A New Family of High Viscosity Polymeric Dispersions for Cleaning Easel Paintings

Cloth Basics

Ottmar Brandau , in Stretch Blow Molding, 2012

Relevant Parameters

Four, temperature, and co-polymer content all play a office in determining how far the cloth stretches during yielding and what forcefulness is required to stretch information technology further (Fig. two.17). Temperature conditioning allows the operator to improve the blow molding process by making sure parts of the preform hotter or colder – changing the way in which they will stretch.

Figure ii.17. Several factors at piece of work, determining the natural stretch ratio.

The objective of preform pattern (or selection) and blow molding processes is to properly friction match up the natural stretch ratio of the preform at the accident molding conditions with the pattern stretch ratios of the preform/bottle combination.

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A STUDY ON THE INVERSION OF STERIC CONFIGURATION IN THE STEREOSPECIFIC POLYMERIZATION OF PROPYLENE

G. NATTA , I. PASQUON , in Stereoregular Polymers and Stereospecific Polymerizations, 1967

Intrinsic viscosity measurements were performed on the different fractions. The following results were obtained:

(1)

the percentage of extractable polymer with each solvent increases by decreasing the pressure. This variation is clearly observed only if ane operates at low pressures, i.e. lower than atmospheric pressure.

(2)

The melting temperature of the extracts obtained, as seen by the polarizing light microscope, does not practically change by varying the force per unit area of the polymerization.

(iii)

The crystallinity of the north–octane extract and of the residual to the extraction is practically independent of the polymerization pressure.

(4)

The pct of boiling η –octane extractable fraction increases by increasing the concentration of the aluminum alkyl introduced in the catalytic system.

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Eco Friendly Flocculants: Synthesis, Characterization and Applications

G.P. Karmakar , in Encyclopedia of Renewable and Sustainable Materials, 2020

Characterization of the Synthesised Flocculants

The intrinsic viscosities [η] at 30±0.1°C of the graft copolymers take been evaluated every bit per standard procedures and are given in Table 1 . From the intrinsic viscosity values, the approximate molecular weights of the grafted products have been calculated using the following equations ( Mendelson, 1969):

(ane) $\left[\eta \right]=\mathrm{half-dozen.eight}\times {10}^{-4}{\left({\mathrm{Mn}}^{-}\right)}^{0.66}$

(2) $\left[\eta \right]=\mathrm{vi.31}\times {10}^{-5}{\left({\mathrm{Mn}}^{-}\right)}^{0.80}$

The above relationships have been used for evaluating the molecular weight of the graft copolymers of polyacrylamide (Erciyes et al., 1992). The results obtained are given in Table i.

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Dilute solution viscometry of polymers

Wei Lu , Jimmy Mays , in Molecular Label of Polymers, 2021

7.2 Relationship between intrinsic viscosity and molecular weight

The intrinsic viscosity is not a directly measure of polymer molecular weight; instead it is a measure of the size of a polymer coil in solution, with units of dL/one thousand or mL/g. The values of the intrinsic viscosity for a given polymer sample of a item molecular weight volition vary with the pick of solvent and temperature, equally these factors influence the size of the polymer concatenation. In a thermodynamically skilful solvent, the polymer chain will expand to enhance the favorable interactions with the solvent. In a thermodynamically poor solvent, the concatenation will contract in size due to the less favorable interactions with the solvent, or even precipitate if solvent quality is too poor. In a thermodynamically skilful solvent, the intrinsic viscosity generally does not vary much with temperature, However, in a poor solvent, temperature has a strong touch on whorl dimensions. Conscientious selection of solvent and temperature is essential to achieving Flory theta conditions, where the second virial coefficient from calorie-free handful is zero and the whorl assumes the same judge conformation that information technology assumes in an baggy cook.

Mark [40, 41] and Houwink [42] demonstrated, empirically and independently, a full general relationship between intrinsic viscosity and molecular weight

(7.ten) $\left[\eta \right]={\mathit{KM}}^a$

where K and a are constants for a particular polymer-solvent pair in a specific solvent and temperature. Eq. (vii.ten) is at present commonly known equally the Mark-Houwink relationship and information technology provides a very convenient style to estimate polymer molecular weight. This equation is valid for an extremely wide range of polymers of various chemical structures and conformational characteristics. The Polymer Handbook [43] contains an extensive listing of Marker-Houwink parameters for various polymers, allowing molecular weight to exist estimated by measuring intrinsic viscosity. The Mark-Houwink exponent a provides insight into polymer concatenation conformation. For compact spheres a  =   0, whereas for rigid rod polymers a  =   1.8. For random coil polymers, a varies betwixt 0.v (random coil under Flory theta atmospheric condition) and 0.viii (thermodynamically proficient solvent). Mark-Houwink relationships are mostly valid and linear for high molecular weight polymers, M  >   10,000   thousand/mol. Lower molecular weight polymers showroom not-Gaussian behavior (concatenation stiffening) due to their inherently short chains. Thus employing Mark-Houwink parameters and intrinsic viscosities to guess molecular weights of low molecular weight polymers is susceptible to large errors.

In establishing empirical Marking-Houwink relationships for polymers, information technology would be ideal to work with monodisperse polymers, eliminating the question of which average molecular weight to employ in Eq. (7.10). Of course, given that synthetic polymers are invariably polydisperse, this is very rarely possible. Thus Marking-Houwink relationships are empirically established using well-fractionated polymers or polymers made by living/controlled polymerization techniques in order to limit polydispersity. Generally, the molecular weight (weight-average) is then measured by light scattering, although other methods of molecular weight conclusion (osmometry, mass spectrometry, etc.) may be employed.

The question as well arises as to which average molecular weight is obtained from Eq. (7.10) for a polydisperse polymer. The viscosity-average molecular weight, K _v , is the average derived via measurements of intrinsic viscosity, and it is defined as [44].

(seven.xi) $M_v=\mathrm{Thou}\mathrm{\Sigma }{N}_i{{\mathrm{Yard}}_i}^{1+a}/\mathrm{\Sigma }{N}_i{M}_i$

where N _i is the number of molecules of molecular weight G _i and Chiliad and a are the Mark-Houwink coefficients. Upon inspection of Eq. (7.11) information technology is obvious that One thousand _v is mostly betwixt number-average molecular weight M _n and weight-average molecular weight M _w but closer to the latter.

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THERMODYNAMICS AND MOLECULAR CONFIGURATION OF ATACTIC POLYPROPYLENE IN SOLUTION

F. DANUSSO , G. MORAGLIO , in Stereoregular Polymers and Stereospecific Polymerizations, 1967

ABSTRACT

The intrinsic viscosity of atactic polypropylene fractions was determined in ii Θ solvents at 34°C in isoamylacetate and at 58°C in isobutylacetate, and in a series of different solvents, in the whole range of temperatures from 20° to 70°C. The results are discussed according to Fox and Flory'south theory. The average statistical dimensions of the unperturbed macromolecules decrease with the increment in temperature. The expansion coefficients [α] in the different solvents were calculated; from these values the thermodynamic interaction parameters, reported in Table 1, were also calculated.

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Molecular weight of polymers used in biomedical applications

O. Dragostin , L. Profire , in Label of Polymeric Biomaterials, 2017

2.ii.ii.ii Experimental method

The intrinsic viscosity can be assigned to a single molar mass. Viscometric methods are based on the fact that the viscosity of a liquid, in which the polymer is dissolved, increases along with the polymer concentration.

Practically, an Oswald viscometer needs to exist used, a serial of dilutions of polymer solution must be fabricated and until the viscosimetric measurements for the polymer solution are identical to that of the original solvent, the menstruum rates must be measured. Therefore a polymer solution of known concentration is aspired to higher bulb (Fig. 5.4), post-obit that the air penetration is allowed, causing the leakage of the solution under its own weight. The time needed for the solution to flow is recorded. The same functioning is repeated for increasingly dilute polymer solution. According to Poiseuille'southward law, the flow time for polymer solution is proportional to the viscosity of the solution, so to its concentration, and inversely proportional to the density [18]:

Fig.5.4. Illustration of a Cannon-Fenske viscometer.

(5.8) $T=\eta /\rho$

where T is the menstruum time, ɳ is the viscosity of the polymer solution, and ρ is the density of the polymer solution.

From the experimental method point of view, Kwaambwa et al. [32] have used viscometric methods for determining One thousand_n , Grand_westward , K₅ , and M_z values of polyisoprene. For this purpose, and besides to accomplish a complete dissolution of the polymer, a polymer stock solution has been prepared by suspending the flask in an ultrasonic bath for x   min. The stock solution has further been used in preparing different concentrations. The flow times of the different polymer concentration solutions take been measured with a viscometer suspended in a h2o bathroom at 25°C. Nosotros also have to consider the menstruation time of the solvent, which has been measured at the end of the experiment (ɳ ₀ in formula 5.6). The Mark-Houwink formula, every bit described earlier, is linearized by plotting ln [ɳ] against Yard_five [32].

Peng et al. [33] reported a study carried out on hyaluronic acid, produced past Bacillus subtilis, which is recognized as a safe strain and ideal jail cell factory. The molecular weight of hyaluronic acid was confirmed with classical viscometry, the measurements being made in NaCl buffer (pH   =   seven). Viscosity analysis output was used to compare the results to multiple-angle laser low-cal scattering detector (MALLS). MALLS is a technique for determining absolute molar mass and particle size in a solution by taking into account how low-cal, from a laser source, is scattered. The difference betwixt the ii methods was insignificant: one.54   ×   10^half-dozen  Da (Viscosity) and i.51   ×   10⁶  Da (MALLS).

Sperger et al. [34] have calculated, in their work, the molecular weight of sodium alginate by determining the viscosity of corresponding aqueous solutions. The viscosimetric molecular weight was calculated co-ordinate to the following equation, depending on the intrinsic viscosity:

(5.9) $M_v={\left(\left[\eta \right]/0.023\right)}^{1/0.984}$

Thus starting from this formula Thou_v values between 63 and 541   kDa have been obtained, considering that intrinsic viscosity was between 1.35 and 11.26   dL/g.

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Molecular weight and molecular weight distribution

Kenji Kamide , Toshiaki Dobashi , in Physical Chemistry of Polymer Solutions, 2000

Answer

The intrinsic viscosity [η] is defined by

(8.22.3) $[\eta ]=\underset{\text{c}\to 0}{\text{lim}}\frac{{\eta }_{\text{sp}}}{\text{C}}$

where

(viii.22.1) ${\eta }_{\text{sp}}{=\eta }_{\text{r}}-1=\frac{\eta }{{\eta }_0}-\mathrm{ane}$

η_r, η and η₀ are the relative viscosity and the viscosities of the solution and solvent, respectively and C is the concentration. If concentration dependence of η_sp is negligible,

(9.xviii.i) ${\eta }_{\text{sp}}=\text{C}\underset{\text{c}\to 0}{\text{lim}}\frac{{\eta }_{\text{sp}}}{\text{C}}=\text{C}[\eta ]$

For i thursday component, Eqs. (8.30.xix) and (9.18.1) read

(9.18.ii) ${\eta }_{\text{sp},\text{i}}{=\text{One thousand}}_{\text{m}}{\text{C}}_{\text{i}}{\text{M}}_{\text{i}}^a$

where C_i and Chiliad_i are the concentration and the molecular weight, respectively, of i thursday component. Since the total η_sp is the sum of η_sp of each component, η_sp,i,

(ix.18.three) ${\eta }_{\text{sp}}=\sum _{\text{i}}{\eta }_{\text{sp},\text{i}}$

Substitution of Eq. (9.18.ii) for η_sp,i in Eq. (9.18.3) yields

(9.18.4) ${\eta }_{\text{sp}}=\sum _{\text{i}}{\text{K}}_{\text{m}}{\text{Grand}}_{\text{i}}^a{\text{C}}_{\text{i}}={\text{1000}}_{\text{chiliad}}\sum _{\text{i}}{\text{Chiliad}}_{\text{i}}^a{\text{C}}_{\text{i}}$

From Eqs. (eight.30.nineteen) and (nine.18.1),

(9.18.v) ${\eta }_{\text{sp}}{=\text{Thou}}_{\text{m}}{\left({\text{K}}_{\text{5}}\right)}^a\text{C}$

where

(9.eighteen.six) $\text{C}=\sum _{\text{i}}{\text{C}}_{\text{i}}$

is the total polymer concentration. Past comparing Eqs. (9.18.four) and (9.xviii.5), we have

(9.18.7) ${\text{One thousand}}_{\text{thousand}}{\left({\text{One thousand}}_{\text{v}}\right)}^a{\text{C}=\text{K}}_{\text{m}}{\left({\text{M}}_{\text{five}}\right)}^a\sum {\text{C}}_{\text{i}}{=\text{M}}_{\text{thou}}\sum {\text{Thousand}}_{\text{i}}^a{\text{C}}_{\text{i}}$

And so Eq. (9.18.seven) is rewritten as

(9.18.8) ${\text{M}}_{\text{v}}={\left[\frac{\sum _{\text{i}}{\text{C}}_{\text{i}}{\text{G}}_{\text{i}}^a}{\sum _{\text{i}}{\text{C}}_{\text{i}}}\right]}^{\frac{\mathrm{ane}}{a}}$

C_i is related to the weight fraction of i-mer, f_west(Chiliad_i), every bit

(9.eighteen.9) ${\text{C}}_{\text{i}}\left(\sum _{\text{i}}{\text{C}}_{\text{i}}\right){\text{f}}_{\text{w}}\left({\text{K}}_{\text{i}}\right)$

Exchange of Eq. (9.18.9) for Q in Eq. (9.xviii.8) yields (Refer also to Eq. (nine.iii.7))

(nine.xviii.ten) $\begin{array}{ll}{\text{M}}_{\text{v}}& ={\left[\frac{\sum _{\text{i}}\left(\sum _{\text{i}}{\text{C}}_{\text{i}}\right){\text{f}}_{\text{w}}\left({\text{M}}_{\text{i}}\right){\text{Thousand}}_{\text{i}}^a}{\sum _{\text{i}}\left(\sum _{\text{i}}{\text{C}}_{\text{i}}\right){\text{f}}_{\text{westward}}\left({\text{M}}_{\text{i}}\right)}\right]}^{\frac{1}{a}}={\left[\frac{\sum _{\text{i}}{\text{f}}_{\text{w}}\left({\text{One thousand}}_{\text{i}}\right){\text{M}}_{\text{i}}^a}{\sum _{\text{i}}{\text{f}}_{\text{w}}\left({\text{M}}_{\text{i}}\right)}\right]}^{\frac{1}{a}}={\left[\sum _{\text{i}}{\text{f}}_{\text{w}}\left({\text{M}}_{\text{i}}\right){\text{M}}_{\text{i}}^a\right]}^{\frac{\mathrm{one}}{a}}\\ & ={\left[{\int }_0^{\infty }{\text{M}}^a{\text{f}}_{\text{w}}\left(\text{M}\right)\text{dM}\right]}^{\frac{1}{a}}={\left[\frac{{\int }_0^{\infty }{\text{Yard}}^{a+1}{\text{f}}_{\text{n}}\left(\text{Thou}\right)\text{dM}}{{\int }_0^{\infty }{\text{Mf}}_{\text{n}}\left(\text{One thousand}\right)\text{dM}}\right]}^{\frac{\mathrm{one}}{a}}\end{array}$

Similarly, the viscosity-average degree of polymerization is expressed as

(9.18.xi) ${\text{n}}_{\text{five}}={\left[{\int }_0^{\infty }{\text{northward}}^a{\text{f}}_{\text{w}}\left(\text{n}\right)\text{dn}\right]}^{\frac{1}{a}}={\left[\frac{{\int }_0^{\infty }{\text{northward}}^{a+1}{\text{f}}_{\text{northward}}\left(\text{n}\right)\text{dn}}{{\int }_0^{\infty }{\text{nf}}_{\text{n}}\left(\text{n}\right)\text{dn}}\right]}^{\frac{\mathrm{ane}}{a}}$

Eq. (9.18.11) is rewritten as

(9.eighteen.12) ${\text{n}}_{\text{5}}={\left[\frac{{\mu }_{a+1}}{{\mu }_{\mathrm{one}}}\right]}^{\frac{1}{a}}$

where μ _a is a thursday moment of the caste of polymerization.

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Characterization of long-concatenation branching in polymers

Wei Lu , Jimmy Mays , in Molecular Characterization of Polymers, 2021

8.ii.1.ii Intrinsic viscosity

The measurement of intrinsic viscosity is simple and very accurate, even at very low molecular weights, and may be carried out online with SEC or other polymer chromatographic separation techniques via viscosity detectors (encounter Affiliate 7 for more detailed discussion). Since branched polymers are smaller than linear polymers of the same molecular weight, their intrinsic viscosities will be smaller, and an intrinsic viscosity-based branching parameter g′ may be defined as follows.

(8.12) $\mathrm{one\; thousand}\prime ={\left[\eta \right]}_{\mathit{br}}/{\left[\eta \right]}_l$

where [η] _br is the intrinsic viscosity of the branched polymer and [η] ₅₀ is the intrinsic viscosity of the linear polymer of the same type and molecular weight. The smaller the value of g′, in general the greater the extent of branching.

Early theoretical piece of work by Stockmayer and Fixman [one] and Zimm and Kilb [23] for star polymers yielded values of thou′ for such materials [24]. Even so, these early on theories failed to adequately take into account the extremely complex hydrodynamic interactions within polymers (draining upshot) [ten]. Only for star polymers and a few other model branched architectures have substantially improved theoretical or Monte Carlo results for g′ been generated [25–28]. Since theory relating g′ to the extent of branching is far less well developed than theory relating 1000 to extent of branching, it is thus highly desirable to know the human relationship between g′ and thousand.

Nonfree draining polymer linear chains may be described by the Flory-Fox equation [23].

(8.13) $\left[\eta \right]=6^{2/\mathrm{iii}}\Phi <S^{\mathrm{ii}}>{}^{3/2}{\mathrm{Chiliad}}^{-1}$

where Φ is a constant. If the same expression is also valid for branched polymers, g′ may exist related to m by the relationship

(viii.14) $g\prime =g^{3/\mathrm{two}}$

Zimm and Kilb [24] calculated theoretically the intrinsic viscosities of several unperturbed star-branched polymers, taking into business relationship hydrodynamic interactions, and derived a very different relationship between g and g′

(8.15) $g\prime =m^{1/2}$

As we volition see afterwards in this chapter, experiments take shown that the relationship between one thousand′ and thou depends on the branching architecture and, possibly, on solvent thermodynamic quality every bit well. A more full general expression

(8.16) $k\prime =g^{\varepsilon }$

is thus required, allowing the extent of branching to exist calculated from Eq. (8.xvi) based upon measurement of m′ and converting it to g, taking into account the branched compages and excluded volume.

Equally a rule, ɛ values close to one/ii are constitute for lightly branched systems and star polymers, whereas values closer to iii/ii are found for more highly branched polymers such as combs [29]. Think that the equations relating thousand to extent of branching are calculated for unperturbed chains (Flory theta conditions), and the k′ values are generally measured in thermodynamically good solvents. However, the proposition of Scholte that thousand′ tin be assumed to exist approximately contained of the thermodynamic quality of the solvent appears to be justified on the basis of his review of the literature [9]. More importantly, Kratochvil and Netopilik [30] have noted that ɛ tin can only be expected to exist a molecular weight independent empirical abiding for a set of branched molecules having the aforementioned molecular compages. For fractions of a randomly branched polymer, such as low-density polyethylene, the compages will vary equally a function of molecular weight (lower molecular weights less branched, higher molecular weights more highly branched), and thus the ɛ parameter itself will become molecular weight dependent.

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Soft Colloids

Martien Cohen Stuart , ... Hans Lyklema , in Fundamentals of Interface and Colloid Science, 2005

2.4c The intrinsic viscosity

Figure 2.23 gives intrinsic viscosities for three aqueous samples of potassium poly(styrene sulphonate) solutions every bit a role of the reciprocal Debye length. The data are taken from a systematic and experimental written report by Davis and Russel ¹⁾ ; the Yamakawa model can be found in ref. ²⁾ . The chain accuse is expressed every bit the ratio l _B/l _c of the Bjerrum length over the distance between next charges. Every bit this ratio > 1, no condensation is expected. Notation the logarithmic scale: [η] varies past a factor of 10ⁱⁱⁱ. The [η] values are easily a cistron of x² college than those for the corresponding uncharged polymers considering of the concatenation expansion. As expected, [η] increases with 1000 and with κ⁻¹: the lower the electrolyte concentration, the more extended the chain is. In the low salt limit, the values for extended rods are approached. To the left, at high c _{table salt}, the polyelectrolyte effect is suppressed and θ weather are approached. Here, the polyelectrolyte behaves as a non–draining Gauss–blazon gyre. The drawn curves are based on the hydrodynamic theory by Yamakawa and Fuji ⁱ⁾ , combined with earlier work for such chains by Odijk ²⁾ and Fixman and Skolnick ³⁾ . For theoretical groundwork, run into sec. 2.3c. Nosotros note that this reasonably accounts for the experimental trends. Key factors are chain stiffness (or for that matter, persistence length) and the excluded volume. Every bit a trend, thermodynamic quantities are more easily deemed for than hydrodynamic ones.

Figure 2.23.. Intrinsic viscosities of potassium poly (styrene sulphonate). Sample parameter as in the central. — rod limit. Drawn: Yamakawa model.

(Redrawn from Davis and Russel, loc. cit.)

More than to the quantitative side, it appears that [η] is, as a starting time approximation, proportional to M ^1/2. For a multifariousness of systems this has been observed, for instance for poly(α–L–glutamic acid) in NaCl solution and diverse values of c _NaCl, ^(four) for poly(mono methyl itaconate) in organic solvents at various degrees of neutralization ⁵⁾ , for sodium poly(acrylate) in aqueous NaBr solutions and at different degrees of dissociation ^six) and for oligo– and poly(methylmethacrylates) in acetonitrile, n–butylchloride and benzene ⁷⁾ , where a lower gradient than 1/ii was establish for the depression M samples. This proportionality is theoretically predicted by the familiar Stockmayer–Fixman equation ⁸⁾

[2.iv.xi] $\left[\eta \right]/M^{1/2}={\text{Grand}}_0+0.51{\Phi }_0\text{B}{G}^{1/\mathrm{ii}}$

Hither, B is a second virial coefficient, Φ₀ is the Flory (or Flory–Fox) constant introduced in [2.4.7] and 1000 ₀ is too a constant (contained of G), which equals

[2.four.12] ${\text{K}}_0={\Phi }_0\frac{{〈r_0^2〉}^{\mathrm{three}/\mathrm{ii}}}{\mathrm{Thousand}}$

where 〈r ₀ ²〉^1/two is the r. k.southward. finish–to–stop distance under Θ conditions. Equation [2.iv.xi] works well if the chain is not too expanded. A plot of [η]/Chiliad ^1/2 as a office of Thou ^1/2 (a Stockmayer–Fixman plot) helps to assess the (hydrodynamic) virial coefficient.

Intrinsic viscosities of polyelectrolytes typically depend on the electrolyte concentration c _s, on the line charge and on the mode this charge is distributed. As a starting time approximation for c _southward ≫ c _p, ane may expect [η](c _p) to scale as c _s ^−1/2. This scaling will hold when the polyelectrolyte behaves every bit a coil, expanded by intramolecular repulsion. A quick browse of the formulas for electrical interaction Gibbs energies shows these to scale with c _s ^−1/2 provided ψ^d or σ^d are constants. Deviations from the c _{due south} ^−1/ii law are expected for electrostatic (ψ^d and/or σ^d are not constant but volition regulate) and conformational reasons (for loftier chain charges, the molecule assumes a rather rod–type conformation, see sec. ii.3). Past way of illustration we give a few illustrations, emphasizing the c _s ^−1/ii role and accompanying deviations.

Figure 2.24 illustrates the expected trends for a weak polyelectrolyte. The data are plotted in terms of the parameter B in the Stockmayer–Fixman equation. This parameter is independent of M and has the dimensions of intrinsic viscosity, i. eastward. of a reciprocal weight concentration (in these experiments, decilitres per gram). One may await B to consist of an electrical and a non–electrical function, which according to the figure, are linearly additive:

Figure 2.24. Electrolyte concentration dependence of the intrinsic viscosity for NaPAA in NaBr solutions of concentration c _s (mol dm⁻³). Given is the parameter B in [two.4.11]. The caste of dissociation is indicated.

(Redrawn from Noda et al. loc. cit.)

[two.iv.13] $\text{B}={\text{B}}_{\text{non-e1}}+{\text{B}}_{\text{el}}$

[2.4.14] ${\text{B}}_{\text{el}}=\text{const}.f\left(\alpha \right){\text{C}}_{\text{s}}^{-1/\mathrm{ii}}$

where f(α) is a function of the degree of ionization. It appears that B _not–el is independent of c _southward and α; this must be an intrinsic macromolecular parameter. The part f(α) is substantially a measure of the relation σ^d(σ^o). As is always found, upon increasing σ^o further increases of α go gradually less active in increasing σ^d (or the 'active' fraction). The trends of fig. 2.24 appear to be rather representative; they accept as well been reported (in less particular) by Satoh et al. (loc. cit.) for poly(α–L–glutamic acrid) in NaCl.

Figures 2.25a and b are meant to illustrate the lyotropic furnishings for a strong polyelectrolyte solution. These measurements take been carried out as a office of the shear charge per unit γ˙. The intrinsic viscosity increases somewhat with decreasing γ˙ simply maintains the same ionic specificity, of which the trends are typical. For instance, these have also been observed by Cohen and Priel ²⁾ , though at lower c _s. The differences between the different counterions reflect their specific bounden to the chain; increased binding leaves less charge in the diffuse (i.e. interaction–agile) function. So, it is seen that the binding increases from z ₊ = 1 to z ₊ = 2 and for fixed z ₊, according to Li⁺ < Na⁺ < Thousand⁺ and Mg²⁺ < Ca²⁺ < Ba²⁺. This is the familiar sequence for sulphate groups; it is a. o. reflected in the c. m.c. of dodecylsulphate micelles ³⁾ and in the surface pressure of Gibbs monolayers of the respective surfactants ⁴⁾ .

Figure 2.25.. Ion specificity in the intrinsic viscosity of Na poly(styrene sulphonate) equally a part of the electrolyte concentration. Measurements at non-naught shear (γ˙ = 1000 s⁻¹). Redrawn from Jiang et al. ¹⁾ .

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Molecular Weight Determination of Polyethylene Terephthalate

Shady Farah , ... Abraham J. Domb , in Poly(Ethylene Terephthalate) Based Blends, Composites and Nanocomposites, 2015

Determination of PET Molecular Weight 144

8.2.i

Intrinsic Viscosity Method145

8.two.1.1

Decision of Intrinsic Viscosity from Melt-Flow Index 147

8.2.two

Decision of Molecular Weight by the Mark–Houwink Equation 147

viii.ii.3

Decision of Molecular Weight by Carboxyl and Hydroxyl End Grouping Analysis Methods 148

8.2.4

Average Molecular Weight Determination of Polyesters by NIR Spectroscopy 148

eight.ii.5

Stop Group Decision of PET by NMR Spectroscopy 149

eight.ii.6

Determination of Molecular Weight by Gel Permeation Chromatography 149

8.2.half-dozen.one

Methods for Obtaining Molecular Weight from GPC 151

8.2.6.2

Simplified Molecular Weight Method 151

8.2.6.3

Dawkins Method 151

8.2.vi.4

Mobile Stage for the Determination of Molecular Weight of PET past GPC 152

8.2.half dozen.5

Examples for Molecular Weight Decision Using GPC 152

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