Gas diffusion in partially crystalline polymers part I: Concentration dependence

In this work, a phenomenological model for the gas diffusion in partially crystalline polymers using differential effective medium theory is presented. By making an analogy with the power law known as Archie's law which relates the d.c. conductivity of a brine saturated porous rock to its porosity; we show that gas diffusion through semicrystalline polymers can be described in a similar way. It is assumed that the diffusion coefficient in the crystalline region is zero, while in the amorphous region it is given by a free volume model, and an effective diffusion coefficient D^eff, is obtained using the mentioned analogy. The variation of D^eff upon concentration is analyzed through its free volume dependence. The crystallinity dependence is considered through an average chain immobilization factor 〈β〉 which is explicitely derived. Finally, the results of this model are compared with experimental data given by Kreituss and Frisch, obtaining a good agreement. © 1996 John Wiley & Sons, Inc.     

Plastic yielding of partially crystalline polymers

Measurements are described of characteristic stress-strain properties in tension for several representative partially crystalline polymers prepared by cooling from the melt. Striking differences were found in the natural draw ratio, ranging from 2x to 11x. They are interpreted in terms of a simple molecular model of the yielding process in which polymer chains, folded to different degrees in the crystallites, are pulled taut. Values of yield and draw stress were found to be of the same order as the free energy U_m of melting, suggesting that yielding and drawing take place by stress-induced disruption of crystallites, analogous to melting. The mechanical work of drawing was similar to, but generally larger than, that required for melting, ranging from U_m to about 4U_m. The difference is attributed to strain energy of drawn material and possible recrystallization during drawing.     

Segmental mobility model for diffusion of gases in polymers

Diffusion of small molecules in polymers is described quantitatively in terms of segmental mobility processes. The diffusion coefficient depends on a diffusive jump length, which is characteristic of the polymer, and a jump frequency, which is equated to the segmental mobility rate. The presence of a particular solute increases mobility of the surrounding polymer segments by a predictable amount, which is related to the partial molar volume of the solute. The theory is fit to experimental diffusion data, and partial molar volumes are calculated from the fitting parameters. Good agreement with experimental partial molar volumes is obtained.     

Surface diffusion and relaxation of partially adsorbed polymers

We studied by lattice simulation the surface diffusion and relaxation of isolated, self‐avoiding polymers partially adsorbed onto a flat surface. The key parameters describing the system are the number of segments in the chain, N, the adsorption energy of a segment, expressed as a dimensionless surface temperature T_s, and the segmental friction factor on the surface relative to that in the bulk, ζ_s/ζ_b. The simulation data indicate Rouse scaling of the surface diffusion coefficient, D_∥, and in‐plane relaxation time, τ, versus N for all values of T_s and ζ_s/ζ_b studied. A simple application of the Rouse model to a partially adsorbed chain, which ignores fluctuations in adsorbed trains, yields a formula for D_∥ with the correct N‐scaling. It can account for the effects of T_s when ζ_s/ζ_b is finite (≲10), but it fails when ζ_s/ζ_b diverges, predicting no surface diffusion at all, whereas simulations indicate finite surface mobilities facilitated by a caterpillar‐like motion. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1146–1154, 2000     

The function of twinning during the deformation of partially crystalline polymers

Summary A crystallographic process calledc-twinning is proposed which enhances the understanding of the deformation-orientation behaviour of partially crystalline polymer systems. As has been shown with polyethylene it is able to explain some of the main features of the unaxial extension experiment without great difficulty, in cooperation with other known phenomena. The ability of performingc-twinning is supposed to be the reason for the possibility that a semicrystalline polymer may undergo large deformations.

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Zusammenfassung Es wird ein kristallographischer Prozeß vorgeschlagen, diec-Zwillingsbildung, der das Verständnis des Deformations-Orientierungsverhaltens teilkristalliner Polymersysteme vervollständigt.Am Beispiel des Polyäthylens wird gezeigt, wie er im Zusammenspiel mit bekannten Prozessen zwanglos einige der typischen Erscheinungen bei uniaxialer Dehnung erklärt.Es ist zu vermuten, daß die Möglichkeit derc-Zwillingsbildung bestimmend dafür ist, ob ein teilkristallines Polymersystem zu großen Deformationen fähig ist.

     

Direct evaluation of the electron density correlation function of partially crystalline polymers

A discussion of the general properties of the one-dimensional electron density correlation function K(z) of a partially crystalline polymer with lamellar structure shows that application of a graphical extrapolation procedure permits direct determination of the crystallinity, the specific inner surface, and the electron density difference η_c ? η_a. The procedure is based upon the occurrence of a straight section in the “self-correlation” range of K(z). Curved and nonparallel lamellae do not invalidate the concept. In the case of heterogeneous samples composed of partially crystalline and totally amorphous regions, some of the parameters of the experimentally obtained correlation function, as for example the invariant K(0), are affected and may lose their definiteness. Use of the method is demonstrated in a detailed discussion of the correlation functions measured for a sample of lowdensity polyethylene at 25 and 100°C.     

Effect of microheterogeneities on the diffusion of gases through glassy polymers

The diffusion of gases through glassy polymers is studied and the effective diffusion coefficient D^eff is represented as the result of the superposition of two fundamental mechanisms, namely slipping and hopping. D^eff is calculated by a two-point correlation method. Comparisons are made with experimental data of Meares for diffusion coefficients of Kr, O₂, He, and A in poly(vinyl acetate) in the glassy state. Good fits are obtained and yield significant parameters.     

On the procedure of constructing phase diagrams of partially crystalline polymer-liquid systems

The procedure of constructing phase diagrams of partially crystalline polymer-liquid systems, which is based on a difference in refraction indexes of a pure liquid and its solutions in partially crystalline and high-elasticity polymer was proposed.     

Liquid crystalline polymers

The suitabilities of thermo-optometry and differential scanning calorimetry for the characterization of certain copolyethers were compared. Under certain conditions, such polymers do not exhibit the endotherm signal corresponding to the solid/liquid crystalline transition in the DSC curves. Thermo-optometry provides evidence of these phase transitions into the liquid crystalline state, and is a very useful additional method.     

Effect of amorphous sequences on the longitudinal acoustic modes in partially crystalline polymers. I. Transfer matrix method

A novel theoretical scheme is developed which enables the determination of the LAM-like vibrations of polymer chains made up of crystalline and amorphous parts as they occur in partially crystalline structures. The boundary conditions effective at the junction points are formulated in terms of the compliances of the associated amorphous sequences. These compliances can be derived from their eigenfrequencies and eigenvectors in a disconnected state. The treatment uses a matrix formalism which can be extended to include bending and torsional motions in a general state of vibration of the crystalline stem. A first numerical example demonstrates that the LA mode of a crystalline stem can be strongly perturbed by the coupling to the adjacent amorphous sequences. Interpretation of frequencies and line shapes of observed LA modes should always include these coupling effects; their neglect can lead to considerable errors.     

Empirical relation for diffusion of gases in hydrocarbon polymers: Interpretation in terms of fractional free volume

An empirical relationship between the diffusion coefficients of gases in three polyethylenes and their diffusion coefficient in natural rubber is given. The diffusion coefficients are given within a relative error of 4.7%. This relationship is interpreted according to the fractional free volume theory. The ratios of the fractional free volumes in the polyethylenes to the fractional free volume in natural rubber are derived.     

State of radon in crystalline polymers

The state of radon in crystalline polymers, polyethylene and polypropylene, has been studied by methods of macro- and microauto-radiography. Radon-222 was introduced into the samples by diffusion from the gas phase at various temperatures and time intervals. Effects on the state of radon of such factors as density and polymer crystallinity, extent of macromolecular chain branching, spherulite radius, content of different admixtures, -ray photon irradiation dose or irradiation with accelerated electrons, etc., were investigated. In pure polymers, radon was found to be in an atomically dispersed state. Radon forms thermally stable accumulations at the surface as well as in the bulk of the material due to admixtures, gas bubbles and crazes. The probable effect of radon's tendency to form accumulations on the kinetics of its diffusion in crystalline polymers is discussed.     

Ciliation and lamellae in crystalline polymers

Molecular cilia, the uncrystallized portions of chains already partly attached to polymer crystals, exert a profound influence on the course of polymeric crystallization with ultimate responsibility for the divergence of adjacent lamellae which leads to spherulitic growth. Their effective size and pressure have been measured, in α-polypropylene, from electron microscopic measurements of the separation and maximum curvature of lamellae in row structures. That cilia exist and extend the effective region occupied by a lamella beyond the geometrical confines of its fold surfaces is important for crystallization theory and may well have implications for the connection of lamellae into networks and for gelation.     

Advances in liquid crystalline conjugated polymers

We review advances in liquid crystalline (LC) conjugated polymers by focusing on (i) ferroelectric and (ii) photoresponsive LC conjugated polymers. In Part 1, LC polyphenylene derivatives were synthesized through substitution of fluorine‐containing chiral LC groups into side chains. Poly(para‐phenylene) [ P1 ] and poly(meta‐phenylene) [ P2 ] derivatives showed chiral smectic C phases responsible for ferroelectricity. They exhibited quick response to electric field, giving switching times of <1 s between two bistable states. The spontaneous polarization (P_S) of P2 remained unchanged even after the electric field became zero, affording the residual polarization (P_R) whose value was the same as that of P_S. This indicates that P2 has a potential memory function based on FLC nature. In Part 2, poly(para‐phenylenevinylene) [ P5 ] and poly(bithienylene‐phenylene) [ P6 ] derivatives were synthesized by introducing dithienylethene moieties into side chains. Drastic quenching of fluorescence occurred when the photoresponsive moiety changed from an open form to a closed one upon an irradiation of ultraviolet light. The quenched fluorescence was recovered through a photoisomerization from the closed form to the open one. Macroscopically aligned P6 film exhibited a linearly polarized fluorescence with significant anisotropy. Reversible quenching and emitting behavior in anisotropic fluorescence was controlled by the photochemical switching. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2463–2485, 2009     

Influence of local chain dynamics on diffusion of gases in polymers as determined by pulsed field gradient NMR

Diffusion of gases in polymers below the glass transition temperature, T_g, is strongly modulated by local chain dynamics. For this reason, an analysis of pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements considering the viscoelastic behavior of polymers is proposed. Carbon‐13 PFG NMR measurements of [¹³C]O₂ diffusion in polymer films at 298 K are performed. Data obtained in polymers with T_g above (polycarbonate) and below (polyethylene) the temperature set for diffusion measurements are analyzed with a stretched exponential. The results show that the distribution of diffusion coefficients in amorphous phases below T_g is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below T_g requires long diffusion times, which suggests fluctuations of local chain density on a macroscopic scale may occur. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 231–235, 2010