Lamellar height

The fold length or lamellar height can be increased by raising the crystallization temperature, as well as by increasing the pressure. The fold length for many polymers increases linearly with the reciprocal difference between the melting point and the crystallization temperature (see Figure... 

Figure 10-7. Illustration of the formation of primary P, secondary S, and tertiary T, nuclei. Growth in the -- - direction produces no new surfaces, but growth in the — direction does. Liam, Lamellar height L.v, lamellar length bo, lamellar thickness (approximately the same size as the molecular diameter). The nucleus forms in the Ls direction, and the crystal grows in all three directions by deposition of other molecules.

Thus, the critical theoretical lamellar height decreases with increasing supercooling (Tf, Tcrya). This has been observed for actual lamellar heights (Figure 10-9). 

Figure 10-9. Dependence of the lamellar height Liam on the reciprocal undercooling for poly(4-methyl pentene-1), poly(ethylene), and poly(oxymethylene) for experiments carried out in different solvents (after A. Nakajima and F. Hameda).

Consequently, the thermodynamic melting temperature Tm can be obtained by extrapolation from a plot of the melting temperature Tm against the number of monomeric units per lamella, that is, the lamellar height (Figure 10-13). 

Fiywv ()- 0. Mean lengths of the crystalline and amorphous portions of the lamellar height of polylethylene) as inferred from small-angle X-ray measurements carried out at different temperatures. All experiments were carried out on the same material (after K. V. Fulcher, D. S- Brown, and R. E. Wetioii). 

Most of the melting points reported in the literature do not apply to perfect crystals of infinitely long chains (T ) or even to perfect crystals of finite chains (T ). They are more often the melting points Tm of polymers of finite molecular weight, indefinite lamellar height, and containing defects, that is, not perfect crystals. 

If the degree of polymerization is sufficiently large, the lamellar height (also called the fold height [3]) at a given crystallization temperature is practically independent of the molar mass. On the other hand, the lamellar thickness for all semicrystalline polymers shows a considerable... 

The behavior of the internal energy, heat capacity, Euler characteristic, and its variance ( x ) x) ) the microemulsion-lamellar transition is shown in Fig. 12. Both U and (x) jump at the transition, and the heat capacity, and (x ) - (x) have a peak at the transition. The relative jump in the Euler characteristic is larger than the one in the internal energy. Also, the relative height of the peak in x ) - x) is bigger than in the heat capacity. Conclude both quantities x) and x ) - can be used to locate the phase transition in systems with internal surfaces. 

Unlike the bulk morphology, block copolymer thin films are often characterized by thickness-dependent highly oriented domains, as a result of surface and interfacial energy minimization [115,116]. For example, in the simplest composition-symmetric (ID lamellae) coil-coil thin films, the overall trend when t>Lo is for the lamellae to be oriented parallel to the plane of the film [115]. Under symmetric boundary conditions, frustration cannot be avoided if t is not commensurate with L0 in a confined film and the lamellar period deviates from the bulk value by compressing the chain conformation [117]. Under asymmetric boundary conditions, an incomplete top layer composed of islands and holes of height Lo forms as in the incommensurate case [118]. However, it has also been observed that microdomains can reorient such that they are perpendicular to the surface [ 119], or they can take mixed orientations to relieve the constraint [66]. 

In this situation, the equilibrium thickness at any given height h is determined by the balance between the hydrostatic pressure in the liquid (hpg) and the repulsive pressure in the film, that is n = hpg. Cyril Isenberg gives many beautiful pictures of soap films of different geometries in his book The Science of Soap Films and Soap Bubbles (1992). Sir Isaac Newton published his observations of the colours of soap bubbles in Opticks (1730). This experimental set-up has been used to measure the interaction force between surfactant surfaces, as a function of separation distance or film thickness. These forces are important in stabilizing surfactant lamellar phases and in cell-cell interactions, as well as in colloidal interactions generally. 

Fig. 21. Ziggurat-like structure obtained by SFM after annealing at 170 °C for one day a thin film of symmetric P(S-fo-MMA) diblock copolymer (Mw=57,000 g/mol). A step height of 29 1 nm corresponds to the lamellar periodicity. Reproduced from [261]...

Fig.25. Surface structures formed on mica upon adsorption of P(S-fc-4VP) 330-130 from chloroform [279]. The 2.5x2.5 pm2 height images were obtained by contact mode SFM. Depending on the solution concentration, the morphology developed from small islands on the left to lamellar morphology on the right. The solution concentrations are indicated above the micrographs. The drawing below illustrates the transition from the A dot-like to B stripe-like morphology caused by variation of the block-length ratio. Courtesy of P. Eibeck and M. Moller...

Fig. 31 Variation of the size of the elementary dendrimer cylinder as a function of generation number (G ). is the diameter and h the height of the cylinder (i.e. lamellar periodicity)...

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