1 Introduksi
1.1 Latar Belakang
Distribusi ukuran partikel (Particle Size Distribution / PSD) adalah karakterisasi fundamental untuk material powder, emulsi, dan suspensi karena mengontrol flowability, solubility, bioavailability, texture, dan stability produk. Pada pangan: ukuran partikel kakao menentukan smoothness cokelat (target $d_{50} < 30$ μm), ukuran droplet emulsi minyak menentukan stabilitas creaming (Stokes' law), dan ukuran spray-dried powder menentukan rehydration (Schubert, 1987). Pada farmasi: PSD aktif farmasi mengontrol disolusi dan bioavailability (Noyes-Whitney equation).
Pengukuran modern: laser diffraction (Malvern Mastersizer, range 0.01–3500 μm, dasar Mie theory), dynamic light scattering (DLS, untuk nanopartikel < 1 μm), sieve analysis klasik (sieve series ASTM E11), dan microscope image analysis. Output standar adalah distribusi kumulatif Q3(x) (volume-weighted) atau Q0(x) (number-weighted), dengan metrik kunci $d_{10}$, $d_{50}$, $d_{90}$ (Allen, 2003; ISO 9276-2:2014).
1.2 Tujuan Modul
Modul Particle Size Distribution di SQalytics ditujukan untuk:
- Menghitung metrik distribusi: $d_{10}$, $d_{50}$ (median), $d_{90}$, mean $D[4,3]$ (De Brouckere) dan $D[3,2]$ (Sauter), span = $(d_{90} - d_{10}) / d_{50}$.
- Mendukung distribusi log-normal fit: $\mu_g$, $\sigma_g$ (geometric mean & SD).
- Memvisualisasikan frequency distribution + cumulative distribution (histogram + sigmoid).
- Mendukung input format: histogram bin (sieve series) atau raw measurement list (DLS).
- Audiens: mahasiswa S2 teknologi pangan/farmasi yang menjalankan sieve analysis atau laser diffraction, peneliti formulasi powder/emulsi, QC ingredient sourcing.
1.3 Posisi di Antara Alternatif
Pilih Particle Size Distribution untuk karakterisasi ukuran. Untuk distribusi viskositas vs shear (kinetika), pakai Rheology / Flow Curve. Untuk stabilitas emulsi via zeta potential, gunakan Colloid / Emulsion Stability. Untuk kalibrasi instrumen atau band ratio, pakai Standard Curve atau Band Ratio Index. Untuk uji statistik perbandingan PSD antar batch, lanjut ke Compare Many Groups.
2 Metode
2.1 Dasar Teoretis
Distribusi kumulatif volume-weighted $Q_3(x)$ — fraksi volume partikel dengan ukuran $\leq x$:
$$ Q_3(x) = \frac{\int_0^x q_3(x') \, dx'}{\int_0^\infty q_3(x') \, dx'} $$dengan $q_3(x)$ density distribusi volume.
Percentile sizes $d_{10}$, $d_{50}$, $d_{90}$:
$$ Q_3(d_{10}) = 0.10, \quad Q_3(d_{50}) = 0.50, \quad Q_3(d_{90}) = 0.90 $$Span (lebar distribusi, dimensionless):
Tipikal: span < 1 monodisperse, 1–2 narrow, > 2 broad. Untuk emulsi tunggal-emulsifier biasanya span 1.0–1.5.
Mean diameters (Allen, 2003):
$$ D[4,3] = \frac{\sum n_i d_i^4}{\sum n_i d_i^3} \quad \text{(De Brouckere, volume-weighted)} $$ $$ D[3,2] = \frac{\sum n_i d_i^3}{\sum n_i d_i^2} \quad \text{(Sauter, surface-weighted)} $$$D[3,2]$ proporsional dengan specific surface area — penting untuk dissolution/reaktivitas. $D[4,3]$ untuk volume-related properties.
Log-normal distribution — model umum untuk PSD pangan dan farmasi:
$$ q_3(x) = \frac{1}{x \sigma_g \sqrt{2\pi}} \exp\!\left[-\frac{(\ln x - \mu_g)^2}{2 \sigma_g^2}\right] $$dengan $\mu_g = \ln(d_{50})$ geometric mean dan $\sigma_g$ geometric standard deviation. Untuk log-normal: $\sigma_g = \sqrt{d_{84}/d_{16}} = \sqrt{d_{50}/d_{16}}$.
Specific surface area (asumsi partikel spherical):
$$ S_v = \frac{6}{D[3,2]} $$dengan $S_v$ m²/cm³ bila $D[3,2]$ dalam μm.
2.2 Persamaan Inti
Span: $\text{Span} = (d_{90} - d_{10})/d_{50}$
Sauter mean: $D[3,2] = \sum n_i d_i^3 / \sum n_i d_i^2$
De Brouckere mean: $D[4,3] = \sum n_i d_i^4 / \sum n_i d_i^3$
Log-normal density: $q_3(x) = (x \sigma_g \sqrt{2\pi})^{-1} \exp[-(\ln x - \mu_g)^2 / (2 \sigma_g^2)]$
Specific surface area: $S_v = 6 / D[3,2]$
2.3 Asumsi & Batas Validitas
| Asumsi | Konsekuensi jika dilanggar | Cara cek di SQalytics |
|---|---|---|
| Partikel spherical (laser diffraction) | $D[3,2]$ bias untuk irregular shape | Kombinasikan dengan microscopy |
| Refractive index sampel benar (Mie theory) | Distribusi shifted di laser diffraction | Catat RI di metadata |
| Dispersi cukup (tidak agglomerated) | PSD bias ke high | Pakai surfactant atau sonikasi |
| Sieve mesh kalibrasi (ASTM E11) | $d_{50}$ bias | Kalibrasi sieve berkala |
| Distribusi unimodal | Log-normal fit fails untuk multi-modal | Modul flag bila $R^2 < 0.95$ |
| Sample volume cukup (≥ 0.5 g powder) | High variability | Replicate ≥ 3 |
3 Cara Kerja
3.1 Step-by-Step di SQalytics
- Buka
Particle Size Distributiondari domain Kimia. - Muat tabel input:
- Histogram bin mode: kolomSize_um(bin midpoint) +Volume_pct(frekuensi volume).
- Raw measurement mode: kolomParticle_id+Diameter_um. - Pilih distribution type:
volume-weighted(Q3, default laser diffraction) ataunumber-weighted(Q0, DLS number). - (Opsional) Aktifkan log-normal fit untuk $\mu_g$ + $\sigma_g$.
- Klik
Run Particle Size Analysis. - Tinjau hasil:
- TabSummary— $d_{10}$, $d_{50}$, $d_{90}$, span, $D[4,3]$, $D[3,2]$, $S_v$.
- TabFrequency Plot— histogram + log-normal fit overlay.
- TabCumulative Plot— Q3 sigmoid curve dengan percentile markers.
- TabResult Table.
Setelah hasil utama tampil di Step 4, gunakan Step 5 opsional untuk mengirim PSD distribution atau cumulative undersize ke Publication Graph Studio (PGS). Di sana Anda bisa lanjut mengatur typography, legend, preview Print, lalu ekspor SVG/PNG/PDF untuk kebutuhan publikasi.
3.2 Template Tabel Input + Contoh Data Sintetis
Mode histogram (sieve series):
| Size_um | Volume_pct |
|---|---|
| 10 | 1.2 |
| 25 | 4.5 |
| 50 | 12.8 |
| 100 | 28.4 |
| 200 | 32.5 |
| 400 | 16.2 |
| 800 | 3.8 |
| 1600 | 0.6 |
3.3 Contoh Luaran
| Metric | Value | Interpretasi |
|---|---|---|
| $d_{10}$ | 28.4 μm | 10% partikel < 28 μm |
| $d_{50}$ (median) | 142.5 μm | Median bulk powder |
| $d_{90}$ | 412.0 μm | 90% < 412 μm |
| Span | 2.69 | Broad distribution |
| $D[4,3]$ De Brouckere | 175.2 μm | Volume-mean (sensitivity to coarse) |
| $D[3,2]$ Sauter | 95.6 μm | Surface-mean (dissolution proxy) |
| $S_v$ specific surface | 0.063 m²/cm³ | Surface area per unit volume |
| Log-normal $\mu_g$ | 4.96 (= ln 142.5) | Geometric mean |
| Log-normal $\sigma_g$ | 0.78 | Geometric SD (broad) |
| $R^2$ log-normal fit | 0.987 | Good unimodal fit ✓ |
Compare Many Groups untuk uji statistik $d_{50}$ antar batch atau ke Colloid / Emulsion Stability bila konteks beralih ke droplet emulsi."
4 Kesimpulan
4.1 Relevansi Real-World
- Cokelat refining — target $d_{50}$ < 30 μm untuk mouth-feel smooth.
- Spray-dried powder (milk, instant coffee) — $d_{50}$ 100–300 μm untuk dispersibility.
- Emulsi minuman — $d_{50}$ < 1 μm untuk creaming stability.
- Tablet farmasi — $D[3,2]$ mengontrol disolusi (Noyes-Whitney).
- Roasted coffee grinding — $d_{50}$ vs extraction yield espresso (~ 200–400 μm).
- Tepung terigu — $d_{50}$ ~ 70–150 μm vs gluten development.
4.2 Where to Go from Here
⚙ Troubleshooting Cepat
i Riwayat Revisi
| Tanggal | Revisi | Penulis |
|---|---|---|
| 2026-05-12 | Migrasi MD v2 → HTML final dengan figure publikasi + caption Elsevier-style (W1 batch malam 12 Mei) | Claude |
| 2026-05-12 | Draft v2 publikasi (KaTeX $d_n$/span/Sauter/log-normal + APA Allen/ISO/Schubert/McClements) | Claude |
4 Referensi
- Allen, T. (2003). Powder sampling and particle size determination. Elsevier. https://doi.org/10.1016/B978-0-444-51564-3.X5051-0
- International Organization for Standardization. (2014). ISO 9276-2: Representation of results of particle size analysis — Part 2: Calculation of average particle sizes/diameters and moments from particle size distributions. ISO.
- Schubert, H. (1987). Food particle technology. Part I: Properties of particles and particulate food systems. Journal of Food Engineering, 6(1), 1–32. https://doi.org/10.1016/0260-8774(87)90019-7
- Rawle, A. (2003). Basic principles of particle size analysis. Malvern Instruments Technical Note.
- McClements, D. J. (2015). Food emulsions: Principles, practices, and techniques (3rd ed.). CRC Press. https://doi.org/10.1201/b18868