Particle Size Distribution and TiO2 Opacity

The opacity of titanium dioxide in coatings and plastics depends critically on particle size — and not just the median size, but the entire particle size distribution (PSD). Two grades with identical median diameter can deliver meaningfully different hiding power in practice, because the shape of the distribution determines how many particles fall in the optimal scattering window. Getting this right is one of the most impactful levers in paint formulation optimization.

The physics of light scattering by TiO2 particles

Light scattering by spherical particles is described by Mie theory. Scattering efficiency peaks when the particle circumference equals roughly one wavelength of the scattered light. For visible light spanning 400–700 nm, the optimal scattering diameter is approximately 200–350 nm (0.20–0.35 μm). TiO2's exceptionally high refractive index (2.75 for rutile) shifts the optimum toward the lower end — approximately 0.20–0.28 μm — because the high refractive index contrast with the binder medium makes even slightly smaller particles highly effective scatterers.

Below the optimum (particles smaller than ~180 nm), scattering efficiency per particle drops steeply. Nano-TiO2 at 15–30 nm primary particle size is so far below the visible wavelength window that it scatters essentially no visible light — the particles are transparent to the eye while still absorbing UV. This is the deliberate design of sunscreen-grade nano TiO2: UV protection without white cast.

Above the optimum (particles larger than ~400 nm), scattering efficiency also declines. Large particles feel gritty in coatings, cause anilox blinding in fine-screen flexo printing, and contribute to sedimentation in liquid systems. A 0.6 μm particle provides less hiding per unit weight than a 0.25 μm particle and creates handling problems in premium applications.

Why PSD width matters as much as median size

Two grades with D50 = 0.26 μm can deliver very different opacity if one has a tight PSD (span = 0.8) and the other has a broad PSD (span = 1.3). The span is defined as (D90 − D10) / D50. A broad PSD means a significant fraction of particles are outside the 0.18–0.35 μm optimal window — either too small (transparent) or too large (inefficient scatterers). Both fractions represent paid-for TiO2 that delivers sub-optimal hiding.

Chloride-process TiO2 has inherently narrower PSD than sulfate-process because the vapor-phase particle formation at 1400–1500°C produces more uniform nucleation and growth. Typical chloride-process span: 0.7–0.9. Typical sulfate-process span: 1.0–1.3. This PSD difference explains most of the 5–10% hiding-power advantage that chloride grades hold over sulfate grades at similar D50.

A bimodal PSD — with peaks at both 0.20 μm and 0.60 μm — is particularly problematic. Despite a D50 that may appear acceptable, the coarse fraction causes dispersion problems and the fine fraction contributes little hiding. Bimodal distributions sometimes arise from inadequate bead-mill dispersion or from mixing two lots with different PSDs. Laser diffraction analysis (volume-weighted distribution) reveals bimodality that D50 alone cannot detect.

Measuring and specifying PSD for procurement

Laser diffraction (Malvern Mastersizer, Beckman Coulter LS, Horiba LA series) is the industry standard for TiO2 PSD measurement. The instrument reports D10, D50, D90, and optionally the full volume-weighted distribution curve. Measurement can be done wet (particles dispersed in isopropanol with ultrasound) or dry (air dispersed). Wet measurement is more reproducible for fine TiO2.

Standard CoA values for coating-grade chloride rutile: - D10: 0.14–0.18 μm - D50: 0.24–0.28 μm - D90: 0.38–0.48 μm - Span: 0.70–0.90

For sulfate rutile, D50 may be similar but span is typically 1.0–1.3 and D90 extends to 0.55–0.70 μm.

When evaluating a new grade, request the full PSD curve, not just D50. Ask the supplier to confirm whether the measurement is volume-weighted or number-weighted (they are very different — volume-weighted is the relevant one for opacity prediction). Confirm wet or dry measurement conditions.

PSD effects beyond opacity: rheology and dispersion

PSD affects coating rheology in ways that matter at the production scale. A narrow-PSD grade tends to pack more efficiently in high-solids formulations — particles of nearly uniform size can organize into more ordered arrangements, reducing viscosity at a given solids loading. A broad-PSD grade with a coarse tail tends to increase high-shear viscosity and can cause grind-out problems in roller mill or bead-mill dispersion.

In plastic masterbatch, PSD width affects screen pressure in extrusion. A coarse tail (D90 > 0.6 μm) in masterbatch TiO2 can accelerate screen pack fouling and increase screen-change frequency — a significant cost in high-volume production. Premium masterbatch grades specify maximum coarse particle content (e.g., > 45 μm sieve residue ≤ 0.005% by weight) to control this.

SEMITI grade PSD specifications

SEMITI 706 and 706W (premium chloride rutile): D50 0.24–0.27 μm, span 0.75–0.85. Optimized for highest hiding efficiency in premium architectural and industrial coatings.

SEMITI 996 and 902 (universal chloride rutile): D50 0.25–0.29 μm, span 0.80–0.95. Balanced hiding and cost for standard applications.

SEMITI 298 (sulfate rutile): D50 0.25–0.30 μm, span 1.0–1.2. Broader distribution; acceptable for economy coatings, rubber, and paper where color and hiding tolerance is wider.

SEMITI A100 (anatase): D50 0.18–0.24 μm, span 0.9–1.1. Finer than rutile grades; designed for fiber delustering and paper where softer, finer particles are preferred over maximum hiding.

Request PSD data alongside the standard CoA when qualifying a new TiO2 grade — it is the single most informative document for predicting application performance beyond what the CoA summary numbers reveal.

The crowding effect and optimal volume fraction

At high TiO2 loadings, particles pack so closely that their scattering fields overlap and interfere destructively — each additional particle adds less hiding than the previous ones. This non-linearity is the crowding effect, and it has direct implications for formulation optimization.

Optimal volume fraction: The critical spacing for maximum scattering efficiency is approximately one particle diameter between particle centers — equivalent to a volume fraction of about 18–22% TiO2 by volume in the dried film. Above this, crowding reduces efficiency; below it, particles are too sparse for maximum hiding.

In practical terms for a typical architectural latex paint: - At 15% TiO2 by weight (volume fraction ~10%): slightly below optimum — hiding efficiency per gram is high but total hiding could be higher - At 20–22% TiO2 by weight (volume fraction ~14–16%): near-optimal for most latex systems - At 30% TiO2 by weight (volume fraction ~20%): crowding zone begins — each additional kg provides diminishing returns

Extender optimization: One practical way to manage crowding is strategic use of extender pigments. Calcium carbonate, kaolin, talc, and synthetic silica do not contribute hiding but occupy space in the film. In a flat latex paint where TiO2 is used at 20% by weight plus 15% kaolin, the kaolin occupies volume that prevents TiO2 particles from crowding each other — effectively acting as a spacing agent. This "spacing effect" of extenders can recover 10–15% of the hiding efficiency lost to crowding at high TiO2 loadings, reducing the total TiO2 needed without losing contrast ratio.

The optimal extender for crowding management has particles sized 2–5× the TiO2 particle (0.5–1.5 μm), which maximizes spatial separation without contributing excessive rheology. Kaolin (D50 ~1–2 μm) and precipitated calcium carbonate (PCC, D50 0.5–1 μm) are the most effective spacers.

PSD measurement: instrument settings and common errors

Laser diffraction PSD measurement of TiO2 is straightforward but requires careful technique. Errors in sample preparation produce misleading results.

Critical instrument settings: - Dispersion: TiO2 must be fully dispersed before measurement. Minimum: 60-second ultrasonic probe (50 W) in isopropanol with 0.1% dispersant (e.g., Darvan 821A). Inadequate ultrasound leaves agglomerates intact — the measured D50 will be higher than the true primary particle size. - Refractive index input: set TiO2 RI = 2.75 (rutile) or 2.50 (anatase), imaginary component 0.001. Incorrect RI input biases the entire PSD calculation — some labs default to generic particle RI and get systematically wrong results. - Concentration: maintain obscuration in the instrument's valid range (typically 2–8% obscuration for Malvern Mastersizer). Too high = multiple scattering (artificially narrow PSD); too low = poor signal-to-noise. - Measurement runs: take 3 replicate measurements and average. Standard deviation between runs should be < 0.01 μm on D50 for a well-dispersed sample.

Dry vs. wet measurement: Dry measurement (air dispersed) is faster but often gives D50 10–20% higher than wet measurement because some agglomerates survive the dry dispersion air jet. Wet measurement (isopropanol + ultrasound) is the reference method for specification comparison. When comparing PSD data from different sources, always confirm whether wet or dry measurement was used — mixing methods introduces a systematic bias.

Volume-weighted vs. number-weighted distribution: Laser diffraction reports volume-weighted PSD by default. Number-weighted PSD gives much more weight to small particles. For hiding power, volume-weighted is the relevant distribution — it correlates with the mass fraction of TiO2 in each size bin, which is what determines optical performance. Number-weighted PSD of TiO2 shows an enormous peak at the smallest sizes that is irrelevant to hiding and misleading for grade comparison. Always specify volume-weighted when requesting PSD data.