Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T _g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T _g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T _g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation. Received 21 March 2000 and Received in final form 4 December 2000     

The phase behaviour of single polyethylene chains with and without fixing one end

The phase behaviour of a single polyethylene chain is studied by using molecular dynamics simulations. A free chain and a chain with fixing one end are considered here, since the atomic force microscope （AFM） tip can play a significant role in polymer crystallization in experiment. For a free chain, it is confirmed in our calculation that the polymer chain exhibits an extended coil state at high temperatures, collapses into a condensed state at low temperatures, i.e. the coil-to-globule transition that is determined by a high temperature shoulder of the heat capacity curve, and an additional liquid-to-solid transition that is described by a low temperature peak of the same heat curve. These results accord with previous studies of square-well chains and Lennard-Jones homopolymers. However, when one of the end monomers of the same chain is fixed the results become very different, and the chain cannot reach an extended coil-like state as a free chain does at high temperatures, i.e. there exists no coil-to-globule-like transition. These results may provide some insights into the influence of AFM tip when it is used to study the phase behaviour of polymer chains. If the interaction force between AFM tip and polymer monomers is strong, some monomers or one of them can be seen as being fixed by the tip, which is similar to our simulation model, and it is also found that AFM tip could induce polymer crystallization.     

Polymer thin films and surfaces: Possible effects of capillary waves

It is discussed how the proximity of a free surface or mobile interface may affect the strain relaxation behavior in a viscoelastic material, such as a polymer melt. The eigenmodes of a viscoelastic film are thus derived, and applied in an attempt to explain the experimentally observed substantial shift of the glass transition temperature of sufficiently thin polymer films with respect to the bulk. Based on the idea that the polymer freezes due to memory effects in the material, and exploiting results from mode-coupling theory, the experimental findings of several independent groups can be accounted for quantitatively, with the elastic modulus at the glass transition temperature as the only fitting parameter. The model is finally applied discussing the possibility of polymer surface melting. A surface molten layer is predicted to exist, with a thickness diverging as the inverse of the reduced temperature. A simple model of thin polymer film freezing emerges which accounts for all features observed experimentally so far. Received 8 August 2001     

Investigation into defects occurring on the polymer surface during the photolithography process

With a view to improving the realisation of polymer optical waveguide some features relevant to the photolithography process are analysed. This paper focuses on defects that occur on the surface of polymer layers involved in the process. For example, depending on the heat treatment or the deposited material, some worm-like defects appear on the polymer surface. When they occur, the waveguide surface roughness becomes too high (about one hundred nm and more). This means that the optical performance of the waveguides is too poor. In this document, we show the changes in temperature on polymer film surfaces which are coated with a thin inorganic layer and the occurrence of these defects is observed. This work confirms that the defect occurrence is clearly linked to the glass transition temperature. The paper reports that, in some cases, the adjustment of thermal properties by annealing can advantageously shift the glass transition, without changing the target optical properties.     

Is the dynamics of polystyrene films consistent with their glass transition temperature?

Experiments in the past 1.5 decades have found that the glass transition temperature of polymer films can be noticeably different from the bulk when the film thickness is decreased below ∼100  nm. On the other hand, many dynamic measurements have found results inconsistent with the observed change in the glass transition temperature. One frequently cited reason is that the dynamic properties being probed may not be directly related to the glass transition. Viscosity is a property traditionally used to characterize the dynamic slowing down occurring to a material at the glass transition. In this paper, we report experimental result showing that the viscosity of polystyrene films supported by oxide-coated silicon decreases with decreasing film thickness, consistent with the observed glass transition temperature of the films.     

Mechanical properties of thin confined polymer films close to the glass transition in the linear regime of deformation: Theory and simulations

Over the past twenty years experiments performed on thin polymer films deposited on substrates have shown that the glass transition temperature T(g) can either decrease or increase depending on the strength of the interactions. Over the same period, experiments have also demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous, on the scale of a few nanometers. A model for the dynamics of non-polar polymers, based on percolation of slow subunits, has been proposed and developed over the past ten years. It proposes a unified mechanism regarding these two features. By extending this model, we have developed a 3D model, solved by numerical simulations, in order to describe and calculate the mechanical properties of polymers close to the glass transition in the linear regime of deformation, with a spatial resolution corresponding to the subunit size. We focus on the case of polymers confined between two substrates with non-negligible interactions between the polymer and the substrates, a situation which may be compared to filled elastomers. We calculate the evolution of the elastic modulus as a function of temperature, for different film thicknesses and polymer-substrate interactions. In particular, this allows to calculate the corresponding increase of glass transition temperature, up to 20 K in the considered situations. Moreover, between the bulk T(g) and T(g) + 50 K the modulus of the confined layers is found to decrease very slowly in some cases, with moduli more than ten times larger than that of the pure matrix at temperatures up to T(g) + 50 K. This is consistent with what is observed in reinforced elastomers. This slow decrease of the modulus is accompanied by huge fluctuations of the stress at the scale of a few tens of nanometers that may even be negative as compared to the solicitation, in a way that may be analogous to mechanical heterogeneities observed recently in molecular dynamics simulations. As a consequence, confinement may result not only in an increase of the glass transition temperature, but in a huge broadening of the glass transition.     

Viscosity,glass transition and activation energy of solid cis-polyisoprene and trans-polyisoprene blends

Blends of cis-polyisoprene (CPI) and trans-polyisoprene (TPI) have been prepared by solution casting to study viscosity, glass transition temperature and activation energy for the glass transition. The viscosity of blends having different weight ratios has been obtained through a single experiment measuring storage and loss modulus using the dynamic mechanical analyser technique. The glass transition temperature is determined through the temperature at which the minimum of temperature derivative curve of viscosity falls. The activation energy of glass transition and fragility index have been obtained by employing the Vogel–Fulchar–Tammann (VFT) equation by assuming non-Arrhenius behaviour of viscosity of polymer blends. Results indicate that both glass transition and activation energy for the glass transition are influenced by composition and crosslink density of the blend.     

Viscoelastic dynamics of polymer thin films and surfaces

The strain relaxation behavior in a viscoelastic material, such as a polymer melt, may be strongly affected by the proximity of a free surface or mobile interface. In this paper, the viscoelastic surface modes of the material are discussed with respect to their possible influence on the freezing temperature and dewetting morphology of thin polymer films. In particular, the mode spectrum is connected with mode coupling theory assuming memory effects in the melt. Based on the idea that the polymer freezes due to these memory effects, surface melting is predicted. As a consequence, the substantial shift of the glass transition temperature of thin polymer films with respect to the bulk is naturally explanied. The experimental findings of several independent groups can be accounted for quantitatively, with the elastic modulus at the glass transition temperature as the only fitting parameter. Finally, a simple model is put forward which accounts for the occurrence of certain generic dewetting morphologies in thin liquid polymer films. It demonstrates that by taking into account the viscoelastic properties of the film, a morphological phase diagram may be derived which describes the observed structures of dewetting fronts. It is demonstrated that dewetting morphologies may also serve to determine nanoscale rheological properties of liquids.Received: 1 January 2003, Published online: 14 October 2003PACS: 47.50. + d Non-Newtonian fluid flows - 68.47.Mn Polymer surfaces - 68.60.Dv Thermal stability; thermal effects     

The kinetics of the structural relaxation process in PHEMA-silica nanocomposites based on an equation for the configurational entropy

The enthalpy relaxation of polymer-silica nanocomposites prepared by simultaneous polymerization of poly(2-hydroxyethyl methacrylate) (PHEMA) and tetraethyloxysilane, TEOS, a silica precursor, is investigated. Both the glass transition temperature, T_g, and the temperature interval of the glass transition, ΔT _g , increase as the silica content in the sample does. Structural relaxation experiments show that the temperature interval in which conformational motions take place broadens as the silica content in the hybrid increases. A phenomenological model based on the evolution of the configurational entropy during the structural relaxation process, the SC model, has been used for determining the temperature dependence of the relaxation times during the process. The results show an increase of the fragility of the polymer as the silica content increases, a feature that can be related to the broadening of the distribution of relaxation times characterized by the β parameter of the stretched exponential distribution. On another hand the silica content increase produces a significant change of the relaxation times in the glassy state.     

Evidence of glass transition in thin films of maleic anhydride derivatives: Effect of the surfactant coadsorption

The glass transition temperature of poly (maleic anhydride-alt-1-octadecen) and poly (styreneco-maleic anhydride) cumene-terminated thin films has been measured by mechanical relaxation of Langmuir films of these polymers. The dynamical properties show glass-like features (non-Arrhenius relaxation times and non-Debye mechanical response) interpreted by the coupling model. The glass transition temperature values determined by a mechanical relaxation experiment (step-compression) agree very well with those obtained by surface potential measurements. It is found that the glass transition temperature values in thin films decrease by about 100K as compared with those corresponding to the bulk polymers. The coadsorption of the water-insoluble surfactant DODAB decreases the glass transition temperature.     

Molecular simulation study of the glass transition in a soft primitive model for ionic liquids

In this paper, we present a molecular dynamics study of the glass transition for a soft-core primitive model for ionic liquids, in which cations are fully flexible chains of tangent soft spherical monomers, being the positively charged monomer at one of the ends of the chain, and anions as charged soft spheres. We have monitored transport coefficients such as the self-diffusion coefficients and the shear viscosity, as well as correlation functions such as the mean-square displacement, the self-intermediate scattering function, and probes of heterogeneous dynamics such as the van Hove distribution function and the four-points susceptibility. The analysis of these properties indicates that, for a given pressure, the glass transition shows a weak temperature dependence on the cation length, occurring first for short-chain than for long-chain ionic liquids.     

Lactone polymers. V. Viscoelastic properties of poly-ε-caprolactone and poly-ε-thiocaprolactone

The viscoelastic properties of crystalline poly-ε-caprolactone and poly-ε-thiocaprolactone have been characterized and compared by stress relaxation and dynamic mechanical studies. The glass transition temperature of poly-ε-thiocaprolactone was shown to be -40°C at 1 Hz and appeared to be independent of the degree of crystallinity. The rate of viscoelastic relaxation for each polymer was independent of linear strain rate of a decade range. The density of each polymer over a wide temperature range was used to reduce the individual time-dependent modulus values to an arbitrary reference temperature. This reduction of stress relaxation data to a standard mechanical state obviated the requirement of vertical shift factors for construction of the respective master curves. The distribution of relaxation times was correlated with the glass transition and the crystalline melt temperature range for each polymer.     

Two simultaneous mechanisms causing glass transition temperature reductions in high molecular weight freestanding polymer films as measured by transmission ellipsometry

We study the glass transition in confined polymer films and present the first experimental evidence indicating that two separate mechanisms can act simultaneously on the film to propagate enhanced mobility from the free surface into the material. Using transmission ellipsometry, we have measured the thermal expansion of ultrathin, high molecular-weight (MW), freestanding polystyrene films over an extended temperature range. For two different MWs, we observed two distinct reduced glass transition temperatures (T(g)'s), separated by up to 60 K, within single films with thicknesses h less than 70 nm. The lower transition follows the expected MW dependent, linear T(g)(h) behavior previously seen in high MW freestanding films. We also observe a much stronger upper transition with no MW dependence that exhibits the same T(g)(h) dependence as supported and low MW freestanding polymer films.     

Some relevant parameters affecting the glass transition of supported ultra-thin polymer films

We have measured, the thickness dependence of the glass transition temperature T(g)( h), using ellipsometry at variable temperature, for poly(methyl-methacrylate) (PMMA) of various tacticity in confined geometry. We report that several factors significantly affect T(g)( h): i) polymer microstructure (stereoregularity of PMMA) related to local dynamics; ii) interfacial interactions; iii) conformation of the polymer chains. These results raise many fundamental questions on the origin of the thickness-dependent glass transition. Why and how do the interactions with the substrate significantly affect T(g)( h)? Does T(g)( h) depend on the modifications of conformational parameters of the chains (their entropy)? What is the correlation between local dynamics and T(g)( h) in thin films? The aim of this paper is to summarise these open questions, which should stimulate further investigations in the thin polymer film scientific community.     

Pressure, temperature, and thickness dependence of CO2-induced devitrification of polymer films

The glass transition temperature is known to increase with decreasing film thickness h for sufficiently thin poly(methyl methacrylate) films supported by silicon oxide substrates. We show that this system undergoes a CO2 pressure-induced devitrification transition, P(g), which is film thickness dependent, P(g)(h)=DeltaP(g)+P(bulk)(g). P(bulk)(g) is the bulk glass transition and DeltaP(g) can be positive or negative depending on T and P. The phenomenon of retrograde vitrification, wherein the polymer exhibits a rubbery-to-glassy-to-rubbery transition upon changing temperature isobarically, is also shown to occur in this system and it is film thickness dependent.     

The glass transition of thin polymer films: some questions, and a possible answer

A simple and predictive model is put forward explaining the experimentally observed substantial shift of the glass transition temperature, T_g, of sufficiently thin polymer films. It focuses on the limit of small molecular weight, where geometrical `finite size' effects on the chain conformation can be ruled out. The model is based on the idea that the polymer freezes due to memory effects in the viscoelastic eigenmodes of the film, which are affected by the proximity of the boundaries. The elastic modulus of the polymer at the glass transition turns out to be the only fitting parameter. Quantitative agreement is obtained with our experimental results on short chain polystyrene (M_W = 2 kg/mol), as well as with earlier results obtained with larger molecules. Furthermore, the model naturally accounts for the weak dependence of the shift of T_g upon the molecular weight. It explains why supported films must be thinner than free standing ones to yield the same shift, and why the latter depends upon the chemical properties of the substrate. Generalizations for arbitrary experimental geometries are straightforward.     

Phase diagram of magnetic polymers

We consider polymers made of magnetic monomers (Ising or Heisenberg-like) in a good solvent. These polymers are modeled as self-avoiding walks on a cubic lattice, and the ferromagnetic interaction between the spins carried by the monomers is short-ranged in space. At low temperature, these polymers undergo a magnetic induced first order collapse transition, that we study at the mean field level. Contrasting with an ordinary point, there is a strong jump in the polymer density, as well as in its magnetization. In the presence of a magnetic field, the collapse temperature increases, while the discontinuities decrease. Beyond a multicritical point, the transition becomes second order and -like. Monte Carlo simulations for the Ising case are in qualitative agreement with these results. Received 11 February 1999     

Freedericksz transition in polymer-stabilized nematic liquid crystals

We have constructed polymer-stabilized nematic liquid crystals by photopolymerizing diacrylate monomers in the nematic phase. The orientation of the liquid crystal was controlled by the polymer network. We studied the Freedericksz transition in these systems. Experimentally we studied the transition by measuring the capacitance of the liquid crystal cells as a function of applied voltage. The transition was affected profoundly by the dispersed polymer network. The threshold was higher with shorter interpolymer network distance. Theoretically we studied the systems using a two-dimensional model in which the polymer networks were represented by parallel cylinders with random location. The interaction between the liquid crystal and the polymer network was described by the boundary condition imposed by the polymer network. By fitting the experimental data, we found that the polymer cylinders had diameters of a few submicrons, and a substantial amount of liquid crystal was trapped inside the cylinders.     

Fast magic-angle spinning proton NMR studies of polymers at surfaces and interfaces

Solid-state proton NMR with fast magic-angle sample spinning has been used to study the structure and dynamics of polymers and the water interface in porous glass composites. The composites were prepared by photopolymerization of poly(ethyl acrylate) and other acrylate formulations in a high surface-area rigid glass matrix with 40-A interconnected pores. High resolution solid-state proton spectra were obtained for polymer films and composites with 15 kHz magic-angle sample spinning at temperatures above the polymer glass transition temperature. The solid-state proton spectra can be detected with high sensitivity and used to determine the composition of polymer and water filling the pores. These results and spin diffusion studies using 1H-29Si 2D heteronuclear correlation and wideline separation NMR show that the polymer fills the central 30 A of the pore, and that the remaining volume is filled with surface hydroxyl groups and water.     

Temperature dependence of the slip length in polymer melts at attractive surfaces

Using Couette and Poiseuille flows, we extract the temperature dependence of the slip length, delta, from molecular dynamics simulations of a coarse-grained polymer model in contact with an attractive surface. delta is dictated by the ratio of bulk viscosity and surface mobility. At weakly attractive surfaces, lubrication layers form; delta is large and increases upon cooling. Close to the glass transition temperature Tg, very large slip lengths are observed. At a more attractive surface, a sticky surface layer is built up, giving rise to small slip lengths. Upon cooling, delta decreases at high temperatures, passes through a minimum, and grows for T-->Tg. At strongly attractive surfaces, the Navier-slip condition fails to describe Couette and Poiseuille flows simultaneously. The simulations are corroborated by a schematic, two-layer model suggesting that the observations do not depend on details of the computational model.