Measuring the nematic order of colloidal fd virus by xray diffraction

Abstract

The orientational distribution function of the nematic phase of the semi-flexible rod-like virus fd is measured by x-ray diffraction as a function of concentration and ionic strength. The angular distribution of the scattered intensity from a single-domain nematic phase of fd arises from only the single particle orientational distribution function at high angle but it also includes spatial and orientational correlations at low angle. Experimental measurements of the orientational distribution function from both the interparticle and intraparticle scattering were made to test whether the correlations present in interparticle scatter influence the measurement of the single particle orientational distribution function. It was found that the two types of scatter yield consistent values for the nematic order parameter. It was also found that x-ray diffraction is insensitive to the orientational distribution function's precise form, and the measured angular intensity distribution is described equally well by both Onsager's trial function and a Gaussian. At high ionic strength the order parameter S of the nematic phase coexisting with the isotropic phase approaches theoretical predictions for long semi-flexible rods S=0.55, but deviations from theory increase with decreasing ionic strength. The concentration dependence of the nematic order parameter was also found to better agree with theoretical predictions at high ionic strength, indicating that electrostatic interactions have a measurable effect on the nematic order parameter. The measured x-ray order parameters are also shown to be proportional to the measured birefringence and the saturation birefringence of fd is measured, enabling a simple, inexpensive way to measure the order parameter.