Batch Simulation · Module 01

Sorption Isotherm.

Fit Freundlich, Langmuir, and Polanyi–Dubinin–Manes isotherms to your data, or set the parameters by hand. Log–log plots with 95 % confidence bands.

How it works

Three sorption models.

Upload a CSV and the models are fitted with 95 % confidence intervals. Or set the parameters yourself. All curves share one log–log scale.

Freundlich

Empirical

C_s = K_Fr · C_w^n_Fr

Power-law model for heterogeneous surfaces. n_Fr < 1 indicates favourable sorption.

Langmuir

Monolayer

C_s = (Q_max · K_L · C_w) / (1 + K_L · C_w)

Monolayer sorption on uniform sites with saturation at Q_max.

Polanyi–Dubinin–Manes

Pore-filling

C_s = V_Oρ_O · exp[ −( −RT ln(C_w/S)/E )^b ]

Pore filling, extended to water via the Polanyi potential.

01

Upload data

CSV file, two columns: C_w, C_s (no header).
02

Pick a model

Open Models and pick one or more. Tune by hand or click Auto-Fit.
03

Inspect & export

Turn on 95 % CI bands. Pin compounds to compare. Save as PNG.

01

Single compound

Load data, then Auto-Fit. Pin compounds to compare them.

Upload data

CSV · two columns · no header

Compound name (optional), shown in the legend

Choose CSV file

Two columns: C_w, C_s

Need to compare compounds? Pin the current dataset and load a new CSV.

Models

Toggle one or more · tune parameters

Freundlich Empirical Show

C_s = K_Fr · C_w^n_Fr

K_Fr

n_Fr

Langmuir Monolayer Show

C_s = (Q_max · K_L · C_w) / (1 + K_L · C_w)

K_L

Q_max

Polanyi–Dubinin–Manes Pore-filling Show

C_s = V_O · ρ_O · exp[ −( −RT · ln(C_w / S) / E )^b ]

Check Fit next to a parameter to include it in optimization.

V_O [cm³/kg] Fit

E [kJ/mol] Fit

ρ_O [g/cm³] Fit

S [mg/L] Fit

T [K] Fit

b [−] Fit

Advanced: fitting bounds

Restrict optimisation to a specific search domain.

Parameter

Lower

Upper

K_Fr n_Fr K_L Q_max V_O E ρ_O S T b

Plot settings

Title, axes, units, legend labels

Plot title

Freundlich label

Langmuir label

PDM label

Data label

Plot 1 X min (log)

Plot 1 X max (log)

Plot 2 X min (log)

Plot 2 X max (log)

Plot 1 Y min (log)

Plot 1 Y max (log)

Plot 2 Y min (log)

Plot 2 Y max (log)

Plot 1 X unit

Plot 1 Y unit

Plot 2 X unit

Plot 2 Y unit

Use ^ for superscripts. E.g. mg L^-1.

Pre-analysis

Statistics · outliers · cleaning

Upload a CSV first to run pre-analysis.

01

C_s vs C_w

Raw concentration · log-log

Concentration

C_s [mg g^-1]

Upload data or enable a model.

C_w [mg L^-1]

02

C_s vs C_w / S

Normalized by solubility · log-log

Activity

C_s [mg g^-1]

Mirrors Plot 1, normalised by solubility.

C_w / S [-]

02

Global analysis: C_s vs C_w/S

Concentrations are normalised to each compound's solubility (C_w/S). All datasets are fitted together.

Add compound

CSV · solubility · density

Compound name

S [mg/L]

ρ_O [g/cm³]

Choose CSV file

Two columns: C_w, C_s

No compounds added yet.

Models (normalized)

Toggle one or more · tune parameters

Freundlich Empirical Show

C_s = K_Fr^* · (C_w/S)^n_Fr

K_Fr^*

n_Fr

Langmuir Monolayer Show

C_s = (Q_max · K_L^* · (C_w/S)) / (1 + K_L^* · (C_w/S))

K_L^*

Q_max

Polanyi–Dubinin–Manes Pore-filling Show

C_s = V_O · ρ_O,mean · exp[ −( −RT · ln(C_w / S) / E )^b ]

Density ρ_O,mean is auto-computed.

V_O [cm³/kg] Fit

E [kJ/mol] Fit

ρ_O,mean [g/cm³]

T [K]

b [−] Fit

Advanced: fitting bounds

Restrict optimisation to a specific search domain.

Parameter

Lower

Upper

K_Fr^* n_Fr K_L^* Q_max V_O E

Plot settings

Title, axes, units, legend labels

Plot title

Freundlich label

Langmuir label

PDM label

X min (log)

X max (log)

Y min (log)

Y max (log)

X unit

Y unit

Use ^ for superscripts. E.g. mg L^-1.

G

C_s vs C_w / S

Global fit · all compounds aggregated · log-log

Global

C_s [mg g^-1]

Add compounds to begin.

C_w / S [-]