Theory of neutron scattering from condensed matter
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...ntageous, P(k;t) = ∫ ddre−ik·r P(r;t), and P(k;t) is known as the (self-)intermediate scattering function [11,12]. It can be measured directly by neutron scattering employing the spin-echo technique [13] or, on larger length scales, by photon correlation spectroscopy [14]. The momentum transferred from the sample to the photon or neutron is then simply ~k. For the diffusion propagator, one readily ca...
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...Simple liquids at normal temperatures (well above Tg) have viscosities near 0.1 Pa s, values of the order of 1012 Pa s are achieved near Tg. This same effect can be induced by increasing the pressure. However, it is an experimental challenge to measure the viscosity over several decades under elevated pressure, and thus different measurement techniques are used. Figure 1 illustrates most of the techniques for high-pressure viscosity measurements; all have some limitations with respect to both pressure and viscosity range. Using a falling body viscometer, Bridgman (1926) was the first to measure precise viscosities at pressures of up to 1.2 GPa. In this type of viscometer, the liquid and a cylindrical weight are enclosed in a cylinder, with an attached bellows to transmit the pressure. The entire apparatus is mounted inside a high-pressure chamber, with pressure generated by a hydraulic press. The viscosity is determined from the descent under gravity of the weight in the liquid, with the range of measurable η only about three decades. To extend this range, Bridgman (1964) utilized a swinging vane apparatus which provided viscosities of up to about 105 Pa s at pressures of as high as 3 GPa....
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...Simple liquids at normal temperatures (well above Tg) have viscosities near 0.1 Pa s, values of the order of 1012 Pa s are achieved near Tg. This same effect can be induced by increasing the pressure. However, it is an experimental challenge to measure the viscosity over several decades under elevated pressure, and thus different measurement techniques are used. Figure 1 illustrates most of the techniques for high-pressure viscosity measurements; all have some limitations with respect to both pressure and viscosity range. Using a falling body viscometer, Bridgman (1926) was the first to measure precise viscosities at pressures of up to 1....
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...The short-range order (amorphous halo) may be enhanced by lower temperature, as reflected in a steeper and narrower peak S(Q). The peak also shifts to larger Q (closer packing) with decreasing T or increasing pressure (Alba-Simionseco et al 1998). The structure factor also depends on the interactions among atoms. For example, for a LJ liquid (figure 12), simulations reveal (Chandler and Weeks 1970) that the main features of S(Q) depend on the repulsive part of the potential, but not on the attractive part (which in any case is neglected in many simulations (Bernu et al 1987, Roux et al 1989, Nauroth and Kob 1997)). Experimental results for the S(Q) of OTP under high pressure were reported by Tölle (2001). By comparing the static structure factor measured under isothermal, isobaric, isochoric and isochronic (constant τ) conditions (figure 13), Tölle observed that for constant T or P ‘S(Q) evolves continuously, it is nearly identical along an isochore and an isochron’....
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...Some amber, formed by polymerization and vitrification of tree resin, is more than 300 million years old. Utilization of naturally-occurring glasses dates to the beginning of recorded history. For example, around 75 000 BC, tools were made from obsidian, a silica glass formed from quenched volcanic lava. The first synthetic glasses, silicate artifacts, appeared in Mesopotamia and Egypt, about 3500 years ago. However, glazed (vitreous) surfaces were produced as early as the 5th millennium BC. A verse in one of the oldest books of the bible (about 2000 BC) indicates the great value of vitreous material in antiquity: ‘Gold and glass cannot equal [wisdom]’ (Job 28:17, ASV). Modern glass-making is a highly developed technology, used to produce not only inorganic glasses but also metallic glasses and many plastics. It is a testament to the complexity of the process that despite such a long history, the factors governing vitrification are still vigorously investigated. Near the glass transition, viscosities become so large that the material behaves as a solid, yet retains the microscopic disorder of the liquid state. Small changes in thermodynamic conditions can alter the time scale for molecular motions from nanoseconds to a duration exceeding the human lifespan. Because of the complexity of the supercooled dynamics, theoretical efforts remain at the model-building stage and a quantitatively accurate theory of real materials is lacking. There are many routes to the glassy state: (i) thermal quenching at a rate sufficient to avoid crystallization; (ii) application of hydrostatic pressure; (iii) condensation of gas at low temperature (e.g. include the water in comets and the Mt Palomar mirror); (iv) solvent evaporation or sublimation; (v) irradiation of crystalline materials to disrupt the unit cell; (vi) using chemical methods, such as polymerization, hydrolysis of organosilicon compounds, or condensation of chemically reacted vapours (e.g. to produce fibre optics). Although theorists often ascribe vitrification to an underlying thermodynamic transition, from an experimental viewpoint the glass transition is a kinetic process, associated with departure from the equilibrium liquid structure, as the experimental time-scale becomes shorter than the characteristic time for the relevant molecular motions. Although this transition is accompanied by spectacular changes in physical properties (above Tg the material assumes the shape of its container, while the glass can serve as the container), there are no changes in the molecular configuration. Both the liquid and glassy states lack long-range order (no translational symmetry) and are distinguished by their dynamic, rather than static, properties. Historically, studies of the dynamics of molecules approaching the glassy state are focused on the effect of temperature, owing in part to experimental convenience. Isobaric measurements of relaxation times and viscosities are carried out as a function of temperature. (Previous studies relied on the less useful method of scanning temperature and measuring the response to a fixedfrequency perturbation.) While much has been learned from these studies, more groups have begun to exploit pressure as an experimental variable. This has led to important insights into glass formation in liquids and polymers. The earliest use of pressure to study the dynamics was probably the dielectric measurements of Gilchrist et al (1957) on propanol and glycerol at pressures as high as 100 MPa....
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...Hole model of Simha–Somcynsky. The model of Simha and Somcynsky (SS) (1969) is based on the cell model for polymers originally proposed by Prigogine and Mathot (1952)....
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