Dynamic structure factor polymer solution

The dynamical properties of polymer molecules in solution have been investigated using MPC dynamics [75-77]. Polymer transport properties are strongly influenced by hydrodynamic interactions. These effects manifest themselves in both the center-of-mass diffusion coefficients and the dynamic structure factors of polymer molecules in solution. For example, if hydrodynamic interactions are neglected, the diffusion coefficient scales with the number of monomers as D Dq /Nb, where Do is the diffusion coefficient of a polymer bead and N), is the number of beads in the polymer. If hydrodynamic interactions are included, the diffusion coefficient adopts a Stokes-Einstein formD kltT/cnr NlJ2, where c is a factor that depends on the polymer chain model. This scaling has been confirmed in MPC simulations of the polymer dynamics [75]. 

For non-interacting, incompressible polymer systems the dynamic structure factors of Eq. (3) may be significantly simplified. The sums, which in Eq. (3) have to be carried out over all atoms or in the small Q limit over all monomers and solvent molecules in the sample, may be restricted to only one average chain yielding so-called form factors. With the exception of semi-dilute solutions in the following, we will always use this restriction. Thus, S(Q, t) and Sinc(Q, t) will be understood as dynamic structure factors of single chains. Under these circumstances the normalized, so-called macroscopic coherent cross section (scattering per unit volume) follows as... 

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

Recently a very detailed study on the single chain dynamic structure factor of short chain PIB (M =3870) melts was undertaken with the aim to identify the leading effects limiting the applicability of the Rouse model toward short length scales [217]. This study was later followed by experiments on PDMS (M =6460), a polymer that has very low rotational barriers [219]. Finally, in order to access directly the intrachain relaxation mechanism experiments comparing PDMS and PIB in solution were also carried out [186]. The structural parameters for both chains were virtually identical, Rg=19.2 (21.3 A). Also their characteristic ratios C =6.73 (6.19) are very similar, i.e. the polymers have nearly equal contour length L and identical persistence lengths, thus their conformation are the same. The rotational barriers on the other hand are 3-3.5 kcal/mol for PIB and about 0.1 kcal/mol for PDMS. We first describe in some detail the study on the PIB melt compared with the PDMS melt and then discuss the results. 

On the other hand, Doi and Onuki (Doi and Onuki 1992) proposed both a dynamic structure factor S(q,t) and a time-dependent modulus G(t), considering the dynamic coupling between stress and composition in polymer solutions and blends ... 

Finally the book reaches properties that are determined by the collective properties of the dissolved polymers, including the dynamic structure factor, the polymer slow mode, the zero-shear viscosity, and linear and nonlinear viscoelasticity. Chapter 11 treats the dynamic structure factor S(q,t) of polymer solutions as... 

Depolarized light scattering spectroscopy was applied by Degiorgio, et al. to solutions of a fiuorinated latex polymer(10). The orientations of pairs of spheres are uncorrelated, so as discussed in Section 10.4 the VH spectrum is determined entirely by the self- part of the dynamic structure factor appropriate analysis of the VH spectrum determines both Ds and the rotational diffusion coefficient Dr. Degiorgio, et al. found that Ds(4>) and Dr(4>) are both accurately described, for... 

This chapter has considered measurements of the dynamic structure factor S q, t) of polymer solutions. Here behaviors of the first cumulant, the polymer slow mode, and the high-frequency Rayleigh-Brillouin spectrum have been considered. Neutron spin-echo methods as supplements to light scattering spectroscopy were noted. Results on Ki and the Rayleigh-Brillouin spectrum are readily summarized. The discussion of the slow mode is considerably more extended, but leads to a comparison with modem models for glass formation. 

M. Benmouna and A. Z. Akcasu. Temperature effects on the dynamic structure factor in dilute polymer solutions. Macromolecules, 11 (1978), 1187-1192. 

The dynamical structure factor S q,t) has been derived for various models, but no experimental attempts have been made to analyze the shape of S q,t) for polymer solutions in a good solvent. The... 

Fluorescence is also a powerful tool for investigating the structure and dynamics of matter or living systems at a molecular or supramolecular level. Polymers, solutions of surfactants, solid surfaces, biological membranes, proteins, nucleic acids and living cells are well-known examples of systems in which estimates of local parameters such as polarity, fluidity, order, molecular mobility and electrical potential is possible by means of fluorescent molecules playing the role of probes. The latter can be intrinsic or introduced on purpose. The high sensitivity of fluo-rimetric methods in conjunction with the specificity of the response of probes to their microenvironment contribute towards the success of this approach. Another factor is the ability of probes to provide information on dynamics of fast phenomena and/or the structural parameters of the system under study. 

There is a host of other intriguing phenomena associated with the structure and dynamics of stars, which we only list here. The inhomogeneous monomer density distribution in Fig. 2 is responsible for temperature and/or solvency variation in analogy to polymer brushes attached on a flat solid surface [198]. In fact, multiarm star solutions display a reversible thermoresponsive vitrification (see also Sect. 5) which, in contrast to polymer solutions, occurs upon heating rather than on cooling [199]. Another effect is the organization of multiarm stars in filaments induced by weak laser light due to action of electrostrictive forces [200]. This effect was recently attributed [201] to local concentration fluctuations which provide localized-intensity dependent refractive index variations. Hence, the structure factor speciflc to the particular material plays a crucial role in the pattern formation. 

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