Properties of Dilute Solutions

now that the thermodynamics have been covered, we know how to get the polymer into solution, but how the polymer chains are organized in the solution is also important. Let us initially assume that the polymer is in a fairly dilute solution, therefore we can assume that there are very few entanglements between the polymer chains. Entanglements begin to set in when the dimensionless Berry number (Be), the product of intrinsic viscosity and concentration, exceeds unity [18]  

FIGURE 7.5 The effects of solvent power and temperature on a polymer molecule in solution. 

For typical polymer-solvent systems, this usually works out to a few percent polymer. 

In the limit of infinite molecular weight (the minimum possible AS), the situation where AH = TAS is known as the 6 or Flory condition. For a polymer of infinite molecular weight in a particular solvent, the 6 temperature equals the UCST, indicating that the solution is on the brink of phase separation. Under these conditions, the polymer-solvent and polymer-polymer interactions are equal, and the solution behaves in a so-called ideal fashion with the second virial coefficient equal to 0, etc., and the MHS exponent (Eq. 5.18) a = Q.5. 

For a given polymer, 6 conditions can be reached at a fixed temperature by adjusting the solvent to give a 9 solvent or with a particular solvent by adjusting the temperature to reach the 9 or Flory temperature. Any actual polymer will still be soluble under 9 conditions, of course, because of its lower-than-infinite molecular weight and consequently larger AS. 

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P. E. Rouse. The theory of nonlinear viscoelastic properties of dilute solutions of scaling polymers. J Chem Phys 27 1273-1280, 1953. 

We have reported the absorption properties of dilute solutions of PET dissolved in HFIP and assigned the foil owing,absorptions ... 

Andon, R.J.E., Counsell, J.F., Tees, E.B., Martin, J.F., and Mash, MJ. Thermodynamic properties of organic oxygen compounds. Part 17. Tow-temperature heat capacity and entropy of the cresols, Trans. Faraday Soc., 63 1115-1121,1967. Andon, R.J.E., Cox, J.D., and Herington, E.F.G. Phase relationships in the pyridine series. Part V. The thermodynamic properties of dilute solutions of pyridine bases in water at 25 °C and 40 °C, J. Chem. Soc. (London), pp. 3188-3196, 1954. Andrades, M.S., Sanchez-Martin, M.J., and Sanchez-Camazano, M. Significance of soil properties in the adsorption and mobility of the fungicide metalaxyl in vineyard soils, J. Agric. Food Chem., 49(5) 2363-2369, 2001. 

Rouse, P.E. A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 21,1272-1280 (1953). 

Boggs FW, Tompson J (1966) Flow properties of dilute solution of polymers Part I Mechanism of drag reduction U.S. Rubber Co. Research Center Report on Contract No. Nonr. 3123(00)... 

Raoult s law is directly responsible for two other properties of dilute solutions the elevation of the boiling point and the depression of the freezing point. 

An independent empirical confirmation of this relation was discussed in Section 6.2.4. The relation was mention in Section 2.5 and used at the choice of specific values of the parameters for calculation of dynamic properties of dilute solutions in Section 6.2.2. 

The mentioned phenomena are among the remarkable properties of diluted solutions and are determined solely by the numbor of molos of substance dissolved in one unit of volume of the solution, not by the nature of that substance. Such properties, being functions of molar concentration only, are called colligative properties. 

References to other investigations of the properties of dilute solutions of the nitrate are appended.1... 

It was van t Hoff, winner of the very first Nobel prize in chemistry, who perceived an analogy between the properties of dilute solutions and the gas laws. We will see that many physical properties of dilute solutions, such as the amount of light scattered or the viscosity, can be written as a virial equation in the number of molecules (moles), N, or concentration of solute, c. We have written a general form of a virial equation in Equation 12-4, using the quantity P to represent some measured property of the solution and P0to represent the property of the pure solvent. 

As we mentioned earlier in this section, it was van t Hoff who saw an analogy between the properties of dilute solutions and the gas laws. Just as an equation of state can be written for an ideal gas, so can an equation of state be written for an ideal solution in terms of its osmotic pressure, as shown in Table 12-2. It is then a straightforward matter of remembering the definition of a mole (the weight of something divided by its molecu-... 

Since the density p appears in a dimensionless combination here, the concentration dependence of the chemical potential comes with a choice of concentration units. The first term on the right side of Eq. (3.1) expresses the colligative property of dilute solutions that the thermodynamic activity of the solute, is proportional to its concentration, p. The excess chemical potential accounts for intermolecular interactions between the solution molecules, and is given by the potential distribution theorem (Widom, 1963 1982) ... 

Problem 3.6 exercises your ability to compute nonlinear rheological properties of dilute solutions. 

In the history of physical chemistry dilute solutions were regarded as specially important, as their behaviour is governed by simple laws. A dilute solution is a solution in which the concentration of one component (the solvent) preponderates greatly over that of all the others. The physical properties of dilute solutions differ therefore only slightly from those of the pure solvent. Their thermal properties are connected with the... 

Raoult s law forms the basis for four properties of dilute solutions, which are called colllgative properties (derived from Latin colligare, meaning to collect together ) because they depend on the collective effect of the number of dissolved particles rather than on the nature of the particular particles involved. These four properties are ... 

If the polymer volume fraction in solution is below the overlap volume fraction 0, the solution is called dilute (p<4> ). The average distance between chains in dilute solutions is larger than their size. Therefore, polymer coils in dilute solutions are far from each other swimming happily in surrounding solvent. Most properties of dilute solutions are very similar to pure solvent with slight modifications due to the presence of the polymer. 

The discussion of luminescence has, up to the present, been based on the properties of dilute solutions in which the analyte molecules were presumed not to interact with one another. It has already been established that at high absorbance at the wavelength of excitation, deviations from linearity of the fluorescence in-tensity-versus-concentration relationship may occur because of the exponential variation of luminescence intensity with concentration. However, over a wide range of solute concentrations, solute-solute interactions may also account for loss of luminescence intensity with increasing solute concentration. 

The physical properties of dilute solutions of certain surface-active substances, when plotLed as a function of solution concentration, show a more or less sharp break, which occurs at roughly the same point lor different properties. Typical examples are the breaks in the curves of surface tension, electrical conductivity, and osmotic pressure, as illustrated schematically in Figure 11.1. The... 

Thermodynamic properties of liquid Mn-Si, Fe-Sn, and Ga-Pb solutions have been determined over the entire composition ranges thermodynamic properties of dilute solutions of Cu and Sb in liquid tin and of Cd in liquid lead have also been measured. 

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