Particle or Macromolecular Shape by SAXS

SAXS encodes structural information through the scattering intensity profile, which reflects the internal pairwise distances within the particle. Through indirect Fourier transformation, this information is converted into the pair distance distribution function (PDDF), a real-space representation of all distances between points inside the particle.

From the PDDF, SAXS provides:

• Overall particle shape, distinguishing globular, rod-like, disk-like, or more complex geometries
• Characteristic dimensions, such as maximum particle dimension (Dmax), radii, or aspect ratios
• Internal symmetry and compactness, inferred from the PDDF profile shape
• Presence of extended or flexible domains, visible through long tails or broadened distributions
  

  Figure 1. PDDF obtained from lysozyme solution SAXS data using XSACT Pro, showing a compact globular profile. PDDF is obtained through a Bayesian approach, with no information loss. The user input of auxiliary values such as the maximum distance within the particle (D_max) of the smoothness parameter are not required.

Figure 2 Comparison between the PDDF of a spherical particle (40 nm in diameter) and a cylindrical particle (40 nm length and 4 nm diameter.), illustrating how shape information is encoded in real-space distance distributions.

Modern Bayesian approaches [1], as implemented in XSACT Pro, extract the PDDF with minimal user input and without loss of structural information, ensuring a robust and objective reconstruction.

SAXS shape determination applies to a wide range of nanoscale systems, particularly those that are monodisperse or moderately polydisperse.

Typical samples include:

• Protein solutions, including monomeric and oligomeric species
• Dilute nanoparticles in aqueous or organic media
• Surfactant assemblies and micelles, including block-copolymer micelles
• Lipid-based colloidal systems such as liposomes or vesicles
• Polymeric or inorganic nano-objects stable in suspension

Because SAXS measurements are performed in solution or in soft-matter environments, they preserve the native, hydrated structure of the particle.

SAXS offers unique advantages for determining shape at nanometer resolution:

These features make SAXS a powerful method for elucidating particle and macromolecular geometry in biostructural research, nanomaterial design, drug delivery systems, soft-matter physics, and colloidal science.