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THE AMORPHOUS STATE. Reporter: Zhao Xiaopeng. Amorphous polymers do not contain any crystalline regions, “crystalline” polymers generally are only semicrystalline , containing appreciable amounts of amorphous material. When a crystalline polymer is melted, the melt is amorphous.
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THE AMORPHOUS STATE Reporter: Zhao Xiaopeng
Amorphous polymers do not contain any crystalline regions, “crystalline” polymers generally are only semicrystalline, containing appreciable amounts of amorphous material. When a crystalline polymer is melted, the melt is amorphous. Depending on temperature and structure, amorphous polymers exhibit widely different physical and mechanical behavior patterns. THE AMORPHOUS POLYMER STATE
At low temperatures, amorphous polymers are glassy, hard, and brittle. As the temperature is raised, they go through the glass–rubber transition. Tg is defined as the glass transition temperature. Above Tg, cross-linked amorphous polymers exhibit rubber elasticity.
THE AMORPHOUS POLYMER STATE • EXPERIMENTAL EVIDENCE REGARDING AMORPHOUS POLYMERS • CONFORMATION OF THE POLYMER CHAIN • MACROMOLECULAR DYNAMICS • CONCLUDING REMARKS
THE AMORPHOUS POLYMER STATE • Solids and Liquids • Possible Residual Order in Amorphous Polymers?
Solids and Liquids • An amorphous polymer does not exhibit a crystalline X-ray diffraction pattern, and it does not have a first-order melting transition. • The older literature often referred to the amorphous state as a liquid state.Water is a noncrystalline (amorphous) condensed substance and is surely a liquid. • Polymers such as polystyrene or poly(methyl methacrylate)at room temperature are glassy, taking months or years for significant creep or flow. • Today, amorphous polymers in the glassy state are better called amorphous solids.
Possible Residual Order in Amorphous Polymers? • A pot of spaghetti, where the spaghetti strands weave randomly in and out among each other. • The model would be better if the strands of spaghetti were much longer, because by ratio of length to diameter. • One group of experiments finds relative positions of adjacent strands have short regions where they appear to lie more or less parallel. • Our knowledge of the amorphous state remains very incomplete, and this area of polymer science are the subjects of intensive research at this time.
EXPERIMENTAL EVIDENCE REGARDING AMORPHOUS POLYMERS • Short-Range Interactions in Amorphous Polymers • Long-Range Interactions in Amorphous Polymers
Methods that measure short-range interactions can be divided into two groups
One of the most powerful experimental methods of determining short-range order in polymers utilizes birefringence • n1 and n2 are the refractive indexes for light polarized in two directions 90° apart. • If a polymer sample is stretched, n1 and n2 are taken as the refractive indexes for light polarized parallel and perpendicular to the stretching direction.
Long-Range Interactions in Amorphous Polymers • Small-Angle Neutron Scattering • Electron and X-Ray Diffraction • General Properties
Small-Angle Neutron Scattering(SANS) • For small-angle neutron scattering, the weight-average molecular weight, Mw, and the z-average radius of gyration, Rg, may be determined
The quantity P(θ) is the scattering form factor • R(θ) is the scattering intensity known as the “Rayleigh ratio” • W represents the sample-detector distance • Vs is the scattering volume • Iθ/I0is the ratio of scattered radiation intensity to the initial intensity
From data such as presented in Figure, both Rg and Mw may be calculated.
Electron and X-Ray Diffraction • Under various conditions, crystalline substances diffract X-rays and electrons to give spots or rings. • According to Bragg’s law, these can be interpreted as interplanarspacings. • Amorphous materials, including ordinary liquids, also diffract X-rays and electrons, but the diffraction is much more diffuse, sometimes called halos.
Electron and X-Ray Diffraction • For low-molecular-weight liquids, the diffuse halos have long been interpreted to mean that the nearest-neighbor spacings are slightly irregular and that after two or three molecular spacings all sense of order is lost. • The situation is complicated in the case of polymers because of the presence of long chains. • Questions to be resolved center about whether or not chains lie parallel for some distance, and if so, to what extent.
Electron and X-Ray Diffraction • X-ray diffraction studies are frequently called wide-angle X-ray scattering, or WAXS. • The first scattering maximum indicates the chain spacing distance. • The diffracted intensity is plotted in the y-axis multiplied by the quantity s.
In analyzing WAXS data, the two different molecular directions must be borne in mind. • (a) conformational orientation in the axial direction, which is a measure of how ordered or straight a given chain might be. • (b) organization in the radial direction, which is a direct measure of intermolecular order. • WAXS measures both parameters.
General Properties • For many common polymers the density of the amorphous phase is approximately 0.85 to 0.95 that of the crystalline phase • Using computer simulation of polymer molecular packing, scientists studied the relative alignment of polyethylene chains expected from certain models. • They calculated the angle between pairs of chains (from the center of one bond to the center of the next), which showed a small but clear tendency toward alignment between closely situated molecular segments. • However, no long-range order was observed.
CONFORMATION OF THE POLYMER CHAIN • One of the great classic problems in polymer science has been the determination of the conformation of the polymer chain in space. • The detailed arrangement in space must be determined by other experiments and, in particular, by modeling. • The resulting models are important in deriving equations for viscosity, diffusion, rubbery elasticity, and mechanical behavior.
The Freely Jointed Chain • n links • each of length l • linear sequence • no restrictions on the angles
Kuhn Segments • The Kuhn segment length is the basic scale for specifying the size of a chain segment providing a quantitative basis for evaluating the axial correlation length • The Kuhn segment length, b, depends on the chain’s end-to-end distance under Flory θ-conditions, or its equivalent in the unoriented, amorphous bulk state, rθ，where L represents the chain contour length
The Random Coil • The term “random coil” is often used to describe the unperturbed shape of the polymer chains in both dilute solutions and in the bulk amorphous state. • There is a distribution in end-to-end distances for random coils, even of the same molecular weight. • The distribution of end-to-end distances can be treated by Gaussian distribution functions(see Chapter 9). • The most important result is that, for relaxed random coils, there is a well-defined maximum in the frequency of the end-to-end distances, this distance is designated as r0.
Models of Polymer Chains in the Bulk Amorphous State • The earliest models included both rods and bedspring-like coils. • X-ray and mechanical studies led to the development of the random coil model. • In this model the polymer chains are permitted to wander about in a space-filling way as long as they do not pass through themselves or another chain.
Models of Polymer Chains in the Bulk Amorphous State • There are some better-developed models. They range from the random coil model to the highly organized meander model. • Several of the models have taken an intermediate position of suggesting some type of tighter than random coiling. • The most important reasons why some polymer scientists are suggesting nonrandom chain conformations in the bulk state include the high amorphous/crystalline density ratio, and electron and X-ray diffraction studies, which suggest lateral order.
MACROMOLECULAR DYNAMICS • The Rouse–Bueche Theory • Reptation and Chain Motion • Nonlinear Chains • Experimental Methods of Determining Diffusion Coefficients
The Rouse–Bueche Theory • This theory begins with the notion that a polymer chain may be considered as a succession of equal submolecules. • Each long enough to obey the Gaussian distribution function, that is, they are random coils in their own right. • The Rouse –Bueche theory is useful especially below 1% concentration. • While it does not speak about the center-of-mass diffusional motions of the polymer chains, the theory is important because it serves as a precursor to the de Gennesreptationtheory,described next.
Reptation and Chain Motion • The de GennesReptation Theory • Fickian and Non-Fickian Diffusion
Pierre-Gilles de Gennes • Nobel Prize for Physics1991 • Methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers
The de GennesReptation Theory • The Rouse–Bueche theory was highly successful in establishing the idea that chain motion was responsible for creep, relaxation, and viscosity • Quantitative agreement with experiment was generally unsatisfactory
The de GennesReptation Theory • The snakelike motion is called reptation. • The chain is assumed to have certain “defects,” each with stored length b • When the defect crosses mer B, it is displaced by an amount b
The tubes are made up of the surrounding chains. • (a) Initial position. • ( b) The chain has moved to the right by reptation. • ( c) The chain has moved to the left, the extremity choosing another path.
Fickian and Non-Fickian Diffusion • D is the three-dimensional self-diffusion coefficient • X is the center-of-mass distance traversed in three dimensions • t represents the time
Fickian and Non-Fickian Diffusion • A simple case of Fickiandiffusion,noting the time to the one-half dependence. The reptation model of de Gennes supports the t1/2dependence • According to the scaling laws for interdiffusion at a polymer–polymer interface, the initial diffusion rate as the chain leaves the tube goes as t1/4, representing a case of non-Fickian diffusion.
Nonlinear Chains • The discussion above models the motion of linear chains in a tube. Physical entanglements define a tube of some 50 Å diameter. • This permits the easy passage of defects but effectively prevents sideways motion of the chain.
The basic diffusion steps for a branched polymer. • Note motion of mer C, which requires a fully retracted branch before it can take a step into a new topological environment
Two possibilities exist for translational motion in branched polymers. • First, one end may move forward, pulling the other end and the branch into the same tube. • This process is strongly resisted by the chains as it requires a considerable decrease in entropy to cause a substantial portion of a branch to lie parallel to the main chain in an adjacent tube. • Instead, it is energetically cheaper for an entangled branched-chain polymer to renew its conformation by retracting a branch so that it retraces its path along the confining tube to the position of the center mer. • Then it may extend outward again, adopting a new conformation at random
Experimental Methods of Determining Diffusion Coefficients • Two general methods exist for determining the translational diffusion coefficient, D, in polymer melts • (a) by measuring the broadening of concentration gradients as a function of time • (b) by measuring the translation of molecules directly using local probes such as NMR.
The slices are scanned in an IR microdensitometer to obtain the broadened concentration profile, from which D is evaluated.
The stars diffuse almost three orders of magnitude slower than linear polymer, illustrating the detriment that long side chains present to reptation.
CONCLUDING REMARKS • The amorphous state is defined as a condensed, noncrystalline state of matter, many polymers are amorphous under ordinary use conditions. • In the amorphous state the position of one chain segment relative to its neighbors is relatively disordered. • The chains are highly entangled with one another, with physical cross-links appearing at about every 600 backbone atoms. • While the amorphous polymer state is “liquid-like ” in the classical sense, if the polymer is glassy, a better term would be “amorphous solid,” since measurable flow takes years or centuries.
