José M. Carella

Limited-supply diffusion in the liquid polystyrene–glassy poly(phenylene oxide) pair. Further results in extended times scale

Diffusion between a liquid polystyrene and a glassy poly(phenylene oxide) matrix is experimentally studied over a wide range of temperatures and diffusion times, using confocal Raman microspectroscopy. A specially designed experimental setup allows precise direct following of time evolution of the chemical composition profiles along the diffusion path. A direct and precise quantification is made for the experimental errors involved in two methods used for Raman measurements. An already proposed diffusion model is used to predict the time evolution of the advancing composition profiles along the diffusion path, and gives precise results. Experimental thermodynamic and kinetic data taken from literature are used for the model calculations, and excellent agreement with experimental results is obtained. Diffusion slow down is confirmed at the lowest diffusion temperature used, and probable causes are discussed.

Modeling the fractionation process in TREF systems. II. Numerical analysis

Temperature raising elution fractionation (TREF) allows qualitative short chain branching (SCB) analysis in copolymers. In order to make the analysis quantitative, information on how such fractionation occurs must be incorporated into the interpretation of TREF spectra. In a previous work a model of the fractionation was proposed and some preliminary results given. In this article a rigorous mathematical analysis of the solution of the fractionation model is presented by defining two problems. The direct problem, of little practical use, helps to understand the fractionation process. The inverse problem consists in obtaining the distribution of crystallizable lengths (DCL) (directly related to the SCB distribution) from the TREF spectrum. This last problem (i.e., the main interest of this work) is explained in detail. TREF experiments are simulated solving the so-called direct problem using DCLs of different shapes. The synthetic TREF spectra are then processed using the inverse algorithm. The synthetic experiments demonstrate the adequacy of the proposed algorithm as a tool of analysis. A linear ethylene polymer was used to test, experimentally, the numerical procedure. The results obtained are in agreement with those obtained in earlier studies on the same sample by Raman spectroscopy.

Calculation and experimental verification of concentration profiles for selected species at the interphase generated by diffusion in polymer pairs

A method for calculating diffusion rates for individual species in concentrated regime is outlined. The effects of monomeric friction coefficient, Flory-Huggins thermodynamic interaction parameter, individual species molecular weights, local molecular weights distribution, and local T g are precisely calculated. The method is used to calculate individual concentration profiles generated by diffusion of multicomponent polymer blends, and experimentally tested. Polystyrene with a bimodal molecular weight distribution is allowed to diffuse in a blend of polyphenylene oxide and polystyrene. Local physical properties change markedly along the interdiffusion path and, therefore, this is a demanding test for the proposed calculation method. The simulated concentration profiles are compared with results obtained by using two independent experimental techniques: Raman spectroscopy and dynamic mechanical analyzer (DMA). The total polystyrene (PS) concentration profiles, calculated using the proposed method, agree well with Raman spectroscopy results. Simulated DMA results-which are sensitive to the PS species molecular weight distribution-obtained using the concentration profiles, calculated for each PS molecular weight species agree well with the experimental DMA results. Calculations based on average molecular weights give incorrect results.

Development of a simple experimental method to measure interphase composition profiles generated by diffusion in polymers

An experimental method to determine interphase composition profiles in amorphous polymers pairs and polymer-solvent pairs is presented. The method is based on the measurement of dynamic mechanical properties of slender composite beams, and well-established properties of amorphous polymer homogeneous blends and solutions. The method does not require tracers. A simple calibration procedure is included in the description, and some results for a polystyrene-polystyrene pair are used to illustrate the method application.

Interphase evolution in polymer films by confocal Raman microspectroscopy.

Liquid-glassy polymer diffusion is an important topic in polymer physics, with several mechanistic aspects that still remain unclear. Here we describe the use of confocal Raman microspectroscopy (CRM) to study directly several features of interphase evolution in a system of this type. The interphase studied was generated by contact between liquid polystyrene (PS) and glassy polyphenylene oxide (PPO). Interphase evolution on thin films made from these polymers was followed by depth profiling in combination with immersion optics. We also applied regularized deconvolution to improve the spatial resolution of the measurements. With the help of these techniques, we examined interphase PPO concentration profiles and kinetics of interphase evolution in the range 120–180 °C, well below the glass transition temperature of the PPO-based films (185 °C). Overall, the experiment captures the most important features needed to discern the mechanistic factors that control this process. In this sense, confocal Raman microspectroscopy emerges as one of the best experimental techniques for the study of diffusion kinetics in this type of system.

A generalized method to calculate diffusion rates in polydisperse systems. Further results on Rouse dynamics in the concentrated regime

Experiments designed to thoroughly test a recently proposed generalized method to calculate diffusion rates in polydisperse systems have been carried out. Polydisperse polystyrene (PS) samples were allowed to diffuse in a poly(phenylene oxide) (PPO) matrix. Designed blends were made from anionically polymerized PS with molecular weights which cover most of the ranges where Rouse dynamics control the diffusion processes. The diffusion temperatures range from (T g - 1 K) to (T g + 105 K), causing the monomeric friction factor values for PS to change by up to seven orders of magnitude along the diffusion coordinate. Calculations performed with the above mentioned method agree with Raman and DMA experimental data.

A generalized method to calculate diffusion rates in polydisperse systems. Application to miscible polymer pairs in the concentrated regime

Abstract A generalized method for calculating diffusion rates in polydisperse systems, valid in the concentrated regime, is outlined. In the formulation of the method the discrete variable that describes the molecular size, is replaced by a continuous variable in the same range. This replacement diminishes the number of degrees of freedom but keeping the essential physics of the original statement. The effects of monomeric friction coefficient, Flory-Huggins thermodynamic interaction parameter, individual species molecular weights, local molecular weights distribution and local Tg are consistently included in the model. The method is used to calculate concentration distribution profiles generated by diffusion of polydisperse polymers blends, and experimentally tested. For this purpose polystyrene with discrete (bimodal and tetramodal) molecular weight distributions and polystyrene with wide and continuous molecular weight distributions were used to simulate polydisperse systems. They are allowed to diffuse in a blend of polyphenylene oxide and polystyrene. The simulated concentration profiles are compared with results obtained by using two experimental techniques based on independent physical properties, which give complementary information: Raman spectroscopy and DMA. The total PS concentration profiles calculated using the proposed method agree well with Raman spectroscopy results. Simulated DMA results—which are sensitive to the PS species molecular weight distribution—obtained using the concentration profiles calculated for each PS molecular weight species, agree well with the experimental DMA results. Calculations based on average molecular weights on the other hand, give incorrect results.

A solution for an ill-conditioned inverse problem. A composite slender beam in bending tests

The bending stiffness of composite beams measured at different temperatures can be used to determine interphase composition profiles generated by polymer-polymer interdiffusion, or solvent diffusion into one face of the polymer beam. A suitable method to solve the inverse problem thus generated is presented here, which allows calculation of beam composition profiles. A simple numerical procedure is also outlined. Error propagation analysis is included, together with a precise guide to minimize experimental error.

Finite element model of interdiffusion and reaction in polydisperse polymer blends

Numerical modelling of polymer blends production and processing, while technologically important, poses a considerable computational challenge when one or more of the polymer species is polydisperse. The mathematical formulation of such problems, where molecular weight distribution may range over several hundreds—which are very frequent in practice—leads to a huge set of coupled differential equations. In this work a numerical technique is presented that reduces the problem to a manageable number of degrees of freedom while keeping the essential physics of the original statement. For this purpose the distributions of molecular degrees of polymerization are approximated by continuous variables, and the set of concentration profiles replaced by a continuous field. The resulting equations are then reexpressed in weak form as a Galerkin integral identity and discretized using finite elements. Mass conservation and interchange chemical reactions as transesterification are treated using Lagrange multipliers. The accuracy of the technique—which can also be applied to the monodisperse case—is assessed through a number of simulations, and comparisons with experimental results published earlier. Copyright