Interfacial Separation of Particles (Studies in Interface Science)
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It is negligible for colloidal microparticles, whilst it has a nonnegligible role in controlling the attachment energies of nanoparticles to the fluid interfaces. Thus, the contributions of the line tension to the particle attachment at fluid interface become important in the nanoscale due to the role of several aspects such as the heterogeneity in surface roughness and chemical nature of the particles in the modification of the wettability of the particles in relation to that of macroscopic surfaces [ 55 , 56 ].
The role of the line tension decreases rapidly with the increase of the particle size as was pointed out by Isa et al.
The line tension decreases the contact angle in relation to that expected for a macroscopic wetted surface [ 60 ]. Furthermore, it is important to consider the important role played for the line tension in the energetic landscape of particle-laden interface, controlling the transition wetting-drying of the particles for the fluid interface [ 60 ], which was also evidenced independently by Bresme and Quirke using molecular simulation [ 61 ]. However, they found values for the line tension that were at least one order of magnitude higher than those obtained previously from experimental data [ 60 ].
This discrepancy might be associated with the different line tension dependence on the surface tension between the fluid phases and the solid, obtained via simulations and experiments. Despite the important role of the line tension on the particles attachment, for the sake of simplicity no further discussion on the role of the line tension will be included [ 62 ].
The complete understanding of the attachment of particles to fluid interfaces requires the evaluation of the energies involved in the process.
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Thus, the total energy associated with the attachment of particles to the fluid interface can be obtained by the difference between the energies of the particle at the interface and in the bulk suspension. For the simplest case that considers small particles attached to an arbitrary interface and small enough for the gravity effects being negligible, the attachment energy, , is given by The sign allows identifying the relative position of the centre of the particle in relation to the interfacial plane.
Indeed, represents the situation of those particles with their centre above the interfacial plane, whereas represents the situation of particles with the centre below the interfacial plane. The formation of interfacial layers of conventional surfactants, the adsorption-desorption equilibrium takes place in time scales ranging between milliseconds and several seconds. However, it is known that the attachment of particles to fluid interfaces can be considered in most cases an irreversible process, being the energies involved in the attachment many times the thermal energy , being the Boltzmann constant and the temperature.
As a consequence, once the particles arrive to the interface they remain trapped in a quasi-2D layer, and only small fluctuations from the equilibrium positions in the direction perpendicular to the interfacial plane are expected due to thermal or capillary deformations of the interface.
This does not mean that once the particles arrive to the interface they remain attached at fixed positions; the real scenario implies the continuous diffusion of the particles along the 2D plane in addition to the small fluctuations above and below the interfacial plane. The reversibility-irreversibility of particles attachment at fluid interfaces was addressed both theoretically and experimentally by Wi et al. However, for smaller particles, a true thermodynamic equilibrium between the bulk phases and the interface is established, with the line tension playing a central role in the energetic landscape.
It is worth mentioning that the role of the reversibility or irreversibility of particles attachment to fluid interfaces is essential for controlling the structure of interfacial assemblies of particles because they have a central role in the particle interactions at the interface and in the layer response to external mechanical perturbations, for example, collision between droplets in an emulsion [ 64 ].
In the last twenty years, several experimental techniques have been developed for the determination of the contact angle of particles at fluid interfaces: This is due to the different assumptions used to calculate the contact angle from the raw data. A detailed discussion of the different methods for the determination of the contact angle of particles attached to fluid interfaces was presented by Maestro et al.
One of the most important problems related to the determination of the contact angle of particles at fluid interfaces comes from the type of contact angle evaluated advancing or receding. Many variables can modify the wettability and consequently the attachment energy of particles at fluid interfaces. The most important of them is probably the HLB of the particles, which is affected by the chemical nature of both particles and of the two phases adjacent to the interface.
This balance can be easily tuned either by physical or chemical medications of the particles surfaces. In the former case, species able to modify the surface activity of the particles e. An alternative method, with increasing interest nowadays, is the fabrication of particles with asymmetrical wettability, the so-called Janus particles [ 4 , 90 , 91 ].
The effect of the particles size on the contact angle of particles is accounted for among the most studied effects. This can be interpreted in terms of a constant contribution of the line tension to the particle wetting once a threshold value for the particle size is reached in agreement with the results by Isa et al. Several authors have pointed out that a decrease of the effective charge density of the particles leads to the increase of the contact angle of the particles [ 77 , 93 ]. The reason is the partial hindering of the electrostatic barrier associated with the repulsion of the particles, which plays a central role in the control of the particle adsorption.
In this context, the differences of dielectric constant between the two fluid phases, and consequently the chemical nature of the fluid interface, determine the attachment of particles at the interface due to the existence of image-particle interactions associated with the presence of particles close to the two-phase boundaries. Thus, electrodipping forces drive the particles towards the phase with higher dielectric constant. The chemical nature of the particles surface plays also a central role in the wettability control. Similar effects were found by chemical grafting of poly glycerol-monomethacrylate chains to polystyrene latex particles.
The wettability of the particles can be also modified by the physical adsorption of surfactant to the surface of the particles as was evidenced by Maestro et al. They pointed out that a complex balance between the hydrophobic and the electrostatic interactions established in the mixed particle-surfactant system governs the contact angle. Thus, the concentration of surfactant in the solution plays a key role in the control of the particle wettability. The results also evidenced that the maximum value for the contact angle of the particles is associated with the neutralization of the particle surface charge by the adsorption of surfactant molecules.
Further increases of the surfactant concentration lead to the rehydrophilization of the particles and consequently to the contact angle decrease. A similar behavior was found by Binks et al. Also, the wettability can be modified by small molecules such as alcohols [ 67 , 91 ]. This latter effect was attributed to the formation of solvent layers onto the particle surface which modify their surface nature and consequently the contact angle at the fluid interfaces.
Following with the role of the particle surface nature on the contact angle of particles at fluid interfaces, it is important to consider the role of roughness and porosity; these two features play a more important role as the particle size decrease [ 21 , 67 ]. The increase of the roughness and porosity of the particles leads to the increase of the contact angle in such a way that can be qualitatively explained assuming a classical Cassie-Baxter model [ 95 ].
This is related to the existence of asymmetric wetting along the contact line, thus defining different pinning-depinning phenomena of the particles at the interface. Furthermore, the roughness and porosity of the particles can influence the adsorption of surface active modifiers onto the particles. Theoretical calculations by Nonomura and Komura [ 95 ] showed that the wetting of particles depends on the interfacial tensions between the particles and the liquid phases, the particle sizes, and the fraction of the surface area of the particle that is in contact with the external liquid phase.
This later leads to the asymmetric wetting of the particles due to their roughness, which can be well described on the bases of the Cassie-Baxter model, especially for those particles with a high roughness. Despite the potential importance of these aspects in the contact angle of particles at fluid interface, no systemic studies on their role have been addressed. Additionally, the effect of the methodology use for the preparation of the particle-laden interface cannot be neglected in the understanding of the contact angle of particles at fluid interfaces [ 39 ]. For those particle layers obtained from the adsorption of the particles from bulk dispersions to the interface, a subtle balance of energies is expected interactions fluid-fluid and fluid-particles , which determines the most probable contact angle of the particles at the interface.
On the contrary, for spread monolayers, the particles are directly deposited at the interface independently of their contact angle. The HLB is one of the most important parameters governing the position of particles at the interface. However, in contrast to that occurring for surfactant in which the HLB determines the portioning of the molecules between the interface and the two adjacent fluids phase, in most cases for particle-laden interfaces once the particles arrives to the interface they remain trapped irreversibly and no partitioning of the particles between the fluid phases can be expected due to the high attachment energies involved, which overcome many times the thermal energy as was discussed above [ 96 ].
Thus, the classical equations of state Langmuir, Frumkin, etc. In order to overcome these problems for the thermodynamic description of the particle-laden interface, new models considering their specific features have been developed in recent years [ 48 , 98 ]. The first attempt to provide a thermodynamic description of particle-laden interface was performed by Binks [ 6 ] on the bases of the Volmer and van der Waals equations. The model considered that each particle behaves as common surfactant molecule.
However, the model fails and provides unrealistic dependences of the surface tension on the interfacial coverage. This is explained taking into account the big difference that exists between the behavior of particles and common surfactant at the interfaces, and the different interactions at the interface.
Additionally, the different length scales for particles and common surfactants are expected to play a key role in the thermodynamic behavior of particle-laden interface, and a correct thermodynamic model must consider this fact. Using several assumptions the model provides an expression for the surface pressure , with being the surface tension of the particle-laden interface and the surface tension of the pure fluid interface -area isotherm [ 48 , 98 ] that reads as follows: Consider that is the so-called cohesion pressure that is related to the balance of energies existing at the interface, depending strongly on the contact angle of the particles at the fluid interface, and accounts for the organization and degree of packing of the particles at the interface.
This model predicts a thermodynamic behavior rather independent of the particle size and the nature, providing a good description for the behavior of both soft and hard particles. Figure 2 shows some examples of the application of the aforementioned thermodynamic model to experimental isotherms.
These results pointed out a rather good agreement between the experimental results and the theoretical model before the collapse of the monolayer at lower areas. However, the validity of this model has been tested with a small number of systems so far. Basically, most of the research focused on the steady state behavior of particle-laden interface is based on surface tension-surface concentration isotherms.
However, this is not easily evaluable for particle-laden interfaces, and only when the particles are directly spread at the interface it is possible to obtain this type of relations. Several authors have given results of the steady state of particle-laden interfaces [ 33 , 43 , 53 , , ]; however a description of the experimental results in terms of theoretical models, such as Frumkin or Langmuir, is difficult and no systematic studies are available.
On the contrary, a theoretical description of the isotherm of the system containing particles is rather difficult. Similar synergetic effect has been observed for other types of mixtures such as protein-surfactant and polyelectrolyte-surfactant systems [ 22 , , ]. It is worth mentioning that the bare silica particles do not present any surface activity and a surface tension value close to that of pure water was found for them independent of their bulk concentration as was discussed previously by Ravera et al.
The comparison of mixed dispersion of PA and silica nanoparticles with this dispersion in which silica nanoparticles are combined with conventional surfactant such as CTAB and DTAB showed strong differences in the ability to produce surfactant decorated nanoparticles depending on the surfactant nature, whereas for CTAB or DTAB decorated silica nanoparticles an almost negligible change on the surface tension for the lowest surfactant concentrations was observed due to the low interfacial coverage; a higher efficiency of PA was found for the preparation of surfactant decorated nanoparticles with interfacial activity [ 33 , 34 , 37 ].
Thus, it is possible to assume that ionic surfactants are less efficient for modifying the hydrophobicity of particles than fatty acids such as PA. Increasing the surfactant concentration, the effectiveness of the ionic surfactant to increase the hydrophobic character of the complexes is enhanced, favoring their attachment at the interface. An additional contribution to the incorporation of the particles to the interface can be associated with the interaction of the hydrophobic tails of the surfactant decorated particles at the interface [ 53 , , ].
The study of the interaction of carbon soot particles with anionic surfactant has pointed out the absence of appreciable modifications of the pure surfactant layer due to the presence of carbon particulates. This is ascribed to the fact that carbon is strongly hydrophobic and the surfactant interaction occurs by hydrophobic interactions, thus leading to the hydrophilization of the particles. The consequence is a depletion of surfactant that is expected from the interface due to its interaction with the particles, but no particle incorporation to the interface occurs [ ]. The results found for carbon soot-anionic surfactant mixtures contrast with those found for silica nanoparticles—trimethylalkylammonium bromides ones.
In this latter case, there is a depletion of surfactant molecules from the bulk dispersion due to their interaction with the particles and the subsequent adsorption onto their surface. Therefore it is expected that only a residual amount of surfactant remains free in the solution [ 33 , 34 ], explaining the decrease of the interfacial tension due to the attachment of particle-surfactant complexes at the fluid interface rather than the adsorption of free surfactant molecules, as it is expected for the aforementioned systems containing carbon soot [ ].
The complex scenario found for the formation of particle-laden layers obtained by mixtures of particles and surfactant contrasts with that found for the formation of layers with polymer grafted particles, where the chemical nature of the polymer chains controls the particle adsorption [ ]. This can affect the synergetic effect of the particle-surfactant interaction as was shown by Santini et al.
In order to obtain a complete description of particle-laden interfaces it is necessary to characterize the morphological and structural features of the interfacial films. Information on these aspects can be obtained by two different approaches: The second one is based on the analysis of the position of the particles with respect to the adjacent phases, which is related to the contact angle of the particles. Several authors have shown that the organization of complexes at the interfacial layers depends on the packing density [ 50 , 52 ] and therefore on the coverage of the interfacial layer.
This can be rationalized considering the effect of the surfactant concentration on the incorporation of the particles to the interface [ 53 ], so that the number and size of the interfacial aggregates increase till the formation of a close packed film. This system showed the formation of isolated particle islands, at the lowest surfactant concentration, that coalesce with the increase of the PA concentration to form a close-packed particle monolayer see Figure 4.
Additional information on the organization of particles at the interface can be obtained from ellipsometry experiments. Similar results were found for the effect of the degree of silanization on silica particles by Zang et al. Thus, it is possible to assume that the wettability of the particles determines their position in relation to the interfacial plane. Their results pointed out clearly that the increase of the surfactant concentration leads to a transition from a low packed film thickness several times smaller than the particle diameter to a closed packed monolayer with a thickness comparable to the particle diameter.
Liquid water at liquid-solid and liquid-gas interfaces behaves as a separate thermodynamic system from bulk water [ ]. Liquid water at interfaces can be investigated using x-ray reflectivity [ ], vibrational sum-frequency generation spectroscopy VSFG [ ] and atomic force microscopy [ ]. Gas at air-water and other gas-water interfaces behaves like a flat hydrophobic surface b with the difference that the van der Waals interactions between the liquid and gas surfaces are negligible.
The surface will be strongly attracted to probes approaching from the gas side at distances of about a micrometer and jumping into contact when still over nm distant [ ], thus showing the long-range nature of the attractive van der Waals forces. Interfacial water absorbs light differently to bulk water with both absorptions at nm [ ] and at nm [ ] being described. The structure of the surface is not completely understood but some information has been determined.
The necessarily under-coordinated water molecules at the surfaces of both ice and water form similar ice-like, low-density phases that are hydrophobic, stiffer, superfluidic and thermally more stable than the bulk water [ ]. Under pressure at hydrophobic surfaces, liquid water shows increasing ice-like order. However, the pressure response is opposite to that of hexagonal bulk ice, indicating that ice-like order is not to be confused with the presence of real ice [ ]. Hydrogen bonding in the surface is stronger than in the bulk [ ] and this has an effect on the osmotic pressure but some hydrogen bonding is lost, giving a more reactive environment [ ] and greater ice nucleation [ ].
The increased strength of surface water hydrogen bonds is partially due to the reduced competition from neighboring water molecules [ ] but has little effect on their vibrational lifetime [ ]. This stronger bonding is due to lower anti-cooperativity and compensation for the increased chemical potential on the loss of some bonding.
This surface hydrogen-bonding gives rise to long-range specific ion effects on the aerial surfaces where tiny amounts of dodecahedral cluster -stabilizing ions such as ClO 4 - affect the water clustering around distant similar ions such as I - [ ]. The diffusion within the surface is increased for some surface molecules but decreased for others and depends on the number of hydrogen bonds and size of the water clusters [ ]. In addition, the surface water structuring varies less with temperature than the bulk. Refractive index study of the water-air surface reveals it to be about 1. Recent vibrational spectroscopy shows this surface to be relatively homogeneous [ a,c ] although this work is questioned [ b ].
About a quarter of the water molecules each have a 'dangling' O-H group [ , ] pointing at a slight angle out of the water [ , , ] whilst slightly more have 'dangling' acceptor electron positions [ ] similar to water-hydrophobe surfaces, creating a slight negative charge on the surface. This indicates that although there is little change in water's hydrogen bonding length at the interface, these hydrogen bonds are stiffer in terms of their rotation, as happens at other hydrophobic surfaces.
The density, dielectric permittivity, [ b ] and dipole moment of interfacial water change from their bulk water values to that of the gas over a distance of less than about a nanometer. Ions, including hydrogen and hydroxide ions, and other solutes will behave differently at the surface to their behavior in the bulk.
Perhaps the most important property of the surface, after the surface tension, concerns how it affects the local ion distribution. Some ions prefer the surface as shown by their effect on the surface tension Jones-Ray effect [ ] and bubble coalescence.
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Certainly, the surface pH may be several pH units different from that of the the bulk pH [ ]. Strong acids like HCl and particularly HNO 3 re-associate at the interface [ ], so allowing their evaporation. However weak acids, such as formic and acetic acids, have a strong surface preference but dissociate more rapidly when at the surface, so reducing evaporation [ ]. Thus the suface is more complex than that suggested by vibrational sum frequency generation see elsewhere for an hypothesis. Charge transfer causes the surface to reflect the charge on the ions close to the surface [ ], usually anions.
An additional effect is charge transfer where the outside water molecules contain more hydrogen-bond acceptors whereas the water molecules just to the inside of the slip-plane contain an excess of hydrogen-bond donors [ ]. Aqueous radicals also prefer to reside at such interfaces [ ], as do some molecular species that prefer to hydrogen bond on the outside of clathrate-like structures; superoxide c for example [ ]. The presence of radicals at the surface is further shown by their release when microbubbles collapse [ ].
Excess electrons have been found to be stable at the surface of ice for several minutes [ ]. Small cations kosmotropes , but see ion effects in foams are found away from the interface towards the bulk where their requirement for efficient hydration may be satisfied and as they cannot easily be stripped of the bound water by the interface. Also, there is a very large electrostatic solvation free energy cost that prevents adsorption of low polarizability ions at hydrophobic interfaces such as oils or air [ ]. Such cations only approach the interface in response to the surface negative charge.
In acid solutions, oxonium ions point away from the surface as they only poorly accept hydrogen bonds but strongly donate three , with their oxygen atom pointing at the surface [ ]. This encourages these ions to sit in the surface layer [ ] in the absence of competing anions such as OH - see interfacial ions and can lead to the charging of hydrophobic surfaces in acid solution [ ]. Mostly however at neutral pHs, there is a lower concentration of hydrogen ions than anions at the surface. The zeta potential of the surface of water is considerable and changes markedly with solute concentration mV for deionized water [ ], mV for 0.
This is due to a surface charge density varying from about an electron per nm 2 for pure water to about an electron per 10 nm 2 for 0. The charge at the surface of deionized water with air is similar to that found on small oil droplets in water [ c]. The aerosol mists formed at waterfalls see left are found to be negatively charged [ ].
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If a charge lies on the outside of the interface then its image charge is attractive in the liquid phase as shown at the bottom of the diagram. Water coats all hydrophilic surfaces open to ambient atmospheres that are not dried and the first absorbent layer is generally held strongly. Importantly this layer will affect the properties of the surface including their electrical properties and can cause negative resistance [ ]. The viscosity of water at hydrophilic surfaces may be orders of magnitude greater than that in the bulk but may be reduced considerably by light nm [ ]. Disrupting the 'unstirred layer' next to a surface has pronounced effects on the surface charge and surface chemistry which can last for several minutes after the stirring has ceased [ ].
Therefore under flow conditions, all surfaces should be considered as dynamic including gas-liquid interfaces where there are continuous molecular evaporations and condensations. The reduced density and stronger hydrogen bonds within the surface will both contribute to the stabilization of water clusters; particularly that of ES over CS full and partial clustering. Small gas molecules bind to these surface clusters due to multiple van der Waals dispersion interactions plus the good fit between the gas molecules and the clusters.
There is no possibly-negative influence caused by the necessary closure of the clusters within the bulk. This offers an explanation for the greater solubility of the hydrophobic gases at the interface as they can occupy clathrate-type water dodecahedra. They are also thought important in clathrate hydrate formation at liquid-gas interfaces [ ].
This is also supported by the exceptionally small difference in surface density from the bulk density as shown by the abnormally large pressure coefficient of the surface tension. Interestingly, the air-water interface may give rise to chiral selectivity and recognition [ ]. The surface may, therefore, act as the isotropic bulk cannot.
It presents a mechanism for the choice of chirality early in the formation of life's molecules; for example, the D-series of carbohydrates and the L-series of amino acids. Even simple neutral organic pollutants such as phenol have been shown to significantly affect the interfacial water structure [ ]. Recently, it has been discovered that the charge on the interface affects the freezing point of supercooled water [ ]. On a surface with no electric field, water droplets were found to freeze at around For each sample, four micrographs were analyzed and the results averaged.
In this section, a brief outline of the self-consistent field SCF computations will be given. We employ the numerical lattice approximation by Scheutjens and Fleer SF-SCF , which is a versatile tool for computing the thermodynamic properties of, e. In essence, it is an extension of Flory—Huggins theory 7 to include gradients.
For a detailed background on this approach, we refer to other publications. In SF-SCF, the system is represented by lattice sites and molecules are composed of one or more segments, with one segment exactly filling one lattice site. It is a mean-field approach in which each segment interacts with an average potential due to the other segments; the objective of SCF is to obtain concentration profiles that are self-consistent and to minimize the free energy for a given system. Various geometries are possible, such as planar, cylindrical, or spherical, with gradients in one, two, or three dimensions.
In the present work, the focus is on a flat interface, so we consider a planar geometry with gradients in one direction x -axis. To model the experimental system, our SCF computations involve two polymers A and B dissolved in a theta solvent S , i. These polymers will be denoted A , A , and B for short. Relevant physical quantities can be extracted from the SCF computations.
The volume fraction profiles also give insight into the interfacial excess of each component. This can be quantified by computing. The interfacial excess can only be computed when the position x Gibbs of the Gibbs dividing plane is fixed. This definition has the advantage that the Gibbs plane coincides with the symmetry plane for a symmetrical system e.
One may wonder why we did not choose the location of the Gibbs dividing plane such that the excess of the solvent is zero. Since our computations start from and include the symmetric case, we choose not to use the definition of zero interfacial excess of solvent. It is important to realize that the amount of polymer adsorbed depends on the volume available to the polymer in the bulk phase due to the influence of the translational entropy of the polymers.
Experiments have shown that this effect is most important when the polymer solution is dilute. This is also true for the self-consistent field calculations carried out, and it was explicitly verified that the bulk volume the number of lattice layers was always chosen large enough so that all properties adsorptions, density profiles are independent of the number of lattice layers. It is given by 1 , In this section, results from our experiments and self-consistent field computations are described and discussed.
First, phase diagrams and results for the interfacial tensions are presented. Subsequently, interfacial density profiles are shown and discussed in terms of the interfacial excess of the components. Finally, the relation between interfacial excess and interfacial tension is discussed in terms of the Gibbs adsorption equation. In the experiments, the mass density of the pure polymers is about 1. When additionally a smaller variant of polymer A is introduced to the system, the binodal is shifted away from the vertical axis in the phase diagram.
This indicates that, although small polymer A does preferentially situate in the A-rich phase, significant amounts of small polymer A do remain in the B-rich phase. The agreement between experiment and SCF computations is near-quantitative. Effect on the phase diagram of adding a small polymer to a mixed solution of two larger polymers. The systems consist of dextran 70 kDa with gelatin kDa in a 1: The points indicate the measured coexisting phases, and the curves are to guide the eye. There is a modest difference in the absolute magnitudes of the tension between experiment and theory, but the trends are almost quantitatively the same: This is consistent with the observation that the interfacial tension decreases with decreasing degree of polymerization at fixed tie-line length.
Effect of a small polymer on the interfacial tension of a mixed solution of two larger polymers from a experiments and b self-consistent field computations. In other words, it appears that the effect of polydispersity on the interfacial tension as modeled by the addition of the smaller polymer component is stronger at larger tie-line lengths and that, in this sense, the effect is quantitatively different from just a decrease in the average degree of polymerization. This point is addressed in more detail in a later part of this section. In order to investigate whether the addition of small polymers to a high molar mass system leads to a higher or lower interfacial tension, one should in some way take the fact into account that the phase diagram itself depends on the polymer chain length.
Therefore, to account for the shift in the location of the critical point, we elected to compare results at equal tie-line length. We found that the small polymers adsorb at the interface, leading to a small but significant lowering of the interfacial tension consistent with our self-consistent field calculations. Still, it could be questioned whether the tie-line length is the most appropriate way of comparing different systems.
Another method would be to scale the polymer concentrations with their critical concentrations, for instance, but this requires a very precise determination of the polymer concentrations at the critical point to avoid systematic errors. This is, however, experimentally especially difficult.
The tie-line length has the advantage that it does not require normalization and is easily accessible experimentally for our system. Additionally, comparing systems at equal tie-line length ensures that on average the concentration differences across the interface are the same, ensuring that the density profiles and interfacial widths are similar. We now turn our attention to the interfacial density profiles and the corresponding interfacial excesses of the various components. It is clear, especially in the top and bottom panels, that the polymers are depleted from the interface and that there is a local excess of solvent.
The reason for this phenomenon lies in the fact that unfavorable contacts between polymers A and B at the interface are reduced in this way. The result is also that the interfacial tension is significantly reduced compared to the hypothetical scenario in which the density of solvent across the interface would be constant.
Interfacial Separation of Particles: Volume 20
Additionally, the phase that is enriched in small polymer A contains more solvent due to the higher osmotic pressure of the smaller polymer. The profiles are centered around the Gibbs dividing plane dashed vertical lines located such that the interfacial excesses of polymers A and B are equal. It turns out that the profile of A is shifted about 2. The interfacial excess of solvent is always positive; therefore, the excess of the polymers is, in total, always negative.
When both A and A are present, the small component shows positive adsorption, in line with the reasoning in the previous paragraph, at the expense of a slightly reduced adsorption of solvent.
The Gibbs plane is located such that the excess filled regions of polymers A and A in total is equal to that of polymer B At first glance, it may seem surprising that the system partially exchanges a positive excess of solvent for a positive excess of small polymer to decrease the interfacial tension. After all, according to the Gibbs adsorption equation.
To resolve this apparent contradiction, we consider the implications of the Gibbs adsorption equation in more detail. Let us consider the dependence of the interfacial tension as a function of the position in the phase diagram, i. According to eq 8 , this leads to.