From two-dimensional model networks to microcapsules

Rheol Acta (2002) 41: 292–306 DOI 10.1007/s00397-002-0233-3

Heinz Rehage Martin Husmann Anja Walter

Received: 28 August 2001 Accepted: 17 January 2002 Published online: 9 May 2002
Springer-Verlag 2002

H. Rehage (&) Æ M. Husmann Æ A. Walter Institute of Physical Chemistry, University Essen, Universita¨tsstr. 2–5, 45141 Essen, Germany E-mail: [email protected]

ORIGINAL CONTRIBUTION

From two-dimensional model networks to microcapsules

Abstract The synthesis of microcapsules for technical, cosmetic, and pharmaceutical purposes has attracted much interest in recent years. The design of new capsules requires profound knowledge of their mechanical properties. Rheological studies provide interesting information on intrinsic membrane features and they can also be used to obtain information on bursting processes and shearinduced release of encapsulated compounds. In this article we shall discuss the basic rheological properties of different types of ultra-thin membranes, which can be used to form stable capsules walls. We have also analyzed the typical structures of these cross-linked films using Brewster-angle microscopy. Tiny oil or water droplets, which are surrounded by ultra-thin membranes, form simple types of

Introduction Typical capsules consist of a liquid core enclosed by a membrane of solid-like or rubber-elastic properties. Such structures are often recognized in nature as living cells (Chang 1972, 1997, 1998). One well-known example for such a biological type of microcapsule is the red blood cell. A human erythrocyte consists of a lipid bilayer that is coupled at well-defined anchor points to a two-dimensional spectrin network, which confers elastic forces to the liquid like phospholipid-bilayer. As a consequence, the red blood cell is easily shearable,

microcapsules. In addition to the interface shear rheology, we have measured the Young’s modulus (elongational modulus) and the Poisson ratio using a modified spinning drop apparatus. The shear-induced deformation and orientation of microcapsules was investigated in optical rheometers (rheoscopes). In the regime of small deformations the results were in fairly good agreement with a theoretical model recently proposed by Barthe`s-Biesel. Due to the simple synthesis and well-defined structure, microcapsules can also serve as model systems to understand the complicated flow properties of red blood cells (erythrocytes). Keywords Microcapsule Æ Interfacial polymerization Æ Ultra-thin network Æ Young’s modulus Æ Surface elasticity

but strongly resistant to any increase in the local surface area. It turns out that the stability of red blood cells is highly dependent upon the rubber-elastic properties of the supporting spectrin network. The unique combination of elastic and viscous forces leads therefore to interesting mechanical properties of the red blood cells. Besides their presence in biological systems, microcapsules are frequently used as small containers in pharmaceutical, cosmetic or chemical industry (Chang 1972. Most of these applications are associated with the controlled release of active ingredients at well-

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defined external conditions (Patwardhan and Das 1983). Detailed knowledge of wall properties such as stability or elasticity is essential to design tailor-made capsules with controlled release properties. Mechanical forces such as swallowing (101–102 s–1), stirring (101– 103 s–1), or rubbing (104–105 s–1) are often linked to undesired deformation and breaking processes of the capsule walls. It is therefore interesting to understand the rheological properties of these artificial cells. In this publication, we shall first discuss the basic features of ultra-thin membranes, which can be used to construct stable capsule walls. In the second part, we shall focus our attention on the deformation and bursting process of capsules under the influence of centrifugal or shear forces. The present article gives a review of our work in this area, and this topic was presented as plenary lecture at the Golden Jubilee Meeting of the German Rheological Society in Berlin, May 14–16, 2001.

Experimental results Two-dimensional model networks Ultra-thin cross-linked membranes have been prepared with different techniques at the water surface or at the interface between oil and water (Achenbach et al. 2000; Burger et al. 1995; Husmann et al. 1999). These structures can be formed using the self-associating properties of tensio-active molecules such as surfactants, phospholipids, or proteins. Extensive investigations of the rheological properties of protein layers were performed by Dickinson and others (Dickinson 1997, 1998, 1999; Dickinson and Wasan 1997; Faergemand et al. 1997). It turns out that protein films tend to form cross-linked network structures at fluid interfaces, and these properties are very often used in the food industry in order to stabilize creams, foams or emulsions. In this article we shall only focus on artificial membranes, which were synthesized from surfactant molecules or polymers. Ultra-thin cross-linked membranes can be categorized, depending on the nature and strength of bonding forces. Two extreme cases are often observed in colloidal systems: transient networks and permanent structures. When the cross-linking process is a result of chemical reactions, the structures are always of the permanent type. As well as chemically cross-linked membranes, networks can also be formed by physical contact. In this case, the crosslinking reaction occurs by a process of self-association. This physical contact is caused by attractive interactions, including, for example, complex formations, Coulomb forces, hydrogen bonds, and hydrophobic interactions.

Physically cross-linked membranes Polyamide networks The best known heterogeneous polycondensation reaction carried out at the oil-water interface is a variant of the Schotten-Baumann reaction, in which dicarboxylic acid dichlorides react with diamines or dioles (polyamide formation). This polycondensation reaction can be carried out in a two-phase system. The dicarboxylic acid dichloride dissolved in organic liquids like carbon tetrachloride and the polar diamine is miscible in hydrophilic phases like water. At the interface between oil and water both compounds react, and a thin film of polyamide is formed, which can be removed from the interface using a glass tube (‘‘nylon rope trick’’). Depending on the concentrations of the chemical compounds, the formation of the flat polyamide membrane can take several hours. A typical example showing the kinetics of surface gelation is summarized in Fig. 1 (Walter 1999). We have plotted the two-dimensional storage modulus l¢, which describes the elastic properties of the sample, as a function of the reaction time (Walter et al. 2000, 2001). Such curves can be obtained using surface rheometers. Details of sample preparation and experimental equipment needed for such measurements have been extensively described in previous publications (Achenbach et al. 2000; Burger et al. 1995; Pieper et al. 1998; Walter et al. 2000, 2001). It is evident that the network shown in Fig. 1 exhibits striking elastic properties, although the reaction only leads to the formation of linear polymer chains. Besides the presence of entangled macromolecules, the cross-linking process is due to the formation of small crystals, which lead to multifunctional junction points (Walter et al. 2000, 2001). If trifunctional compounds are used in place of

Fig. 1. Time-sweep experiment for the reaction between 10 mmol/l 1,6-diaminohexane with 1 mmol/l sebacic acid-dichloride (x=2 rad/s, c=0.2%, T=200 C, water-silicon oil interface)

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diols or diamines, one obtains chemically cross-linked networks instead of physically stabilized coherent phases. The cross-linking reactions are terminated as soon as l¢ has reached its finite plateau value. In the present case, the evolution of l¢ starts immediately after mixing the two chemical compounds at the liquid interface. The plateau value is reached after a reaction time of approximately 1 h (see Fig. 1). The actual time span is highly dependent upon the concentration of the monomeric compounds. Since it is possible to terminate the polycondensation reaction at any instant by exchanging the solvent, we can use this method to synthesize membranes with different elastic properties. Polyamide membranes can be used to synthesize polymers of very high molecular mass, which are physically cross-linked by crystallized regions. Polyamide microcapsules are ideal model systems on grounds of their simple synthesis, non-toxic properties, and defined structure.

Fig. 2. The two-dimensional storage and loss modulus as a function of the angular frequency for a Span 65 film formed at the interface between dodecane and water. (c=0.5 mmol/l, T=20 C)

Networks stabilized by hydrogen bonds It is well known that the surfactant Span 65, trioctadecanyl ester of sorbic acid, has a tendency to form very stable emulsions. Because of these special features, this surface-active compound is frequently used in technical applications. Typical examples of these technologies include the formation of foams, microcapsules, or concentrated emulsions. Enhanced emulsion stabilities are often correlated with large values of the surface viscosity or elasticity (Edwards et al. 1991). It is interesting to note that ultra-thin films formed by adsorption of SPAN 65 molecules exhibit such viscoelastic features. Relevant data are summarized in Fig. 2 (Rehage et al. 2001). Span 65 molecules are only soluble in dodecane, and due to the surface activity of this detergent a monomolecular film instantaneously forms at the interface to water (Rehage et al. 2001). The rheological data of such films exhibit typical properties of a generalized Maxwell material. In the regime of high frequencies, the two dimensional storage modulus l¢(x) attains a plateau value, and under these conditions the elastic response of the sample is dominant. It turns out, that l¢(x)>>l¢¢(x) for xk>>1. The plateau value describes the rubber-elastic properties of the sample. With decreasing angular frequency, the viscous properties become more important. In this regime, relaxation processes occur and the solution behaves as a liquid (terminal zone). The intersection point, where l¢(x)=l¢¢(x), is characterized by an average value of the relaxation time. This average relaxation time describes the dynamic features of the ultra-thin networks. In monolayers of surfactant molecules, stress decay can

only occur by rupture processes of junction points. We can conclude therefore, that the Span 65 networks are fluctuating, and are continuously constructed and destroyed by the formation and breaking of cross-linking points. In such systems the relaxation time describes an average lifetime or breaking time of the junction points. Under experimental conditions, where the frequency is short in comparison to the reciprocal lifetime, a junction point cannot open during one oscillatory cycle. Under this regime, the adsorbed layer behaves as a permanent cross-linked network. A completely different structure results for small angular frequencies. Here, we detect numerous breaking and reformation processes within the time scale of observation. As a consequence, an applied shear stress will completely relax and a fluid-like behavior results. The intermediate frequency range is characterized by an ambivalent behavior where both processes occur simultaneously. This regime is characterized by striking viscoelastic properties. The experimental data of the concentration dependence of the surface shear modulus suggests that hydrogen bonds may be responsible for this special behavior. This seems, however, not to be the only source of cross-linking processes because the surfactant SPAN 60, a similar compound, does not show the formation of these supermolecular structures (Rehage et al. 2001). The number of paraffin chains generally indicates the difference between these surface-active molecules: SPAN 65 has an average value of three and SPAN 60 only one of these hydrophobic chains. Since it is well known that long paraffin chains interact by van-der-Waals attractions, there may also be a combination of hydrogen

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bonds and hydrophobic forces, which finally leads to the observed dynamic cross-linking process. Membranes stabilized by Coulomb interactions If cationic or anionic surfactants are combined with multivalent counter ions, networks with rubber-elastic features are often formed at fluid interfaces (Achenbach et al. 2000; Rehage et al. 1997). In this case ionic surfactant molecules are cross-linked by oppositely charged counter-ions. Typical properties of these ultra-thin membranes are summarized in Fig. 3. Figure 3 gives information on the cross-linking reactions of such a film at the pure water surface. The surfactant concentration is far below the cmc (critical micelle concentration), so that most of the molecules are solved as monomers. After addition of multivalent counter ions (cerium sulfate), the surface gelation process sets in, taking around 2 h until the network is completely formed. Since the diffusion of surfactants molecules to the surface is complete within milliseconds, the characteristic gelation time must be a cooperative process, occurring immediately after forming the surfactant film. This might be a special coagulating process, as proposed by the Smoluchowski theory (Husmann et al. 1999). It is easy to see that these ultra-thin membranes have viscoelastic properties. As well as rheological measurements, the process of surface gelation can also be observed by Brewster-Angle-Microscopy. Relevant results are summarized in Fig. 4 (Achenbach et al. 2000). Dark areas represent the pure water surface, whereas white colors are due to the presence of surfactant aggregates. These images clearly demonstrate the different stages of cross-linking as a function of

Fig. 3. The two-dimensional storage modulus l¢ and loss modulus l¢¢ of CTAB (cetyl trimethyl ammonium bromide) as a function of the reaction time t (CTAB, c=6·10–7 mol/l, counterions: cerium(IV)-sulfate, c=10–3 mol/l, x=10 rad/s, deformation c=0.2%, T=20 C)

time. At the beginning (after 30 min) separate aggregates can be detected, since they are only partially linked to each other. After 1 h the number of junction points is significantly increased. There are also some areas, however, in which the network was not yet completely formed. These experimental results are in general agreement with percolation theories, predicting increasing clusters as the reaction proceeds (Figon et al. 1999; Daboul et al. 2000; Heo et al. 1999; Jan and Stauffer 1998; Stauffer 1997, 1998; Stauffer and Chang 1999). After a reaction time of 2 h, large aggregates, where the molecules are tightly linked, can be observed. Due to this dense packing, individual fragments within these aggregates can no longer be resolved by means of Brewster-Angle-Microscopy. After 2.5 h, a homogeneous film occupies the entire visible area. These observations are consistent with results obtained by shear rheological measurements of films at similarly low surfactant concentrations (see Fig. 3) (Achenbach et al. 2000). Ultra-thin networks, stabilized by Coulomb forces, can be formed by a large number of anionic or cationic surfactants. It is interesting to note that all structures we have investigated so far exhibit similar properties. The basic network structure consists of disc-like aggregates having typical diameters of several micrometers in the vicinity of the sol-gel transition. The aggregates are in close contact, forming infinite large clusters of fractal geometry. These networks have many pores, but with increasing surfactant concentration the uncovered areas become much smaller and a homogeneous film structure is formed. Since these membranes are easy to synthesize, they may be used in technical applications for the stabilization of emulsion droplets and foams.

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Fig. 4. Brewster-angle-microscope-images of CTAB and cerium(IV)-sulfate after various reaction times (CTAB c= 5·10–7 mol/l, cerium(IV)-sulfate c=10–3 mol/l, pH=2)

Chemically cross-linked membranes Ultra-thin membranes formed by radical reactions In previous investigations, we have used the radical polymerization of surface-active methacrylate diesters, in order to synthesize ultra-thin networks at the interface between oil and water (Burger et al. 1995; Burger and Rehage 1991, 1992, 1998; Rehage and Burger 1993). Methacrylate diesters are soluble in oil (e.g., dodecane) but quasi-insoluble in polar liquids such as water. At the interface between oil and water, however, monomolecular films of adsorbed molecules are formed upon instantaneously. On irradiation with ultraviolet light at a wavelength of 254 nm, a photoreaction sets in which finally leads to the cross-linked film (Burger et al. 1995; Burger and Rehage 1991, 1992, 1998; Rehage and Burger 1993). It turns out that the membranes prepared by these techniques exhibit rubber-elastic properties. We have analyzed the two-dimensional sol-gel transition, the kinetics of gelation, and the rheological properties of the cross-linked films. The scaling behavior was in excellent agreement with percolation theories (Burger et al. 1995; Burger and Rehage 1991, 1992, 1998; Rehage and Burger 1993). We also observed a power-law relaxation behavior in the vicinity of the sol-gel transition. This is consistent with experimental results first published by Winter and others (Chambon et al. 1986; Chambon and Winter 1985; Winter 1987, 1994, 1997; Winter et al. 1994; Winter and Mours 1997). It is interesting to note that the coherent structure of these membranes can be observed

Fig. 5. Brewster-angle microscopy image of 1,12-dodecandioldimethacrylate at the pure water surface (surface excess: 1.05 nm2/ molecule, T=20 C, 12 h irradiation time)

by means of Brewster-Angle-Microscopy in the vicinity of the sol-gel transition. The image at Fig. 5 represents the sol state after starting the surface polymerization. Dark areas represent the uncovered water surface. It is easy to see that large ring-shaped network clusters are formed. This observation is in fairly good agreement with percolation theories (Stauffer and Aharony 1995). Relevant data concerning the pore size in these twodimensional networks can be obtained by electron spin resonance measurements (Burger et al. 1995). Using spin labels of significantly different sizes that were diffusing from the aqueous environment into the oil phase, it was possible to determine the average mesh

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size of the interfacial network structure (Bredimas et al. 1983; Burger et al. 1995). In a recent publication, we have also investigated the elongational rheological properties of these membranes (Pieper et al. 1998). For these measurements, we have developed a new experimental technique that consists of measuring the deformation of a microcapsule in the spinning drop apparatus (Pieper et al. 1998). The theoretical analysis of the deformation process allows calculation of an interface apparent elastic Young’s modulus. Comparison of the surface shear modulus with the Young’s modulus allowed evaluation of the Poisson ratio of the cross-linked films.

Ultra-thin membranes formed by polycondensation reactions Chemically cross-linked membranes can also be synthesized using polycondensation reactions. This can be achieved by spreading organosiloxane compounds on the surface of acid or alkaline water. In this paper we focus upon interfacial polycondensation of octadecyltrichlorosilane. The surface gelation can be divided into hydrolysis and subsequent condensation. The chlorosilane is soluble in oil. Due to extreme reactivity with water molecules, hydrolysis of the chlorosilane to a silanol occurs with ease:

Fig. 6. The two-dimensional storage modulus l¢ and the loss modulus l¢¢ of a polyoctadecyl-siloxane membrane as a function of reaction time t (dodecane-water interface, c=0.1 mmol/l, T=23 C; x=1 rad/s, c=0.025%)

The generated silanol molecules have a tendency to condensate spontaneously. Therefore, a silanol reacts in a second step either with a second silanol:

or with an chlorosilane to produce a siloxane:

Fig. 7. The two-dimensional storage modulus l¢, the modulus l¢¢ and the magnitude of the complex viscosity [arrowvertex]g*[arrowvertex] as a function of angular frequency x (dodecane-water interface, c=0.1 mmol/l, T=23 C; c=0.2%)

The formation of highly stable siloxane groups accounts for the fact that the fast polycondensation can occur at room temperature. Typical results concerning the surface gelation of octadecylsiloxane membranes are summarized in Fig. 6 (Husmann 2001). To prepare a flat film 100 ml water was poured into the beaker that served as outer cylinder. The biconical disc of the surface rheometers was carefully brought into contact with the water/air surface to avoid formation of air bubbles. Afterwards, the water surface was covered with 10 ml dodecane. This solvent contained a fresh solution of octadecyltrichlorosilane.

The increase of l¢ describes the evolution of crosslinking as a function of reaction time. After a time span of about 2 h both moduli reach near constant values and the polymerization is complete. In this regime elastic properties are dominant. The ultra-thin networks formed by organosiloxane compounds exhibit striking rubber-elastic properties. This is evident from Fig. 7, where a frequency sweep test was performed (Husmann 2001). The flatness of the l¢ curve over the whole frequency range indicates the negligible influence of relaxation processes. This behavior is characteristic of a permanently cross-linked network, in which the junctions remain stable as a function of time. Besides these permanent interactions, the small contribution of hy-

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drogen bonds, which act as additional cross-linking points, should be taken into account. These fluctuating bonds can eventually be formed between sterically hindered, non-reacting silanol groups. Additional measurements concerning the viscoelastic properties can be obtained from strain sweep experiments. In these dynamic tests, the deformation is varied at a constant angular velocity. Relevant results of these measurements are summarized in Fig. 8. The elastic modulus remained constant up to a certain deformation, indicating a region of linear viscoelastic response. The value of the critical strain amplitude is approximately 5%. For three-dimensional rubber-elastic networks, rupture starts to occur at deformations between 10% and 500% (Ferry 1980; Vinogradov and Malkin 1980). The smaller value in this case can be attributed to the existence of short elastically effective chains and to a lower degree of conformational changes in two-dimensional systems.

It is possible to study the molecular structure of organosiloxane films at the water surface by means of Brewster-Angle-Microscopy images. Typical results are summarized in Fig. 9 (Husmann 2001; Husmann and Rehage 2001). The image at Fig. 9a describes a membrane in the solstate that already contains some finite clusters. These aggregates resemble honeycombs, in which the aggregates have no close contact to each other. This structure can be interpreted as a skeleton of two-dimensional foam with many defects. In the gel-state (Fig. 9b) the uncovered areas are much smaller. The film consists of roughly spherical particles that are in close contact forming a dense twodimensional network. The geometry appears to be of fractal nature. Furthermore, a kind of crumpling or buckling of the flat surface is indicated by optically homogeneous stripes. We must conclude therefore, that these films are not completely flat, but slightly folded (Achenbach et al. 2000; Husmann 2001). This interesting observation will be discussed in the following paragraphs. Investigation of microcapsules All polymerization techniques discussed so far can be used for the synthesis of microcapsules. In this case, oil droplets are suspended in water and the polymerization is initiated at the interface between the two immiscible fluids. In the following paragraphs we shall briefly discuss the deformation process of microcapsules, which might be induced by centrifugal fields or simple shear flow. Spinning capsule technique

Fig. 8. The two-dimensional storage modulus l¢ and the loss modulus l¢¢ as a function of the strain amplitude c (dodecane-water interface, c=0.1 mmol/l, T=23 C; x=1 rad/s) Fig. 9a,b. Brewster-anglemicroscopy images of the network structure formed by octadecyltrimethoxysilane monomers at the surface of water: a sol state (surface concentration: 2 molecules/nm2); b gel state (surface concentration: 4 molecules/nm2)

In order to measure the dilatation properties of thin membranes, we injected microcapsules into the rotating

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tube of the spinning-drop tensiometer (Husmann et al. 1999; Pieper et al. 1998). Details of the apparatus and all experimental procedures are extensively described in the publication of Pieper et al. (1998). The essential part of the spinning drop tensiometer consists of a horizontally aligned glass tube filled with water. The investigated capsule was synthesized near the center of the tube. Creaming of the microcapsules, caused by the density differences between oil and water, was avoided by constant tube rotation. At elevated centrifugal forces the capsules are not only aligned but also deformed as a result of their elastic shells. The shape and size of the capsules was recorded during tube rotation by means of a video camera (Pieper et al. 1998). In a number of experiments the particle deformation caused by the action of centrifugal forces was measured at different speeds of the rotating tube. Typical microcapsules observed at different centrifugal fields, are shown in Fig. 10 (Achenbach et al. 2000; Husmann 2001). For small values of the tube velocity (less than 3000 rpm) the capsule is slightly off center. The radius of these particles is about 0.5 mm. At low values of the angular frequency gravity is important, and the theoretical analysis of the deformation of these particles becomes complicated. At the limit of larger centrifugal forces, buoyancy effects may be ignored. According to the theory of D. Barthe`s-Biesel, capsule deformation can be described by the simple equation (Pieper et al. 1998) lb s D ¼ lþb ¼ Dqx2 a3  5þm 16Es

ð1Þ

This equation is valid at the limit of small capsule deformations. D is the capsule deformation, l denotes the longest and b the shortest axis of the deformed particle. The difference in density between the oil inside the capsule and the continuous water phase outside is Dq. x denotes the angular frequency of the rotating tube and a is the radius of the capsule in the quiescent state. Parameter Es describes the two-dimensional Young’s modulus (surface elongational modulus) of the ultra-

Fig. 10a–c. Polyorganosiloxane microcapsules observed at different speeds of the rotating tube: a 1000 rpm; b 5000 rpm; c 10,000 rpm. The horizontal line represents the axis of symmetry of the tube

thin membrane and mS the surface Poisson ratio. The surface shear modulus lS and the Young’s modulus are related by (Pieper et al. 1998): Es ls ¼ 2ð1þm sÞ

ð2Þ

Replacing ES in Eq. (1) yields lb s ¼ Dqx2 a3  32l5þm D ¼ lþb ð1þms Þ s

ð3Þ

Equation (3) depends on two different parameters – the surface shear modulus ls and the Poisson ratio ms. Since the shear modulus can be measured independently at flat interfaces using surface rheometers, it is possible to calculate ms from the deformation of the capsules. Relevant results are represented in Fig. 11 (Husmann 2001). At low centrifugal forces the deformation of the spinning capsule is a linear function of –Dqx2a3, as predicted from Eq. (3). After each experiment at elevated rotational speeds, we went back to the small tube rotation of 500 rpm. Using this condition the microcapsule should be near spherical, and any deviation from this quiescent shape indicates the occurrence of irreversible membrane modifications. It is easy to see that up to a centrifugal force of 5·10–2 N/m the microcapsule can be reversibly deformed. At this threshold value, the stretching is approximately 1%. This is of the same order as the limit of linear viscoelastic response, observed from strain-sweep experiments (see Fig. 8). Above this limit, the membrane becomes irreversibly deformed. The last point of the diagram corresponds to capsule breakup. This is clearly evidenced by analyzing the capsule shape (Fig. 12). The dispersed particles have evidently lost their elliptical shapes, and are no longer axis-symmetric. On close inspection it becomes clear that the microcapsules always burst at one of their poles (caps). This observation is consistent with the mechanical model proposed by Barthe`s-Biesel and others (Pieper et al. 1998). Figure 13 provides more insights into the load-bearing capacity of the membrane (Husmann 2001).

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Fig. 11. The capsule deformation D as a function of the centrifugal force –Dqx2a3 (outer phase: glycerol-water mixture, g=0.22 Pas, oil-phase: 0.2 mmol/l octadecyltrichlorosilane solved in p-xylene)

Fig. 13. Vector plot of the mechanical load of the membrane along the capsule contour

Fig. 12. Capsule bursting, induced by centrifugal forces

The capacity of mechanical load bearing, represented by vector arrows, attains maximum values at the poles (caps). The force deforming the capsule is generated by pressure differences between the inner and outer phase of the dispersed particle. Figure 13 describes why network rupture occurs randomly at one of the two poles of the microcapsules. From the linear part of Fig. 11 it is possible to calculate ms if the surface shear modulus is known from independent measurements. Relevant results are summarized in Fig. 14 (Husmann et al. 1999; Husmann 2001). It is worthwhile to mention that the two-dimensional Poisson ratio attains negative or positive values (Fig. 15). This parameter measures the strain in the transverse direction, which results from a longitudinal extension. A positive value of ms ratio corresponds to a material that shrinks transversally when it is stretched longitudinally. For membranes the behavior is different, and it appears that negative values of ms are also possible. From mean field calculations and Monte Carlo simulations, Boal et al. (1993) calculated ms for different

Fig. 14. The Poisson ratio mS and the Young’s modulus ES as a function of interface concentration Gm of the monomers (octadecyltrimethoxysilane microcapsules, formed from dodecane droplets which were suspended in the water phase)

types of tethered networks. For self-avoiding and phantom networks, the Poisson ratio varied between –1 and +1. For large deformations ms was always positive; however at intermediate deformations, negative values were obtained (Boal et al. 1993). These results can be understood by imaging a crumpled sheet of paper, which stretches in the direction perpendicular to that of stress. Presently, it is not clear whether the ultra-thin crosslinked membranes can really be compared to a phantom or self-avoiding network structure. The values of ms that were obtained, are at least, in general agreement with these theoretical predictions (Achenbach et al. 2000). It is interesting to note that the cross-linked polyorganosiloxane membranes show some folding phenomena, even in the quiescent state (see Fig. 9). These

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Fig. 15. Simple illustration showing the existence of negative twodimensional Poisson numbers. If a crumbled sheet of paper is stretched, it will simultaneously move in longitudinal and transversal directions

small deviations from the true planar surface seem to be responsible for the negative Poisson numbers measured. Shear induced deformation of microcapsules Red blood cells can change their shapes in response to local flow conditions. A similar phenomenon is observed with microcapsules if their walls consist of viscoelastic membranes. One of the first experiments describing interesting relations between particle deformation and shear thinning behavior was performed by Bredimas et al. (1983). Chang and Olbricht (1993a, 1993b) succeeded in confirming theoretical predictions by means of flow induced capsule deformation experiments. These authors investigated diethylene-triamine/sebacoyldichloride polyamide capsules brain-stembricht 1993a, 1993b). In comparison to the relatively few experimental studies, significant theoretical progress was achieved. Large deformations and burst of capsules in elongational flow was treated in a recent paper (Li et al. 1988). The flow of capsules into pores was described in Queguiner and Barthe`s-Biesel (1997). Suspensions of artificial two-dimensional capsules in shear flow were analyzed in Breyiannis and Pozrikidis (2000). The transient response of capsules under varying flow conditions was summarized in the publication of Diaz et al. (2000). Eggleton and Popel (1998) calculated large deformations of red blood cells and microcapsules in simple shear flow. Electrohydrodynamic effects on the deformation and orientation of a liquid capsule in linear flow were calculated by Ha and Yang (2000). Kwak and Pozrikidis (2001) discussed the influence of bending stiffness on the deformation of capsules in uniaxial extensional flow. Barthe`s-Biesel and others published extensive simulations of capsules in shear or extensional flow (Barthe`s-Biesel 1996, 1998; Barthe`s-Biesel and Chhim

1981; Barthe`s-Biesel and Rallison 1981). In order to compare these simulations with experimental data, we have synthesized chemically cross-linked polyamide microcapsules. These systems were prepared by interfacial polycondensation of 4-aminomethyl-1,8-diaminooctane and sebacoyl dichloride at the silicon oil-water interface (Walter et al. 2000, 2001). After synthesis, the capsules were inserted into an optical flow cell with Couette geometry (rheoscope). This apparatus was equipped with an inverse microscope. A high-speed video camera allowed detailed analysis of particle deformation and orientation. By rotating the cylinders in opposite directions, a linear shear field was induced within the gap. We measured the orientation and deformation of microcapsules as a function of the shear rate. The technical equipment used for these measurements is extensively described in Walter et al. 2000, 2001). It turns out that the shear-induced deformation of microcapsules is dependent upon the constitutive law of the enclosing membrane. For further analysis we shall focus only on a Mooney-Rivlin-type behavior of the capsule wall. This special constitutive law often holds for polymer systems. In this context, the membrane is considered as a three-dimensional volume incompressible material of negligible thickness. According to a model, recently proposed by Barthe`s-Biesel, a simple correlation between the capsule deformation and the elastic modulus describing of the wall material exists (Barthe`s-Biesel 1996, 1998; Barthe`s-Biesel and Chhim 1981): l  b 25 gs ac_ g ac_ D¼ ¼  þ Oð s Þ2 :::::: ð4Þ lþb 4 Es Es The capsule deformation D is defined as described in the spinning capsule experiments. The constant Es describes an effective two-dimensional elastic modulus which is composed of two modes of deformation, namely pure shear and area dilatation. Since the dilatation modulus of ultra-thin cross-linked membranes is approximately 3–4 times larger than the two-dimensional shear modulus, we can initially assume that Es is not significantly different from the surface Young’s modulus. gs describes the viscosity of the outer solvent phase, a the radius of the quiescent capsules, and c_ the shear rate. The ratio gs ac_ =Es is sometimes denoted as capillary number C. This constant is described by the ratio of deforming and restoring forces. Function O, which is dependent upon the square of the capillary number, denotes a more complicated expression, which can be calculated from the theories of Barthe`s-Biesel (Barthe`s-Biesel 1996, 1998; Barthe`s-Biesel and Chhim 1981). At the limit of low deformations this term is small and can be ignored. If we measure the deformation and orientation of microcapsules in simple shear flow, we can use Eq. (4) to obtain information on the membrane elasticity. The shear-induced deformation of microcapsules is visualized in Fig. 16 (Walter 1999).

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These images show a capsule in its quiescent state and under the action of shear forces. The deformed capsule has obtained an ellipsoidal shape and the orientation angle does not change very much as a function of the shear rate. During the course of different rheooptical measurements we noticed that the deformation and orientation angle of microcapsules do not remain constant, but fluctuate slightly. Similar observations were first reported by Chang and Olbricht (Chang and Olbricht 1993a, 1993b). A typical example is summarized in Fig. 17 (Walter 1999). The observed periodic effect is certainly not caused by any malfunction of the rheoscope, since oscillations were not measured for analogous emulsion droplets. Close inspection reveals that the oscillations of the deformation D and orientation angle v are linked. Both functions are sinusoidally oscillating with the same angular frequency xosc, and a well-defined phase shift of p/2 exists between them. In order to obtain more information about this phenomenon, we measured the membrane rotation time (tank-threading motion). This can be achieved by adsorbing tracer particles at the membrane surface. This procedure is shown in Fig. 18 (Walter 1999). We used aluminum tracer particles to evaluate the circulation frequency of the membrane. This parameter is often denoted as tank-threading time ttt.. Within the limits of experimental error there exists a simple relation Fig. 16. Photographs of a polyamide microcapsule subjected to shear rates of 0 s–1, 5 s–1, 12 s–1, and 25 s–1. The radius of the quiescent capsule is 208 lm. Polyamide microcapsules were formed by emulsifying an aqueous solution in silicon oil. (Aqueous phase: 10 mmol/l 4-aminomethyl-1,8diaminooctane dissolved in 10 mmol/l sodium carbonate; oil phase: silicone oil containing 1 mmol/l sebacoyldichloride 4aminomethyl-1,8-diaminooctane)

between the membrane rotation period and the oscillation time (Walter et al. 2001): ttt tosc  ð5Þ 2 It is interesting to note that such an equation was recently proposed by numerical simulations of Ramanujan and Pozrikidis (1998). These authors calculated oscillation effects for oblate spheres with initial deformation of D=0.05. In this model, membrane oscillation is supposed to be caused by the capsule’s asymmetric region, which periodically changes its position and thereby induces shape oscillations. We may therefore conclude that the oscillation phenomenon is linked to small deviations from the quiescent spherical shape. Diffusion processes can cause such irregularities, as can buoyancy and small shear forces, which are always present during capsule synthesis. Close inspection revealed that we never succeeded in synthesizing perfect spherical microcapsules. The maximum initial deformation of our particles was D=0.03; corresponding to an axis ratio b/l=0.97. This is only a minor deviation from the globular shape, but is significant enough to stimulate membrane oscillations. We conclude, therefore, that even slight irregularities of the wall material or small deviations from the initial spherical state can induce the described sinusoidal phenomenon. In optical rheometers (rheoscopes) we can observe the capsule deformation as a function of the shear rate.

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regime of small shear forces the droplet is oriented in a direction of 45 in respect to the streamlines. At increasing velocity gradients the droplet becomes more and more oriented in the direction of flow. For microcapsules, surrounded by Money-Rivlin-type membranes, the theoretical model proposed by Barthe`s-Biesel predicts a shear rate independent orientation angle v (Barthe`s-Biesel 1998): v ¼ 450

Fig. 17. Sinusoidal deformation of a polyamide microcapsule observed in simple shear flow for different values of the shear rate

Typical measurements are summarized in Fig. 19 (Walter 1999; Walter et al. 2000, 2001). This diagram shows average values of the sinusoidal size variation. Under the regime of small shear rates, a linear curve is observed. From the gradient of this line, it is possible to calculate Es according to Eq. (4). For polyamide capsules of various sizes and different elastic shells, we measured surface Young’s moduli which were about 3.5 times larger than the corresponding two-dimensional shear moduli (Walter et al. 2000, 2001). Since Es is approximately equal to the Young’s modulus we can use Eq. (2) in order to calculate the Poisson number. In twodimensional systems, ms can attain values between –1 and +1 (Pieper et al. 1998). For polyamide capsules we obtain m0.75. In contrast to organosiloxane membranes, we observed only positive values, indicating the absence of crumbling phenomena. In contrast to siloxane membranes, polyamide shells are much thicker, and this might be one reason for the different behavior of both materials. As well as measuring the shear-induced deformation, it is also possible to determine the orientation of microcapsules during flow. Typical measurements are shown in Fig. 20 (Walter 1999). The emulsion droplet behaves as predicted by the theory of Barthe`s-Biesel and Rallison (1981). In the Fig. 18. Visualization of the membrane rotation time with tracer particles for a polyamide microcapsule at a constant shear rate of 12 s–1

ð6Þ

For other types of constitutive membrane laws, however, the orientation angle does not remain constant (Barthe`s-Biesel 1998; Walter et al. 2000, 2001). Equation. (5) is only valid for microcapsules surrounded by Mooney-Rivlin type membranes. It is evident that the experimental data are not in agreement with Eq. (5). In the regime of small shear rates, the curve does not reach the limiting value of 45. This may be due to small deviations from the initial spherical state as discussed before. The decrease of the orientation angle with increasing shear rate can be understood if, in addition to elastic forces, viscous forces are also acting within the membrane. This assumption is supported by measurements of the two-dimensional loss modulus. Such data are represented in Fig. 21. We observe a rubber-elastic plateau, and at high frequencies a transition towards the glassy state. At all angular velocities, l¢ is larger than l¢¢. The decrease of the loss modulus at high frequencies represents an artifact caused by inertia problems of the rheometers torque transducer. Figure 21 shows that the polyamide membranes have mainly elastic properties, but viscous forces are also observed. The simple assumption of the existence of Mooney-Rivlin type membranes is therefore only a crude approximation, and the real constitutive law of the enclosing network is more complicated. Further experiments investigating these phenomena are still in progress.

Conclusions All experiments, discussed before, are consistent with theoretical predictions under a regime of small shear rates, deformations, or shear forces. Up till now, we

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Fig. 19. Polyamide capsule deformation as a function of shear rate, a=222 lm

Fig. 21. The two-dimensional storage and loss modulus as a function of the angular frequency for a chemically cross-linked polyamide membrane. (Aqueous phase: 10 mmol/l 4-aminomethyl1,8-diamino-octane dissolved in 10 mmol/l sodium carbonate; oil phase: silicone oil containing 1 mmol/l sebacoyl dichloride 4-aminomethyl-1,8-diaminooctane)

Fig. 20. The orientation angle as a function of the shear rate for an emulsion droplet and a polyamide microcapsule

polymer physics, membranes are generally treated as two-dimensional analogon of macromolecules. Like polymer chains, which are usually coiled in solution, it is supposed that membranes also tend to change their conformations depending on the temperature or nature of solvents. The crumbling transitions of membranes are therefore an interesting and actual topic in polymer physics (Drossel and Kardar 2000; Kantor and Kardar 1996a, 1996b, 1999; Kardar 2000; Takeoka et al. 1999; Vilgis 1992; Wiese and Kardar 1999). Besides the question of initial membrane roughness, we detected another folding phenomenon, which only occurs during flow. A typical example is shown in Fig. 22 (Walter et al. 2001). It is evident that the polysiloxane microcapsule is folded parallel to its orientation. We may call this effect shear induced folding, because the membrane crumbling

understand mainly the linear viscoelastic response of ultra-thin membranes. At elevated shear forces, more complicated effects occur. These phenomena can only be described if the constitutive laws of the membranes are known. The intrinsic film properties depend upon many chemical parameters. They are influenced by the adsorption process of monomers, the polymerization time, monomer concentration, temperature, polarity of the solvents, interfacial tensions, and transport properties of chemical compounds across the fluid interfaces. We have observed a broad distribution of different membrane types, and this leads to various flow properties. Even at the limit of linear viscoelastic response, we have detected two phenomena which are not yet well understood. The first problem is related to the flatness of membranes. In

Fig. 22. Shear induced deformation of an organosiloxane microcapsule, a=343 lm

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is observed during flow. It is interesting to note that such phenomena were not detected for polyamide capsules. As discussed in the first paragraph, organosiloxane membranes in the quiescent state already show small folding effects (see Fig. 9); however during shear flow this phenomenon becomes much more pronounced. Comparable processes are often observed in daily life, for example, when shearing a sheet of paper or tissue. From a theoretical point of view, folding should be related to the bending resistance of the membranes, but this parameter has not as yet, been included into theoretical models describing the properties of microcapsules. For vesicles and lipid membranes, however, bending seems to be the main factor influencing shape and thermal fluctuations (undulations) (Dobereiner et al. 1997; Dobereiner and Seifert 1996; Hackl et al. 1997; Seifert 1997, 1999; Wortis et al. 1997). The second problem, observed even at small deformations, is due to slight deviations from the initial spherical capsule shape. It turns out that during capsule synthesis, stirring actions, gravity effects, reaction heats, or diffusion processes produce small forces which tend

to deform the capsules. Disturbances caused by these effects are generally small, but are large enough to induce membrane oscillation. It is interesting to note that such complicated phenomena were never observed in spinning capsule experiments. From a chemical point of view it is also much easier to synthesize capsules for experiments in centrifugal fields, because the density difference between oil and water must not be adjusted to zero. Particle creaming or sedimentation is automatically compensated by the tube rotation. Spinning capsule techniques therefore offer a more appropriate way to compare experimental data with theoretical models. At the present moment we use this method to analyze the stability, burst, and deformation of non-spherical capsules. This work will continue and is still in progress. Acknowledgements Financial support of this work by grants of the ‘‘Deutsche Forschungsgemeinschaft’’ SFB 1690, a French-German PROCOPE research project organized by the ‘‘Deutsche Akademischer Austauschdienst’’ (DAAD) and the ‘‘Fonds der Chemischen Industrie’’ are gratefully acknowledged. Thanks are due to M. Madani and R. Ko¨nig for technical assistance. We benefited greatly from the collaborations with D. Barthe`s-Biesel.

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