Microrheology of Single Polymer Chains Compressed Under Finite Obstacles

             

Principal Investigator

Edith M. Sevick

Research School of Chemistry

Projects

w55 - VPP

One of the most vigorous research topics in modern soft condensed matter over the past decade has
been the imaging and manipulation of individual polymer chains. This has been made possible by advances in microscopy, particularly in fluorescence microscopy, atomic force microscopy (AFM), and optical/magnetic tweezers, and has lead to a number of investigations of single macromolecules, particularly those of biological origin such as DNA and actin. These kinds of experiments have inspired new topics for theoretical and computational study. These include the deformation of chains in strong flows and the collision of field-driven chains with fixed obstacles.
 
           

 

What are the results to date and the future of the work?

Another recent topic is the compression of a surface-tethered polymer by an obstacle that is not much larger than the unperturbed chain. This can be realised experimentally by compressing a chain with an AFM tip, or by the impaction of a membrane-tethered biopolymer by a cellular object.

 

 

 

 

 

While the compression of a chain might seem well-understood, we found that at a critical compression, the end-fixed chain forms a highly-stretched umbilical tether which extends to the edge of the compressing obstacle such that a large portion of the chain can escape from underneath the obstacle. This escape transition is an activated process; i.e. the stretching of the umbilical tether is energetically costly. Thus, the time required for a chain to find its escape route can be long and can be measured by discontinuities in the compressive force profile. We are interested in finding the time required for the chain to escape and the change in the compressive force due to this partial chain escape. More interestingly, we are interested in exploring the dynamics of this end-tethered chain when the obstacle sinusoidally compresses the chain over a range of frequencies. Experimentally, this scenario occurs in (1) tapping mode

             
Appendix A -

             
       

AFM, and (2) the aggregation of sonically-agitated colloidal particles to which polymers are loosely adsorbed. The compressive force profile should reflect the dynamics of the escape process and this might then be used as a rheological measure for surface-bound polymers. We explore this by "doing" the experiment on computer, i.e. we use Langevin simulation to monitor the polymer chain and to measure the compressing force.

The results of the project are not yet published as there is one further set of simulations to perform. However, with the results in hand, we are fairly confident of the results and interpretations. In essence, this project constructed simulated force profiles from various compression patterns. First, we explored quick compression (i.e. fast lowering of the obstacle against the chain) followed by sustained compression in order to explore the dynamics of the escape process. These results fit very well with both model and theory. We have not yet completed the complementary simulations where the compressed chain is suddenly de-compressed. This is necessary to find the time required for the chain to retract. This retraction time should be much shorter than the time required for the chain to escape as retraction is not an activated event. In addition, we have performed many simulations where the polymer is compressed sinusoidally and these results have proven very interesting. By monitoring the maximum height and radial extents of the chain versus the obstacle height, we can very easily determine when the chain has escaped. We note that when the chain escapes, we find a marked reduction in the compressive force. When the compressive force is averaged over many cycles, we unexpectedly found that the average compressive force shows a maximum at an intermediate compression frequency. We understand this to indicate that there is an intermediate frequency for which escape of the chain is less likely to occur. This is a particularly important result for the micro/nano-rheology of surface-bound chains.

The above results have been the topic of several invited seminars/contributed conference papers in Europe/US/Australia and will be submitted for publication after the final set of simulations have been performed.

What computational techniques are used?

In a Langevin simulation, we are interested in time and length scales for which the inertial effects become negligible. Thus the simulation solves for the chain displacement which occurs when the sum of the forces acting along points in the chain contour is set to zero. These forces consist of a deterministic force, a negative drag force related to the drag coefficient and velocity, and random forces due to the surrounding solvent. These random forces are characterised by a Gaussian distribution with zero mean and variance related to the thermal energy.

The simulations are completed in three dimensions and with the N=100 monomers in the chain. The positions of the monomers are monitored in time and the compressive force is simply the force that the monomers impose upon the compressing cylinder.

Publications

P.M. Saville, E.M. Sevick, Collision of a Field-Driven Polymer with a Finite-Sized Obstacle: A Brownian Dynamics Simulation, Macromolecules, 32, 1999, 892-899.

       
- Appendix A