Systematic development of coarse-grained polymer models

Abstract

The coupling between polymer models and experiments has improved our understanding of polymer behavior both in terms of rheology and dynamics of single molecules. Developing these polymer models is challenging because of the wide range of time and length scales. Mechanical models of polymers have been used to understand average heological properties as well as the deviation a single polymer molecule has from the average response. This leads to more physically significant constitutive relations, which can be coupled with fluid mechanic simulations to predict and understand the theological response of polymer solutions and melts. These models have also been used in conjunction with single molecule polymer experiments. While these have provided insight into the dynamics of polymers in rheological flows, they have also helped to design single molecule manipulation experiments. Promising research in this area includes DNA separation and stretching devices. A typical atomic bond has a length of 10-10m and vibration time scale of 10-14s. A typical experiment in a microfluidic device has lengths of order 10-5m and times of order 102s. It is not possible to capture these larger length and time scales of interest while capturing exactly the behavior at the smaller length and time scales.

(cont.) This necessitates a process of coarse-graining which sacrifices the details at the small scale which are not necessary while retaining the important features that do affect the response at the larger scales. This thesis focuses on the coarse-graining of polymers into a series of beads connected by springs. The function which gives the retractive force in the spring as a function of the extension is called the spring force law. In many new microfluidic applications the previously used spring force laws produce significant errors in the model. We have systematically analyzed the coarse-graining and development of the spring force law to understand why these force laws fail. In particular, we analyzed the force-extension behavior which quantifies how much the polymer extends under application of an external force. We identified the key dimensionless group that governs the response and found that it is important to understand the different constraints under which the polymer is placed. This understanding led to the development of new spring force laws which are accurate coarse-grained models by construction. We also examined the response in other situations such as weak and strong flows.

(cont.) This further illustrated the disadvantages of the previous force laws which were eliminated by using the new force laws. This thesis will have practical impact because the new spring force laws can easily be implemented in current polymer models. This will improve the accuracy of the models and place the models on firmer theoretical footing. Because the spring force law has been developed independently of other coarse-grained interactions, this thesis will also help in determining the best parameters for other interactions because they will not need to compensate for an error in the spring force law. These new spring force laws will help form the framework of coarse-grained models which can help understand a wide range of situations in which the behavior at a small scale affects the large time and length scale behavior.