meter just before the measurements were taken. The ionic strength was adjusted with KC1 solutions. For the emulsion samples prepared by this procedure, it was observed that the primary emulsions gave reproducible measurements of the diffusion coefficient even after storage for several months.

220

Light-scattering

technique

The diffusion coefficient and hydrodynamic radius were studied by quasielastic light scattering and the gyration radius was determined by intensity analysis. Quasi-elastic light scattering The translational-diffusion coefficient was measured by homodyne detection. An Ar’ laser (wavelength 514.5 nm), Spectra Physics model 165, was used as a light source. The sample was placed in a thermostatted cyclindrical cell immersed in an index-matching bath. The scattered light was observed with a photomultiplier, amplified, and fed into a discriminator connected to a 64-channel K7025 Malvern digital correlator. An interference filter was used to eliminate unwanted stray light. The autocorrelation function was computed in a multibit mode and analysed using a Commodore CBM 3032 computer. A 0.05 mg ml-’ aqueous solution of polystyrene latex spheres of known diameter (109 nm) was used to calibrate the apparatus before each set of measurements. For each sample and scattering angle, several sampling times ranging from 2 to 30 ps were used and the logarithm of the normalized correlation function was fitted to the first- and second-order time polynomials using the cumulants method of Koppel and co-workers [16, 171. The fits corresponding to a given sampling time 7 gave a decay time rate P 1 (or I’,). The mean decay time rate, P , was then obtained by extrapolation to zero sampling time and the polydispersity factor p2/r2 was calculated from the slope of the variation of P 1 with P 17. The mean apparent translation-diffusion coefficient was then calculated by using the formula D, = F/q2, where the scattering wave-vector, q, is related to the scattering angle 8, the incident wavelength X and the continuous-phase refractive index n by q = (4nn/X) sin (0 12). At the limit of infinite dilution, where interactions between particles are disregarded, the diffusion coefficient D, gives the mean hydrodynamic radius [18], thus: RH = kBT/6nqD,o

(2)

where 7 is the viscosity of the continuous phase. For most emulsion samples r = l/rc was plotted against sin’ (f312): the plots are straight lines, determined by the least-squares method with an accuracy of 2%. The slopes are then the measured coefficient D,. In most cases, then, only the scattering at 90” was measured. Intensity analysis The intensity measurement provides another means of size and mass determination and can be used as an indicator of the eventual evolutions of the emulsion size. If the particles are greater than h/20, the scattered intensity

221

depends on the scattering angle 8, and the radius of gyration determined by studying the plots of d(B) defined [19] as: d(0) =

RG can be

(3)

The “molecular weight” M of the particle can then be deduced by studying the scattered intensity as a function of concentration, C, according to the methods described in Refs [14, 201

z =-& p$2A*C]

(4)

where RO is the Rayleigh factor (proportional to the intensity) at angle 0, and P(0) = 1 - iR&q’ is the scattering factor. A2 is a second virial coefficient and K = (27r”/nh4)(n0 dn/dc)*, where n, is the refractive index of the continuous phase, N is the Avogadro number and dn/dc is the specific refractive index increment of the emulsion. The index increment was measured with a Isopelem 2312 differential refractometer. The emulsions studied showed dn/dc = 0.153 cm3 g-l and K = 3.875 X 10e7 cm* g-’ mol. Benzene was used as a standard to calibrate the apparatus. The Rayleigh factor of benzene was taken from the data of Ref. [21]. RESULTS

AND DISCUSSION

Diffusion

coefficient

study and hydrodynamic

radius

The influence on D, of the dilution, the ratio of the surfactants, the ionic strength and the glucose content of the emulsion has been investigated. Effect

of dilution and size of the emulsion

droplets

The distribution of the droplet sizes was determined by measurements of the diffusion coefficient of dilute emulsions and by polydispersity analysis. The dilution plays a very important role from two points of view. Practically speaking, it is necessary to give a transmission that is sufficient for the QLS measurements and to reduce the multiple scattering, which is only negligible for volume fractions $ < @0/1OO. Dilution increases the distance between droplets so that the interactions between them are reduced and the measured coefficient D, is then a better reflection of the intrinsic diffusion properties of the emulsions. The variation of D, at very low ionic strength as a function of relative volume fraction & is given in Fig. 1. In the range of $J < 1$,,/100, D, exhibits a linear variation with the volume fraction and can be expressed as D, = Da0 (1 + (u@) where D, = 4.51 X lo-‘* m* s-’ and (Y - 25. The value of D, at infinite dilution permits the evaluation of the hydrodynamic radius of the droplets from the Stokes-Einstein formula [2].

222

-p-f-r

0.2

‘-1

d

P

0.6

1.0 0,.102

Fig. 1. Variation of Drzo versus the dilution The initial volume fraction is @0 = 0.27.

expressed

as the relative volume

fraction

c#+.

If one takes D, = (4.5 + 0.1) lo-‘* mz s-l, the hydrodynamic diameter of the droplets, 2Rn, is found to be - 97 * 2 nm. From light scattering data, it is common practice to describe the distribution by the normalized variance of D, represented by the degree of polydispersity pz/rz [7]. From Eqn (2), the In R, distribution can then be estimated. However, in all measurements made, almost single exponential correlation functions were observed with a small polydispersity factor which was always about 2%; rarely, this factor attained 10%. Thus, taking into account the experimental accuracy of about l-2%, the distribution of RH (or In RH) should be very narrow and its normalized variance can be represented by the normalized variance of D, i.e. the degree of polydispersity. The variance increases slightly with more concentrated emulsions and with higher salinities. Moreover, it was observed that, when filtered with 0.22~ym or 0.45~ym Millipore filters, the emulsions had practically the same D,, the same order of polydispersity, and comparable intensities. Thus, if the filtration is included in the preparation, one can be sure of having a very narrow distribution of sizes. This plays a very important role in pharmaceutical use. The overall variation of D, and the variance at very small 4 (down to Go/10 000) suggest that the droplets can be considered as stable with respect to the dilution [ll] . Influence of HLB and of the treatment temperature Figure 2 shows a maximum value of Da at about 8.60 for a HLB in the range 8.50-8.65. The minimum of the emulsion size is almost reached at

223

855 Fig. 2. Variation the critical range. TABLE

865

860

of the apparent translational-diffusion Emulsion +,/lOOO.

(X

D&o

of the translational-diffusion coefficient and hydrodynamic frozen or heated at 7°C. The last column is for comparison Freezing < -10°C

2R,

coefficient

versus

HLB

in

1

Variation previously

D,

HLB

1O1’ m* so’)

2.43 171

(nm)

Polydispersity

(normalized

variance)

0.4

80°C

4.20 103.5 0.2

120°C (autoclave) 3.24 134.2 0.2

radius of emulsions

Preparation 70°C 4.51 97 0.02

this point and it is believed that the finest emulsions correspond to the greatest stability. The Da coefficients measured at 20°C of an emulsion previously heated (or cooled) are listed in Table 1. It can be seen that the mean size of the emulsion has changed. One notes also the increase in the polydispersity factor. It is believed that the emulsions could be broken by these operations. This effect is important and is probably related to the variation in the hydrophilic properties of surfactants with temperature T, the cloud points being 58 and 6O”C, respectively. When T is raised, flocculation and coalescence are favoured and subsequent cooling to ambient temperature does not restore the size distribution entirely; hence the polydispersity is larger. Influence

of pH

The influence of pH on a very dilute emulsion, $,,/lOOO, has been studied. Contrary to what might be expected on the basis of observations made in

224

. Fig. 3. Variation

of Dz,2o versus pH of emulsion

e0 /lOOO.

zeta-potential studies, the present measurements showed that in the pH range 3-10, there is little or no variation in Da (Fig. 3). This result is, however, in good agreement with that of Depraetere et al. [6]. By means of photomicrography these authors observed that with a surfactant HLB in the range 8-12.4, there is no significant permanent change in the appearance of emulsions changing the pH from 4 to 9.5. Below pH - 2.8-2.9, the coefficient Da drops drastically. This drastic decrease in Da may reflect flocculation or coalescence. Indeed, as the particles are negatively charged (as shown from zeta-potential measurements [6]) the addition of hydrogen ions can reduce their charge and thereby reduce the Debye-Hi_ickel double layer, which results in a weakening of repulsive forces between droplets [22]. On the other hand, there is a possibility of an alteration in the structure of the surfactant layer beyond the observed threshold of the pH value, which can result in coagulation [23] . The possibility of binding between oxyethylene groups with hydrogen ions has been shown [24], and a decrease in the zeta potential following the decrease in pH was observed [6]. Influence of KC1 and glucose content It is well known that electrolytes can reduce the potential barrier of interactions between droplets, thereby favouring flocculation [lo, 221. However, for the emulsions used here, stabilized with simulsol 92 + simulso196 (HLB of 8.50), and with an electrolyte content as high as 1 M KCl, the coefficient Da is decreased by only a few percent.

225

i

“E ”

gx 3 n

0

b

5.

3.

0

1 Glucose

content

(Mel

I“

)

4. Influence of glucose content on D. (a) Uncorrected D,,,, ; (b) viscosity-corrected was made as if all the glucose content was in the dispersDaw,O The viscosity correction ing’ phase. Fig.

The presence of D-glucose affects the emulsion coefficient DzzO, as can be seen from Fig. 4. This coefficient was corrected for viscosity according to the standard method, on the assumption that all the glucose content was in the continuous phase, and using viscosity values given in the CRC Handbook [25]. Although the variation in the value of DzzO as a function of glucose content (from 0 to 1 M) is small (around lo%), it is significantly higher than the experimental standard deviation (-2%). Intensity

data

The hydrodynamic size of the droplets is quite large compared with X/20. A study of the intensity variation with respect to the scattering angle 19 showed that the plot of d(cos 0 ) = [1(19)/l(n - 8 ) - l] versus cos 0 is a straight line (Fig. 5). A radius of gyration, RG = 31 nm, is deduced from the slope according to Eqn (3). The scattering factor at 0 = 90” is P(B) = 1 - : R&q* = 0.833 and the mass of the droplets can then be determined by the concentration dependence plot of KCIRgO. From the limit at infinite dilution (KC/R,,), = 6.0 X lo-’ mol g-l, a molecular weight of 200 X lo6 g mol-’ was found for the “dry” droplets, with an accuracy of 5%. If the W/W ratios of the oil and surfactants is known, the mass of the oil core can be deduced, and then from the density, a radius of 42 + 1 nm can be estimated for the oil. Alternatively, from

226

0.1 Fig. 5. Angular

0.2

CL3

dissymmetry

04

0.5

of emulsion

case scattered

intensity:

@ = a0 /lOOO, pH 5.3.

the density measurements, it can be deduced that the mean density p of the droplets is about 0.8880 and a radius R of about 45 nm can be found for each dry droplet. The value of R is slightly smaller than the hydrodynamic radius RH = 48 f 1 nm. The surfactant layer thus might have a thickness of about 3.2 nm and at most is equal to 6.0 nm. It should be noted that the lengths of the two types of surfactant molecule are 1.0 nm and 4.5 nm [6]. There may be a thin layer of bound water surrounding the droplets. DISCUSSION

There are many powerful methods of measuring very small submicrometre sizes, such as electron micrography or neutron scattering, but light scattering is almost the only practical method applicable to emulsions. The use of electron micrography is not easy because of the difficulties involved in the sample preparation, taking into account the oily nature of the emulsion. Neutron scattering requires exacting material and time conditions, owing to the importance of the positioning of the sources. Compared to these methods, light scattering experiments are quick. With a micro-computer, only a few minutes are necessary to produce the diffusion coefficient Da and in most cases, the size RH can be determined easily by using the Stokes-Einstein relation. However, one precaution must be taken. The conversion of the measured apparent coefficient Da to size is not always direct because, although Da is related to shape and size, it is also influenced by interactions between droplets, either with each other or with counterions in the continuous phase [15]. Da reflects the diffusion coefficient of a single particle in the hydrodynamic field of the solvent only when these interactions are disregarded: hence the necessity of the extrapolation to infinite dilution. In some dilute systems, such as the emulsion @,,/lOOO studied here, with a

227

particle concentration C, - 1.0 X lo’* droplets ml-‘, the mean distance between droplets is about 1 pm, which is ten times their size, so that interaction between them is entirely negligible. Therefore the use of the Stokes-Einstein relation for determining the size can be justified in a single experiment. The variation of D, with $, which shows a virial coefficient Q: - 25, cannot be explained from the hard sphere model which gives 01 = 1.45. Moreover, the droplets are charged, as shown by zeta-potential measurements [6] and by other measurements from electrophoretic light-scattering (ELS) experiments carried out by the present authors (to be published). When the emulsion droplets were subjected to an electric field, a frequency shift of the scattered light was observed and the mobility p could be deduced. From the value of P and the diffusion coefficient Dao, the effective charge 2 was estimated using the relation [26] z=- k,T e

-Y Da0

(4)

where kB is the Boltzmann constant, T is the absolute temperature and e is the elementary charge. Note that the measurement of mobility by ELS does not give the structural charge of the molecule directly but rather an “effective charge” related to the ion distribution around the plane of shear at the surface of the particle. A negative effective charge 2 = 130 was observed at 2 X 10e4 M KCl. This small charge is probably a result of the difference between the dielectric constants of water and the droplet constituents and other causes not well known. Although it is believed that with an emulsion stabilized with non-ionic surfactants such as those used here, the steric effect must play the first important role, the electrostatic effect cannot be disregarded [22]. Thus the interactions can be treated within the framework of the theory of Derjaguin-Landau--Verwey-Overbeek (DLVO) which considers a Coulombic long-range repulsion and a London-van der Waals short-range attraction [22, 27, 281, and the virial coefficient can be calculated according to a method used by Corti et al. [lo]. From the effective charge 2, an approximate estimate at low ionic strength of the repulsive potential energy V, was made according to the formula [21]

v, =

.2?e*

exp (-2KR3c)

2eR( 1 + RR)*

1+x

(r - 2R)

(KR < 1)

is the relative distance between the droplets, e is the 2R dielectric constant of the continuous phase and K-’ is the Debye-Hiickel thickness. By taking the Hamaker constant to be between lo-l4 and lo-‘* erg for the attraction, at an ionic strength 2.10e4 M KCl, a height in the range 21-29k,T was found for the potential barrier. On this basis (i) a first where x g

228

estimation showed that the calculated virial coefficient is 28 for R = 45 nm, almost unaffected by the attraction term. This is in good agreement with the observed value; (ii) with this barrier the emulsions studied can already have a relative stability [29]. This interaction, combined with the steric effect, must greatly enhance the stability. A sample prepared according to the method described above gave reproducible results even after many days, and as already mentioned, the primary emulsions can be stored in sealed ampoules for many months. CONCLUSION

Light scattering is shown to be useful for investigating the hydrodynamic properties of oil-in-water emulsions stabilized with mixtures of surfactants around a critical HLB. It is believed that for fluid emulsions, the stability is essentially conditioned by sizes which must be of the order of - 0.1 pm. Moreover, for pharmaceutical use by the intravenous route, the sizes must be strictly controlled because particle sizes must be smaller than 5 pm. Although the light-scattering technique, like other methods [30-321, requires an appropriate dilution, it has permitted the determination of sizes with very good accuracy. It has also been possible to show the behaviour of the emulsions on dilution, on addition of salt, change of pH, etc. and thus to contribute to an insight into their stability. ACKNOWLEDGEMENT

The authors to use facilities

are indebted to Professor Hanss for his generous permission for the measurements on electrophoretic light scattering.

REFERENCES 1 2 3 4 5 6 7 8 9 10

P. Becher, Emulsions: Theory and Practice, Reinhold, New York, NY, 1965, 382 pp. P.H. Elworthy and A.T. Florence, J. Pharm. Pharmacol., 21 (1969) 705. M. Seiller, J. Legras, F. Puiseux and A. Le Hir, Ann. Pharm. Fr., 28 (1970) 425. P. Becher, S.E. Trifiletti and Y. Machida, in A.L. Smith (Ed.), Theory and Practice of Emulsions Technology, Academic, London, 1976, pp. 271-280. B. Vincent, Adv. Colloid Interface Sci., 4 (1973) 193. P. Depraetere, A.T. Florence, F. Puiseux and M. Seiller, Int. J. Pharm., 5 (1980) 291. J.C. Brown, P.N. Pusey, J.W. Goodwins and R.H. Ottewill, J. Phys. A, Math. Nucl. Gen., 8 (1975) 664. A.M. Cazabat, D. Langevin, J. Meunier and A. Pouchelon, Adv. Colloid Interface Sci., 16 (1982) 175. J.D. Nicholson, J.V. Doverty and J.H.R. Clarke, in I.D. Robb (Ed.),Microemulsions, Plenum, New York, NY, 1982, pp. 33-47. M. Corti and V. Degiorgio, in V. Degiorgio, M. Corti and M. Giglio (Eds), Light Scattering in Liquids and Macromolecular Solutions, Plenum, New York, NY, 1979, pp. 111-124.

229

11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29 30 31 32

P. Turq,

M. Drifford, M. Hayoun, A. Perera and J. Tabony, J. Phys. Lett., 44 (1983) L471. B.J. Berne and R. Pecora, Dynamic Light Scattering, Wiley, New York, NY, 1976, 376 pp. A.M. Cazabat, D. Langevin and A. Pouchelon, J. Colloid Interface Sci., 73 (1980) 1. K.E. van Holde, Physical Biochemistry, Prentice-Hall, Amsterdam, 1971. J.M. Schurr, CRC Crit. Rev. Biochem., 4 (1977) 371. D. Koppel, J. Chem. Phys., 57 (1971) 4814. P.N. Pusey, D.W. Shaeffer, D.E. Koppel, R.D. Camerini and R.M. Franklin, J. Phys. (Paris), Colloq., 33 (1972) Cl. B. Chu, Laser Light Scattering, Academic, New York, NY, 1974. C.Y. Young, J.P. Missel, N.A. Mazer, G. Benedek and M.C. Carey, J. Phys. Chem., 82 (1978) 1375. R. Chiang, in J. Brandrup and E.H. Immegut (Eds), Polymer Handbook, part IV, Wiley, New York, NY, 1967, pp. 315-330. E.R. Pike, W.R. Pomeroy and J.M. Vaughan, J. Chem. Phys., 62 (1975) 3188; J. Ehl, C. Loucheux, C. Reiss and H. Benoit, Makromol. Chem., 75 (1964) 35. E.J.W. Verwey and J.Th.G. Overbeek, Theory of the Stability of Lyophobic Colloids, Elsevier, Amsterdam, 1948. B. Vincent, in D.H. Everett (Ed.), Colloid Science, Vol. 1, The Chemical Society, London, 1973, pp. 221-237. B. Wurzschmitt, Z. Anal. Chem., 130 (1950) 105; P. Depraetere, Thesis, University of Caen, 1980. R. Weast, Handbook of Chemistry and Physics, CRC Press, Cleveland, OH, 1976, p. D230. B.R. Ware, Adv. Colloid Interface Sci., 4 (1974) 1. T.D. Vu, F. Puiseux and J. Paris, Labo-Pharma Probl. Tech., 257 (1976) 739. B. Goldstein and B.H. Zimm, J. Chem. Phys., 54 (1971) 4408. J.T. Davies and E.K. Rideal, Interfacial Phenomena, Academic, New York, NY, 1963,480 pp. A.J. Moes, in F. Puiseux and M. Seiller (Eds), Galenica 5 (Emulsions et Milieux Disperses), Technique et Documentation, Paris, 1983, pp. 343-371. M.J. Groves and D.C. Freshwater, J. Pharm. Sci., 57 (1968) 1273. R.W. Limes and B.V. Miller, Powder Technol., 24 (1979) 91.