The effect of crystallite shape on small-angle X-ray scattering

Gerasimov, V. I.; Genin, Ya.V.; Kitaigorodsky, Alexander I.; Tsvankin, D.Ya.

doi:10.1007/bf01507523

Cited by 34 publications

(26 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let a% be the structure parameter of the n-th lattice cell (p = 1 ..... K) and H(a%) the statistical function which gives the relative probability of the representation of a specific set of structure parameters in a given lattice. Then (6) where H= and H. are normalized.…”

Section: ~N(r) = E~n(r --Rn)mentioning

confidence: 99%

“…This procedure, however, requires thoroughly measured curves and the model seems to be relatively insensitive towards parameter variation. Tsvankin [3][4][5][6] developed a structure model basing on the concept of the linear paracrystalline lattice. Buchanan [7] modified this theory and described an evaluation method that has been widely applied in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…It should be noted that this procedure is relatively unproblematic for linear lattices. In case of a threedimensional lattice, however, only very special structures fulfill the relations (5) and (6).…”

mentioning

confidence: 97%

See 2 more Smart Citations

Analysis of the small-angle X-ray scattering of linear polyethylene by a paracrystalline lattice model

Brämer

Gerdes

Wenig

1983

Colloid & Polymer Sci

View full text Add to dashboard Cite

Three paracrystalline lattice models for the interpretation of the small angle scattering of polyethylene are discussed: The "lattice model", the "stapel model, (often referred to as the lamellar stack model) and the "proportional model". While the applicability of the first model is restricted, the latter models differ in the statistical assumptions of lamellar and interlamellar thickness distributions. The principal advantage of the proportional model over the stapel model is its applicability through the adjustment of only three parameters : long period, crystallinity and one statistical parameter. Small angle X-ray curves of linear polyethylene are interpreted by the proportional model. The results are in good agreement with stapel model calculations.

show abstract

Section: ~N(r) = E~n(r --Rn)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of the small-angle X-ray scattering of linear polyethylene by a paracrystalline lattice model

Brämer

Gerdes

Wenig

1983

Colloid & Polymer Sci

View full text Add to dashboard Cite

show abstract

“…Blundell (1969) generalized the one-dimensional model for arbitrary density variations within the crystalline regions. The effect of crystallite shape (quasi-one-dimensional model) was examined by Gerasimov, Genin, Kitaigorodskij & Tsvankin (1972). A critical review of onedimensional models is given by Crist (1973;Crist & Morosoff, 1973).…”

Section: Introductionmentioning

confidence: 99%

Investigation of the superstructure of polymers during deformation by synchrotron radiation

Wilke¹,

Bratrich²

1991

J Appl Cryst

View full text Add to dashboard Cite

Firstly a short review of some frequently used models for fibre structures is given. Then a model, based on a three-dimensional monoclinic paracrystalline macrolattice is described. This model allows the calculation of the two-dimensional intensity distribution for the small-angle scattering from semicrystalline polymers with different orientational states. The parameters of the model result from comparison with the measured intensity. The method of analysis is applied to low-density polyethylene deformed uniaxially at different temperatures. The use of synchrotron radiation makes it possible to follow the destruction and rebuilding of the superstructure. A reversible change of the superstructure during stretching and relaxing was found for different draw ratios for very high-molecular-weight polyethylene samples.

show abstract

“…The presence of equatorial scattering indicates that a detectable variation in electron denhas been associated with crystallites that exist in a form that more closely resembles a lamellae sity exists in the direction perpendicular to the fiber axis, while its incoherence implies that the structure than a fibrillar structure. 40 Consider now the coherent meridional scattering that ocdensity modulation is not regular or periodic in nature. Some researchers focused on extracting curs only in the drawn/heat-set filaments.…”

mentioning

confidence: 99%

Effect of initial take-up speed on properties and structure of as-spun and drawn/heat-set poly(ethylene terephthalate) filaments

Hotter

Cuculo

Tucker

et al. 1998

J. Appl. Polym. Sci.

View full text Add to dashboard Cite

ABSTRACT:The effect of initial take-up speed on the properties and structure of both as-spun and drawn/heat-set poly(ethylene terephthalate) filaments was characterized through measurements of birefringence, percent crystallinity, tensile properties, high temperature shrinkage, loss tangent temperature dependence, DSC melting behavior, and wide-angle (WAXS) and small-angle X-ray scattering (SAXS). While a steady trend toward improved as-spun filament orientation and tensile properties occurred with increasing initial take-up speed, the reduced drawability of these more structured precursor filaments resulted in corresponding drawn/heat-set filaments that were of relatively lower overall orientation and tensile strength. The observed trends in tenacity, initial modulus, and high temperature shrinkage of the drawn/heat-set filaments appeared to be well correlated with the extent and distribution of amorphous phase rigidity as perceived through inferences made from the loss tangent temperature dependence. The WAXS patterns of the drawn/heat-set samples indicated that these filaments all possess a well-developed and highly oriented crystalline structure. Application of a simple two phase model allowed the determination of an amorphous orientation factor, which for the drawn/heat-set filaments was generally found to decrease as the draw ratio imposed in order to achieve comparable levels of elongation to break decreased. The SAXS patterns of the drawn/heat-set filaments indicated that comparable long period spacings exist in all cases and that a transition from a four-point pattern to a two-point bar-shaped pattern occurred when the precursor filament possessed some significant amount of as-spun crystallinity.

show abstract

The effect of crystallite shape on small-angle X-ray scattering

Cited by 34 publications

References 4 publications

Analysis of the small-angle X-ray scattering of linear polyethylene by a paracrystalline lattice model

Analysis of the small-angle X-ray scattering of linear polyethylene by a paracrystalline lattice model

Investigation of the superstructure of polymers during deformation by synchrotron radiation

Effect of initial take-up speed on properties and structure of as-spun and drawn/heat-set poly(ethylene terephthalate) filaments

Contact Info

Product

Resources

About