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Kenneth Kusima edited this page Jan 24, 2026 · 32 revisions

Quantitative Analysis Methodology: TAP–MS Calibration

This repository implements a rigorous quantitative analysis workflow for Temporal Analysis of Products (TAP) mass spectrometry data. Unlike steady-state MS analysis, which often relies on relative intensity ratios, TAP requires the conversion of time-resolved electrical signals (counts or Amps) into absolute molar flux ($\text{nmol} \cdot \text{s}^{-1}$).

Because TAP experiments rely on the precise analysis of transient pulse shapes (moments analysis), maintaining strict mass balance is critical. This software achieves this using a dual-factor calibration logic:

  1. Dynamic Normalization: Using an internal inert standard (e.g., Argon) to correct for pulse-to-pulse variations in reactor state.
  2. Static Calibration: Using a species-specific factor to account for fundamental ionization physics.

1. The Physical Model

The fundamental equation used to transform the raw mass spectrometer signal $S(t)$ into molar flux $\Phi(t)$ is derived from the requirement that the integral of the signal must equal the known injected molar amount.

The master equation implemented in the code is:

$$ \Phi_X(t) = \underbrace{\left[ S_X(t) - B \right]}_{\text{Net Signal}} \times \underbrace{K_{pulse}}_{\text{Machine State}} \times \underbrace{\alpha_X}_{\text{Chemical Identity}} $$

Nomenclature

Symbol Unit Description
$\Phi_X(t)$ $\text{nmol} \cdot \text{s}^{-1}$ Molar Flux of species $X$ leaving the reactor.
$S_X(t)$ $\text{a.u.}$ Raw Intensity signal from the mass spectrometer at time $t$.
$B$ $\text{a.u.}$ Baseline background signal (vacuum level) to be subtracted.
$K_{pulse}$ $\frac{\text{nmol} \cdot \text{s}^{-1}}{\text{a.u.}}$ Intensity-to-Flux Constant. A dynamic scalar derived from the inert tracer in the current pulse.
$\alpha_X$ Dimensionless Calibration Factor. A static scalar representing the relative detection efficiency of species $X$ vs. the inert reference.

2. Parameter Definitions & Derivation

A. Intensity-to-Flux Constant ($K_{pulse}$)

  • Code Variable: config['conv']
  • UI Label: Intensity -> Flux Conversion
  • Nature: Dynamic (Recalculated for every pulse/peak)

Purpose: This factor normalizes the data against the "machine state" at the exact moment of the experiment. It compensates for variables that drift over time, such as detector gain, vacuum chamber pressure, and slight variations in the pulse valve injection size.

Derivation: It is calculated by integrating the signal of the co-pulsed inert tracer (e.g., Argon) where the injected amount is known (calibrated sample loop).

$$ K_{pulse} = \frac{N_{Ar, injected}}{\int_{0}^{\infty} S_{Ar}(t) , dt} $$

** Implementation Note:** In multi-peak experiments (e.g., pump-probe), this value is defined separately for each peak (e.g., c_global_0, c_global_1) to account for different loop volumes or detector drift between events.

B. Calibration Factor ($\alpha_X$)

  • Code Variable: calibration_factor
  • UI Label: Calibration Factor (AMU X)
  • Nature: Static (Determined offline, constant for the species)

Purpose: This is a material constant that corrects for the fact that the mass spectrometer is not equally sensitive to all molecules. It encapsulates the ratio of probabilities for Ionization ($\sigma$), Transmission ($T$), and Fragmentation ($f$).

Derivation: This factor is determined in a separate offline calibration experiment where a binary mixture of known composition (e.g., 50% Ar / 50% Reactant) is pulsed repeatedly.

$$ \alpha_X = \frac{Sensitivity_{Ar}}{Sensitivity_{X}} = \frac{\sigma_{Ar} \cdot T_{Ar} \cdot f_{Ar}}{\sigma_X \cdot T_X \cdot f_X} $$

Once determined, this value is "hard-coded" or entered once for the specific AMU and remains constant across all experiments involving that species.

3. Algorithm Implementation

The software processes .tdms files through a strict pipeline to ensure that the resulting flux curves form a valid probability density function for kinetic modeling.

Step 1: Baseline Subtraction

Before any scaling, the vacuum background must be removed. This is critical because even a small DC offset, when integrated over the long tail of a TAP pulse, will result in significant mass balance errors.

# Code Logic
corrected_raw = raw_vals - baseline_offset

Step 2: Piecewise Time-Domain ConversionTAP experiments often involve complex sequences (e.g., pump-probe) where different logic applies to different time segments. The code uses boolean masking to apply the specific $K_{pulse}$ and $\alpha_X$ to the correct time window.Python# The Master Equation in Code
# eff_conv combines the machine state (conv) and chemical physics (calibration_factor)
eff_conv = config['conv'] * calibration_factor

# Apply conversion only to the specific time window (mask)
flux_column[mask] = corrected_raw[mask] * eff_conv
Step 3: Transport Validation (Knudsen Criterion)After conversion, the software integrates the flux curve $\Phi(t)$ to calculate the zeroth moment ($M_0$) and validates the transport regime. Reliable kinetic data requires that the reactor operates in the Knudsen diffusion regime, validated by the dimensionless shape factor:$$H_p \cdot t_p \approx 0.3 \quad (\text{For inert transport})$$Where $H_p$ is the peak height normalized by area ($H_p = F_{peak} / M_0$) and $t_p$ is the time to peak.

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