Relaxation spectra of polymers and phenomena of electrical and hydrophobic recovery: Interplay between bulk and surface properties of polymers

On Applicability of the Relaxation Spectrum of Fractional Maxwell Model to Description of Unimodal Relaxation Spectra of Polymers

The relaxation time and frequency spectra are vital for constitutive models and for insight into the viscoelastic properties of polymers, since, from the spectra, other material functions used to describe rheological properties of various polymers can be uniquely determined. In recent decades the non-integer order differential equations have attracted interest in the description of time-dependent processes concerning relaxation phenomena. The fractional Maxwell model (FMM) is probably the most known rheological model of non-integer order. However, the FMM spectrum has not yet been studied and used to describe rheological materials. Therefore, the goal of the present paper was to study the applicability of the relaxation spectrum of FMM to the description of the relaxation spectra of polymers. Based on the known integral representation of the Mittag-Leffler two-parameter function, analytical formulas describing relaxation time and frequency spectra of FMM model were derived. Monotonicity of the spectra was analyzed and asymptotic properties were established. Relaxation frequency spectrum grows for large frequencies with a positive power law, while the relaxation time spectrum decays for large times with a negative power of time. Necessary and sufficient conditions for the existence of the local extrema of the relaxation spectra were derived in the form of two trigonometric inequalities. A simple procedure for checking the existence or absence of the spectra extrema was developed. Direct analytical formulas for the local extrema, minima, and maxima are given in terms of model fractional and viscoelastic parameters. The fractional model parameters, non-integer orders of the stress and strain derivatives of FMM uniquely determine the existence of the spectrum extrema. However, the viscoelastic parameters of the FMM, elastic modulus, and relaxation time affect the maxima and minima of the relaxation spectra and the values of their local peaks. The influence of model parameters on their local extrema was examined. Next, the applicability of the continuous-discrete spectrum of FMM to describe Baumgaertel, Schausberger and Winter (BSW) and unimodal Gauss-like relaxation spectra, commonly used to describe rheological properties of various polymers, was examined. Numerical experiments have shown that by respective choice of the FMM parameters, in particular by respective choice of the orders of fractional derivatives of the stress and strain, a good fit for the relaxation modulus experiment data was obtained for polymers characterized both by BSW and Gauss-like relaxation spectra. As a result, a good approximation of the real spectra was reached. Thus, the viscoelastic relaxation spectrum of FMM, due to the availability of the two extra degrees of freedom (non-integer orders of the stress and strain derivatives), provides deep insights into the complex behavior of polymers and can be applied for a wide class of polymers with unimodal relaxation spectra.

On Recovery of a Non-Negative Relaxation Spectrum Model from the Stress Relaxation Test Data

The relaxation spectra, from which other material functions used to describe mechanical properties of materials can be uniquely determined, are important for modeling the rheological properties of polymers used in chemistry, food technology, medicine, cosmetics, and many other industries. The spectrum, being not directly accessible by measurement, is recovered from relaxation stress or oscillatory shear data. Only a few models and identification methods take into account the non-negativity of the real spectra. In this paper, the problem of recovery of non-negative definite relaxation spectra from discrete-time noise-corrupted measurements of relaxation modulus obtained in the stress relaxation test is considered. A new hierarchical identification scheme is developed, being applicable both for relaxation time and frequency spectra. Finite-dimensional parametric classes of models are assumed for the relaxation spectra, described by a finite series of power-exponential and square-exponential basis functions. The related models of relaxation modulus are given by compact analytical formula, described by the products of power of time and the modified Bessel functions of the second kind for the time spectrum, and by recurrence formulas based on products of power of time and complementary error functions for frequency spectrum. The basis functions are non-negative. In result, the identification task was reduced to a finite-dimensional linear-quadratic problem with non-negative unknown model parameters. To stabilize the solution, an additional smoothing constraint is introduced. Dual approach was used to solve the stated optimal identification task resulting in the hierarchical two-stage identification scheme. In the first stage, dual problem is solved in two levels and the vector of non-negative model parameters is computed to provide the best fit of the relaxation modulus to experiment data. Next, in second stage, the optimal non-negative spectrum model is determined. A complete scheme of the hierarchical computations is outlined; it can be easily implemented in available computing environments. The model smoothness is analytically studied, and the applicability ranges are numerically examined. The numerical studies have proved that using developed models and algorithm, it is possible to determine non-negative definite unimodal and bimodal relaxation spectra for a wide class of polymers. However, the examples also demonstrated that if the basis functions are non-negative and the model is properly selected for a given type of the real spectrum (unimodal, multimodal), the optimal model determined without non-negativity constraint can be non-negative in the dominant range of its arguments, especially in the wide neighborhood of the spectrum peaks.

Two-Level Scheme for Identification of the Relaxation Time Spectrum Using Stress Relaxation Test Data with the Optimal Choice of the Time-Scale Factor

The viscoelastic relaxation spectrum is vital for constitutive models and for insight into the mechanical properties of materials, since, from the relaxation spectrum, other material functions used to describe rheological properties can be uniquely determined. The spectrum is not directly accessible via measurement and must be recovered from relaxation stress or oscillatory shear data. This paper deals with the problem of the recovery of the relaxation time spectrum of linear viscoelastic material from discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation test. A two-level identification scheme is proposed. In the lower level, the regularized least-square identification combined with generalized cross-validation is used to find the optimal model with an arbitrary time-scale factor. Next, in the upper level, the optimal time-scale factor is determined to provide the best fit of the relaxation modulus to experiment data. The relaxation time spectrum is approximated by a finite series of power-exponential basis functions. The related model of the relaxation modulus is proved to be given by compact analytical formulas as the products of power of time and the modified Bessel functions of the second kind. The proposed approach merges the technique of an expansion of a function into a series of independent basis functions with the least-squares regularized identification and the optimal choice of the time-scale factor. Optimality conditions, approximation error, convergence, noise robustness and model smoothness are studied analytically. Applicability ranges are numerically examined. These studies have proved that using a developed model and algorithm, it is possible to determine the relaxation spectrum model for a wide class of viscoelastic materials. The model is smoothed and noise robust; small model errors are obtained for the optimal time-scale factors. The complete scheme of the hierarchical computations is outlined, which can be easily implemented in available computing environments.

A Class of Algorithms for Recovery of Continuous Relaxation Spectrum from Stress Relaxation Test Data Using Orthonormal Functions

The viscoelastic relaxation spectrum provides deep insights into the complex behavior of polymers. The spectrum is not directly measurable and must be recovered from oscillatory shear or relaxation stress data. The paper deals with the problem of recovery of the relaxation spectrum of linear viscoelastic materials from discrete-time noise-corrupted measurements of relaxation modulus obtained in the stress relaxation test. A class of robust algorithms of approximation of the continuous spectrum of relaxation frequencies by finite series of orthonormal functions is proposed. A quadratic identification index, which refers to the measured relaxation modulus, is adopted. Since the problem of relaxation spectrum identification is an ill-posed inverse problem, Tikhonov regularization combined with generalized cross-validation is used to guarantee the stability of the scheme. It is proved that the accuracy of the spectrum approximation depends both on measurement noises and the regularization parameter and on the proper selection of the basis functions. The series expansions using the Laguerre, Legendre, Hermite and Chebyshev functions were studied in this paper as examples. The numerical realization of the scheme by the singular value decomposition technique is discussed and the resulting computer algorithm is outlined. Numerical calculations on model data and relaxation spectrum of polydisperse polymer are presented. Analytical analysis and numerical studies proved that by choosing an appropriate model through selection of orthonormal basis functions from the proposed class of models and using a developed algorithm of least-square regularized identification, it is possible to determine the relaxation spectrum model for a wide class of viscoelastic materials. The model is smoothed and robust on measurement noises; small model approximation errors are obtained. The identification scheme can be easily implemented in available computing environments.

Investigation of the Impact of Cold Plasma Treatment on the Chemical Composition and Wettability of Medical Grade Polyvinylchloride

The impact of the Corona, dielectric barrier discharge, and low pressure radiofrequency air plasmas on the chemical composition and wettability of medical grade polyvinylchloride was investigated. Corona plasma treatment exerted the most pronounced increase in the hydrophilization of polyvinylchloride. The specific energy of adhesion of the pristine and plasma-treated Polyvinylchloride (PVC) tubing is reported. Plasma treatment increased markedly the specific free surface energy of PVC. The kinetics of hydrophobic recovery following plasma treatment was explored. The time evolution of the apparent contact angle under the hydrophobic recovery is satisfactorily described by the exponential fitting. Energy-dispersive X-ray spectroscopy of the chemical composition of the near-surface layers of the plasma-treated catheters revealed their oxidation. The effect of the hydrophobic recovery hardly correlated with oxidation of the polymer surface, which is irreversible and it is reasonably attributed to the bulk mobility of polymer chains.

Plasma treatment switches the regime of wetting and floating of pepper seeds

Cold radiofrequency plasma treatment modified wetting and floating regimes of pepper seeds. The wetting regime of plasma-treated seeds was switched from the Wenzel-like partial wetting to the complete wetting. No hydrophobic recovery following the plasma treatment was registered. Environmental scanning electron microscopy of the fine structure of the (three-phase) triple line observed with virgin and plasma-treated seeds is reported. Plasma treatment promoted rapid sinking of pepper seeds placed on the water/air interface. Plasma treatment did not influence the surface topography of pepper seeds, while charged them electrically. Electrostatic repulsion of floating plasma-treated seeds was observed. The surface charge density was estimated from the data extracted from floating of charged seeds and independently with the electrostatic pendulum as σ≈1-2μC/m².

Composition and Stability of Plasma Polymer Films Exhibiting Vertical Chemical Gradients

Controlling the balance between stability and functional group density in grown plasma polymer films is the key to diverse applications such as drug release, tissue-engineered implants, filtration, contact lenses, microfluidics, electrodes, sensors, etc. Highly functional plasma polymer films typically show a limited stability in air or aqueous environments due to mechanisms like molecular reorganization, oxidation, and hydrolysis. Stabilization is achieved by enhancing cross-linking at the cost of the terminal functional groups such as -OH and -COOH, but also -NH₂, etc. To overcome such limitations, a structural and chemical gradient was introduced perpendicular to the surface plane; this vertical gradient structure is composed of a highly cross-linked base layer, gradually changing into a more functional nanoscaled surface termination layer. This was achieved using CO₂/C₂H₄ discharges with decreasing power input and increasing gas ratio during plasma polymer deposition. The aging behavior and stability of such oxygen-functional vertical gradient nanostructures were studied in air and in different aqueous environments (acidic pH 4, neutral pH ≈ 6.2, and basic pH 10). Complementary characterization methods were used, including angle-resolved X-ray photoelectron spectroscopy (ARXPS) and time-of-flight secondary ion mass spectrometry (ToF-SIMS) as well as water contact angle (WCA) measurements. It was found that in air, the vertical gradient films are stabilized over a period of months. The same gradients also appear to be stable in neutral water over a period of at least 1 week. Changes in the oxygen depth profiles have been observed at pH 4 and pH 10 showing structural and chemical aging effects on different time scales. The use of vertical gradient plasma polymer nanofilms thus represents a novel approach providing enhanced stability, thus opening the possibility for new applications.