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Band Broadening Correction for SEC

Source: R/step_sec_band_broadening.R
step_sec_band_broadening.Rd

step_sec_band_broadening() creates a specification of a recipe step that corrects for axial dispersion (band broadening) in SEC chromatograms. This improves the accuracy of molecular weight distribution measurements.

Usage

step_sec_band_broadening(
  recipe,
  measures = NULL,
  method = c("tung", "emg"),
  sigma = NULL,
  calibration_peak = NULL,
  tau = NULL,
  iterations = 1,
  damping = 0.5,
  role = NA,
  trained = FALSE,
  skip = FALSE,
  id = recipes::rand_id("sec_band_broadening")
)

Arguments

recipe

A recipe object.

measures

Character vector of measure column names to process. If NULL, all measure columns will be processed.

method

Correction method. One of:

  • "tung" (default): Tung's linear correction

  • "emg": Exponentially Modified Gaussian deconvolution

sigma

Spreading parameter (standard deviation of the instrumental broadening function) in the same units as the location axis (typically minutes or mL). If NULL, must provide calibration_peak.

calibration_peak

A measure_tbl or data frame with location and value columns representing a narrow standard peak used to estimate sigma.

tau

Exponential time constant for EMG method. If NULL with EMG method, estimated from calibration_peak.

iterations

Number of iterations for iterative correction. Default is 1 for Tung's method (single pass). Higher values may improve correction but can introduce instability.

damping

Damping factor (0-1) to prevent over-correction and instability. Default is 0.5. Lower values are more conservative.

role

Role for generated columns.

trained

Logical indicating if the step has been trained.

skip

Logical. Should the step be skipped when baking?

id

Unique step identifier.

Value

An updated recipe with the new step added.

Details

Band broadening in SEC occurs due to:

  • Axial diffusion during elution

  • Non-ideal column packing

  • Extra-column volume (tubing, connections, detector cell)

This causes:

  • Artificially broadened peaks

  • Underestimated Mn (number-average MW)

  • Overestimated dispersity (Mw/Mn)

Tung's Method (default):

The observed chromatogram F(V) is related to the true distribution W(V) by: $$F(V) = \int W(V') G(V - V') dV'$$

where G is a Gaussian spreading function with standard deviation sigma. Tung's linear correction approximates: $$W(V) \approx F(V) - \sigma^2 \frac{d^2 F(V)}{dV^2}$$

EMG Method:

Models band broadening as convolution with an Exponentially Modified Gaussian, which better handles asymmetric peak shapes caused by tailing.

Sigma Determination:

The spreading parameter sigma should be determined from a narrow molecular weight standard (e.g., polystyrene with PDI < 1.05). Use estimate_sigma() to calculate sigma from such a standard.

Note

  • Correction is applied to the signal, not to molecular weight values

  • Large corrections (> 50% change in peak width) may indicate unreliable sigma or poor chromatographic conditions

  • This step preserves the area under the curve (mass conservation)

References

Tung, L. H. (1966). Method of calculating molecular weight distribution function from gel permeation chromatograms. Journal of Applied Polymer Science, 10(3), 375-385.

See also

estimate_sigma() for determining the spreading parameter

Other sec-chromatography: step_sec_baseline(), step_sec_detector_delay(), step_sec_exclude_regions(), step_sec_integration_window(), step_sec_mw_averages(), step_sec_mw_distribution(), step_sec_mw_fractions(), step_sec_peaks_deconvolve(), step_sec_peaks_detect(), step_sec_peaks_refine()

Examples

if (FALSE) { # \dontrun{
library(recipes)
library(measure)

# Using a known sigma value
rec <- recipe(~., data = sec_data) |>
  step_measure_input_long(signal, location = vars(time), col_name = "ri") |>
  step_sec_baseline() |>
  step_sec_band_broadening(sigma = 0.05) |>
  prep()

# Estimating sigma from a narrow standard
narrow_std <- estimate_sigma(narrow_standard_peak)
rec <- recipe(~., data = sec_data) |>
  step_measure_input_long(signal, location = vars(time), col_name = "ri") |>
  step_sec_baseline() |>
  step_sec_band_broadening(sigma = narrow_std$sigma) |>
  prep()
} # }