Calculator Inputs
Contrast Matching Graph
Example Data Table
| Example | Dry SLD | Shell SLD | Shell Fraction | Estimated Match | Use Case |
|---|---|---|---|---|---|
| Protein in mixed water | 1.95 | 0.30 | 10% | About 34% | Find a low protein contrast condition. |
| Polymer particle | 0.80 | 0.20 | 5% | About 19% | Screen blend contrast before beamtime. |
| Silica-rich particle | 3.45 | 1.00 | 8% | About 54% | Match solvent near inorganic phase. |
| Deuterated component | 6.10 | 4.50 | 12% | About 91% | Highlight hydrogenated partner phase. |
Formula Used
Solvent scattering length density
ρsolvent = ρH2O + (D2O% / 100) × (ρD2O − ρH2O)
Effective particle scattering length density
ρparticle = (1 − h) × ρdry + h × ρshell
Here, h is the shell or hydration volume fraction.
Contrast and match point
Δρ = ρparticle − ρsolvent
Match %D2O = 100 × (ρparticle − ρH2O) / (ρD2O − ρH2O)
Relative signal estimate
Irelative = scale × concentration × (Δρ)² + background
P(q) = [3 × (sin(qR) − qR cos(qR)) / (qR)³]²
How to Use This Calculator
- Enter the dry scattering length density of the particle.
- Add a shell or hydration SLD when the particle has a bound layer.
- Set the shell fraction as a percentage of particle volume.
- Keep default H2O and D2O values, or edit them for your solvent data.
- Enter the planned D2O percentage for the trial measurement.
- Add concentration, scale, background, radius, and q range.
- Press the calculate button to view results above the form.
- Use the graph, CSV file, and PDF report for planning notes.
Small Angle Neutron Scattering Contrast Matching Guide
Why Contrast Matters
Small angle neutron scattering often depends on contrast. Contrast is the difference between the scattering length density of the dispersed material and the surrounding solvent. When the difference is large, the particle signal is strong. When the values match, the particle becomes nearly invisible to neutrons.
How Matching Works
Contrast matching uses mixed solvents to find that invisible point. A common mixture uses light water and heavy water. Heavy water has a much higher scattering length density. By changing the heavy water percentage, the solvent value moves across a wide range. The match point is the percentage where the solvent equals the effective particle value.
What the Tool Calculates
This calculator models that idea with practical controls. Enter the dry particle scattering length density, solvent end point values, hydration fraction, concentration, and instrument scale. The tool estimates the solvent value, the hydrated particle value, the contrast term, and a relative signal. It also generates a contrast curve across the selected mixture range.
Hydration and Shell Effects
Hydration is important for many proteins, polymers, gels, and porous solids. Bound solvent can shift the apparent particle value. A dry material may match at one percentage, while a hydrated material may match at another percentage. The hydration correction gives a simple first estimate of that shift.
Limits of the Estimate
The calculated intensity is not a full SANS model. It is a planning estimate based on contrast squared. Real data also depends on particle shape, size distribution, structure factor, incoherent background, detector setup, transmission, and counting statistics. Still, contrast squared is very useful because it shows why signals rise or vanish as the solvent mixture changes.
Planning Measurements
Use the graph to choose useful measurements. Points far from the match point provide strong particle contrast. Points near the match point can hide one component and reveal another. This is helpful in multicomponent systems, such as proteins in detergent, polymer blends, nanoparticles with shells, or complexes in solution.
Exporting Results
Export the table when comparing several trial conditions. Save the PDF for lab notes, proposals, or beamtime planning. Review units carefully, because scattering length density is commonly reported in 10⁻⁶ Å⁻². Consistent units keep match point estimates reliable and easier to discuss with instrument scientists. Document assumptions so later reviews remain transparent too.
FAQs
What is contrast matching in SANS?
Contrast matching adjusts solvent scattering length density until one component has little contrast. The matched part scatters weakly, while other unmatched parts remain visible.
What units should I use for SLD?
Use 10⁻⁶ Å⁻² for all scattering length density inputs. The calculation assumes every SLD field uses the same unit basis.
Why does D2O percentage change the solvent SLD?
D2O has a higher scattering length density than H2O. A mixed solvent is estimated by linear interpolation between those two endpoint values.
What does the shell fraction mean?
It represents the approximate volume share assigned to hydration, coating, or shell material around the dry particle core.
Is the intensity estimate a complete SANS fit?
No. It is a planning estimate based on contrast squared, concentration, scale, background, and a simple sphere form factor.
What happens near the match point?
The contrast approaches zero. Particle scattering becomes weak, so background and other sample components may dominate the measured signal.
Can I use this for proteins?
Yes, for early planning. Use reliable protein SLD, hydration assumptions, buffer composition, and instrument guidance for stronger experimental design.
Why might the match point be outside 0% to 100%?
The particle SLD may fall outside the solvent range. Another contrast agent or different solvent system may be needed.