Compares experimental branching data against theoretical predictions from different branching models to identify the most likely architecture.
Usage
measure_branching_model_comparison(
g,
mw,
g_prime = NULL,
models = c("random", "star", "comb", "hyperbranched"),
branch_frequency = NULL
)Arguments
- g
Numeric vector of experimental g ratios (Rg^2 branched / Rg^2 linear).
- mw
Numeric vector of molecular weights (same length as
g).- g_prime
Optional numeric vector of g' ratios (IV branched / IV linear).
- models
Character vector of models to compare. Default compares all:
"random": Random trifunctional branching (Zimm-Stockmayer)"star": Star polymers (variable arms)"comb": Comb architecture"hyperbranched": Hyperbranched/dendritic
- branch_frequency
For fitting: assumed constant branching frequency (branches per 1000 Da). If NULL, estimated from data.
Value
A list of class branching_model_comparison containing:
- model_fits
Data frame with fit statistics for each model
- best_model
Name of the best-fitting model
- predictions
Data frame with predicted g for each model
- experimental
Input experimental data
Details
Model Equations:
Random trifunctional (Zimm-Stockmayer): $$g = \left[\left(1 + \frac{n_b}{7}\right)^{1/2} + \frac{4n_b}{9\pi}\right]^{-1/2}$$
Star polymer (f arms): $$g = \frac{3f - 2}{f^2}$$
Comb polymer (n_b branches): $$g \approx \frac{1}{1 + 2n_b/3}$$
Hyperbranched (degree of branching DB): $$g \approx \left(\frac{1}{1 + DB \cdot n/2}\right)^{0.5}$$
Model selection uses residual sum of squares and AIC-like criteria.
References
Zimm, B.H. and Stockmayer, W.H. (1949). J. Chem. Phys., 17, 1301-1314.
Burchard, W. (1999). "Solution Properties of Branched Macromolecules." Adv. Polym. Sci., 143, 113-194.
Examples
# Compare models for branched polymer data
mw <- c(50000, 100000, 200000, 500000)
g_exp <- c(0.85, 0.72, 0.58, 0.42)
comparison <- measure_branching_model_comparison(g_exp, mw)
print(comparison)
#> Branching Model Comparison
#> ============================================================
#>
#> Model Fit Summary:
#> ------------------------------------------------------------
#> model parameter r_squared rmse aic
#> random 0.04648146 0.9887283 0.01699313 -17.24806
#> star 1.11325520 0.9470407 0.03683411 -11.05914
#> comb 0.00502421 0.9670907 0.02903611 -12.96221
#> hyperbranched 0.09231394 0.9932768 0.01312403 -19.31498
#> ------------------------------------------------------------
#>
#> Best Model: hyperbranched (lowest AIC)
#> R-squared: 0.9933
#> RMSE: 0.0131
#> Parameter: 0.0923
#>
#> Note: Lower AIC indicates better fit with penalty for complexity.
#> Consider physical plausibility when selecting the final model.