Nanodispersions: Interactions, Stability, and Dynamics

704 Pages·2010·26.551 MB·English

by  Eli Ruckenstein, Marian Manciu (auth.)

Nanodispersions
·
Eli Ruckenstein Marian Manciu
Nanodispersions
Interactions, Stability, and Dynamics
123
EliRuckenstein MarianManciu
DepartmentofChemical DepartmentofPhysics
andBiologicalEngineering UniversityofTexasatEIPaso
UniversityatBuffalo 500W.UniversityAvenue
EIPasoTX79968
TheStateUniversityofNewYork
PhysicalScienceBldg.210
303FurnasHall
USA
BuffaloNY14260-4200 [email protected]
USA
[email protected]
ISBN978-1-4419-1414-9 e-ISBN978-1-4419-1415-6
DOI10.1007/978-1-4419-1415-6
SpringerNewYorkDordrechtHeidelbergLondon
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Preface
ThisbookcontainsanumberofpaperspublishedbyRuckensteinandcoworkersonthetopic
ofnanodispersions.Aerosolsarethefocusofthefirstchapterwhichfeaturesamodelforthe
stickingprobabilityasthemaincontribution.Oneconcludesthat,whentheparticlesaresmall
enough, the dissociation rate can become sufficiently large for doublets to reach equilibrium
with single particles. However, above a critical radius for the particles, the doublets become
stableandtheirconcentrationincreaseswithtime,providingnucleiforaerosolgrowth.
The second chapter examines the deposition of Brownian particles on surfaces when the
interactionforcesbetweenparticlesandcollectorplayarole.Whentherangeofinteractions
betweenthetwo(whichcanbecalledtheinteractionforceboundarylayer)issmallcompared
tothethicknessofthediffusionboundarylayeroftheparticles,theinteractionscanbereplaced
byaboundarycondition.Thishastheformofafirstorderchemicalreaction,andanexpression
is derived for the reaction rate constant. Although cells are larger than the usual Brownian
particles,thedepositionofcancercellsorplateletsonsurfacesistreatedsimilarlybutonthe
basisofaFokker-Plankequation.
Micellar aggregates are considered in chapter 3 and a critical concentration is defined on
the basis of a change in the shape of the size distribution of aggregates. This is followed by
the examination, via a second order perturbation theory, of the phase behavior of a sterically
stabilized non-aqueous colloidal dispersion containing free polymer molecules. This chapter
is also concerned with the thermodynamic stability of microemulsions, which is treated via
a new thermodynamic formalism.Inaddition, amolecular thermodynamics approach is sug-
gested,whichcanpredictthestructuralandcompositionalcharacteristicsofmicroemulsions.
Thermodynamicapproachessimilartothatusedformicroemulsionsareappliedtothephase
transitioninmonolayersofinsolublesurfactantsandtolamellarliquidcrystals.
SternhasnotedthatthetraditionalPoisson-Boltzmannapproachleadstoanionicdensityin
thevicinityoftheinterfacewhichexceedstheavailablevolume.Thisanomalycanbecorrected
bytakingintoaccountthehydrationofions.ThisissueisexaminedinChapter4.Thischapter
also examines the Helfrich force [Helfrich, W. Z. Naturforsch. 1978, 33a, 305], a repulsion
generated by thermallyundulating interfaces. Together withthehydration force,thisforce is
responsibleforthestabilityofneutrallipidbilayers.IncontrasttotheHelfrichtheory,which
isvalidonlyatlargeseparationsbetweenbilayers,thepresenttheoryalsoprovidestheexpo-
nentialbehaviourthatisobservedexperimentallyatsmallseparations.Anequationisderived
fortheforcegeneratedbetweentwochargedplatesimmersedinanelectrolytesolution,which
containssmallchargedparticles,bycouplingdoublelayeranddepletionforces.Itisalsoshown
viaMonteCarlosimulationsthatinconcentratedcolloidalsystems,pairwiserepulsiveinterac-
tionsbetweenparticlescangenerateacollectiveattractiveinteraction.
Chapter5isconcernedwithspecificioneffectsduetoionhydrationforcesandisbasedon
theStructureMaking/StructureBreaking(SM/SB)model.Thestructuremakingionsprefer
the bulk water and are repelled by the surface, while the structure breaking ions disturb the
order of bulk water and are expelled toward the interface. The model was used to calculate
theforcebetweentwoparallelplates.Therearenumerousexperimentsthatpointoutthatthe
v
vi Preface
+ −
cations(exceptH )arerepelledbytheair-waterinterface,whereastheanions(exceptF )are
accumulatedthere.ItisshownthatthesimpleSM/SBmodelcanaccountfortheseobservations
quantitatively.
Chapter6emphasizesthat,asthedoublelayerforce,thehydrationforceisaconsequenceof
electrostatic interactions. In the latter case, the interactions are between neighboring dipoles,
and a theory in which the hydration and double layer forces are treated in a unified manner
isproposed.Thedipolesofthesurfacealignthedipolesoftheneighboringwatermolecules;
the dipoles of the partially aligned water molecules, in turn, partially align the next layer of
molecules,andsoon.Thusadecayingpolarizationfieldisgenerated.Theoverlapofthepolar-
ization fields of two plates brought close enough generates repulsion. Whereas in the tradi-
tionalcontinuumtheoryauniformdipolarfieldonasurfacedoesnotgenerateanelectricfield
outside,thediscretenatureofthewatermoleculesisconsideredtoberesponsibleforthegen-
eration of a local field, which is calculated by assuming that water is organized in ice-like
layers.Inaddition, inour“polarization model”thesurface charge is increasingly neutralized
with increasing electrolyte concentration and replaced with dipoles. As a consequence, the
repulsive force due to charges is diminished whereas that due to dipoles is increased as the
ionicstrengthincreases.Atlowionicstrengthstherepulsionisdecreasedastheionicstrength
increases (particularly because of the screening of the electric field). At high ionic strengths
theincreasingnumberofsurfacedipolesgeneratedbytheincreasingionicstrengthcausesan
increaseinrepulsion.
Chapter7examinesanumberofconsequencesofthepolarizationmodelpresentedabove.
Oneofthemostsignificantistheexistenceofaminimumintherepulsiveinteractionsbetween
colloidalparticlesasafunctionofelectrolyteconcentration,anoldexperimentalresult,which
remained unexplained for 75 years. Voet reported that stable solutions of various metals (Pt,
Pd) and salts (sulfides, halides) in highly concentrated solutions of acids (sulfuric, phospho-
ric)coagulateduponthedilutionwithwater,hencebydecreasingtheelectrolyteconcentration
[Voet,A.Thesis,Amsterdam,1935Seealso:Kruyt,H.R.ColloidScience;Elsevier:Amster-
dam,1952].Thiseffectcanexplain(i)thelightscatteringobservationsregardingtheapofer-
ritinmoleculesatvariousNaCH3COOconcentrationswhichrevealhighrepulsionathighionic
strengths, as well as (ii) the restabilization of protein-covered latexes at high ionic strengths.
Thepolarizationmodeliscombinedwiththermalundulationstoexplainthebehaviourofcom-
monandNewtonblackfilmsaswellastheswellingofneutrallipidbilayersinducedbysimple
salts. This theory, combined with ion-hydration forces, is extended to rough silica surfaces,
whichdisorganizethestructureoftheinterfacialwater.
The last chapter, Chapter 8, is devoted to the interactions between grafted polyelectrolyte
brushes, which exhibit peculiar repulsive and attractive interactions. Several approaches are
suggested. First, a general theory is developed, based on a simple cubic lattice model and
matrixformalism,whichisusedtocalculatethestericinteractionbetweentwograftedpoly-
electrolytebrushes.Anotherapproachbasedonanapproximatepartitionfunctionissuggested
to treat the steric repulsion between grafted polymer brushes, leading to simple equations
for both neutral and charged grafted brushes. A general formalism for double layer interac-
tions between polyelectrolyte brushes is proposed and it is shown that the net interactions
can become attractive, due to the bridging generated by the polyelectrolyte chains between
plates.Consequently,therepulsivestericinteractionscompetewithattractivebridgingforces.
Asimplemodeltocalculatetheavailableareaforcompetitiveadsorptionofmoleculesisalso
proposed.
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
1 Coagulation,dissociationandgrowthofaerosols . . . . . . . . . . . . . . . . . . 1
2 DynamicsofdepositionofBrownianparticlesorcellsonsurfaces . . . . . . . . 67
3 Stabilityofdispersions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
4 Non-DLVO colloidal interactions: excluded volumes, undulation
interactions,depletionforcesandmany-bodyeffects . . . . . . . . . . . . . . . . 325
5 Non-DLVO colloidal interactions: specific ion effects explained by
ion-hydrationforces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
6 PolarizationModel:aunifiedframeworkforhydrationanddouble
layerinteractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459
7 PolarizationModelandionspecificity:applications . . . . . . . . . . . . . . . . 511
8 Polymerbrushes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607
vii
Introduction to CHAPTER 1
Coagulation, dissociation and growth of aerosols
1.1 G. Narsimhan, E. Ruckenstein: “The Brownian Co- coefficient are expressed as functions of the Knudsen
agulation of Aerosols over the Entire Range of Knud- number for various Hamaker constants [1.1].
sen Numbers: Connection between the Sticking Prob- The model was tested using Monte-Carlo simulations
ability and the Interaction Forces” JOURNAL OF (for selected values of the Hamaker constant) over the en-
COLLOID AND INTERFACE SCIENCE 104: 2 tire range of the Knudsen number [1.2]. For large particles,
(1985) 344–369. the Brownian coagulation coefficient agrees well with the
1.2 G. Narsimhan, E. Ruckenstein: “Monte Carlo Simula- Fuchs interpolation formula and with the analytical expres-
tion of Brownian Coagulation over the Entire Range sion obtained in [1.1]. For sufficiently small particles [1.2],
of Particle Sizes from Near Molecular to Colloidal: the coagulation coefficient agrees very well with the lower
Connection between Collision Efficiency and Inter- bound obtained analytically [1.1]. For intermediate particle
particle Forces,” JOURNAL OF COLLOID AND sizes, the range of interparticle attractive forces becomes
INTERFACE SCIENCE 107: 1 (1985) 174–193. comparable to the particle size. This enhances the coagula-
1.3 G. Narsimhan, E. Ruckenstein: “Dissociation Kinetics tion coefficient, which acquires values even greater than for
of Doublets of Aerosol Particles,” JOURNAL OF the free molecular limit.
COLLOID AND INTERFACE SCIENCE 116: 1 The coagulation of aerosols is typically regarded as a re-
(1987) 278–287. sult of the short-range van der Waals attraction between
1.4 G. Narsimhan, E. Ruckenstein: “A Possible Nuclea- particles; when two particles come sufficiently close to
tion Type of Mechanism for the Growth of Small each other, they can coagulate. This is true if the particles
Aerosol Particles,” JOURNAL OF COLLOID AND are large enough and hence the potential well due to van der
INTERFACE SCIENCE 116: 1 (1987) 288–295. Waals and Born interactions is sufficiently deep; it is not
accurate if the particles are too small and the potential well
Traditional approaches to Brownian coagulation account so shallow that the particles are able to escape from it. In
for the interaction between particles through a phenome- the latter case, the coagulated aerosol doublets can acquire
nological sticking probability, which is usually assumed to enough energy from the collision with other molecules to
be unity. A model is proposed for the Brownian coagula- dissociate. A novel theoretical treatment, based on the as-
tion coefficient of electrically neutral aerosol particles, sumption that the time scale of oscillations within the well
which takes into account the interparticle van der Waals is much shorter than the time scale of Brownian motion,
attraction and Born repulsion [1.1]. A “sphere of influ- allows one to average the Fokker-Plank equation over the
ence”, which has a thickness equal to the correlation positions of the doublet and leads to a one-dimensional
length of the relative Brownian motion of two particles is Fokker-Plank equation in terms of the energy of the relative
suggested; within this region, the relative motion of the motion of the constituents of the doublet [1.3]. The average
particles is considered free molecular, whereas outside lifetime of a doublet can thus be calculated. It is shown that
this region it is described by a Fokker-Plank equation. For in air at 298 K, the average dissociation time increases
very small particles, the sticking probability becomes van- dramatically, from 10-7 to 10-1 seconds, as the radius
ishingly small, while for sufficiently large particles it is changes from 15 to 50 Ǻ. The doublets formed by particles
virtually unity. In contrast to earlier models, the expres- with a radius larger than 50 Ǻ are found to be extremely
sion derived for the coagulation coefficient of large parti- stable [1.3].
cles displays the proper continuum and free molecular Very small aerosol particles can be generated via physi-
limits and agrees well with the Fuchs empirical formula cal or chemical nucleation, and their subsequent growth is
[1.1]. Upper and lower bounds of the ratio between the due either to condensation on the surface of the particles or
coagulation coefficient and the Smoluchowski coagulation to the Brownian coagulation of the particles themselves. If
E. Ruckenstein, M. Manciu, Nanodispersions, DOI 10.1007/978-1-4419-1415-6_1, © Springer Science+Business Media, LLC 2010
2 Nanodispersions

the particles are sufficiently large, the latter process is irre- rates of coagulation and dissociation increases as the parti-
versible (i.e., the sticking probability is unity). However, as cle size increases, becoming zero at a critical particle radius.
noted above, for very small particles there is a non- For particles that are sufficiently small compared to the criti-
negligible chance for the doublet to dissociate, because the cal radius, the doublets become unstable and can reach a dy-
interaction between the two particles leads to a shallow namic equilibrium with the single particles. For particles that
potential well. The rate of formation of doublets is calcu- are large compared to the critical size, the doublets are stable
lated as suggested in [1.1] and the rate of dissociation is and their concentration increases with time. They provide
calculated as indicated in [1.3]. The difference between the nuclei for aerosol growth [1.4].
Coagulation, dissociation and growth of aerosols 3
4 Nanodispersions