Determining the Characteristics of Ultrathin Polymer Films: A Spectroscopic Ellipsometry Approach.

Ellipsometry is a powerful and convenient technique that is widely used to determine the thickness and optical characteristics of polymer thin films. The determination is accomplished by modeling the measured change in the polarization of an electromagnetic wave upon interacting with the thin film. However, due to the strong statistical correlations between the fit parameters in the model, simultaneous determination of the thickness and the refractive indices of optically anisotropic ultrathin films using ellipsometry remains a challenge. Here, we propose an approach that can be used to obtain reliable values of both the thickness and the optical anisotropy of ultrathin polymer films. The approach was developed by performing spectroscopic ellipsometry measurements on thin films of hydrophobic polystyrene and hydrophilic chitosan of thickness between a few tens to a few hundred nm and whose absolute value of the birefringence differed by approximately an order of magnitude. Careful consideration of the characteristics of the root mean squared error of the fits obtained by modeling the ellipsometry data and the statistical correlations between the fit parameters formed the basis of the proposed approach.

Probing the tightly bound layer in poly(vinyl alcohol) thin films using swelling measurements.

A strongly adsorbed, tightly bound polymer layer can exist at the polymer/substrate interface in polymer thin films and polymer nanocomposites. The characteristics of the tightly bound layer have long been of interest because of its effect on physical properties. However, direct investigations are challenging as the layer is buried deep within the sample. A common approach to access the tightly bound layer is by rinsing or washing away the loosely bound polymer using a good solvent. While this enables direct investigations of the tightly bound layer, it is unclear if the layer remains unperturbed by the preparation process. Therefore, in situ techniques that can probe the tightly bound layer without strongly perturbing it are preferable. In previous work (P. D. Lairenjam, S. K. Sukumaran and D. K. Satapathy, Macromolecules, 2021, 54, 10931-10942), we introduced an approach to estimate the thickness of the tightly bound layer at the chitosan/silicon interface using swelling of nanoscale thin films when exposed to solvent vapour. To determine the general validity of the approach, in this work we investigated the swelling of poly(vinyl alcohol) (PVA) thin films using two independent techniques: spectroscopic ellipsometry and X-ray reflectivity. We found that the swelling kinetics for thin films of initial thickness in the range 18-215 nm could be described by a single time-dependent swelling ratio, c(t), provided we account for a tightly bound layer of thickness 15 nm at the polymer/substrate interface. Consistent with the conclusions from the swelling measurements, electron density profiles determined by modeling X-ray reflectivity data clearly indicated the existence at the polymer/substrate interface of a 15 nm thick layer of a slightly higher density than the rest of the film. The early-time diffusion coefficient of H2O in PVA determined from the temporal evolution of the mass uptake of the solvent vapour was found to decrease by 3-4 orders of magnitude when the film thickness decreased by approximately an order of magnitude.

Efficient on the fly calculation of time correlation functions in computer simulations.

Time correlation functions yield profound information about the dynamics of a physical system and hence are frequently calculated in computer simulations. For systems whose dynamics span a wide range of time, currently used methods require significant computer time and memory. In this paper, we discuss the multiple-tau correlator method for the efficient calculation of accurate time correlation functions on the fly during computer simulations. The multiple-tau correlator is efficacious in terms of computational requirements and can be tuned to the desired level of accuracy. Further, we derive estimates for the error arising from the use of the multiple-tau correlator and extend it for use in the calculation of mean-square particle displacements and dynamic structure factors. The method described here, in hardware implementation, is routinely used in light scattering experiments but has not yet found widespread use in computer simulations.

Significance of cross correlations in the stress relaxation of polymer melts.

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor.

Rheology and microscopic topology of entangled polymeric liquids.

The viscoelastic properties of high molecular weight polymeric liquids are dominated by topological constraints on a molecular scale. In a manner similar to that of entangled ropes, polymer chains can slide past but not through each other. Tube models of polymer dynamics and rheology are based on the idea that entanglements confine a chain to small fluctuations around a primitive path that follows the coarse-grained chain contour. Here we provide a microscopic foundation for these highly successful phenomenological models. We analyze the topological state of polymeric liquids in terms of primitive paths and obtain parameter-free, quantitative predictions for the plateau modulus, which agree with experiment for all major classes of synthetic polymers.