Thermal Diffusivity Of Polymers Research Articles

Measuring thermal diffusivity when the principal axes are unknown a priori

The thermal diffusivity of polymers may develop anisotropy due material possessing or mechanical loading. The orientation of the anisotropy may not be visually apparent. An analytical study has been performed where the four non-zero components of the diffusivity tensor are estimated for a specimen with in-plane anisotropy. Sensitivity coefficients were calculated for each of the non-zero components of the diffusivity tensor at the four measurement locations. The amplitude of the sensitivity coefficients suggest that the signal received at each sensor is sufficient for estimating the parameters, while the character of the coefficients over time suggests that the parameters are independent. Small values of in-plane anisotropy lead to negligible errors (< 0.4%) in the estimated parameters when the off-diagonal diffusivity is neglected. Larger differences in anisotropy require the estimation of the off-axis terms, which is possible with the addition of a fourth sensor to the extended flash diffusivity method. This additional measurement may be used to verify assumptions of thermally orthotropic behavior in materials.

The Role of Solubility in Thermal Field-Flow Fractionation: A Revisited Theoretical Approach for Tuning the Separation of Chain Walking Polymerized Polyethylene.

The influence of the polymer solubility on the separation efficiency in thermal field-flow fractionation (ThFFF) was investigated for a polymer model system of differently branched chain walking polyethylenes in five different solvents, which were selected depending on their physical parameters. The understanding of polymer thermal diffusion has been elucidated using a revisited approach based on the latest thermal diffusion prediction model by Mes, Kok, and Tijssen combined with the Hansen solubility theory. Thereby, a significant improvement in the precision of the thermal diffusion prediction and the separation efficiency has been achieved by implementation of the temperature dependency on Hansen solubility parameters. In addition, we demonstrate a method for validation of the segmental size of polymer chains with varying topology by using the revisited thermal diffusion prediction approach in inverse mode and experimental thermal diffusion data.

Numerical Modeling of 193-nm Excimer Laser Ablation on CR-39 Polymer

Laser polymer processing has evolved into an important field of applied and fundamental research. Allyl diglycol carbonate or CR-39 is considered an important polymer for use in optical and medical applications since it is a hard and infusible thermoset plastic that is insoluble in all solvents. The temperature distribution of CR-39 when subjected to irradiation during 193-nm excimer laser ablation was investigated. An effective simulation was developed to reflect the effects of polymer thermal diffusion, laser fluence, beam geometry, and number of pulses. A two-dimensional finite element model was used to predict the temperature distribution and ablation depth in the plastic CR-39 polymer under the 193-nm laser ablation process. The photochemical threshold ablation fluence was 750 mJ/cm2 for a single laser pulse, but dropped to 240 mJ/cm2 for repetitive laser pulses. At higher fluence, thermal effects exhibited a slight contribution to the ablation process. For fluence ≥ 750 mJ/cm2, the ablation depth increased abruptly. It can thus be inferred that the rate of temperature increase with pulse number increased concomitantly with the fluence. Thus, thermal effects are a significant factor in the ablation process.

Separation and composition distribution determination of triblock copolymers by thermal field-flow fractionation

Thermal field-flow fractionation (ThFFF) is used to separate a linear triblock copolymer of polystyrene, poly(tert-butyl acrylate), and poly(methyl methacrylate) by composition. Fractions were collected and subjected to off-line NMR analysis. The resultant mole fraction versus retention time plots for each of the three polymer components confirmed the success of the separation and yielded the composition distribution of the copolymer. The composition distribution was also obtained using a second approach that involved solving a series of equations comprised of polymer thermal diffusion coefficients and quasi-elastic light scattering, differential refractometry, and UV detector responses. Both sets of data showed similar trends of composition variations in each polymer component as a function of retention time. However, discrepancies were observed in the mole fraction values. The ability to compositionally separate and to determine composition distribution of copolymers is important as demonstrated by the presence of diblock impurities in the ThFFF with off-line NMR results.

Thermal diffusivity of polymers by modified angström method

The nature of the molecular structure of plastics makes the properties of such materials markedly temperature dependent. In addition, the continuous increase in the utilization of polymeric materials in many specific applications has demanded knowledge of their physical properties, both during their processing as raw material, as well as over the working temperature range of the final polymer product. Thermal conductivity, thermal diffusivity and specific heat, namely the thermal properties, are the three most important physical properties of a material that are needed for heat transfer calculations. Recently, among several different methods for the determination of the thermal diffusivity and thermal conductivity, transient techniques have become the preferable way for measuring thermal properties of materials. In this work, a very simple and low cost variation of the well known Angström method is employed in the experimental determination of the thermal diffusivity of some selected polymers. Cylindrical shaped samples 3 cm diameter and 7 cm high were prepared by cutting from long cylindrical commercial bars. The reproducibility is very good, and the results obtained were checked against results obtained by the hot wire technique, laser flash technique, and when possible, they were also compared with data found in the literature. Thermal conductivity may be then derived from the thermal diffusivity with the knowledge of the bulk density and the specific heat, easily obtained by differential scanning calorimetry.

Thermal diffusivity of polymers by the laser flash technique

The nature of the molecular structure of plastics makes the properties of such materials markedly temperature dependent. Thermal conductivity, thermal diffusivity and specific heat, namely the thermal properties, are the three most important physical properties of a material that are needed for heat transfer calculations. Nowadays, several different techniques for the determination of the thermal diffusivity and thermal conductivity may be found in the literature. Recently, transient techniques have become the preferable way for measuring thermal properties of materials. In this work, the laser flash technique is employed in the experimental determination of the thermal diffusivity of some selected polymers. Measurements were carried out from room temperature up to 160 °C. Disc shaped samples 10 mm diameter and 0.3–1 mm thickness were prepared either by hot pressing the polymer powder, or by cutting the discs from long cylindrical commercial bars. The reproducibility is excellent, and the results obtained were checked against results obtained by the hot wire technique, and when possible, they were also compared with data found in the literature. The laser flash technique mostly employed in the determination of thermal properties of ceramics and metals may also be considered as a suitable method for measuring thermal properties of polymers.

Prediction of Polymer Thermal Diffusion Coefficients from Polymer-Solvent Interaction Parameters: Comparison with Thermal Field Flow Fractionation and Thermal Diffusion Forced Rayleigh Scattering Experiments

In this study a model that allows the qualitative prediction of polymer thermal diffusion coefficients from polymer-solvent interaction parameters is presented. The Flory-Huggins lattice theory served as a starting point for the thermal diffusion model. From this model it follows that D T is determined by the temperature dependence of the polymer-solvent interaction parameter ( h ), the segmental mobility of the polymer chain, and the polymer concentration. In agreement with literature data, the model predicts that D T is independent of the molecular mass of the polymer, D T increases with temperature, and D T is strongly dependent on the interaction between the polymer and the solvent. Furthermore, it follows from the model that D T should decrease with concentration. A good qualitative agreement with experimental data has been found. In order to study the potentials of the model, the D T values of polystyrene (PS) in several solvents were predicted. The required temperature-dependent polymer-solvent interaction parameters were calculated from Hildebrand's solubility parameters of the polymer and of the solvent. The solvent's solubility parameters were estimated using Lee and Kesler's generalized thermodynamic equations of state. The polymer solubility parameters were taken from the literature. Lack of data complicated the comparison. However, a good agreement for PS in THF, MEK, dioxane, and cyclohexane was found. Thermal diffusion values predicted for PS in several aromatic solvents were, however, significantly low. Still, the overall result is satisfactory considering the fact that the Flory-Huggins theory is a highly simplified polymer-solvent theory that was never intended to be used for quantitative purposes. Polymer thermal diffusion model Thermal field-flow fractionation Polymer-solvent interaction parameter Thermal diffusion forced Rayleigh scattering

Micro-thermal field-flow fractionation: New challenge in experimental studies of thermal diffusion of polymers and colloidal particles

The theoretical principles and methodological aspects of the thermal field-flow fractionation applied to study the thermal diffusion of the macromolecules in solution and colloidal particles in suspension were developed. The theoretical analysis indicated that the miniaturization of the separation channel for thermal field-flow fractionation should improve the performance of this technique. A new microchannel was conceived and built. The experimental results obtained for polymer samples with an extended range of molar masses from relatively low up to ultrahigh and for the colloidal particles confirmed that the achieved resolution is the same but the versatility of the microchannel is superior to that of the standard size channels owing to the substantial decrease in the heat energy flux. This important improvement allows us to achieve very high resolution when applying constant-field-force operation, it makes it much easier to program the temperature drop which is an advantageous operational mode from the viewpoint of the time of analysis, and it extends considerably the range of perfectly controlled temperatures of the cold and hot walls. The sample amount needed for one analysis can be as small as a few nanograms.

Soret Coefficients for Aqueous Polyethylene Glycol Solutions and Some Tests of the Segmental Model of Polymer Thermal Diffusion

A thermogravitational cell is used to measure Soret coefficients (s) for dilute binary aqueous solutions of ethylene glycol, diethylene glycol, triethylene glycol, tetraethylene glycol, and polyethylene glycol (PEG) fractions with average molecular weights from 200 to 20,000 g-mol−1. The cell design allows the top and bottom halves of the solution column to be withdrawn and injected into a high-precision HPLC differential refractometer detector for analysis. Previously reported mutual diffusion coefficients D and the measured Soret coefficients are used to calculate thermal diffusion coefficients DT. s and D vary with the PEG molecular weight M as M+0.53 and M−0.52, respectively; hence, DT = sD is essentially independent of M. The segmental model of polymer thermal diffusion predicts DT = DsegUS/RT2, where Dseg is the segment diffusion coefficient, US the solvent activation energy for viscous flow, R the gas constant, and T the temperature. The predicted DT values, although independent of M, are too large by a factor of five. Additional tests of the segmental model are provided using literature data for polystyrene + toluene, n-alkane + CCl4, and n-alkane + CHCl3 solutions. Agreement with experiment is not obtained. In particular, the measured DT values for the alkane solutions are negative.

Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short-Hot-Wire Method

In this paper, the thermal conductivity and thermal diffusivity of four kinds of polymer melts were measured by using the transient short-hot-wire method. This method was developed from the hot-wire technique and is based on two-dimensional numerical solutions of unsteady heat conduction from a wire with the same length-to-diameter ratio and boundary conditions as those in the actual experiments. The present method is particularly suitable for measurements of molten polymers where natural convection effects can be ignored due to their high viscosities. The results have shown that the present method can be used to measure the thermal conductivity and thermal diffusivity of molten polymers within uncertainties of 3 and 6%, respectively. Further, the thermal conductivity and thermal diffusivity of solidified samples were also measured and discussed.

Effect of Channel Orientation on Thermal Diffusion and Polymer Retention in Thermal Field-Flow Fractionation

The ThFFF retention of polymers is enhanced in certain liquid mixtures. Previous studies of thermal diffusion in such mixtures indicate that the enhancement is due to an additional solubility-based force induced by a solvent gradient in the channel. The partitioning of solvent mixtures in a temperature gradient was shown to be correlated to solvent density, just as the thermal diffusion of polymers is correlated to polymer density. This work examines the density effect more closely by looking at the effect of channel orientation on both polymer retention and the partitioning of liquids. A difference in the profiles of solvent partitioning with channel orientation indicates the presence of convection currents in an inverted ThFFF channel, yet polymer retention is independent of channel orientation in homogeneous solvents as well as solvent mixtures. The results indicate that the effect of density on polymer retention is rooted in thermal diffusion and not convection, but that either the previously proposed mechanism of enhanced retention is incorrect or convection currents are confined to the channel edges, becoming significant only in the tapered regions of the channel. Finally, the effect of polymer concentration on retention is more pronounced in mixed carrier liquids.

Cold Wall Temperature Effects on Thermal Field-Flow Fractionation

Thermal field-flow fractionation is a powerful tool for separating and characterizing lipophilic polymers. The construction of calibration curves is required for converting retention data into molecular weight distributions because thermal diffusion of polymers in solution is not well understood. Retention behavior is determined by the physicochemical properties of the polymer and solvent and should be independent of and apply to any thermal field-flow apparatus. Among these properties is the effect of the cold wall temperature which has been studied in some detail and found to be very important in retention behavior. In addition, temperature effects on thermal diffusion have been measured. †Current address: Thera Tech, 410 S. Chipeta Way, Salt Lake City, UT 84112. †Deceased: October 24, 1996.

Study of thermal diffusion of polybutadiene and polytetrahydrofuran in various organic solvents

The thermal diffusion coefficient (Dτ) was determined for polybutadiene and polytetrahydrofuran (i.e., polyoxytetramethylene) standards of different molecular masses in various organic solvents. The combination of thermal field-flow fractionation retention data with diffusion data from dynamic light scattering or diffusion NMR experiments yielded the thermal diffusion coefficients. In agreement with earlier work on thermal diffusion of polymers in solution, the thermal diffusion coefficient was found to be independent of the molecular mass of the polymers. However, this work once more indicates that the Dτ value is strongly influenced by the chemical composition of both the polymer and the solvent. © 1996 John Wiley & Sons, Inc.

Study of thermal diffusion of polybutadiene and polytetrahydrofuran in various organic solvents

The thermal diffusion coefficient (Dτ) was determined for polybutadiene and polytetrahydrofuran (i.e., polyoxytetramethylene) standards of different molecular masses in various organic solvents. The combination of thermal field-flow fractionation retention data with diffusion data from dynamic light scattering or diffusion NMR experiments yielded the thermal diffusion coefficients. In agreement with earlier work on thermal diffusion of polymers in solution, the thermal diffusion coefficient was found to be independent of the molecular mass of the polymers. However, this work once more indicates that the Dτ value is strongly influenced by the chemical composition of both the polymer and the solvent. © 1996 John Wiley & Sons, Inc.

A New Holographic Grating Technique for the Measurement of Diffusion and Thermal Diffusion of Polymers in Solution

Abstract Despite being a fundamental transport property, thermal diffusion in polymer solutions is still poorly understood, and reliable experimental data are scarce. After a brief review of previous experimental techniques and results, the application of forced Rayleigh scattering to the study of diffusion and thermal diffusion in polymer solutions is discussed. Due to the μm diffusion lengths, equilibration times are reduced to typically 100 ms, and signal averaging allows noise reduction. From a single experiment three different diffusion coefficients are obtained without the need for chain labeling: the thermal diffusivity, the translational diffusion coefficient, and the thermal diffusion coefficient. An improved setup, allowing convection-free heterodyne detection, is discussed. Results for polystyrene in toluene and ethyl acetate are reported, and the measured translational diffusion coefficients are compared with data obtained from photon correlation spectroscopy.

Reassessment of Khazanovich's Theory of Thermal Diffusion of Polymers in Solution

Reassessment of Khazanovich's Theory of Thermal Diffusion of Polymers in Solution

Thermal bending associated with heat conduction by holographic interferometry

An experimental technique using real-time holographic interferometry combined with digitized image processing has been developed to measure the thermal diffusivity of polymers. This technique uses a cantilever beam or an annular disk with one side subjected to a pulse of radiant energy from a photographic flash. The resulting thermally induced deflection is measured by holographic interferometry. The observed deflection is due to a resultant thermal moment induced by a temperature gradient through the thickness. As time goes on, the heat conducts from the exposed surface through the thickness, resulting in a decrease of the bending moment and transverse deflection. It is shown that the deflection is proportional to the thermal moment, and the thermal diffusivity can be retrieved by moment analysis without deriving the analytical solution to the thermomechanical problem.

Thermal diffusivity of polymers by flash radiometry: correlation between thermal diffusivity and fine structure of poly(ethylene terephthalate)

The thermal diffusivity D of poly(ethylene terephthalate) (PET) film is measured by flash radiometry and the correlation between thermal diffusivity and supramolecular structure of PET is discussed. It is found that D increases stepwise with increasing temperature of heat treatment in the range 100–240°C for 1 h, corresponding to the stepwise increase of crystallite size. Also D increases with increasing time of heat treatment in the range 20–80 min at 220°C, reflecting a change of crystallite form from the thermodynamically unstable one to the more stable one. The in situ measurement of D on isothermal crystallization shows that the large increase of D due to first-order crystallization is followed by the gradual and small increase of D due to second-order crystallization. The value of D measured at room temperature for the sample whose D was levelled out on isothermal crystallization has a specific feature: the plot of D against isothermal crystallization temperature has a distinct sharp peak around 107°C and this result is explained as relating to the Avrami exponent calculated from the initial slope of the variation of D on isothermal crystallization. Boiling of a film sample in aqueous phenol solution gives rise to increasing D up to 50 vol% of phenol content, but above this content D decreases. The increase of D is mainly due to the progress of crystallinity by liquid-induced crystallization and the decrease of D is ascribed to the larger contribution of microvoids, which causes phonon scattering.

On-Line Coupling of Thermal Field-Flow Fractionation with Low-Angle Laser Light Scattering

Abstract The analysis of a polymethyl methacrylate sample dissolved in dimethylformamide is performed by using a low-angle laser light scattering photometer attached to a thermal field-flow fractionation channel and a differential refractometer. Relevant theoretical light scattering equations for flow-through operation are outlined. It is shown that the calibration curve of the separation system can be constructed in situ during the course of separation, without using any calibration standard. The average molecular weights as well as the molecular weight distribution curves of the polymer have been determined. The sensitivity of the light-scattering photometer has been measured, and it is compared to that of the differential refractometer in terms of signal-to-noise ratios. The various sources of errors in the molecular weight determination are discussed, and the potential of the coupling for physicochemical studies on the thermal diffusion of polymers is indicated. In spite of some inherent problems, this coupling is expected to have a very bright future if reliable low-angle light-scattering instruments can be made available at moderate prices.

Thermal diffusivity of polymers by the flash method

We have adopted the flash method to the measurement of thermal diffusivity α of polymers in the temperature range 100–400K. The pulsed radiant energy from a flash tube is applied to the ‘front’ side of a suspended sample disc, and α is deduced from the exponential decay time constant of the subsequent transient temperature difference between the ‘front’ and the ‘back’ side, while correction against radiation loss is made by measuring the much longer decay time of the back-side temperature. Calibration runs on polycarbonate (PC) samples of several thicknesses show that the method is quick, precise and fairly accurate, and the results obtained are in reasonable agreement with previous determinations. We have also carried out measurements on polyoxymethylene (POM), poly (vinylidene fluoride) (PVF 2) and poly (ethylene terephthalate) (PET) and computed their thermal conductivities. Results on POM and PVF 2, which are semicrystalline, are analysed in the framework of several two-phase models, and the effect of crystallization (produced by annealing) on the glass transition behaviour of PET has also been studied.