Simultaneous Birefringence-dichroism Apparatus & Couette flowcell
The optical properties of a sample can also reveal information concerning microstructure. Two frequently measured bulk optical properties are birefringence and dichroism. Birefringence can be simply described as a difference in the real part of the refractive index in one coordinate direction relative to another and is caused by optical anisotropy in a material. It is sometimes referred to as double refraction, which occurs when light travels through an anisotropic crystal and is broken up into two rays. These rays are polarized with respect to each other and travel at different velocities. The first, referred to as the ordinary ray, obeys Snell¡¯s law, while the second, the extraordinary ray, does not. The phenomenon is illustrated in Figure 1.
Figure 1. Example of the phenomena of birefringence.
In polymeric liquids, intrinsic birefringence is caused by anisotropy in the segmental polarizability, where the value of the polarizability along the axis of the polymer is different than that orthogonal to it. When a polymer solution or melt is subjected to a sufficiently strong deformation, polymer chains tend to align with the flow direction. Such a change in the microscopic orientation of polymer chains can be detected by passing polarized light through the sample, as a change in the light¡¯s polarization state can be correlated with microstructure.
Additionally, form birefringence can arise when there is a difference between the refractive index of a macromolecule or particle and the solvent, or oriented anisotropic particles are present in solution. In the case of anisotropic particle suspensions, the form birefringence increases with the degree of orientation. Form effects also lead to changes in the attenuation of polarized light. If the particles are sufficiently small compared with the wavelength of light, they act as dipole scatterers and generate an anisotropic attenuation of the light, known as dichroism . For suspensions of anisotropic nanoscale particles in polymer liquids, both of the constituent species will contribute to the birefringence; however, any measured dichroism derives solely from particle orientation.
Thus, rheo-optics has proven to be a valuable tool for non-invasively probing fluid microstructure in well-defined flow fields. For example, Schmidt and co-workers reported the mechanical rheology and birefringence of polyethylene oxide/laponite clay/ water solutions . Li et al. studied the birefringence polystyrene Boger fluids in axisymmetric stagnation flow [4, 5]. Finally, Oberhauser and co-workers performed flow birefringence experiments to examine the response of entangled polystyrene solutions to step changes in shear rate in Couette flow [6, 7].
In order to ultimately study the response of polymer-clay solutions in steady and transient shear flow, we borrowed ideas from Fuller and co-workers and assembled an apparatus to perform simultaneous birefringence and dichroism experiments [8-10]. A detailed schematic of the experiment is shown in Figure 2.
Figure 2. Schematic of the simultaneous birefringence and dichroism experiment.
In short, monochromatic light from a Helium-Neon laser passes through a polarizer oriented at 90¡ã, a photoelastic modulator (PEM) oriented at 45¡ã, and a quarter wave plate oriented at 0¡ã before passing along the vorticity direction of a circular Couette flow cell. A tepper motor with precise computer control will drive the outer cylinder, providing accurate and reproducible steady and transient shear flows. After leaving the flow cell, the beam is split into two equally intense beams, one of which goes directly to a detector (dichroism) and the other of which passes through a quarter wave plate oriented 0¡ã and a polarizer oriented at -45¡ã going to another detector. By means of Fourier analysis, the intensity signals can be decomposed and manipulated to obtain the magnitude of the birefringence and dichroism as well as their principle axis of orientation. The mathematical analysis used to calculate the birefringence and dichroism are presented in appendix A.
Data are acquired using a data acquisition board (National Instruments, Inc.) and decomposed and extracted using four digital lock-in amplifiers (Stanford Research Systems, Inc.). LabVIEW code (National Instruments, Inc.) to control the flow cell and obtain real-time data was written with the assistance of undergraduate researcher Russell Prestipino. A schematic representation of how rheo-optical data was acquired and analyzed is shown in Figure 3.
Figure 3. Schematic of the rheo-optical data acquisition system.
The circular Couette flow cell was fabricated by Kineoptics (Slidell, LA). The flowcell consists of two coaxial cylinders. The inner cylinder is stationary and removable with diameter of 45mm. The rotating outer cylinder with diameter of 47mm is driven by a microstepper motor with a Gemini controller provided by Parker Hannifin Corp. The flow is confined within the 1mm gap between the outer and inner cylinders. By rotating outer cylinder, inertial flow instabilities are suppressed.[Drazin and Reid,(1985)].
1. Fuller, G.G., Optical Rheometry of Complex Fluids. 1995, New York: Oxford University Press.
2. Onuki, A. and M. Doi, Flow birefringence and dichroism of polymers. I. General theory and application to the dilute case. Journal of Chemical Physics, 1986. 85(2): p. 1190-7.
3. Schmidt, G., A.I. Nakatani, and C.C. Han, Rheology and flow-birefringence from viscoelastic polymer-clay solutions. Rheologica Acta, 2002. 41: p. 45-54.
4. Li, J.-M., et al., Flow Birefringence and Computational Studies of A Shear Thinning Polymer Solution in Axisymmetric Stagnation Flow. Journal of Non-Newtonian Fluid Mechanics, 1998. 74: p. 151-193.
5. Li, J.-M., et al., Birefringence and Computational Studies of A Polystyrene Boger Fluid in Axisymmetric Stagnation Flow. Journal of Non-Newtonian Fluid Mechanics, 2000. 91: p. 189-220.
6. Oberhauser, J.P., K. Pham, and L.G. Leal, Rheo-optical Studies of The Response of Entangled Polymer Solutions to Step Changes in Shear Rate. Journal of Rheology, 2004. 48(6): p. 1229-1249.
7. Oberhauser, J.P., K. Pham, and L.G. Leal, Erratum:"Rheo-Optical Studies of The Response of Entangled Polymer Solutions to Step Changes in Shear Rate"[J.Rheol. 48, 1229-1249(2004)]. Journal of Rheology, 2005. 49(2): p. 569-569.
8. Frattini, P.L. and G.G. Fuller, The dynamics of dilute colloidal suspensions subject to time-dependent flow fields by conservative dichroism. Journal of Colloid and Interface Science, 1984. 100(2): p. 506-518.
9. Johnson, S.J., P.L. Frattini, and G.G. Fuller, Simultaneous Dichroism and Birefringence Measurements of Dilute Colloidal Suspensions in Transient Shear Flow. Journal of Colloid and Interface Science, 1985. 104(2): p. 440-455.
10. Fuller, S.J.J.a.G.G., Flowing colloidal suspensions in non-Newtonian suspending fluids: decoupling the composite birefringence. Rheologica Acta, 1986. 25: p. 405-417.