Challenges and opportunities in polymer theory


  • Zhen-Gang Wang

    Corresponding author
    1. Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125
    • Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125
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I wish to start by thanking the editor of this special issue for inviting me to write in the viewpoint section. The invitation is both an honor and an opportunity: it requires me to think beyond the specific tasks in my daily work routine and take a broader, longer term view of our field. This is a valuable exercise that all of us—especially the younger researchers—would benefit from doing from time to time.

In last year's special issue, seven leaders in polymer science presented their views on some of the big questions or intriguing puzzles in our field. I share many of the views expressed by these authors. In particular, I believe that closer interaction between polymer science and biology and the molecular and structural design and engineering of polymers for functional applications will be two of the most important directions for polymer science. These are, in my opinion, also two of the most promising and fertile areas for polymer theory.

The history of polymer science is one of the greatest triumphs of science and engineering and indeed of human intelligence and ingenuity. Today, polymer science is a grand edifice built on solid foundations supported by chemistry and physics. In the area of polymer theory, the introduction of modern many-body theoretical concepts and techniques from statistical mechanics and condensed-matter physics has allowed many polymer physics problems to be formulated and studied with elegance and rigor. The treatment and understanding of excluded-volume effects and correlations in dilute and semidilute solutions and the elucidation and prediction of self-assembly of block copolymers are two obvious examples that come to mind. However, if we survey the current polymer theory literature, the vast majority of the work is concerned with the thermodynamic, structural, and dynamic properties of polymer solutions, melts, and solids (both glassy and crystalline or semicrystalline). I grant that these are some of the most important properties of polymers, and these properties often underlie many functional applications (biological, biomedical, electrical, optical, etc.), but often we stop short of directly confronting the end-functional properties. Although I have no doubt that there remain and will continue to be many important fundamental problems of this nature that are by all means fully deserving of study, there is currently a gap between this level of polymer physics and the functional level associated with the various applications of polymers.

Considerable opportunities exist in the application of polymer physics to biology and biotechnology/bioengineering. Biopolymers have always been part of polymer science. Indeed, much of the motivation for understanding polyelectrolytes initially derived from biomacromolecules such as DNA and proteins. The physics of polyelectrolytes will remain one of the central areas of research for polymer theory in the foreseeable future. There are other problems that are inspired by biopolymers, such as the study of topological knots and links and the inclusion of twist degrees of freedom in polymer models, but with a few notable exceptions, studies of these phenomena have been limited by and large to addressing the underlying polymer physics problems, not the biological problems themselves. I believe the time is ripe for polymer theorists to directly tackle the biological questions involving polymer physics. I will use DNA looping in a lac repressor in Escherichia coli as an example to illustrate the kind of insight that polymer physics can provide for a real biological problem. The lac repressor functions by clamping two operator sites along the double-stranded DNA to form a loop,1 thus impeding the RNA polymerase from reading the gene and producing the enzymes that degrade lactose.2, 3 The level of repression is intimately related to the probability of the loop formation, as demonstrated beautifully in experiments by Müller et al.,4 in which noncoding DNA segments were inserted into the looping region, which showed that the repression was maximum at a separation of 70 base pairs. Here there is obviously a fundamental polymer physics question: what is the free energy of loop formation between two sites separated by a given number of base pairs in a long DNA chain? This is a variant of the Jacobson–Stockmayer factor for the cyclization of a linear polymer. The question can be studied at various levels, the simplest one being that of an elastic rod5 or a wormlike chain6 forming a loop with some fixed angle. More sophisticated models that account for the sequence effects at base levels can and have been constructed.7 However, the biological question is the level of gene repression. Making the connection from the probability of loop formation to the level of gene expression requires knowledge of the biochemistry of this gene regulatory system and a thermodynamic or kinetic model. Two groups, that of Crothers7 and that of Hwa, Kondev, and Phillips,8 have recently bridged the polymer physics question of loop formation to the biological question of gene repression through a relatively simple thermodynamic model and achieved remarkable agreement with experiments. The modeling effort from loop formation to gene expression is relatively straightforward, but this step is essential in answering the biologically relevant question.

Another area that can be a fertile playground for polymer theory is semiconducting polymers or, more generally, organic optoelectrical materials. Semiconducting polymers are an attractive class of materials because they combine the optical and electronic properties of semiconductors with the processing advantages and mechanical properties of polymers. These materials hold enormous promise as the materials for the next generation of optoelectrical devices, such as light-emitting diodes, transistors, molecular switches, photovoltaic cells, chemical and biological sensors, and large-area flexible displays. Research in this area is rapidly expanding. Although the fundamental processes in these applications are quantum-mechanical in nature, the processing conditions, such as the casting-solvent quality, blend composition, and morphology, can significantly affect the optoelectrical properties of the materials through the chain conformation and intra- and interchain contacts.9, 10 For example, by protonating the conjugated ionomer poly[2,5-bis(N-methyl-N-hexyl amino)phenylene vinylene] in the nonpolar solvent o-xylene, Nguyen and Schwartz11 found a large blueshift in the photoluminescence spectrum in a dilute solution. The same system under semidilute conditions, on the other hand, showed a redshift in the photoluminescence spectrum. The photoluminescence blueshift in the dilute solution was attributed to the shortened conjugation length of the polymer upon shrinkage of the chain (due to twisting of the polymer backbone), whereas the redshift in the semidilute solution was caused by polymer–polymer aggregation. Similarly, Nilsson and Inganäs12 made DNA sensors that were based on the conformation change in the luminescent zwitterionic polythiophene derivative induced by complexation with DNA. These results clearly demonstrated strong coupling between the chain conformation and chain–chain interactions on the one hand and the optoelectrical properties on the other. A problem that should be particularly interesting to polymer theory is the effect of the morphology in blends or block copolymers of semiconducting polymers (with other semiconducting or nonconducting polymers). Blending is one of the trademarks of polymer technology for producing composite materials with physical properties that are different from those of the pure components, and it has spawned many theoretical studies in polymer mixture thermodynamics and phase-separation dynamics. The supramolecular organization and interfacial heterojunctions of the polymers are crucial for determining the optoelectrical properties of the semiconducting polymers.13–17 This is especially true for blends of p-type and n-type polymers, for which the creation and dissociation of the electron-hole pairs (excitons) take place at or near the interfaces.10 The key question is how to relate chain packing and orientation at the interfaces, as well as blend morphology, to the optoelectrical properties of the material. A theoretical understanding connecting the conformation and microstructure of the polymers with the quantum dynamics of energy and electron transfer should be a worthwhile endeavor.

Future applications of polymers will increasingly involve specialty polymers for their functional properties. Polymer physics, and particularly polymer theory, will be enriched by embracing this future trend. For a polymer theorist to make meaningful contributions in this respect, two major efforts are required. The first is simply a willingness to commit the time and energy to learn a new subject (or subjects) to truly understand what the issues are. Often this involves a language barrier, especially in the case of biology. However, the matter is merely one of perseverance. The second effort will require that we overcome a psychological barrier: we have a penchant for universal behaviors and scaling laws and do not like to bother with molecular details. However, it is often the molecular details that dictate the specific functional properties. The beauty of Nature (as well as the manmade world) lies in both its unity and diversity; there can also be unity in diversity and vice versa. Furthermore, an in-depth understanding of the specific issues is often necessary before an understanding of universal behaviors emerges. I believe the rewards will be plentiful enough to make the efforts worthwhile.


I thank several theoretical and experimental friends for helpful comments and suggestions. I specially thank Rachel Segalman for suggesting several key references in the area of semiconducting polymers.