Computer-Controlled Double-Beam UV-Vis Spectrophotometer
Records high-resolution extinction spectra (absorbance A vs wavelength λ from 400 to 750 nm) of colloidal gold sols using matched 10.00 mm quartz cuvettes with ±0.1 nm wavelength accuracy.
Chemistry / Gold Nanoparticles & Mie Scattering
FREE TO EXPLORELABORATORY 50 · NATURAL SCIENCES
Synthesis and Localized Surface Plasmon Resonance of Gold Nanoparticles via Mie Scattering Theory
Synthesize colloidal gold nanoparticles via Turkevich citrate reduction of tetrachloroauric acid, record localized surface plasmon resonance (LSPR) extinction spectra, and evaluate Mie scattering theory and electrodynamic phase retardation to extract the intrinsic dipolar plasmon wavelength λ₀ = 512.6 nm and retardation slope. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
MEASURE · CALIBRATE · ANALYSE
Your virtual chemistry laboratory.
LSPR EXTINCTION WAVELENGTH Λ_MAX—
MEASUREMENT STATUS
Ready to dispense 20.0 nm of liquid.
Adjust d V, then weigh the dispensed aliquot.
Mass observations are determined by the high-precision thermodynamic equation of state for pure liquid water. Readings reflect thermal equilibrium and analytical balance force restoration.
Physical chemistry assumptions and metrological limits
['The linear Mie retardation model λ_max = λ₀ + S · d applies strictly to spherical, monodisperse particles in the diameter regime d = 10 to 60 nm; for particles d > 80 nm, quadrupolar and octupolar plasmon modes induce pronounced non-linear spectral distortion.', 'Non-spherical nanoparticle morphologies (such as gold nanorods, nanotriangles, or core-shell particles) break spherical symmetry and exhibit two or more distinct plasmon resonance bands (transverse and longitudinal LSPR), which cannot be modeled by simple spherical Mie theory.', 'Colloidal destabilization, electrolyte addition (e.g. NaCl), or surfactant displacement induces plasmonic coupling between adjacent particles, generating coupled inter-particle dimer modes that red-shift the spectrum into the near-infrared (~650–800 nm).'] The physical chemistry simulation model evaluates aqueous suspensions of spherical colloidal gold nanoparticles (bulk gold density ρ = 19.32 g/cm³, molar mass M = 196.97 g/mol, conduction electron density N = 5.90 × 10²² cm⁻³) in deionized water (n_m = 1.333, ε_m = 1.777) at 25.00 °C (298.15 K). Theoretical Mie plasmon parameters: intrinsic dipolar plasmon resonance wavelength for gold nanospheres in water in the quasi-static limit (d → 0) is λ₀ = 512.60 nm, corresponding to the Fröhlich condition ε₁(512.6 nm) = −2 ε_m = −3.554. Across the diameter regime d = 10.0 to 60.0 nm, electrodynamic phase retardation induces a linear bathochromic shift with theoretical slope S = dλ_max/dd = 0.4400 nm/nm. For the six standard nanoparticle core diameters d = [10.0, 15.0, 20.0, 30.0, 45.0, 60.0] nm, the corresponding LSPR peak extinction wavelengths are λ_max = [517.0, 519.2, 521.4, 525.8, 532.4, 539.0] nm. Ordinary least-squares linear regression yields an empirical slope S = 0.44000 nm/nm and Y-intercept λ₀ = 512.600 nm with Pearson correlation coefficient R² = 1.000000000. The extracted intrinsic dipolar plasmon wavelength λ₀ = 512.60 nm shows perfect concordance (0.0000% difference) with the authoritative literature benchmark (512.60 nm, Haiss et al., Anal. Chem. 2007). Multi-point regression insulates the analysis from minor cuvette reflection losses, stray light, and slight variation in colloid optical density.
Analytical chemistry apparatus & tools.
Precision Heating Mantle and Magnetic Stirrer with PID Controller
Maintains vigorous boiling at 100.0 ± 0.5 °C with high-speed vortex stirring (800 rpm) during citrate addition to ensure instantaneous, uniform nucleation and narrow size distribution.
Three-Neck Round-Bottom Reaction Flask (250 mL) with Allihn Reflux Condenser
Enables solvent-loss-free Turkevich reduction of tetrachloroauric acid under reflux, preventing concentration changes during boiling.
Spectroscopic-Grade Tetrachloroauric Acid Standard (HAuCl4·3H2O)
Ultra-pure auric chloride precursor (purity ≥ 99.99%, M = 393.83 g/mol) dissolved in Milli-Q deionized water to provide standardized Au(III) ions.
Analytical Grade Trisodium Citrate Dihydrate (Na3C6H5O7·2H2O)
Bifunctional reagent acting simultaneously as mild reducing agent (reducing Au(III) to Au(0)) and electrostatic capping agent imparting negative citrate surface charge.
Aqua Regia Glassware Decontamination & Passivation Bath
3:1 v/v mixture of concentrated HCl and HNO3 to dissolve all trace residual gold seeds and particulate nucleation centers from glassware prior to synthesis.
FOLLOW THE METHOD
A reason behind every step.
Synthesize colloidal gold nanoparticles via Turkevich citrate reduction of tetrachloroauric acid, record localized surface plasmon resonance (LSPR) extinction spectra, and evaluate Mie scattering theory and electrodynamic phase retardation to extract the intrinsic dipolar plasmon wavelength λ₀ = 512.6 nm and retardation slope. Suggested independent volumetric settings: 10.0, 15.0, 20.0, 30.0, 45.0, 60.0 nm.
01
Glassware Aqua Regia Decontamination and Surface Passivation
Clean all glassware (reflux flask, condenser, magnetic stir bar, and volumetric pipettes) with freshly prepared aqua regia (3:1 HCl:HNO3) under a fume hood to strip all catalytic gold nuclei. Rinse with 10 volumes of 18.2 MΩ·cm Milli-Q deionized water and oven dry at 110 °C.
02
Preparation of Gold(III) Precursor and Citrate Reductant Solutions
Prepare 100.0 mL of 1.00 mM tetrachloroauric acid (HAuCl4) by dissolving 39.38 mg HAuCl4·3H2O in ultra-pure water. Separately prepare 50.0 mL of 38.8 mM (1.0 wt%) trisodium citrate dihydrate (Na3C6H5O7·2H2O) using Class-A volumetric flasks.
03
Turkevich Citrate Reduction and Colloidal Gold Synthesis
Transfer 50.0 mL of 1.00 mM HAuCl4 solution into the three-neck flask equipped with an Allihn reflux condenser. Heat to vigorous boiling (100 °C) under 800 rpm magnetic stirring. Rapidly inject 5.0 mL of hot trisodium citrate solution. Observe the color transition from faint yellow to colorless, dark gray/black (nucleation), deep purple, and finally brilliant ruby-red within 3–5 minutes. Continue boiling for 15 minutes, remove heat, and stir until cooled to 25 °C.
04
Synthesis of Size-Graded Colloid Series (10 nm to 60 nm)
Repeat the Turkevich synthesis across variable citrate-to-gold precursor ratios (or obtain calibrated monodisperse gold nanoparticle standards with TEM core diameters d = 10.0, 15.0, 20.0, 30.0, 45.0, and 60.0 nm). Dilute aliquots with deionized water to bring optical absorbance within the linear spectrophotometer range (0.3 to 1.2 AU).
05
UV-Vis Spectrophotometric Scanning and Extinction Baseline Calibration
Fill matched 10.00 mm quartz cuvettes with Milli-Q water to record the 100% transmission baseline from 400 to 750 nm. Rinse the sample cuvette twice with the colloidal gold sol, fill to the fill-line, and acquire the extinction spectrum at 0.5 nm sampling intervals. Locate the maximum extinction peak wavelength λ_max and record absorbance A_max.
06
Mie Scattering Linear Regression and Intrinsic Plasmon Resonance Extraction
Plot the experimental localized surface plasmon resonance (LSPR) extinction peak wavelength λ_max (nm) on the Y-axis against nanoparticle core diameter d (nm) on the X-axis across the six standard samples. Perform ordinary least-squares linear regression to extract the electrodynamic retardation slope S = dλ_max/dd and the Y-intercept λ₀ (intrinsic dipolar plasmon wavelength), comparing with theoretical Mie calculations.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into quantitative chemical insight.
Points are your recorded gravimetric observations. The regression line validates the linear mass-volume proportionality and extracts density.
ORDINARY LEAST-SQUARES FIT · m = ρ·V + m₀
\lambda_{\max} = S \cdot d + \lambda_0 \implies \lambda_{\max} = 0.440 \cdot d + 512.60
| # | Nanoparticle Core Diameter d (nm) | LSPR Extinction Wavelength λ_max (nm) | Nanoparticle Core Diameter d (nm) | LSPR Extinction Wavelength λ_max (nm) | Remove |
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