Estimates the Mark-Houwink K and a (alpha) parameters from intrinsic viscosity and molecular weight data.
Arguments
- mw
Numeric vector of molecular weights.
- intrinsic_visc
Numeric vector of intrinsic viscosities (same length as
mw).- weights
Optional numeric vector of weights for weighted regression. Use concentration or signal intensity as weights for SEC data.
- mw_range
Optional numeric vector of length 2 specifying the MW range to use for fitting. Data outside this range is excluded.
- log_fit
Logical. Perform fit in log-log space (recommended)? Default is
TRUE.
Value
A list of class mh_parameters containing:
- K
Mark-Houwink K parameter
- a
Mark-Houwink a (alpha) exponent
- r_squared
R-squared of the fit
- n_points
Number of data points used
- mw_range
MW range of the data
- fit
The fitted linear model object
Details
The Mark-Houwink equation relates intrinsic viscosity to molecular weight:
$$[\eta] = K \cdot M^a$$
In log form: $$\log([\eta]) = \log(K) + a \cdot \log(M)$$
The parameters K and a depend on:
Polymer-solvent system
Temperature
Polymer microstructure (tacticity, branching)
Interpretation of 'a' exponent:
a ~ 0.5: Theta solvent (polymer coil collapsed)
a ~ 0.5-0.8: Good solvent (typical range)
a ~ 0.8: Rigid rod or extended chain
a < 0.5: Branched or compact structures
Examples
# Estimate Mark-Houwink parameters from triple-detection data
mw <- c(10000, 25000, 50000, 100000, 250000)
iv <- c(0.15, 0.28, 0.45, 0.72, 1.2)
mh <- measure_mh_parameters(mw, iv)
print(mh)
#> Mark-Houwink Parameters
#> ========================================
#>
#> K = 3.8112e-04
#> a = 0.652
#>
#> R-squared: 0.9981
#> Data points: 5
#> MW range: 10000 - 250000
#>
#> Equation: [eta] = K * M^a
# K = 0.000114, a = 0.716 (typical for PS in THF)