Deformation and bursting of nonspherical polysiloxane microcapsules in a spinning-drop apparatus

Journal of Colloid and Interface Science 282 (2005) 109–119 www.elsevier.com/locate/jcis

Deformation and bursting of nonspherical polysiloxane microcapsules in a spinning-drop apparatus M. Husmann a , H. Rehage a,∗ , E. Dhenin b , D. Barthès-Biesel b a Institute of Physical Chemistry, University Essen, Postfach, 45141 Essen, Germany b Génie Biologique, UMR CNRS 6600, Université de Compiègne, BP 20-529, 60205 Compiègne, France

Received 12 February 2004; accepted 14 August 2004 Available online 12 October 2004

Abstract We analyze the deformation and bursting process of nonspherical organosiloxane capsules in centrifugal fields. Measurements were performed in a commercial spinning-drop tensiometer at different values of tube rotation. A theoretical analysis of the mechanics of initially ellipsoidal elastic shells subjected to centrifugal forces is developed where the deformation of the capsule is predicted as a function of the initial geometry and membrane elastic properties. For different types of organosiloxane membranes the Poisson number varies between 0 and 0.9. This phenomenon points to a considerable reduction of the membrane thickness at the onset of mechanical stress. Membrane-breaking processes always initiated at one of the pole ends of the capsules. Such rupture processes can be interpreted in terms of the derived theoretical model.  2004 Elsevier Inc. All rights reserved. Keywords: Capsule; Spinning-drop tensiometer; Surface shear modulus

1. Introduction Ultrathin, cross-linked films with gel-like properties are frequently found in biological systems [1,2]. A typical example represents the outlying membrane of Klebsiella bacteria (Fig. 1) [1,2]. The cell membrane of these organisms consists of two double layers of phospholipids. In the gap between both membranes, a highly elastic murein network is present. This protein network is firmly attached to the fluidlike phospholipid double layers. The coupling of viscous and elastic forces leads to an increased stability of the bacteria membrane. Another well-known example for the presence of such structures 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. This cross-linked protein network confers elastic forces to the fluid-like lipid membrane. Consequently, the red blood cell * Corresponding author. Fax: +49-201-183-3951.

E-mail address: [email protected] (H. Rehage). 0021-9797/$ – see front matter  2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.08.129

is easily shearable, but strongly resists to any increase of the local surface area. It turns out that the stability of red blood cells depends very much on the rubber-elastic properties of the supporting spectrin network. The unique combination of elastic and viscous forces leads, hence, to interesting mechanical cell properties. Natural membranes consist of a broad mixture of different types of phospholipids, and they contain a large number of incorporated proteins. These structures are rather complicated. We decided to synthesize well-defined artificial microcapsules in order to investigate basic relationships between membrane properties and particle stretching. Encapsulated droplets generally consist of an internal newtonian liquid, enclosed by a viscoelastic, deformable layer (skin, shell or membrane) that is usually semipermeable. These particles are suspended in another liquid of Newtonian flow characteristics. Despite of this simple architecture, artificial capsules still possess typical features of biological cells because their membranes enclose fluid compartments of microscopic dimensions [3]. As the elastic shells of these particles can easily be modified by means of chemical reactions, mi-

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Fig. 1. Schematic drawing of the murein network of Klebsiella bacteria.

crocapsules represent ideal model systems for advanced rheological research. Specific advantages of artificial capsules are caused by simple synthesis and the possibility to vary systematically size, shape and structure [3]. It is even possible to modify the nature, thickness, porosity or elasticity of the enclosing membrane, which finally leads to the synthesis of tailor-made capsules covering a wide range of different material properties. In particular, viscoelastic layers around fluid droplets seem to tolerate large mechanical forces, and therefore these structures prevent coalescence and bursting processes, thus leading to an improved stability of microcapsule suspensions. Artificial capsules offer the possibility to investigate intrinsic membrane properties independently from other parameters. We can synthesize, for instance, the capsule membrane in flat form at the interface between oil and water. This special technique allows determining intrinsic elastic and viscous membrane properties by means of surface rheometers [4–11]. In addition, we can investigate the molecular structure using Brewster angle microscopy. In former investigations, we used such experiments in order to examine the two-dimensional sol–gel transition, the kinetics of surface gelation, relaxation effects and transient membrane properties [4–10,12]. In these experiments it was also possible to explore the regime of linear viscoelasticity and critical shear stress [10,13]. In addition to these investigations, one could also visualize these ultrathin cross-linked films using Brewster Angle and video-enhanced microscopy [9,10,14,15]. Parallel to these investigations we can use special computer programs as molecular dynamics, force field methods or dissipative particles dynamics (DPD) to calculate microscopic structures and physical properties as interfacial tensions [16,17]. As the capsule stability crucially depends on the nonlinear constitutive laws of membrane deformation, it is essential to investigate all these parameters in order to understand the complicated mechanical properties of these artificial particles. The basic relationship between membrane properties and capsule deformation is of biophysical and physiological interest and this topic shall be the main sub-

ject of this publication. Besides these scientific investigations, capsules are frequently used in technical products [3]. This holds for chemical, medical, pharmaceutical, cosmetically and food industry. Successful encapsulation, transportation and controlled release of the capsule content depend crucially on the nature of the separating interfaces [3]. Complex mechanical forces are exerted on membranes during various technical applications, and these often limit the stability of dispersed particles. On grounds of these problems, it is interesting to study the burst and deformation of microcapsules under the onset of mechanical forces. Bredimas et al. were probably the first, who investigated microcapsules in simple shear flow [18]. The results clearly indicated the presence of the shear-induced orientation and stretching processes. By analyzing the capsule deformation, it was possible to measure an effective Young modulus of the enclosing membrane [18]. Later on, Chang and Olbricht presented an extensive analysis of Nylon microcapsules in simple shear flow [19,20]. The results were in fairly good agreement with theoretical models. The apparent surface elastic moduli measured by capsule compression and flow induced particle deformation coincided within the limits of experimental error [20]. Besides these investigations, a more complicated shear-induced capsule oscillation phenomenon was observed. In recent publications, we could show that this phenomenon was attributed to small deviations from the quiescent, spherical state [21,22]. During capsule synthesis, stirring actions, gravity effects, reaction heats or diffusion processes can lead to small flow fields, which tend to deform the capsules. The average deviation from the true, spherical state of the polyamide capsules was of the order of 2–3% [21,22]. Disturbances caused by these effects are generally small, but evidently large enough to induce membrane oscillations. These phenomena are described by a theory, recently proposed by Ramanujan et al. [23,24]. Besides these results, we also noticed a second phenomenon, which was not described in literature before [11,21,22]. Some of the capsules showed membrane folding in the direction parallel to their principal axis of orientation. This effect points to the existence of a finite bending modulus, which stands in competition to shear and dilation properties. Up to now, such shear-induced membrane crumbling is not completely understood. Whereas all these investigations were made with globular capsules, there is even more lack of knowledge for anisometric particles. Red blood cells or rod-like bacteria are excellent examples for the biological presence of elongated, nonglobular shapes. Because the deformation behavior of such biological cells is of foremost interest, we shall focus in this article on the deformation properties of nonspherical artificial microcapsules. Up to our knowledge, such measurements were not performed before. Anisometric particles can be synthesized in a spinning-drop tensiometer. This instrument is commercially available to measure surface tensions between two insoluble liquids. For capsule investigations, we introduce droplets containing surface-active organosiloxane monomers. These molecules tend to adsorb

M. Husmann et al. / Journal of Colloid and Interface Science 282 (2005) 109–119

at the interface between oil and water. The surrounding films were formed by polycondensation reactions where water molecules act as a cross-linking agent. For small values of the tube rotation, we obtained quasi-spherical capsules, but at elevated values of the centrifugal forces, we succeeded in synthesizing ellipsoidal capsules. In the subsequent sections of this publication, we shall analyze the deformation behavior of these artificial capsules and the bursting process induced by centrifugal fields. These measurements are new and cover a broad range of different applications; ranging from capsule stability to the defined release of incorporated chemical compounds.

2. Deformation of an initially ellipsoidal capsule in a spinning-drop-device The analysis of the deformation of an initially spherical capsule in a spinning drop device was recently performed and used to analyze experimental measurements conducted on spherical capsules [12]. However, it is also of interest to study the deformation of nonspherical capsules and to assess the effect of the initial geometry on the particle overall deformability. As will be explained in the experimental section, ellipsoidal capsules can be synthesized in a spinning drop apparatus and then subjected to increasing or decreasing centrifugal forces. In this case, the former published analysis has to be modified to account for a non spherical initial shape of the capsule. Correspondingly, a spheroidal capsule is considered with axial length 2βb and radius b in its quiescent state. Alternatively, the geometry can be characterized by the value of the Taylor parameter D = (L − B)/(L + B), where L and B denote, respectively, the length and breadth of the capsule profile. The initial Taylor parameter of the ellipsoidal capsule D0 is thus given by:

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with density ρi + ρ (ρ > 0). The axes of revolution of the tube and of the capsule are aligned, buoyancy effects due to gravity are assumed to be much smaller than centrifugal forces, so that the problem is fully axisymmetric. This last assumption implies that the ratio between gravitational and centrifugal effects is small. g  1. rsph ω2

(4)

Here, g denotes the acceleration due to gravity. A system of cylindrical coordinates (r, θ, z) is used with the Oz-axis aligned with the common axis of the tube and capsule. The position of a material point on a membrane meridian curve (θ = constant) is defined by the angle φ (φ ∈ [0, π]) between the unit outer normal vector n and the Oz-axis (Fig. 2). The load on the capsule is due to centrifugal forces only and is normal to the interface
 1 r2 2 q = ρω2 rsph (5) P− n, 2 2 rsph 2 P is the unknown pressure inside the capwhere ρω2 rsph sule. We restrict the analysis to the case where the capsule deformations are small and apply the linear theory of elastic shells [25]. This assumption means that the ratio α between centrifugal and elastic forces is small:

α=

3 ρω2 rsph

µ

=

T  1, µ

(6)

3 measures the resultant tension exerted where T = ρω2 rsph by centrifugal forces on the membrane. The principal tensions in the membrane Nφ and Nθ are directed along respectively the meridian and parallel curves.

βb − b β − 1 (1) = . βb + b β + 1 Also, the radius rsph of the sphere with the same volume is given by: D0 =

4π 3 4π 3 βb = r ⇒ rsph = bβ 1/3. (2) 3 3 sph The capsule is filled with an incompressible liquid of density ρi and is enclosed by an infinitely thin elastic membrane with surface shear modulus µ , surface Young modulus Es and surface Poisson ratio νs . These elastic parameters are related by the classical relations [13] Es = 2µ (1 + νs ).

(a)

(3)

The case νs = 1 corresponds to a membrane that is area incompressible, i.e., that has an infinite area dilation modulus. The bending resistance of the membrane is neglected. The capsule is placed inside a cylindrical tube of radius R(R > b), rotating around its axis with steady angular velocity ω. The tube is filled with another incompressible liquid

(b) Fig. 2. Schematics of capsule deformation (a): initial state of the capsule; (b) capsule deformed in a spinning tube device.

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In the limit of small deformations, the axisymmetric membrane equilibrium equations are expressed on the initial ellipsoidal shape [25]. d (rNφ ) − r1 Nθ cos φ = 0, dφ
 Nφ Nθ 1 r2 2 + = ρω2 rsph P− , 2 r1 r2 2 rsph

(7a) (7b)

where r1 and r2 are the principal radii of curvature of the ellipsoid, given by: r1 = r2 =

β 2b (sin2 φ + β 2 cos2 φ)3/2 b (sin2 φ + β 2 cos2 φ)1/2

,

(8a)

.

(8b)

The solution of the equilibrium equations is straightforward.
 1 r2 P 2 3 r2 − Nφ = ρω rsph (9a) , 2 rsph 2 8 rsph 
 r2 1 r2 2 3 P− Nθ = ρω rsph 2 rsph 2 rsph
 r22 1 r2 P − − (9b) . 2 r1 rsph 2 8 rsph Assuming that the membrane material satisfies a twodimensional form of Hooke’s law, the principal deformations εθ and εφ are linear functions of the elastic tensions [13]: εφ = εθ =

1 2µ (1 + νs ) 1 2µ (1 + νs )

(Nφ − νs Nθ ),

(10a)

(Nθ − νs Nφ ).

(10b)

To obtain the deformed profile of the ellipsoid, we have to relate the displacement of the membrane material point to the deformation. Following Flügge, we find that [25]: ∂v/∂φ + w , r1 v cotan φ + w εθ = , r2 εφ =

the result is to compute the difference between the final and initial Taylor deformation parameter D of the capsule. [βb + w(0)] − [b + w(π/2)] β − 1 − . [βb + w(0)] + [b + w(π/2)] β + 1 (13) In the limit of small deformations v, w and D are all proportional to α. In the case of an initially spherical capsule (β = 1, D0 = 0), the integration of Eqs. (11a) and (11b) can be performed analytically and the deformation is given by [12]:

D = D − D0 =

5 + νs 32(1 + νs ) 3 ρω2 rsph 5 + νs

D = α =

=

3 ρω2 rsph

(14) (5 + νs ). µ 32(1 + νs ) 16Es As shown by Pieper et al. this equation allows the determination of the surface Poisson ratio, provided that surface shear modulus µ is known [12]. Then, the surface Young modulus can also be determined from Eq. (3). For an initially spheroidal capsule, the analytical solution is complicated, and it is simpler to integrate Eqs. (11a) and (11b) numerically for different values of β and νs . The variation of D/α as a function of the ellipsoid axis ratio β is shown on Fig. 3 for different values of the surface Poisson ratio νs in the interval [0, 1]. The case νs = 1 has to be excluded (area incompressible membrane), because an axisymmetric capsule cannot deform while keeping its volume and surface area constant. In all cases, D/α decreases as the axis ratio of the capsule increases. This means that as β increases, the capsule is less amenable to deformation by centrifugal forces. This is probably due to the specific geometry considered here where the deviation from sphericity and the principal direction of stretch are aligned. The influence of the surface Poisson ratio is weak. In the limit of small deformations and for slightly ellipsoidal shapes

(11a) (11b)

where the displacement u of a membrane material point is contained in the meridian plane and is defined by: u = vτ + wn,

(12)

where τ is a unit vector tangent to a meridian curve (Fig. 2). Inserting Eqs. (9a) and (9b) in Eqs. (10a) and (10b), we find that εθ and εφ are proportional to α. Similarly from Eqs. (11a) and (11b), v and w must also be proportional to α. The integration of Eqs. (11a) and (11b) with the condition that the capsule volume remain constant, allows the determination of v, w and P , from which the deformed profile of the capsule can be inferred. A convenient way to express

Fig. 3. Variation of the additional deformation D/α as a function of the initial axis ratio β of an ellipsoidal capsule, for different values of the surface Poisson ratio νs . The points represent experimental data for predeformed capsules with interface II.

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Table 1 Coefficients of the linear correlation between D/α and β for β ∈ [0.97, 1.25] νs

m

p

R2

0 0.25 0.5 0.75 0.85 0.9

−0.341 −0.292 −0.269 −0.280 −0.315 −0.307

0.495 0.422 0.382 0.381 0.413 0.402

0.998 0.990 0.993 0.997 0.997 0.997

(β ∈ [0.97; 1.23]), D/α is found to vary linearly with β with correlation coefficients R 2 larger than 0.99: D (15) = mβ + p. α The values of the linear correlation coefficients are given as a function of νs in Table 1. As will be shown in the last section, this model allows analyzing the experimental data of spinning capsules and thus obtaining an estimate for the value of the Poisson ratio.

3. Materials and methods 3.1. Surface polymerization Octadecyltrichlorosilane (ODTClS) was purchased from ABCR-company (A better choice for research chemicals) and used without further purification (95% purity). Cetyltrimethylammoniumbromide (CTAB), dodecane, p-xylene, and glycerol was obtained from Fluka (p.a. grade). All solvents were dried by means of molecular sieves. Water was obtained from an ultra pure water system (Seralpur PRO 90 CN, USF Seral). Mixtures between water and glycerol and usage of different oils such as dodecane and xylene allowed adjusting the density between the polar and hydrophobic phases to desired values. These solvent variations were necessary in order to generate enough forces to deform and break the capsules in the spinning-drop tensiometer. All chemical compounds were stored under argon. Membrane formation was induced by the interfacial polycondensation of octadecyltrichlorosilane at the interface between oil and water. The reaction can be divided into hydrolysis and subsequent condensation [10]. The chlorosilane is extremely reactive and hydrolysis to a silanol takes easily place. ≡SiCl + H2 O −→ ≡SiOH + HCl. The generated silanol molecules have the tendency to condensate spontaneously. Therefore, a silanol reacts in a second step either with a second silanol. 2≡SiOH −→ ≡Si–O–Si≡ + H2 O or with a chlorosilane to produce linear chains of siloxanes. ≡SiCl + ≡SiOH −→ ≡Si–O–Si≡ + HCl.

Fig. 4. Schematic drawing of an amorphous organosiloxane film structure at the interface between a hydrophilic and hydrophobic phase.

Due to this special polycondensation scheme, very stable siloxane groups were formed already at room temperature. Up to now, various interface sensitive methods have been used to characterize these films. On silicon–silicon dioxide (Si/SiO2 ) substrates a film thickness of about 2.5 ± 0.2 nm for a complete monolayer was calculated by means of lowangle X-ray reflectivity and ellipsometry by Wassermann et al. [26]. It was also possible to determine the area occupied by each alkysiloxane group which was in the order of 0.21 ± 0.03 nm2 [26]. Between the alkyl chains cannot be a large pore volume, because in the tightest possible crystalline packing the hydrocarbon tails needs surface areas of about 0.18 nm2 /alkyl-chain [27]. Furthermore, the critical surface tension of 2 × 10−2 N m−1 observed for films on a SiO2 matrix indicates a highly ordered CH3 surface [28]. According to these experiments, Ulmann supposed that the alkyl chains are orientated in a tilt angle of
15◦ [29]. This leads to the postulation of a cyclic trimer with chair conformation in which alkyl chains are connected at the axial position. Such a structure is schematically shown in Fig. 4. 3.2. Surface rheology The shear rheological properties of flat cross-linked membranes were evaluated in the Rheometrics fluidspectrometer RFS II, using a modified shear system. The measuring cell consisted of a quartz dish (diameter 84 mm) and of a thin biconical titanium plate (angle 2◦ , diameter 60 mm), which could be placed exactly at the interface between oil and water. The dish was first filled with the aqueous phase containing glycerol in order to increase the viscous resistance. The titanium plate was then positioned at the water surface, and a solution of octadecyltrichlorosilane in xylene was poured upon. We measured the torque required to hold the plate stationary as the cylinder was rotated with a sinusoidal angular frequency ω. In such experiments, the two-dimensional storage modulus µ and the two-dimensional loss modulus µ can be evaluated from the amplitude and phase angle of the stress and deformation signals. Evaluation of these data and more details concerning the measurements and sample preparation are extensively described in Refs. [4–10,12,21,22,30]. In a series of experiments, we studied different types of two-dimensional networks. Interface I corresponded to the polymerization at the

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phase boundary between dodecane and water. As we have observed with surface rheometers that the polymerization time of octadecyltrichlorosilane decreases to a large extent by addition of small traces of cationic surfactants, the water phase contained a highly dilute solution of 5 × 10−6 mol l−1 cetyltrimethylammoniumbromide (CTAB). The polymerizing monomer octadecyltrichlorosilane was solved in the dodecane phase at different concentrations. Interface II was especially designed to form nonspherical capsules and to induce particle bursting. In order to reduce the formation of air-bubbles we also increased the viscosity of the external phase. In this case, the polar phase consisted of a glycerol– water mixture with a viscous resistance of η = 0.22 Pa s. The hydrophobic phase was composed of a dilute solution of 0.2 mmol l−1 Octadecyltrichlorosilane in p-xylene. Typical values of the equilibrium surface shear modulus are summarized in Table 2. 3.3. Spinning capsule experiment A commercial spinning-drop tensiometer Krüss SITE 04 was used to study the deformation of microcapsules under the action of centrifugal forces. A schematic drawing of such an apparatus is shown in Fig. 5. The maximum operating speed of the glass tube was limited to 10,000 rpm. Above this value, vibrations set in and leaking occurred from the tube sealing. Before starting an experiment, the tube was first cleaned and filled with the aqueous water/glycerol solution. Special caution was neces-

sary to avoid air bubbles and dust particles. At low rotational speeds (of the order of 1000 rpm) an oil droplet (xylene or dodecane) containing the dissolved octadecyltrichlorosilane phase was injected with a syringe. This droplet was still approximately spherical at this rotation speed, and it was held stationary due to the action of centrifugal forces. Under those conditions the polymerization reaction took place, and a stable microcapsule was thus formed. Depending on the monomer concentration and the oil phase the polymerization times changed between 5–30 min, and before increasing the rotational speed, we waited for additional two hours. After that period, all cross-linking reactions were terminated (see Fig. 6). An initially spherical capsule could be deformed by increasing the tube rotation. The shape and size of the capsule was recorded by means of a video-camera. The optical system was calibrated with steel wires of known thickness in order to compensate for optical distortions due to the lens effects of the glass tube and to the refractive indices of the solvents. The capsule diameter and length could then be measured using digital image analysis. Nonspherical capsules were synthesized at elevated tube rotations. The measuring process of these particles was the same as for globular shapes. Various capsule sizes and two different interfaces were studied.

Table 2 The equilibrium shear modulus of ultrathin cross-linked membranes as a function of the monomer concentration for different interfaces Membrane Interface I Interface I Interface I Interface I Interface I Interface II Interface II

Monomer concentration c (mmol l−1 ) 40 20 10 6 5 0.1 0.2

Surface shear modulus µ (N m−1 ) 0.494 0.393 0.223 0.113 0.075 0.378 0.474

Fig. 6. Evolution of the two-dimensional surface modulus µ and the two-dimensional loss modulus µ as a function of the polymerization time (ω = 1 rad s−1 , γ = 0.025, T = 20 ◦ C). Network formation with octadecyltrichlorosilane (c = 0.1 mmol l−1 ) at the phase boundary p-xylene/water (interface II).

Fig. 5. Schematic drawing of the spinning capsule experiment.

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4. Results 4.1. Spherical capsules Before describing the typical behavior of nonspherical capsules, we shall just discuss the deformation properties of initial globular shapes. First, the kinetics of surface gelation were measured at the flat interface by means of surface rheometers. Typical results are represented in Fig. 6. We have measured the evolution of the two-dimensional storage modulus µ and the two-dimensional loss modulus µ as a function of the polymerization time t. These data represent the kinetics of surface gelation. Immediately after the onset of polymerization, mainly linear chains were formed. In this regime, µ is still very small. The twodimensional sol–gel transition occurs at about 6.5 min. At exactly this point, a supermolecular network phase is formed spanning the whole sample. During the surface reaction, more and more monomers are connected to this network and the elasticity, which depends upon the density of junction points, is steadily increasing. At about one hour, all reactions are terminated and the curve attains a plateau value. At these conditions elastic properties are more pronounced that viscous features. The polymerization times, which are measured by these experiments, are controlled by the diffusion of reactive monomers towards the fluid interface and by cross-linking reaction time constants. In measurements of interfacial tensions we reached concentration depended stationary values after several minutes. This suggests that the adsorption kinetics of monomers have striking effects on the polymerization reactions. Typical relaxation properties of the ultrathin membranes are summarized in Fig. 7. We have plotted here the twodimensional relaxation modulus µ (t) as a function of the time t. It is evident, that µ (t) attains a plateau. The slight decrease at long times might be induced by the release of entangled chains, which also contribute to the cross-linking process. These effects, however, are small compared to the stability of junctions points formed by chemical polycondensation reactions. The equilibrium surface shear modulus of interface I and II was measured as a function of the monomer concentration. Relevant results are summarized in Fig. 8 for interfaces I and II [10,30]. In all experiments we have observed, that in the regime of small concentrations nearly all octadecyltrimethoxysilane molecules diffuse towards the interface where they react to form a two-dimensional, ultrathin network. The surface excess concentration Γ is then simply given by the total number of molecules divided by the area of the fluid interface. In Fig. 8 we have simultaneously plotted the twoand three-dimensional monomer concentration. It is easy to see that there exists an exponential relation between surface shear modulus and the number of reacting monomers. It is interesting to note, that in the case of interface I, a well-defined threshold value of 3.4 mmol l−1 is needed

Fig. 7. The two dimensional relaxation modulus µ (t) as a function of time t (γ = 1%, T = 20 ◦ C). Network formation with octadecyltrichlorsilane (c = 0.1 mmol l−1 ) at the phase boundary p-xylene/water (interface II).

Fig. 8. The surface shear modulus as a function of the surface concentration Γ and the initial bulk concentration c of octadecyltrimethoxysilane in the oil phase (interface I and II).

to induce two-dimensional gel-formation (gelation threshold). Below this concentration, we never succeeded in forming coherent, two-dimensional network structures. For interface II we measured a much lower threshold concentration of about 0.02 mmol l−1 . From these experiments it is evident, that the organic solvent has marked influence on the twodimensional gelation process. This knowledge and the measured data of viscoelastic membrane properties were used to synthesize tailor-made microcapsules. In a series of experiments, we systematically compared the rheological properties of flat membranes with the deformation properties of microcapsules. In order to investigate the question, whether the surface polymerization at flat or curved interfaces leads to identical membrane structures, we also investigated microcapsules in simple shear flow using optical rheometers (rheoscopes) [11,12,21,22]. Within the limits of experimental error, the surface shear moduli determined by interfacial rheometers and by measuring the flow-induced deformation of microcapsules where identical [11,12,21,22]. We can, hence, conclude, that the mechanical properties of the synthesized flat and curved membranes where very similar.

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The centrifugal field-induced deformation of microcapsules with interface I is summarized in Fig. 9. For three different surface concentrations we obtained straight lines. As the surface shear moduli µ of these membranes were independently measured by means of surface rheometers (see Fig. 8), we can calculate the surface Poisson ratio from the slope of these curves using Eq. (14). Typical results are summarized in Fig. 10. At the surface concentration of 3.6 molecules·nm−2 near the sol–gel transition (3.4 molecules·nm−2 ), large deformations and a negative value of the Poisson ratio νs = −0.44 are observed. We cannot exclude that the fragile network structure, formed at these conditions, is not destroyed or changed during the measurements. In the vicinity of the sol– gel transition, the network contains a large number of pores,

Fig. 9. Deformation of three different initial spherical capsules as a func3 at different values of the monomer tion of the membrane tension ρω2 rsph surface concentration. Interface I, T = 20 ◦ C.

where the oil phase is in direct contact with water. Forces acting at this interface may, therefore, be influenced by fluidlike interfacial tensions. This single point might thus be an artifact. The other results for νs are all of the order of zero, slightly negative or positive. The Poisson ratio measures the strain in the transverse direction which results from longitudinal extension. A positive value corresponds to a material that shrinks transversally when it is stretched longitudinally. Negative values of the Poisson number describe a membrane that is elongated transversally when stretched longitudinally. Mean field calculations and Monte Carlo simulations performed by Boal et al. for different types of tethered networks recently suggested that νs may vary between −1 and +1 [31]. In these investigations, positive values were found for large deformations and negative Poisson numbers seemed to be linked to intermediate and small deformations [31]. The values of νs = 0 represent an intermediate case where the action of a force does not affect other directions. For ultrathin membranes, this corresponds to processes, where the film thickness decreases during stretching. It is interesting to note, that surface Poisson numbers of the order of zero were also observed in ultrathin membranes of aminomethacrylates [12]. From a chemical point of view, these are quite different materials, but they show the same characteristic properties as thin films of organosiloxanes. We can, hence, conclude that a surface Poisson number of zero belongs to a more general behavior, which does not depend on the actual type of the investigated material. Due to the action of centrifugal forces, capsules can be destroyed within the spinning-drop tensiometer. As the tube rotation cannot be increased to a large extent (problem of sealing leaking), network rupture occurs at elevated values of ρ, rsph or low values of µ . Typical results of such experiments are summarized in Fig. 11. In this experiment we started at a tube rotation of 500 rpm. After terminating the surface polymerization, the rotation speed was stepwise increased. We investigated the particle deformation, and after each measurement the cap-

Fig. 10. Surface Poisson number νs as a function of the surface excess Γ of organosiloxane monomers for different capsules. Interface I, T = 20 ◦ C.

Fig. 11. Microcapsule deformation D as a function of the centrifugal force 3 (interphase II). ρω2 rsph

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3 = 80 mN m−1 , see largest deformation in Fig. 11). Fig. 12. Microcapsules, destroyed by the action of centrifugal forces (interface II, ρω2 rsph

sule was again examined at the initial state (500 rpm). These experiments were performed in order to detect any trace of permanent deformation. It is easy to see that up to a resultant 3 = 65 mN m−1 , a deformed capsule tension, T = ρω2 rsph relaxes back to a spherical shape. The measuring point at 80 mN m−1 shows a striking deviation from this simple rule. Under these conditions, the particle remains permanently deformed even at low values of tube rotation. Typical images of such a microcapsule are shown in Fig. 12 where it is clear that the capsule is no longer symmetric. It is worthwhile to mention that membrane rupture always occurs at one of the pole ends where, as shown by Eqs. (9a) and (9b), the two elastic tensions are maximal and given by: 3 Nφ = Nθ = ρω2 rsph

P . 2β 4/3

(19)

This prediction is in excellent agreement with Fig. 12, where membrane damage seems to occur exactly at these extremities.

Fig. 13. Capsule deformation D as a function of the centrifugal force 3 (interphase II). ρω2 rsph

4.2. Nonspherical capsules When microcapsules are synthesized at elevated tube rotations, it is possible to investigate the influence of initial anisotropy on the deformation process. Typical results are shown for a capsule with interface II in Fig. 13. The value of parameter rsph is computed from the volume of the capsule assuming the shape to be axisymmetric. The capsule was 3 = synthesized at a resultant centrifugal tension of ρω2 rsph −1 25 mN m (open circle in Fig. 13). The particle formed at this condition has a stretched membrane, since lowering the tube rotation results in a decrease of deformation. However, in contrast to spherical microcapsules, the deformation could not be reduced to zero even at very small values of the angular velocity. Conversely, when the angular frequency of the tube was increased above the value where synthesis was performed, the capsule deformation increased. The experimental results exhibit a linear variation of the Taylor parameter D with the centrifugal tension T . 3 = D0 + AT . D = D0 + Aρω2 rsph

(20)

A is the slope of the linear correlation and D0 describes the value of the zero tension initial anisotropy of the capsule,

Fig. 14. Deformation D of capsules as a function of the centrifugal force 3 for eleven capsules summarized in Table 3 (interphase II). Open ρω2 rsph circles describe conditions where the capsules where synthesized.

from which it is easy to deduce the axis ratio β (Eq. (1)). For 3 3 large values of ρω2 rsph (ρω2 rsph > 80 mN m−1 ), a sharp deviation from the linear correlation (20) was observed. This phenomenon is due to irreversible network damage. Capsules with interface II were synthesized at different values of the tube rotation rate, resulting in particles with different sizes and shapes (Fig. 14). For each particle the linear

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Table 3 Parameters of ellipsoidal capsules. Capsule reference

Γm (molecules·nm−2 )

rsph (mm)

D0

β

A (mN m−1 )

µ A

1 2 3 4 5 6 7 8 9 10 11

23.3 24.5 35.7 21.8 26.3 27.1 26 25.9 22.7 27 29.1

0.58 0.61 0.89 0.54 0.65 0.68 0.65 0.65 0.57 0.67 0.72

−0.206 −0.03 0.103 0.464 1.297 3.02 5.2 5.44 6.04 7.2 8.6

0.996 1 1.0022 1.011 1.026 1.062 1.1097 1.115 1.1286 1.1555 1.187

0.202 0.208 0.226 0.187 0.173 0.154 0.135 0.139 0.146 0.121 0.105

0.095 0.098 0.106 0.088 0.081 0.072 0.063 0.065 0.069 0.057 0.049

correlation of the small deformation results, gives the value of D0 (and then β) and A, with regression coefficients larger than 0.99. As the chemical reactions of membrane formation were nearly identical for all capsules, they all should have similar rheological network properties, with a shear modulus µ = 0.47 N m−1 , measured directly in the shear rheometer. Then Eq. (20) may be rewritten as: D − D0 = µ A. (21) α The results are summarized in Table 3. It is interesting to note that the slope A of the deformation curves does decrease with β as predicted by the theory. The experimental value of D/α can now be plotted as a function of β (see Fig. 3). We find that for all capsules, the Poisson ratio νs lies between 0.75 and 0.9, a value that is quite larger than the one obtained for capsules with interface I (Fig. 10). Changing the solvents has evidently marked effects on the molecular structure of the ultrathin, cross-linked membranes. In this context, it is interesting to note, that the surface shear modulus depends very much on the nature of the unpolar liquid (Table 2). Compared to dodecane, we need much lower monomer concentrations in xylene for the synthesis of ultrathin membranes, and the gelation threshold is shifted towards smaller concentrations. We can, hence, conclude that different solvents have marked influence on the surface polymerization reactions.

of νs of order 0.5 or larger point to a reduction of the membrane thickness during stretching. For interface I, we also obtained negative values or Poisson numbers of the order of zero. These results describe a striking influence of organic solvents on the process of surface gelation. Besides analyzing the deformation, we have also investigated the bursting process of capsules. We observed membrane rupture processes initiating at the poles of the particles, as predicted by the theory. It is interesting, to note, that centrifugal fields can successfully be used to synthesize nonspherical capsules. These particles are interesting and they might even have technical applications on grounds of their special shape and size. Nonspherical capsules are characterized by relatively large surface areas and this can improve accumulation times in the stomach or intestine walls. Such capsules are interesting for advanced methods of controlled release of drugs. The development of new techniques to enable the production of nonspherical microcapsules is currently representing an innovative field of research.

Acknowledgments We gratefully acknowledge the financial support by grants of the Deutsche Forschungsgemeinschaft (SFB 681/8-3), of France–Germany Procope Project (Charactérisation mécanique des capsules et des interfaces polymérisées), and of CNRS-PICS Program.

5. Summary and conclusions In this publication we have analyzed the deformation behavior of microcapsules in centrifugal fields. A mechanical model of the deformation of initially ellipsoidal capsules has been derived, but had to be solved numerically. In the range of small deformations, both theory and experiments predict a linear dependency between the capsule deformation and the applied centrifugal forces. The comparison between experimental results and theoretical predictions, together with independent measurements of the membrane shear modulus, allowed the determination of the surface Poisson ratio νs . For interface II, we obtained values between 0.5 and 0.9. Values

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