Core-shell particles at fluid interfaces : performance as interfacial stabilizers
Buchcic, C. - \ 2016
Wageningen University. Promotor(en): Martien Cohen Stuart, co-promotor(en): R.H. Tromp; Marcel Meinders. - Wageningen : Wageningen University - ISBN 9789462578968 - 140
stabilization - stabilizers - particles - colloidal properties - adsorption - interface - fluids - stabilisatie - stabiliseermiddelen - deeltjes - colloïdale eigenschappen - adsorptie - grensvlak - vloeistoffen (fluids)
There is a growing interest in the use of particles as stabilizers for foams and emulsions. Applying hard particles for stabilization of fluid interface is referred to as Pickering stabilization. By using hard particles instead of surfactants and polymers, fluid interfaces can be effectively stabilized against Ostwald ripening and coalescence. A drawback of the use of hard particles as interfacial stabilizers is that they often experience a pronounced energy barrier for interfacial adsorption and that hard particles are very specific with regard to the type of fluid interface they can adsorb to. Soft particles, on the other hand, are known as good stabilizers against coalescence and they spontaneously adsorb to a variety of different fluid interfaces.
The aim of this thesis was to investigate core-shell particles comprising a hard core and soft shell with regard to their interfacial behaviour and their ability to act as sole stabilizers for foams and emulsions. We hypothesised that the presence of the soft shell allows for easier interfacial adsorption of core-shell particles compared to the hard core particles only. To test this hypothesis, we prepared core-shell particles comprising a solid polystyrene (PS) core and a soft poly-N-isopropylacrylamide (PNIPAM) shell. To ascertain the effect of shell thickness, we prepared a range of core-shell particles with different shell thicknesses, containing identical core particles. We found that core-shell particles are intrinsically surface active and can generate high surface pressures at the air-water interface and oil-water interfaces, whereas core particles seemed to experience a large energy barrier for interfacial adsorption and did not lower the surface tension. We also confirmed by microscopy that core-shell particles are actually adsorbing to the fluid interface and form densely packed interfacial layers. Further, we found that a certain critical thickness of the soft shell is necessary in order to ensure facile interfacial adsorption. If the PNIPAM shell on top of the core particles is well above 100nm thick, particle adsorption at the air-water interface was found to be diffusion limited.
By gentle hand-shaking we were able to produce dispersion of air bubbles and emulsion droplets solely stabilized by core-shell particles. The resulting bubbles still underwent Ostwald ripening, albeit slowly. For oil-in-water emulsions of hexane and toluene, both of which have a relatively high solubility in the continuous phase, we found that core-shell particles can stop Ostwald ripening. The resulting emulsion droplets adopted pronounced non-spherical shapes, indicating a high elasticity of the interface. The high stability and the remarkable non-spherical shape of the emulsion droplets stabilized by core-shell particles were features we also observed for fluid dispersion stabilized by hard particles. This shows that in terms of emulsion stability core-shell particles behave similar to hard particles as interfacial stabilizer.
As to why the differences between the stability of bubble and oil dispersions arise could not be finally answered. Yet, microscopic analysis of the interfacial configuration of core-shell particles at the air-water interface reveals some peculiar insights which may suggest that core-shell particles adsorb in a polymer-like fashion with the soft PNIPAM shells adsorbing to the air-water interface only, while the hard PS cores reside in the continuous phase.
In summary, we showed that core-shell particles with a hard core and a soft shell can indeed combine the advantageous properties of hard and soft particles. The soft shell enables spontaneous adsorption to a variety of fluid interfaces. Despite their spontaneous adsorption, core-shell particles strongly anchor and do not spontaneously desorb from the fluid interface again. Further, the hard core provides enough rigidity to the core-shell particles to allow the establishment of a stress bearing interfacial particle network. This network eventually stops Ostwald ripening in oil-in-water emulsions. Our results therefore show that in the case of oil-water interfaces, core-shell particles can perform better than solely hard particles as interfacial stabilizers.
Colloids at liquid interfaces: dynamics and organization
Ershov, D.S. - \ 2014
Wageningen University. Promotor(en): Jasper van der Gucht, co-promotor(en): Martien Cohen Stuart. - Wageningen : Wageningen University - ISBN 9789461738943 - 127
colloïden - oppervlaktechemie - grensvlak - oppervlakteverschijnselen - capillairen - vloeistoffen (liquids) - colloids - surface chemistry - interface - surface phenomena - capillaries - liquids
This thesis deals with spherical microparticles trapped at liquid interfaces. It focuses on two aspects of their behavior: firstly, the effect of the curvature of a liquid interface on interparticle interactions and their organization; secondly, the mobility of particles at visco-elastic interfaces.
In Chapter 2of this thesis we showed that it is possible to induce capillary interactions between spherical microparticles with homogeneous surface chemistry by tailoring the curvature of the liquid interface. If the interfacial curvature is anisotropic, the constraint of constant contact angle along the contact line can only be satisfied if the interface is deformed locally. These deformations create excess surface area, which changes when two particles approach each other. This leads to a change in the surface free energy, which manifests itself as a capillary interaction between the particles.
To study the effect of curvature on the interactions between particles, we created oil-water interfaces of different shape (ellipsoid, dumbbell, torus and squares) and added spherical negatively charged particles that adsorbed at these interfaces. On all these interfaces, we observed quadrupolar capillary interactions that organized the particles into square lattices. The order of this organization increased with increasing curvature anisotropy, indicating that capillary interactions are stronger as well. By contrast, on flat interfaces or on spherical droplets with homogeneous curvature, no attractive interaction was observed and only at very high surface coverage did the particles order in a hexagonal lattice, as a result of repulsive interactions.
In Chapter 3we studied the interface deformations around particles at curved interfaces and the resulting capillary interactions theoretically. We used the finite element method to solve the Young-Laplace equation for the shape of the interface around a particle and calculated the interaction potential between the particles numerically.
The main finding of these calculations is that for an anisotropically curved interface, with two different local principal curvatures, the particle deforms the interface in two ways simultaneously: concave deformation along one principal direction and convex – along the other, thus creating a deformation field with quadrupolar symmetry. Two particles with such deformations interact favorably only if the overlapping deformations are similar (concave-concave, convex-convex), which occurs when they approach each other along one of the two principal directions. Since the two local principal directions are always perpendicular, particles interacting along them will tend to arrange into a square pattern.
As a consequence of the quadrupolar deformation field, two particles approaching each other along a line forming 45 degrees with the principal axes will repel each other (which is confirmed by our observations), because in this case the deformation fields overlap with four different “petals” (2 pairs of concave-convex), and the excessive surface area doesn’t reduce upon approaching, but increases. A system of two particles oriented at an angle with respect to the principal axis is therefore subjected to a torque rotating the axis of the system so that it gets aligned with one of the two principal directions. The torque magnitude reaches its maximum when the system’s axis is at an angle of 45 degrees with respect to the principal direction and decreases to 0 when the axis is aligned with one of the principal directions.
The family of interaction potentials we obtained allows for calculating the minimum deviatoric curvature needed to initialize capillary interactions strong enough to compete with thermal energy, so that a stable organization can be expected. The calculated value was very close to the deviatoric curvature where ordering was observed experimentally in Chapter 2.
In Chapter 4we studied the mobility of 3 mm polystyrene particles in a monolayer of 1.5 mm core-shell microparticles deposited at flat air-water interfaces; all the particles present in the system were stabilized by negative charges.
In this exploratory chapter we made an attempt to characterize the mechanical properties of such monolayers by analyzing the mobility of the larger tracer particles in the monolayer. With increasing particle density of the monolayer, we observed that the mean-square displacement of the tracer particles was reduced, which can be interpreted as an increase of the viscosity of the monolayer. At very high densities the motion of the particles became subdiffusive and confined, pointing at elasticity of the monolayer. We also studied correlated movements between neighboring particles in an attempt to do two-point interfacial microrheology. A comparison between the one-point and two-point methods shows clear indications of heterogeneous dynamics of the tracer particles. Our results therefore call for a further development of two-point microrheology at interfaces.
In Chapter 5we used tracer particles to study the properties of thin cross-linked actin networks deposited at the surface of oil droplets. These networks are a model system for the intracellular actin cortex. We used the generalized Stokes-Einstein relation to extract the complex frequency-dependent shear modulus of such networks from the movement of the added tracer particles. We studied the effects of the length of actin filaments and the cross-linker concentration on the mechanical properties of these layers.
The advantage of this system is that actin networks are freely accessible from the water phase, and therefore can be subjected to in-situ addition of cross-linkers, enzymes or other chemicals of interest. Using this, we managed to show strong stiffening after addition of myosin motor proteins and ATP, which we ascribed to contraction of the actin-myosin network.
Freesia groeimodel: Ontwikkeling van een groeimodel voor gebruik door telers
Labrie, C.W. ; Visser, P.H.B. de; Buwalda, F. ; Helm, F.P.M. van der - \ 2011
Bleiswijk : Wageningen UR Glastuinbouw (Rapporten GTB 1075) - 35
freesia - groeimodellen - grensvlak - droge stof - groei - kwekers - klimaatfactoren - teelt onder bescherming - nederland - freesia - growth models - interface - dry matter - growth - growers - climatic factors - protected cultivation - netherlands
Abstract Wageningen UR Greenhouse Horticulture conducted in close cooperation with the Dutch freesia sector research on the effects of climate on dry matter production of Freesia plants. The relationships were established on the basis of photosynthesis, growth and climate data measured in greenhouses of Freesia growers. The relationships were incorporated in a dynamic growth model that correctly simulated the dry matter growth in a series of trials. A user-friendly interface was satisfactorily developed interactively with a number of Freesia growers. The model can be used by growers to find the most optimal combination of climate factors for Freesia growth at given plant age and greenhouse settings.
Van eiwitten in platland tot bionanotechnologie in Wageningen
Norde, W. - \ 2010
Wageningen : Wageningen Universiteit - ISBN 9789085855767 - 28
eiwitten - oppervlakten - grensvlak - nanotechnologie - bionanotechnologie - oppervlaktechemie - oppervlakteverschijnselen - proteins - surfaces - interface - nanotechnology - bionanotechnology - surface chemistry - surface phenomena
Polymer vs. surfactant : competitive adsorption at the solid-liquid interface
Postmus, B.R. - \ 2008
Wageningen University. Promotor(en): Martien Cohen Stuart; Frans Leermakers. - [S.l. : S.n. - ISBN 9789085049289 - 143
polymeren - oppervlaktespanningsverlagende stoffen - adsorptie - grensvlak - polymers - surfactants - adsorption - interface
The research described in this thesis focuses on the competitive adsorption of nonionic polymer and nonionic surfactant on a silica surface. These type of systems are interesting from both an academical and a technological viewpoint. Our academic interest stems simply from the observation that we had a hard time predicting the (adsorption) behaviour of the system beforehand. The technological relevance of our study can be attributed to the observation that technological applications are often complex mixtures containing a large variety of additives. The interactions between all these different components, such as the formation of mixed aggregates or co-adsorption, are quite complex. For applications, these interactions are very important since the properties of a mixture on a microscopical scale can be used to manipulate the macroscopical behaviour. Or, in the case of undesirable macroscopic behaviour, a detailed knowledge about the microscopic interactions can be used to improve on the situation.
We have restricted ourselves to relatively simple complex mixtures, i.e. we have chosen a well-defined model system consisting of homodisperse components. This model system is an aqueous mixture of the nonionic polymer PEO with the nonionic surfactant CnEm. To study the adsorption behaviour of this mixture, we have chosen to use a flat silica surface as a model surface. The CnEm surfactants adsorb (on a hydrophilic surface such as silica) with their head groups. Because the head groups consist entirely of EO segments, the binding mechanism of the surfactants to the silica is exactly the same as the PEO binding mechanism, namely H-bonding. By evaluating the competitive adsorption of the system, we are effectively investigating the subtle effects of layer structure. By making small changes to the choice of surfactant architecture, polymer length or solvent quality, large changes in layer structure can be induced.
Reflectometry was used to look at the competitive adsorption from mixtures containing PEO and CnEm. There are several methods to test this competitive adsorption. In the case of simultaneous adsorption, the polymer and surfactant are allowed to adsorb from a mixture. It is also possible to study adsorption sequentially, i.e. first adsorb component A, and then sequentially try to displace component A with component B. We decided to start by doing sequential adsorption experiments, because these are easier to control. In such an experiment, the PEO is allowed to adsorb onto the surface from a solution with 5 mg PEO/L. Care was taken to insure that the layer was in its steady state. Next, the flow of PEO solution was replaced by the background solution, and subsequently by a solution containing only surfactants. The concentration of the surfactant solution was 110-4 mol/L for all surfactants except for C12E3, where solubility problems demanded the use of a lower concentration c = 610-5. Still, all surfactant solutions had a concentration higher than the CMC. The results of these experiments can basically be grouped in two categories. Upon changing to the surfactant solution, the adsorbed amount would either increase sharply, or the adsorbed amount would remain constant. In the first case where the adsorbed amount would increase until the amount that the surfactant would also reach from a single component solution. Furthermore, subsequent rinsing of this layer would result in a total dissolution of the layer, and hence, the adsorbed amount would go to zero. Since this is typical surfactant behaviour, we can conclude that the surfactant displaces the polymer as it adsorbs.
To better understand the experimental observations, we have developed an SCF model. In this model, it is possible to calculate the charge on the silica surface as a function of the pH and the ionic strength. This yields titration curves that can be compared with experimental titration curves. Our calculated results correspond quite well with literature data.
One can also use the model to make predictions about the adsorption of PEO on our silica surface. It is possible to go to concentrations much lower than those that are experimentally accessible. We have made predictions about the response of the adsorbed polymer layer upon changes in ionic strength and pH. The results show that PEO adsorption is relatively insensitive for the ionic strength at pH ≈ 7, but at pH ≈ 10, the ions can displace the polymer quite well. This type of behaviour is also found experimentally. Every time that we perform a calculation (and we do find a solution), we obtain the mean field free energy and the most likely conformation of the system. By looking at the profiles of the most likely conformation, i.e. plotting the volume fraction of a species versus the distance from the surface, we can see that the adsorbed polymer inhibits the adsorption of salt. Hence, the polymer and the salt are in competition for adsorption.
The behaviour of CnEm surfactants can also be evaluated with the model. Here we use exactly the same parameters that we used for the PEO. Again, we started by evaluating the surfactant bulk behaviour. Instead of investigating the first occurrence of a micelle, we have defined a more experimentally relevant CMC. We have evaluated that concentration where the volume fraction of micelles is approximately equal to the volume fraction of unimers. Based upon this criterion we have calculated the CMC and the corresponding micellar size for a number of surfactant architectures and for a number of ionic strengths. We have also evaluated surfactant adsorption isotherms. These calculated adsorption isotherms feature a first order transition at the CSAC. By evaluating the behaviour of the CSAC, we have found that the CSAC shifts to a higher concentration when the pH or the ionic strength is increased. We identified conditions for which the CSAC > CMC, which effectively implies that the surfactant does not adsorb anymore. We compared these predicted results to data measured using a reflectometer, and we find that the model predicts the experimental results quite well.
The next step is to use the model to try and reproduce the displacement results. We have defined systems that include both PEO and CnEm, at some pH and ionic strength. To determine which component adsorbs from a mixture, we evaluate the response of the CnEm to the competing polymer. The surfactant starts adsorbing at some concentration (CSAC). If the surfactant concentration is lower than the CSAC, then the PEO will adsorb (we assume that the pH and ionic strength are such that the PEO is capable of adsorbing). For surfactant concentrations higher than the CSAC but lower than the CMC, the surfactant will preferentially adsorb. In the case of CSAC > CMC, the surfactant will not adsorb. Typically, the polymer will adsorb in this case, however, one can think of situations (high pH and high ionic strength) where the polymer will also stay in solution.
Using the method described above, we can model the competitive adsorption of PEO and CnEm. We can evaluate the response of the surfactant to competing species, such as PEO of length N. By identifying for every surfactant architecture that polymer length N where CSAC = CMC, we can make predictions about the adsorption from mixtures.
Lipid bilayers and interfaces
Kik, R.A. - \ 2007
Wageningen University. Promotor(en): Martien Cohen Stuart; Frans Leermakers, co-promotor(en): Mieke Kleijn. - [S.l.] : S.n. - ISBN 9789085048374 - 169
elektrische dubbellaag - lipiden - grensvlak - oppervlakte-eiwitten - ionensterkte-effecten - electrical double layer - lipids - interface - surface proteins - ion strength effects
In biological systems lipid bilayers are subject to many different interactions with other entities. These can range from proteins that are attached to the hydrophilic region of the bilayer or transmembrane proteins that interact with the hydrophobic region of the lipid bilayer. Interaction between two membranes is also very common. To gain more insight into the thermodynamic, structural and mechanical consequences we experimentally and theoretically investigated the interactions of a lipid bilayer with various types of interfaces. More specifically, we have analysed the transmembrane protein-lipid interaction by a computational self-consistent field method and have studied the adhesion of vesicles onto gold experimentally. Some aspects of the latter problem were also analysed theoretically. There exists a computationally inexpensive, yet qualitatively accurate and realistic method to molecularly model the bilayer membrane in the presence of surfaces, namely the self-consistent field theory. This approach makes use of a large number of approximations. Important ones are: the discretisation of space by using a lattice, the non-self-avoidance of chains implying freely jointed chains and the replacement of binary interactions by an external potential leading to the (local) mean field ansatz. When a transmembrane hydrophobic inclusion is present in the lipid membrane the bilayer around it is disturbed. The structural perturbation of the lipid bilayer around these inclusions have an exponentially decaying wave-like appearance. There are many factors that influence this. The most important ones are the shape of the inclusion, the hydrophobic length of the inclusion, the local interaction between the inclusion and the bilayer, the hydrophobic bilayer thickness and the mechanical characteristics of the lipid bilayer. At distances larger than the bilayer thickness the wavelength and the decaylength of this exponentially decaying wave are exclusively determined by the mechanical and structural properties of the bilayer. This means that the wavelength and the decaylength can be described by the thickness, the bending modulus and the area compression-expansion modulus of the bilayer. The amplitude and the offset of the perturbation are on the other hand set by the properties of the inclusion. Indeed, the hydrophobic length mismatch, i.e., the difference between the hydrophobic length of the inclusion and the hydrophobic thickness of the lipid bilayer, and the contact interaction between the inclusion and the lipid bilayer are the key variables. The free energy of insertion is mainly determined by the contact interaction energy between the inclusion and the lipid bilayer and it shows a parabolic dependence on the hydrophobic length mismatch. The free energy of insertion is minimal at a hydrophobic length mismatch where the bilayer perturbations are minimal. We argued that there is a subtle interplay between the entropy loss of the lipid tails adjacent to the surface and the contact interaction between the inclusion and the lipid tails. Important for the biological performance, we found that overlap of the perturbed regions of the bilayer around two or more inclusions can cause attractive or repulsive interaction between such inclusions depending on the distance between them. This non-monotonic interaction force with the distance between inclusions, is directely linked to the non-monotonic structural perturbations mentioned already. This lipid mediated free energy of interaction between the inclusions can be divided into three different regimes each with their own length scale. These are the short-range segmental, the intermediate-range conformational and the long-range elastic contributions. The short-range contribution is only present when one or two lipids are in between the inclusions. This interaction depends strongly on the Flory-Huggins interaction between the inclusion and the lipid tails. The intermediate-range contribution is present at separations on the length scale of approximately the bilayer thickness. This interaction shows an exponentially decaying dependence on the separation between these inclusions and is a consequence of the confinement of the lipid tails in between these inclusions. The long-range contribution is determined by the elastic properties of the bilayer and has an exponentially decaying wave-like appearance, with a wavelength that is the same as the perturbation wave length of the bilayer. Our SCF analysis complements available simulations on the one hand and mesoscopic models on the other. Moreover, they may help to analyse experiments and explain observations in biomembranes. In the second part of this thesis we examined the adhesion of negatively charged DOPG vesicles and zwitterionic DOPC vesicles to a gold surface using quartz crystal microbalance and surface plasmon resonance techniques. Gold has a hydrophilic surface where lipid vesicles adsorb intact. When the vesicle radius was above approximately $40$ nm the DOPC vesicles completely cover the surface, whereas below this radius the surface coverage decreases with decreasing vesicles size. When spherical vesicles adsorb onto a surface they deform. The shape deformation of the adsorbed vesicles increases with increasing vesicles size. The diminished deformation for the smaller vesicles results in a relatively small interaction area between the vesicles and the gold surface resulting in less lipid-surface interactions. Self-consistent field model calculations on a single vesicle are in line with these experimental results. The calculations showed that the relative deformation of the vesicles has a linear dependence on the vesicles radius. They furthermore showed that below a certain minimal vesicle radius the deformation is completely absent resulting in a lipid-surface interaction energy that vanishes. Self-consistent field calculations further indicate that the lipid-surface interaction can be divided into three different regimes. In the weak interaction regime the adhesion of the vesicles is not accompanied by drastic changes in the bilayer structure and the vesicle is deformed elastically. In this case the adhesion of the vesicles is energetically favourable over the adhesion of an equally sized bilayer patch. The adhesion of lipid vesicles to the gold surface can most likely be categorised in this regime. In the second intermediate interaction regime the adsorbed vesicles are energetically unfavourable compared to equally sized bilayer patches. The deformation of these vesicles remain in the elastic regime and therefore they do not transform into an adsorbed lipid bilayer patch. In the strong interaction regime the adsorption of the vesicles is strongly energetically unfavourable compared to equally sized bilayer patches and this interaction is so strong that local molecular rearrangements take place to increase the bilayer curvature. This results in adsorbed vesicles that are very susceptible to fusion and/or rupture. An interesting prediction is that the adsorption energy of a vesicle does not depend on the bilayer rigidity. This means that the adsorption energy is a constant, and fixed by the interaction energy between the lipid molecules and the surface. At the same time the deformations of the vesicles increase with diminishing rigidity, which means that although the interaction is the same, the vesicles with different rigidity can be present in different interaction regimes. As already mentioned, lipid vesicles adsorb intact onto a gold surface. However, on many other surfaces lipid vesicles transform after adsorption into a supported lipid bilayer. We studied the importance of electrostatic interactions for the adhesion strength of DOPC and DOPG vesicles to a gold surface. This was done by varying the pH, the ionic strength and an externally applied electrostatic potential. Varying the pH of the solution has an effect on the protonation of the oxide groups present at the gold surface. As a consequence the surface charge ranges from a positive charge below pH$=5$ to negative charge above pH$=5$. In the case of negatively charged DOPG vesicles, we showed that there is a relation between the adsorbed amount and the pH. The adsorbed amount was larger at low pH compared to high pH and remained approximately constant in the pH range $6-10$. There is still some adsorption in this pH range, from which it can be concluded that besides the electrostatic interaction also other interactions, such as the van der Waals or other chemical interactions, play a role. The ionic strength has a rather strong influence on the adhesion of DOPG vesicles, while the adsorbed amount of DOPC vesicles remains approximately constant. Both experiments and self-consistent field modelling showed that the adsorbed amount decreases with decreasing ionic strength. This relation can be attributed to the fact that the headgroup density of the DOPG vesicle decreases with decreasing ionic strength, which results in less favourable non-electrostatic lipid-surface interactions. The externally applied potential had no effect on the adsorption DOPG vesicles. This can be attributed to the fact that externally applied potential can only be varied over a limited range, because otherwise redox reactions reaction at the gold surface start to play a role. This means that the surface potential range is too small to influence the interaction energy of the DOPG and the DOPC bilayer. With self-consistent field modelling it was shown that if redox reaction did not occur and the externally applied potential could be varied over a larger range, the interaction energy between the lipid bilayer and the gold surface could be divided into four different regimes. These regimes vary from weakly attractive to strongly attractive. It can be concluded that the adhesion of DOPG vesicles onto gold is parly determined by electrostatic interactions. Because the vesicles are weakly bound to the gold surface, the electrostatic interaction can influence the adsorption of intact vesicles. However they are never strong enough to induce transition of the adsorbed vesicles to a flat supported bilayer. In the case of DOPC vesicles the electrostatic interactions have a negligible effect The organisation of proteins in lipid membranes is identified as one of the central issues in molecular biology. We have tried to unravel the role of the lipid matrix in the protein insertion problem. Our results may be important, for example in the case of transmembrane proteins with multiple transmembrane $\\alpha$-helices, because the short-range lipid-mediated interactions of these transmembrane helices can directly influence the quaternary structure of these proteins. Besides generic issues discussed in the present thesis there are numerous molecular specific aspects. These problems will undoubtelly attract many scientific activities in the years to come. Lipid vesicles at surfaces attracted a lot of attention in the last ten years. Vesicles adhesion is used frequently to generate supported lipid bilayers. Such interfacial layers gives the opportunity to study the properties and interactions of these lipid bilayers and use these layers in biotechnological applications. We tried to unravel some details of the interactions of lipid layers with a gold surface. Our results may be used to understand why in some cases supported bilayers are formed while in other vesicles stay intact at the surface. Understanding this will give us the opportunity to control the fusion of lipid vesicles on a surface. Fusion of vesicles in a plane is also an issue in biological processes such as the formation of the cell plate in plant cell division.
Interfacial Transport Phenomena (Second edition)
Slattery, J.C. ; Sagis, L.M.C. ; Oh, E.S. - \ 2007
New York (US) : Springer - ISBN 9780387384382 - 830
engineering - mechanica - materialen - thermodynamica - oppervlakten - grensvlak - engineering - mechanics - materials - thermodynamics - surfaces - interface
Gives a presentation of transport phenomena or continuum mechanics focused on momentum, energy, and mass transfer at interfaces. This work includes a discussion of transport phenomena at common lines or three-phase lines of contact, and a theory for the extension of continuum mechanics to the nanoscale region immediately adjacent to the interface.
Interfacial properties of water-in-water emulsions and their effect on dynamical behavior
Scholten, E. - \ 2006
Wageningen University. Promotor(en): Erik van der Linden, co-promotor(en): Leonard Sagis. - Wageningen : - ISBN 9789085043669 - 148
emulsies - grensvlak - oppervlaktespanning - dynamica - gelatine - dextraan - arabische gom - emulsions - interface - surface tension - dynamics - gelatin - dextran - gum arabic
Keywords: biopolymer mixtures, water-in-water emulsions, phase separation, interfaces, tension, bending rigidity, permeability, droplet deformation, morphology.The objective of this work was to investigate interfacial properties of biopolymer-based water-in-water emulsions, and to determine the effect of these interfacial properties on the kinetics of phase separation and the deformation behavior of emulsions droplets in shear flow. Since the experimental determination of interfacial properties, such as interfacial thickness and bending rigidity is difficult, we have developed a model that determines these parameters from the experimentally accessible interfacial tension and the interaction potential of the dissolved biopolymers. From the results we could conclude that the thickness of these water/water interfaces is much larger than for oil/water interfaces. The bending rigidities for these interfaces were found to be very large compared to those of water/oil interfaces. The permeability of these interfaces was tested with the spinning drop and the droplet relaxation method. These water/water interfaces were found to be permeable to all ingredients in the system at long time scales (spinning drop experiments) and permeable to water for short time scales (droplet relaxation after cessation of a flow field). This permeability was incorporated into the description of the droplet relaxation time, from which the interfacial tension and the permeability can be deduced simultaneously. Due to the permeability, both the spinning drop method and the droplet relaxation method (without contribution of permeability) cannot be used to measure the interfacial tension accurately. Furthermore, both bending rigidity and permeability were incorporated into the description of coarsening ofbicontinuousstructures during phase separation. We found four different regimes for coarsening depending on whether the process is dominated by interfacial tension, bending rigidity or permeability.
Basics of macroscopic properties of adsorbed protein layers formed at air-water interfaces based on molecular parameters
Wierenga, P.A. - \ 2005
Wageningen University. Promotor(en): Fons Voragen; M.R. Egmond, co-promotor(en): Harmen de Jongh. - Wageningen : WUR - ISBN 9789085043270 - 171
eiwitten - adsorptie - grensvlak - oppervlakte-interacties - fysicochemische eigenschappen - proteins - adsorption - interface - surface interactions - physicochemical properties
The importance of protein characteristics on the role of proteins in forming and stabilising interfaces is studied. This study offers a new understanding of adsorbed protein layers.
Equilibrium polymers in solution and at interfaces
Gucht, J. van der - \ 2004
Wageningen University. Promotor(en): Gerard Fleer; Martien Cohen Stuart, co-promotor(en): N.A.M. Besseling. - [S.I.] : s.n. - ISBN 9789058089632 - 293
polymeren - hydrofiele polymeren - evenwicht - grensvlak - waterstofbinding - reologische eigenschappen - visco-elasticiteit - polymers - hydrophilic polymers - equilibrium - interface - hydrogen bonding - rheological properties - viscoelasticity - cum laude
cum laude graduation (with distinction)
Complex coacervate core micelles in solution and at interfaces
Burgh, S. van der - \ 2004
Wageningen University. Promotor(en): Martien Cohen Stuart, co-promotor(en): Arie de Keizer. - [S.I.] : S.n. - ISBN 9789085040194 - 128
micellen - polymeren - grensvlak - colloïdale eigenschappen - micelles - polymers - interface - colloidal properties
Detailed characterization of adsorption-induced protein unfolding
Engel, M.F.M. - \ 2004
Wageningen University. Promotor(en): Ton Visser; Sacco de Vries, co-promotor(en): Carlo van Mierlo. - [S.l.] : S.n. - ISBN 9789085040019 - 125
runderserumalbumine - alfa-lactalbumine - moleculaire structuur - grensvlak - fysische eigenschappen - adsorptie - spectroscopie - bovine serum albumin - alpha-lactalbumin - molecular conformation - interface - physical properties - adsorption - spectroscopy
Polyelectrolyte behaviour in solution and at interfaces
Klein Wolterink, J. - \ 2003
Wageningen University. Promotor(en): Martien Cohen Stuart; Willem van Riemsdijk, co-promotor(en): Luuk Koopal. - [S.I.] : S.n. - ISBN 9789058088390 - 184
elektrolyten - grensvlak - oplossingen - elektrochemie - electrolytes - interface - solutions - electrochemistry
|Entering and spreading of protein-stabilized emulsion droplets at the expanding air-water interface
Hotrum, N.E. ; Cohen Stuart, M.A. ; Vliet, T. van; Aken, G.A. van - \ 2003
In: Food Colloids, Biopolymers and Materials / Dickinson, E., van Vliet, T., Cambridge : Royal Society of Chemistry - ISBN 9780854048717 - p. 192 - 199.
emulsies - schuim - schuimen - eiwitten - caseïnaten - grensvlak - mechanische eigenschappen - emulsions - foams - foaming - proteins - caseinates - interface - mechanical properties
Colloids and interfaces in life sciences
Norde, W. - \ 2003
New York; Basel : Marcel Dekker - ISBN 9780824709969 - 433
colloïden - colloïdale eigenschappen - grensvlak - oppervlaktespanning - emulsies - schuim - reologische eigenschappen - studieboeken - oppervlaktechemie - colloids - colloidal properties - interface - surface tension - emulsions - foams - rheological properties - textbooks - surface chemistry
Thermodynamic and mechanical properties of curved interfaces : a discussion of models
Oversteegen, M. - \ 2000
Agricultural University. Promotor(en): J. Lyklema; F.A.M. Leermakers; P.A. Barneveld. - S.l. : S.n. - ISBN 9789058081780 - 148
thermodynamica - grensvlak - capillaire opstijging - thermodynamics - interface - capillary rise
Although relatively much is known about the physics of curved interfaces, several models for these kind of systems seem conflicting or internally inconsistent. It is the aim of this thesis to derive a rigorous framework of thermodynamic and mechanical expressions and study their relation to previous models.
In chapter 2 interfaces are described mathematically. It turns out that their curvatures can generally be determined by two independent coefficients, viz. the total and the Gaussian curvature. These degrees of freedom of a system must be accounted for in the thermodynamic expression for the internal energy and are conjugated to the bending stress and torsion stress, respectively. The curvatures can then be taken as intensive variables, as has been done by Gibbs, or as extensive variables, as proposed by Boruvka and Neumann. The two ways of accounting for curvature leads to different definitions of the interfacial tension. In the former way the curvatures can be fixed when changing the interfacial area, whereas in the latter the area times the curvature must be constant upon variation of the interfacial area. Consequently, the interfacial tension according to Boruvka and Neumann incorporates bending as well as stretching work. Hence, for homogeneously curved interfaces, the difference between the two interfacial tensions is the bending work.
It follows from a quasi-thermodynamic description that the interfacial work according to Gibbs can be described mechanically as the volume integral of the excess pressure profile. Writing the volume element in terms of the curvatures, the interfacial tension according to Gibbs can be expressed in terms of the zeroth, first, and second bending moments, respectively. Using their thermodynamic definitions, the bending and torsion stress can also be given mechanically, i.e., in terms of the excess pressure profile. Subsequently, using the relation between the interfacial tension of Gibbs and that of Boruvka and Neumann is expressed in terms of the bending moments. The newly derived equations differ significantly from those known in the literature. However, it is shown that the Laplace equations of capillarity derived from either the thermodynamic or the mechanical route are consistent.
The mechanical and thermodynamic notion of `pressure' are scrutinized in chapter 3. The mechanical or virial route to the pressure is reviewed as a result of the forces exerted by the momenta and interactions of the particles per unit area. The mechanical pressure turns out to be a tensor quantity and is used to recover results known in the literature. Since the interactions cannot be assigned unambiguously to one position in space, the local pressure is found to be equivocal.
A lattice model allowing spatial gradients is elaborated. The grand potential density of a system, which is the work of changing the volume of the system reversibly, is identified as the scalar thermodynamic pressure. For a bulk system, the grand potential density recovers the Kamerlingh-Onnes virial expansion of the pressure and has the same features as the reduced van der Waals pressure. Moreover, it has been shown that in the continuous limit the Helmholtz energy of the lattice gas can be written as the Landau expression for the free energy. For an inhomogeneous system of monomers, pressure profiles are found from the grand potential density that have similar features as those found from the virial route. That is, in the vicinity of an interface both tensile and compressive regions are observed. In the model by Szleifer et al. the tensile, i.e., negative region of the locale pressure is omitted. Since that region may be necessary to obtain low interfacial tensions for some systems, an important feature of their `pressure' has been ignored. Since the reference state of the energy of the lattice model can be chosen freely, it is concluded that the thermodynamic pressure can neither be given unambiguously.
The bending and torsion stress of a monomer liquid-vapour interface are determined from their mechanical expressions using two definitions of the local pressure. The expressions as derived in chapter 2 turn out to give unique consistent results, whereas the expressions known in the literature give ambiguous outcomes for the thermodynamically well-defined parameters. The latter is physically unacceptable. Since, unlike the virial route to the pressure, the thermodynamic pressure of the lattice model yields by definition a unique expression for the grand potential, it is concluded that this lattice model is a useful tool to model curved interfaces.
A phenomenological description of the curvature dependence of the interfacial tension is given in chapter 4. Up to first order in the curvature, the change of the interfacial tension is determined by the Tolman length. A second order description is given by the Helfrich equation, which, in turn, is determined by the bending modulus and the saddle-splay modulus. These Helfrich constants turn out to be the (derivatives of the) bending and torsion stresses of the planar interface, respectively. As a consequence of the different mechanical expressions for the bending and torsion stress, the Helfrich constants cannot be obtained from the properties of the planar interface only but also require the curvature dependence of the bending moments. This difference with the equations known in the literature can be traced back to the difference of the definition of the pressure from either a virial or thermodynamic route. It is shown that for a simple liquid-vapour interface the extra terms are needed when the pressure is found from the grand potential density. Only then are the Tolman length and the mechanically obtained Helfrich constants consistent with a parabolic fit to the interfacial tension.
The Helfrich constants of the simple liquid-vapour interface can be determined as a function of the intermolecular interactions. It is shown that a van der Waals density functional theory and its asymptotic expressions reproduce the Helfrich constants found from the lattice model in the vicinity of the critical point. Away from the critical point the square gradient of the van der Waals theory is not sufficient to account for the changes in the density profile across the interfacial region.
The phase behaviour of a bilayer membrane is considered in chapter 5. In order to model surfactants, the lattice gas model is extended to chain molecules. It is thought that each segment of the chain emerges from its predecessor such that the end of the chain can be considered as a diffusing particle obeying the Fokker-Planck equation. The grand potential density is again identified as an (ambiguous) local pressure. By choosing proper interactions, the formation of surfactant vesicles can be modelled.
For this study, the non-ionic surfactant C 12 E 5 is modelled. The interfacial tension of the vesicle is determined as a function of its radius. The resulting Helfrich constants determined both mechanically and from a parabolic fit to the interfacial tension are consistent. Keeping the hydrophobicity of the tail group constant, the Helfrich constants of the vesicle are obtained as a function of the hydrophilicity of the head group. It is found that for very hydrophilic head groups the bending modulus has an almost constant positive value, whereas the saddle-splay modulus is negative. This is thus interpreted that the membranes are relatively rigid. When the hydrophilicity decreases, the bending modulus becomes less positive and the saddle-splay modulus less negative. This renders less rigid bilayers, allowing large collective fluctuations, i.e. undulations, of the membranes. Hence, owing to steric hindrance, the spacing between a set of bilayers increases with decreasing hydrophilicity. For moderate hydrophilicity, the bending modulus is decreasingly positive. However, the saddle-splay modulus becomes positive which favours the formation of handles between the undulating bilayers. When the hydrophilicity is relatively low, the Helfrich constants seem to diverge because the head groups do not longer hydrated and the system phase-separates into surfactant and solvent rich phases. Since all these phases have been observed experimentally, it is concluded that the lattice model is a potentially valuable tool to study surfactant systems.
More information can be found onthe author's homepage.
|Fundamentals of interfacial and colloid science Vol III: Liquid-fluid interfaces
Lyklema, J. - \ 2000
San Diego : Academic Press - ISBN 9780124605237 - 785
colloïden - colloïdale eigenschappen - grensvlak - oppervlakte-interacties - oppervlaktechemie - oppervlakteverschijnselen - colloids - colloidal properties - interface - surface interactions - surface chemistry - surface phenomena
This volume deals with various aspects of surface tensions and interfacial tensions. Together with the phenomenon of adsorption (enrichment of molecules at interfaces), these tensions constitute the basic characteristics of interfaces. The authors try to keep the treatment systematic and deductive. Recurrent features are that each chapter begins, as much as possible, with the general thermodynamic and/or statistical thermodynamic foundations and the various phenomena are presented in order of increasing complexity. The requirement that the work be both a reference and a textbook is reflected in its being comprehesive as far as the fundamentals are concerned and in its didactic style.
Surfactants, interfaces and pores : a theoretical study
Huinink, H. - \ 1998
Agricultural University. Promotor(en): J. Lyklema; A. de Keizer. - S.l. : Huinink - ISBN 9789054857921 - 122
oppervlaktespanningsverlagende stoffen - grensvlak - chemische structuur - chemische samenstelling - surfactants - interface - chemical structure - chemical composition
The aim of this study was to investigate the behavior of surfactants in porous media by theoretical means. The influence of curvature of a surface on the adsorption has been studied with a mean field lattice (MFL) model, as developed by Scheutjens and Fleer. An analytical theory has been developed to interpret the MFL results. The chapters three and four, which form the core of this thesis, have been devoted to the background and the outcomes of both theories. These theories contain various approximations and therefore limitations. In the flanking chapters two and five attempts to overcome two of these approximations have been described. First, the MFL theory considers water as built up from isotropic monomers. As a consequence, the theory cannot predict the characteristic behavior of water. An alternative model could be the Besseling theory, which is based on the quasi- chemical approach. Some elaborations of this water model have been reported in chapter two. Second, the MFL theory, as used in the chapters three and four, always assumes homogeneous surfactant layers, which is inherent to its mean field approximation. However, it is well known that adsorption layers of surfactants often consist of discrete aggregates. The Herzfeld model has been chosen to study the discrete nature of the adsorbed layer. The theory and its outcomes, dealing with aggregation and ordering behavior of surfactant aggregates at interfaces, have been described in the last chapter.
In chapter two a lattice model for water, developed by Besseling, has been extended by incorporation of the electrostatic interactions of the water molecules with each other and with an external electrostatic field. This could have been the first step towards a better description of water near charged interfaces or in charged pores and electrosorption phenomena. The waterwater and water-field interactions have been treated with the reaction field approach of Onsager. Expressions have been obtained for the dielectric constant of the water in an external field.
At low field strengths, the predicted permittivity is close to the experimental one. The temperature dependence has also been reproduced. The dipolar correlation factor has been obtained by using the Clausius-Mossoti equation for the refractive index and the Kirkwood-Fröhlich expression for the dielectric constant. The predicted correlation factor and its temperature
An analytical theory for nonionic surfactants in hydrophilic cylindrical pores has been developed in chapter three. The adsorption has been approximated with a phase transition model. Above a certain surfactant concentration a monolayer of isolated molecules converts into a bilayer. With the help the thermodynamics of phase transitions, the surfactant chemical potential at phase transition could be related to the curvature of the pore. The shift in this chemical potential due to the curvature is in first approximation proportional to the curvature constant of the bilayer. A molecular model, mean field type has been used to interpret this curvature energy. Both the curvature energy and the surface tension can be calculated from the excess grand potential density profile. The curvature constant has been calculated from the profile of a flat layer, which is allowed as long as this profile is not very sensitive to the curvature. An equation, which relates the chemical potential at phase transition, the curvature, the structure of the layer and the affinity, has been derived.
Our model predicts that the chemical potential of phase transition decreases with decreasing pore radius. The adsorbed bilayer becomes more stable when the pore - radius decreases. Experiments confirmed these trends. If the affinity of the adsorbed layer for the surface increases, the curvature influence on the chemical potential of phase transition increases.
To test the analytical theory and to obtain generic knowledge about the influence of curvature on surfactant adsorption, MFL calculations have been performed, which have been described in chapter four. Contrary to the analytical model, the MFL theory allows changes in the structure of the adsorbed layer with curvature.
The position of the phase transition in a curved system has been calculated as a function of the adsorption energy and the size of the tails and the headgroups. No matter what parameters were used, the MFL calculations always predicted that the surfactant chemical potential of phase transition decreases with decreasing pore radius, which confirmed the outcome of the analytical model. Especially the adsorption energy turned out to have a strong influence on the sensitivity of phase transition for the curvature. The shift in the chemical potential of the phase transition becomes stronger with increasing adsorption energy, as has also been predicted with the analytical theory.
The most important approximation of the analytical theory, which has been tested with MFL calculations, is the curvature independency of the structure of the adsorbed layer. The surface tension of an adsorbed bilayer has been calculated as a function of the curvature for different chemical potentials. The curvature constant has been obtained as a function of the chemical potential by fitting these curves and calculating it from the excess grand potential density profile of a flat layer. It turned out that the last procedure, which is also used in the analytical theory, underestimates the value of the curvature constant. As long as this constant has a considerable value, the error made by this procedure does not effect the essential physics. Therefore it may be concluded that the analytical theory still captures the important physics despite its severe assumptions.
Both the analytical theory and the MFL model neglect the existence of discrete surfactant aggregates at the surface. To remedy this shortcoming, in chapter 5 the Herzfeld model has been applied to the adsorption of rod-like aggregates at a solid- water interface. The adsorbed layer was represented as a collection of rod-like polydisperse particles embedded in a monolayer of surfactants. An equilibrium condition has been derived, stating that the intrinsic excess grand potential of a rod of a given length plus its hard rod chemical potential has to be zero. The intrinsic excess grand potential has been divided into cap and body contributions, which are in principle the only two input parameters of the model. To calculate the hard rod chemical potential, the Herzfeld lattice model has been used. Rods are represented as rectangles. These rectangles have been placed on a square lattice. As a consequence the number of possible orientations of a rod is two.
By combining the Herzfeld model and the equilibrium condition, expressions for the length distributions in both directions have been obtained. With these distributions expressions were derived for the total number of rods, the average aspect ratio and the standard deviation of this aspect ratio, all in both directions. The distributions have exponential forms, with decay parameters equal to the average aspect ratio minus one and the standard deviation of the aspect ratio. The close relationship between the average aspect ratio and its standard deviation has made clear that size fluctuations are very important in systems with large rods.
Calculations have been performed on isotropic systems. Adsorption isotherms have been calculated for different cap Helmholtz energies. These isotherms show that the surfactants already adsorb in large amounts when the aggregates as such are not stable. However the collection of aggregates is stabilized by the translational entropy. If the caps become more unfavorable the co-operativity of the adsorption increases, because the length of the adsorbed aggregates increases. Adsorption isotherms have also been obtained for systems, which are allowed to order. It has been shown that at a certain surfactant chemical potential a second order isotropic- nematic phase transition occurs. After this transition the growth of the aggregates is promoted in the direction of alignment and inhibited in the direction perpendicular to that.
The isotropic-nematic transition line has been calculated. It turned out that ordering can take place at much lower surface densities of rods when the average aspect ratio increases. The cap fraction is inversely proportional to the average aspect ratio minus one to the power two at the transition line. Although this expression could not be derived, the close resemblance with an equation, derived for monodisperse rods, confirmed that it is an exact outcome of the model. With the formula found, a relation between surface density at the transition line and the Helmholtz energy of the end caps has been derived, which showed that the nernatic ordering takes place at lower rod densities when the caps become more unfavorable.
In the end of my study it has become more and more evident that the phase behavior of surfactants at interfaces should be at least as rich as in solution. As experimental techniques to investigate the structure of micelles at a surface are becoming available (e.g. AFM), we expect that the possible morphologies will become known to us in increasing detail in the near future. This thesis may assist the explorations, directed to fill the gaps in our knowledge of the behavior of surfactants at the solid-water interface, and thus allows us to use surfactants more effective in its applications.
The influence of spreading particles on the stability of thin liquid films
Bisperink, C.G.J. - \ 1997
Agricultural University. Promotor(en): A. Prins; H.J. Bos. - S.l. : Bisperink - ISBN 9789054857174 - 214
oppervlakten - grensvlak - dispersie - gassen - schuim - oppervlakteverschijnselen - surfaces - interface - dispersion - gases - foams - surface phenomena
The influence of spreading particles on the stability of thin liquid films was investigated. Due to the spreading of a particle, i.e. an oil droplet, over a surface of a thin liquid film the latter becomes thinner and may rupture. The following steps in the whole process were distinguished: 1) transport of the particle to the film surface, 2) dewetting of the particle ensuring physical contact between the particle surface and the film surface, 3) spreading of the particle over the film surface and 4) movement of the film bulk liquid induced by the surface movement due to spreading material.
An attempt was made to develop a theory that describes the spreading process quantitatively. It describes the film thinning process as a result of the liquid drag due to the surface motion initiated by the spreading material by using the parameters film thickness, droplet radius, liquid bulk viscosity, liquid bulk density and the surface rheological properties of the oil droplet and the film liquid.
Model systems of foaming liquid and lipid material were used to study this spreading process. The latter was done on a relative macroscopic scale over bulk surfaces which is different compared to the dimensions and conditions which are valid for spreading particles on a foam film. It was assumed that the developed theory could be applied to both dimensions. The experimental results pointed in this direction. This was verified by the experimental results of introducing small spreading emulsion droplets on thin liquid films. A clear correlation between the above mentioned parameters and film rupture initiated by the spreading droplets was found.
Polymer adsorption theory : universal aspects and intricacies
Linden, C.C. van der - \ 1995
Agricultural University. Promotor(en): G.J. Fleer; F.A.M. Leermakers. - S.l. : Van der Linden - ISBN 9789054854203 - 106
oppervlakten - grensvlak - polymeren - oppervlakteverschijnselen - surfaces - interface - polymers - surface phenomena
The work presented in this thesis is based on the theory for polymer adsorption by Scheutjens and Fleer (SF). Roughly, the thesis can be divided into two parts: the first two chapters consider the original theory from a new viewpoint, attempting to find universal laws and to establish connections with analytical theories. The last three chapters are devoted to extensions of the theory to more intricate systems.
In chapter 1 polymer adsorption from dilute solution is studied. We try to find the universal behaviour in the volume fraction profile as predicted by De Gennes from scaling arguments. In this analysis, three regimes are distinguished: close to the surface a proximal regime , which is dominated by the numerous contacts between polymer and surface, next to that a central regime , where the volume fraction profile decays as a power law which is independent of solution concentration and polymer chain length, and finally a distal regime with an exponential decay towards the bulk volume fraction. With the SF theory these regimes can indeed be found provided the polymer chains are sufficiently long (more than, say, 5000 segments). However, the exponent in the power law regime does depend on solution concentration and polymer chain length. Extrapolation to infinite chain length yields the proper mean-field exponent. Although in general mean-field theories (like the SF theory) can yield incorrect exponents, they tend to predict the proper trends, so that it can be expected that a chain length dependence is actually present. In *-solvents, where the mean-field treatment is thought to be exact because the second virial coefficient vanishes, an additional regime is found in between the central and distal regime. Its origin is, as yet, unclear.
The volume fraction profile is also the main topic in chapter 2, which discusses polymers adsorbing from a semi-dilute solution in a good solvent. In a semi- dilute solution the correlation length is independent of chain length, and it is found that this correlation length and the adsorption energy are the only parameters determining the volume fraction profile. Thus, in contrast to the case of dilute solutions in chapter 1, the profile for adsorption from semi-dilute solutions is independent of the polymer chain length. The free energy equation derived by SF is shown to be equivalent to that obtained in analytical mean-field theories if it is assumed that all segments of a polymer chain are distributed within the system in a similar way. Such an assumption is called a ground-state approximation. This ground-state approximation can also be used to extract the adsorbed volume fraction profile (comprising only the polymer chains touching the surface) from the overall profile. This has been done by Johner et al . Their results compare well with SF calculations when the bulk concentration is high and the adsorption energy low, but the agreement is much less when this is not the case, possibly due to the larger influence of tails under these conditions. When a bidisperse polymer mixture adsorbs from a semi-dilute solution the overall profile is not affected, even though the individual components may show a very different profile.
In chapter 3 we leave the case of simple flexible homopolymers and consider the influence of partial rigidity within the chain. Rigid polymers possess less conformational entropy, and hence adsorb more easily than flexible polymers. Chain stiffness is modelled by excluding direct backfolding and defining an energy difference between a straight and a bent conformation of two consecutive bonds, where the straight conformation is more favourable. When all parts of the polymer are equally stiff, a persistence length can be defined, which increases with the energy difference. Using this persistence length, the radius of gyration of a stiff polymer in solution can be rescaled to a flexible one with a smaller number of segments. However, it turns out that this procedure does not work out well for adsorption from dilute solution: the scaling laws in the central regime as found in chapter 1 are altered. The critical adsorption energy decreases with increasing persistence length, in full agreement with an equation formulated by Birshtein, Zhulina and Skvortsov. The situation gets complicated when only part of the polymer is stiff. As the stiffer par's lose less entropy upon adsorption, they adsorb preferentially. This effect leads to copolymer adsorption behaviour, even when there is no difference in interaction energy between the stiff and the flexible moieties.
Entropic effects play a major role also in chapter 4, where the adsorption of comb polymers is considered. Comb polymers consist of a backbone and a (large) number of teeth, hence they have a large number of chain ends per molecule. These ends prefer to protrude into the solution to form dangling tails. As a result, combs tend to adsorb in a conformation where the backbone is preferentially on the surface and the teeth stick out. This leads to relatively thin adsorbed layers, and if the distance between the branch points of the comb is small compared to the tooth length a depletion zone develops adjacent to the adsorbed layer. For comb copolymers it is found that if the teeth adsorb preferentially over the backbone segments the critical adsorption energy is lower than in the case where the backbone adsorbs, even though both types of molecules have the same number of adsorbing segments. At the point of desorption only a few segments are on the surface, and a polymer in which only the tooth segments adsorb loses less entropy than a polymer adsorbing with its backbone.
Finally, in chapter 5 we consider chemical surface heterogeneity by incorporating in the chain statistics a probability that a surface site has a particular adsorption energy. The surface can be constructed such that, on average, no energetic interaction between the polymer and the surface is present. Nevertheless, adsorption can take place on such a surface, provided "adsorbing sites" (sites with a favourable adsorption energy) are grouped together. The distribution of adsorbing sites determines largely the adsorption behaviour. If the driving force for adsorption is high, more polymer adsorbs on a surface with an equal distribution of adsorbing sites, as more of the available surface can be used. On the other hand, at low adsorption energy, it is more favourable to have the adsorbing sites group together, so that little of the non-adsorbing sites are in contact with the polymer.
In conclusion, universal behaviour is found only in the case of flexible, linear homopolymers adsorbing from a semi-dilute solution in a good solvent. In all other cases studied (dilute solutions, chain rigidity, chain branching and surface heterogeneity) the structure is more intricate. Although the meanfield character of the Scheutjens-Fleer theory is definitely a serious approximation, it does enable the modelling of a large variety of equilibrium systems, even at high concentrations, providing an abundance of detailed information. It is worthwhile to continue to check its assumptions and predictions with other theories and obviously with experiment. The volume fraction profile determines the properties of the system and is also very sensitive to the approximations used in the model. Therefore, precise and unambiguous measurements of the density profile remain of the utmost importance.