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Advances in Colloid and Interface Science 161 (2010) 2947

Contents lists available at ScienceDirect

Advances in Colloid and Interface Science1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302. A new single drop methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.1. Coaxial capillary pendant drop method overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2. Physics of subphase exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3. Surfactant and small amphiphile exchange: equilibrium and dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.1. Convection-enhanced adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2. Desorption kinetics and reversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3. Sequential surfactant adsorption and replacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4. Polymer and macromolecule adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1. Thermodynamic equilibrium and convection-enhanced transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2. Desorption kinetics and reversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.3. Competitive adsorption and displa

5. Soft interfacial nanocomposites and nano5.1. Prerequisites for interfacial nanoco

5.1.1. Strong polyelectrolytes .5.1.2. Weak polyelectrolytes .

Corresponding author. Tel.: +1 610 330 5820; fax:E-mail address: [email protected] (J.K. Ferri).

0001-8686/$ see front matter 2010 Elsevier B.V. Aldoi:10.1016/j.cis.2010.08.002ContentsKeywords:AdsorptionDesorptionKineticsConvectionSurfactantProteinPolymerMacromoleculeAssemblyInterfaceStructureNanomechanicsElasticityNanomembraneViscoelasticRheologyConstitutiveSoft matterprobed by perturbing an interface or adjoining bulk phase from the equilibrium state. Many methodsdesigned for studying kinetics at uiduid interfaces focus on removing the system from equilibriumthrough dilation or compression of the interface. This modies the surface excess concentration i and allowsthe species distribution in the bulk Ci to respond. There are only a few methods available for studying uiduid interfaces which seek to control Ci and allow the interface to respond with changes to i. Subphaseexchange in pendant drops can be achieved by the injection and withdrawal of liquid into a drop at constantvolumetric ow rate RE during which the interfacial area and drop volume VD are controlled to beapproximately constant. This can be accomplished by forming a pendant drop at the tip of two coaxialcapillary tubes. Although evolution of the subphase concentration Ci(t) is dictated by extrinsic factors such asRE and VD, complete subphase exchange can always be attained when a sufcient amount of liquid is used.This provides a means to tailor driving forces for adsorption and desorption in uiduid systems and insome cases, fabricate interfacial materials of well-dened composition templated at these interfaces. Thecoaxial capillary pendant drop (CCPD) method opens a wide variety of experimental possibilities.Experiments and theoretical frameworks are reviewed for the study of surfactant exchange kinetics,macromolecular adsorption equilibrium and dynamics, as well as the fabrication of a wide range of softsurface materials and the characterization of their mechanics. Future directions for new experiments are alsodiscussed.

2010 Elsevier B.V. All rights reserved.cement . . . . . . . . . . . . . . . . . . .membranes . . . . . . . . . . . . . . . . .mposite synthesis . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .

+1 610 330 5059.

l rights reserved.terfaces in the presence of surface active species are often

Available online 11 August 2010 Adsorption equilibrium is the state in which the chemical potential of each species in the interface and bulk

is the same. Dynamic phenomena at uiduid ina b s t r a c ta r t i c l e i n f oFrom surfactant adsorption kinetics to asymmetric nanomembrane mechanics:Pendant drop experiments with subphase exchange

James K. Ferri a,, Csaba Kotsmar b, Reinhard Miller c

a Department of Chemical and Biomolecular Engineering, Lafayette College, Easton, PA 18042, USAb Department of Chemical Engineering, The University of Texas at Austin, Austin, TX 78712, USAc Max Planck Institut fr Kolloid and Grenzchenforschung, D-14424 Golm/Potsdam, Germany

j ourna l homepage: www.e lsev ie r.com/ locate /c is. . . . . . . . . . . . . . . . . . . . . . . . . . 37

. . . . . . . . . . . . . . . . . . . . . . . . . . 38

. . . . . . . . . . . . . . . . . . . . . . . . . . 38

. . . . . . . . . . . . . . . . . . . . . . . . . . 38

. . . . . . . . . . . . . . . . . . . . . . . . . . 38

..g p..utiv.c m.....

30 J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947consists of a coaxial double capillary which allows for in-situ internalsubphase exchange in single pendant drops.

The aim of this review is to provide an overview and examples ofthe many applications of the coaxial capillary pendant drop (CCPD)method. A summary of the method and dynamics of subphaseexchange is given in Section 2. Section 3 describes experiments andtheoretical frameworks for surfactants and small amphiphiles dealingwith desorption [12] and reversibility of adsorbedmolecules [13], andsequential adsorption of different surfactants [14]. In Section 4,experiments concerning macromolecules and biomacromolecules aswell as experiments with interfacial mixtures of small and largemolecules are described. Protein desorption kinetics [15,16], molec-ular displacement, specically of proteins by surfactants [17] and thepenetration of surface active molecules into an existing surface layer

second liquid of species concentration C2, using Microinjector 2(M2). The drop volume VD or area AD is maintained constant viafeedback control using the drop shape and the withdrawal of liquidfrom the droplet interior at the same volumetric ow rate (RE) usingM1. During the exchange, the concentration of each species in thedrop, i.e. C1(t) and C2(t), evolves continuously from the initialdistribution, C1(t=0)=C1, and C2(t=0)=0, to the nal distribu-tion, C1(t=)=0 and C2(t=)=C2,. The surface tension before,during, and after the exchange can be monitored using drop proleanalysis tensiometry.

2.2. Physics of subphase exchange

The simplest description of the evolution of the subphase5.1.3. Protein and biomacromolecules . . . . . . . . . .5.2. Adsorption of non-ionic polymers to lipid monolayers . . . .5.3. Electrostatic assembly of asymmetric nanocomposites of stron5.4. Polysaccharides, peptides and weak polyelectrolyte assemblies5.5. Proteins and nanobiomembranes . . . . . . . . . . . . . .5.6. Metrology of nanomembrane mechanics: elasticity and constit

6. Future directions . . . . . . . . . . . . . . . . . . . . . . . . .6.1. Physicochemical mechanics of surface materials: surface elasti

nanoparticles and their composites . . . . . . . . . . . . .6.2. Diffusive transport through nanocomposite surface materials .6.3. Closure . . . . . . . . . . . . . . . . . . . . . . . . . .

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction

The study of equilibrium and exchange kinetics of surfactants,macromolecules, and their assemblies at immiscible uid and softinterfaces as well as the rheology of such structures are subjects ofinterest in both science and a wide range of technological applica-tions. Substantial interest in particular non-equilibrium propertiescomes from all elds of application dealing with foams and emulsions,as discussed in [13]. As most practical systems are based on multi-component adsorption layers, studies of adsorption kinetics frommixed solutions [4], penetration of one component into an establishedadsorbed layer [5], and viscoelastic phenomena in well-denedinterfacial nanocomposites are extraordinarily important.

Not many experimental techniques are suitable for the study ofequilibrium and exchange kinetics or rheology and constitutivebehavior of liquid-supported surface material assemblies. Classictechniques to prepare well-dened interfacial composites employ theuse of a Gibbs or Langmuir monolayer at the interface of a Langmuirtrough followed by the transfer of the monolayer from one reservoirto another via a translating barrier to exchange the subphase [6,7].Often studies undertaken with this method are limited because of thelarge subphase volume required. Additionally, highly stable surfacelayers are required because of the interfacial hydrodynamic shearwhich arises from the motion of the adjacent bulk during transfer.

Drop and bubble methods are more suitable for such experimentsbecause they allow for more stringent control of the environmentalconditions and therefore, more uniform temperature, pressure andconcentration at the interface, smaller amounts of material needed,and a much higher interface/volume ratio than in conventionalLangmuir troughs.

Svitova et al. describe a modied pendant bubble method whichthey term continuous ow tensiometry (CFT) which utilizes aconvection cell to exchange the external bulk liquid [8]. A pendantbubble is formed in a cuvette and remains during the exchange, andthe interfacial tension is monitored by axisymmetric bubble shapeanalysis. Another approach was presented by Wege et al. [911] that[18] are detailed. Section 5 outlines fabrication and metrology of soft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39olyelectrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . . 40. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41e behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44odulii of surfactants, macromolecules,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

elastic interfacial nanocomposites and nanomembranes using non-specic adsorption of polymers [19] and polyelectrolytes of oppositecharge with electrostatic layer-by-layer assembly [20] and interfacialchemistry.

There are obviously many applications not yet realized, such asinvestigations of interphase transport phenomena. These and othermore sophisticated experiments, for example studies of the effect ofsolvent conditions such as pH and/or ionic strength [21], compositionof mixed solvents [22] on interfacial rheology, and moleculartransport through surface composite layers are described in Section 6.

2. A new single drop methodology

Axisymmetric drop shape analysis (ADSA) has emerged as apowerful tool for the study of equilibrium and dynamic adsorption atuid/uid interfaces [23]. Recently a technique was introduced inwhich the drop subphase is exchanged using coaxial capillaries toexchange the volume of the drop interior [911]. For most of theexperiments described in this review, a commercially availablependant drop tensiometer PAT-1D (Sinterface Technologies, Berlin,Germany) was used [24].

2.1. Coaxial capillary pendant drop method overview

In the hydrostatic version of the pendant drop method, a drop(5bVDb15 L) of surfactant solution is formed at the tip of a capillary.A silhouette of the drop is cast onto a CCD camera and digitized. Thedigital images of the drop are recorded over time and t to the YoungLaplace equation to accurately (0.1 mN/m) determine surfacetension. Specially constructed tips for the pendant drop apparatussuch as the concentric capillaries described in CabrerizoVilchez et al.[11] are used for subphase exchange experiments. A schematic isshown in Fig. 1.

An experiment is performed as follows. A liquid drop of speciesconcentration C1, is formed using Microinjector 1 (M1) and allowedto quiesce. The drop subphase is then exchanged by the injection of aconcentration can be derived if the drop subphase is assumed to be

To visualize spatiotemporal distribution of subphase concentra-tion, experiments were performed using an aqueous solution of alow molecular weight dye (Brilliant Green, C2,=3.3 mg/mL,

ce [16]. a) Experimental set-up, and b) schematic of drop subphase exchange.

31J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947perfectly mixed. For a perfectly mixed drop subphase, the concentra-tion of species 1 is described by [12]:

C1 t = C;1 exp t = 2:1

where is the residence time of the liquid in the drop =VD/RE.The concentration of species C2, (i.e. C1,=0)

C2 t = C;2 1 exp t = 2:2

Experiments which measure the rate of exchange can beperformed using simple liquids, for example, using water and binarymixtures of water and ethanol [12] or DMSO and chlorobenzene [25].See Fig. 2a. In most cases the experimentally measured characteristicexchange time constant NVD/RE as shown in Fig. 2b indicates that thedrop is not perfectly mixed.

However, the details of the dynamics of the subphase exchange areimportant to equilibrium and kinetic experiments. For equilibrium it isimportant to quantify the volume of uid required to achieve completeexchange. Additionally, in order to separate interfacial exchangekinetics from the dynamics of the subphase exchange process, theevolution of the subphase concentrationmust be described as a functionof the extrinsic conditions such as capillary tip geometry, average andlocal uid velocity, and subphase concentration.

Direct numerical simulation of the liquid velocity in the dropprovides details of the ow structure on a microscopic level, i.e. uid

Fig. 1. Schematic of coaxial capillary pendant drop technique, as in Referenstreamlines, velocity distribution, and concentration distribution, andon amacroscopic level, can be used to determine the overall residencetime of liquid in the drop. The spatiotemporal species distribution canalso be calculated to determine the rate at which the drop subphaseattains compositional uniformity. In general, the velocity distributionis described by the solution of the NavierStokes equation:

vt + v v

= P +

2v + g 2:3

which describes the velocity vector eld v(t,x,y,z) in terms of theintrinsic uid properties, viscosity , density , and the pressure P.The species continuity equation accounts for both convective anddiffusive transport of each species Ci(t,x,y,z) in the drop subphase by

Cit + v Ci = Di

2Ci 2:4

where Di is the diffusion coefcient of the species in the liquid phase.Solution of Eqs. (2.3) and (2.4) subject to appropriate boundary andinitial conditions yields v and Ci.Fig. 2. Macroscopic characterization of rate of subphase exchange. a) Surface tension() versus time for water exchange with 2% (v:v) aqueous ethanol. C1,=0 andC2,=2% (v:v) ethanol for 0.2 L/s, solid line is best t to Eq. (2.1), dashed line is thecalculated evolution of bulk concentration of ethanol from Eq. (2.2). b) Time constant vs. exchange ow rate RE as measured; symbols () and () from Reference [11] andsymbols () from Reference [22]; error bars represent 95% condence and solid line is for perfect mixing.

D26106 cm2/s); see Reference [26] for details. Fig. 3a showsthe evolution of dye distribution for the exchange ow rateRE=0.2 L/s. Direct numerical simulation of the velocity andconcentration distribution using Eqs. (2.3) and (2.4) in cylindricalaxisymmetry and appropriate boundary conditions are shown inFig. 3b. Further details of the simulation as well as the impact ofstructure formation on the boundary condition at the airwaterinterface are provided in [26].

3. Surfactant and small amphiphile exchange: equilibrium anddynamics

The equilibrium and kinetics of surfactant and small amphiphileexchange at uid interfaces draw awide range of interest for scientistsand engineers; see Reviews [2731]. The simplest framework whichrelates the equilibrium surface excess concentration eq,1 of smallmolecules to their equilibrium bulk concentration C,1 is the Langmuiradsorption isotherm

x1 =eq;1;1

=C;1

a1 + C;1 3:1

where a1 =11

is the equilibrium adsorption constant, ,1 is the

maximum packing of the surfactant in a monolayer, and x1 is the

surfactant may then be calculated solving Eq. (3.2) if the timedependence of the Cs,1(t) is known; c.f. Section 2.2 for details.

Eq. (3.2) can be non-dimensionalized to elucidate the competitionbetween the intrinsic physicochemical kinetics and the rate ofconvective exchange of the drop subphase by scaling the surfaceexcess concentration by the equilibrium surface excess concentration1~eq,1, the subphase concentration by the equilibrium subphaseconcentration, Cs,1 ~C,1, and time by the convective exchangetimescale, t~.

32 J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947fractional coverage of the interface.The kinetics of surfactant exchange can be described by a mass

balance at the interface [32]:

1 t t = 1Cs;1 t ;11 t

11 t 3:2

Eq. (3.2) describes the rate of change of the surface excessconcentration (t) as the difference between the adsorptive uxwhich is the product of the adsorption kinetic rate constant 1, theinstantaneous subphase concentration Cs,1(t), and the space avail-able on the interface, i.e. the difference between the maximumsurface concentration ,1 and the surface concentration 1(t). Thedesorptive ux is equal to the product of the desorption kineticconstant 1 and 1(t). The evolution of the surface concentration of

Fig. 3.Microscopic characterization of subphase exchange dynamics: experiment andsimulation. a) Subphase exchange with Brillant Green (C2,=3.3 mg/mL) atRE=0.2 L/s, and b) direct numerical simulation of species distribution and velocitycontours using Eqs. (2.3) and (2.4) for the same experimental conditions as in a) and

constant surface tension boundary condition. See Reference [26] for details.In non-dimensional form, Eq. (3.2) becomes

x1 1 t

t = 1 k1Cs;1 t

1x1 1 t

x1 1 t

h i 3:3where the dimensionless variables 1 =

1eq;1

, Cs;1 =Cs;1C;1

, and t =t,

and the x1 =eq;1;1

is the equilibrium fractional coverage of species 1,

and the adsorption number, k1 =1C;11

is a scaled bulk concentration

of species 1.When desorption kinetics aremuch faster than convection,i.e. 11, a local equilibrium exists between the bulk and theinterface, and the surface concentration is described by

x11 t

=k1C s;1 t

1 + kCs;1 t

3:4

In this case, the surface excess concentration evolution isdetermined only by the rate of convective exchange.

The equilibrium and dynamic surface tensions eq and (t)corresponding to Langmuir adsorption are described by the surfaceequation of state,

eq = o + RT ;1 ln 1x1 3:5

and

t

= o + RT ;1 ln 1x1 1 t 3:6

where o is the surface tension of the surfactant-free interface and RTis the product of the gas constant and the temperature.

In this section, experiments studying the adsorption dynamics ofsurfactants and small amphiphiles using the CCPD method areillustrated using a homologous series of phosphine oxide surfactantswhich are reasonably described by the Langmuir framework. SeeTable 1 and Reference [33] for details of equilibrium data and modelconstants.

3.1. Convection-enhanced adsorption

Convective exchange adsorption experiments are performed byformation of a pendant drop of surfactant solution followed bycontinuous injection of the same surfactant solution into the dropsubphase and withdrawal of uid from the drop at the samevolumetric ow rate. This convection can enhance the rate and extentto which an apparent equilibrium state is reached. A discussion ofthese two effects and representative experiments follows.

Table 1Langmuir isotherm constants for CnDMPO surfactants.

CnDMPOn

a (mol/L) (mol/m2)

8 4.12104 3.40106

10 4.39105 3.64106

12 5.88106 4.39106

14 5.85107 4.44106

replacing its subphase with water, a driving force for surfactantdesorption is established. Eq. (3.3) subject to the initial condition,

process is a function of the dimensionless groups, 1, which is the

Fig. 4. Dynamic surface tension of C10DMPO () at a bulk concentration ofC=1104 mol/L: rapid adsorption, no bulk depletion. Solid line is the dropinterfacial area; dashed line is the equilibrium surface tension as predicted withLangmuir model.

Fig. 5. Dynamic surface tension of C14DMPO at a bulk concentration of C=6106 mol/Lfor static () adsorption and convection exchange () experiments: adsorption depletionand shift in apparent equilibrium. Solid line is the drop area, dashed line is the equilibrium

33J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947Consider a semi-innite surfactant solution immediately after theformation of an interface. Surfactant adsorbs at the interface depletingthe local concentration in the bulk and a concentration gradient fromthe bulk to the interface is initiated. Often bulk diffusion is themechanism controlling the rate of surfactant adsorption. Thecharacteristic diffusion time scale D for surfactant adsorptiondepends on how effective the surface depletes the bulk of surfactantand on the diffusion coefcient of surfactant in the bulk solution.

D =h21D1

3:7

where the adsorption depth, h1, can be dened from the ratio of theequilibrium surface concentration of a surfactant to the bulkconcentration, i.e.

h1 =eq;1C;1

3:8

which can be calculated from an equilibrium model such as Eq. (3.1)[31]. Eqs. (3.7) and (3.8) show that the smaller is the concentration;the larger is the adsorption depth and the diffusion timescale.Therefore, experiments which study surfactants at low concentrationscan require long equilibration times. Low concentration pendant dropexperiments also present an additional difculty; surfactant adsorp-tion can deplete the bulk concentration shifting the apparentequilibrium. This occurs because at low concentration, the bulkphase does not act as an innite reservoir of surfactant. This effect canbe qualitatively predicted by the depletion number, Sb,

Sb;1 =ADeq;1VDC;1

3:9

where AD is the total interfacial area and VD is the total volume of thependant drop. The depletion number is a ratio of the equilibriummassof surfactant adsorbed at the interface to the total amount ofsurfactant available in the bulk. When Sb1, the pendant drop canbe treated as an innite reservoir. The larger is Sb, the greater the shiftof the apparent adsorption equilibrium. Convective exchange of thedrop subphase during adsorption experiments mitigates both of theseeffects.

The following experiments for the surfactant C10DMPO illustrate.At a bulk concentration C=1104 mol/L, the adsorption depth, h, is2.5105 m. The diffusion timescale for surface tension equilibrationis about 6 s. Under typical experimental conditions (VD=15 L,AD=25 mm2), the depletion number is about 5102. This predictsa rapid equilibration with respect to the timescales in the experiment,and the depletion number suggests that the pendant drop will behaveas an innite reservoir of surfactant. These expectations are conrmedby the data shown in Fig. 4. The surface tension is unchanging over allobserved times and agrees with the equilibrium value as predicted bythe Langmuir isotherm.

For the surfactant C14DMPO at a bulk concentration ofC=6106 mol/L, the adsorption depth as predicted by the constantsof the Langmuir model given in Table 1 is about 6104 m suggestingthat the diffusion timescale for adsorption equilibration is on the orderof hours. The depletion number for the experiment Sb is nearly unity. InFig. 5, the surface tension relaxation is shown for both static andconvection-enhanced adsorption equilibrations. In the case of noexchange (i.e. static pendant drop), bulk depletion alters the apparentequilibrium, however continuous exchange accelerates the approach toequilibrium and the extent to which equilibrium is reached; the longtime asymptote for the exchanged subphase is well described by theLangmuir model.

Acceleration of adsorption kinetics can be accomplished in

situations where there is no bulk depletion effect. These situations 1 t = 0

= 1, describes the dynamic surface concentration and can

be readily integrated via the RungeKutta method. The desorptionarise typically for macromolecules which have long timescales at low(to moderate) concentration, cf. Section 4.1 for examples.

3.2. Desorption kinetics and reversibility

Surfactant desorption kinetics can be measured in experimentswhere a pendant drop of surfactant solution is formed, and thensubsequently the drop subphase is replaced with an aqueous phase,free of surfactant. Experiments may be designed to measure both therate of desorption (and therefore desorption kinetic constants) andthe extent to which desorption occurs. A discussion of theory andexperiments follows.

Consider an interface of a pendant drop having an equilibriumdistribution of the surfactant adsorbed from the adjacent bulk phase.If the bulk concentration of the surfactant in the drop is depleted bysurface tension as predicted with the Langmuir model.

ratio of the convection and desorption timescales, the adsorptionnumber, k, and the fractional interfacial coverage, x1. When theconvective timescale is much smaller than the desorption timescale,the subsurface concentration during the exchange is negligible andthe surface concentration is desorption-controlled [34], i.e.

1 t

= exp 1t

3:10As desorption proceeds, the surface tension increases. The rate of

this increase can be recast in dimensionless form by scaling thesurface tension by its equilibrium lowering according to:

t

= t eq

oeq= 1

ln 1x1 1 t

ln 1x1 3:11

Fig. 6 shows the dimensionless time evolution of the surfacetension as a function of the ratio of convection to adsorptiontimescales (1) for a xed adsorption number k1, representing theeffect of varying either the surfactant physical chemistry (i.e. the

1 t t = 1Cs;1 t 1 t 2 t 11 t 3:12

2 t t = 2Cs;2 t 1 t 2 t 22 t 3:13

where i and i are the adsorption and desorption kinetic rateconstants of each component respectively. Note that in Eqs. (3.12) and(3.13), themaximum surface concentration is assumed to be the samefor each component, which is reasonable for homologous surfactantspossessing the same polar moiety.

The evolution of the surface concentration of surfactant may thenbe calculated solving Eqs. (3.12) and (3.13) together with Eqs. (2.2)and (2.3) to describe the evolution of the bulk concentration of eachcomponent. These may be rearranged, scaling time by the convectiontimescale, ,

1 t

= 1 k1Cs;1 t

1 t 2 t

1t h i 3:14

34 J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947desorption coefcient 1) or the exchange ow rate RE.Consider the variation of surfactant physical chemistry at a xed

exchange rate. As the desorption coefcient increases, the increase in becomesmore rapid. However this effect has an upper bound.Whendesorption is essentially instantaneous, the interface maintains a localequilibrium with the bulk phase as described by Eq. (3.4); this is thedashed curve in Fig. 6. This suggests that the study of a homologousseries of surfactants, viz. n-alkanes conjugates of the same hydrophilicmoiety, at a xed exchange rate should be able to identify thepresence of a desorption barrier and demonstrate its dependence onhydrocarbon chain length. Finally, consider the effect of the exchangeow rate. The greater is RE the more rapid is the exchange forcing thebulk concentration towards zero. In this case, the solutions toEqs. (3.3) and (3.10) converge, i.e. the process is desorption-controlled and independent of exchange rate. The effect of adsorptionnumber on the surface tension increase for a xed surfactant physicalchemistry and exchange ow rate have also been reported.

Data is presented in Fig. 7 which shows the surface tension anddrop area versus time for C8, C10, C12, and C14DMPO at bulkconcentrations having an equilibrium surface tension of 45 mN/m.Here, the temporal axis was rescaled so that (t=0) occurs at theinitiation of exchange. In these experiments, the exchange rate anddrop volume for each experiment were constant so the convectiontimescale is the same in each experiment so that the only adjustable

Fig. 6. Desorption kinetics for different surfactant physical chemistries and exchangeow rates at a xed adsorption number (k=10). (1) =1.0, (2) =0.1 and (3)

=0.01. Desorption-control shown for (=0.01).parameter is the desorption coefcient 1. Eq. (3.3) was integratedusing the form of C1(t) given in Eq. (2.2) with the best t value for from the experiment. The desorption coefcients for each surfactantwere reported [12]; these values (s1) are 4.1103 (C8), 2.8103

(C10), 2.1103 (C12), and 5.5104 (C14).

3.3. Sequential surfactant adsorption and replacement

Finite surfactant sorption kinetics during sequential subphaseexchange can give rise to non-equilibrium surface concentrations andthereby non-equilibrium surface tensions. Consider an interfacehaving an equilibrium distribution of the rst surfactant (component1) adsorbed from the adjacent bulk phase. A mass balance for eachsurfactant can also be written at the interface which describes the rateof change of the surface concentration, i, of each component as adifference between adsorptive and desorptive kinetic uxes. Theadsorptive ux of each species is proportional to the bulk concentra-tion, Ci, of that species and the space available on the interface; i.e. thedifference between the maximum surface concentration, , and thetotal instantaneous surface concentration, 1+2. Assuming negligi-ble interactions among adsorbed species, the desorptive ux of eachcomponent is linearly proportional to its surface concentration. For abinary system, the sorption kinetic equations are:

Fig. 7. Desorption kinetics of surfactants: CnDMPO. Scaled surface tension C8 (),C10 (), C12 (), and C14 () versus time.t

2 t t

= 2 k2 Cs;2 t

1 t 2 t

2 t

ih 3:15where t=

t. Eqs. (3.14) and (3.15) show that the evolution of the

surface concentration of each species in a binary system depends on

four dimensionless groups: the adsorption numbers ki =iC;ii

which

are scaled bulk concentrations and the desorption coefcients i.When these kinetic constants are sufciently large, Eqs. (3.14) and

(3.15) reduce to the LangmuirHinshelwood equilibrium adsorptionisotherms [35] for a binary system in which adsorption follows a localequilibrium with convective exchange, as in Eq. (3.4) for a unarysystem:

x1 t

=

1 t

=k1C

1 t

1 + k1C 1t + k2C 2 t

3:16

x2 t

=

2 t

=

k2C2 t

3:17

35J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947 1 + k1C 1 t + k2C2 t

The surface tension evolution is dictated by the surface concen-tration via the equation of state which relates the dynamic surfacetension (t) to the surface concentrations 1(t) and 2(t).

t

= o + RT ln 11 t

2 t

24

35 3:18

where o is the surface tension of the surfactant-free interface and RTis the product of the gas constant and the temperature.

When the adsorption number for each component is the same (i.e.ki=const.), the equilibrium interfacial coverage and therefore thesurface tension are the same prior and subsequent to the exchange.This same behavior is displayed when the sorption kinetic constantsof both species are identical. However, the surface tension during asequential exchange of surfactants with different desorption coef-cients manifests a temporal dependence that depends on bothmagnitude of the difference and the sequence in which the exchangeoccurs. Representative experiments demonstrating minima andmaxima in the dynamic surface tension during the exchange areshown in Fig. 8. This was demonstrated to be consistent withinterfacial over- and under-population during the exchange processusing the theory described in this section and assuming species

Fig. 8. Sequential adsorption of surfactants: C10DMPO and C14DMPO. Surface tension

() versus time.concentrations of the form given in Eqs. (2.1) and (2.2). Furtherdetails were reported earlier by Gorevski [14].

4. Polymer and macromolecule adsorption

Adsorption of proteins and their interaction with other biocom-patible/biodegradable macromolecules or low molecular-weightsurfactants at liquid interfaces are of high relevance to food,pharmaceutical and cosmetic industrial applications. Central pro-blems associated with polymers and macromolecules at liquidinterfaces are those of adsorption and thermodynamic equilibrium,dynamic surface tension, adsorption and desorption kinetics, and theinteractions in interfacial mixtures of surfactants andmacromolecules[3644].

4.1. Thermodynamic equilibrium and convection-enhanced transport

Proteins and macromolecules desorb from interfaces into puresolvents very slowly [4548]. The reason is likely the high Gibbs freeenergy of adsorption. One can assume that the adsorption kinetics ofhigh molecular weight species at surfaces is an irreversible process, inanalogy to kinetically irreversible or unidirectional chemical reac-tions, neglecting the reverse ux of material from the surface into thebulk [49,50].

The adsorption of macromolecules at solid or liquid interfaces is inmany cases kinetically irreversible, i.e. the adsorption and interfacialtension of a solution calculated from the extrapolation to innite timedepends signicantly on the conditions under which the adsorptionlayer was formed, rather than solely on the macromolecule concen-tration. Convective transfer of the molecules from the bulk to thesolution interface can enhance the adsorption process, and can lead toincreased adsorbed amounts of the molecules in equilibrium at thesame bulk concentration caused by the shorter time needed for theunfolding of adsorbedmacromolecules [50]. Therefore, the adsorptionisotherm and surface tension isotherm for protein solutions derivedfrom thermodynamic ormolecular statistical considerations can fail todescribe such a system.

Fainerman et al. [50] investigated the adsorption kinetics of threedifferent proteins, -casein, -lactoglobulin and human serumalbumin (HSA) at the at the air/water interface with and withoutforced convection. (These experiments were performed using abubble prole analysis tensiometer and CFT similar to Svitova [8] asshown in Fig. 9a.) The adsorption experiments were performed atdifferent solution concentrations with the three different proteinsboth with and without forced convection. The data indicate asignicant difference between the adsorption rates in case of allproteins at all concentrations in the two different types of experi-ments. With forced convection, both the rate of surface tensiondecrease and consequently the adsorption rate were approximatelyone order of magnitude larger. Fig. 9b represents the differences in thecase of 107 mol/L BLG solutions. It was also shown that theequilibrium surface tensions, i.e. the values extrapolated to innitetime, are independent of the adsorption rate. Fig. 9c shows that for thetwo experiments with 5109 mol/L -casein solutions the limitingsurface tension values are the same to within the experimental error.Similar results were found for HSA and BLG solutions.

It can be seen that the rate of protein adsorption, even thoughvaried in a wide range, does not affect the equilibrium surface tensionof the solution, and consequently the adsorption. Therefore, despitethe essential irreversibility of the protein adsorption kinetics at liquidinterfaces [51], this process is thermodynamically reversible. Thisbehavior may be caused by the fact that the characteristic time forconformational change is essentially shorter than the time necessaryto attain the equilibrium state in experiments with forced convection.

The adsorption equilibriumof poly(ethyleneoxide)poly(propylene

oxide)poly(ethylene oxide), hereafter PEO/PPO/PEO, was studied in

36 J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947the presence and absence of convective exchange [19]. At highconcentration, the interface reaches equilibrium under convectiveexchange under comparable time scales to diffusion alone, seeFig. 10a. However, at lower concentration the diffusion timescale ismuch longer and convection greatly enhances the rate of approach to an

Fig. 9. a) Pendant bubble external convective exchange as described in References [8,37];b) dependence of surface tension on time for BLG solution (concentration 107 mol/l)with () andwithout () forced convection; RE=25 L/s; c) surface tension as function ofinverse time for 5109 mol/L -casein solutions with () and without () forcedconvection; solid lines represent approximations to innite time.equilibrium state; see Fig. 10b However, in both cases, the long timeasymptotes of the dynamic surface tension between both convectiveexchange and diffusion alone are the same suggesting that athermodynamic equilibrium is reached in either case. Furthermore,Fig. 10b provides an illustration of acceleration of adsorption kineticsevenwhenadsorptionequilibriumis accessiblebydiffusion asdiscussedin Section 3.1. Although polymers are traditionally thought to havefrozen, unresponsive structures at interfaces, these studies suggest thatthe polymer is highly mobile in the adsorbed layer and readilyrearranges at the interface. Similar results have been reportedelsewhere; for additional discussion see Reference [52] and Section 5.2.

4.2. Desorption kinetics and reversibility

The study of the desorption kinetics of proteins and macromole-cules can also be used to elucidate the energy of the adsorbed layer.For example, the desorption of PEO/PPO/PEO was studied [53,54]; itwas shown that these macromolecules are kinetically irreversible onthe timescale of available experiments; see Fig. 11 for representativedata of dynamic surface tension versus time during subphase washoutusing the CCPD method.

Desorption kinetics of different proteins, -casein and -lacto-globulin were studied as a function of the initial surface concentrationof protein. Adsorption layers were prepared by adsorption from

Fig. 10. Dynamic surface tension of PEO/PPO/PEO. a) C1,=6.4107 mol/L; exchangeRE=0.5 L/s () and diffusion only (). b) C1,=1.6107 mol/L; exchangeRE=0.5 L/s and diffusion only.

protein solutions of different concentrations and the kinetics and

the competition between desorption and degradation at longertimescales.

4.3. Competitive adsorption and displacement

Mixtures of proteins and low molecular weight surfactants areapplied in many practical systems due to favorable propertiesachieved by the synergist effects [4]. Small surfactants adsorb rapidlyand provide interfaces low interfacial tension for emulsication orfoaming processes, and the proteins adsorb more slowly and form arather stable layer preventing systems from coalescence.

A number of studies on mixed proteinsurfactant systems towhich a broad spectrum of experimental characterization techniqueswere applied are summarized in Reference [4]. The CCPD methodallows for a quantitative comparison of the properties of adsorptionlayers fabricated via sequential (component by component) andsimultaneous adsorption (from a mixed solution).

Experimental protocol and results from mixed -casein/C12DMPO(non-ionic surfactant) and mixed -casein/DoTAB (cationic surfac-tant) systems are in detail in References [56,57]. Although theadsorption isotherms of these mixed layers obtained in the twodifferent ways are very similar, after subphase exchange theirequilibrium states are substantially different due to differences inthe composition. Figs. 13 and 14 present the measured dynamic

Fig. 11. Desorption of PEO/PPO/PEO; C1,=9.5107 mol/L. Surface tension () anddrop area (solid line) vs. time. It is assumed to be kinetically irreversible onexperimental timescales observed.

37J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947extent of desorptionwere studied [34]. It was found that desorption ofproteins from liquid interfaces depends on the conditions underwhich they have been adsorbed. At low concentrations, theadsorption process takes a relatively long time and the moleculeshave enough space and time to adsorb and unfold at the interface. Inthe case of higher bulk concentrations the adsorption is faster and theadsorbing molecules strongly compete with each other from thebeginning of the process. Fig. 12 shows representative data for -casein supporting that rate and extent of desorption for proteinsolutions are a function of surface coverage. It was observed that at allconcentrations and for both proteins, only a small fraction of theadsorbed molecules desorbs. Additionally, the surface tension changeis little, which suggests irreversible adsorption. This nding wascontradictory to other results in literature [55], therefore, additionaltheoretical analyses were performed. These showed that the relativedesorption for proteins is 104108 times slower than that for usualsurfactants. Hence, experiments performed on timescales O(104 s) areunable to discriminate between the reversibility and the irreversibil-ity of adsorbed proteinmolecules; additional complications arise fromFig. 12. Desorption of -casein with varying monolayer concentrations: comparison ofdesorption kinetics from adsorption layers formed from C1,=5108 () 1107

() 5107 () mol/L; RE=0.2 L/s.surface tensions during the bulk exchange with buffer solution(washing-out) of a pendant drop with mixed -casein/C12DMPOadsorption layers (increasing concentrations of C12DMPO) built upwith sequential and simultaneous adsorption, respectively. Surfac-tants are able to displace/replace proteins from the surface because oftheir high surface activity, high concentration, and ability to modifybiomacromolecules, especially in the adsorbed state. Note that bysubphase exchange, surfactants and small amphiphiles can becompletely removed from the airwater interface due to their lowadsorption energy. Additionally, protein/surfactant complexes of lowsurface activity, i.e. anchored at the interface via only a few adsorbedsegments, also desorb easily. However, free protein molecules notdisplaced by the surfactant, remain in the surface layer. Increasingconcentration of C12DMPO used during the assembly of the mixedlayers leads to increasing amounts of displaced/replaced proteins,shown by signicantly lower surface tensions after the adsorptionprocess and much higher values after the subsequently performed

Fig. 13. Dynamic surface tensions during the dropbulk exchange process with buffersolution (washing-out) after simultaneous adsorption experiments with differentC12DMPO concentrations (A: 5106 mol/L; B: 105 mol/L; C: 3105 mol/L;D: 4105 mol/L; E: 5105 mol/L; F: 8105 mol/L) and a xed -casein

6concentration of 10 mol/L.

nanocomposites with well-dened composition, architecture, andprocessing conditions is possible. There are two essential prerequi-sites: 1) a driving force for interfacial assembly and 2) a kinetichindrance to disassembly; i.e. slow desorption kinetics. There alsoexists an ancillary requirement; 3) the constituents of the compositeshould partition relatively weakly to the solid interfaces contacted bythe exchange liquid in the experimental set-up to prevent large scalefouling. These requirements are addressed for representative systemsof strong polyelectrolytes, weak polyelectrolytes, and protein-basednanomembranes.

5.1.1. Strong polyelectrolytesStrong polyelectrolytes possess high degree of counter-ion

dissociation and are therefore highly soluble in aqueous systems.This satises 3) but necessitates an electrostatic template at the airwater interface. For this, a monolayer of insoluble moleculespossessing a charged headgroup must be spread on the surface ofthe drop, and the lm is brought to the desired state of compressionand therefore surface charge density by varying the drop volumeusing microsyringe (M1). A number of different phospholipidmonolayers [9,19,74] have been demonstrated to endure the process

38 J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947washing-out process. At the highest surfactant concentrations, thesurface tension of solution does not reach that of the pure bufferbecause of the (small amount) of protein remaining at the airwaterinterface. The exchange experiments demonstrate that in sequentialadsorption, proteins and surfactants interact only in the adsorptionlayer. In this case, the surface tension reaches much higher values inFig. 13, i.e. protein displacement by surfactant was more effective ascompared to the replacement from a layer formed via simultaneousadsorption in Fig. 14. Surface dilational rheological experiments withmixed -casein/C12DMPO and -casein/DoTAB adsorption layersconrmed this nding.

5. Soft interfacial nanocomposites and nanomembranes

Soft surface nanocomposites have scientic and practical applica-tions spanning elds from electro-optical [5861] and mechano-sensitive materials [6264] to biofunctional surfaces for the stimula-tion of cell proliferation, differentiation, and gene expression [6571].

Ultrathin surface materials can be categorized according to thenature and strength of bonding forces by which they are formed, andstrategies ranging from physical forces such as electrostatic and

Fig. 14. Dynamic surface tensions during the dropbulk exchange process with buffersolution (washing-out) after simultaneous adsorption experiments with differentC12DMPO concentrations (A: 5106 mol/L; B: 105 mol/L; C: 3105 mol/L;D: 4105 mol/L; E: 5105 mol/L; F: 8105 mol/L) and a xed -caseinconcentration of 106 mol/L.hydrophobic interactions to interfacial chemistry can be employed,see References [72,73] for examples. In this section we discussprerequisites for nanomembrane fabrication using the coaxialcapillary pendant drop method and describe experiments includingadsorption to insoluble monolayers by non-ionic macromolecules,electrostatic templating and layer-by-layer assembly of polyelectro-lytes, and representative interfacial covalent crosslinking chemistry ofpolysaccharides, peptides, and proteins. Particularly, we reviewresults for polyelectrolyte multilayer assemblies including poly-(styrene sulfonate) (PSS) with poly-(allylamine hydrochloride)(PAH) or poly-(acrylic acid) (PAA), hyaluronic acid (HA)poly(L-lysine) (PLL), and brin-based nanomembranes. Strategies for metrol-ogy and materials characterization are also described. In most cases,electrostatic complexation, hydrophobic association, or covalent cross-linking at the airwater interface leads to the formation of supramo-lecular networks which confers mechanical rigidity that is outside thedescription provided by equilibrium surface thermodynamics; i.e. Gibbselasticity. A continuum framework for data analysis is described.

5.1. Prerequisites for interfacial nanocomposite synthesis

The CCPD method permits subphase exchange with a relativelylow convective disturbance to the interface, therefore fabrication ofunder a wide range of experimental conditions, viz. monolayer lmpressure, drop volume, and exchange ow rate see Fig. 15.

After the monolayer is deposited and brought to the desired stateof compression, the subphase of the drop is then exchanged with asubphase containing a polyelectrolyte of opposite charge to the lipid.Alternate cycles of polycation (PC) and polyanion (PA) and intermit-tent rinsing with aqueous monovalent electrolyte result in afreestanding polymeric nanocomposite with a thickness dened bythe number of adsorbed layers; see Fig. 16.

This sequential assembly of oppositely charged strong polyelec-trolytes at the airwater interface results in nanocomposites of well-dened composition and transverse dimension. The free energychanges as measured by ADSA during the adsorption cycles can beused to provide information on the dynamics of structure formation inthe nanocomposite, as shown in Fig. 17. Further details of adsorptiondynamics are reported in Reference [20].

5.1.2. Weak polyelectrolytesWeak polyelectrolytes have a solution chemistry-dependent

degree of dissociation; therefore under some conditions aqueoussolubility is considerably less than for strong polyelectrolytes. Thispresents an experimental difculty associated with 3). Additionally,changing solution conditions between alternate layers can result in

Fig. 15. Surface pressure isotherm of l-DPPC: monolayer surface pressure versus area

per molecule; effect of surface coverage and rate of exchange.

desorption and simplex formation as shown below in Fig. 18. Thesurface tension increases concomitant with PAH (pH=6.0) adsorp-

macromolecular adsorption at soft surfaces. One of the difculties in

Fig. 16. Schematic of freestanding asymmetric polyelectrolyte nanomembranefabrication at the airwater interface using lipid templating.

Fig. 18. Desorption of polyelectrolyte monolayer and simplex formation. Surface tensionversus time for (dis)assembly of weak polyelectrolyte bilayer: DMPG(PAH/PAA)1.CPAH,=1mg/mL, CPAA,=1mg/mL; RE=0.2 L/s; pH=6.0 for PAH; pH=9.0 for PAA;CNaCl=0.5 mol/L. Surface tension during DMPGPAH adsorption (), NaCl wash (), andDMPGPAHPAA adsorption (). Solid line is the drop area.

39J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947tion as in Fig. 17. However, after exchange with PAA (pH=9.0), thereis a decrease in surface tension that is consistent with PAA/PAHsimplex formation and desorption. Because the surface equation ofthe state of the insoluble layer is very sensitive to small impurities, thesurface tension of the interface during compression and expansioncan serve as an indicator of polymer adsorption. Fig. 19 shows theexpansion and compression of the lipid monolayer before and aftercontact with the polyelectrolyte solutions. The complete reversal ofPAH adsorption underscores the notion of the reversible nature of theadsorbed polymer layer as well as the importance of maintainingconstancy of solution chemistry, which is well known in any layer-by-layer assembly of weak polyions [75,76].

5.1.3. Protein and biomacromoleculesProtein, virus, or reactive nanoparticle-based nanomembranes

[77,78] can be synthesized by covalent network formation throughnon-specic, viz. using divalent complexing agents such as Ca++,polycondensation reactions, or biochemically specic reactions, suchas the cleavage of brinogen by thrombin to form brin bers [79].Because most proteins have large surface afnity and low rates ofdesorption, the uid interface can be used to template the transverseconnement required to produce a nanomembrane. When thekinetics of desorption are a priori unknown, they can be measuredusing methodology outlined in Section 3.2; see for exampleFig. 17. Surface tension versus time for the assembly of strong polyelectrolyte bilayer:DMPG(PAH/PSS)1. CPAH,=1 mg/mL, CPSS,=1 mg/mL; RE=0.2 L/s; pH=6.0;CNaCl=0.5 mol/L. Surface tension during DMPGPAH adsorption (), NaCl wash(), and DMPGPAHPSS adsorption (). Solid line is the drop area.studying lipidpolymer interactions by adsorption onto a monolayerat the airwater interface is the ambiguity in the initial condition ofthe mixed monolayer. Previous studies, for example as in Reference[83], investigated the mixed monolayer by rst spreading the lipidonto a Langmuir trough containing a subphase free of polymer andrepresentative data for brinogen in Fig. 20. In this case, adsorptionis driven by the hydrophobicity of the reactants satisfying 1); howeverin some situations, condition 3) is problematic, particularly when thesubphase is not completely exchanged.

5.2. Adsorption of non-ionic polymers to lipid monolayers

Non-specic adsorption of macromolecules at soft and solidinterfaces represents a wide range of technologically importantproblems ranging from immunoassay specicity [80] to reverseosmosis membrane ltration fouling [81,82]. In the eld of surfacescience, understanding the kinetics of adsorption and equilibration atsoft interfaces remains a largely unsolved problem. An insoluble lipidmonolayer spread at the airwater interface can be used as arepresentative system to study both the kinetics and structure ofFig. 19. Phospholipid monolayer expansion/compression isotherm and equation ofstate before and after disassembly of strong polyelectrolyte (PAH) monolayer bysequential adsorption of (PAA). Surface tension during dilation of DMPG only () andafter DMPGPAHPAA adsorption (). Solid line is the drop area.

Fig. 21. Adsorption of the triblock polymer onto the lipid monolayer. Surface pressureversus lipid area per molecule for l-DPPC and PEO/PPO/PEO (C1,=2.4105 mol/L).Exchange rate RE=0.2 L/s. PEO/PPO/PEO (); PEO/PPO/PEO adsorption onto l-DPPC(). Solid line is the l-DPPC alone.

40 J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947subsequently injecting a concentrated polymer solution into thesubphase below the lipid monolayer. In this case, the polymer mustdiffuse to uniformity in the bulk to reach adsorption equilibrium.Spreading the lipid on a subphase of the polymer solution is alsoprecluded because the preexisting adsorbed phase lowers the surfacetension and attenuates the Marangoni effect by which homogeneousspreading of the lipid is accomplished.

The CCPDmethod can be used to study the equilibriumpenetrationof a wide variety of polymers and copolymers into phospholipidmonolayers as a function of polymer bulk concentration. Uniformadsorption of polymer onto the lipid is achieved by rst spreading theinsoluble monolayer onto the pendant water drop and replacing theoriginal subphase for a polymer solution. Compression isotherms canbe used to gain insight into the large deformation response of themixed system and controlled studies of the response of the interfacialtension to periodic area perturbations can be used to obtain thedilational rheological parameters of the interfacial layer and providesinformation about the rate of exchange of matter between the surfaceand the subphase and the relaxation kinetics in the monolayer.

Fig. 21 shows representative data for the adsorption of the PEOPPOPEO copolymer onto a DPPC monolayer. Here, it can be seen that

Fig. 20. Kinetically irreversible adsorption of brinogen at airwater interface. Surfacetension () vs. time for brinogen (C1,=1mg/mL; 10 mM Ca++). Desorption drivenby complete subphase exchange with pure water. Solid line is the drop area.the surface pressure of the penetrated monolayer is approximatelythe same as for adsorption of the polymer only. This is due to therelatively low surface pressure of the preexisting monolayer; the lipidis in the liquid expanded state. However, as the lipid molecular area isdecreased by compression, the surface pressure increases in a waythat is consistent with squeeze-out of the polymer from the lipidmonolayer. This implies reversible adsorption of the polymer andsuggests that the desorption timescale for the same copolymer at theairwater interface shown in Fig. 10 is much longer than theexperimental observation. It is also possible to measure theviscoelasticity of the interfacial nanocomposites prepared using thismethod; data for the PEO/PPO/PEODPPC system suggests someinteraction between the lipid and the copolymer in the adsorbedlayer; see Reference [19] for details.

5.3. Electrostatic assembly of asymmetric nanocomposites of strongpolyelectrolytes

Ultrathin freestanding polyelectrolyte lms have recently receivedincreasing attention due to their potential use as micromechanicalsensors, actuators, and barrier materials [8486]. An increasingnumber of experimental results have shown that thin lms exhibit asignicantly different behavior as compared to bulk materials, i.e.transport, glass transition, and stress to failure, although themechanisms responsible for these phenomena are still not fullyunderstood.

Recently, the CCPD method was used to fabricate and characterizethe mechanics of strong polyelectrolyte multilayers as described inSection 5.1.1. Fig. 22 shows the mechanical response of strongpolyelectrolyte multilayers as a function of thickness and the surfacetension response of strong polyelectrolyte nanomembranes DMPG(PAH/PSS)n under dilation and compression. It is shown that strongpolyelectrolyte nanocomposites are likely to be elastomeric structuresthat stretch semi-reversibly upon large deformation with an increas-ing dependence of the lm surface elastic modulus on lm thicknessand template charge density; see Reference [87] for details.

The effect of strong polyelectrolyte molecular weight and solventionic strength on the elastic modulus of the nanomembrane was alsostudied by Cramer and Ferri [88]. Fig. 23 shows the dependence ofsurface and bulk elastic moduli on anion (13 kDa and 70 kDa)molecular weight and salt concentration. For either molecular weight,there is a transition corresponding to a decrease in elastic modulusdemonstrating a saloplastic effect [89]. A lowering of the yield stressand a decrease in the surface elastic modulus were also observed forFig. 22. Mechanics of strong polyelectrolyte asymmetric membranes at airwaterinterface. Synthesis conditions: C1,=1mg/mL; CNaCl=0.5 mol/L; exchange rateRE=0.2 L/s. Surface tension and drop areas versus time for DMPG(PSS/PAH)n;n=1 (), 2 (), 3 (). Solid line is the drop area.

increases in ionic strength. The bulk elastic modulus E is related to thesurface elastic modulus Es via E=Es/h where h is the nanomembranethickness. Additionally, it was reported that for strong polyelectrolytemultilayers out of plane coupling is limited to about two layers. Themagnitude of the elastic modulii found for strong polyelectrolytes isconsistent with elastomeric rubbers. For such materials, some degreeof a reversibility and viscoelastic response would be expected; bothwere experimentally observed [87]. Studies of other polyelectrolytenanomembranes using CFT at the airwater interface are reported inReferences [90,91].

5.4. Polysaccharides, peptides and weak polyelectrolyte assemblies

Strong polyelectrolytes have a high degree of dissociation andtherefore interlayer interactions are stronger; lm growth is linear inthe number of layers. Weak polyelectrolytes have a lower degree ofdissociation and weaker interlayer interactions, consequently the lmgrowth is exponential in the number of layers [92]. The mechanicalproperties of weak polyelectrolyte multilayers have been studied by avariety of techniques [9396].

among biopolymers [79,100,101]. The surface stress response to

Fig. 24. Surface tension (symbols) and drop area (solid line) versus time for DMPG(PAH/PSS)2 () and DMPG(PLL/HA)2 (). Solid line is the drop area.

Fig. 25. Surface tension and drop area versus time for DMPG(PLL/HA)2 () and

41J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947Differences in the mechanics of strong and weak polyelectrolytelms as studied by the CCPD method are manifold. Consider the datashown in Fig. 24 which compares the surface tension response todilation for two bilayers (n=2) for strong (PSS/PAH) and nanocompo-sites for weak polyelectrolytes hyaluronic acid (HA) and poly(L-lysine)(PLL). The strong PE pair exhibits a linear (elastic) relationship betweenstress and area for up to 10%areal dilation. Theweakpolyelectrolyte pairshows plastic ow over a relatively low deformation.

The surface modulus of DMPG(HA/PLL)n as a function of lmgrowth was shown in Reference [97] to be approximately constant for(2bnb6) signifying no increase in the surface elastic modulus for anincrease in membrane thickness. A constant surface modulus whichaccompanies increasing lm thickness signies a decreasing bulkmodulus. The decrease was also conrmed independently for (HA/PLL)n using the colloidal probe AFM technique in Reference [67].

The mechanical strength of the membrane can be modied viapolycondensation of HA and PLL to form an interlayer amide. Fig. 25shows surface tension as a function of deformation for DMPG(HA/PLL)2 as assembled and after covalent crosslinking.

Fig. 25 demonstrates that the surface tension (i.e. stress response)of the interface during dilation exceeds the limit as dened for a Gibbssurface layer. That is, when the surface tension is a function of thesurface density of adsorbed species only, the surface stress has anupper bound of the surface tension of the pure solvent subphase;

Fig. 23. Effect of solvent strength on the elasticity of strong polyelectrolytenanomembranes. Surface modulus Es (N/m) () and bulk modulus E (MPa) () of

DMPG(PSS/PAH)3 as a function of aqueous sodium chloride concentration.o=72 mN/m for airwater. As can be seen in the surface stressresponse for the crosslinked and non-crosslinked HA/PLL (n=2), thecrosslinked membrane displays elastic behavior over a signicantlywider range of strain and also demonstrates fracture. Additionally,Fig. 26 shows the increase in the deviation from the YoungLaplaceequation with increasing dilation which occurs for the crosslinkednanomembrane. This systematic deviation from the YoungLaplaceequation suggests that a fundamental assumption of the Laplaceequation is violated as deformation increases; see Section 5.6 fordiscussion and alternative framework for drop shape analysis forelastic nanomembranes.

5.5. Proteins and nanobiomembranes

Recent developments in producing biocompatible materials haveenabled numerous demonstrations that cells can be extremelysensitive to changes in the mechanical properties of their substratesunder chemostatic conditions [98]. Proteins perform a diverse array oftasks in living cells, including signal transduction, metabolic andcatalytic functions, and mechanical support [99]. Because mechanicalforces can lead to protein domain deformation and unfolding, this isan important subject in molecular biomechanics.

The viscoelasticity of the protein brin is unique and remarkableDMPG(PLL/HA)2 after crosslinking () for 12 h under constant drop area.

ination of brin nanomembranes was investigated. Fig. 27 compares

Fig. 26. Deviation from the YoungLaplace versus drop area for the deformation ofDMPG(PLL/HA)2 () and DMPG(PLL/HA)2 after crosslinking ().

42 J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947Progress in the understanding of the mechanical performance ofnanomaterials fabricated atmesoscopic size has been limited due to thelack of suitable instrumentation and methods; particularly because themetrology of nanomaterials at intermediate (104b lb102 m) lengthscales is difcult to access. Therefore, the elaboration of bothexperimental methodology and theoretical framework for theirinterpretation is of signicant importance in advancing both the sciencethe surface tension during deformation of a brinogenmonolayer anda brin nanomembrane at the airwater interface. As in Fig. 25, thesurface tension exceeds that of the pure solvent o which demon-strates the impact of covalent structure on interfacial stress response.The non-linear nature of the surface stress as a function of strain andthe absence of fracture also illustrates the role of internal structure onmaterial response.

5.6. Metrology of nanomembrane mechanics: elasticity and constitutivebehaviorFig. 27. Comparison of the interfacial stress response of native brinogen () beforeand after biochemical crosslinking with thrombin () to form a brin nanomembrane.Synthesis conditions are Cbrinogen,=1mg/mL; Cthrombin,=20 units/mL; 10 mmol/LCaCl2. Surface tension of native brinogen () and after biochemical crosslinking withthrombin () during drop dilation. Solid line is the drop area.and technology of mesoscopic materials transversely constrained tomolecular and supramolecular dimensions.

Although there have been advances in nanomaterials character-ization based on compressive loading [102,103], this section isrestricted to a review of the theoretical framework for a two-dimensional (i.e. ultrathin) nanomembrane of a linearly elasticcontinuum of arbitrary, axisymmetric curvature under tension. Seefor example Reference [104] for further details.

Consider an axisymmetric curved elastic membrane subject to aninternal pressure, for example a pendant drop. A point on themembrane is characterized by the cylindrical coordinates (r, , z) andthe surface coordinates (, ). The undistorted state is given byaxisymmetric shape, which can be expressed as r0(z0) or 0(z0). Whensubjected to a tensile load such as ination, this shape deforms. Themotion of a point during a rotationally symmetric ination can beexpressed as r(z0) and z(z0) or (z0) so that knowledge of thesefunctions species the shape of the membrane in the deformed state.The surface coordinate 0 is related to the cylindrical coordinates (r0,z0) by d0 =

r20 z0 + 1

qdz0, where the prime denotes differentia-

tion with respect to z0. Similarly, in the deformed state, the surface

coordinate (z0) is related to the cylindrical coordinates r and z by

d z0 =r 2 z0 + z2 z0

qdz0. Therefore, the stretches of the mem-

brane in the directions of the surface coordinate lines are:

1 =d z0 d0 z0

=

r2 z0 + z2 z0

qr20 z0 + 1

q

2 =r z0 r0 z0

5:1

where the subscript (1) denotes an extension in the surface direction and the subscript (2) denotes an extension in the surface direction .

As the dilation of themembrane proceeds, surface stresses developin the membrane in response to its stretching. For isotropic materials,the stretches and stress are collinear. In linear elasticity, the physicalcomponents for the stress tensor T11=T1 of the membrane are

T1 =Gs

1s211 + s

221

h i5:2

where surface stress in the orthogonal direction (2) is obtained byexchanging of indices (1) and (2).

The local force balance in the membrane requires that thedivergence of the stress in the membrane equals the jump of pressureacross it. The force balance has two tangential components and onenormal component. The normal and the tangential () components ofthe force balance are

T11

1 r

2s 1 r

+ T21r

1 r

2s= p

T1z0

1rrz0

T2T1 = 0

5:3

and the tangential () component is identically satised. The pressurejump [p] across the membrane arises from hydrostatics, i.e.p = p 0 + gz z0 .The geometric and constitutive relationships can be substituted into

the equations of equilibrium to form a coupled system of non-linearpartial differential equations for the deformed shape of the droplet;namely r(z0) and z(z0). For purely elastic surface materials, Eqs. (5.1)through (5.3) form coupled two point boundary value equations which

can be converted to initial value problems by appropriate substitution.

properties such as constitutive behavior and structurepropertyrelationships in soft surface materials. Comparable methods whichrely on small amplitude perturbation to extract parameters such aselasticity, see for example Reference [24], are incapable of describingbehavior observed under large deformation; typically surface strainsEsi =

12

2i1

b0:1. Although the strain eld of the pendant drop

ination is not strictly isotropic, this approximation signicantlysimplies data reduction; the constitutive law for the extra surfacestress in linear elasticity is = Gs 1 + s1s

21

or simply = K AA0 .ADSA measures the total surface stress S; the extra surface stress can be found by assuming ()=eq, or the surface tension of theinterface in the undeformed state, and subtracting.

First consider the constitutive behavior of the nanocompositeDMPG(PAH/PSS)2 for tensile loading and unloading shown iscompared to DMPG alone in Fig. 28. In the gure, an initial region oflinear elasticity (constant K) can be seen followed by yielding and atransition to plasticity. The dilational modulus of the lipid alone isconstant for the entire deformation. In each experiment, the drop areais held constant after reaching an areal dilation of 60%. It can also benoted that a stress relaxation is observable for the polyelectrolyte

43J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947Solutions of these equations yield p(z0), 1(z0), 2(z0), T1(z0), T2(z0),and most importantly the deformed conguration r(z0) and z(z0) as afunction of the constitutive parameters, c.f. Gs and s in Eq. (5.2). Notethat as a consequence of elasticity, all dependent variables are afunction of the initial conguration, i.e. z0. Comparison of r(z) tomeasured ination proles form the basis of an inverse method todetermine the constitutive parameters of the nanomembrane.

For purely viscous interfaces, the surface stress is isotropic andindependent of history. Now, the shape of the drop depends only onthe thermodynamic surface tension and the pressure jump across theinterface, i.e. r=r(z) only not z0.

In this case, the momentum balance reduces to the YoungLaplaceequation:

r z r z

2r z z2

r z z 2

1" #

1 +r z z

2" #32= p 5:4

where is the surface tension, r(z) is the shape of the drop in thedeformed conguration, and [p] is the pressure jump across theinterface. Solution of Eq. (5.4) has been extensively documented [24].

Accordingly, there are different mechanisms of interfacial elastic-ity. For a liquid interface, the isotropic surface stress is a function ofsurface excess concentration, []. Dilation of the interface results in alocal or global dilution of the surface excess concentration . The Gibbsadsorption equation species that as surface excess concentrationdecreases, surface tension increases. For liquid interfaces, the Gibbs

elasticity EG = lnA relates changes in surface tension to changes in

area, i.e. deformations which dilute the surface excess concentrationare resisted. Controlled perturbation of the liquid interface can beused to measure the complex modulus E, which contains bothstorage (surface equation of state) and dissipation (interfacialtransport and relaxation kinetics) contributions [105109].

For a solid interface, the surface stress is related to the strainenergy which describes the intrinsic capacity of the material to storeenergy and the deformation history of the material. The isotropicmembrane stress = 12 T1 1;2 + T2 1;2 is the average of thetwo principle stresses from Eq. (5.2).

Fluid interfaces which support ultrathin soft nanocomposites candisplay liquid and solid-like mechanical responses. The total interfa-cial stress in surface direction 1, S1, can be written as the sum of thethermodynamic surface tension and the membrane contribution, i.e.S1 = + T1 1;2 . This approach was recently used to separatesurface tension effects from nanomembrane contributions in Picker-ing emulsion deformation; see Reference [77] for details.

The total isotropic surface stress measured by ADSA is the result ofboth contributions as shown in Eq. (5.5).

S = + 1;2 5:5

For isotropic materials, when the principle stretches are approx-imately equal (12), the principle stresses are equal; theapplication of ADSA for interfacial stress measurement is reasonable.

It should be noted that because all materials are viscoelastic, themacroscopic behavior depends on the ratio of the timescale forinternal relaxation R and the timescale of an experimental observa-tion O known as the Deborah number, De=R/O. For De1macroscopic behavior is elastic, for De1 it is viscous, and for De~1it is viscoelastic. Therefore, the difference of applicability betweenEqs. (5.1)(5.3) and Eq. (5.4) to describe the shape and state of stressof the interface arises not from the difference between solids andliquids, but rather the capacity of the interface to support a non-zerodeviatoric stress =S1S2.

The CCPD method can be used to prepare liquid-supported elasticnanomembranes (i.e. asymmetric nanocomposites), and this set-up in

conjunction with ADSA can be used as a test frame to study materialnanocomposite but not for the lipid alone. By rescaling the surfacestress according to the equilibrium relaxation,

t 0eq0

, the relaxation

time constant for a simple Maxwell model, E=E0e( t/) can bebounded by the experimental data; see Fig. 29. These results suggestthat more complicated expressions for linear or non-linear viscoelas-ticity may apply.

The recoverable energy during deformation can be calculated fromthe loading and unloading curves as measured during ination anddeation. Fig. 30 shows the evolution of average extra surface stressduring loading and unloading for the DMPG(PSS/PAH)3 as a functionof surface dilation. The plasticity index, = ACBC

AC, can be used to

describe the fraction of the deformation that is irreversible and cangive insight into the internal structure of the nanomaterial. In thiscase, the plasticity index is 0.30, indicating that 30% of thedeformation is unrecoverable. The impact of processing conditions,for example solvent annealing, and polyelectrolyte molecular weighton elastic modulus, yield stress, and plasticity as discussed further inReference [88].

The extra surface stress as a function of surface strain for a brinnanomembrane is shown in Fig. 31. It can be noted that the strain-stiffening effect gives rise to a dilational modulus of the form K=K0exp[(/)/0]; for these data K04.5 mN/m and 00.14. Thehyperelastic material response can also be noted in this case; b0.05.See Reference [97] for further experimental details.

Fig. 28. Extra surface stress versus areal dilation for DMPG(PAH/PSS)2 () and DMPG

only ().

and separate intrinsic surface mechanics from the kinetics effects that

Fig. 29. Surface stress relation versus time for DMPG(PAH/PSS)2 (): experiment andtheory (simple Maxwell model) for =10, 25, and 40 s. Surface stress during relaxation() vs. time. Solid lines are the theory for differing characteristic relaxation times(=10, 25, and 40 s).

Fig. 31. Constitutive behavior for protein-based nanocomposite: hyperelasticity andstrain-stiffening in extra surface stress versus areal dilation for brin nanomesh;h70 nm; preparation conditions are the same as in Fig. 27. Loading () andunloading ().

44 J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947The effect of internal molecular structure on nanomembranestress response and constitutive behavior is apparent. Fig. 32compares the extra surface stress and deviation from the GaussLaplace equation for the crosslinked linear biopolymers and theprotein-based membrane. Interestingly, the low deformationmodulus of both nanomembranes is approximately the same;only large deformation is able to discriminate between the differentmaterials. Although the specic origin of the strain-stiffening effectis unclear (either due to protein tertiary molecular structure orsuperstructure of the brous mesh itself), the difference issignicant.

6. Future directions

Continuation of investigations of surfactant and protein adsorp-tion kinetics and reversibility is relatively straightforward, howeverthe CCPDmethod provides access to a fairly wide range of systematicinvestigations on the mechanics of well-dened nanocompositesand structureproperty relationships for materials beyond thosedescribed in Section 5. Additionally, studies of diffusion and

molecular transport in these materials should also be accessible

Fig. 30. Plasticity in the strong polyelectrolyte nanomembrane DMPG(PSS/PAH)3under large deformation: loading (AC) and unloading (CB) hystereses in extra surfacestress versus areal dilation.arise due to the dynamics of adsorption between the interface and thebulk that occurs at the elevated bulk concentrations typically requiredusing the CCPD method. A brief outline of both types of experimentsis also provided.

6.1. Physicochemical mechanics of surface materials: surface elasticmodulii of surfactants, macromolecules, nanoparticles and theircomposites

Both sequential and co-adsorption provide means to fabricatesurface materials of well-dened composition and morphology;Fig. 33 illustrates permutations between some of the basic buildingblocks available for surface modication. In many cases, the interfacecan be designed to be a kinetically irreversible structure which canprovide engineered functionality for a variety of applications, many ofwhich are referenced in the preceding sections. Because the subphasecan be effectively exchanged using the CCPD method, it is possible tomeasure dilational modulii of interfacial nanocomposite materialsFig. 32. Comparison of the impact of covalent intramembrane nanostructure:nanomembrane of crosslinked linear polyelectrolyte DMPG(HA/PLL)2 () and brin(): extra surface stress and deviation from GaussLaplace equation versus arealdilation. Solid lines are the sum of the error between the observed shape and GaussLaplace equations.

surface equations and state and transport; polymer and soft nanocomposites; nanoparticles

45J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947for fabrication. A wide variety of constitutive behavior such as thosedescribed in Section 5 would be directly accessible.

6.2. Diffusive transport through nanocomposite surface materials

Fig. 33. Surface mechanical properties of interfacial nanocomposite materials: surfactantand nanoparticle composites.Interphase transport phenomena remain a relatively unex-plored area in interface science [110112]. Fick's law is thesimplest constitutive law that describes molecular transport; itrelates the ux of a material through a continuous medium to theconcentration gradient of that material and its transport coef-cient. For the transport of small solutes through the nanocompositematerials shown in Fig. 33, the continuum approximation may bereasonable; this requires the characteristic length scale of thesolute l(A) to be much smaller than the transverse dimension ofthe interface h.

The rate of transport of A per interfacial area (or simply ux of A)through the interface (i) in dilute limit is given by

NA = DA;iCAr 6:1

where NA is the ux with respect to a xed frame of reference, i.e.the drop interfacial area S, DA,i is the diffusion coefcient of species

A through the interfacial composite, andCAr is the concentration

gradient normal to the interface. The gradient can be written interms of the concentration in the () phase CA, the concentrationin the () phase CA, and interface thickness, h, using CAr

CB CA

h .This approximation attributes all resistance to mass transfer to theinterface; however boundary layer effects in both phases may beeasily included.

For interphase transport, the driving force must be adjusted toreect the difference in solute partitioning between phases;C*

;A = f C

A

CA where CA

*, is the () phase concentration inequilibrium with the () phase concentration and f CA

is the

thermodynamic function that describes equilibrium partitioning

Fig. 34. Interphase transport through interfacial nanocomposite materials: a) solventpermeation, b) solute permeation and interphase transport, and c) nanomembranepermeability and dialysis.

46 J.K. Ferri et al. / Advances in Colloid and Interface Science 161 (2010) 2947of species A between the () and () phases. Substitution intoEq. (6.1) yields an expression for the permeability of theinterface p:

p =NA

CAC*;

A

6:2

where p is the product ofDA,i and h. For a given interfacial composite, pis an intrinsic material property. Therefore, it provides additionalinformation concerning the internal structure of the material, as wellas itself being a technologically relevant parameter.

Fig. 34 summarizes a variety of experiments which can bedesigned to assess the transport of solvents and soluteswith relativelylarge gas phase solubilities, interphase transport of solutes which aremutually soluble in immiscible phases, and solutes which are solubleonly in a single (for example aqueous) phase.

6.3. Closure

Subphase exchange in pendant drops provides a means to tailordriving forces for adsorption and desorption in uiduid systemsand in some cases, fabricate surface materials of well-denedcomposition at these interfaces. Since a complete exchange canalways be attained, the CCPD method opens a wide variety ofexperimental possibilities, previously not achievable with moretraditional methods, including a new framework for assessingmechanics and transport of soft surface materials.

Acknowledgments

This workwas nancially supported by projects of the DLR (50WM0640 and 0941), the DFG SPP 1273 (Mi418/16-2), and the NSF(CMMI) Award 0729403.

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