XPCS is an experimental technique which can be used, for example, to study protein dynamics in solution.
Figure 1: Schematic of the XPCS technique. |
When a coherent beam (parallel and no frequency distribution) falls on an object with static or dynamic disorder, a random array of bright and dark spots are created by the irregular interference of scattered waves from different parts of the object. This is called speckle pattern. As the scattering parts fluctuate (due to dynamics), the speckle pattern also fluctuates. By probing such fluctuations, it is possible to obtain the information about the sample dynamics. X-ray photon correlation spectroscopy (XPCS) exploits this mechanism to study the dynamics using a high brilliance synchrotron X-ray source. In this technique, a series of images are collected over time using an area detector which records intensity fluctuations in q-space (reciprocal space, i.e. length scale, L ~ 2 π/q) with time as schematically shown in Figure 1. Such an intensity fluctuation can be quantified by the intensity auto-correlation function (ICF) ![]() |
In many cases g2(q,t) can be described by an exponential decay function
![]() ![]() ![]() ![]() Figure 2: (Left): A time correlation function (TTC), and (right): χT showing dynamical heterogeneity |
There are several synchrotron beamlines specialized in XPCS, e.g.
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Figure 3: ESRF at night. |
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We studied bovine protein Immunoglobulin G (IgG, purchased from
Sigma Aldrich) in the presence of polyethylene glycol (PEG). The
solution was filled in a 1.5 mm quartz capillary tube. XPCS was
performed using a heating stage (Linkam, UK) on the sample stage to
change the sample temperature. The measurement was performed in
transmission geometry with an incident beam of 8.5 keV and sample to
detector distance of 21.3 m at PETRA III, P10, DESY, Hamburg,
Germany. The beam dimension was 100x100 μm2. Figure 4
shows a TTC at a quench temperature of -2 °C at q = 0.0011
A-1. |
Figure 4: (Left): TTC for a quench from 37 °C to -2 °C for IgG-PEG showing a slowing down of the dynamics, middle: Intensity correlation functions extracted from the diagonal cuts of the TTC, right: the relaxation time as s function of sample age. Line profiles at different sample age (tage), represents the ICF as a function of tage. The broadening of the bright regime shows a slowing down of the dynamics with sample age. The diagonal cuts of this TTC at different sample ages are shown in the middle panel of Figure 4. The colorbar shows the sample age in seconds. The relaxation time τ extracted from these ICFs are plotted as a function of tage in the right panel of Figure 4. The slowing down of the dynamics with tage can be observed here. |