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Broad Standard Calibration for SEC/GPC

Source: R/step_sec_broad_standard.R
step_sec_broad_standard.Rd

step_sec_broad_standard() creates a specification of a recipe step that fits a calibration curve using a polydisperse (broad) molecular weight standard with known Mn and Mw values.

Usage

step_sec_broad_standard(
  recipe,
  measures = NULL,
  broad_standard = NULL,
  known_mn = NULL,
  known_mw = NULL,
  fit_type = c("linear", "quadratic"),
  method = c("hamielec", "integral"),
  reference_mwd = NULL,
  integration_range = NULL,
  extrapolation = c("warn", "none"),
  output_col = "mw",
  log_output = TRUE,
  role = NA,
  trained = FALSE,
  skip = FALSE,
  id = recipes::rand_id("sec_broad_standard")
)

Arguments

recipe

A recipe object.

measures

Character vector of measure columns to apply calibration to. If NULL, uses all measure columns.

broad_standard

A data frame containing the broad standard chromatogram:

  • location (or time, volume, retention, elution_time, elution_volume): Elution position

  • value (or signal, response, intensity, ri, uv): Detector response

known_mn

Known number-average molecular weight (Mn) in Daltons.

known_mw

Known weight-average molecular weight (Mw) in Daltons.

fit_type

Type of calibration curve:

  • "linear" (default): log10(M) = C1 + C2*V (classic Hamielec)

  • "quadratic": log10(M) = C1 + C2V + C3V^2

method

Calibration method:

  • "hamielec" (default): Optimize to match Mn and Mw

  • "integral": Use cumulative MWD matching (requires reference_mwd)

reference_mwd

Optional data frame for integral method containing the known cumulative molecular weight distribution of the broad standard:

  • mw: Molecular weight values (Daltons)

  • cumulative: Cumulative weight fraction (0 to 1)

Required when method = "integral". Can be obtained from the standard's certificate of analysis or determined by light scattering/viscometry.

integration_range

Optional numeric vector c(min, max) specifying the elution range to use for the broad standard. If NULL, auto-detects peak region.

extrapolation

How to handle data outside the calibration range:

  • "warn" (default): Extrapolate but warn

  • "none": Return NA for out-of-range values

output_col

Name for the output molecular weight column. Default is "mw".

log_output

Logical. If TRUE (default), output column contains log10(MW). If FALSE, output contains MW in Daltons.

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

This step implements broad standard calibration methods for SEC/GPC, which use a single polydisperse standard with known molecular weight averages instead of multiple narrow standards.

Hamielec Method:

Based on Balke, Hamielec, LeClair, and Pearce (1969). The original method assumes a linear calibration relationship, though this implementation also supports a quadratic extension for better fit over wide MW ranges:

$$\log_{10}(M) = C_1 + C_2 \cdot V$$

The algorithm simultaneously optimizes coefficients C1 and C2 (and C3 for quadratic fits) using Nelder-Mead optimization to minimize the squared relative errors between calculated and known Mn and Mw values.

Integral/Cumulative Match Method:

The integral method matches the entire cumulative MWD shape rather than just Mn and Mw. This requires a reference cumulative distribution (reference_mwd) typically obtained from the standard's certificate or measured by light scattering/viscometry. The algorithm optimizes calibration coefficients to minimize the sum of squared differences between the calculated and reference cumulative distributions.

This method is more robust than Hamielec because it uses the full distribution shape, not just two moments. It's particularly useful when the standard's MWD shape is well-characterized.

When to Use Broad Standard Calibration:

  • QC labs running the same polymer type repeatedly

  • When narrow standards aren't available for your polymer

  • When you have a well-characterized in-house reference material

  • Provides "absolute" molecular weights for the same polymer type

Limitations:

  • Results are only valid for polymers with similar hydrodynamic behavior

  • Linear calibration may not fit well over very wide MW ranges

  • Requires well-characterized broad standard (accurate Mn and Mw)

  • Integral method requires full cumulative MWD data

References

Balke, S.T., Hamielec, A.E., LeClair, B.P., and Pearce, S.L. (1969). Gel permeation chromatography. Industrial & Engineering Chemistry Product Research and Development, 8(1), 54-57.

See also

Other sec-calibration: load_sec_calibration(), save_sec_calibration(), sec_calibration_standards, sec_pmma_standards, sec_ps_standards, step_sec_conventional_cal(), step_sec_universal_cal()

Examples

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

data(sec_triple_detect)

# Create broad standard chromatogram data
broad_std <- data.frame(
  time = seq(10, 20, by = 0.1),
  signal = dnorm(seq(10, 20, by = 0.1), mean = 15, sd = 1.5)
)

# Apply broad standard calibration
rec <- recipe(~., data = sec_triple_detect) |>
  step_measure_input_long(
    ri_signal,
    location = vars(elution_time),
    col_name = "ri"
  ) |>
  step_sec_baseline() |>
  step_sec_broad_standard(
    broad_standard = broad_std,
    known_mn = 50000,
    known_mw = 150000
  ) |>
  prep()

# Check calibration results
tidy(rec, number = 3)
} # }