Theta solution intrinsic viscosity

Intrinsic viscosity measurements revealed a conformational transition upon heating from 26 to 40 °C, while the UV absorbance of the solution was insensitive to the change. The entropy parameters for PA were also discussed in light of the Flory-Krigbaum correlation between the second virial coefficient and theta temper-... 

Comparison of the limiting viscosity numbers determined in deionized water with those determined in 1 molar sodium nitrate shows a 20 per cent decrease in copolymer intrinsic viscosity in the saline solution. These results are consistent with previous studies using aqueous saline solutions as theta solvents for 2-propenamide polymers(47) Degree of hydrolysis controls the value of limiting viscosity number for the hydrolyzed copolymers in distilled water. 

Staudinger showed that the intrinsic viscosity or LVN of a solution ([tj]) is related to the molecular weight of the polymer. The present form of this relationship was developed by Mark-Houwink (and is known as the Mark Houwink equation), in which the proportionality constant K is characteristic of the polymer and solvent, and the exponential a is a function of the shape of the polymer in a solution. For theta solvents, the value of a is 0.5. This value, which is actually a measure of the interaction of the solvent and polymer, increases as the coil expands, and the value is between 1.8 and 2.0 for rigid polymer chains extended to their full contour length and zero for spheres. When a is 1.0, the Mark Houwink equation (3.26) becomes the Staudinger viscosity equation. 

The intrinsic viscosity in a theta solution is labeled Equation (3-39) can thus be expressed as follows for theta conditions ... 

In a better solution than that provided by a theta solvent the polymer coil will be more expanded. The radius of gyration will exceed the which is characteristic of the bulk amorphous state or a theta solution. If the polymer radius in a good solvent is times its unperturbed /-g, then the ratio of hydrodynamic volumes will be equal to a and its intrinsic viscosity will be related to [ /] by... 

Other factors affecting retention volume are the viscosity of the mobile phase, the sizes of gel pores, and the effective size of the solute molecules. Of these, the former two can be ignored, because they exhibit either no effect or only a small effect. The effective size of a solute molecule may also change with changing column temperature. The dependence of intrinsic viscosity on column temperature for PS in chloroform, tetrahydrofuran, and cyclohexane were tested [5]. The temperature dependence of intrinsic viscosity of PS solutions was observed over a range of temperatures. The intrinsic viscosity of PS in tetrahydrofuran is almost unchanged from 20°C up to 55°C, whereas the intrinsic viscosity in chloroform decreased from 30°C to 40°C. Cyclohexane is a theta solvent for PS at around 35°C and intrinsic viscosity in cyclohexane increased with increasing column temperature. 

The viscosity method makes use of the fact that the exponent, a, in the Mark-Houwink equation (see Frictional Properties of Polymer Molecules in Dilute Solution), rj = KM° , is equal to 0.5 for a random coil in a theta-solvent. A series of polymers of the same type with widely different known molecular weights is used to determine intrinsic viscosities [t ] at different temperatures and hence a at different temperatures. The theta-temperature can thus be determined either by direct experiment or, if it is not in the measurable range, by calculation. 

If the universal constancy of is accepted, it is possible to calculate the average dimensions of polymer molecules in solution merely from knowledge of their intrinsic viscosities and molecular weights. More particularly, it is possible to calculate the natural, or unperturbed, dimensions of the polymer chain from the knowledge of intrinsic viscosity in a theta solvent [28,29]. 

Problem 3.24 The intrinsic viscosity of polystyrene of molecular weight 3.2x10 in toluene at 30°C was determined to be 0.846 dlVg. In a theta solvent (cyclohexane at 34°C) the same polymer had an intrinsic viscosity of 0.464 dL/g. Calculate (a) unperturbed end-to-end distance of the polymer molecule, (b) end-to-end distance of the polymer in toluene solution at 30°C, and (c) volume expansion factor in toluene solution. (3> = 2.5x10 mol )... 

The intrinsic viscosity of different fractions of cis-1,4-polybutadiene (PB) was measured in isobutyl acetate at 20.5°C. Based on the viscometric results [F. Danusso, G. Moraglio, and G. Gianotti, J. Polym. Sci, 51, 475 (1961)] given below, determine whether theta conditions have been attained in the solution. 

Viscosity measurements were made on solutions of fractionated cis-1,4-polybutadiene samples in toluene at 30°C and in n-heptane at —1°C (theta temperature), yielding the following values of intrinsic viscosities (in dL/g) ... 

Hadjichristidis and coworkers [230] studied the hydrodynamic behavior, in dilute solution, of miktoarm stars of the types A2B and A2B2 where A, B = PS, PI, and PBD in solvents good for both segments or theta for one of the arms and good for the others. Analysis of the results suggests that the experimentally determined values of intrinsic viscosity, [q], viscometric radius, Rv, and Rh for the copolymers are higher than the ones calculated from homopolymer star data. The phenomenon was perceived as an indication of repulsive interactions between A and B chains, which tend to increase the sizes of the individual chains and of the star molecule as a whole [230]. A similar conclusion was reached from SEC experiments on polystyrene-poly-f-butylacrylate miktoarm stars with equal number of branches of the two components [243]. The phenomenon, in this case, was more pronounced as the molecular weight of the branches increased. 

This equation applies for polymeric solutions under theta conditions. Theta conditions are those at which excluded volume effects (expansion of the dimensions of the ideal coil) are exactly compensated by polymer solvent interactions (Chapter 25). The dependence between intrinsic viscosity and MW is given by the Mark-Houwink-Sakurada equation (see also Chapter 1) ... 

Equations (19) and (20) are valid in theta solvent. The more compact structure and the lack of chain ends result in different chemical and physical properties of cyclic polymers, including lower translational friction coefficients, higher glass transition temperatures [167], faster crystallization [168], higher refractive index [169], higher density [170], higher critical solution temperature [167], and lower intrinsic viscosity [167, 171, 172]. 

The intrinsic viscosity (IV) is physically related to the "hydrodynamic volume" of the chain (its volume during flow), so that when the chain dimensions (as defined by end-to-end distance) increase in the solution, the IV will increase en suite. In practice, a large deviation is found between IV in a "bad" solvent (worst conditions at the so-called theta (0) state, where a = 0.5), and in an "excellent" one (where high values of IV are fotmd and a = 0.8). 

The solution viscosity of cyclic polymers is lower than those of their linear analogues. The viscosity of cyclic and linear PS was preferentially studied and compared in cyclohexane, a theta solvent. Quite similar intrinsic viscosity ratios, [>/]c/[>/]i/ were determined by several research groups for this system for instance, values of 0.64-0.70 depending on the molar mass, of 0.67, and of 0.65 are reported. However, at high molar masses (>20 000gmor ), the ratio of intrinsic viscosities was found to approach unity.A similar tendency was reported also for cyclic and linear poly(2-vinylpyridine) and polybutadiene. For cyclic and linear PDMS, the ratio of intrinsic viscosities, [r ]cl[h] i under 0-conditions in bromohex-ane at 18 °C, was found to be equal to 0.66. ... 

In viscosimetric measurements the product KnX[q] is a measure for the solvent quality that describes these additional interactions and the expansion of the coil by the solvent molecules (similar to the exponent a of the [/j]-M-relationship see The influence of the solvent quality on the [/j)-M-relationship in Chap. 6). Solely at theta-conditions the Huggins constant is zero and therefore the product KhX[/jP. At theta-conditions, the long-range interactions between polymer segments are compensated by the solvent even at higher concentrations (see Chap. 8). In this case, the specific viscosity /jgp of a dilute solution increases linearly with the concentration and the reduced viscosity is independent of the concentration and is equivalent to the intrinsic viscosity. 

The intrinsic viscosity [r ] of a polymer increases with rising solvent quality (see Solvent in Chap. 5) due to the increased solvating envelope of the polymer chain. An increased effective volume of the chain leads to an expansion of the polymer coil and therefore to an increased intrinsic viscosity (see Fig. 5.2). The solvent quality can also be seen in the exponent a of the [q]-M-relationship. In the case that the interactions of the solvent molecules with the chain are so small that the coil is not contracted or expanded, theta-conditions are reached and the coil has its unperturbed dimensions in solution. A theta solvent is referred to as a thermodynamically poor solvent. In this solution state a theoretical value for the exponent a=0.5 can be derived (the required Eqs. 8.22 and 8.33 are discussed in detail in A deeper insight into in Chap. 8). This value of a=0.5 is also experimentally observed as shown in Fig. 6.7 for the theta system poIy(styrene) in cyclohexane (T=34.5 C). 

The chemical structure of a polymer can also cause a contraction of the polymer coil compared to the unperturbed dimensions at theta-conditions. In this case the exponent a of the [ ]]-M-relationship shows values of a<0.5. A contraction of the coil occurs if the attractive intramolecular interactions between the polymer segments become larger than the interactions with the solvent molecules. In extreme cases, the solvent is forced out of the polymer coil and the chain segments start to form compact aggregates. The density of the polymer coil is then independent of the molar mass and the intrinsic viscosity is constant. In this case the exponent a is zero. An example is shown in Fig. 6.12 for compact glycogen in aqueous solution. 

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. 

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