Flexibility characterization

The chain flexibility characterized by the number of monomers in the statistical segment s is also reflected in the magnitude of phase transition (Fig. 3). At a constant charge fraction i = 0.012 and c = 0, the extent A and the critical value of %c decrease with decreasing flexibility. 

FIGURE 52 The dependence of conversion degree Q on polymer chain statistical flexibility, characterized by characteristic ratio C, for PUAr. 

Similar linear dependences for SP - OPD with various were obtained in Ref. [7] and they testify to molecular mobility level reduction at decrease and extrapolate to various (nonintegral) values at = 1.0. The comparison of these data with the Eq. (1.5) appreciation shows, that reduction is due to local order level enhancement and the condition = 1.0 is realized at values, differing from 2.0 (as it was supposed earlier in Ref [23]). This is defined by pol5miers sfructure quasiequilibrium state achievement, which can be described as follows [24]. Actually, tendency of thermodynamically nonequilibrium solid body, which is a glassy polymer, to equilibrium state is classified within the fimneworks of cluster model as local order level enhancement or (p j increase [24-26], However, this tendency is balanced by entropic essence straightening and tauting effect of polymeric medium macromolecules, that makes impossible the condition (p j= 1.0 attainment. At fully tauted macromolecular chains = 1.0)

polymer structure achieves its quasiequilibrium state at d various values depending on copolymer type, that is defined by their macromolecules different flexibility, characterized by parameter C. ... 

Let us note, that the chain flexibility, characterized by parameter C, in one form or another is included in all relationships, adduced above for estimation. Hence, for correct determination it is necessary to define the temperature dependence [18], whieh ean be estimated with the help of the equation [43] ... 

For the observed distinetions explanation it is necessary to point out, that the Eqs. (2.8) and (2.12) take into consideration only molecular characteristic, namely, maeromolecule flexibility, characterized by the value C. Although the Eq. (2.12) takes into account additionally topological factor (traditional macromolecular binary hooking network density v ), but this factor is also a function of [40, 42], The Eqs. (2.16) and (2.5) take into account, besides C, the structural organization of HDPE noncrystalline regions within the frameworks of cluster model of polymers amorphous state structure [5] or fractal analysis with the aid of the value [22], Hence, HDPE noncrystalline regions structure appreciation changes sharply the dependence DJJ). 

Such flexibility allows tliese materials to be stmcturally characterized and tlien assembled into a wide variety of configurations for furtlier experiments. 

The mechanical properties of rigid foams vary considerably from those of flexible foams. The tests used to characterize these two classes of foams are, therefore, quite different, and the properties of interest from an application standpoint are also quite different. In this discussion the ASTM definition of rigid and flexible foams given earlier is used. 

Compressive Behavior. The most kiformative data ki characterising the compressive behavior of a flexible foam are derived from the entire load-deflection curve of 0—75% deflection and its return to 0% deflection at the speed experienced ki the anticipated appHcation. Various methods have been reported (3,161,169—172) for relating the properties of flexible foams to desked behavior ki comfort cushioning. Other methods to characterize package cushioning have been reported. The most important variables affecting compressive behavior are polymer composition, density, and cell stmcture and size. 

If necessary, the fit can be improved by increasing the order of the polynomial part of Eq. (9-89), so that this approach provides a veiy flexible method of simulation of a cumulative-frequency distribution. The method can even be extended to J-shaped cui ves, which are characterized by a maximum frequency at x = 0 and decreasing frequency for increasing values of x, by considering the reflexion of the cui ve in the y axis to exist. The resulting single maximum cui ve can then be sampled correctly by Monte Carlo methods if the vertical scale is halved and only absolute values of x are considered. 

To extract the conformational properties of the molecule that is being studied, the conformational ensemble that was sampled and optimized must be analyzed. The analysis may focus on global properties, attempting to characterize features such as overall flexibility or to identify common trends in the conformation set. Alternatively, it may be used to identify a smaller subset of characteristic low energy conformations, which may be used to direct future drug development efforts. It should be stressed that the different conformational analysis tools can be applied to any collection of molecular conformations. These... 

Extensive use of the three-dimensional solubility parameters for predicting adhesion seems not to have been made, although its additional flexibility should make it successful over a wider range of conditions than the single-parameter approach. Some recent studies involving dental adhesion employed the method with success. Asmussen and Uno fl40 successfully correlated the shear bond strength of various dental adhesive resins, characterized in terms of their three-... 

Ultrafiltration utilizes membrane filters with small pore sizes ranging from O.OlS t to in order to collect small particles, to separate small particle sizes, or to obtain particle-free solutions for a variety of applications. Membrane filters are characterized by a smallness and uniformity of pore size difficult to achieve with cellulosic filters. They are further characterized by thinness, strength, flexibility, low absorption and adsorption, and a flat surface texture. These properties are useful for a variety of analytical procedures. In the analytical laboratory, ultrafiltration is especially useful for gravimetric analysis, optical microscopy, and X-ray fluorescence studies. 

A more complicated, but flexible, system has been reported by Blomberg et al. (46). Here, size exclusion chromatography (SEC), normal phase EC (NPLC) and GC were coupled for the characterization of restricted (according to size) and selected (according to polarity) fractions of long residues. The seemingly incompatible separation modes, i.e. SEC and NPLC, are coupled by using an on-line solvent-evaporation step. 

These types of behavior characterizes the many different plastics available (Table 7-1). Some tough at room temperature, are brittle at low temperatures. Others are tough and flexible at temperatures far below freezing but become soft and limp at moderately high temperatures. Still others are hard and rigid at normal temperatures but may be made flexible by copolymerization or adding plasticizers. 

Two approaches to the attainment of the oriented states of polymer solutions and melts can be distinguished. The first one consists in the orientational crystallization of flexible-chain polymers based on the fixation by subsequent crystallization of the chains obtained as a result of melt extension. This procedure ensures the formation of a highly oriented supramolecular structure in the crystallized material. The second approach is based on the use of solutions of rigid-chain polymers in which the transition to the liquid crystalline state occurs, due to a high anisometry of the macromolecules. This state is characterized by high one-dimensional chain orientation and, as a result, by the anisotropy of the main physical properties of the material. Only slight extensions are required to obtain highly oriented films and fibers from such solutions. 

As was shown by Floryl), starting from a certain concentration, it is impossible in principle (for purely geometric reasons) to fill a larger fraction of the volume with these chains when they are randomly arranged. This critical concentration depends on chain flexibility which Flory characterized by the fraction f of folded (gauche) isomers in a polymer molecule... 

Figure 4 (curve 1) shows that in the absence of extension the distribution function W(fi) lies in the range 0 < /S < 0.2 for relatively long chains. In other words, in the absence of external forces, crystallization of flexible-chain polymers always proceeds with the formation of FCC since in the unperturbed melt the values of /3 are lower than /3cr. For short chains, the function W(/3) is broader (at the same structural flexibility f) (Fig. 4, curve 2) and the chains are characterized by the values of > /3cr, i.e. they can crystallize with the formation of ECC. Hence, at the same crystallization temperature, a... 

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