polymers
technical activities 1997

THEORY AND MODELING

Materials science and engineering is on the threshold of a fundamental transformation. Spectacular advances in computer processor power, memory, and computational methodologies now allow researchers to simulate highly complex materials behavior and microstructures. In FY97, the MSEL Theory and Modeling Program's activities continued their focus on the behavior and properties of materials over length scales extending from atoms to bulk materials. For example, MSEL researchers performed molecular dynamics simulations to study relaxation and glass formation in supercooled liquids, employed mesoscopic phase field and reaction-diffusion models of alloys, polymers and liquid crystals to study phase behavior, stability, separation kinetics, and morphological evolution in these materials, designed cellular automata models to investigate solidification in alloys, and developed finite-element software tools to model solder drops in microelectronic interconnects, domain formation in micromagnetic materials, and mechanical properties of composite microstructures.

In FY97 MSEL's Center for Theoretical and Computational Materials Science (CTCMS) facilitated numerous interactions between industry, academia, NIST and other government labs in the development and application of state-of-the-art theoretical and computational science techniques to industrially important materials and materials processing problems. To use more effectively the nation's talents and resources, the CTCMS integrates ongoing research at various institutions by forming temporary multi-disciplinary and multi-institutional research teams as required to attack key materials issues. The CTCMS has three principal activities, all operating interactively: planning, research, and technology transfer. Workshops are held as the first step in defining technical research areas with significant technological impact, identifying team members, and in building and designing the infrastructure for collaborative research. NIST, in its unique position as a "third Party" liaison, is well suited to play a national role in this planning process. The CTCMS provides an infrastructure and support for its members, including an interactive World Wide Web information server, and modern computing and workshop facilities. In FY97, CTCMS researchers within MSEL developed powerful new materials modeling tools and addressed critical technical issues in the areas of microelectronic interconnect design, Green's functions and boundary element methods applied to mechanical properties, microstructure and dynamics of glass formation, standards in micromagnetics modeling, morphological control of polymer-based liquid crystal display materials, and object-oriented finite-element modeling of composite microstructures.

Significant Accomplishments

A path-integral description is deduced and explicitly calculated using fractional calculus methods for the virial coefficient of flexible polymers with objects having complex shape and general interaction (dendrimers, colloid particles, proteins). This theory is potentially important for describing the role of particle shape and polymer-particle interaction on the binding of polymers to filler particles. This contribution also introduces new mathematical methods which should be broadly applicable to condensed matter.

Developed a statistical mechanics based theory that connects the kinetics of glass formation to the underlying thermodynamics. This leads to a formula to replace the Vogel-Fulcher law.

Discovered a new polymer phase transition involving a polymer molecule threading a membrane separating two solutions. The transition is first-order.

Theory and Modeling of Polymer Phase Transitions

E. A. Di Marzio

Objectives

The objectives are: i. Develop a relationship between the kinetic properties and thermodynamic properties of glass forming systems. ii. Discover, classify and understand all the polymer phase transitions. iii. Determine how different phase transitions couple to one another. iv. Use polymer phase transitions as models for self-assembly. v. Investigate the coupled phase transitions as technology opportunities.

Technical Description

The principle of detailed balance is taken to connect thermodynamic properties to the kinetic properties of polymer glasses and compared the results with the classical Vogel-Fulcher law for the temperature dependence of, e.g., the viscosity.

A statistical mechanical analysis of a polymer molecule which is allowed to translocate through a small hole in an otherwise impenetrable partition separating two solutions shows that the molecule undergoes a first-order phase transition. A classification scheme is developed for coupled pairs, triplets, etc. of polymer phase transitions. An attempt is being made to collect, catalogue, and classify the various examples of coupled polymeric phase transitions in order to determine what technology opportunities exist in the area of self-assembly.

External Collaborations

Arthur J-M Yang while at Armstrong World Industries; now at Industrial Science and Technology Network, Inc.

Arnold Mandell, Emory University

Planned Outcomes

  • A model for the temperature dependence of the viscosity of glass forming polymers from a rigorous statistical mechanics basis.
  • A methodology for classifying phase transitions in polymers.

 

Accomplishments

  • Developed a statistical mechanics based theory that connects the kinetics of glass formation to the underlying thermodynamics. This leads to a formula to replace the Vogel-Fulcher law. Derived formulas for the frequency dependence of viscosity and dielectric susceptibility.
  • Discovered a new first-order polymer phase transition. It is that of a polymer molecule threading a membrane separating two solutions. In addition, an important insight was obtained which shows why linear macromolecules display phase transitions in abundance.
  • Investigated the extent to which self-assembly in polymeric systems can be viewed as thermodynamic phase transition phenomena. It is concluded that self-assembly in polymers is essentially nothing more than the equilibrium, kinetic and pattern formation aspects of polymeric phase transitions.

 

Outputs

Publications

E. A. Di Marzio and A. J-M Yang, Configurational Entropy Approach to the Kinetics of Glasses, J. Research NIST, 102, 135 (1997).

E. A. Di Marzio, The Use of Configurational Entropy to Derive the Kinetic Properties of Polymer Glasses, ACS Books, Symposium on Polymer Glasses, San Francisco, April, 1997, in press.

E. A. Di Marzio and A. Mandell, Phase Transition Behavior of a Linear Macromolecule Threading a Membrane, J. Chem. Phys., in press.

Presentations

E. A. Di Marzio, The Glass Transition in Polymers, Chemical Engineering Department, Johns Hopkins, Baltimore, MD, October 1996.

E. A. Di Marzio, Phase Transitions in Polymers: Their use as Models for Self-Assembly, Physics Department, University of Maryland, Baltimore Campus, October 1996.

E. A. Di Marzio, Phase Transitions in Polymers: Their use as Models for Self-Assembly, Polymer Science Department, University of Massachusetts, Amherst, MA, October 1996.

E. A. Di Marzio, The Glass Transition in Polymers, Polymer Science Department, University of Massachusetts, Amherst, MA, October 1996.

E. A. Di Marzio, The Use of Configurational Entropy to Derive the Kinetic Properties of Polymer Glasses, American Chemical Society Meeting, San Francisco, CA, April 1997.

Theory and Modeling of the Properties of Polymer Blends, Films and Solutions

J. F. Douglas

Objectives

The objectives are: i. describe the influence of solvent quality on the morphology of adsorbed and grafted polymer layers, ii. develop theoretical approach for deducing shift of phase boundary for polymer blends under steady shear in the two phase region, iii. introduce novel fractional calculus methods for solving boundary value problems involving rough surfaces such as polymers, iv. investigate influence of blend incompatibility on the tendency for block copolymers to become localized at the interface of phase separated blends and v. calculate swelling of polymers subject to a power law potential to describe chain swelling of block copolymers over a range from weak to strong segregation.

Technical Description

The properties of polymer blends, films and solutions are studied through analytical path-integration and other functional (integral equation, renormalization group, fractional calculus) methods, and analytic calculations for lattice models of polymers in combination with numerical calculations based on polymer lattice models of interacting polymers, numerical simulation of polymer layer deposition processes, and lattice gas simulations of phase separation of fluids with surfactants.

Accomplishments

  • Developed theoretical method for deducing shift of critical temperature of blends in the two-phase region under conditions of steady shear. Provided interpretation to renormalization of critical exponents ($ and <) in diluted polymer blends. Results used to predict the exponent governing the shear shift of the critical temperature.
  • The inhomogeneity of polymers adsorbed and grafted on surfaces is modeled by a generalized random sequential adsorption model in which the adaptability of chain shape to changes in surface accessibility in the deposition process is modeled by taking the size of depositing species to be variable. Properties of polymer layers grown adsorbed under non-equilibrium conditions are shown to be qualitatively different from polymer films at equilibrium and predictions of the model are verified experimentally.
  • Numerical calculations with Bruce Berghosian of Boston University indicate that surfactants such as block copolymers exert a very different influence on phase separation depending on the degree of fluid immiscibility. For weak segregation the surfactant exerts a weak influence on the phase separation kinetics, while the coarsening is arrested in the strong segregation regime where the surfactant becomes localized at the interfaces between the phase separated domains.
  • A path-integral description is deduced and explicitly calculated using fractional calculus methods for the virial coefficient of flexible polymers with objects having complex shape and general interaction (dendrimers, colloid particles, proteins). This theory is potentially important for describing the role of particle shape and polymer-particle interaction on the binding of polymers to filler particles. This contribution also introduces new mathematical methods which should be broadly applicable to condensed matter.
  • Model calculations are applied to the swelling of block copolymers from the disordered to ordered regimes and to the density profile of end-tethered polymer layers with a parabolic potential interaction modeling the interchain interactions in the grafted layer. Renormalization group calculations were performed to describe the influence of chain excluded volume on the density profile of end-grafted brushes.

 

External Collaboration

Modeling of the deposition of polymer layers under non-equilibrium conditions was performed in collaboration with Professor Steve Granick of the University of Illinois and Dr. Hildegard Schneider of 3M Corporation.

Outputs

Publications

J. Yu, J. Douglas, E. Hobbie and C. Han, Homogenization of Polymer Blends Under Shear, Phys. Rev. Ltrs., 78, 2664 (1997).

J.F. Douglas, Some Applications of Fractional Calculus to Polymer Science, Advances in Chemical Physics, in press.

J.F. Douglas, H. Schneider, P. Frantz, R. Lipman and S. Granick, Origin and Characterization of Conformational Heterogeneity in Adsorbed Polymer Layers, Journal of Physics: Condensed Matter, 9, 7699 (1997).

M. Trache, W. McMullen and J.F. Douglas, Segmental Concentration Profiles of End-Tethered Polymers with Excluded Volume and Surface Interactions, J. Chem. Phys., 105, 4798 (1996).

J.F. Douglas and K.F. Freed, Modification of Continuum Chain Model of Surface-Interacting Polymers to Describe the Crossover between Weak and Strong Polymer Adsorption,

Macromolecules, 30, 1813 (1997).

C. Donati, J.F. Douglas, W. Kob, S.J. Plimpton, P.H. Poole and S.C. Glotzer, String-Like Clusters in a Supercooled Liquid, Phys. Rev. Ltrs, submitted.

J.F. Douglas, C.M. Guttman, A. Mah and T. Ishinabe, Spectrum of Self-Avoiding Walk Exponents, Physical Review E, 55, 738 (1997).

J.A. Given, J.B. Hubbard and J.F. Douglas, A First-Passage Time Algorithm for the Hydrodynamic Friction and Diffusion-Limited Reaction Rate of Macromolecules, J. Chem. Phys., 106, 3761 (1997).

Presentations

Jack Douglas and Mark Mansfield, Treatment of Fluctuation Effects in Mean-Field Models of Chain Stretching, American Physical Society March Meeting, Kansas City, MO, March 1997.

Jack Douglas, Coping with Complex Boundaries, American Mathematical Society, April 1997.

Jack Douglas, Transport Properties of Complex-Shaped Particles and Polymers, Chemistry Department, New York University, New York, NY, August 1997.

J.F. Douglas, R. Lipman, A. Karim and S. Granick, Models of the Influence of Excluded Volume on the Formation of Polymer Layers, American Chemical Society, Las Vegas, NV, September 1997.

J.F. Douglas, A Model of the Viscoelasticity and Mass Transport in Glass Forming Liquids, Third International Discussion Meeting on Relaxations in Complex Systems, Vigo, Spain , July 1997.