Counterion and Polyelectrolyte Dynamics as viewed by Neutron Spin
Echo Spectroscopy
Polyelectrolytes differ in chain
dynamics and equilibrium structure from neutral polymers due to the
presence of long-ranged electrostatic interactions. This manifests
as strong interactions in solutions for both synthetic and biopolymers
as observed by aggregation and multimode relaxations. Describing these
relaxations requires new experimental methods to test current theories
and simulations.
Control of polymer dynamics with
designed self assembly, externally supplied fields (e.g., electric,
flow, or magnetic), or patterned substrates requires overcoming Brownian
motion as well as inter and intra molecular structural correlations.
Current examples include small molecule and polymer associations for
drug design and biological processes and the docking of polyamides
to the minor groove of DNA or motor protein motion along microtubules.
These examples rely on intermolecular forces including hydrogen bonding
and electrostatics which are balanced by an entropic loss. For biopolymers
such as DNA and proteins, the association between counterions and
chain is electrostatic in origin. In order to design new technologies
with charged polymers the fundamental time scales and length scales
of polymer and counterion association need to be quantified.
Charged polymers present a challenge
due to the long-range electrostatic interactions and coupled dynamics
between small, fast-moving counterions and polymers. The observed
multimode dynamics and large scale structure in these systems are
influenced by ionic strength, viscosity, and charge valence, but the
molecular origin of the dynamics remains to be experimentally ascertained
due to the limited number of techniques able to measure the solution
behavior at the nanoscale. We have used small angle neutron scattering
(SANS) to characterize the equilibrium structure and the pico to nanosecond
dynamics by neutron spin echo (NSE) spectroscopy. In particular, NSE
provides structural information between 60 nm and 3 nm and time scales
between 45 ps and 100 ns.
We have measured the statics and
dynamics of labeled counterions and polyelectrolytes through the partial
structure factors for a model system composed of poly(styrene sulfonate)
(PSS) and counterions including sodium, magnesium, and tetramethylammonium
(TMA+). An example of the dynamic structure factor for NaPSS in D2O
taken for several values of the scattering wave vector (Q) is shown
in Fig. 1.
Figure 1. Normalized intermediate
scattering function for NaPSS in D2O at 46gL-1.
The labeled counterion dynamics
were measured for a TMA+ PSS system and exhibit a Q dependent diffusion
coefficient, shown in Fig. 2. A diffusive slowing down near the static
correlation peak is observed signifying the coupled internal polymer
relaxations and counterions on the nanoscale.
Figure 2. Inverse effective diffusion
coefficient from NSE and scattered intensity from SANS versus Q for
TMA-PSS in D2O at 46gL-1.