Excluded-volume parameter

The parameter a which we introduced in Sec. 1.11 to measure the expansion which arises from solvent being imbibed into the coil domain can also be used to describe the second virial coefficient and excluded volume. We shall see in Sec. 9.7 that the difference 1/2 - x is proportional to. When the fully... 

The excluded volume unfortunately does not reduce to a simple expression. According to Eq. (60), it depends first of all on the thermodynamic parameters as expressed through J it depends also on... 

In it the pressure P is found in terms of temperature T and volume per particle v. The interactions enter through two parameters uq, the excluded volume per particle, and a, the binding energy per particle at unity density in a bulk fluid. The equation of state arose as an extension of the ideal gas law,... 

In the classical theories of polyelectrolytes, the chain expansion is characterized by the electrostatic excluded volume parameter, zel with ... 

A theoretical investigation of the use of NMR lineshape second moments in determining elastomer chain configurations has been undertaken. Monte Carlo chains have been generated by computer using a modified rotational isomeric state (RIS) theory in which parameters have been included which simulate bulk uniaxial deformation. The behavior of the model for a hypothetical poly(methylene) system and for a real poly(p-fluorostyrene) system has been examined. Excluded volume effects are described. Initial experimental approaches are discussed. 

The strong point of molecular dynamic simulations is that, for the particular model, the results are (nearly) exact. In particular, the simulations take all necessary excluded-volume correlations into account. However, still it is not advisable to have blind confidence in the predictions of MD. The simulations typically treat the system classically, many parameters that together define the force field are subject to fine-tuning, and one always should be cautious about the statistical certainty. In passing, we will touch upon some more limitations when we discuss more details of MD simulation of lipid systems. We will not go into all the details here, because the use of MD simulation to study the lipid bilayer has recently been reviewed by other authors already [31,32]. Our idea is to present sufficient information to allow a critical evaluation of the method, and to set the stage for comparison with alternative approaches. 

Ky is the Flory-Huggins interaction parameter between the i and j monomers. In Eq. 6.6, the matrices have a dimension (m) (m). We note that the s-depen-dence of the excluded volume matrix is solely determined by the contribution of the bare susceptibility yoo(Q> ) he invisible matrix component 0 . Finally, combining Eq. 6.6 with Eq. 6.1 the response function in the interacting system is given by ... 

N is the total number of monomers, (p the polymer volume fraction and Pi and Pi/2 the form factors of the total copolymer and of the single blocks respectively. 12=Vd=Vh is the excluded volume interaction parameter which relates to the second virial coefficient A2=vN/ 2Mc). 

Fig. 3. Theoretical density profile of dendritic structures of generations 2-7 [12]. The radial volume fraction properly normalized to unity at the center of the molecule is plotted against the radial distance to the origin. All data has been calculated assuming a realistic excluded volume parameter of the segments of the dendrimer. Reproduced with permission from [12]...

The DNA-nucleosome interaction parameters are not known at present. In most of the theoretical work it is deemed negligible compared to the DNA-DNA and nucleosome-nucleosome interaction, except for a hard-core excluded volume interaction. Nevertheless, recent work on the mechanism of nucleosome repositioning [67] assumes that the DNA can dynamically detach from the nucleosome surface and reattach in different conformations, such that it is conceivable that distant DNA segments may also transiently bind to open regions of the DNA-binding surface of the nucleosome. 

This is certainly true of the simple properties, such as the molecular weight of a mixture. For the van der Waals equation of state, the parameter b stands for the excluded volume due to the molecule, which suggests that the linear additive relation, or the arithmetic mean, may be appropriate for an ideal mixture ... 

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