HPLC Simulator

The simulator calculates each compound’s retention time and peak width, represents its detector response as a Gaussian peak, and adds the peaks together. Detector noise and a signal offset are then added at evenly spaced sampling times across the run.

Retention time. The retention factor depends on temperature and mobile-phase composition:

log₁₀(k′) = m_wT + b_w + (m_φT + b_φ)φ

Here T is temperature in °C, φ is the volume fraction of solvent B (0–1), and the coefficients describe the compound’s behavior on the selected stationary phase. For an isocratic run, the detected retention time is:

t_R = t₀(1 + k′) + t_tube,   t₀ = V₀/F

V₀ is the column hold-up volume, F is flow rate, and t_tube is the post-column tubing delay. In gradient runs, composition is interpolated between programmed points, delayed and smoothed by the system volumes, and used to track each compound through the column as its retention factor changes.

Peak width. Column efficiency follows the reduced van Deemter relationship:

h = A + B/ν + Cν,   H = h d_p,   N = L/H

ν is reduced mobile-phase velocity, d_p is particle diameter, L is column length, and N is the theoretical plate count. Peak width is expressed as the Gaussian standard deviation, σ. For isocratic runs, the simulator combines the broadening contributions as:

σ² = t_R²/N + τ² + σ_tube² + (V_inj/F)²/12

τ is the detector time constant, σ_tube² is tubing-dispersion variance, and V_inj is injection volume. All times and volumes in these equations use consistent units. For gradient runs, the column term is approximated by [t₀(1 + k′_elution)]²/N, and the injection-volume term is omitted. Efficiency and tubing dispersion use the initial gradient composition.

Detector response. This simulator uses a simplified, ideal detector that responds equally to all compounds at the same molar concentration. Real detectors generally have compound-dependent responses. For example, a UV absorbance detector gives a stronger response to compounds that absorb more strongly at the selected wavelength. A mass spectrometer’s response depends on ionization and ion detection; compounds that ionize readily or are already ionic can give stronger responses, depending on the ionization method and measurement conditions.

With the ideal-detector assumption, each compound contributes a peak of the form:

c_i(t) = [n_i/(F σ_i√(2π))] exp[−(t − t_R,i)²/(2σ_i²)]

n_i is the injected amount, calculated from sample concentration and injection volume. This sets the peak area; a narrower peak has a greater height for the same amount. The total chromatogram is the sum of these concentrations, plus the offset and simulated detector noise.

Other relationships connect solvent composition and temperature to viscosity and diffusion, column geometry and porosity to hold-up volume and velocity, and flow resistance to backpressure. Post-column tubing adds delay, dispersion, and pressure drop. These calculations explain how changing a condition affects the separation and instrument requirements.

Retention is calculated from log₁₀(k′) = m_wT + b_w + (m_φT + b_φ)φ, with T in °C and φ the organic volume fraction. The last two coefficients describe −S, following the original data convention. Supply coefficients for both solvents.

Random unknowns follow the original synthetic-compound distributions; they are not measured compounds. Noise is regenerated when the chromatogram is recalculated and stays fixed during zooming, panning, and display-only changes. Its standard deviation is the noise parameter divided by the square root of the detector time constant, converted from nM to µM.