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Continuously curved chain

Figure 35 shows how the equilibrium transition curves of [(Ala-Gly-Pro)n]3Lys-Lys shift to higher temperatures with increasing chain length. The continuous curves represent the numerical fit to the experimental transition data. [Pg.193]

The chain overlap parameter has been very successful at superimposing the data from the systems without hydrophobic modification, producing the continuous curve. However, it is clear from Flynn s work that once the hydrophobes are introduced into the polymer the viscosity rapidly increases at lower values of the chain overlap parameter. Increasing the mole percentage of hydrophobes also increases the viscosity at lower values of the chain overlap parameter. The position and number of the hydrophobes on a chain are important in determining the structure that forms and the onset of the increase in viscosity. The addition of side chains to hydroxyethyl cellulose modifies the network modulus as a function of concentration. This is discussed further in Section 2.3.4. [Pg.208]

Figure 4.10 shows a plot of He as a function of f for different PE and paraffin samples crystallized from the melt. The calculated continuous curve was derived using b = 20 nm. The deviation of the experimental data from the calculated curve is due to the wide range of b values obtained (b = 6-26 nm), corresponding to the widely different structures examined (CEPE crystals, chain-folded lamellae, low-density (LD) PE and linear paraffins). Comparison of experimental and calculated He data for PE emphasizes the parallel increase in the b parameter derived from mechanical data (14-26 nm) and in determined thermodynamically (79-91 mJ m ) for a series of samples with different molecular weights (56000-307000) (Balta Calleja et al, 1990b) (see also Section 4.3). [Pg.95]

The area s can thus be used as a curvilinear coordinate to locate a point on the continuous curve. Therefore, the configuration of a Brownian chain is defined by the vectorial function r(s) (where r(s) is the continuous limit of r ). [Pg.47]

A continuous random chain can be considered as a curve defined by a vector function r(s) with 0 < s < S. However, it would not be right to conceive such a chain as a unidimensional object. In fact, a close relation exists between the dimensionality of a chain and the exponent v. [Pg.55]

In Edwards s theory (1966),12 the chains are represented by continuous curves. The interaction between chains is transformed so as to be replaced by an external random potential whose effect is mathematically equivalent. The chain behaviour in this external potential is studied in an approximate manner, and subsequently, the result is averaged over the set of potentials. [Pg.318]

As the distribution (P)qualiuii 168) gives the probability of a specific chain conformation with fj) = 0, n,. -, j n) ihis conformation > can be assumed as a discrete representation of the continuous curve fl(s), so that... [Pg.281]

A three-dimensional contour surface (0.15 fin A ) of nuclear distribution of lithium atoms is shown in Fig. 14.17. The probability density of lithium nuclei strictly distributes into the continuous curved one-dimensional chain along the [010] direction, which is consistent with the computational predictions by Morgan et al. [22] and Islam et al. [23]. Other atoms, Fe, P, and O remained to be localized at the initial positions even after MEM analysis. Given the two possible diffusion paths in Fig. 14.11, the microscopic reason of the diffusimi anisotropy can be the difference... [Pg.467]

Fig. 9a, b. Intra-chain pair density function radial distance a dotted curve result of bulk NPT Monte Carlo simulation of a 32-chain 24-mer (n-tetracosane) system at 450 K and 0.1 MPa dashed curve result from fast sampling of continuous unperturbed chains curves are neatly identical b dotted curve result from bulk NPT Monte Carlo simulation of a 10-chain 78-mer ( polyethylene ) system at 450 K and 0.1 MPa dashed curve result from fast sampling of continuous unperturbed chains... [Pg.263]

Fig. IOl Probability distribution of torsion angle idative to trans, (< > — 4>(t)). SoM curve, result of bulk NPT Monte Carlo simulation of a 32-drain 24-mer (n-tetiaoisane) syston at 450 K and 0.1 MPa. Dashed curve, result of Cast sanq>lii% rtf continuous unperturbed chains. Oirves are neaity idmtical... Fig. IOl Probability distribution of torsion angle idative to trans, (< > — 4>(t)). SoM curve, result of bulk NPT Monte Carlo simulation of a 32-drain 24-mer (n-tetiaoisane) syston at 450 K and 0.1 MPa. Dashed curve, result of Cast sanq>lii% rtf continuous unperturbed chains. Oirves are neaity idmtical...
The two PRISM predictions are shown in Fig. 1 la as dashed and dotted curves. We can see there that both PRISM predictions are almost indistinguishable from each other as a result of the to(r) from the bulk NPT simulation and from the continuous unperturbed chains being almost indistinguishable. However, both PRISM predictions are definitely distinguishable from the exact results from the NPT MC simulation. At small r, the PRISM prediction for g(r) rises more rapidly than the exact g(r), resulting in a bulging shape PRISM also underpredicts the first peak. [Pg.266]

Since (3.4b) gives the probability of a particular chain configuration To = 0, Fj,..., r , it is clear that this chain configuration r can be taken to be the discrete representation of the continuous curve r(j). Therefore let... [Pg.24]

Although the force constants for a vibration are the same for all erf the units of the chain, the frequency of a given vibration will depend upon its phase angle 0. A plot of the vibrational fr uent versus the ph e angle falls on a smooth, continuous curve over a limited frequency range, and is called the dispersion curve since it shows the dispersion of the frequency from all of the oscillators in phase to all of the oscillators exactly out of phase. [Pg.324]

The polymer chain is then treated as a continuous curve and space is dis-... [Pg.493]

We observe a plateau, characteristic for ideal chains, and then a rise at higher q s, for distances shorter than the persistence length where the microscopic chain structure takes over control. The peculiar shape of the curve in this range reflects specific properties of polycarbonate and indeed, these can be reproduced by calculations on the basis of the RIS model. The continuous curve represents the theoretical results, and even if the agreement is not perfect, it describes the main characteristics qualitatively correctly. [Pg.66]

A continuous lipidic cubic phase is obtained by mixing a long-chain lipid such as monoolein with a small amount of water. The result is a highly viscous state where the lipids are packed in curved continuous bilayers extending in three dimensions and which are interpenetrated by communicating aqueous channels. Crystallization of incorporated proteins starts inside the lipid phase and growth is achieved by lateral diffusion of the protein molecules to the nucleation sites. This system has recently been used to obtain three-dimensional crystals 20 x 20 x 8 pm in size of the membrane protein bacteriorhodopsin, which diffracted to 2 A resolution using a microfocus beam at the European Synchrotron Radiation Facility. [Pg.225]

In a poor solvent (cyclohexane at 5°C), a polymer chain takes on a condensed globular state because constituent molecules are repulsed by the solvent molecules. Nanofishing of this chain revealed a perfectly different force-extension curve, as shown in Figure 21.5. It was observed that constant force continued from about 30 to 130 nm after nonspecific adsorption between a... [Pg.585]


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Continuous curves

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