Trends in Colloid and Interface Science VI

347 Pages·1992·7.24 MB·English

by  M. H. G. M. Penders, A. Vrij (auth.), C. Helm, M. Lösche, H. Möhwald (eds.)

Progress in Colloid & Polymer Science • Vol. 89
PROGRESS IN COLLOID SCIENCE & POLYMER
Editors: H.-G. Kilian (Ulm) and G. Lagaly (Kiel)
Volume 98 )2991(
Trends in Colloid
and Interface Science VI
Guest Editors:
.C Helm, M. L6sche, and H. M6hwald (Mainz)
D (
4
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Preface
This special issue contains the major portion of Combining a meeting of national and interna-
lectures and posters presented at a conference that tional societies requires a balance of potentially con-
combined the 35th biannual meeting of the flicting interests. The selection process inevitably
Deutsche Kolloidgesellschaft and the 5th annual disappointed some, yet we hope that most par-
meeting of the European Colloid and Interface ticipants felt that the program was evenly balanced
Society. It was held at the Johannes Gutenberg- between national interests and scientific fields. eW(
Universit/it Mainz, FRG, September, 25--28, 1991, also ensured that our group is only sparingly
and brought togethera bout 300 participants from 71 represented in contributions to this volume).
countries. We at the Institute of Physical Chemistry of the
Although there was an emphasis on partially University of Mainz are grateful to the members of
ordered systems, the following wide range oft opics our group, especially those who, instead of prepar-
was covered in the program: ing presentations of their own work, helped in
organizing and holding the conference. We were
elcitraP and allemaL noitcaretnI Environments in Fluid delighted by compliments concerning the con-
ladiolloC :selcitraP Size dna Mobility ference organization as well as about its scientific
Rheology dna Stability level. We hope that this has contributed to progress
ladiolloC under Suspensions Stress in science, as well as to international collaboration
seitreporP ecafruS and noitprosdA in this field. Especially, it was interesting to meet
sreyalonoM at the ecafretnI retaW~riA and talk with people from former Communist
raluceloM dna evitcelloC Dynamic seitreporP countries.
Phase dna snoitisnarT Phase smargaiD We also acknowledge the financial support of our
corporate sponsors (Bayer AG, BASF AG, Coulter
Electronics GmbH, Henkel KGaA, Hoechst AG,
The highlight of the conference was the lecture of
Hoffmann-La Roche AG, Hiils AG, LAUDA Dr. R.
the 1991 Nobel laureate .P G. de Gennes, who was
Wobser GmbH & Co. KG, Malvern Instruments
awarded the Wolfgang-Ostwald Prize of the
GbmH, Partikel-Analytik HMS Elektronik, Riegler
Deutsche Kolloidgesellschaft (designated to honor a
& Kirstein Ultrathin Organic Film Technology), in-
lifetime achievement).
stitutions (Johannes Gutenberg-Universit~it Mainz,
We are grateful to the ECIS International Commit-
and the Royal Society of Chemistry), the two spon-
tee for assisting us in selecting a quarter of the 071
soring Societies, and the Deutsche Forschungsge-
original submissions for oral presentations. This re-
meinschaft.
quired tough decisions which were based pre-
dominantly, but not totally on scientific grounds.
Consequently, poster presentations received much
time and space during the conference and were On behalf of the local organizers,
allocated the same amount of space as oral con-
tributions in this volume. C. A. Helm, M. L6sche, H. M6hwald
Contents VII
stnetnoC
Preface ............................................................................................. V
Penders MHGM, VrAi:j Modeling of solvation interactions in non-polar dispersions of colloidal particles using
the liquid state theory of adhesive hard sphere mixtures .............................................. 1
Jardali FS, Woodcock :VL Monte Carlo investigations of the order-disorder transition in colloidal-sphere suspensions 9
Eriksson JC, Ljunggren S: The Laplace equation and Winsor microemulsions ............................. 20
Johansson L, Elvingson C, Skantze U, L6froth J-E: Diffusion and interaction in gels and solutions .......... 25
Saric A, Despotovic R, Trikic S: On mutual interactions in polycomponent surfactant systems .............. 30
Zemb Th, Belloni L, Dubois M, Marcelja S: Osmotic pressure of highly charged swollen bilayers ........... 33
Huruguen ,PJ Zemb Th, Pileni MP: Influence of proteins on the percolation phenomenon in AOT reverse
micelles: Structural studies by SAXS ................................................................ 39
Sobisch T: The use of methyl orange for the characterization omfi celles in aqueous nonionic surfactant solutions 44
Hagenbiichle M, Graf C, Weber R: Structural order of Tobacco-Mosaic-Virus in aqueous solutions determined
by static and dynamic light scattering ............................................................... 49
Paillette M: A phase electric birefringence study of interdroplet attractions in water-in-oil microemulsions ... 53
Anton ,P K6berle ,P Laschewsky A: Structure and properties of zwitterionic polysoaps: Functionalization by
redox-switchable moieties .......................................................................... 56
Asnaghi D, Carpineti M, Giglio M, Sozzi M: Fractal aggregation of polystyrene spheres in the crossover region
between DLCA and RLCA ......................................................................... 60
Antonietti M, Lohmann S, Bremser W: Polymerization in microemulsion -- size and surface control of ultrafine
latex particles ..................................................................................... 62
Zhou Z, Hilfiker R, Hofmeister U, Eicke H-F: Interconnection of microemulsion droplets with block-copolymers 66
Lombardo D, Mallamace ,F Micali N, Vasi C, Sciortino F: Direct measurements by light scattering of the self diffu-
sion in dense macromolecular solutions ............................................................. 17
Mallamace ,F Micali N, Vasi C, Bansil R, Pajevic ,S Sciortino :F Micro-phase separation in cross-linked gels:
Depolarized light scattering results .................................................................. 77
Lombardo D, Mallamace ,F Majolino D, Micali N: Evidence by light scattering of long-range structures connected
with the percolation transition in water-decane-AOT microemulsions ................................... 82
Herzog ,B Huber K: Solubilization of a water-insoluble dye: A light scattering study ...................... 87
Akcasu AZ, N/igele G, Klein R: Interdiffusion in polymer mixtures ...................................... 89
Alarc6n-Waess O, Medina-Noyola M: Collective diffusion in colloidal suspensions: A generalized Langevin
equation approach ................................................................................. 95
Motte L, Lebrun A, Pileni MP: Influence of the preparation mode on the size of CdS particles synthesized "in
situ" in reverse micelles ............................................................................ 99
Lisiecki I, Boulanger L, Lixon ,P Pileni MP: Synthesis of copper metallic particles using functionalized surfactants
in w/o and o/w microemulsions .................................................................... 301
Jain TK, Billoudet ,F Motte L, Lisiecki I, Pileni MP: Photochemical studies of nanosized CdS particles synthesiz-
ed in micellar media ............................................................................... 601
Pons R, Solans C, Steb6 MJ, Erra ,P Ravey JC: Stability and rheological properties of gel-emulsions ........ 011
Aveyard R, Binks ,PB Fletcher PDI, eY :X Coalescence lifetimes of oil and water drops at the planar oil-wateri nter-
face and their relation to emulsion phase inversion ................................................... 411
Magny ,B Iliopoulos I, Audebert R, Piculell L, Lindman :B Interactions between hydrophobically modified
polymers and surfactants ........................................................................... 811
Nika G, Paleos CM, Dais ,P Xenakis A, Malliaris A: Aggregational behavior of polymeric micelles of methacrylate
functionalized quarternary ammonium salts .......................................................... 221
Palberg ,T Wi/rth M, KOnig ,P Simnacher E, Leiderer P: Resonant phenomena in colloidal crystals .......... 521
Angelova MI, Sol6au ,S M616ard Ph, Faucon ,FJ Bothorel P: Preparation of giant vesicles by external AC electric
fields. Kinetics and applications .................................................................... 721
Bondarev VN: Ordering phenomena in gyrotropic electrolytes ........................................... 231
VIII Contents
Bossis G, Lemaire E, Persello ,J Petit L: Structuration and elasticity of electrorheologicalf luids ............. 531
Deggelmann M, Kramer H, Martin C, Weber R: Electrophoretic mobility of aqueous colloidal suspensions in the
gas and liquid-like phase ........................................................................... 041
Marion G, Sahnoun ,S Mendiboure ,B Dicharry C, Lachaise :J Reflectometry study of interbubble gas transfer
in liquid foams .................................................................................... 541
Sz6nyi S, Watzke HJ, Cambon A: Perfluoroalkyl bilayer membranes prepared from saturated amphiphiles with
fluorocarbon chains ................................................................................ 941
Sa'idi Z, Boned C, Peyrelasse :J Viscosity-percolation behavior of waterless microemulsions: A curious
temperature effect ................................................................................. 651
Decher G, Schmitt :J Fine-Tuning of the film thickness of ultrathin multilayer films composed of consecutively
alternating layers of anionic and cationic polyelectrolytes .............................................. 061
Sawodny M, Schmidt A, Urban C, Ringsdorf H, Knoll :W Photoreactions in Langmuir-Blodgett-Kuhn multilayer
assemblies of liquid crystalline azo-dye side-chain polymers ........................................... 561
Bilinski ,B Wojcik :W The surface dehydroxylation and rehydroxylation of controlled porosity glasses ....... 071
Chibowski E, Holysz L: Changes in barite surface free energy due to its surface precoverage with
tetradecylamine chloride (TDAC1) or sodium dodecylsulphate (DDSO4Na) .............................. 371
Seidel :J Microcalorimetric study of cetylpyridinium-chloride adsorption onto different oxides .............. 671
Klumpp E, Heitmann H, Lewandowski H, Schwuger :JM Enhancing effects during the interaction of cationic
surfactants and organic pollutants with clay minerals ................................................. 181
Szymanowski ,J Cierpiszewski R: Interfacial activity of acidic organophosphorus extractants and interfacial
mechanism of metal extraction ...................................................................... 681
Rheinl/inder ,T Klumpp E, Rossbach M, Schwuger :JM Adsorption studies on pesticide/cationic surfactant/ben-
tonite systems ..................................................................................... 091
Raudino A: Modulation of reaction rate at inhomogeneous charged interfaces by electrohydrodynamic effects 194
Qiu x, Ruiz-Garcia ,J Knobler CM: Phase transitions and domain structures in ester and acid monolayers .. 791
Kim ,S uY H: Lateral diffusion of macromolecules in monolayers at the air/water interface ................. 202
Akamatsu S, Rondelez :F Two-dimensional pattern formation in Langmuir monolayers .................... 209
Aschero G, Piano E, Pontiggia C, Rolandi R: Electronic speckle pattern interferometry used to characterize
monolayer films ................................................................................... 412
Caminati G, Ahuja RC, M6bius D: Photo-induced electront ransfer in monolayers: effect of acceptorl ocation at
the interface ...................................................................................... 812
Caminati G, Gabrielli G, Barni E, Savarino ,P M6bius D: Dye/dihexadecylphosphate monolayers: a spectroscopic
and thermodynamic study ......................................................................... 223
Gabrielli G, Puggelli M, Gilardoni A: Mixed monolayers: Support acidity, two-dimensional phases and
compatibility ...................................................................................... 227
Sluch MI, Vitunovksy AG: Aggregation of cyanine dyes in Langmuir-Blodgett films ....................... 233
Bonosi ,F Caneschi A, Martini G: Spreading isotherms and electron spin resonance of nitronylnitroxide mono-
and multilayers ................................................................................... 235
Lunkenheimer K, Laschewsky A: Adsorption properties of soluble surface active stilbazium dyes at the air-water
interface .......................................................................................... 239
Sch6nhoff M, L6sche M, Meyer M, Wilhelm C: Incorporation of membrane proteins into lipid surface
monolayers: Characterization by fluorescence and electron microscopies ................................ 243
Nickel ,D Nitsch C, Kurzend6rfer ,P .v Rybinski :W Interfacial properties of surfactant mixtures with alkyl
polyglycosides .................................................................................... 249
Aliotta ,F Fontanella ME, Magazd S, Maisano G, Majolino D, Migliardo P: Dynamical properties of lecithin-based
microemulsions ................................................................................... 253
Aliotta ,F Migliardo ,P Donato DI, Turco-Liveri ,V Bardez E, Larrey :B Local hydration effects in reversed micellar
aggregates ........................................................................................ 258
Schubert ,V-K Strey R, Kahlweit M: Similarities of aqueous and nonaqueous microemulsions .............. 263
Caniparoli ,PJ Gains N, Zulauf M: Influence of stigmastanyl phosphorylcholine on the size, mass, and shape
of taurocholate/lecithin/cholesterol mixed micelles .................................................... 268
F6rster G, Brezesinski G, Wolgast S: Polymorphism of phosphatidylcholines varied in the hydrophobic part. 172
Schurtenberger ,P Magid ,JL Lindner ,P Luisi PL: A sphere to flexible coil transition in lecithin reverse micellar
solutions ......................................................................................... 472
Bertolini ,D Cassettari M, Salvetti G, Tombari E, Veronesi ,S Squadrito G: Thermodynamic properties of water
in reverse micelles ................................................................................. 872
Bertolini ,D Cassettari M, Salvetti G, Tombari E, Veronesi S, Squadrito G: Time-dependent heat capacity of
aqueous solutions of biomolecules .................................................................. 182
Sager ,W Sun ,W Eicke H-F: Is the AOT/water/oil system really simple? Conductivity measurements in ionic and
nonionic microemulsions ........................................................................... 284
Contents IX
Graciaa A, Ben Ghoulam M, Marion G, Lachaise J: Effect of anionic surfactant structure on critical concentra-
tions and compositions of sodium alkylbenzene sulfonate/polyoxyethylene octylphenol/tetradecyltrimethyl-
ammonium bromide mixed micelles ................................................................. 288
Onori G, Santuci A: An infrared study of micelle formation in AOT-H20-CC14 solutions ................... 293
Onori G, Santucci A: Effect of 1-alcohols on micelle formation and hydrophobic interactions ............... 297
Heindl A, Kohler H-H, Strnad J: Molecular theory of rod-shaped micelles ............................... 302
Bartusch G, D6rfler H-D, Hoffmann H: Behavior and properties of lyotropic-nematic and lyotropic-cholesteric
phases ........................................................................................... 307
L6onard A, Maillet JC, Dufourcq J, Dufourcq :JE Bilayer thickness from lipid-chain dynamics: Influence of
cholesterol and electric charges. A 2H-NMR approach ................................................. 513
Cametti C, DeLuca ,F D'Ilario A, Maraviglia ,B Misasi R, Sorice M, Bordi ,F Macri MA: Structural alteration of
lymphocyte membrane induced by gangliosides. A conductometric study .............................. 913
Cametti C, DeLuca ,F D'Ilario A, Briganti G, Macri MA, Maraviglia :B Dielectric dispersion in the ripple phase
of DPL mixtures in water .......................................................................... 324
Petit C, Lixon ,P Pileni MP: Structural change in AOT reverse micelles induced by changing the counterions 328
Laggner ,P Koynova R, Tenchov :B Dis-interdigitation of phospholipid bilayers by low amounts of cholesterol 332
B6ta A, Lohner K, Laggner P: X-ray studies on the near-equilibrium pathways of the pretransition in DPPC
multilayer liposomes ............................................................................... 333
Colotto A, Lohner K, Laggner P: Low-dose effects of melittin on phospholipid structure. Differences between
diester and diether phospholipids .................................................................. 334
Degovics G, Laggner ,P Tritthart J: Fractal dimensions and BET-surfaces in wet and dry portland cement paste 335
Author Index ....................................................................................... 336
Subject Index ....................................................................................... 338
Progress in Colloid & Polymer Science Progr Colloid nryloP icS 89:1--8 )2991(
Modeling of solvation interactions
in non-polar dispersions of colloidal particles
using the liquid state theory of adhesive hard sphere mixtures
M. H. G. M. Penders and A. Vrij
Van't Hoff Laboratorium voor Fysische en Colloidchemie, University of Utrecht, The Netherlands
:tcartsbA Colloidal particles dispersed in a non-polar solvent are modeled by
a binary mixture of large spheres in a "solvent" of small spheres using the
liquid state model of adhesive hard sphere mixtures. The discrete nature of
the solvent molecules is explicitly taken into account. Solvation forces can be
described fairly well using both solvent-solvent and solvent-solute interac-
tions. By increasing the solvent-solvent interaction, keeping the solvent-
solute interaction constant, the effective attraction between the large colloidal
particles increases. The isothermal osmotic compressibility goes to infinity
when the adhesive strength between the solvent molecules becomes very
high and phase separation may occur ("poor" solvation). By increasing the
solute-solvent interaction, keeping the solvent-solvent interaction constant,
the effective repulsion between the large particles increases ("good" solva-
tion). -- When the solvent density is small (near the "critical" value),
however, solvent-solute interactions may ultimagely lead again to effective at-
tractions between the large spheres, if the adhesive strength between the sol-
vent and solute particles is large enough. This phenomenon may be inter-
preted in terms of "bridge formation".
yeK :sdrow Solvation interactions; adhesive drah_ spheres; structure factors;
colloidal _dispersions; binary serutxim_
1. Introduction If, however, there is a preferential solvation, not
of solvent molecules, but of chain ends of the sur-
The action of solvent molecules plays an impor- face layers of opposing particles, effective attraction
tant role in the building up of interaction forces in forces between the particles result. In other words:
colloidal systems containing particles stabilized by a work is gained when chain/solvent contacts are
protective surface layer of chain molecules. If the replaced by chain/chain plus solvent/solvent con-
particle core is composed of material with a refrac- tacts. Such forces are, in fact, directly measurable
tive index comparable to that of the solvent, the van using macroscopic mica surfaces covered with
der Waals-London attraction forces between the chain molecules ,2 3.
cores are small 1. The interaction forces between In this paper, we elucidate such complex interac-
the colloidal particles are then dominated by the tions with the help of a fluid state model in which
chain-chain and chain-solvent interactions of the the suspension is modeled as a two-component
opposing protective layers of the touching particle mixture of large and small spheres having certain
surfaces. adhesive interactions.
If there is a preferential solvation of chain (ends) An important characteristic in the statistical
by solvent molecules, repulsive forces will already description is that the solvent is not merely describ-
be felt before the bare chain segments are actually ed as a continuous background, but possesses a
in contact, because the removal of solvent discrete nature. The discrete nature of the solvent
molecules requires work ("good" solvation). molecules was already considered by Chan et al.
2 Progress in Colloid & Polymer Science, Vol. 89 (1992)
et al. ,6 7, Jamnik et al. 8 and by our group sphere system of "pure solvent" using a semi-
,9 .101 permeable membrane that is permeable to the small
Henderson 5 gave an explicit expression for the spheres, but impermeable to the large spheres. The
solvent contribution to the force between colloidal volume fraction of the "pure solvent" is denoted
particles using a hard sphere model. Hansen et al. with ~° 1 . In the case of d~/d22 ~* 1 the following ap-
,6 7 used a binary hard sphere mixture and con- proximate relation between 10 and 0~ can be given:
cluded that due to the presence of small solvent
molecules the effective repulsion between the large
10 --- 0~(1 -- ~2). )1(
particles decreases. According to them, phase
separation may occur when the size ratio of the two
species is less than 0.2, and the partial packing frac- In Eq. )1( ~° 1 can be regarded as the volume frac-
tions of the two species are comparable.
tion of the small spheres in the volume available
Chan et al. 4, and Jamnik et al. 8 investigated
once the volume occupied by the large spheres has
the effects of solute/solvent size ratio on the solvent been subtracted. The relation in Eq. (1) is exact for
mediated potential of mean force between solutes at
a binary hard sphere mixture with d11/d22 ~ 0
infinite dilution using a binary mixture of hard
,6 9.
solutes dispersed in a "solvent" of hard spheres
In this paper the partial structure factor )K(22$
with surface adhesion (sticky spheres). Jamnik et al.
(denoted as S )K( in the rest of the paper) will be us-
found 8 that, at critical conditions of the model ed to describe the interactions between the large
fluid, the solvation force between the macropar- particles (denoted as 2) dispersed in a "solvent" of
ticles tends to vanish in parallel with the increasing small particles (denoted as 1). Here, K is the
compressibility of the fluid.
magnitude of the wave vector.
In this paper, we present results of model calcula- The structure factor at zero wave vector S (K = 0)
tions of the osmotic isothermal compressibility and can be related to the osmotic isothermal com-
structure factors concerning binary mixtures of pressibility (3p2/311/)~ ' (see, e.g., ,9 17):
large particles dispersed in a "solvent" of small par-
ticles, taking both solvent-solute and solvent-sol-
vent interactions into account. For the model S(K = )O = kT(Op2/aFl), I , )2(
calculations the Baxter theory of adhesive hard
spheres 11, 21 is used; the calculations are based
with H being the osmotic pressure of the mixture in
on the PY-approximation in the Ornstein-Zernike
osmotic equilibrium with the small spheres, 20j the
equation as worked out by Barboy 13, 41 and Per-
number density of particles 2, x/ 1 the chemical
ram and Smith 15, 16. The direct interaction bet-
potential of the "solvent", k the Boltzmann constant,
ween the large spheres is neglected.
and T the absolute temperature. For dilute disper-
In section II the relevant equations for a binary
sions S(K = 0) can be written as:
mixture are given. In section III the influence of
stickiness (solvent-solvent and solvent-solute in-
teractions) on the osmotic compressibility and S(K = 0) = 1/(1 + )2P2B2 ~- 1- 2B2P 2 , )3(
structure factor for a binary mixture of large spheres
in a "solvent" of small spheres will be discussed,
making use of the theory presented in section II. where B 2 is the osmotic second virial coefficient.
To describe short-range interactions between par-
The results of model calculations concerning the
ticles the polydisperse adhesive hard sphere model
solvation interactions in colloidal dispersions will
can be used 13--16. The adhesive interaction
be shown.
potential between particles i and j, Vij(r ), which is
a limiting form of the square well potential, is defin-
2. Theoretical background
ed by
We consider a binary mixture of large spheres
f
with pair diameter 22d and volume fraction 2~¢ in a
)F(j,V
"solvent" of small spheres with pair diameter l~d ~n r ~< j~a
12rij(dij- aij)/di/ j~rc < r < d~j,
and volume fraction .hO The two-sphere mixture is kT
r .>> dij )4(
considered to be in osmotic equilibrium with a one-
sredneP and Vrij, Interactions of lyophilic colloids in a non-polar solvent 3
)bT(
with d~.- jiTr allowed to be infinitesimally small,
= ¢1 q- ¢2'
and j~r being the stickiness parameter for particles i
and j, which goes to infinity in the case of hard and for B 2
sphere interactions.
3
The structure factor S (K) is a function of the set of
1 + - -
parameters .lj~t;I In the case of hard sphere interac- B2/VHs =
tions 2 0 goes to zero. The parameter set )2ij ) and/'ij
are connected by the following relation:
x
, (8)
~7
-- Z P.d (GG - 612iy + lyj~, + 18)
6 y with
V m = (rd6)d3=. (9)
j~2q'/ jid
)5(
-- 12(1 -- )3~ ~ jjdiid = 0 .
In the limit of rll and 21r *-- oo (or ;t n = 212 = 0)
Eqs. (6) and (8) give the expression for a binary hard
In most cases the coefficients ./.,2{ } for given/'ii can sphere mixture. In the case of 21~ = 0 the solvent-
only be found numerically. solute interactions disappear. By decreasing r n (or
In the next section, we discuss the case of a binary increasing the stickiness between the solvent
mixture where both the solvent-solvent and sol- molecules) "poor" solvation is simulated. In the
vent-solute interactions are taken into account 11'/( limit of 2u = 0 the solvent-solvent interactions
< co, 2~r < o0). The direct attractions between the disappear, and by decreasing 21/ "good" solvation
large particles are taken to be zero for simplicity is simulated. All three cases are described in more
22r( = co). This implies that the emphasis on the detail elsewhere 10.
interaction between the large (colloidal) particles is To obtain both coefficients 112 and 21~ Eq. (5) has
on the indirect interactions through the solvent. A to be solved. In this case a quartic equation in 212
more detailed description about the method of is found. Some results of model calculations for a
calculation of the structure factor can be found binary mixture of large colloidal spheres in a "sol-
elsewhere 10. vent" of small spheres with a pair diameter ratio
d22/dll = 160 are given in Figs. 1--8.
In Figs. 1 and 2 In 1/S (K = 0) is plotted against
3. Solvation interactions in binary mixtures the volume fraction of the large spheres ~ (which
equals ~2) for a binary mixture of large hard
For a binary system of large colloidal spheres spheres in a "solvent" of small adhesive hard
(denoted as 2) in a "solvent" of small spheres spheres with ~° 1 = 0.40 at different/'n-values (/'12 =
(denoted as 1) with solvent-solvent and solute-sol- 22'/ = oo). The volume fraction of the solvent ~1 is
vent interactions (rll < oo, 21'/ < oo and 22'/ = )0o taken to be equal to 0~1 -- 120 (see also Eq. (1)).
the following expressions for S(K = 0), which is The curve denoted with/, presented in Figs. 1 and
proportional to the osmotic isothermal com- 2, represents the ln1/S(K =0) vs. ¢ plot for
pressibility, and the second virial coefficient B 2 can monodisperse hard spheres in a solvent, which is
be given in the case of d11/d22 ---* 0: regarded as a continuous background. This curve
(1 -- 02)2(1 + 2~3 -- 3q~ 2 -- J.llq~l) 2
(6)
S(K = O) =
~11@1( 1 + 2q~2 -- q~l) )t12(~12 -- 6)01q~2 ) ~ 2
1+2~3 -- 1 -- 3~ -- 1 -- 3~
appears to be nearly linear over a large volume frac-
with
tion range.
At r u = oo, i.e., in the case of a binary hard
iO = (rc/6)Pid )a7( sphere mixture, the initial slope of the lnl/S(K =