Dilute good solvent

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... 

At sufficiently high temperatures, the solvent is gbbd, with three regimes. There is a dilute good solvent regime at concentrations... 

Plot the size r of a labelled section of n consecutive Kuhn monomers of a chain for different regions of the diagram in Fig. 5.1. (i) Dilute -solvent (ii) semidilute -solvent (iii) dilute poor solvent (iv) two-phase region (v) concentrated poor solvent (vi) dilute good solvent (vii) semidilute good solvent (viii) concentrated good solvent. 

As noted above, in a dilute good solvent Rgj where Rg is independent of polymer concentration within the dilute concentration range. Using the subscript s for semidilute and d for dilute, the scaling law can be written... 

The first model that took into account excluded volume effects was the selfavoiding-walk (SAW), which was introduced about 60 years ago [65, 66]. Each monomer occupies a lattice site on a simple cubic lattice. The bond length between adjacent monomers is fixed by the lattice constant and the bond angles are restricted by the geometry of the lattice. This model is well-suited to describe generic polymers in dilute, good solvent conditions and exhibits the correct scaling behavior... 

Prepared by the dehydration of benzamide. Hydrolysed by dilute acids and alkalis to benzoic acid. Good solvent. benzopheDone,C]3HioO,PhC(0)Ph. Colourless rhombic prisms, m.p. 49 C, b.p. 306°C. Characteristic smell. It is prepared by the action of benzoyl chloride upon benzene in the presence of aluminium chloride (Friedel-Crafts reaction) or by the oxidation of di-phenylmethane. It is much used in perfumery. Forms a kelyl with sodium. 

Molecular weights of PVDC can be determined directly by dilute solution measurements in good solvents (62). Viscosity studies indicate that polymers having degrees of polymerization from 100 to more than 10,000 are easily obtained. Dimers and polymers having DP < 100 can be prepared by special procedures (40). Copolymers can be more easily studied because of thek solubiUty in common solvents. Gel-permeation chromatography studies indicate that molecular weight distributions are typical of vinyl copolymers. 

The adsorption transition also shows up in the behavior of the chain linear dimension. Fig. 6(a) shows the mean-square gyration radii parallel, i gl, and perpendicular, to the adsorbing plate. While these components do not differ from each other for e for e > ej i g strongly increases whereas Rh decreases. In the first case (non-adsorbed chain) oc oc N as a dilute solution in a good solvent in the bulk. For adsorbed chains R /N 0 for oo because the thickness is finite it is controlled by the distance e- e from the adsorption threshold, but does not diverge as N oo. The adsorbed chain follows in fact a... 

These core-shell type microspheres have very interesting structural features in that the cores are hardly crosslinked and the shell chains are fixed on the core surface with one end of the shell chains. The other end of the shell chains is free in good solvents for the shell chains. As the result of such a specific structure, the solubilities of the core-shell type polymer microspheres are governed by, not the core, but by the shell sequences, and the core-shell structures do not break even in the dilute solution [9,10]. 

Relationships between dilute solution viscosity and MW have been determined for many hyperbranched systems and the Mark-Houwink constant typically varies between 0.5 and 0.2, depending on the DB. In contrast, the exponent is typically in the region of 0.6-0.8 for linear homopolymers in a good solvent with a random coil conformation. The contraction factors [84], g=< g >branched/ <-Rg >iinear. =[ l]branched/[ l]iinear. are another Way of cxprcssing the compact structure of branched polymers. Experimentally, g is computed from the intrinsic viscosity ratio at constant MW. The contraction factor can be expressed as the averaged value over the MWD or as a continuous fraction of MW. 

In general, each molecule in a very dilute solution in a good solvent (low xi) will tend to exclude all others from the volume which it occupies. This leads to the concept of an excluded volume from which a given... 

Below a critical concentration, c, in a thermodynamically good solvent, r 0 can be standardised against the overlap parameter c [r)]. However, for c>c, and in the case of a 0-solvent for parameter c-[r ]>0.7, r 0 is a function of the Bueche parameter, cMw The critical concentration c is found to be Mw and solvent independent, as predicted by Graessley. In the case of semi-dilute polymer solutions the relaxation time and slope in the linear region of the flow are found to be strongly influenced by the nature of polymer-solvent interactions. Taking this into account, it is possible to predict the shear viscosity and the critical shear rate at which shear-induced degradation occurs as a function of Mw c and the solvent power. 

The viscosity of the oxidized polymer (VIII) was determined using DMF as a solvent. Chloroform was not a good solvent because it was too volatile and resulted in poor reproducibility. The reduced viscosities are plotted against polymer concentration (Figure 6). Polymer VIII behaved like a polyelectrolyte, the reduced viscosities increased sharply on dilution in a salt free solution. The addition of 0.01 M KBr did not completely suppress the loss of mobile ions however, at 0.03 M KBr addition a linear relationship between the reduced viscosities and concentration was established. 

Based on the analogy between polymer solutions and magnetic systems [4,101], static scaling considerations were also applied to develop a phase diagram, where the reduced temperature x = (T — 0)/0 (0 0-temperature) and the monomer concentration c enter as variables [102,103]. This phase diagram covers 0- and good solvent conditions for dilute and semi-dilute solutions. The latter will be treated in detail below. 

Fig. 39. Crossover from 0- to good solvent conditions in dilute solutions. Calculated characteristic frequencies, normalized to 0-conditions, as dependent on reduced temperature for two different chain lengths N at various values of (QS). To the right of each curve the increase in Qred (q,x) between t = 0 and t = 0.9 is given...

Fig. 42. NSE spectra of a dilute solution under good solvent conditions (PDMS/d-toluene, T = 373 K). a S(Q,t)/S(Q,0) vs. time t b S(Q,t)/S(Q,0) as a function of the Zimm scaling variable (H(Q)t)2/3. The solid lines result from fitting the dynamic structure factor of the Zimm model (see Tablet) simultaneously to all experimental data using T/r s as adjustable parameter...

Fig. 44. Double logaritmic plot of Q(Q)/Q2 vs. Q for various dilute solutions under good solvent conditions visualize the crossover from segmental to monomer diffusion [119]. The solid lines result from fitting the theoretical predictions of Akcasu et al. [94] to the experimental data using B = 0.38 and T s and a = / as adjustable parameters. The dotted lines are the corresponding predictions for 0 conditions. (Reprinted with permission from [119]. Copyright 1981 American Chemical Society, Washington)...

The crossover from 0- to good solvent conditions in the internal relaxation of dilute solutions was investigated by NSE on PS/d-cyclohexane (0 = 311 K) [115] and on PDMS/d-bromobenzene(0 = 357K) [110]. In Fig. 45 the characteristic frequencies Qred(Q,x) (113) are shown as a function of t = (T — 0)/0. The QZ(Q, t) were determined by fitting the theoretical dynamic structure factor S(Q, t)/S(Q,0) of the Zimm model (see Table 1) to the experimental data. This procedure is justified since the line shape of the calculated coherent dynamic structure factor provides a good description of the measured NSE-spectra under 0- as well as under good solvent conditions. 

Fig. 45a, b. Segmental diffusion in dilute solutions at the crossover from - to good solvent conditions. Reduced characteristics frequencies Qred (Q,x) vs. x = (T — )/ at different Q-values a PDMS/d-bromobenzene b PS/d-cyclohexane. (b reproduced with permission from [115]. Copyright 1980 The American Physical Society, Maryland)... 

On macroscopic length scales, as probed for example by dynamic mechanical relaxation experiments, the crossover from 0- to good solvent conditions in dilute solutions is accompanied by a gradual variation from Zimm to Rouse behavior [1,126]. As has been pointed out earlier, this effect is completely due to the coil expansion, resulting from the presence of excluded volume interactions. 

Fig. 46. Segmental diffusion in a dilute PDMS/d-bromobenzene solution at the crossover from to good solvent conditions. Reduced characteristic frequencies Qred (Q, x) vs. Q at different x-values. Comparison between experimental results ( ) and theoretical predictions (-). according to [98].

Chain and ring macromolecules are topologically distinct. Thus it is not surprising that many differences in their microscopic properties are observed [127], Besides many other experimental techniques, which were applied to specify these differences, NSE was used to compare the center of mass diffusion and the internal relaxation of linear and cyclic PDMS systems in dilute solutions under good solvent conditions [120,128,129]. An important parameter for these investigations was the molecular mass, which was varied between 800 and 15400 g/mol and which was almost identical for the corresponding linear (L) and ring (R) systems. 

Elastic and quasi-elastic (NSE) neutron scattering experiments were performed on dilute solutions of linear poly(isoprene) (PIP) polymers and of PIP stars (f = 4,12,18) [150]. In all cases the protonated polymers were dissolved in d-benzene and measured at T = 323 K, where benzene is a good solvent. Figure 50 shows the results of the static scattering profile in a scaled Kratky representation. In this plot the radii of gyration, obtained from a fit of the... 

Fig. 58a, b. Segmental diffusion in semi-dilute polymer solutions. Schematic view of the Q-dependence of the relaxation rates Q(Q) at a fixed concentration. a Good solvent conditions b -conditions. (Reprinted with permission from [168]. Copyright 1994... 

It is generally accepted that in semi-dilute solutions under good solvent conditions both the excluded volume interactions and the hydrodynamic interactions are screened owing to the presence of other chains [4,5,103], With respect to the correlation lengths (c) and H(c) there is no consensus as to whether these quantities have to be equal [11] or in general would be different [160],... 

Under good solvent conditions the dynamics of semi-dilute solutions was investigated by NSE using a PDMS/d-benzene system at T = 343 K and various concentrations 0.02 c < 0.25. The critical concentration c as defined by (112) is 0.055. 

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