Polymers parentheses

Fig. 16 Compression stress (a) - Hencky strain (sh) curves for gels of )0-glucan samples from oat oatlOO (2.12) and oat200 (2.13), barley bar 100 (2.80) and bar200 (3.04), wheat whe200 (3.66), and lichenan lie 100 (24.49) with cellotriosyl/cellotetraosyl ratios given in parenthesis. Polymer concentration, 8% w/v and gel curing temperature 25 °C...

The parenthesis in Equation 19 is the probability that a randomly selected monomer unit bound in the polymer chain belongs to the sol fraction, and therefore, the meaning of the above equation is obvious. At conversion 4 the weight fraction of the primary molecules which were formed at x=0 is given by ... 

Most of the polymers are better known by their trivial names or trade names. Polymers prepared from single polymers are denoted by prefixing poly- to the name of the monomer, e.g., polyethylene, polypropylene, Polyacrylonitrile, polystyrene, etc. If the monomer has substituents or has a multi-worded name, the name of the monomer is enclosed in parenthesis after the prefix poly-, e.g., poly (methyl methacrylate), poly (vinyl alcohol), etc. Condensation polymers like that derived from ethylene glycol and terephthalic acid are named as poly (ethylene terephthalate). 

Table 8 2PA properties of selected polymers. The solvent used in the measurement is indicated in parenthesis after the molecular formula and the average number of repeating units. The cross sections reported are the contributions per repeat units... 

Fig. 13 Bond lengths of the rhombohedral C60 polymer around the interfullerene bonds (A). Experimentally proposed values are also shown in parenthesis [39], Both values generally show good agreement with each other...

Figure 5.32. Impedance plots for single cells at ambient temperature, a Nation 117. Cell voltage and ohmic drop corrected potential (in parenthesis) ( ) 0.9 V (0.9 V) ( ) 0.8 V (0.81 V) (A) 0.70 V (0.76 V) ( ) 0.6 V (0.74 V) ( ) 0.5 V (0.74 V). b Nafion 112. Cell voltage and ohmic drop corrected potential (in parenthesis) ( ) 0.9 V (0.9 V) ( ) 0.8 V (0.81 V) (A ) 0.70 V (0.73 V) ( ) 0.6 V (0.67 V) ( ) 0.5 V (0.61 V). Plots were corrected for the high-frequency resistances. Left detail of the high-frequency regions [29]. (Reprinted from Journal of Electroanalytical Chemistry, 503, Freire TJP, Gonzalez ER. Effect of membrane characteristics and humidification conditions on the impedance response of polymer electrolyte fuel cells, 57-68, 2001, with permission from Elsevier.)...

Values for the respective polymer support are indicated in the parenthesis)... 

In searching for a polymer in this table, note that the sorter of the word processing software used in its generation sorts all characters (and not just letters) in a particular order. A parenthesis precedes a square bracket, a square bracket precedes a number, the numbers are ordered in an ascending sequence, and letters are ordered in the usual alphabetical order after numbers so that the following "alphabetical" order is used (, [, 1,2,...,8,9,10,1 l,...,a,b,...,y,z. 

Note that by defining the terms in parenthesis as pseudokinetic or apparent rate constants (Table 12.4) Equations 12.42 and 12.43 are identical to those describing the MWD of the live polymer in a homopolymerizafion. 

Simple vinyl polymers are named by attaching the prefix poly to the monomer name. For example, the polymer made from styrene becomes polystyrene. However, when the monomer name consists of more than one word or is preceded by a letter or a number, the monomer is enclosed in parenthesis with the prefix poly. Thus polymers derived from vinyl chloride or 4-chlorostyrene are designated polyfvinyl chloride) and poly(4-chlorostyrene), respectively. This helps to remove any possible ambiguity. 

The first term in parenthesis on the right-hand side of eg. fi2.42l reflects entropic effects that arise from the number of possible ways that macromolecules and solvent can be arranged in space this term is also known as the combinatorial contribution. The second term on the right-hand side is the enthalpic contribution and arises from differences between polymer-polymer and polymer-solvent interactions this term is also referred to as the residual contribution (not to be confused with the residual properties introduced earlier, which measure deviations from the ideal-gas state). Even if this term is zero (i.e., x = o), the solution is nonideal due to the size difference between polymer and solvent. 

With poly(vinyl chloride) or poly(methyl methacrylate), however, the parentheses should always be used because the term without them is ambiguous. Writing all polymer names with parenthesis (e.g., poly(ethylene)) would still be correct. 

Figures in parenthesis refer to polymer molar mass in kD. 

Figure 5.59 Energy required (kj kg ) to reach the transition temperature of each polymer. (Number in parenthesis in the legend is 7, or 7g.)...

Data on virgin unreinforced polymer in parenthesis. Source Author s own files ... 

The structure of a polymer is generally displayed by representing it as a parenthesized expression with a subscript letter outside the closing parenthesis. Two such expressions are commonly used ... 

The grouping in the parenthesis of Equation 10.10 can be related to the characteristic ratio and is nearly independent of the polymer molecular weight the dependence of intrinsic viscosity on solvent quality is therefore proportional to the product aM. In theta solvents, a is unity (the intrinsic viscosity scales with and in good solvents a is proportional to (the intrinsic viscosity scales with M ). Comparison with Equation 10.1 suggests that the Mark-Houwink parameter should lie in the range 0.5 expansion factor if theta conditions for the polymer solution are known. 

Table 9.1 Density (p) at 35 °C, d-spacing (dsp) frinn parenthesis) for membranes based on polymers obtained wide angle X-ray diffraction, fractional liee volnme (v), by polycondensation of 3,3 -diaminobenzidine with dif-and water uptake at 35 °C (H2O per polymer repeat unit in ferent dicarboxylie acids...

The phosphoric acid uptakes (H3PO4 per polymer repeat unit in parenthesis) were recorded gravimetrically after equilibrating the membranes in 16.2 mol L H3PO4 (the bromine containing polymers were equilibrated in 14.3 mol H3PO4). All membranes were prepared by solution casting from DMAc. All data are from reference [5]... 

The structural entity which repeats over and over again in the polymer, i.e., the structure within the parenthesis in Eq. 1 or 2 or 3, is referred to as the polymer repeat unit. 

Figure 1 shows the gel permeation chromatography (GPC) profiles of the representative polycondensation products PSEG(l/7), PSEG(2/7) and PYSE(l/7), where the numbers in parenthesis (m/n) denote the number of Si atoms in siloxane and ethylene glycol units in OEG, respectively. The polymers thus obtained were viscous liquids, and the number average molecular weights of the products were in... 

Polymer Synthesis and Characterization. Table I lists a representative sample of the polymers prepared. The molar ratios of the monomers used in the polymerization are listed in parenthesis behind the monomer. Polymerization reactions proceeded without incident. The dissolution of the bulk polyiners in DMF required a few hours since the DMF was added to the flask in 25 mL portions. 

Reynolds number. It allows one to assume that the role of processes related with hydrodynamies decreases with the increase of surface coverage with the polymer, 0. As a first approach, it can be assumed that this decrease occins exponentially. If that is so, it can be shown that the relationship between the adsorption rate and the Reynolds number will be described by the third term in parenthesis on the right-hand side of Eq. (138) (see Appendix 1). 

Is it easier to wet a PS, a poly(vinyl chloride) (PVC) (40 mN m ) or a Teflon (PTFE) (18 mN m ) smface Which of the three polymers is easiest to wet and which is the most difficult to wet Explain briefly your answer. The numbers in parenthesis are the critical surface tension values at 20 °C. 

Figure 12.10 DLVO term for steric repulsion. The first term (the one squared in parenthesis) is simply the volume fraction of the polymer in the layer. Different expressions are obtained for the three different geometries Indicated here as the overlap volume (vq) dp = sphere diameter (m), H = distance between two objects (m), X = thermodynamic interaction parameter (estimation requires thermodynamic model) (dimensionless), M2 = molecular weight of adsorbed polymer (kg mol ), p = molar volume (m moC ), C2 = surface layer concentration of adsorbed polymer (mol m ), 8 = adsorbed layer thickness (m)...

The homopolymerization of ethylene is often carried out with a mixture containing four components monomer (M), polymer (P), diluent (D) and initiator (I). The phases which may co-exist are solids (c), liquid (1), vapor (g) and a supercritical fluid phase (s) which may upon a change of temperature, pressure or composition separate into a liquid and a vapor phase. The components coexisting in a given phase will be written within a parenthesis, the phase will be labeled with a superscript and coexistence of two or more phases will be indicated by a slash (/) for example, the notation (MD) /(MPDI) indicates that a vapor and... 

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