Multi-Angle Light Scattering Processing for SEC

step_sec_mals() creates a specification of a recipe step that processes multi-angle light scattering (MALS) detector signals to determine absolute molecular weight and radius of gyration at each elution slice.

Usage

step_sec_mals(
  recipe,
  mals_col = NULL,
  concentration_col = NULL,
  dn_dc = NULL,
  dn_dc_column = NULL,
  wavelength = 658,
  solvent_ri = 1.333,
  angles = 90,
  formalism = c("zimm", "debye", "berry"),
  calibration_constant = NULL,
  output_mw = "mw_mals",
  output_rg = "rg",
  min_signal = 0.01,
  role = NA,
  trained = FALSE,
  skip = FALSE,
  id = recipes::rand_id("sec_mals")
)

Arguments

recipe: A recipe object.
mals_col: Name of the MALS detector measure column. For single-angle detectors (RALS/LALS), this is the only signal needed.
concentration_col: Name of the concentration measure column (from step_sec_concentration() or similar).
dn_dc: Refractive index increment (mL/g). Required for absolute MW.
dn_dc_column: Column containing sample-specific dn/dc values.
wavelength: Laser wavelength in nm. Default is 658 (common for MALS).
solvent_ri: Solvent refractive index. Default is 1.333 (water). Common values: water = 1.333, THF = 1.407, toluene = 1.497.
angles: Numeric vector of detection angles in degrees. For single-angle detectors, provide just one value (e.g., 90 for RALS). Default assumes a 90-degree detector.
formalism: Angular extrapolation method for multi-angle data: "zimm" (default), "debye", or "berry".
calibration_constant: MALS instrument calibration constant. If NULL, results are in relative units. Obtain from toluene standard calibration.
output_mw: Name for the molecular weight output column. Default is "mw_mals".
output_rg: Name for the radius of gyration output column. Default is "rg". Only calculated if multiple angles are provided.
min_signal: Minimum signal threshold (as fraction of max) below which MW is set to NA. Default is 0.01.
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, containing absolute MW (and optionally Rg) at each elution point.

Details

Light scattering provides absolute molecular weight without calibration standards. The fundamental relationship is:

$$\frac{K \cdot c}{R(\theta)} = \frac{1}{M_w} \cdot P(\theta) + 2A_2 c$$

where:

K is the optical constant
c is the concentration
R(theta) is the excess Rayleigh ratio
Mw is the weight-average molecular weight
P(theta) is the particle scattering function
A2 is the second virial coefficient

The optical constant K is calculated as: $$K = \frac{4\pi^2 n_0^2 (dn/dc)^2}{N_A \lambda^4}$$

Formalisms for Angular Extrapolation:

Zimm: Kc/R vs sin^2(theta/2) - best for random coils
Debye: Kc/R vs sin^2(theta/2) - similar to Zimm
Berry: sqrt(Kc/R) vs sin^2(theta/2) - better for large particles

Single-Angle vs Multi-Angle:

Single angle (RALS/LALS): Provides Mw only, assumes P(theta) ~ 1
Multi-angle (MALS): Provides both Mw and Rg from angular dependence

Note

Accurate results require:

Known and accurate dn/dc value
Calibrated instrument (calibration_constant from toluene)
Accurate concentration from RI detector
Clean baseline and aligned detectors

Examples

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

# Single-angle (90 degree) light scattering
rec <- recipe(~., data = sec_triple_detect) |>
  step_measure_input_long(ri_signal, location = vars(elution_time), col_name = "ri") |>
  step_measure_input_long(mals_signal, location = vars(elution_time), col_name = "mals") |>
  step_sec_baseline() |>
  step_sec_ri(dn_dc = 0.185) |>
  step_sec_concentration(detector = "ri", injection_mass = 0.2, flow_rate = 1.0) |>
  step_sec_mals(
    mals_col = "mals",
    concentration_col = "ri",
    dn_dc = 0.185,
    wavelength = 658,
    angles = 90
  ) |>
  prep()
} # }