Effects of thermal and mechanical history on the viscoelastic properties of rigid poly(vinyl Chloride)

The effects of processing variables on the solid state properties of rigid PVC were studied by evaluating dynamic mechanical and tensile properties for thin film specimens of two different resins. The dynamic measurements were performed over the temperature range ?1]60 to 85°C, encompassing both the low temperature β transition and above ambient a transition (T_g). Engineering tensile strengths and energies to fracture were obtained at ambient conditions for several rates of elongation. Test specimens were prepared by solvent casting and compression molding techniques and subsequently were subjected to various thermal-mechanical histories. The results obtained were similar for both types of specimens and are described below. The various thermal histories considered include: (1) quick quenching from 225°C (samples referred to as “untreated”); (2) very slow (equilibrium) cooling after annealing at T_g; (3) quick quenching from T_g. In addition, the effects of frozen stresses were examined by systematically varying the stresses imposed on samples during the cooling processes 2 and 3. Increasing the load level imposed on specimens during equilibrium cooling resulted in enhancements of the β transition loss dispersion and tensile yield strength. Changes in loading during process 3, however, had little effect on the cooled specimens. But process 3 does alter the relaxation spectrum below T_g so that additional molecular relaxation is induced between T_β and T_α as much as 45°C below the a transition. The anomalous tan δ dispersions thus produced are accompanied by diminished tensile yield strengths and greatly increased energies to fracture. The most extreme case was encountered for the “untreated” specimens which were rapidly quenched from 225°C. The loss tangent data indicate remarkable differences in the region between T_β and T_α. When comparing the dynamic mechanical data with the fracture energy results for the same samples we note that increases in the intensity of the T < T_g anomalous dispersion correlate with increasing energies to fracture. On the other hand, the β transition intensity does not directly correlate. One molecular model which is consistent with these observations assumes that elongation induces a dilation of the polymer. Since most polymers possess Poisson ratios less than 0.5, the dilation will create extra internal volume (including free volume) in the polymer network. The increase in internal volume as elongation proceeds has the net effect of shifting the conditions of testing toward higher temperatures on a molecular relaxation scale permitting a higher level of molecular mobility at ambient conditions. As a sample continues to elongate one of two consequences is encountered: the imposed deformation cannot be accommodated by the available molecular mobility and the specimen fractures; or the deformation results in dilation to the extent that the response properties are shifted into a region of the relaxation spectrum where molecular mobility is sufficient for the specimen to accommodate the imposed deformation and yielding occurs. Yielding is expected if the effective temperature shifts as far as T_g before the sample fractures. In a case where there are additional molecular relaxation possibilities prior to the a transition, such as those in the anomalous dispersion region between T_β and T_α, sufficient dilation for yielding will be encountered before the normal T_g is reached. The anomalous T < T_g relaxation process thus tends to promote increased elongation and higher energies to fracture in PVC.     

Nanoparticle Distribution in Three‐Layer Polymer–Nanoparticle Composite Films: Comparison of Experiment and Theory

The distribution of hydrophobic nanoparticles deposited on a hydrophilic polymer film is investigated by scanning electron microscopy, transmission electron microscopy, and atomic force microscopy before and after spin‐coating a polymer solution on the particle film and drying it at room temperature. Various polymers and solvents are used. To reach equilibrium, all investigated systems are annealed additionally above the glass transition temperature (T_g) of the polymers. The compatibility of the interacting components is estimated by calculating their surface energy, solubility, and mutual interaction parameters. The experimental results show a redistribution of the particles on both interfaces of the polymer film. This corresponds to the calculated immiscibility of particles and polymers. The distribution of the nanoparticles at the interfaces is related mainly to the vapor pressure of the solvent, that is, kinetic effects during spin‐coating. Only minor contributions result from surface energy, solubility, and interaction parameters.     

Yielding behavior of glassy polymers. III. Relative influences of free volume and kinetic energy

The free-volume model for interpreting the initial yielding behavior of glassy polymers is extended to include kinetic energy influences. Molecular mobility is assumed to be determined by the product of the probabilities of attaining sufficient local free volume to allow molecular rearrangement, and kinetic energy to overcome restraining forces. Yielding then is initiated at the point where the free-volume increase resulting from the dilational component of the applied stress is sufficient to bring the local molecular mobility to that characteristic of the unstressed polymer at T_g.

Expressions are derived for the temperature and strain-rate dependences of the initial yield strain (defined as the proportional limit on the tensile stress-strain curve) and compared with experimental data for poly(methyl methacrylate). The extended model is found to afford no substantial improvement over a simple free-volume model, indicating that relaxational processes in the glassy state-at least in the range T_g to (T_g - 100°C)-are governed principally by freevolume changes.     

Temperature behavior of the Kohlrausch exponent for a series of vinylic polymers modelled by an all-atomistic approach

The Kohlrausch-Williams-Watt (KWW) function, or stretched exponential function, is usually employed to reveal the time dependence of the polymer backbone relaxation process, the so-called α relaxation, at different temperatures. In order to gain insight into polymer dynamics at temperatures higher than the glass transition temperature T _g , the behavior of the Kohlrausch exponent, which is a component of the KWW function, is studied for a series of vinylic polymers, using an all-atomistic simulation approach. Our data show very good agreement with published experimental results and can be described by existing phenomenological models. The Kohlrausch exponent exhibits a linear dependence with temperature until it reaches a constant value of 0.44, at 1.26T _g , revealing the existence of two regimes. These results suggest that, as the temperature increases, the dynamics progressively change until it reaches a plateau. The non-exponential character then describes subdiffusive motion characteristic of polymer melts.     

An apparent double glass transition in semicrystalline polymers

Thermal expansion and/or specific heat and/or dynamic mechanical loss data reveal the presence of two glass-like transitions in bulk crystallized polyethylene, polypropylene, polybutene-1, polypentene-1, cis-and trans-polyisoprene (natural), poly-4-methylpentene-1, isotactic polystyrene, poly(vinyl alcohol), nylon 6, the oxide polymers ?(CH₂)_nO?, with n = 1 to 4, polyethylene terephthalate, polyvinylidene fluoride, polyacrylonitrile, and polyvinylidene chloride. We designate the lower of these as T_g(L), which appears identical with the conventional T_g at zero crystallinity. The higher one, designated as T_g(U), is strongly increased with increasing levels of cystallinity. The differnece ΔT_g = T_g(U) ? T_g(L) tends to approach zero as the fractional crystallinity, X, approaches zero. For a X of 0.5 [Ptilde] 0.1, ΔT_g is about 50°C and T_g(U)/T_g(L) is about 1.2 with temperatures in °K. The increases in coefficient of thermal expansion, (Δα)_L and (Δα)_U, at these two transitions seem to depend on crystallinity and morphology in the expected manner for polyethylene and polypropylene: for × = 0.5–0.7, (Δα)_U is stronger than (Δα)_L; for X χ 0, (Δα)_L is stronger than (Δα)_U. Such data are not available for the other listed polymers. Some atactic polymers, poly-4-methylpentene-1, and polystyrene also seem to have a double T_g, the upper of which we tentatively ascribe to the presence of Geil-Yeh types of local order. Since polyethylene, polyvinylidene fluoride, and polyvinylidene chloride exhibit the apparent double T_g, tacticity, per se, is not necessary to produce it. Special care must be exercised to distinguish T_g(U) from the crystalline phase α_c relaxation occurring at temperature T_c. It is shown that T_c for well-annealed crystalline material tends to occur at about 0.83 to 0.85 T_M where T_M is the crystalline melting point in °K. Hence T_c is very close to the temperature at which rate of bulk crystallization is a maximum. While the phenomenon of a double T_g seems clear, its origin is in doubt. We suggest that T_g(L) and T_g(U) arise from tkie presence of different types of amorphous material. For example, polymer molecules not incorporated in the crystallites and/or cilia might give rise to T_g(L). Morphological entities under greater restraint, such as tie molecules or loose loops, might give rise to T_g(U). Conversely, pseudocrystalline structures (smectic or nematic) might be responsible for T_g(U), at least in polypropylene, poly-4-methylpentene-1, and possibly in some nylons.

Data available in the literature do not permit making a definite choice between different possible origins of the apparent double glass transition. Indeed, the origin may vary from polymer to polymer.     

Application of a new structural theory to polymers. ii. transition states for amorphous polymers and copolymers

A recently developed nonequilibrium thermodynamic theory of continuum rheology is combined with a generalized definition of thermomechanical transitions, to produce a single equation for interrelating the basic variables (stress o, strain rate ε, pressure p, temperature T, and structure ?) at a transition. Specialization of ? to represent uncrosslinked polymers leads to incorporation of molecular weight M as a variable. New predictions are thus made for the glass transition [T_g(M), T_g(p), T_g(ε) and others] and compared successfully with data. Particularly remarkable are the results that 1/T_g is a piecewise linear function of In M, and T is piecewise linear with p. Comparable results and confirmation with data arise when applying the theory to the liquid-liquid transition, T _ll (M). For random copolymers, application of a single mixing rule to the transition equation leads to a prediction of T_g as a function of composition and the T_gi for the homopolymers (components i). This relationship reduces, in various cases, to several familiar equations in which the parameters were simply empirical, thus providing an interpretation of those parameters and defining restrictions applicable to each case. Finally, an alternative interpretation of ? in terms of free volume allows the theory to be extended to other systems, including those with small molecules.     

Amorphous structure heat: Temperature dependence of heats of solution for polystyrene in toluene and ethylbenzene

When a polymer is dissolved in a solvent, the heat measured is a sum of a polymer-solvent interaction term and a term related to the structure that existed in the solid polymer relative to its amorphous liquid state. This latter contribution, termed the “residual” heat, can have an endothermic contribution due to the fusion of crystalline regions and an exothermic contribution due to the disruption of structure in noncrystalline amorphous regions. For atactic polystyrene between 30 and 110°C, it is shown that the “residual” heat is exothermic, decreases linearly with temperature differences below T_g, and extrapolates to zero in the vicinity of T_g. The existence of an exothermic heat above T_g is probably related to a 160°C transition in polystyrene. This “residual” heat was further observed to be independent of the pressure at which the polystyrene was glassified.     

Confinement and processing effects on glass transition temperature and physical aging in ultrathin polymer films: Novel fluorescence measurements

Fluorescence intensity measurements of chromophore-doped or -labeled polymers have been used for the first time to determine the effects of decreasing film thickness on glass transition temperature, T _g, the relative strength of the glass transition, and the relative rate of physical aging below T _g in supported, ultrathin polymer films. The temperature dependence of fluorescence intensity measured in the glassy state of thin and ultrathin films of pyrene-doped polystyrene (PS), poly(isobutyl methacrylate) (PiBMA), and poly(2-vinylpyridine) (P2VP) differs from that in the rubbery state with a transition at T _g. Positive deviations from bulk T _g are observed in ultrathin PiBMA and P2VP films on silica substrates while substantial negative deviations from bulk T _g are observed in ultrathin PS films on silica substrates. The relative difference in the temperature dependences of fluorescence intensity in the rubbery and glassy states is usually reduced with decreasing film thickness, indicating that the strength of the glass transition is reduced in thinner films. The temperature dependence of fluorescence intensity also provides useful information on effects of processing history as well as on the degree of polymer-substrate interaction. In addition, when used as a polymer label, a mobility-sensitive rotor chromophore is demonstrated to be useful in measuring relative rates of physical aging in films as thin as 10 nm. Received 21 August 2001     

Dynamic light scattering in solid polymers

The viscosity of an amorphous polymeric solid above its glass transition [T _g (T,P)] increases as the temperature of the solid is decreased or the pressure is increased. Under changes in temperature or pressure, molecular subunits in the polymeric solid undergo configurational changes. Such changes or relaxations have a distribution of relaxation strengths and times. As the solid is cooled or as the hydrostatic pressure on the solid is increased, the relaxation strengths increase and the relaxation times increase. These changes in relaxation or dynamic properties are very dramatic as the empirical T _g is approached. Near T _g the polymeric solid is no longer in volume equilibrium; continued cooling or pressuring at a time rate faster than the average relaxation time will produce a polymeric glass. This glass is a nonequilibrium, amorphous solid. If the glass is held at a fixed temperature and pressure very close to, but below, T _g , the volume of the glass will be observed to relax to its equilibrium value. For temperatures and pressures well below T _g , equilibrium is a much more conjectural concept since the relaxation times become extremely long. It has been proposed^1,2 that there is a characteristic temperature T _g at which an amorphous polymer undergoes a second-order transition to an equilibrium glass with zero configurational entropy (i.e., a noncrystallizable solid).     

Measuring surface and bulk relaxation in glassy polymers

We present a comprehensive study of gold nanoparticle embedding into polystyrene (PS) surfaces at temperatures ranging from T _g + 8 K to T _g − 83 K and times as long as 10⁵ minutes. This range in times and temperatures allows the first concurrent observation of and differentiation between surface and bulk behavior in the 20nm region nearest the free surface of the polymer film. Of particular importance is the temperature region near the bulk glass transition temperature where both surface and bulk processes can be measured. The results indicate that for the case of PS, enhanced surface mobility only exists at temperatures near or below the bulk T _g value. The surface relaxation times are only weakly temperature dependent and near T _g , the enhanced mobility extends less than 10nm into the bulk of the film. The results suggest that both the concept of a “surface glass transition” and the use of glass transition temperatures to measure local mobility near interfaces may not universally apply to all polymers. The results can also be used to make a quantitative connection to molecular dynamics simulations of polymer films and surfaces.     

Cold flow of glassy polymers. II: Ductility,impact resistance,and unoccupied volume

A definition of maximum fractional unoccupied volume, f = 1.0 – (d_a/d_c), is presented for amorphous crystallizable polymers, f differs for various polymers at T_g, depending on the conformability of the polymer. It is large, at T, for sterically hindered or bulky polymers but low for flexible polymers. There is a reasonably good correlation between f and impact strength. In addition, one can explain the effect of “antiplasticizers.”     

Relaxation times and energy barriers of rubbing-induced birefringence in glass-forming polymers

The relaxations of rubbing-induced birefringence (RIB) in several glass-forming polymers, including polycarbonate and polystyrene (PS) derivatives with various modifications to the phenyl ring side group, are studied. Significant relaxations of RIB are observed at temperatures well below the glass transition temperature T _g . The relaxation times span a wide range from ∼ 10 s to probably geological time scale. Physical aging effects are absent in the RIB relaxations. The model proposed for the interpretation of RIB in PS describes well the RIB relaxations in all the polymers investigated here. The energy barriers are of the order of a few hundred kJ/mol and decrease with decreasing temperature, in opposition to the trend of Vogel-Fulcher form for polymer segmental relaxations above T _g . The relaxation behaviors of different polymers are qualitatively similar but somewhat different in quantitative details, such as in the values of the saturated birefringence, the shape of the initial barrier density distribution functions, the rates of barrier decrease with decreasing temperature, and the dependence of relaxation times on temperature and parameter , etc. The RIB relaxations are different from any of the other relaxations below T _g that have been reported in the literature, such as dielectric relaxations or optical probe relaxations. A microscopic model for the relaxations of RIB is much desired.     

Effects of gas temperature on optical and transport properties of a-Si:H films deposited by PECVD

Effects of silane temperature (T _g) before glow-discharge on the optical and transport properties of hydrogenated amorphous silicon (a-Si:H) thin films were investigated. The optical measurements show that the refractive index increases with increasing T _g. The transport characterizations show that when T _g increases, the dark conductivity increases. However, the temperature coefficient of resistance decreases. In addition, after holding at 130°C for 20 h, the resistance variation, ΔR/R, of the films deposited at T _g = room temperature (10.8%) is much larger than those deposited at silane temperatures of 80°C (3%) and 160°C (2%). This can be attributed to different rates of defect creation in a-Si:H films caused by various T _g.     

Structural changes in glassy poly(ethylene terephthalate)

Structural changes in glassy poly(ethylene terephtbalate) and their effects on its crystallization, melting, and various properties were studied. Quenched, annealed below T_g, crystallized, and drawn samples were studied using calorimetry, wide-and small-angle X-ray diffraction, mechanical spectroscopy, and stress-strain analysis. All results indicate some level of order in the glassy polymer which can be increased by annealing below T_g. This order still exists at tempertures above T_g and affects the properties of the polymer.     

Effect of filler and cooling rate on the glass transition of polymers

Fillers have been reported to raise, have no effect upon, or to lower the glass transition temperature T_gof polymers. In those studies, comparisons have been made between filled and unfilled polymers having equal thermal histories. In the work report here, however, the thermal history (cooling rate) was also varied. Two systems, polystyrene-silica and epoxy-rubber were studied. The glass transitions were measured by using a differential scanning calorimeter and a method of analysis first described by Ellerstein and later elaborated upon by Flynn. The data could be represented by a linear plot of the log of cooling rate versus T_gor T_g ^?1. For the polystyrene system, the filled material had a larger negative slope for the plot of log cooling rate versus T_g ^?1 so that after fast cooling the filled material had a lower T_g than the unfilled material. However, when the cooling rate was lowered, the T_g of the filled and unfilled materials approached each other, and for very slow cooling (annealed samples) the filled material had a higher T_g than the unfilled one. For the epoxy-rubber system, the rubber lowered the T_g by an amount which increased with cooling rate. Thus the extent and even the direction of the change in T_g with filler is shown to be dependent upon thermal history. It is shown that the slope of the plot of log cooling rate versus T_g ^?1 or T_g is related to an activation energy. A new simplified method of correcting T_g for DSC instrument thermal lag is described.     

Scattering studies from polymer blends

An ultraquenching technique was used to prepare thin (ca. 1000 Å) amorphous films of polypivalolactone and poly(4-methyl-pentene-1). These films were characterized by electron microscopy, electron diffraction, and dynamic mechanical analysis. Other ultraquenched films of these polymers were crystallized by annealing for various times in the vicinity of their glass transition temperatures. Electron microscopy and electron diffraction were used to follow the reorganization of their structures.

Evidence for a double T_g in polypivalolactone (PPVL) was found, with crystallization of annealed, ultraquenched films occurring just above T_g (L) = 270°K. A T_g (U) = 340°K was noted. When the disordered glass was annealed above T_g (L), polypivalolactone crystallized into the a crystal form, which is composed of antiparallel chain segments, suggesting a chain-folded crystallization mechanism.

Poly(4-methyl-pentene-1) (P4MP1) gave evidence for T_g (L) = 220°K and T_g (U) = 325°K by dynamic mechanical analysis. However, morphology and electron diffraction showed that significant crystallization of ultraquenched polymer did not occur until T_g (U) was reached. X-ray data also supported this conclusion, which is explained by the lower density of the crystal phase of P4MP1 (compared to amorphous material) below 320°K. Long-term annealing of films at T_g (U) resulted in the formation of single-crystal structures, again indicative of a mechanism of chain-folded crystallization from the glass.     

Correlation between glass transition temperature and thermal expansion coefficients of polymers: Its interpretation and implication

A new approach pertaining to the hole and lattice theories of polymeric systems is developed to interpret the universal inverse relationship between the glass transition temperature (T_g) and the difference in thermal expansion coefficients for liquid and glassy polymers (δ α). The success of this particular theoretical consideration rests upon the familiar hypothesis of the iso-free volume state at T_g and the entropy contribution to the hole-polymer segment interaction energy. Based on the experimental data available, we have established the free volume fraction at T_g, v_g = 0.025, which is identical with the assessment of the empirical Williams-Landel-Ferry (WLF) equation for the temperature-dependence shift factor a_T. However, appreciably higher values of v_g are reported by other contemporary models. The present findings justify an alternative form of the WLF equation with the product T_g, δ α playing the role of δ α. The universality of this novel expression is demonstrated, by means of statistical analysis, to be remarkably more warrantable than its original version.     

Amorphous linear polyethylene: Annealing effects

The effect of annealing amorphous linear polyethylene films prepared by an improved ultraquenching technique at temperatures just below and above a dynamic mechanical relaxation peak (torsion braid) observed at ∽190K has been characterized by electron microscopy and torsion braid analysis. Based on the results described, this peak is believed related to the lower glass transition temperature T_g(L), the T_g of wholly amorphous linear polyethylene, whereas the β peak at 260K is T_g (upper). Annealing just below T_g (L) results in a growth in size of the nodules observed in the as-quenched samples, whereas annealing above T_g (L) can result in the growth of single crystal-like structures, spherulites, and shish-kebobs. Storage of the crystallized samples at room temperatures results in a decrease in size of the relaxation peak during subsequent torsion braid spectroscopy measurements. The results indicate significant amounts of molecular motion can occur during crystallization even at T_g.     

Vapor Pressure Assisted Void Growth and Cracking of Polymeric Films and Interfaces

Pores and cavities form at filler particle-polymer matrix interfaces, at polymer film-silicon substrate interfaces as well as in molding compounds of IC packages. Moisture diffuses to these voids. During reflow soldering, surface mount plastic encapsulated devices are exposed to temperatures between 210 to 260°C. At these temperatures, the condensed moisture vaporizes. The rapidly expanding water vapor can create internal pressures within the voids that reach 3–6 MPa. These levels are comparable to the yield strengths of epoxy molding compounds and epoxy adhesives, whose glass transition temperatures T _g range between 150 to 300°C. Under the combined action of thermal stress and high vapor pressure (relative to the yield strength at T _g), both pre-existing and newly nucleated voids grow rapidly and coalesce. In extreme situations, vapor pressure alone could drive voids to grow and coalesce unstably causing film rupture, film-substrate interface delamination and cracking of the plastic package.Vapor pressure effects on void growth have been incorporated into Gurson's porous material model and a cohesive law. Crack growth resistance-curve calculations using these models show that high vapor pressure combined with high porosity bring about severe reduction in the fracture toughness. In some cases, high vapor pressure accelerates void growth and coalescence resulting in brittle-like interface delamination. Vapor pressure also contributes a strong tensile mode component to an otherwise shear dominated interface loading. An example of vapor pressure related IC package failure, known as popcorn cracking, is discussed.     

Concerning free volume quantities and the glass temperature

Free volume quantities proposed earlier by Boyer and Simha in connection with the glass transition are reformulated by taking into account the temperature dependence of the thermal expansivities α _l and α_g for the liquid and the glass, respectively. This necessitates an extrapolation of the liquid to temperatures below Tg which is performed by means of the reduced volume-temperature function established and given a theoretical foundation previously. For the glass, low temperature experimental data, encompassing all relaxations occuring below T_g, are required.

Two polymer series are examined in detail, namely, poly(methacrylates) and poly(vinyl) alkyl ethers, where α_g has been measured between at least 30°K and T_g. Results for poly(methylacrylate) and poly(styrene) are also given. The systematic decrease in the product (αl - αg) · T|_T=Tg with increasing length of the side chain noted previously is considerably reduced but not eliminated when the appropriately corrected expression is substituted instead. However, the free volume fraction related to the quantity αlT|_T=Tg remains more nearly invariant in the polymers analyzed.

An alternative treatment is discussed which considers an occupied volume expanding below T_g by a mechanism of thermal vibrations solely. Experimental and theoretical means of obtaining this quantity arc suggested.