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Calculate Branching Index

Source: R/polymer-analysis.R
measure_branching_index.Rd

Calculates the branching index (g or g') for branched polymers by comparing their properties to linear reference polymers of the same molecular weight.

Usage

measure_branching_index(
  mw,
  rg = NULL,
  intrinsic_visc = NULL,
  reference = "linear",
  mh_linear = NULL,
  rg_linear_fit = NULL,
  method = c("g", "g_prime", "both")
)

Arguments

mw

Numeric vector of molecular weights for branched samples.

rg

Numeric vector of radius of gyration values (for g ratio).

intrinsic_visc

Numeric vector of intrinsic viscosity values (for g').

reference

Type of reference: either "linear" for comparison to linear polymer theory, or a data frame containing linear reference data.

mh_linear

Mark-Houwink parameters for linear reference polymer (list with K and a). Required if reference = "linear" and using g'.

rg_linear_fit

Rg-MW relationship for linear polymer: either a model or a list with slope and intercept for log(Rg) = intercept + slope * log(M).

method

Branching index type:

  • "g": Radius of gyration ratio: g = Rg^2(branched) / Rg^2(linear)

  • "g_prime": Viscosity ratio: g' = [eta](branched) / [eta](linear)

  • "both": Calculate both g and g'

Value

A data frame with columns:

mw

Molecular weight

g

Branching index from Rg (if calculated)

g_prime

Branching index from viscosity (if calculated)

branches_per_molecule

Estimated branch points (Zimm-Stockmayer)

Details

Branching reduces the hydrodynamic size of polymers compared to their linear counterparts. This is quantified by the branching ratios:

Rg-based branching index (g): $$g = \frac{R_g^2(branched)}{R_g^2(linear)}$$

Viscosity-based branching index (g'): $$g' = \frac{[\eta](branched)}{[\eta](linear)}$$

The relationship between g and g' depends on polymer architecture: $$g' = g^\epsilon$$

where epsilon ~ 0.5-1.5 depending on branching type.

Zimm-Stockmayer Model (random branching): $$g = \frac{6}{n_b} \left[ \frac{1}{2} + \frac{(2 + n_b)^{1/2} - 1 - n_b/2}{n_b} \right]$$

where n_b is the number of branch points per molecule.

See also

Other sec-polymer: measure_branching_frequency(), measure_branching_model_comparison(), measure_conformation_data(), measure_mh_parameters(), measure_rg_mw_scaling()

Examples

# Calculate branching index from Rg data
mw <- c(100000, 200000, 500000)
rg_branched <- c(12, 18, 32)
rg_linear <- c(15, 22, 40)  # Reference linear polymer

g <- measure_branching_index(
  mw = mw,
  rg = rg_branched,
  reference = data.frame(mw = mw, rg = rg_linear),
  method = "g"
)