Surface free energies polymer crystals

Fig. 5 Chain deposition on the side surface of a polymer crystal, a and ae are side-surface and end- (fold-) surface free energies, and b is the width of the chain (after [16])...

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. 

Polymer surfaces is a field of increasing interest to both basic and applied research (Eisenriegler, 1993). The aim of this section is to show that microhardness is directly related to surface free energy and, therefore, to the degree of polymer perfection at polymer surfaces and interfaces. Studies have revealed that the morphology (crystal thickness and size of the interlamellar regions) of the polymer nanostructure are the main factors determining the microhardness (Balta Calleja et al., 1997). (See also Section 4.2.3.) The hardness-derived parameter... 

Here oe( ,) is the fold-surface free energy for L = and Ahf is heat of fusion. <5 is a small constant, reflecting the fact that some finite supercooling is required for crystal growth (see Section III.E). Equation 5 can be used for the determination of accurate OeH for the parent polymer. 

According to the secondary nucleation theory, polymer crystals grow by deposition of layers of stems on the side surface of the lamella183 (see Figure 33). Each new layer needs to be nucleated ( secondary or surface nucleation), after which it spreads comparatively rapidly. The main barrier to secondary nucleation is the excess side surface free energy 2blo... 

For polymers manifesting the most common type of crystalline morphology (folded chain lamellae), the "equilibrium" values (asymptotic limits at infinite lamellar thickness) of Tm, of the heat of fusion per unit volume, and of the surface free energy of the lamellar folds, are all lowered relative to the homopolymer with increasing defect incorporation in the crystallites. By contrast, if chain defects are excluded completely from the lamellae, the equilibrium limits remain unchanged since the lamellae remain those of the homopolymer, but the values of these properties still decrease for actual specimens since the average lamella becomes thinner because of the interruption of crystallization by non-crystallizable defects along the chains. 

Silica exists in a broad variety of forms, in spite of its simple chemical formula. This diversity is particularly true for divided silicas, each form of which is characterized by a particular structure (crystalline or amorphous) and specific physicochemical surface properties. The variety results in a broad set of applications, such as chromatography, dehydration, polymer reinforcement, gelification of liquids, thermal isolation, liquid-crystal posting, fluidification of powders, and catalysts. The properties of these materials can of course be expected to be related to their surface chemistry and hence to their surface free energy and energetic homogeneity as well. This chapter examines the evolution of these different characteristics as a function not only of the nature of the silica (i.e., amorphous or crystalline), but also as a function of its mode of synthesis their evolution upon modification of the surface chemistry of the solids by chemical or heat treatment is also followed. 

An alternative possibility arises from considerations related to the development of crystalline structure in polyethylene [22], The main feature of this structure is the periodic folding of the polymer chains in the crystal. Theoretically this is explained within the context of the kinetics of crystal nucleation and growth from solution. According to Cormia, Price, and Turnbull [22], the fold-surface energy in polyethylene crystals is comparable to the end-interfacial energy of rodshaped nuclei. These surface free energies are of the order of 10 to... 

The temperature above which all crystalline order disappears is defined as the melting point of a crystalline polymer. This transition is related to the surface-free energy a, the specific crystal volume Vc, and the heat of fusion AH°° of an infinite large lamellar crystal involving an infinite large linear polymer molecule, by the following equation [288,289] ... 

Polymer crystallization follows a typical nucleation-growth mechanism. According to the classical nucleation theory [1-3], nucleation implies a size threshold for the growth of the crystaUine phase, which is a consequence of rate competition between the body free-energy gain and the surface free-energy penalty. Thus, in the free-energy landscape, crystallization can be described as... 

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