Polystyrene characteristic ratio

Figure 2. Generalized characteristic ratio C q) plotted vs. qjn for three typical polymers polyethylene (PE) at 400 K [11, 21], atactic polystyrene (PS) at 300 K. [14], and poly(dimethyl-siloxane) (PDMS) at 350 K [15],...

Both these polymers have an - A-B structure [14,15], so their characteristic ratio C(q) was obtained through the procedure outlined in Section 2.1.2 see Eqs. (2.1.33H21.35) in particular. Since we were interested in stereoirregular (i.e., atactic) polystyrene for comparison with experimental data, the matrix procedure based on parameters proposed by Yoon, Sundararajan, and Flory [111] was suitably complemented with the pseudostereochemical equilibrium algorithm, which allows units of opposite configuration to be formally interconvertible with fixed relative amounts [36]. In the temperature range 30-70 °C the results may be fairly well expressed by the following analytical forms ... 

The numerical value of Flory s characteristic ratio depends on the local stiffness of the polymer chain with typical numbers of 7-9 for many flexible polymers. The values of the characteristic ratios of some common polymers are listed in Table 2.1. There is a tendency for polymers with bulkier side groups to have higher C c, owing to the side groups sterically hindering bond rotation (as in polystyrene), but there are many exceptions to this general tendency (such as polyethylene). 

Calculate the mean-square end-to-end distance of atactic polystyrene with degree of polymerization 100 assuming that it is an ideal chain with characteristic ratio C = 9.5. (Note that the characteristic ratio is defined in terms of the main-chain bonds of length / = 1.54 A rather than monomers.)... 

Step 21. Calculate the key properties of polymers in dilute solutions. The steric hindrance parameter a is predicted by using equations 12.22-12.26. For polystyrene, the result is 0-2.22. The characteristic ratio is predicted from the value of a, by using Equation... 

The characteristic ratio, C, is much smaller (1.08) for the ABA chains in the large micelles than in the small aggregates formed at weak segregation [34], since most of the chains form loops. Loops appear to be dominant in the micelle formed in A,Ai-dimethyl acetamide by a large triblock copolymer with polystyrene as the soluble internal block and poly(tert-butylstyrene) as the insoluble terminal blocks [26]. 

Let us consider the determination of molecular characteristics S and for butadiene-styrene rubber. As it is known [15], the value of macromolecule diameter square is equal to for polybutadiene - 20.7 and for polystyrene - 69.8 A. Calculating the macromolecule, simulated as cylinder, cross-sectional area for the indicated polymers according to the known geometrical formulae, let us obtain 16.2 A and 54.8 A, respectively. Further, accepting as S for butadiene-styrene rubber mean value of the cited above areas, let us obtain S=35.5 A. Further the characteristic ratio can be determined, which is a polymer chain statistical flexibility indicator [16], with the aid of the following empirical formula [14] ... 

If all torsional angles were assumed to be equally probable, cos (f> = 0 and the equation (2.28) reduces to equation (2.27). The characteristic ratio Coo therefore takes into account all local or short-range steric interactions and is a measure of the flexibility of the polymer chain. Very flexible chains will have values of Coo close to unity. Typical values of Coo are 6.7 for polyefiiy-lene, 10.2 for polystyrene, and about 600 for DNA — much higher than the... 

Neutron-scattering studies on polystyrene solutions have shown that while short-length scale correlations are perturbed, in the same manner as single chains in cood solvent, the large-length scale properties are indeed Gaussian. Daoud predicted that the mean squared end-to-end distance of the chains is swollen relative to a pure. melt but can be described simply by a swollen characteristic ratio Coo(( )... 

Block copolymers based on nitrile rubber and on epoxy and phenolic resins and on polystyrene (50-54) have been intensively studied in Russia The generated block copolymers were investigated by turbidimetric and IR methods. Thermomechanical experiments were also run on fractions. As may be seen from Fig 13, fractions which combine the properties of the polymers (Curves 2,3, and 4) were obtained together with fractions characteristic of the raw rubber (Curve 1) and of the resin (Curve 5). The copolymer is soluble in solvents which are typical for both components. Solubility studies on the products showed that for any given ratio of the original components, 15 to 20% of the resin combines with the rubber. The properties of the block copolymer, however, depend on the initial ratio of components nitrile rubber confers elasticity and the phenolic resin processability. 

This reaction has the characteristics of a dead end polymerization, and the conversion of monomeric MMA to polymer can be controlled via the azo content of the polystyrene and the reaction temperature. The separation of the reaction products into homopolymer and block copolymer was achieved by selective solvent extraction thus, cyclohexane was used to dissolve the homopolystyrene, acetonitrile the homo-poly-MMA and the copolymer was completely soluble in benzene. The compositition of the crude product as a function of the ratio of MMA/prepolymer is shown in Fig. 4.5 58> ... 

Typical chromatograms were observed when polystyrene was py-rolyzed in air and the pyrolytic products were analyzed by gas chromatography. A characteristic peak which was observed on the chromatograms obtained by the pyrolysis of maleic anhydride and the alternating styrene maleic anhydride copolymer but not with polystyrene was used as a reference peak. As shown in Table II, the ratio of the area under... 

The polystyrene simulation followed the experiments of Bell and Edie (12) with good agreement. Figure 14.8 shows the simulation results for fiber spinning nylon-6.6 with a draw ratio of 40. The figure demonstrates the wealth of information provided by the model. It shows the velocity, temperature, axial normal stress, and crystallinity fields along the threadline. We see the characteristic exponential-like drop in diameter with locally (radially) constant but accelerating velocity. However, results map out the temperature, stress, and crystallinity fields, which show marked variation radially and axially. 

FIG. 16.18 Non-Newtonian viscosity ratio for solutions of narrow molecular weight distribution polystyrenes in n-butyl benzene, plotted vs. reduced shear rate q/q0, where qa, equal to the reciprocal of the characteristic time constant Tn, is chosen empirically for each solution. The data were obtained for molecular weights ranging from 160 to 2400 kg/mol and for concentrations ranging from 0.255 to 0.55 g/ml at temperatures from 30 to 60 °C.The full line is calculated with the aid of Eqs. (16.52)—(16.55). From Graessley, Hazleton and Lindeman (1967). Courtesy Society of Rheology. 

As described earlier (Sect. 2.3) Guenet s study of thermally-induced conversion of isotactic polystyrene solutions to rigid gels led to his observation that the ratio, a, of residual adsorbed solvent molecules per phenyl group of polymer, after all of the non-adsorbed liquid has been removed by evaporation in vacuum, is characteristic of the liquid [79-82, 181]. This end-point was established by correlating the heat of fusion of the liquid in the system with the amount of residual sorbed liquid. The composition extrapolated to AH = 0 was taken to be a. He later reported [181] that his thermodynamic protocol is also applicable for the determination of adsorbed liquid by atactic polystyrene. 

Polystyrene Latex (PSL) Bead Solution Filtration Experiments were conducted to obtain filter retention, flow rate, and Ap data for a DI water based PSL bead mix solution prepared using particles ranging from bead diameters of 0.772 to 20 pm. It is a common practice to use PSL bead challenge solutions (created by mixing different size PSL bead standards in specific volumetric ratio to simulate slurry-like particle size distribution for the bead mix solution) to obtain relative quantitative retention data for various filters. These solutions are expected to retain stable PSD and provide more consistent information compared to real CMP slurries, which may change particle characteristics over time. 

High-molecular-weight PM PS is soluble in common solvents and is a good film former. Qualitatively, the overall handling characteristics resemble those of polystyrene. Films of PM PS were cast from toluene solution by a solvent evaporation technique. Other polysilylenes, poly(methylcyclohexylsilylene), poly(methyl-n-pro-pylsilylene), poly(methyl-n-octylsilylene), and a copolymer of dimethyl- and meth-ylphenylsilylene (1 1 ratio) were also prepared by Wurtz coupling by the method of Zhang and West (47). Films of these polymers were also cast from toluene. All polymers form clear transparent colorless films. 

The standard molecular structural parameters that one would like to control in block copolymer structures, especially in the context of polymeric nanostructures, are the relative size and nature of the blocks. The relative size implies the length of the block (or degree of polymerization, i.e., the number of monomer units contained within the block), while the nature of the block requires a slightly more elaborate description that includes its solubility characteristics, glass transition temperature (Tg), relative chain stiffness, etc. Using standard living polymerization methods, the size of the blocks is readily controlled by the ratio of the monomer concentration to that of the initiator. The relative sizes of the blocks can thus be easily fine-tuned very precisely to date the best control of these parameters in block copolymers is achieved using anionic polymerization. The nature of each block, on the other hand, is controlled by the selection of the monomer for instance, styrene would provide a relatively stiff (hard) block while isoprene would provide a soft one. This is a consequence of the very low Tg of polyisoprene compared to that of polystyrene, which in simplistic terms reflects the relative conformational stiffness of the polymer chain. 

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