Hosemann

According to Hosemann-Bonart s model8), an oriented polymeric material consists of plate-like more or less curved folded lamellae extended mostly in the direction normal to that of the sample orientation so that the chain orientation in these crystalline formations coincides with the stretching direction. These lamellae are connected with each other by some amount of tie chains, but most chains emerge from the crystal bend and return to the same crystal-forming folds. If this model adequately describes the structure of oriented systems, the mechanical properties in the longitudinal direction are expected to be mainly determined by the number and properties of tie chains in the amorphous regions that are the weak spots of the oriented system (as compared to the crystallite)9). 

Hosemann R, Bagchi SN (1962) Direct analysis of diffraction by matter, North-Holland, Amsterdam... 

In the classical treatment of the paracrystal, Hosemann [5] refers to the quantity oc/dc as g-factor . 

Juggling with projections and slices results in the Guinier-DuMond equation [64] (Hosemann [5], p. 605-607 Guinier Fournet [65], p. 116-117)... 

Scattering and Disorder. For structure close to random disorder the SAXS frequently exhibits a broad shoulder that is alternatively called liquid scattering ([206] [86], p. 50) or long-period peak . Let us consider disordered, concentrated systems. A poor theory like the one of Porod [18] is not consistent with respect to disorder, as it divides the volume into equal lots before starting to model the process. He concludes that statistical population (of the lots) does not lead to correlation. Better is the theory of Hosemann [158,211], His distorted structure does not pre-define any lots, and consequently it is able to describe (discrete) liquid scattering. The problems of liquid scattering have been studied since the early days of statistical physics. To-date several approximations and some analytical solutions are known. Most frequently applied [201,212-216] is the Percus-Yevick [217] approximation of the Ornstein-Zernike integral equation. The approximation offers a simple descrip-... 

History. Starting from the ID point statistics of Zernike and Prins [116] J. J. Hermans [128] designs various ID statistics of black and white rods. He applies these models to the SAXS curves of cellulose. Polydispersity of rod lengths is introduced by distribution functions, / , (,r)108. Hermans describes the loss of correlation along the series of rods by a convolution polynomial . One of Hermans lattice statistics is namedparacrystalby Hosemann [5,117]. Hosemann shows that the field of distorted structure is concisely treated by the methods of complex analysis. A controversial subject is Hosemann s extension of ID statistics to 3D [63,131,227,228],... 

Figure 8.42. ID structural models with inherent loss of long-range order, (a) Paracrystalline lattice after HOSEMANN. The lattice constants (white rods) are decorated by centered placement of crystalline domains (black rods), (b) Lattice model with left-justified decoration, (c) Stacking model with formal equivalence of both phases (no decoration principle)... 

It is worth noting that in polymer structures the various kinds of long-range positional order of the equilibrium positions of the structural elements may be lost after not too big numbers of repetitions owing to the presence of lattice distortions (different from the thermal one), which have been called distortions of the second kind. According to Hosemann and Bagchi,171 these forms are called paracrystalline modifications. 

Hosemann, R. Bagchi, S. N. Direct Analysis of Diffraction by Matter. North-Holland, Amsterdam, 1962. 

Any homogeneously distorted two-dimensional coordination scheme should be based upon the distance correlation statistics between next neighbors at least. In the case of a two-dimensional lattice construction, this distance correlation principle has been used by Hosemann and coworkers [13] to generate micro-paracrystals of finite size with the help of a computer. The construction procedure (known as spiral-paracrystal ) terminates if a coordination point cannot be assigned to a lattice point. 

From these results, it is concluded that, in a fully reduced catalyst, FeAl204 is not present furthermore, the aluminum inside the iron particle is present as a phase that does not contain iron (e.g., A1203), and this phase must be clustered as inclusions 3 nm in size. These inclusions may well account for the strain observed by Hosemann et al. From the Mossbauer effect investigation then, the process schematically shown in Fig. 17 was suggested for the reduction of a singly promoted iron synthetic ammonia catalyst. Finally, these inclusions and their associated strain fields provide another mechanism for textural promoting (131). 

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