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Theta temperature, pressure

Theta temperature is one of the most important thermodynamic parameters of polymer solutions. At theta temperature, the long-range interactions vanish, segmental interactions become more effective and the polymer chains assume their unperturbed dimensions. It can be determined by light scattering and osmotic pressure measurements. These techniques are based on the fact that the second virial coefficient, A2, becomes zero at the theta conditions. [Pg.106]

Molecular weight from osmotic pressure measurements Degree of polymerization and molecular weight distribution Excluded volume from osmotic pressure measurements Theta temperature from second virial coefficient data Evaluation of charges on macroions from osmotic pressures... [Pg.638]

In order to get the real mass flow from the map, multiply by delta and divide by the square root of theta. The pressure and temperature condition immediately before the turbomachineiy is used, not the ambient measurement. For instance, at the turbine expander, the inlet temperature and pressure will be quite elevated and will change dramatically with a change in some process condition such as combustor firing rate therefore, the look-up value on the map will change. [Pg.255]

The free energy change which takes place when polymer chains interpenetrate is influenced by factors such as temperature, pressure and solvent composition. The point at which this free energy change is equal to zero is known as the 0 (theta)-point and such a solvent is called a 0-solvent. More formally, a 0-point is defined as one where the second virial coefficient of the polymer chains is equal to zero. It can be determined by light scattering and by osmometry. [Pg.238]

Theta temperature n. (1) (0, Flory temperature). d is also the temperature for the polymer solution at which the second virial coefficient in the equation giving molecular weight from osmotic pressure approaches zero. (2) The critical temperature of mixing for a polymer of infinitely high degree of polymerization. [Pg.976]

The reference temperature is not the true theta temperature at which the second virial coefficient of the osmotic pressure vanishes. The latter lies far below due to H-bonding and hydrophobic interaction in addition to the van der Waals interaction in the background. The parameters related to the strength of hydration, such as no, yn, were taken from Section 6.4 for PEO, and Section 6.5 for PNIPAM. [Pg.358]

In addition to studying the solubilization of C02-insoluble polymers by means of emulsifying agents [25], as described in Section 7.1.3, SANS has also been used to study C02-soluble systems such as fluoropolymers and PDMS [24]. In particular, Melnichenko et al. [239] have studied the dimensions of PDMS molecules in CO2 in order to test the prediction of Kiran and Sen [240] that they will adopt ideal configurations, unperturbed by excluded-volume effects, at a critical theta pressure (Pe) as they do in polymer solutions at the theta temperature (T ). Results of experiments on PDMS in CO2 (Figs. 7.39 and 7.40) confirm that the system exhibits both of these phenomena at P 540 bar and T 55 °C. [Pg.493]

The SANS experiments on PDMS in COj were designed to compare the chain dimensions with those in organic solvents and to test the prediction [7] that they will adopt ideal configurations, unperturbed by excluded volume effects, at a critical theta pressure XPo) as they do in polymer solutions at the theta temperature. The effect of temperature on the thermodynamic state of PDMS - COj solution is illustrated in Fig. 4. The concentration fluctuations diverge as the temperature approaches the phase boundaries, which are themselves a function of pressure. When the correlation length decreases to the theoretical value (0) Rg(0)/3 s 41 A, the condition is reached and this demonstrates that, unlike PS-AC, the solvent quality may be changed from the "poor to theta solvent by varying the temperature, as in PS-... [Pg.323]

Fig.6 shows that PDMS may tdso enter the good solvent domain at a theta temperature Te = 65 5 C, as observed in PS-CH solutions [21]- However, unlike organic solvents, diis transition can also be made to occur at a critical tiieta pressure (P - 52 4 MPa) in COj, as illustrated in the inset in Fig.6. To our knowledge, this is die first time that the existence of a theta pressure has been demonstrated experimentally and a more detailed description of tilts phenomenon is given in reference [22]. Fig.6 shows that PDMS may tdso enter the good solvent domain at a theta temperature Te = 65 5 C, as observed in PS-CH solutions [21]- However, unlike organic solvents, diis transition can also be made to occur at a critical tiieta pressure (P - 52 4 MPa) in COj, as illustrated in the inset in Fig.6. To our knowledge, this is die first time that the existence of a theta pressure has been demonstrated experimentally and a more detailed description of tilts phenomenon is given in reference [22].
All the experimental results obtained in the semidilute 0-solutions are consistent with the idea of de Gennes and Brochardthat at the theta temperature, where the second virial coefficient of the osmotic pressure vanishes, the mesh size of the transient gel is not proportional to the correlation length of concentration fluctuations as it is in the case of a good solvent. ... [Pg.303]

Theta conditions in dilute polymer solutions are similar to tire state of van der Waals gases near tire Boyle temperature. At this temperature, excluded-volume effects and van der Waals attraction compensate each other, so tliat tire second virial coefficient of tire expansion of tire pressure as a function of tire concentration vanishes. On dealing witli solutions, tire quantity of interest becomes tire osmotic pressure IT ratlier tlian tire pressure. Its virial expansion may be written as... [Pg.2518]

X-ray diffraction powder patterns were recorded on a CGR Theta 60 instrument, using monochromated CuKa radiation. The adsorption capacities for several adsorbates were measured at room temperature by gravimetry, using a Cahn RH microbalance as proposed by Vaughan and Lussier (3 ). The samples were first treated in air for 5 hours at 480°C. The experiment was performed by passing, over the sample, a stream of nitrogen saturated by the vapor pressure of the sorbate at room temperature, the relative pressure P/Po was then equal to 1. [Pg.240]

Characterization of catalysts The zeolite structure was checked by X-ray diffraction patterns recorded on a CGR Theta 60 instrument using Cu Ka, filtered radiation. The chemical composition of the catalysts was determined by atomic absorption analysis after dissolution of the sample (SCA-CNRS, Solaize, France). Micropore volumes were measured by N2 adsorption at 77 K using a Micromeritics ASAP 2000 apparatus and by adsorption of cyclohexane (at P/Po=0.15) using a microbalance apparatus SET ARAM SF 85. Incorporation of tetrahedral cobalt (II) in the framework of Co-Al-BEA and Co-B-BEA was confirmed by electronic spectroscopy [18] using a Perkin Elmer Lambda 14 UV-visible diffuse reflectance spectrophotometer. Acidity measurements were performed by Fourier transform infrared spectroscopy (FT-IR, Nicolet FTIR 320) after pyridine adsorption. Self-supported wafer of pure zeolite (20 mg/cm ) was outgassed at 673 K for 6 hours at a pressure of lO Pa. After cooling at 423 K, the zeolite was saturated with pyridine vapour (30 kPa) for 5 min, evacuated at this temperature for 30 min and the IR spectrum was recorded. [Pg.579]

Determination of the theta-point It was shown above that at the 0-point the second virial coefficient vanishes. This allows the 0-point to be located by light scattering or osmotic pressure measurements. It can also be found by the rather time-consuming determination of the critical solution temperature extrapolated to infinite molecular weight. [Pg.43]

Fig. 2. (a) Schematic phase diagram of a polymer solution, at constant pressure, using temperature T and volume fraction 0 of the polymer as variables. Phase separation into a dilute or semidilute solution (with volume fraction 0e ex) a more concentrated solution (with volume fraction 0 x)occurs for states (T, 0) that fall in the two-phase region underneath the coexistence curve (binodal). The binodal ends in the critical point 0c(AO, TdN), where N is the degree of polymerization of the polymer. For iV - oo the critical point merges with the theta point of the dilute solution, ie, T = 0,0c(iV oo) = 0. For further explanations cf text,... [Pg.5484]

Hsiao et al. reported a cloud point pressure at approximately 150-170 bar and 40 C for 4 wt% of a PFOA sample (Af = 1,000,000 g/mol) [30], An LCST-type behavior was also noted as a result of the positive dependency of pressure upon increasing temperatures. Through neutron scattering experiments, this high solubility of PFOA could be related to a positive second virial coefficient (A2) in conditions as mild as 207 bar and 45°C in the case of sample with an equal to 36,500 g/mol [31]. However, the theta pressure was not determined. In another set of experiments, the positive A2 was found to be a decreasing function of molecular weight, as expected from the case of polymer solutions in incompressible solvents [32]. A2 was also estimated to be proportional to at the power of -0.4. [Pg.323]


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See also in sourсe #XX -- [ Pg.16 , Pg.18 , Pg.21 , Pg.23 , Pg.25 ]




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