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Rouse-Zimm dynamics

For flexible polymers the structural change due to intramolecular motions must be large enough for the light wave to detect the difference between the various molecular shapes. Only under these circumstances will intramolecular interference affect the lightscattering spectral distributions. An extreme example of this case, the Rouse-Zimm dynamic model of the Gaussian coil, is discussed in detail in Section 8.8. [Pg.177]

The depolarized scattering for the Rouse-Zimm dynamical model of flexible polymer chains (cf. Section 8.8) may also be calculated. Ono and Okano (1971) have performed this calculation for q = 0 (zero scattering angle) and find that the scattered light spectral density is a series of Lorentzians each with a relaxation time characteristic of one of the Rouse-Zimm model modes. However the contribution of each mode to the spectrum is equal. This behavior should be contrasted with that of the isotropic spectrum where the scattering spectrum is dominated by contributions from the longest wavelength modes. [Pg.192]

Some possible approximations have been considered by Cates [56], who concentrated attention on macromolecular entanglements, which play an important role in the description of the behaviour of block polymers [86-89]. Cates believes that the fact that the concept of polymer fractal neglects the effects of macromolecular entanglements is the main drawback of this theory. Nevertheless, Cates [56] introduced several simplifications that make it possible to ignore these effects for dilute solutions and relatively low molecular masses. However, in the opinion of Cates, even in the case of predominant influence of entanglements, theoretical interpretation of this phenomenon is impossible without preliminary investigation of the properties of the system in terms of Rouse-Zimm dynamics, which can serve as the basis for a more complex theory. It was assumed [56] that the effects of entanglement can be due to the substantially enhanced local friction of macromolecules. [Pg.307]

Rouse-Zimm dynamics in a good solvent. Derive the dependence of the relaxation time T on the chain length N, for a dilute polymer solution in a good solvent. [Pg.643]

Table 1. Dynamic structure factors for Rouse and Zimm dynamics... [Pg.16]

In contrast to -conditions a large number of NSE results have been published for polymers in dilute good solvents [16,110,115-120]. For this case the theoretical coherent dynamic structure factor of the Zimm model is not available. However, the experimental spectra are quite well described by that derived for -conditions. For example, see Fig. 42a and 42b, where the spectra S(Q, t)/S(Q,0) for the system PS/d-toluene at 373 K are shown as a function of time t and of the scaling variable (Oz(Q)t)2/3. As in Fig. 40a, the solid lines in Fig. 42a result from a common fit with a single adjustable parameter. No contribution of Rouse dynamics, leading to a dynamic structure factor of combined Rouse-Zimm relaxation (see Table 1), can be detected in the spectra. Obviously, the line shape of the spectra is not influenced by the quality of the solvent. As before, the characteristic frequencies 2(Q) follow the Q3-power law, which is... [Pg.81]

The theoretical prediction of these properties for branched molecules has to take into account the peculiar aspects of these chains. It is possible to obtain these properties as the low gradient Hmits of non-equilibrium averages, calculated from dynamic models. The basic approach to the dynamics of flexible chains is given by the Rouse or the Rouse-Zimm theories [12,13,15,21]. How-ever,both the friction coefficient and the intrinsic viscosity can also be evaluated from equilibrium averages that involve the forces acting on each one of the units. This description is known as the Kirkwood-Riseman (KR) theory [15,71 ]. Thus, the translational friction coefficient, fl, relates the force applied to the center of masses of the molecule and its velocity... [Pg.56]

The incorporation of non-Gaussian effects in the Rouse theory can only be accomplished in an approximate way. For instance, the optimized Rouse-Zimm local dynamics approach has been applied by Guenza et al. [55] for linear and star chains. They were able to obtain correlation times and results related to dynamic light scattering experiments as the dynamic structure factor and its first cumulant [88]. A similar approach has also been applied by Ganazzoli et al. [87] for viscosity calculations. They obtained the generalized ZK results for ratio g already discussed. [Pg.63]

It can also be verified that this formulation is entirely equivalent to the optimized Rouse-Zimm local dynamics approach [55]. [Pg.64]

The complex viscosity, i.e., the viscosity observed in the presence of an oscillatory shear rate, is a dynamic property that can be straightforwardly obtained from the Rouse, or Rouse-Zimm theory as the Fourier transform of the stress time-correlation function. Thus, these theories give [15]... [Pg.64]

A feature of theories for tree-like polymers is the disentanglement transition , which occurs when the tube dilation becomes faster than the arm-retraction within it. In fact this will happen even for simple star polymers, but very close to the terminal time itself when very little orientation remains in the polymers. In tree-like polymers, it is possible that several levels of molecule near the core are not effectively entangled, and instead relax via renormalised Rouse dynamics (in other words the criterion for dynamic dilution of Sect. 3.2.5 occurs before the topology of the tree becomes trivial). In extreme cases the cores may relax by Zimm dynamics, when the surroundings fail to screen even the hydro-dynamic interactions between the slowest sections of the molecules. [Pg.231]

Fig. 5.10 Chain dynamic structure factor of PDMS (a) and PIB (b) in toluene solution at 327 K at the Q-values 0.04 A" (empty circle), 0.06 A (filled circle), 0.08 A" (empty square), 0.10 A (filled square), 0,15 A (empty diamond), 0,20 A (filled diamond), 0,25 A (empty triangle), 0.30 A" (filled triangle), 0.40 A" (plus). Solid lines correspond to fitting curves Rouse-Zimm model for PDMS and Rouse-Zimm with intrachain viscosity for PIB (see the text). (Reprinted with permission from [186]. Copyright 2001 American Chemical Society)... Fig. 5.10 Chain dynamic structure factor of PDMS (a) and PIB (b) in toluene solution at 327 K at the Q-values 0.04 A" (empty circle), 0.06 A (filled circle), 0.08 A" (empty square), 0.10 A (filled square), 0,15 A (empty diamond), 0,20 A (filled diamond), 0,25 A (empty triangle), 0.30 A" (filled triangle), 0.40 A" (plus). Solid lines correspond to fitting curves Rouse-Zimm model for PDMS and Rouse-Zimm with intrachain viscosity for PIB (see the text). (Reprinted with permission from [186]. Copyright 2001 American Chemical Society)...
Only recently has the theory of chain dynamics been extended by Peterlin (J [) and by Fixman (12) to encompass the known non-Newtonian intrinsic viscosity ofTlexible polymers. This theory, which is an extension of the Rouse-Zimm bead-and-spring model but which includes excluded volume effects, is much more complex than that for undeformable ellipsoids, and approximations are needed to make the problem tractable. Nevertheless, this theory agrees remarkably well (J2) with observations on polystyrene, which is surely a flexible chain. In particular, the theory predicts quite well the characteristic shear stress at which the intrinsic viscosity of polystyrene begins to drop from its low-shear Newtonian plateau. [Pg.20]

In the Rouse-Zimm bead spring model of polymer solution dynamics, the long-range global motions are associated with a broad spectrum of relaxation times given by equation (10) and where tj is the relaxation time of the h such normal mode of the chain... [Pg.184]

Several works have been devoted to the theoretical studies of the equilibrium and dynamic properties of dendrimers [13,33,176-184). These studies were complemented by computer simulations [ 185-191 ]. In most studies trifunctional dendrimers were considered (the fimctionality of the branching points was taken to be three, / = 3). The reason for this is two-fold. First, / = 3 holds for polyamidoamine [172] and polyether [173] dendrimers, which were extensively studied experimentally. Second, the number of monomers in a dendrimer increases exponentially with the generation number g, and, for a given g the increase depends on /. Therefore, larger / mean much larger dendritic systems at the same g. This leads to larger connectivity matrices within the GGS (Rouse-Zimm) formahsm and to more densely packed structures when Monte Carlo or molecular dynamics simulations are used. [Pg.242]

Just as the Gaussian chain is the basic paradigm of the statistics of polymer solutions, so is its extension to the bead-spring model still basic to current work in the held of polymer dynamics. The two limiting cases of free draining (no hydrodynamic interaction between beads, characterized by the draining parameter A = 0) and non-free draining (dominant hydrodynamic interaction, A= CO, due to Rouse and Zimm, respectively, are sufficiently familiar that the approach is often known as the Rouse-Zimm model. ... [Pg.230]

Chapter 1 introduces basic elements of polymer physics (interactions and force fields for describing polymer systems, conformational statistics of polymer chains, Flory mixing thermodynamics. Rouse, Zimm, and reptation dynamics, glass transition, and crystallization). It provides a brief overview of equilibrium and nonequilibrium statistical mechanics (quantum and classical descriptions of material systems, dynamics, ergodicity, Liouville equation, equilibrium statistical ensembles and connections between them, calculation of pressure and chemical potential, fluctuation... [Pg.607]

The Rouse-Zimm Model Describes the Dynamics of Viscoelastic Fluids... [Pg.638]

Substituting the preaveraged result of the Oseen tensor and performing the normal mode analysis of the Zimm equation for the various Rouse modes, we can calculate the mean square displacement of the center-of-mass of the chain, mean square displacement of a labeled monomer, translational friction coefficient of the chain, and the relaxation times of the various Rouse modes with the Zimm dynamics (Doi and Edwards 1986). The main results of these calculations are the following. [Pg.188]

The above results are valid only if the time of measurement is longer than the characteristic time for the relaxation of the various Rouse modes of the Zimm chain. The longest relaxation time for a chain with the Zimm dynamics (corresponding to the Rouse mode p = 1), where the hydrodynamic interaction dominates, is called the Zimm time given by... [Pg.189]

The results of Equations 7.46, 7.48, and 7.50 for the Zimm dynamics are entirely consistent with the universal laws expected in Section 7.2.1 and are fully supported by experimental data in dilute solutions. If the hydrodynamic interaction among segments is suppressed in the Kirkwood-Riseman-Zimm equation, then the problem reduces to the Rouse dynamics and all results of Section 7.2.2 are recovered. [Pg.189]

Figure 7.4 In dilute solutions, intrachain hydrodynamic interaction dominates (Zimm dynamics). At higher polymer concentrations, chain interpenetration screens the hydrodynamic interaction, resulting in an apparent Rouse dynamics. Figure 7.4 In dilute solutions, intrachain hydrodynamic interaction dominates (Zimm dynamics). At higher polymer concentrations, chain interpenetration screens the hydrodynamic interaction, resulting in an apparent Rouse dynamics.
Ferry also made seminal measurements on dilute solutions, using a precision shear wave apparatus. The Rouse-Zimm theory of chain dynamics was explored in great detail. [Pg.66]

The theory of cyclization dynamics was first presented by Wileaski and Fixman [WF] (5). A number of curious features of the theory prompted detailed attention by Doi (11), by Perico and Cuniberti (12), and by others (13). The theory is developed in terms of the bead-and-spring Rouse-Zimm [RZ] model (14). Unrealistic in detail, this model is quite useful for describing low frequency, large flmq[>litude chain motions. The RZ model, figure 2, treats the chain as a series of n beads connected by (n-1)harmonic springs of root-mean-squared length b. [Pg.296]


See other pages where Rouse-Zimm dynamics is mentioned: [Pg.48]    [Pg.48]    [Pg.16]    [Pg.65]    [Pg.167]    [Pg.41]    [Pg.62]    [Pg.91]    [Pg.130]    [Pg.193]    [Pg.148]    [Pg.152]    [Pg.34]    [Pg.193]    [Pg.239]    [Pg.25]    [Pg.147]    [Pg.147]    [Pg.153]    [Pg.194]    [Pg.440]    [Pg.565]    [Pg.280]    [Pg.160]   
See also in sourсe #XX -- [ Pg.307 ]




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