Soft Matter Under Electric Field And Shear
Negi, Ajay Singh
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‘Soft condensed matter’ is a newly-emerged sub-discipline of physics concerned with the study of systems that are mechanically soft such as colloids, emulsions, surfactants, polymers, liquid crystals, granular media and various biomaterials including DNA and proteins. These materials display a broad range of interesting microstructures and phase behaviours and have a myriad of applications in the materials, food, paint and cosmetic industries as well as medical technologies. Soft condensed matter physics presents new opportunities and challenges for the development of new ideas and concepts in experimental and theoretical physics alike. Because the field overlaps with many different disciplines, the study of soft matter also offers promising developments to other fields of science including chemistry, chemical engineering, materials science, biology, and environmental science. The behaviour of these systems is dominated by one simple fact: they contain mesoscopic structures in the size range 10 nm to 1 µm that are held together by weak entropic forces. The elastic constants of these materials are 109 times smaller than the conventional atomic materials and hence are easily deformable by external stresses, electric or magnetic fields, or even by thermal fluctuations. We have studied two important classes of soft matter systems in this thesis -colloidal suspensions and surfactant systems. The thesis is divided into two main themes: (a) Effects of electric field on the colloidal suspensions, and (b) Effects of shear on surfactant solutions. Motions of colloidal particles under the influence of applied electric field were observed under a microscope and were studied using image analysis and particle tracking. We have also used tracking of thermal fluctuations of colloidal particles embedded in surfactant gels to study microrheology of surfactant solutions. Linear and non-linear rheology of aqueous solutions of cationic cetyltrimethyl ammonium bromide (CTAB) and anionic sodium-3-hydroxynapthalene-2-carboxylate (SHNC) were studied using bulk rheology in a commercial rheometer. Rheological studies of an anionic surfactant sodium dodecyl sulphate (SDS) in the presence of strongly binding counterion p-toluidine hydrochloride (PTHC) has also been done. Chapter 1 starts with a general introduction to soft condensed matter systems and then we proceed to describe two specific class of soft condensed materials which we have studied in this thesis -colloidal suspensions and surfactant/water systems. After describing different types of colloids, we discuss why colloids are suitable as model systems in condensed matter physics. This is followed by a discussion on the chemical structure, phase behaviour and self assembling properties of surfactant molecules in water. We then discuss the inter-macromolecular forces such as van der Waals interaction, the screened Coulomb repulsion, hydrogen bond, hydrophobic and hydration forces and steric repulsion which are the major players in the interaction in soft condensed matter systems. The systems that have been the subject of our experimental studies, viz. polystyrene colloidal suspensions, CTAB+SHNC, SDS+PTHC and CTAT have also been discussed in detail. Then we have given an overview of effects of electric field on the colloidal suspensions. Two types of geometries have been discussed: one in which the field is parallel to the plates and another when the field is perpendicular to the electrodes. Application of colloidal particles in diagnostic tests (Latex Agglutination Tests) has been discussed after this. Some methods used to enhance the sensitivity of LATs have also been reviewed. This is followed by a theoretical background of linear and non-linear rheology. We have also given an introduction to digital video microscopy, its advantages and discussed few quantities like pair correlation function, structure factor which can be extracted using digital video microscopy and particle tracking. The concluding part of this chapter describes the organization of this thesis. Chapter 2 discusses the experimental apparatus and techniques used in our studies. We describe our setup for applying the electric field to the colloidal particles and imaging and tracking their motion. We also discuss the image processing and analyzing methods for extracting the useful quantities from the digitized images. We have described the various components of the MCR-300 stress-controlled rheometer (Paar Physica, Germany) and the AR-1000N stress-controlled rheometer (T. A. Instruments, U. K.) followed by different experimental geometries that we have used for our experiments. Next we have described the various experiments that can be done using a commercial rheometer. Calculation of surface charge of colloidal particles using a conductivity meter has been demonstrated for our colloidal particle suspensions. We also describe the sample preparation methods employed in different experiments. In Chapter 3, we have discussed our study of clustering of colloidal particles under the influence of an ac electric field as a function of frequency. The field was applied in a direction perpendicular to the confining walls. Two regimes are observed, a low frequency regime where the clusters are isotropic with a local triangular order and a new high-frequency regime where the clusters are highly elongated (anisotropic) with no local order. The crossover from one regime to the other occurs at a critical frequency, fc. The formation of elongated clusters seen at high frequencies is explained in terms of rotation of particles due to a phase lag between the polarization of the electric double layer around a particle and the applied electric field that arises because of inhomogeneities of the conducting surface. We have also observed that the threshold field for the cluster formation, Eth, increases with frequency in both the regimes. We did these studies on two different sizes of particles and found that both Eth and fc were lower for the larger particles. Our model based on particle rotation was able to estimate the value of fc correctly for both the sizes of the particles. Chapter 4 describes a method employing an ac electric field applied perpendicular to the confining walls to increase the sensitivity of recognition of ligands by their corresponding receptors grafted on Brownian latex particles. Application of electric field assists the colloidal micro-particles grafted with receptors to come nearer due to electro-hydrodynamic drag. This increase in the local concentration of the latex particles results in improving the chances of ligand-receptor interaction leading to the aggregation of the latex particles. With this technique we have been able to increase the sensitivity of the ligand-receptor recognition by a factor as large as 50. We have demonstrated the utility of our method using streptavidin as the model receptor and biotinylated RNase A as the model ligand. We have also applied our technique to a commercially available kit for rheumatoid factor (RF) with successful results. The same method was also successfully applied for the detection of typhoid whose antibodies were purified and attached to polystyrene particles by our collaborators from DRDE Gwalior. In Chapter 5, we have studied the statics and dynamics of colloidal particles at different applied electric fields from zero to beyond the threshold field. We have taken a series of time-lapsed images and calculated out the pair-correlation function, mean squared displacement, structure factor, non-Gaussian parameter etc. We have studied both mono-dispersed colloidal system and binary colloidal system (mixture of two different sizes of particles). The aggregates formed in the two cases were analysed with the help of Voronoi polygons to quantify the microscopic structure. In mono-dispersed system, the aggregates formed were two-dimensional hexagonal crystals and we have used this system to study the freezing transition in 2-dimension. The properties of the system in the liquid and the crystalline state satisfy various criteria for the 2-d freezing transition. The first maximum of the structure factor at the voltage at which freezing occurs, is 5.5 as has been suggested for the 2-d freezing. This is reflected in the dynamics of the system also, where the ratio D/D0 falls below 10%, in accordance with the LPS (L¨owen, Palberg, Simon) criterion for freezing in 2-d colloidal systems [Phys. Rev. Lett. 70, 1557 (1993)]. However, in the binary colloidal system the clusters formed were not crystalline but more like 2-d dense liquids. A closer inspection of these clusters reveals that the motion of a smaller subset of particles is cooperative and follows string-like paths. The mean square displacement of such a system shows a plateau in the intermediate times which indicates the “caging” of particles by its neighbours. A peak in non-gaussian parameter indicates the presence of dynamical heterogeneities in the system. In Chapter 6, we have described the use of multiple particle tracking to study the microrheology of semidilute solutions of wormlike micelles and compared the results with those from macrorheology experiments done on the same samples. Two concentrations of CTAT (1.3% and 2%) were used. We observed that, in spite of the mesh size being much smaller than the size of the probe particles, the viscoelastic response function calculated using the one-point microrheology does not match with that measured from macrorheology. This can be attributed to the fact that there is another important length scale in the system, the mean micellar length, and it is comparable to the probe particle size. Two-point microrheology was successful in verifying the macrorheology results for CTAT 1.3% but it fails to do so for CTAT 2%. We attribute this to the fact that in a higher viscosity sample (2%), the hydrodynamic force propagate to a lesser distance, thereby limiting the measurable correlation between the particles and precluding the success of two-point microrheology. Chapter 7 describes a rheological study of aqueous solutions of varying concentration of cationic cetyltrimethyl ammonium bromide (CTAB) and anionic sodium-3-hydroxynapthalene-2-carboxylate (SHNC) kept at a fixed molar concentration ratio [CTAB]/[SHNC] = 2. At this molar ratio, the surfactants self-assemble into wormlike micelles which get entangled above the overlap concentration to form viscoelastic gel. The range of the total surfactant concentration φ varies from 1.17% to 5.16% by weight. We found that, plateau modulus, G0, shows a power law dependence on the surfactant concentration, φ, with an exponent 3, which is higher than the expected value of 2.25 observed for the one-component wormlike micelles. Zero shear viscosity, η0, and relaxation time, τR show a maximum at the surfactant concentration, φmax = 1.9% in contrast to a monotonic increase with φ. We propose that this non-monotonic behaviour is due to the unusual dependence of the average micellar length L ¯on φ, showing a maximum in average micellar length L at φmax. This argument provides a strong support to the model of micellar growth in the presence of electrostatic interactions developed by Mackintosh et. al [Europhys. Lett. 12, 697 (1990)]. The presence of electrostatic interactions also appears in the behaviour of the plateau modulus G0 that exhibits a larger φ dependence than in highly screened micelles. In the non-linear flow experiments, a minimum observed in critical shear rate (the shear rate at which shear thinning starts), ˙γc, at φmax strengthens our arguments. In Chapter 8, we describe the phase behaviour and rheology of SDS+PTHC (sodium dodecyl sulphate + p-toluidine hydrochloride) micellar solutions at different molar ratios α=[PTHC]/[SDS]) of the two components. At low values of α, polarizing microscopy observations reveal a transition from an isotropic to a nematic phase of disk-like micelles, whereas a transition to a lamellar phase occurs at higher α values > 0.5, on increasing the surfactant content. Linear rheology of the isotropic micellar solution reveal a viscous behaviour over a large range of surfactant concentrations. Surprisingly, this also extends to the nematic phase of disk-like micelles observed at α =0.2 and φ =0.35. These systems also exhibit a viscoelastic behaviour over a narrow range of surfactant concentration as reported in earlier studies. The extent of the viscoelastic region of the isotropic micellar solution also decreases with increase in α. Frequency sweep curves in this region, scaled on to a master curve is reminiscent of dilute suspensions of hard spheres or rigid Brownian rods. Consistent with the results from oscillatory shear measurements, the f;ow behaviour examined under steady shear is Newtonian over a large range of surfactant content in the isotropic micellar solution. An interesting result in these studies is the non-monotonic behaviour of the viscosity with increase in surfactant concentration. It is likely that the sharp rise in viscosity arises from a jamming effect of the rigid rods. Dynamic light scattering studies suggest that the drop in viscosity is due to the decrease in the length of the micellar aggregates. This is followed by a change in the morphology of the micelles from rods to disks as indicated by the transition to a nematic phase of disk-like micelles or a lamellar phase. A change in the morphology of micellar aggregates with increase in α is expected in mixed surfactant systems with strongly binding counterions. However, the surprising result is the change in morphology of the micellar aggregates with surfactant content. Such a behaviour is seen in mixed surfactant systems for the first time. The thesis concludes with a summary of our main results and a brief discussion of the scope of future work in Chapter 9.
- Physics (PHY) 
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