Crystallization Analysis Tool

Theoretical Introduction

This tool analyzes the solubility and metastable zone width (MSZW) of a solute in a solvent. The solubility curve (or clear point curve) represents the thermodynamic limit above which the solid phase dissolves completely. The nucleation curve (or cloud point curve) represents the kinetic limit where spontaneous nucleation begins upon cooling. The region between these two curves is the Metastable Zone, a supersaturated state where crystallization can be controlled.

The Van 't Hoff Equation

The relationship between solubility (expressed as concentration, C) and absolute temperature (T) is described by the Van 't Hoff equation. Its exponential form is:

C = e(ΔS/R) * e(-ΔH/RT)

By applying the natural logarithm, we get the linear form, which is fundamental for thermodynamic analysis:

ln(C) = - (ΔH / R) * (1/T) + (ΔS / R)

Where:

By plotting ln(C) versus 1/T, we obtain a straight line. The slope of this line is -ΔH/R, and the y-intercept is ΔS/R. This tool uses this linear regression to calculate the thermodynamic parameters from your solubility data.

1. Data Input

Edit the data directly or add new rows. Press the button at the bottom to update charts and analysis.

Compound NameConcentrationSolvent 1 Name% Solvent 1Solvent 2 Name% Solvent 2Clear Temp (°C)Cloud Temp (°C)

2. Metastable Zone Width (MSZW) Map

Chart Display Options

3. Fit Model Analysis

Solubility Curve

Nucleation Curve

4. Residuals Analysis

This chart helps diagnose the quality of the fit. A good model shows residuals (differences between observed and predicted data) randomly scattered around the zero line, with no obvious patterns.

5. Van 't Hoff Thermodynamic Analysis

This section analyzes the data according to the linearized Van 't Hoff equation to extract thermodynamic parameters.

Why use two different forms?

The linear form (the chart above) is used for the "fit" because it allows for robust and simple linear regression to find the thermodynamic parameters (ΔH and ΔS). Once found, the more intuitive exponential form is used to make all concentration and temperature predictions throughout the tool.

6. Analysis by Concentration

7. Crystallization Yield Calculation

Calculate the theoretical yield for the system based on the selected solubility model.

8. Phase Diagram: Temperature vs. Solvent Composition

Introduction to Phase Diagram Models

This section models how the solubility/nucleation temperature changes with the ratio of two solvents.

  • Jouyban-Acree: A semi-empirical model that describes deviations from ideal behavior through interaction parameters (A₀, A₁, A₂). It is the most accurate model if sufficient data is available.
  • Ideal Mixture: A theoretical model (based on the Yalkowsky-Roseman equation) that shows how the system would behave without specific interactions between components. It is useful as a baseline.
  • Polynomial: A simple mathematical model that fits a curve to the data points, without physical meaning. Useful for a quick visualization.

Note: If increasing the "Fixed Concentration" makes the curve go down, it means the input data describes an exothermic dissolution process (less soluble at higher temperatures), and the model is correctly reflecting this.

9. Calculation Log

10. Export & Session Management