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Micromechanics of Soft Particles

Mingyu Guo, Hans M. Wyss*

Materials that contain soft, deformable particles exhibit a rich range of macroscopic mech- anical properties. Experimental access to the mechanics at the scale of a single particle is the basis for studying and understanding the macroscopic mechanics of these materials. In this paper, we discuss experimental methods that can be used to characterize the mechanics of microscopic soft particles. We focus on the recently developed capillary micromechanics method, which yields the full linear elastic behavior of a single particle. We validate the method by comparing results for the com- pressive modulus to osmotic compression measurements, which provide the most direct and unambiguous measure of compressibility. We find good agreement between the two methods on a system of deformable and com- pressible poly-N-isopropylacrylamide micro- gel particles. Our results thus support the validity of the capillary micromechanics method and suggest that it could be applied to a wide range of materials that consist of deformable soft objects.

Introduction of such materials is still surprisingly poorly understood. The macroscopic mechanical behavior of particle suspensions, Many polymers, complex fluids, and biological materials gels, or glasses often changes qualitatively if soft, deform- contain soft, deformable particles as one of their main able particles are used instead of hard particles. constituents. Examples are latex paints or pastes and A good example for this difference in macroscopic creams used in the food and drug industry, which contain properties is the concentration dependence of the steady soft microgels as fillers, or blood, which contains deform- shear viscosity. For suspensions of hard particles, a drastic able and compressible cells. As opposed to suspensions and increase in viscosity is observed as the concentration of gels that consist of solid particles, the mechanical behavior particles approaches a volume fraction around f 60%,  close to the volume fraction for random close packing fRCP M. Guo, H. M. Wyss of spheres.[1,2] As the particles are not compressible or Institute for Complex Molecular Systems (ICMS), Eindhoven deformable their packing density is restricted to a limiting University of Technology, Eindhoven, The Netherlands concentration, often corresponding to random close pack- Fax: 31 40 244 7355; E-mail: [email protected] þ ing fRCP 64%. However, for soft microgel particles this  M. Guo limit no longer applies. Because the particles are highly Laboratory of Chemical Biology, Department of Biomedical compressible, they can shrink to accommodate more Engineering, Eindhoven University of Technology, Eindhoven, particles within the same volume. As a consequence, the The Netherlands H. M. Wyss viscosity of microgel suspensions depends much less Department of Mechanical Engineering/Polymer Technology, sensitively on concentration than the viscosity of a Eindhoven University of Technology, Eindhoven, The Netherlands suspension of hard particles. Thus, to achieve the same

Macromol. Mater. Eng. 2011, 296, 223–229 ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com DOI: 10.1002/mame.201000359 223 M. Guo, H. M. Wyss

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high levels of viscosity that are observed close to f 60% in technique is the high accuracy with which forces and  hard sphere suspensions, a microgel suspension of much displacements can be measured. However, the technique is higher concentration is required.[3–8] still difficult to apply to many materials, as the measure- It is evident that the macroscopic mechanics ultimately ment has to be performed with the AFM tip fully immersed must be governed by the mechanics at the single particle in the liquid phase while at the same time being able to level. However, a full understanding of the link between the deposit the soft particles at a flat interface. Moreover, macroscopic and the local mechanical properties is still without additional information the method does not allow lacking. While the behavior of suspensions of hard particles for a characterization of the full elastic behavior of the is reasonably well understood, a comparable level of particles as no information is obtained on the deformation understanding still remains elusive for soft particle of the object perpendicular to the direction of the applied systems. force. In analyzing the data from these measurements, it is One important reason for this lack of understanding is usually assumed that the materials are incompressible, the fact that in many cases the mechanical properties at the which corresponds to a Poisson ratio of n 1/2 and to ¼ single particle level have not been measured experimen- an infinite compressive elastic modulus K. While this tally and therefore models that aim at establishing a link assumption makes sense for many materials such as liquid between the macroscopic scale and the single particle scale drops, polymeric melts, and even for gas bubbles in a foam, cannot be properly validated. The detailed effects of it is ill-suited in particular in the case of microgel particles different particle properties can thus not be tested. As a and for biological cells, which, besides being deformable, full understanding of the behavior of these materials must can also easily change their volume. Thus their deformation ultimately be based on the properties at the single particle behavior can deviate significantly from the incompressible level, experimental methods at the scale of a single particle case. are of key importance. In micropipette aspiration[14,15] shown schematically in Here we discuss experimental methods that can be used Figure 1(B), a soft object is located with a microscope and to characterize the elastic properties of microscopic soft approached with the tip of a microcapillary. By applying a particles. Some available methods are shown schematically negative pressure to the capillary the object is partly sucked in Figure 1; these methods are particularly useful for into the capillary; the extent of penetration into the aqueous systems such as for measurements of biological capillary tip is a measure for the elasticity of the object. This cells and for microgel particles. method is frequently employed in the characterization of In atomic force microscopy (AFM) measurements,[9–13] biological cells, as it gives good comparative results and is shown schematically in Figure 1(A), the soft objects are easily applicable using similar techniques and equipment deposited onto a flat surface in water and the location of a also commonly employed for handling andmanipulation of single particle is subsequently identified with the AFM. The single cells. However, the response probed by this method is measurement at the single particle level is performed by dominated by the properties at the surface of a cell and using the AFM tip to directly apply an increasing force to the the localized nature of the measurement provides only top center of the particle and measure the corresponding limited information on the overall elastic properties of the vertical displacement of the tip. The main advantage of this whole object. Further, in the data analysis for micropipette aspiration measurements a Poisson ratio of n 1/2 is ¼ usually assumed; due to the complicated deformation mode of the particle or cell in this measurement it is still difficult to characterize compressible particles or cells. Another method that has been used to characterize the mechanics of soft particles or cells is compression between two parallel plates using a specialized loading cell that combines piezo-controlled micromanipulators with a force transducer capable of resolving forces on the order of 10 nN.[16–18] This method enables a measurement of both the compressive elastic modulus and the shear elastic modulus of a particle or cell, as in addition to measuring a force- extension curve the shape change of the particle or cell can also be directly imaged in a microscope. In this paper we focus on the two simple methods Figure 1. Schematic of methods for measuring the elastic proper- schematically shown in Figure 1(C) and (D), osmotic ties of microscopic soft objects. A) Atomic force microscopy. [19–22] [23] B) Microaspiration. C) Osmotic compression. D) Capillary micro- compression and capillary micromechanics, mechanics. respectively. These experimental methods also allow us

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www.mme-journal.de to clearly separate the measurement of the compressive modulus from that of the shear modulus. Capillary microme- chanics is especially interesting, as it allows for the simultaneous measure- ment of both the compressive elastic modulus K and the shear elastic modulus G in a single measurement. Its validity has been tested previously by comparing its results on polyacrylamide microgel particles to those obtained from compres- sion tests on macroscopic hydrogels of Figure 2. Fabrication of monodisperse microgel particles using a microfluidic device. identical chemical composition.[23] How- A) Glass microcapillary device to produce aqueous drops containing the NIPAM mono- ever, it is not obvious that the elastic mer. Immediately prior to drop formation a solution of catalyst is injected through inlet 3 into the aqueous inner phase containing the NIPAM monomer, the cross-linker and the properties of macroscopic gels should be initiator (injected via inlet 2). This ensures that polymerization takes place only after the identical to those of microscopic microgel drops have been formed, thereby avoiding clogging of the device by polymerization in particles; both finite size effects as well as the inlet channel. B) p-NIPAM particles as collected from the microfluidic device; the a possibly anisotropic structure of the particles appear larger as they are compressed by the microscope slides. The scale bar is m microgel particles could lead to signifi- 100 m. cant differences in the measured elastic 1 properties between the bulk gels and the microgels. Further, via inlet 3 (10 wt.-% TMED, flow rate 600 mL hÀ ). The oil phase (HFE- Á the swelling behavior of macroscopic gels can be signifi- 7500, 3M, containing the surfactant Krytox 157-FSL, duPont) which 1 stabilizes the formed drops is injected at a flow rate of 10 mL hÀ via cantly different from that of microgel particles; even if the Á polymer concentrations during synthesis are identical, inlet 1. By injecting the catalyst into the main aqueous phase immediately prior to drop formation, we ensure that polymeriza- the polymer concentrations in the final gels can exhibit tion does not take place in our device before the drops are formed; significant differences. on the other hand, this also ensures that polymerization of the Thus, in order to validate the capillary micromechanics drops into elastic microgel particles occurs before coalescence and method, here we directly test the method at the scale of the coarsening of drops in the collection vial leads to a significant single particles themselves. To do so we compare the results broadening of their size distribution. As a result, the particles obtained from capillary micromechanics to those obtained collected at the outlet of the device exhibit a narrow size from osmotic compression measurements on a model distribution, as shown in Figure 2(B). The formed particles are system of poly-N-isopropyl-acrylamide (p-NIPAM) micro- subsequently washed by removing the oil phase and the surfactant gel particles. by a series of dilution and centrifugation steps. After swelling in water at room temperature the particles exhibit a narrow size distribution with an average diameter of d 89 3 mm.  Æ Experimental Part

Synthesis of Microgel Particles Results

We produce these poly-N-Isopropylacrylamide (p-NIPAM) particles Osmotic Compression of uniform size distribution by first making droplets of aqueous monomer solution using microfluidics; subsequently we poly- Osmotic compression is the most direct and unambiguous merize these droplets to form p-NIPAM particles. We use glass way to characterize the compressive modulus, as it offers a microfluidic devices similar to those developed by Utada et al.[24]; truly isotropic mode of compression without any shear these devices are constructed by inserting two round capillaries component. Moreover, in contrast to the other methods it into a square capillary from both ends. The spaces between the does not require physical contact with a surface whose round capillaries and the square capillaries thereby serve as surface properties can affect the measurement; instead it additional channels where fluid can be injected or extracted. Our relies purely on osmotic pressure to apply stress to the soft device has three inlet channels and one outlet channel, as indicated object. In our experiments we use solutions of dextran on an image of a typical device, shown in Figure 2(A). Droplets are (Dextran-Leuconostoe #31390, Sigma–Aldrich) M 70 kD formed via flow-focussing of an aqueous inner phase (inlet 2 and 3) w ¼ by a oil outer phase (inlet 1). We use the two inlets on the left side of with a concentration dependence of the osmotic pressure [25] the image to inject the aqueous phase, with the main reactants for that has been well established in previous studies. The the polymerization injected via inlet 2(Monomer: 10 wt.-% NIPAM, osmotic pressure can be approximated by the following fit 2 3 Cross-linker: 0.25 wt.-% Bis-acrylamide, Initiator: 3 wt.-% Ammo- function: Posm c c~ 87 c~ 5 c~ , where c~ c=wt:-%. 1 ð Þ þ Ã þ Ã ¼ nium persulfate, flow rate: 2 000 mL hÀ ) and the catalyst injected As the dextran is larger in size than the mesh size of the Á

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polymer network it cannot penetrate the microgel; this 1 kPa (i), P 2.94 kPa (ii), P 6.06 kPa (iii), and P osm ¼ osm ¼ osm ¼ leads to an unbalanced osmotic pressure between the 10.7 kPa (iv), respectively. inside and the outside of the particle, resulting in a uniform We analyze the particle size as a function of osmotic

compressive stress on the particle, as shown schematically pressure and plot the applied osmotic pressure Posm as a in Figure 3(A). function of the volumetric strain deformation DV/V, as We follow the resulting volume change for different shown in Figure 3(C). The curve exhibits an approximately levels of osmotic pressure directly by microscopy and linear behavior and its slope corresponds to the compres- digital image analysis. We immerse the particles in a small sive elastic modulus. We thus obtain a value of K 17.3 kPa ¼ petri dish and image them using a standard light from a linear fit to the data, shown as a dashed line in microscope; to increase the osmotic pressure we carefully Figure 3(C). Precluding that the dextran does not penetrate add concentrated dextran solution at the edge of the petri the microgel, the osmotic compression measurement is dish, thereby minimizing fluid motion and the resulting the most direct and clean way of measuring the compres- migration of particles outside of the field of view of the sive modulus, as a purely compressive mode of deformation microscope. Moreover, we start our measurements at a is employed in the experiment. dextran concentration of c 2.05 wt.-%, corresponding to ¼ an osmotic pressure P 1 kPa, where the density of the osm  dextran solution exceeds that of the microgel particles, Capillary Micromechanics causing them to float to the surface of the cell. At all higher To access both the compressive elastic modulus K and the levels of pressure the particles remain close to the surface shear elastic modulus G of our particles, we employ the and are thus easily imaged with the microscope. A typical recently developed capillary micromechanics technique. example is displayed in Figure 3(B), where we show a series The experimental setup consists of a tapered glass capillary of images of the same group of p-NIPAM particles at with a taper angle a, as shown schematically in Figure 4(A); increasing levels of dextran concentration: c 2.05 wt.-% (i), the backside of the capillary is connected to a flexible tube. ¼ c 4.07 wt.-% (ii), c 6.07 wt.-% (iii), c 8.1 wt.-% (iv). These At the start of an experiment a dilute suspension of soft ¼ ¼ ¼ concentrations correspond to osmotic pressures of P particles is flown through the capillary by applying a osm ¼

Figure 3. Osmotic compression of microgel particles. A) Schematic Figure 4. Capillary micromechanics measurement. A) Schematic representation. The stress due to the osmotic pressure of the representation of the measurement and the geometrical features dextran solution leads to a compression of the particle. B) Series that are captured in the image analysis. Lband is the length of the of images of the same group of particles taken at increasing contact area of the particle with the wall; Rband is the average levels of osmotic pressure, Posm: i) 1.0 kPa, ii) 2.94 kPa, iii) radius of the particle from the center to the contact area. 6.06 kPa, iv) 10.68 kPa. The scale bar is 100 mm. C) Analysis of B) Capillary micromechanics measurement for p-NIPA particles; the compressive elastic modulus K; plot of Posm as a function of the particle deforms and moves toward the tip (bottom) as p is the volumetric strain deformation DV/V, as analyzed from the increased from left to right: i) 500 Pa, ii) 1500 Pa, iii) 2500 Pa, iv) images. 3500 Pa, v) 4500 Pa. The scale bar is 100 mm.

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www.mme-journal.de pressure p to the flexible tube. Here to apply the pressure wall pressure is derived as p we use the hydrostatic pressure in the tube, which we control by varying the filling height; alternatively, the 1 Rwall pwall p; (1) pressure could also be controlled via an air pressure ¼ g cosa sina 2Lwall f þ regulator. As the diameter of the capillary at the tip is smaller than the diameter of the particles the first particle where a is the taper angle of the capillary and where we that approaches the tip will block the further flow of fluid in have taken into account static friction at the walls with a the capillary. The entire pressure difference p between the net friction force F g cosap 2pR L acting on the f ¼ f wall band band inlet and the outlet of the capillary now falls off across this particle with a friction coefficient gf. particle. The resulting external forces acting on the particle In general, the friction coefficient could be determined cause it to move closer to the tip of the capillary and the from a separate measurement, or it could also be obtained particle deforms both in shape as well as in volume. In from the capillary micromechanics measurements them- equilibrium, when the particle no longer moves or deforms, selves by performing several measurements with different the externally applied stress must balance the internal taper angles and using the dependence on the taper angle elastic stress of the particle. As the particle deformation is to determine the friction coefficient. However, swollen quantified simultaneously using an optical microscope, microgels are known to exhibit very low friction with this enables us to directly quantify the elastic properties of surfaces; this is also illustrated by the fact that in the particle. rheological measurements on concentrated microgels it In the experiments on our p-NIPAM particles we increase is difficult to prevent the occurrence of wall slip.[26] Indeed, the applied pressure p in steps from p 500 Pa to p 4.5 kPa values for the friction coefficient of hydrogels are typically ¼ ¼ 4 3 [27] [23] and monitor the resulting elastic deformation of a as low as g 10À –10À . Following reference, we f ¼ particle, as seen in Figure 4(B). It can clearly be seen in therefore neglect the effects of friction and set g 0 in f ¼ the images that our p-NIPAM particles change not just Equation (1) (we note that the corresponding equation in their shape, but also their volume in the process; this reference [23] contains a typing mistake). shows that, in agreement with the osmotic compression Again following [23] we assume that the stress is isotropic measurements, the particles exhibit a finite compressive inside the particle and identify the externally applied stress elastic modulus. in the flow direction with the applied pressure difference p

To characterize the changing shape of the particles we and in the radial direction with the wall pressure pwall. focus on the contact surface between the particle and Balancing these stresses with the internal elastic stress the glass wall, which is highlighted in the schematic response as a result of the particle deformation yields the illustration shown in Figure 4(A). This contact surface elastic modulus K and the shear elastic modulus G. has the shape of a tapered circular band; we denote The analysis is performed by plotting the characteristic the length of this band along the flow direction as Lband and stress for compression and for shear as a function of the the average radius of this band as Rband, as shown in characteristic strain, as shown in Figure 5(A) and (B), Figure 4(A). In this simple description of the particle deformation the parameters

V, Rband, and Lband are sufficient to describe the shape and volume change of the particle in order to analyze its elastic properties. In equilibrium, the externally applied stress on the particle is balanced by the internal elastic stresses of the particle. This balance allows us to quantify the elastic properties of the material in terms of the compressive elastic modulus K and the shear elastic modulus G. The external forces exerted on the Figure 5. Results from capillary micromechanics measurements on microgel particles. particle by the walls of the capillary are Analysis of A) the compressive modulus K and B) the shear modulus G by plotting the quantified by a wall pressure pwall; this is stress as a function of the strain characteristic for compression and shear, respect- ively.[23] For our p-NIPAM particles (circles) we obtain K 23 kPa and G 3 kPa. To the average force per area acting on the   contact surface between the particle and illustrate the wide range of moduli that can be accessed, we also plot results for poly- acrylamide gels with polymer concentrations of c 4 wt.-% (pluses) and c 5 wt.-% p ¼ p ¼ the glass capillary. From the balance of all (crosses); the respective concentrations of the cross-linker bis-acrylamide are 2.6 and external forces acting on the particle the 5 wt.-% relative to the monomer.

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respectively. Besides the results from our p-NIPAM values of K 17.7 kPa and K 18.5 kPa for the osmotic and ¼ ¼ particles, to illustrate the wide range of properties that the capillary micromechanics measurement, respectively. are accessible we also show results from poly-acrylamide The two methods thus provide comparable results and our microgels with polymer concentrations c 4 wt.-% and results suggest that both methods are valid and useful ways p ¼ c 5 wt.-%; the respective concentrations of the cross- of characterizing the elastic properties of microscopic soft p ¼ linker bis-acrylamide are 2.6 and 5 wt.-% relative to the objects. monomer. For our p-NIPAM particles a linear fit to the data yields a shear elastic modulus of G 2.9 kPa; the data exhibit linear Conclusion and Outlook ¼ behavior up to the highest deformations probed, as shown in Figure 5(B). Materials that consist of microscopic soft objects exhibit a For the compressive modulus of the p-NIPAM particles wide range of properties that are distinctly different from we obtain K 23.4 kPa; however, here the corresponding those of systems that consist of hard particles. The ¼ linear fit may not adequately describe the data, as the local deformability of the particles in these systems adds slope of the data clearly increases with increasing DV/V, as additional degrees of freedom to these systems and thereby shown in Figure 5(A). directly affects their dynamics, their structure, and their To validate the data from the capillary micromechanics mechanical properties at the macroscopic scale. measurements, we compare them directly to the results In order to develop an understanding of the macroscopic from the osmotic compression measurements performed behavior of these materials, knowledge of the properties of on the same p-NIPAM particles. This is the most direct test of a single particle is thus essential. The methods presented the accuracy of the methods, as this comparison is not here enable us to measure the linear elastic behavior at the influenced by relative changes of concentration during single particle level. They thus offer the opportunity to swelling of the particles in water or by inhomogeneous study in detail the link between single particle properties concentrations inside the particle. We limit the capillary and the properties of the whole material at the macroscopic data to volumetric strains smaller than 25% and display scale. both curves in the same graph, shown in Figure 6. For Microgels are ideal model systems for such studies, as clarification also the compressive stress of the first point in their mechanical behavior can easily be controlled in their each data series is subtracted from the curve, which does synthesis, by varying the polymer concentration and the not affect the slope of the curves. We find a surprisingly concentration of cross-linking agents. Moreover, microgels good agreement between the two measurements, with such as p-NIPAM that are sensitive to temperature or other external factors can be used as model systems for systematic studies of the link between the local and the macroscopic mechanics, as in one single experimental system the properties can be conveniently tuned for instance by a change in temperature. The experimental methods presented here should be further improved and accompanied by new approaches that circumvent their current limitations. In capillary micromechanics for instance, only objects large enough to be accurately imaged in a light microscope can be measured. This limits the size of objects that can be measured to a few micrometers or larger; circumventing these limitations will require higher resolution imaging techniques as well as optimized flow devices, where objects can be injected into the tapered capillaries with a separate capillary, without requiring the application of large pressure differences across the tapered capillary. Figure 6. Direct comparison of osmotic compression (squares) and capillary micromechanics measurements (circles) for our p- The influence of static friction should also be adequately NIPAM particles. Plot of the applied pressure difference Dp as incorporated into the analysis, which could enable the a function of the volumetric strain deformation DV/V. For the characterization of soft objects that exhibit significantly capillary micromechanics measurements, Dp (2p Dp)/3. ¼ wall þ higher friction than do microgel particles. Finally, the D < At volumetric strain deformations V/V 0.3 we find good method could be validated by a direct comparison to a finite agreement between the two techniques with K 17.7 kPa ¼ and K 18.5 kPa for the osmotic and capillary measurements, element simulation of the particle deformation process; ¼ respectively. this would enable us to directly quantify the errors that are

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