The Dilute Solution

The number of parameters that have influence on the flow behavior of a polymer solution is, as will be shown in the upcoming chapters, enormous and makes it difficult to interpret the viscosimetric measurements. For this reason, viscosimetric measurements are carried out with dilute sample solutions to minimize the interactions of the single polymer molecules. In this case, only the interactions between the polymer and the solvent are determined. The dilute state of solution is shown in Fig. 4.1. 

The polymer molecules are isolated from each other in solution. They take on the statistically most likely conformation and form a coil. The dimension of this coil in dilute solution is what affects the viscous properties of a polymer solution. Despite of the regional isolation between the coils, as shown in Fig. 4.1, there are interactions that take effect during the flow process. These interactions are only prevented when the state of the so-called ideal dilute solution is reached. In this case, the polymer concentration c O and the single polymer molecule only interacts with the solvent. The following description for the determination of the intrinsic viscosity is based on this idealized state of solution. 

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From these results, the thennodynamic properties of the solutions may be obtamed within the McMillan-Mayer approximation i.e. treating the dilute solution as a quasi-ideal gas, and looking at deviations from this model solely in temis of ion-ion interactions, we have... 

To measure the molecular weight of the molecule, we can modilV equation (B 1.9.23) to take into account the intramolecular interference in the dilute solution range. 

The dilute solution properties of copolymers are similar to those of the homopolymer. The intrinsic viscosity—molecular weight relationship for a VDC—AN copolymer (9 wt % AN) is [77] = 1.06 x 10 (83). The characteristic ratio is 8.8 for this copolymer. 

An extensive investigation of the dilute solution properties of several acrylate copolymers has been reported (80). The behavior is typical of flexible-backbone vinyl polymers. The length of the acrylate ester side chain has Httle effect on properties. 

For this system, the vapor pressure is a function of both temperature and the concentration of water in the dilute solution. 

Do and D o are dilute solution binary diffiisivities. Errors depend on the procedure used to determine the dilute solution diffiisivities. 

For estimating the diffusivity of the dilute solute (10 mole percent) in water, the method of Hayduk and Laudie, Eq. (2-159), applies. 

In tire transition-metal monocarbides, such as TiCi j , the metal-rich compound has a large fraction of vacairt octahedral interstitial sites and the diffusion jump for carbon atoms is tlrerefore similar to tlrat for the dilute solution of carbon in the metal. The diffusion coefficient of carbon in the monocarbide shows a relatively constairt activation energy but a decreasing value of the pre-exponential... 

Here, the solute S is in dilute solution, and tire equation can be used across the enthe composition range of tire A-B binary solvent, when Aa + Ab is close to one. When the concentration of the dilute solute is increased, the more concentrated solution can be calculated from Toop s equation (1965) in the form... 

Define fC = Xm/XaXb and = c /caCb, convert molar concentrations to mole fractions using the dilute solution limit, Eq. (6-25), thus obtaining Using Eqs. (6-21) and (6-22) yields... 

To a hot solution of 20.6 g of sodium in 400 ml of absolute ethanol, there is added a solution of 110 g of phthalide and 110 g of p-methoxybenzaldehyde. A vigorous reaction ensues and one-helf of the alcohol is distilled off over a two hour period. Ice and water are added to the red solution end the diluted solution is ecidified with hydrochloric acid. The resulting gum solidifies end the aqueous phase is removed by decantation. The crude solid is recrystallized twice from two liters of ethenol yielding 2-(p-methoxyphenyl)-1,3-indandione as pale yellow crystals, MP155°-156°C. 

These core-shell type microspheres have very interesting structural features in that the cores are hardly crosslinked and the shell chains are fixed on the core surface with one end of the shell chains. The other end of the shell chains is free in good solvents for the shell chains. As the result of such a specific structure, the solubilities of the core-shell type polymer microspheres are governed by, not the core, but by the shell sequences, and the core-shell structures do not break even in the dilute solution [9,10]. 

At finite temperature the chemical potentials can be calculated as follows. In the dilute solution approximation, the Gibbs free energy is given by ... 

Diffusivity of the liquid light key component is calculated by the dilute solution equation of Wilke-Chang [243]. 

Molecular Weight Determination by Application of Raoult s Law. If a small amount (m in grams) of a nonvolatile, nonionized substance (solute, 2) is dissolved in m, grams of a volatile liquid (solvent, 1), it experiences a lowering of vapor pressure from the pure solvent value (P ) to the solution value (P) at the system temperature. This is a consequence of Raoult s law because the total vapor pressure of the dilute solution (x 1) is given by P = x P + x P = 1 -... 

Salt Concentration Cells. In this type of cell the two electrodes are of the same metal (i.e., copper). These electrodes are immersed completely in electrolytes of the same salt solution (i.e., copper sulfate) but of different concentrations. When the cell is short circuited, the electrodes (anode) exposed to the dilute solution will dissolve into the solution and plate the electrode (cathode) exposed to the more concen-trated solution. These reactions will continue until the solutions are of the same concentration. Figure 4-432 shows a schematic of a salt concentration cell. 

The dilute solutions of elements in solid iron are, at present, the only system for which the thermodynamics has been reasonably well worked out experimentally. The remainder of this section will therefore be devoted to the diagrammatic representation of data for these systems which have been evolved by Richardson... 

For quaternary and more complex alloys a suggestion of Chipman and Sherman might be used. Chipman s school have made use of the symbol c for the rate of change of In y of the dilute solute, C, with small additions of alloying elements, X. Thus for the solution of carbon in iron ... 

It is easy to measure the potential of this system and it has been found that membranes of polystyrene, linseed oil and a tung oil varnish yielded diffusion potentials of 43-53 mV, the dilute solution being always positive to the concentrated. Similar results have been obtained with films of nitrocellulose, cellulose acetate , alkyd resin and polyvinyl chloride . 

Witer is accidentally added to 350.00 mL of a stock solution of 6.00 M HC1. A 75.00-mL sample of the diluted solution is titrated to pH 7.00 with 78.8 mL of 4.85 Af NaOH. How much water was accidentally added (Assume that volumes are additive.)... 

The above procedure may be adapted to the determination of molybdenum in steel. Dissolve a 1.00 g sample of the steel (accurately weighed) in 5 mL of 1 1 hydrochloric acid and 15 mL of 70 per cent perchloric acid. Heat the solution until dense fumes are evolved and then for 6-7 minutes longer. Cool, add 20 mL of water, and warm to dissolve all salts. Dilute the resulting cooled solution to volume in a 1 L flask. Pipette 10.0 mL of the diluted solution into a 50 mL separatory funnel, add 3 mL of the tin(II) chloride solution, and continue as detailed above. Measure the absorbance of the extract at 465 rnn with a spectrophotometer, and compare this value with that obtained with known amounts of molybdenum. Use the calibration curve prepared with equal amounts of iron and varying quantities of molybdenum. If preferred, a mixture of 3-methylbutanol and carbon tetrachloride, which is heavier than water, can be used as extractant. 

Analyses, (a) Original zinc-ion solution. Dilute 2.00 mL (pipette) to 100 mL in a graduated flask. Pipette 10.0 mL of the diluted solution into a 250 mL conical flask, add ca 90 mL of water, 2 mL of the buffer solution, and sufficient of the solochrome black indicator mixture to impart a pronounced red colour to the solution. Titrate with standard 0.01 M EDTA to a pure blue colour (see Section 10.59). 

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