Minimum solution temperature

The lower theta temperature corresponds to the minimum solution temperature extrapolated to infinite chain length. Polymer precipitation at low temperatures comes about because of a poor heat of mixing between polymer and solvent. In a sealed tube at high temperatures, solvent volume expands much more than that of the polymer. Entropic factors make mixing more difficult when there is a large free volume mismatch between solute and solvent. One believes that the polymer dimensions contract as the LCST is approached. Phase separation occurs when it is exceeded. 

In 1960 Freeman and Rowlinson demonstrated that solutions of polyolefins in hydrocarbon solvents may also show LCM [31], These authors reported minimum solution temperatures (supposed to represent critical temperatures LCST) for solutions of polyethylene, poly(isobutylene) and polypropylene in -alkanes (cf. Table 3). These observations were not altogether unexpected. It was known at the time that hydrocarbon mixtures show LCM in the vicinity of the vapor/liquid critical point of the more volatile component if the... 

Most formaldehyde producers recommend a minimum storage temperature for both stabilized and unstabilized solutions. Figure 3 is a plot of data (17,18,122,126) for uiiinhibited (<2.0 wt% methanol) formaldehyde. The minimum temperature to prevent paraformaldehyde formation in unstabilized 37% formaldehyde solutions stored for one to about three months is as follows 35°C with less than 1% methanol 21°C with 7% methanol 7°C with 10% methanol and 6°C with 12% methanol (127). 

Experience in air separation plant operations and other ciyogenic processing plants has shown that local freeze-out of impurities such as carbon dioxide can occur at concentrations well below the solubihty limit. For this reason, the carbon dioxide content of the feed gas sub-jec t to the minimum operating temperature is usually kept below 50 ppm. The amine process and the molecular sieve adsorption process are the most widely used methods for carbon dioxide removal. The amine process involves adsorption of the impurity by a lean aqueous organic amine solution. With sufficient amine recirculation rate, the carbon dioxide in the treated gas can be reduced to less than 25 ppm. Oxygen is removed by a catalytic reaction with hydrogen to form water. 

The mechanical properties of Watts deposits from normal, purified solutions depend upon the solution formulation, pH, current density and solution temperature. These parameters are deliberately varied in industrial practice in order to select at will particular values of deposit hardness, strength, ductility and internal stress. Solution pH has little effect on deposit properties over the range pH 1 0-5-0, but with further increase to pH 5 -5, hardness, strength and internal stress increase sharply and ductility falls. With the pH held at 3-0, the production of soft, ductile deposits with minimum internal stress is favoured by solution temperatures of 50-60°C and a current density of 3-8 A/dm in a solution with 25% of the nickel ions provided by nickel chloride. Such deposits have a coarse-grained structure, whereas the harder and stronger deposits produced under other conditions have a finer grain size. A comprehensive study of the relationships between plating variables and deposit properties was made by the American Electroplaters Society and the results for Watts and other solutions reported... 

The instance we have considered here, that of a polymer in a poor solvent, results in an upper critical solution temperature (UCST) as shown in Figure 2.33. This occurs due to (a) decreased attractive forces between like molecules at higher temperatures and (b) increased solubility. For some systems, however, a decrease in solubility can occur, and the corresponding critical temperature is located at the minimum of the miscibility curve, resulting in a lower critical solution temperature (LCST). This situation is illustrated in Figure 2.34. 

A critical solution temperature (CST) is the minimum temperature for mixing of two substances in all proportions as liquid (Figure 1) or it is the maximum temperature of a binary system for two liquid phases in equilibrium. 

The polyethylene glycols or Carbowaxes and cyanopropylpolysiloxanes are the most common of the polar stationary phases. These phases possess permanent dipoles, and acid-base interaction with solutes is common. These phases are very retentive toward solutes with polar or polarizable functionality. They have lower upper temperature stabilities and higher lower minimum operational temperatures compared to the nonpolar phases. When these phases are cross-linked, the operational upper temperature limits are about 220-270°C and the lower limits about 40-60°C. 

In the system of water-ethanol, the point M corresponds to a minimum boiling temperature of 78.13° and a composition of95.57% ethanol by weight. If any solution of composition of pure water and 95.57% ethanol is distilled, then we get a residue of pure water and a constant minimum boiling mixture of 95.57% alcohol in the distillate. No pure ethanol can be recovered. On the contrary, if a solution of composition between pure alcohol and 95.57% ethyl alcohol is distilled, then we get a mixture containing 95.57% ethanol and pure alcohol. No pure water will be recovered. 

Poly(chloro-p-xylylenes) containing (in theory) about 5, 10, and 20% butyl-p-xylylene were prepared in this way (see illustration on p. 650). The crystalline melting points of the products (XVII) were in the range 220°-250°C. compared with 290°C. for pure poly (chloro-p-xylylene). Solubility characteristics of the products and a sample of poly (chloro-p-xylylene) were studied by heating in a-chloronaphthalene. The solution temperature is the minimum temperature required to dissolve the product with slow heating. The gel temperature is that at which the solution of the product in a-chloronaphthalene sets to a gel on gradual cooling. Results were as follows ... 

Flush the membranes. Membranes should be flushed following cleaning using RO-permeate quality or better water. Pretreated feed water should not be used as components may interact with the cleaning solution and precipitation of foulants my occur in the membrane modules. The minimum flush temperature should be 20°C. ... 

The EPR technique has been used for other alloys as well, including cast (36) and wrought (37,38) duplex stainless, as well as Ni-base alloys (39). Lee (38) used DL-EPR testing to determine the minimum amount of Ti and/or Nb required to render Type 430 SS immune from intergranular attack. In some cases, the details of the experimental method (i.e., solution temperature, KCNS and H2S04 concentrations, scan range) must be modified to differentiate best the levels of sensitization of interest. For example, Scully and Kelly doubled the... 

Figure 19 depicts plots of the temperature of the observed cloud point vs. the weight fraction w2 of CA(2.46) for each solution 55,56). The lower critical solution temperature, LCST, was determined as the minimum temperature of each cloud-point curve. Some CD-solvent systems show the existence of an upper critical solution temperature, UCST, together with LCST (Fig. 20) 57>. 

Unfortunately, the presence of the term in Eq. (5) makes it much more difficult to extract the equilibrium S J) behavior than it was to find (p T) for an Ising magnet. However, the general approach is the same— fmd the S value at which dQdS= 0 and G is a global minimum. The temperature dependence of 5arising from Eq. (5) for a nematic liquid crystal turns out to be quite complicated since there is no analytic solution to the quartic equation arising from 5 QdS = 0. However, the behavior of 5( 7) for 7 < 7j can still be very well approximated by a power-law expression ... 

As tire pressure increases, line C D becomes shorter and shorter (indicated in Fig. 14.17 by lines CD and C"D"), until at point M it dimiirishes to a differential length. For still Irigher pressures (P4) the temperature is above tire critical-solution temperature, and there is but a single hquid phase. The diagram then represents two-phase VLE, and it has the form of Fig. 10.9(d), exhibiting a minimum-boiling azeotrope. 

For the hydrocarbon--CO2 systems studied here, at pressures above the critical pressure (7.383 MPa) and above the critical temperature (304.21 K) of C02 the isobaric x,T coexistence plots of liquid and vapor phases form simple closed loops. The minimum occurs at the lower consolute point or the Lower Critical Solution Temperature (LCST). Since pressure is usually uniform in the vicinity of a heat transfer surface, such diagrams serve to display the equilibrium states possible in a heat transfer experiment. 

In addition, two morphotrophic phase boundaries may intersect within the solid solution system so as to produce a maximum critical temperature (Type II MPD in Fig. 6c) or a minimum critical temperature (Type III MPD in Fig. 6d). The Type II MPD is similar to that of the diopside-jadeite (CaMgSi206-NaAlSi206) solid solution (Carpenter 1980, Holland 1990, Holland and Powell 1996). Each endmember has a monoclinic structure with space group C2/c, but the midpoint of the solid solution, omphacite, has a reduced symmetry (S.G. P2 n) due to an ordering transition. Salje et al. (1991) argue that this midpoint composition actually represents the pure component of the omphacite join. A Type III MPD is observed in the lead phosphate-arsenate system (Bismayer et al. 1986). 

The temperature for salting out need be only as high as is required to prevent crystallization of the salt (R16). For 1.8 M sodiiun sulfate and 2.1 Af sodium sulfite the minimum working temperature is 25°C. A mixture of sulfate and sulfite has been proposed (R7), but solubility is not appreciably increased and the mixture still requires storing in a warm place, i.e., above 25°C, to prevent crystallization. In practice, sulfite holds no advantage over sulfate when a 37 C incubator for storing the concentrated solution is available. Warm sulfite solutions also deteriorate and must be made fresh every week (L8). Furthermore, sulfite increases the danger of albumin denaturation by ether, while sulfate has a protective influence (B31, S4). 

Some binary systems show a minimum at a lower critical-solution temperature a few systems show closed-loop two-phase regions with a maximum and a minimum.) As the temperature is increased at any composition other than the critical composition x = x, the compositions of the two coexisting phases adjust themselves to keep the total mole fraction unchanged until the coexistence curve is reached, above which only one phase... 

Solution. The hot load is of 7000 kW, the hottest stream being at 180 °C. If zl71 j,i=30 °C is assumed for utility/process exchange, the minimum steam temperature is 210 °C, or a saturation pressure of approximately 20 bar. Thermodynamic properties of steam in different conditions as required by the problem are given below (see also Atmex F) ... 

Since sorbents are available in a limited number of particle sizes, a compromise is necessary. An available particle size is selected that is larger but closest to dpopt. The column is made proportionately longer and operated at a slightly higher velocity than Vopt. The retention time, however, will be slightly longer than the theoretical minimum. Elevated temperatures are useful for fast separations because of decreased mobile phase viscosity (q) and increased solute diffusion (Dm). 

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