University of Massachusetts Amherst

Polymer Science and Engineering

Muthukumar Research Group

Theory and Modeling of Polymer Crystallization
When polymers are crystallized from solutions or melts, thin lamellae form with thickness orders of magnitude smaller than extended chain dimensions. Molecular origins of the spontaneous selection of finite thickness are being pursued using a combination of Langevin dynamics simulations and exactly solvable statistical mechanics models. Other related issues being investigated are growth kinetics, effect of externally imposed flow fields on the onset of shish-kebab morphology, role of liquid-crystalline phases in polymer crystallization, and the origin of gigantic chirality in crystals of achiral molecules.

 

figure 1 Spontaneous formation of smectic pearls and their coarsening into lamellae, during the primordial stage of crystallization from solutions.
click on the image to see animation
figure 1 Finite thickness is the equilibrium state (PRL cover of Paul).
click on the image to enlarge the figure
figure 1 Formation of 'shish'kebab' morphology.
click on the image to see animation

Recent Publications

  • Simulations of nucleation and elongation of amyloid fibrils , J. N. Zhang and M. Muthukumar, J. Chem. Phys. 130, 035102 (2009).
  • Shifting Paradigms in Polymer Crystallization, M. Muthukumar, Lect. Notes Phys. 714, 1-18 (2007). PDF file (1.2 MB)
  • Monte Carlo simulations of single crystals from polymer solutions, J. N. Zhang and M. Muthukumar, J. Chem. Phys. 126, 234904 (2007).
  • Continuum theory of polymer crystallization, A. Kundagrami and M. Muthukumar, J. Chem. Phys. 126, 144901 (2007).
  • Modeling polymer crystallization, M. Muthukumar, in Interphases and Mesophases in Polymer Crystallization III (2005), Vol. 191, pp. 241.
  • Fluctuation-assisted crystallization: In a simultaneous phase separation and crystallization polyolefin blend system, X. H. Zhang, Z. G. Wang, M. Muthukumar, and C. C. Han, Macromolecular Rapid Communications 26, 1285 (2005).

 

Polyelectrolyte Physics
Solutions of polyelectrolytes are Coulomb soups of charged strings and are ubiquitous in biological and synthetic systems. The coupling among long-ranged correlations, arising from electrostatic interactions and polymer-connectivity, results in many complex phenomena unknown in uncharged polymeric systems. Theoreticl methods, simulations (Monte Carlo and Brownian Dynamics), and experiments (static and dynamic light scattering, SAXS, WAXS, SANS, NMR, conductometry) are used to investigate the following issues.

  • Effective charge of an isolated polyelectrolyte and the nature of counterion distribution
  • Size of labelled chains and correlations of monomer density of polyelectrolytes in solutions
  • Dynamics and conductivity in polyelectrolyte solutions
  • Micellization of diblock polyelectrolytes
  • Phase diagrams
  • Equation of state of polyelectrolyte gels
  • Effects of semiflexibility on the above
  • Adsorption and pattern recognition
Our experimental systems include polystyrene sulfonate, polyhexadiene sulfonates, monodisperse DNA, microtubules, and FtsZ.

figure 1 Counterion distribution around a polyelectrolyte chain.
click on the image to see animation
figure 1 Measured radius of gyration, correlation length, and estimated Debye length in semidilute polyelectrolyte solutions.
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figure 1 Experimental demonstration of the Ising behavior near the coexistence curve in polyelectrolyte solutions.
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figure 1 Role of semiflexibility in phase behavior.
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Recent Publications

  • Counterion Adsorption on Flexible Polyelectrolytes: Comparison of Theories , R. Kumar, A. Kundagrami, and M. Muthukumar , Macromolecules 42, 1370 (2009).

  • Phase behavior of polyelectrolyte solutions with salt , C. L. Lee and M. Muthukumar, J. Chem. Phys. 130, 024904 (2009).
  • Collapse of Linear Polyelectrolyte Chains in a Poor Solvent: When Does a Collapsing Polyelectrolyte Collect its Counterions? , P. Loh, G. R. Deen, D. Vollmer, K. Fischer, M. Schmidt, A. Kundagrami, and M. Muthukumar, Macromolecules 41, 9352 (2008).
  • Theory of competitive counterion adsorption on flexible polyelectrolytes: Divalent salts , A. Kundagrami and M. Muthukumar, J. Chem. Phys. 128, 244901 (2008).
  • Confinement free energy of flexible polyelectrolytes in spherical cavities, R. Kumar and M. Muthukumar, J. Chem. Phys. 128, 184902 (2008).
  • Phase separation kinetics of polyelectrolyte solutions , S. Kanai and M. Muthukumar, J. Chem. Phys. 127, 244908 (2007).
  • Synthesis and characterization of polyolefin-graft-oligopeptide polyelectrolytes, R. B. Breitenkamp, Z. Ou, K. Breitenkamp, M. Muthukumar, and T. Emrick, Macromolecules 40, 7617 (2007).
  • Microphase separation in polyelectrolytic diblock copolymer melt: Weak segregation limit, R. Kumar and M. Muthukumar, J. Chem. Phys. 126, 214902 (2007).
  • Electrostatic origin of the genome packing in viruses, V. A. Belyi and M. Muthukumar, PNAS, 103, 17174 (2006).
  • Effect of deprotection extent on swelling and dissolution regimes of thin polymer films, A. Rao, S. H. Kang, B. D. Vogt, V. M. Prabhu, E. K. Lin, W. L. Wu, and M. Muthukumar, Langmuir 22, 10009 (2006).
  • Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations, Z. Y. Ou and M. Muthukumar, J. Chem. Phys. 124, 154902 (2006).
  • Langevin dynamics of semiflexible polyelectrolytes: Rod-toroid-globule-coil structures and counterion distribution, Z. Y. Ou and M. Muthukumar, J. Chem. Phys. 123, 074905 (2005).

 

DNA Translocation Through Protein Channels and Synthetic Nanopores How DNA/RNA worms through protein channels and nuclear pores is a fundamental process in life. When a polymer is forced to translocate through a narrow path, its configurational entropy is reduced, resulting in a free energy barrier. This free energy barrier is additionally modulated by potential interactions between the polymer and the pore. We use polymer physics ideas (entropic barrier model), polymer theory, Molecular Dynamics, and Brownian Dynamics to understand the molecular mechanisms of DNA/RNA transport in terms of polymer length and sequence specificity. We compute the translocation time and its distribution, and the ionic current by the Poisson-Nernst-Planck methodology (generalized to polyelctrolytes). The specific systems are DNA/RNA through heptameric alpha-hemolysine protein channel embedded in a phospholipid bilayer, DNA/RNA through synthetic nanopores, and mRNP through nuclear pores.

Animated Description of Polymer Translocation:

figure 1 How ssDNA worms through a-hemolysin channel.

(click on the image to see animation)
figure 1 Simultaneous calculation of polymer conformations and ionic current through a-hemolysin channel.

(click on the image to see animation)
figure 1 Fluctuations of PEG tether inside a-hemolysin channel.

(click on the image to see animation)
figure 1 Stochastic sensing of streptavidin by biotinated PEG tether.

(click on the image to see animation)

Recent Publications

  • Scaling theory of polymer translocation into confined regions , C. T. A. Wong and M. Muthukumar, Biophys. J. 95, 3619 (2008).
  • Polymer translocation through a cylindrical channel , C. T. A. Wong and M. Muthukumar, J. Chem. Phys. 128, 154903 (2008).
  • Langevin dynamics simulations of ds-DNA translocation through synthetic nanopores, C. Forrey and M. Muthukumar, J. Chem. Phys. 127, 015102 (2007).
  • "Polymer translocation through a nanopore. II. Excluded volume effect",C.Y. Kong, M. Muthukumar, J. Chem. Phys., 120 (7): 3460-3466 (2004)
  • Mechanism of DNA transport through pores, M. Muthukumar, Annual Review of Biophysics and Biomolecular Structure 36, 435 (2007).
  • Polymer capture by electro-osmotic flow of oppositely charged nanopores, C. T. A. Wong and M. Muthukumar, J. Chem. Phys. 126, 164903 (2007).
  • Threading synthetic polyelectrolytes through protein pores, R. J. Murphy and M. Muthukumar, J. Chem. Phys. 126, 051101 (2007).

  • Langevin dynamics simulations of genome packing in bacteriophage, C. Forrey and M. Muthukumar, Biophys. J. 91, 25 (2006).

  • Simulation of polymer translocation through protein channels, M. Muthukumar and C. Y. Kong, PNAS, 103, 5273 (2006).
  • Simulations of Stochastic sensing of proteins, C. Y. Kong and M. Muthukumar, JACS, 127, 18252 (2005).

 

http://www.pse.umass.edu