Overlap concentration, polystyrene

In HOPC, a concentrated solution of polymer is injected. The concentration needs to be sufficiently higher than the overlap concentration c at which congestion of polymer chains occurs. The c is approximately equal to the reciprocal of the intrinsic viscosity of the polymer. In terms of mass concentration, c is quite low. For monodisperse polystyrene, c is given as (4)... 

Problems and Worked Examples 183 Problem 3.3 From Eq. (3-4), estimate the overlap concentration in g/cm for polystyrene of... 

The radius of gyration of a polystyrene molecule (M — 3x lO gmol ) was found to be R = lOlOA. Estimate the overlap concentration c in... 

Table 6.1 Critical overlap concentration, C, for polystyrene coils in solution measured by energy transfer between carbazole- and anthracene-labeled polystyrene chains...

Experimental data were obtained for solutions with polymer concentrations varying from w = 0.50% to w = 4.00% or, equivalently, from c = 0.00431 to c = 0.0348 g cm to be compared with the estimated overlap concentration c = 0.0274 g cm-3 [22]. Hence, the experimental results correspond to polystyrene-toluene solutions in the dilute and semidilute solution regime. 

Experimental work on the determination of the depletion layer thickness commenced in this period. The depletion thickness S of polystyrene at a nonadsorbing glass plate was measured using an evanescent wave technique by Aflain et al. [120]. The value found for S was indeed close to the radius of gyration of the polymer. Ausserre et al. [121] measured the depletion thickness of xanthan (a polysaccharide) at a quartz waU below and above the polymer overlap concentration. In dilute solutions, below overlap, S was close to the radius of gyration of... 

The radius of gyration for a polystyrene (MW 30 x 10 ) in benzene solution was found to be 1010 A in a semidilute solution. Estimate the overlapping concentration c in grams per cubic centimeters. 

Second, data for the somewhat more concentrated polystyrene solutions of Ashare whose primary normal stress differences are portrayed in Fig. 2-10 are represented by curves B and C. At 1% concentration, where the molecules overlap somewhat but are probably not entangled, there is a moderate drop in r/, somewhat more than in the extremely dilute solution at 5% concentration, where entanglements probably exist, the non-Newtonian effect is much more pronounced and, over about two decades of 7, ri follows rather closely a power-law relation. It is of interest that the onset of non-Newtonian flow occurs at a much higher shear rate for 1% than for 5% concentration, just as the normal stress differences achieve significant magnitudes at a higher shear rate for 1% than for 5% concentration in Fig. 2-10. Quantitative correlations will be introduced in later chapters. 

III.1 Materials A series of linear PS, star PS and linear PMMA were used in our studies. The characteristics of these polymers are listed in Table 1, where "LPS and "LPM" denote linear PS and linear PMMA, and SPS4", SPS12 denote the 4-arm and 12-arm star PS, respectively. The two star polystyrenes were previously characterized by light scattering in toluene at 25 C. Here we used the overlap concentration obeying the relation... 

The excimer fluorescence of polystyrene (PS) solution has been widely studied since early sixties, predominately for intrachain excimer formation between adjacent pendant phenyl chromophores on the chain in dilute solutions, c < 5.10 g/dl. As the excimer interaction is a very short range interaction between an excited state and a ground state qhromophore at a parallel planar configuration of 0.33-0.35 nm apart, it should be useful to probe the molecular aggregation processes. For the present discussion only the concentration dependence of the intensity ratio < = of the excimer to monomer (isolated excited chromophore) fluorescence will be of interest. Typical fluorescence spectrum of PS in solution is shown in Fig. 2. The overlap between the monomer fluorescence peak (X = 285 nm) and the excimer fluorescence peak (X = 330 nm) is not severe so that simple peak intensity ratio is adequate for the evaluation of < within usual experimental errors. Results of first such investigation by Roots and Nystrom to show a sharp turn at the overlap concentration c (c [n] = 1) were not confirmed. Extensive studies carried out in the author s laboratory showed a peculiar concentration... 

Fig. 3. Universal behaviour of the normalized self-diffusion coefficient DJDq Dq is the diffusion coefficient at infinite dilution) as a function of the reduced concentration c/c, where c is the concentration at which the labelled chains start to overlap, for polystyrene in benzene solutions. The different symbols correspond to different molecular weights in the range 78000-750000. Full symbols correspond to labelled and unlabelled chains having the same molecular weight, while open symbols correspond to a frozen matrix (P>>N) for which a pure reptational behaviour is observed (from Ref. (19)).

Some studies have been made on polymers in marginal solvents, i.e., solvents in which the second virial coefficient is not zero and the scaling exponent v of Rg- M is not near 0.5 or 0.6. Brown and Fundin(26) examined polystyrene in 2-butanone, finding a rapidly-decaying, -dependent mode and a first internal mode whose relaxation rate scaled as at smaller q and at larger q. The relaxation rate of the internal mode appeared to be independent of c at small c and to decrease rapidly with increasing c at larger c. The decrease set in well before the overlap concentration c was attained. 

Fig. 8.9. Power law exponent d as a function of the coil overlap parameter c[ ] at low concentrations. The filled circles are narrow distribution polystyrene solutions (1 77, 316, 318), the open circles are poly(a-methyl styrene) (198, 318). Solvents are chlorinated di-phenyls except the intrinsic viscosity data which were obtained in toluene. Symbols are for polystyrene M= 13.6 x 106, 4 1-8 x 10 , and 0.86 x 106 for poly(a-methyl styrene) O M = 7.5 x 10 , 6 3.3 xlO6, Cr 1.82 xlO6, O- 1.14x10 , a. 0.694x10 , and...

A good dispersion of rubber particles appears to favor the nucleation and growth of a large number of thick crazes uniformly distributed in the polystyrene matrix. This is believed to be an efficient source of energy absorption for the material under mechanical loading. The concepts of stress field overlap and critical volume of stress concentration zone for craze initiation were introduced to explain the observed mechanical behavior of HIPS. 

For polystyrene of molecular weight 10 the overlap therefore occurs above about 2% concentration. Below this concentration, one should therefore use the Flory-Krigbaum theory. 

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