Lateral surface free energy

Lamellar thickness Minimum stable thickness Thickness deviation l — lmin Surface area of the fold surface Width of a stem Thickness of a stem Fold surface free energy Lateral surface free energy... 

In the LH model a nucleus is formed and subsequently spreads by the addition and removal of complete stems, as shown in Fig. 3.8, where ae and a are the fold and lateral surface free energies, a and b are the width and depth of the chains. The probabilities of addition or removal are reflected in the appropriate rate constants using the following notation ... 

In section 3.6.3 we mentioned that in growth on a curved face the strain surface free energy os takes the role the lateral surface free energy tr played in the flat surface case, namely that of a barrier to the formation of the first stem. This analogy cannot be made since, in contrast to surface free energy is associated with the deposition of any stem. Therefore and because of its physical origin (the volume strain) it is closely linked with the free energy of fusion. This is... 

Let e > 0 be the energy gain per segment in the nucleus (in units of kT) and a be the lateral surface free energy per unit area. The free energy Fm>/t per chain in the nucleus of Fig. 11 is given by... 

Consider the cylinder sketched in Figure 1.9 with radius R and length L, where [Pg.19]

The lateral surface free energy a is a key parameter in polymer crystallization, and is normally derived from crystallization kinetics. In polydisperse polymers, where the supercooling dependence of growth rate is affected both by changing... 

One may attempt to derive the ideal shear strength So of the van der Waals solid normal to the chain axis from the value of the lateral surface free energy, a. This value is well known for common polymers such as PE or polystyrene (PS) (Hoffman et al, 1976) or else can be calculated from the Thomas-Stavely (1952) relationship a = /a Ahf)y, where a is the chain cross-section in the crystalline phase, Ahf is the heat of fusion, and y is a constant equal to 0.12. If one now assumes that a displacement between adjacent molecules by Si within the crystal is sufficient for lattice destruction then the ultimate transverse stress per chain will be given by So = cr/31. The values so obtained are shown in Table 2.1 for various polymers. In some cases (nylon, polyoxymethylene, polyoxyethylene (POE)) the agreement with experiment is fair. In the others, deviations are more evident. In order to understand better the discrepancy between the experimentally observed and the theoretically derived compressive strength one has to consider more thoroughly the micromorphology of polymer solids and the phenomena caused by the applied stress before lattice destruction occurs. 

Table 2.1. Comparison of calculated shear strength So and experimentally obtained hardness values for various polymers. The values for their respective unit cell cross-sections a and enthalpies of fusion Ahf are also given. Lateral surface free energy a — Ahf)y. The value of Sq depends on the choice of SI (see text). In this table SI I A has been chosen. (From Baltd Calleja, 1985.)...

From the above discussions, one may get the impression that molecular nucleation is quite appropriate to describe the rate-determining step of both primary crystal nucleation and crystal growth. Furthermore, the situation for molecular nucleation can be quite flexible. According to Eq. (3.10), the substrate for secondary molecular nucleation is not necessarily very smooth, because a terrace step crossing over the nuclei will not affect its lateral surface free energy much. Each event of molecular tiiicleation should be activated by a single macromolecule. Some other macromolecules can be involved in the same event of molecular nucleation and may act in a passive way. 

Lateral surface free energy, a Activation energy for reptation, 9.2-11.5 erg/ crrP 6276 J/mole 11-12 erg/cm ... 

From the several data obtained, Li et al. estimated the PCL/SAN-Flory interaction parameter (%), the PCL crystal surface free energy (a /(erg cm )) and the product GGg where G is the lateral surface free energy [80]. Values of x were approximately independent of SAN content up to 30 wt % with %=-0.33. Values of G and GGg, given in Table 9, decrease with increasing SAN content. The reductions in growth rate were consistent with a combination of reduced PCL concentration at the growth surface, an increase in viscosity of the amorphous material due to the... 

Table 9. Values of PCL crystal surface free energy (Og/Q cm )) and its product with o, the lateral surface free energy in blends of PCL with SAN data taken from [80]...

Crystallites are assumed to be sufficiently large in the direction transverse to the chain axis so that the contribution of the excess lateral surface free energy to Eq. (5.10) can be neglected. Equation (5.9) can be expressed as... 

Figure 8.12 shows the energy map for this process in more detail. The first step, the deposit of the first stem, occurs at rate Aq and involves the lateral surface free energy (IbLcffi) reduced by a fraction of the free energy of crystallization (ij/abL Ag). Note that in this case is defined as being positive for. The... 

It is assumed that the crystallite is sufficiently large in the directions normal to the chain axis so that the influences of the lateral surface free energies can be neglected. By expanding In l— equation (58) becomes... 

Where b is the layer thickness, a is lateral surface free energy, is the fold surface free energy, T[ is the equilibrium temperature, Ah is the enthalpy of fusion and k is Boltzmann s constant. 

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