Fit Rg-MW Scaling Relationship

Fits the power law relationship between radius of gyration (Rg) and molecular weight (MW) to determine polymer conformation.

Usage

measure_rg_mw_scaling(mw, rg, weights = NULL, mw_range = NULL)

Arguments

mw: Numeric vector of molecular weights.
rg: Numeric vector of radii of gyration (same length as mw).
weights: Optional numeric vector of weights (e.g., concentration).
mw_range: Optional numeric vector of length 2 specifying MW range for fitting.

Value

A list of class rg_mw_scaling containing:

nu: Scaling exponent (slope in log-log space)
prefactor: Prefactor K in Rg = K * M^nu
r_squared: R-squared of the fit
conformation: Interpreted polymer conformation
n_points: Number of data points used
fit: The lm fit object

Details

The Rg-MW relationship follows a power law:

$$R_g = K \cdot M^{\nu}$$

where nu (the Flory exponent) indicates polymer conformation:

Interpretation of nu:

nu ~ 0.33: Compact/spherical (collapsed globule)
nu ~ 0.50: Theta solvent (ideal chain)
nu ~ 0.588: Good solvent (swollen coil)
nu ~ 1.0: Rigid rod

Typical Values:

Flexible polymers in good solvent: nu = 0.55-0.60
Branched polymers: nu = 0.40-0.50
Proteins (globular): nu = 0.30-0.35
DNA: nu = 0.58-0.60

References

Flory, P.J. (1953). "Principles of Polymer Chemistry." Cornell University Press.

Examples

# Fit Rg-MW for a linear polymer
mw <- c(10000, 50000, 100000, 500000, 1000000)
rg <- c(4.5, 12, 18, 45, 70)  # nm

scaling <- measure_rg_mw_scaling(mw, rg)
print(scaling)
#> Rg-MW Scaling Analysis
#> ======================================== 
#> 
#> Scaling Law: Rg = K * M^nu
#> 
#> nu (Flory exponent): 0.591
#>   95% CI: [0.574, 0.609]
#> K (prefactor): 1.9661e-02
#> 
#> Conformation: good solvent (swollen coil)
#> 
#> R-squared: 0.9997
#> Data points: 5
#> MW range: 10000 - 1000000