On the micromechanisms of plastic deformation in semicrystalline polymers

Many different molecular processes that cause plastic deformation in polymers can be investigated by transmission electron microscopy (TEM). A short review of those deformation mechanisms is given in this paper using model morphologies and correlating them to the corresponding mechanical behavior.     

Step deformation of solid amorphous polymers

The variation of step deformation kinetics in solids is studied as a function of morphological factors. Oscillations of creep rate at micrometer increments of the amount of deformation, which reflect the step nature of the process, are investigated from an interferogram. It is shown that the plasticization of polymethyl methacrylate by dibutyl phthalate blurs the steps, while their height varies insignificantly. The results are explained using the concept of the netlike structure of amorphous polymers. The data obtained confirm the universal nature of jumps as a mode of evolution of deformation in various solids. The jumps reflect the cooperative nature of motion of kinetic units, and the regular variation of the characteristics of the jumps lends support to the definition of creep as a process of structural self-organization.     

Revision of the model of a fibril with amorphous nodules for oriented soft-chain semicrystalline polymers

A critical analysis of literature data about calculations of small-angle x-ray scattering (SAXS) from a model of a fibril with amorphous nodules (FAN) is made. Changes in the SAXS patterns are reviewed for the effect of stretching the FAN. Possibilities of using the calculation results for interpretation of microdeformational behavior of oriented, flexible chain semicrystalline polymers are analyzed. Invoking the FAN model, a retrospective analysis of some literature data and also analysis of new experimental results obtained by SAXS and wide-angle x-ray scattering methods for oriented samples of cellulose triacetate, poly(vinylidene fluoride-co-hexafluoropropylene), and poly(vinyl alcohol) are carried out.     

Nonequilibrium tensile deformation of amorphous polymers in the rubbery state: Temperature,strain rate,and strain effects. I

We analyze nonequilibrium tensile deformational behavior of an amorphous uncrosslinked random copolymer of styrene and acrylonitrile stretched above its Tg at various temperatures and constant strain rates. The variable investigated is the force required to pull the specimen to a certain strain level. Our results suggest the deformational behavior in the rubbery state can be incorporated in a universal scheme where strain, strain rate, and temperature effects are all superposed, e.g., the effect of strain is identical to the effect of temperature and strain rate. This unexpected result is true within two contiguous but distinct regimes of strain, on both sides of ca. 40% strain, suggesting that non-equilibrium extension at constant pulling speed in the rubbery state occurs by at least two successive mechanisms. Our results also reveal that the physical parameter which should be used to achieve a true superposition of strain rate and temperature data is not as simple as has long been commonly proposed. For instance, we cannot use force alone nor the true stress, nor even the stress divided by strain. The best results are obtained when the function used is a complex function of force and strain. We introduce and explore in depth in this paper and future ones a new method to analyze the data. This method does not impose the choice of the functions which yield superposition and it provides an empirical mean for finding these functions. We have applied our method to other classical elastomers (PIB and SBR) stretched under similar conditions: we find the same conclusions, in particular the same small strain-middle strain transition separating two regimes of deformational behavior in the rubbery state.     

Environmental effects on the tensile deformation of polymers at low temperatures

General experimental results are presented on the environmental effect exerted by nitrogen and argon on the tensile deformation of polymers in the neighborhood of 80° K. The primary features are the large dependence of tensile strength on strain rate and the occurrence of crazing, both of which are absent in helium and vacuum environments. The fracture stress in N₂ and Ar may be less or greater than that in He and vacuum in accordance with the strain rate being low or high, respectively. A brief theory for the low-temperature environmental crazing is presented. A central part of the theory is related to the fact that the adsorption of N₂ and Ar on all polymers around 80° K substantially reduces their surface free-energy by about 25 to 75%.     

A microscopic insight into the deformation behavior of semicrystalline polymers: the role of phase transitions

The deformation behavior of semicrystalline polymers associated with polymorphic transformations under tensile deformation is discussed in the case of syndiotactic polypropylene. We report a phase diagram of this polymer where the regions of stability of the different polymorphic forms are defined as a function of the degree of stereoregularity and deformation. The values of critical strain corresponding to the structural transformations depend on the stereoregularity that affects the relative stability of the involved polymorphic forms and the state of the entangled amorphous phase.     

Chevron morphology in deformed semicrystalline polymers

Chevron morphology was observed using transmission electron microscopy in various semicrystalline polymers deformed in tensile experiments. The morphological and mechanical prerequisites for chevron structure formation in semicrystalline polymers were revealed. It was demonstrated that chevron folding is a common deformation mode which can appear in real, i.e. globally unoriented or partially oriented samples, in areas where the lamellar stacks are oriented perpendicular to the deformation direction. Similarities with the behaviour of other layered systems were found. The mechanism of chevron formation is discussed in the light of the fundamental statements of the folding theories and is related to the specific microstructure of the polymers. The effect of boundary conditions, deformation temperature and macroscopic strain on the characteristics of the chevron structure is described.     

Deformation and entanglement in semicrystalline polymers

Transmission electron microscopy (TEM) of amorphous and semicrystalline isotactic polystyrene (iPS) thin films deformed well below T _g, suggests the same crazing mechanism to operate in both cases. Therefore, by analogy with the amorphous case, highly entangled semicrystalline polymers, such as poly(ether ether ketone) (PEEK) should craze less readily in the glassy-semicrystalline state than iPS, which has a low degree of entanglement. Since this is confirmed by observation, it is reasonable to extend this analogy, and invoke entanglement in order to account for the high fracture resistance of highly entangled semicrystalline polymers, such as polyoxymethylene, using models previously applied to glassy amorphous polymers. There are nevertheless often significant decreases in fracture toughness in polyoxymethylene as the crystallization temperature is raised and/or the molecular weight is reduced, which we attribute to entanglement loss during lamellar folding.     

Distinction between two molecular mechanisms for deformation of glassy amorphous polymers

During deformation of glassy amorphous polymers the rotation of rigid chain segments around skeletal bonds is restricted simultaneously by configurational (intramolecular) and chain-chain (intermolecular) energy barriers. These barriers are modeled in a self-consistent manner for six polymers by use of an approximate analytical treatment. The comparative contribution of these barriers to the small-strain modulus of the bulk solid is used as a basis for distinguishing between two mechanisms of stiffening. With polycarbonate, polyphenylene oxide, and an aromatic polyimide, in which the rigid chain segment is relatively long, the modulus derives its value primarily from the resistance to displacements across chains due to intermolecular barriers. With vinyl polymers such as polystyrene, poly(vinyl chloride) and poly(methyl methacrylate), however, in which the rigid chain segment is short, resistance to displacements along the main chain due to intramolecular barriers contributes equally significantly to the modulus. Our calculations also show that the length of the rigid chain segment, acting as a mechanical moment arm, affects the resistance to intramolecular displacements much more than does the height of the rotational energy barrier.     

Microdeformational behavior of oriented semicrystalline polymers

A new experimental approach to the evaluation of microdeformational properties on the supermolecular level of highly oriented semicrystalline polymer is proposed. It is based on small-angle x-ray scattering measurements in situ during elastic and plastic tensile deformation of oriented samples along the orientation axes. The main idea of this approach consists of consideration of the competition of two processes occurring in uniaxial deformation: (1) intrafibrillar deformation of long periods; (2) mutual interfibrillar slip. A quantitative experimental criterion of inhomogeneity of intrafibrillar deformation is introduced. The combination of inhomogeneous fibril deformation and interfibrillar slip can explain all kinds of relationships between micro- (long period) and macrodeformations. The proposed approach was tested for several highly oriented polymer films and fibers.     

The stress tensor in entangled polymers

In entangled polymeric liquids, a subchain connecting two entanglements is an open system which can exchange particles (Kuhn segments) with its neighboring subchains along the polymer chain. We present a calculation of the subchain mechanical behavior as determined from the grand canonical formalism of statistical mechanics, with different subchains in the same chain sharing the same chemical potential. It is shown that the linear monomer density is a constant, as originally inferred by Doi and Edwards, but the tension is generally different from one subchain to another. Accounting for the latter effect leads to a new tensorial strain measure, somewhat different from that proposed by Doi and Edwards.     

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.     

Melt fracture of entangled polymers*

We construct a model for a slippage plane in a sheared melt, based on a balance between reptation bridging and shear debonding. The resulting state could show up at rather low shear rates and be locally stable. But it is not easy to nucleate: the conventional entangled state is also locally stable. We propose that slippage occurs on solid walls: either at the container surface, or on dust particles floating in the melt. Slippage at solid/melt interfaces was studied (experimentally and theoretically) long ago. There is a critical stress for slippage: our estimate (for strong adsorption of melt chains on the solid) gives (plateau modulus) for typical cases. Thus, melt fracture is expected at moderate stresses, in agreement with observations by S.Q. Wang and coworkers.     

Theoretical approaches to the mechanical relaxation mechanisms in semicrystalline polymers

Two kinds of relaxation mechanisms in semicrystalline polymers, i.e., the primary relaxation mechanism attributed to the noncrystalline phase and the crystalline relaxation mechanism attributed to the crystalline phase, are explained, respectively, in terms of (1) a modified Bueche's model of a one-dimensional vibrating string taking higher-order potential effects into account and (2) Montroll's model of a plane lattice in the form of a vibrating membrane. The modified Bueche's theory of a one-dimensional vibrating string gives a slope in the wedge portion of the relaxation time spectrum of less than – 1/2, when one assumes that the force constants of higher-order potential effects of intra- and intermolecular interaction are negative. The plane lattice model of a membrane vibrating in a lateral as well as in a longitudinal fashion gives a box-type relaxation time spectra over almost the same relaxation time range.     

Morphology of amorphous polymers

It has been suggested that amorphous polymers consist of small domains (30 to 100 A) in which there is local ordering or alignment of neighboring segments. Although free volume remains the primary physical parameter useful in characterizing the properties of amorphous polymers (as percent crystallinity for crystalline polymers), the distribution of the free volume, as determined by the size, interconnection, internal order, etc. of the domains is proposed to also be of importance. The paper reviews electron microscope and electron diffraction evidence for the presence of the domain structure, while also pointing out significant remaining problems.     

Hypersonic relaxation in amorphous polymers

In order to more fully understand the viscoelastic properties of amorphous polymers, it is desireable to have dynamic mechanical data over as wide a range in frequency as possible. One useful technique for studying the high-frequency behavior of polymers is to measure the velocity and attenuation of sound waves in the polymer fluid. When the frequency exceeds 109Hz. the sound waves are called hypersonic acoustic phonons. The present review examines the dynamic data obtained in the GHz frequency range for amorphous polymers.     

Stress relaxation in entangled melts of unlinked ring polymers

Stress relaxation in unlinked ring polymer melts poses an important challenge to our theoretical understanding of entangled polymer dynamics. Recent experiments on entangled unlinked ring melts show power-law stress relaxation with no hint of a rubbery plateau, usually the hallmark of entangled polymers. Here we present a theory for stress relaxation in rings analogous to the successful approach for star polymers. We augment our theory with mesoscale Monte Carlo dynamics simulations of equivalent "lattice animal" configurations. We find a stress relaxation function G(t)～t(-α) with α≈1/2 consistent with experiment, emerging ultimately from the disparate relaxation times of more- and less-central portions of ring conformations.     

Analytic expressions for the statistics of the primitive-path length in entangled polymers

An analytic expression is proposed for the primitive-path length of entangled polymer chains. The expression is derived from statistical mechanics of a chain that is a random walk with randomly scattered entanglements. The only parameters are the number of Kuhn steps in the chain and a dimensionless parameter beta that contains information about the entanglement density and Kuhn step size. The expression is found to compare very favorably with numerical results recently found from examining topological constraints in microscopic simulations. The comparison also predicts well the plateau modulus of polyethylene, suggesting that the slip-link model is a viable intermediate in the search for true ab initio rheology predictions. Since the expression is analytic, it can be used to make predictions where the simulations cannot reach, and hence is applicable for coarse graining.     

Tight and loose shapes in flat entangled dense polymers

We investigate the effects of topological constraints (entanglements) on two-dimensional polymer loops in the dense phase, and at the collapse transition ( -point). Previous studies have shown that in the dilute phase the entangled region becomes tight, and is thus localised on a small portion of the polymer. We find that the entropic force favouring tightness is considerably weaker in dense polymers. While the simple figure-eight structure, created by a single crossing in the polymer loop, localises weakly, the trefoil knot and all other prime knots are loosely spread out over the entire chain. In both the dense and conditions, the uncontracted-knot configuration is the most likely shape within a scaling analysis. By contrast, a strongly localised figure-eight is the most likely shape for dilute prime knots. Our findings are compared to recent simulations.Received: 7 October 2003, Published online: 21 November 2003PACS: 87.15.-v Biomolecules: structure and physical properties - 82.35.-x Polymers: properties; reactions; polymerization - 02.10.Kn Knot theory     

Effects of constrained chain conformations on polymer-solute interactions in semicrystalline polymers

The chemical potential of a solute in a solid polymer includes contributions from solute-polymer chain conformations, Flory-Huggins type interaction, and elastic energy of swelling. Presence of impermeable and rigid crystallites in such systems is expected to affect all these contributions. Theoretical calculations have been performed to check the direct effects of constrained chain conformations in the amorphous domains in semicrystalline polymers. Experimental results are used to determine Flory-Huggins coefficient and elastic modulus. From all these, the primary effects are shown to be on the entropic part of the Flory-Huggins coefficient and an increase in the elastic modulus by one or two order of magnitude. Finally, these results are used to calculate the rates of solvent-induced crystallization to show that these rates can drop to negligible values as the amount of crystals formed rises. Thus, the actual degree of crystallization can lie well below the Flory-Yoon limit.