Using the semidilute unentangled concentration regime to determine the molecular weights of polyelectrolytes
Restricted (Penn State Only)
- Author:
- Han, Aijie
- Graduate Program:
- Materials Science and Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 29, 2022
- Committee Members:
- Robert Hickey, Major Field Member
Enrique Gomez, Outside Unit & Field Member
Ralph Colby, Chair & Dissertation Advisor
John Mauro, Program Head/Chair
Urara Hasegawa, Major Field Member - Keywords:
- Polyelectrolyte solutions
polymer physics
rheology - Abstract:
- Measuring the molecular weight of polyelectrolytes and other ionic polymers has been challenging due to the strong electrostatic repulsion and other complications underlying the conventional methods. Many conventional methods developed for neutral polymers are not ideal for polyelectrolytes. Osmometry (Mn) does not apply to polyelectrolytes since the osmotic pressure is dominated by dissociated counterions. Size exclusion chromatography and static light scattering are reliable methods for neutral polymers in dilute solutions with many assumptions made for simple two-component systems. Applying these two methods to polyelectrolytes with added salt has been popular in the polyelectrolyte field. However, due to the multicomponent nature of polyelectrolyte solutions, corrections such as dn/dc at a constant chemical potential need to be accounted for to address the assumptions that were originally made for two-component systems. Measuring an accurate dn/dc under a constant chemical potential is essential for light scattering, but the data in the literature are fairly scattered. In this dissertation, we developed four methods using the scaling theory of semidilute unentangled polyelectrolyte solutions to estimate the molecular weight. We measured the correlation length (ξ) using small-angle X-ray scattering, the specific viscosity (ηsp), relaxation time (τ) and terminal modulus (G) using rheometry, and the diffusion coefficient (D) using NMR diffusometry. All these properties can be measured with the usual precision of ±5-10%. Combining these measured properties yields the molecular weight of polyelectrolytes. In this work, five nearly monodisperse cesium polystyrene sulfonate (CsPSS) solutions without salt are studied in water, anhydrous ethylene glycol (EG) and anhydrous glycerol, to test each method. The molecular weights are also confirmed by means of static light scattering and intrinsic viscosity measurements in 0.1 M and 0.5 M NaCl aqueous solutions. We found that combining ηsp and ξ relates to the weight-average degree of polymerization (Nw) as since ηsp exhibits slightly stronger power-law dependence on Nw than what the Rouse model expects ( ). The method combining D and ξ yields the number-average molecular weight (Mn) as . We also found that Ferry’s polydisperse Rouse model is correct: τ relates to NzNz+1 and the terminal modulus relates to Nw/NzNz+1 by using binary blends of narrowly distributed CsPSS/EG solutions. To test the universality of these methods tested on narrowly distributed NaPSS and CsPSS, we further extended our study in chapter 5 to various polyelectrolytes from commercial sources such as cesium poly(2-acrylamido-2-methylpropanesulfonate) (CsPAMS) or polyelectrolytes converted from neutral polymers such as quaternizing poly(4-vinyl pyridine) (P4VP) and hydrolyzing sodium styrene-alt-maleic anhydride (SMA). The three methods that mainly involve correlation length measured by SAXS and η, τ and G measured by rheometry are universal for all polyelectrolytes studied with the same coefficient and power-law exponent on degree of polymerization. The method utilizing diffusion coefficient works great on narrowly distributed solutions, but more work is needed to deconvolute the dispersity effects on the curving Stejskal-Tanner plots of polydisperse polyelectrolytes. The entanglement behavior of polyelectrolyte solutions is studied using 2876 K CsPSS in three different solvents. By utilizing time-temperature superposition, we examined the entanglement dynamics of polyelectrolyte solutions over a wide frequency range for the first time. Comparing the master curves of CsPSS/glycerol to entangled neutral polymer solutions, we found that the entangled polyelectrolyte solutions behave as the entangled neutral polymer solutions. Our data also suggest the scaling theory for the entangled polyelectrolyte solutions underestimates the real entanglement concentration ce. Apparently for CsPSS the crossover to neutral polymers is quite close to the entanglement concentration.