Precipitation threshold

Fig. 123.—(a) Phase diagram calculated for three-component systems consisting of nonsolvent [1], solvent [2], and polymer [3] taking Xi==X2=l and Xz equal to 10 (dashed curve), 100 (solid curve), and °° (dotted curve) xi2 = xi3 = 1.5 and X23 =0. All critical points (O) are shown and tie lines are included for the xs = 100 curve. (Curves calculated by Tompa. ) (b) The binodial curve for a 3 = 100 and three solvent ratio lines. The precipitation threshold is indicated by the point of tangency X for the threshold solvent mixture. 

Fig. 22 Static light scattering close to the precipitation threshold. Measurements are performed at constant [Ca2+] by decreasing [NaPA] (route 1). The inert salt level is 0.1 M NaCl. Squared mean square radius of gyration is plotted vs. [NaPA], The symbols denote four different Ca2+ concentrations 3.25 mM ( ) 3.5 mM ( ) 3.75 mM (A) 4.0 mM ( ). Vertical lines indicate precipitation limits which appear as open circles in Fig. 23...

From the experiments just outlined [74-76], a few points are worth being emphasized A powerful procedure was developed to gradually approach phase boundaries of polyelectrolyte precipitation. The approaches can be performed in a highly systematic manner and lead to states which are located extremely close to the precipitation threshold. Approaches could successfully be accompanied by LS experiments. The experiments demonstrated, that the polyelectrolyte chains shrank dramatically in size immediately before the phase boundaries were reached. A sudden increase of the scattering intensity indicated the phase boundaries. These developments give rise to the hope that intermediates may be revealed which have not become accessible in preceding investigations [78-81]. 

Clearly, the phase boundaries lie on top of each other. A closer look reveals a slight decrease in the slope r0 of Eq. (26) according to Ca2+>Sr2+>-Ba2+, which indicates that the larger the bivalent earth alkaline cation is, the smaller is the stoichiometric amount of M2+ necessary to precipitate NaPA. Although based on a different method, the present results suggest a comparison with data from Pochard et al. [73]. In doing so, we have to keep in mind that our own r0 values are of fair accuracy at best because they were evaluated from slopes based on a few data points only. Still, this trend in rQ is the opposite to the observation of Pochard et al. [73]. They found a decrease of the amount of M2+ per COO function at the precipitation threshold, if Ca2+... 

The above observations are in agreement with studies on chain contraction of sodium polymethacrylate (NaPMA) in the presence of Ca2+ and Cu2+ counterions [25]. Static and quasi-elastic light scattering measurements indicate that a PMA chain contracts but does not have a compact spherical structure close to the precipitation threshold. 

We filter a heterogeneous solution before putting it in our NMR tube. Adding a tiny splash of extra solvent to a saturated solution to get below the precipitation threshold may also help minimize the line broadening caused by the microscopic nucleation of colloidal or crystalline particles present in saturated solutions. Alternatively, we... 

The simple thermodynamic model derived in Sect. 2.1 has been useful to get a qualitative insight into the phase separation process. When one intends to apply it to an actual system, the significant influence of polydispersity is clearly evidenced. For example, Fig. 13 shows the experimental cloud-point curve for a DGEBA-CTBN binary mixture, together with binodal and spinodal curves calculated by assuming monodisperse components [66] (curves are arbitrarily fitted to the critical point). The shape of the CPC and precipitation threshold temperature (maximum of the CPC) appearing at low modifier concentrations are a clear manifestation of the rubber polydispersity [77]. 

Toinpa (1956) has called the highest (in case of UCST) or lowest (in the case of LOST) temperature at which phase separation may occur (the maximum or minimum of the phase boundary) a precipitation threshold. 

Figure 3.12. Schematic of the quasibinary section of a ternary (multicomponent) system, Tp, is tile temperature of the precipitation threshold CPC is the cloud-point curve (tlw phase boundary). / stands for the phase coexistence curves at the total polymer concentration V cj and 4. SL is the shadow line. The concentrations of the coexisting...

In strictly binary systems, the precipitation threshold matches the critical temperature aiul the CPC matches the binodal (the phase coexistence curve) (Francis, 1963). The CPC location on a quasibinary section of a polynary sy.stem depends on the MWD function and the thermodynamic properties through x = x(T, V=, MWD). 

A recent approach in polymerization studies in our laboratory is the use of binary fluid mixtures of carbon dioxide with a traditional solvent to increase the precipitation thresholds and thus achieve higher molecular weights [26]. In this context AIBN initiated free-radical polymerization of styrene has been reported in mixtures of carbon dioxide with pentane, toluene and sulfur hexafluoride [26]. 

Type of data cloud points, precipitation threshold (UCST-behavior)... 

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