Douglas Adolf

Calculation of Stresses in Crosslinking Polymers

A general constitutive model is presented for calculating the evolution of stresses in crosslinking polymers. The analysis is valid for thermo- and chemorheologically simple polymers and for time-dependent strain histories where the total strain at any time is not large, such that linear viscoelasticity applies. We identify the material parameters required and outline experimental and theoretical methods for their determination. This formalism is then used to calculate the development of cure stresses for an epoxy wherein the glass transition temperature exceeds the cure temperature during the reaction. Finally, we discuss practical methods of stress minimization through control of the cure cycle.

Stresses during thermoset cure

Production problems attributed to excessive stresses generated during the cure of epoxies led us to develop a formalism to predict these stresses. In our first studies, we developed a fundamental understanding of the complex evolution of viscoelasticity as the cure progresses. We then incorporated these results into a proper tensorial constitutive equation that was integrated into our finite element codes and validated using more complicated geometries, thermal histories, and strain profiles. The formalism was then applied to the original production problem to determine cure schedules that would minimize stress generation during cure. During the pursuit of these activities, several interesting and puzzling phenomena were discovered that have stimulated further investigation. {copyright} {ital 1998 Materials Research Society.}

Verification of the capability for quantitative stress prediction during epoxy cure

We previously developed a formalism to calculate the evolution of stresses during the cure of crosslinking polymers. In the present study, we characterized the chemical kinetics and cure-dependent thermophysical properties for two epoxy systems, the diglycidyl ether of bisphenol A cured by either diethanolamine or a mixture of aromatic amines. Well-defined experiments were performed in which the cure stresses for these two epoxies were measured as a function of time. The stresses predicted by our formalism, using the material parameters obtained for the two systems, agreed well with the measured stresses.

Theory and application of electrically controlled polymeric gels

Presents several applications of ionizable polymeric gels that are capable of undergoing substantial expansions and contractions when subjected to changing pH environments, temperature, electric field or solvent. Conceptual designs for smart, electrically activated devices exploiting this phenomenon are discussed. These devices have the possibility of being manipulated via active computer control as large-displacement actuators for use in adaptive structures. The technology enabling these novel devices is the use of compliant containers for the gels and their solvents, removing the difficulties associated with maintaining a bath for the gels. Though most of these devices are designed using properties discussed in the literature, some presented near the end of this paper make use of conclusions that the authors have drawn from the literature and their own experimental work. Those conclusions about the basic mechanisms of electromechanical gels are discussed in the third part of this paper and a complete set of governing equations describing these mechanisms is presented in the fourth section. This paper concludes with a discussion of some of the ramifications of the above system of equations and a discussion on gel-driven devices and the control of such devices.

Potential energy clock model: Justification and challenging predictions

A recent, nonlinear viscoelastic theory for predicting the thermomechanical response of glassy polymers has been shown to predict behaviors from enthalpy relaxation to temperature-dependent mechanical yield in various modes of deformation quite well. The foundation of this theory rests on a “material clock” that depends on the potential energy of the system. The molecular basis for the clock and the Rational Mechanics framework for the constitutive equation are briefly reviewed. The theory is then used to predict and explain much more complicated behavior of glassy polymers: the change in compressive yield stress during physical aging at different temperatures, the peculiar enthalpic response of glassy polymers previously compressed to different strains, “volumetric implosion” on samples subjected to tensile strains, and the dependence of the shift factor on aging time and applied stress.

General relationships between the mobility of a chain fluid and various computed scalar metrics

We performed molecular dynamics simulations of chain systems to investigate general relationships between the system mobility and computed scalar quantities. Three quantities were found that had a simple one-to-one relationship with mobility: packing fraction, potential energy density, and the value of the static structure factor at the first peak. The chain center-of-mass mobility as a function of these three quantities could be described equally well by either a Vogel-Fulcher type or a power law equation.

Cole–Davidson dynamics of simple chain models

Rotational relaxation functions of the end-to-end vector of short, freely jointed and freely rotating chains were determined from molecular dynamics simulations. The associated response functions were obtained from the one-sided Fourier transform of the relaxation functions. The Cole-Davidson function was used to fit the response functions with extensive use being made of Cole-Cole plots in the fitting procedure. For the systems studied, the Cole-Davidson function provided remarkably accurate fits [as compared to the transform of the Kohlrausch-Williams-Watts (KWW) function]. The only appreciable deviations from the simulation results were in the high frequency limit and were due to ballistic or free rotation effects. The accuracy of the Cole-Davidson function appears to be the result of the transition in the time domain from stretched exponential behavior at intermediate time to single exponential behavior at long time. Such a transition can be explained in terms of a distribution of relaxation times with a well-defined longest relaxation time. Since the Cole-Davidson distribution has a sharp cutoff in relaxation time (while the KWW function does not), it makes sense that the Cole-Davidson would provide a better frequency-domain description of the associated response function than the KWW function does.

Solute mobility and packing fraction: A new look at the Doolittle equation for the polymer glass transition

Molecular dynamics simulations of the diffusion of penetrants in bead-spring polymers were performed along both constant volume and constant pressure paths at several temperatures. By using an effective hard sphere diameter, the packing fractions of these systems were calculated. It was found that all the data for a given polymer type collapsed to a single curve that can be well described using a modification of the Doolittle equation. Data on polymer simulations from the literature was analyzed in this manner and showed similar results. In this work we demonstrate that the packing fraction analysis that is used to describe hard sphere and colloidal systems can also be extended to polymeric systems.

Molecular flexibility effects upon liquid dynamics.

Simulation results for the diffusive behavior of polymer chain/penetrant systems are analyzed. The attractive range and flexibility of simple chain molecules were varied in order to gauge the effect on dynamics. In all cases, the dimensionless diffusion coefficient, D*, is found to be a smooth, single-valued function of the packing fraction, eta. The functions D*(eta) are found to be power laws with exponents that are sensitive to both chain stiffness and particle type. For a specific system type, the D*s for both penetrant and chain-center-of-mass extrapolate to zero at the same packing fraction, eta0. This limiting packing fraction is interpreted to be the location of the glass transition, and (eta0-eta), the distance to the glass transition.

Finite element simulation of the 2D collapse of a polyelectrolyte gel disk

Theoretical models describing the dynamic behavior of the expansion and contraction of polyelectrolyte gels present numerically challenging problems. This paper describes how a method of weighted residuals approach has been used to solve the two-dimensional governing system of equations by finite element analysis. The modulation of the imbibition/expulsion of solvent by a gel disk is studied as an example.