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Universal Calibration for SEC

Source: R/step_sec_universal_cal.R
step_sec_universal_cal.Rd

step_sec_universal_cal() creates a specification of a recipe step that applies universal calibration to determine molecular weight from intrinsic viscosity and retention data.

Usage

step_sec_universal_cal(
  recipe,
  measures = NULL,
  calibration = NULL,
  calibration_col = NULL,
  intrinsic_visc_col = NULL,
  K_sample,
  a_sample,
  K_standard = 0.000114,
  a_standard = 0.716,
  output_col = "mw_universal",
  role = NA,
  trained = FALSE,
  skip = FALSE,
  id = recipes::rand_id("sec_universal_cal")
)

Arguments

recipe

A recipe object.

measures

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

calibration

A calibration object or data frame containing the universal calibration curve (log([eta]M) vs retention).

calibration_col

If calibration is a column name in the data, specify it here.

intrinsic_visc_col

Column containing intrinsic viscosity values. Required for converting between polymer types.

K_sample

Mark-Houwink K parameter for the sample polymer.

a_sample

Mark-Houwink a (alpha) exponent for the sample polymer.

K_standard

Mark-Houwink K for the calibration standard polymer. Default is 0.000114 (polystyrene in THF).

a_standard

Mark-Houwink a for the calibration standard. Default is 0.716 (polystyrene in THF).

output_col

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

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 molecular weight calculated via universal calibration.

Details

Universal calibration is based on the principle that polymers with the same hydrodynamic volume elute at the same retention time, regardless of chemical structure. The hydrodynamic volume is proportional to [eta]M:

$$V_h \propto [\eta] \cdot M$$

The Universal Calibration Curve: $$\log([\eta] \cdot M)_{sample} = \log([\eta] \cdot M)_{standard}$$

At the same retention volume, using Mark-Houwink equations: $$[\eta] = K \cdot M^a$$

We can solve for sample MW: $$M_{sample} = \left(\frac{K_{std} \cdot M_{std}^{1+a_{std}}}{K_{sample}}\right)^{\frac{1}{1+a_{sample}}}$$

Mark-Houwink Parameters (THF, 25C):

  • Polystyrene: K = 0.000114, a = 0.716

  • PMMA: K = 0.000128, a = 0.690

  • Polyisoprene: K = 0.000251, a = 0.728

  • Polybutadiene: K = 0.000457, a = 0.693

Note

Universal calibration requires:

  • Known Mark-Houwink parameters for both standard and sample

  • Calibration with narrow standards (typically polystyrene)

  • Same solvent and temperature for all measurements

For absolute MW determination, consider using MALS detection instead.

See also

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

Examples

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

# Apply universal calibration to convert PS calibration to PMMA
rec <- recipe(~., data = pmma_data) |>
  step_measure_input_long(ri, location = vars(time), col_name = "ri") |>
  step_sec_baseline() |>
  step_sec_universal_cal(
    calibration = ps_calibration,
    K_sample = 0.000128,      # PMMA
    a_sample = 0.690,
    K_standard = 0.000114,    # PS (default)
    a_standard = 0.716
  ) |>
  prep()
} # }