Volume expansion minimum

A hydrogel is formed by a water-soluble polymer that has been lightly crosslinked. Hydrogels swell as they absorb water but they do not dissolve. The volume expansion is limited by the degree of crosslinking. The minimum number of crosslinks needed to form a three-dimensional matrix is approximately 1.5 crosslinks per chain, and this yields the maximum expansion possible without separation of the chains into a true solution. Thus, a hydrogel may be more than 95% water and, in that sense, has much in common with living soft tissues. 

The volume expansions of alkali metals in liquid ammonia are discussed in the light of the current available data. Special emphasis is made of the anomalous volume minimum found with sodium-ammonia and potassium-ammonia solutions. Recent studies of potassium in ammonia at —34° C. were found to exhibit a large minimum in the volume expansion, AV, vs. concentration curve. The results of these findings were compared with the previous results of potassium in ammonia at —45° C. The volume minimum was found to be temperature dependent in that the depth of the minimum increased and shifted to higher concentrations with increasing temperature. No temperature effect was observed on either side of the minimum. These findings are discussed in light of the Arnold and Patterson and Symons models for metal-ammonia solutions. 

Curve 1 is a plot of data from the investigation of Filbert (8) at —45° C. Filbert s results show a pronounced minimum in the volume expansion vs. concentration curve at 0.0AN. The AV value at the minimum is 30 cc./gram-atom as compared with the limiting value of approximately 42 cc./gram-atom at infinite dilution. 

Let us again review the previous findings for the volume expansion of sodium and potassium in liquid ammonia. Filbert (8) reported a volume minimum for sodium in ammonia at —46° C. at approximately 0.03N. Orgell (21) confirmed the existence of this minimum for sodium in ammonia at —45° C. and extended his study to potassium in ammonia at the same temperature. Potassium-ammonia solutions were found to exhibit a minimum at O.OliV which was quite sharp and not nearly as broad as the minimum for sodium at —45° C. More recently, Brendley has investigated the volume expansion of potassium in ammonia at —34° C. Once again a pronounced minimum was found. The potassium data at —45° C. and —34° C. showed differences in the position and... 

Hydration Capacitance Maximum excluded volume Minimum excluded volume effects Coil volume expansion... 

Based on the previous considerations, some authors proposed thermodynamic-based approaches to SAS. De la Fuente Badilla et al attempted to develop a thermodynamic-based criterion for optimum batch antisolvent precipitation (GAS) using a definition of the volume expansion that takes into account the molar volume of the system studied. They analyzed various binary and ternary systems and concluded that the pressure corresponding to a minimum value of the liquid-phase volume expansion coincides with the pressure at which the solute precipitates. In a subsequent work, Shariati and Peters further highlighted the role of SC-CO2 in GAS. It acts as a co-solvent (cosolvency effect) at lower concentrations, whereas at higher concentrations it acts as an antisolvent. 

Subsequently, the relative molar volume expansion (RMVE) was considered (46) to be a more appropriate parameter, and a minimum in the variation of RMVE vs pressure or Xi, was suggested as the criterion for... 

Many important questions and conjectures remain unresolved. It is not known whether these solutions are the only embedded //-surfaces for the five dual pairs of skeletal graphs studied, for example. An important issue is whether or not there exists a bound on the mean curvature attainable in such families for all of the branches studied here, and for the family of unduloids with a fixed repeat distance (Anderson 1986), the dimensionless mean curvature H = HX is always less than n, where X is the sphere diameter in the sphere-pack limit. It is possible that there exists an upper bound on H lower than n that depends on the coordination number, or the Euler characteristic. For the P, D, I, WP, F, and RD branches, the islands over which K > 0 coalesce wih neighboring R regions at a critical mean curvature that is the same (to within an error in H of about 0.15) as the value H corresponding to the local minimum in surface area. We have given what we suspect to be the analytical value for the area of the F-RD minimal surfaces, and for the first nonzero coefficient in both the area and volume expansions about // = 0 in the P family. 

If in a particular mixture, the attractive force between different types of molecule is smaller than that between similar types of molecule, the molecules in the mixture are held together with a smaller force than those in a pure liquid. Thus, the effect during mixing is an endothermic volume expansion and an increase in vapor pressure. There is a positive deviation from Raoult s law which leads to a pronounced maximum for the vapor pressure and therefore to a minimum boiling point (for example, ethanol-water mixture). 

In fact, the rate of relaxation is highest at the start of the volume expansion, decreases to a minimum, and then increases until the end of the experiment. This behavior can be explained in terms of a distribution of relaxation times for volume fluctuations. 

If Sic particles are used to the healing agent, the volume expansion during its oxidation is 80 vol%. Thus, 1.8 times of the interlayer volume is equal to the volume that the formed oxide can be filled wiA the fi ee space between crack walls, XYZ(l-V ), where Ff is the volume fim tion of the fibers and corresponds to Z)fV4/ . Consequently, the minimum thickness of the interlayer can be expressed as,... 

Figure 5(a) shows the effect of the cell density on the radiative conductivity by fixing the volume expansion ratio at 42 and the foam density at 25 kg/ml It is noted that an elevated cell density leads to a weak radiative conductivity. Figure 5(b) describes the effect of the foam density on the radiative conductivity with the cell diameter of 350 pm, 300 pm and 250 pm, respectively. It is believed that there exists an optimum foam density to obtain a minimum radiative conductivity. This optimal foam density tends to shift toward a low value as the cell size increases. 

Upon melting, ice loses its open structure with the "melting" of some fraction of the hydrogen bonds, and so the volume of the Hquid water decreases, reaching a minimum at 4°C above this temperature thermal expansion dominates the density. 

A one-dimensional mesh through time (temporal mesh) is constructed as the calculation proceeds. The new time step is calculated from the solution at the end of the old time step. The size of the time step is governed by both accuracy and stability. Imprecisely speaking, the time step in an explicit code must be smaller than the minimum time it takes for a disturbance to travel across any element in the calculation by physical processes, such as shock propagation, material motion, or radiation transport [18], [19]. Additional limits based on accuracy may be added. For example, many codes limit the volume change of an element to prevent over-compressions or over-expansions. 

LTHW systems are usually under a pressure of static head only, with an open expansion tank, in which case the design operating temperature should not exceed 83°C. Where MTHW systems operating above 110°C are pressurized by means of a head tank, an expansion vessel should be incorporated into the feed and expansion pipe. This vessel should be adequately sized to take the volume of expansion of the whole system so that boiling will not occur in the upper part of the feed pipe. On no account should an open vent be provided for this type of system. MTHW and HTHW systems require pressurization such that the saturation temperature at operating pressure at all points in the circuit exceeds the maximum system flow temperature required. A margin of 17 K (minimum)... 

Bed expansion (freeboard) is 50% minimum (thus, the resin tank must be at least double the volume of the resin requirement). Resin bed expansion is a function of backwash rates and temperature. 

In the flow of a gas through a nozzle, the pressure falls from its initial value Pi to a value P2 at some point along the nozzle at first the velocity rises more rapidly than the specific volume and therefore the area required for flow decreases. For low values of the pressure ratio P2/P1, however, the velocity changes much less rapidly than the specific volume so that the area for flow must increase again. The effective area for flow presented by the nozzle must therefore pass through a minimum. It is shown that this occurs if the pressure ratio P2/P1 is less than the critical pressure ratio (usually approximately 0.5) and that the velocity at the throat is then equal to the velocity of sound. For expansion... 

When multiple compressors are specified, only those required for the initial plant should be purchased. Adequate space must of course be allocated to meet expansion needs. If only one compressor is specified, one large enough to meet expansion needs should be specified. For centrifugal compressors the capacity can easily be varied over a wide range. The designer should, however, check to see that the initial requirements exceed its minimum capacity, which is called the surge point. In the case of reciprocal compressors, either a clearance volume can be added to the compressor cylinders or the suction valve can be removed. See reference 39 for a discussion of this. 

At a volume corresponding to that of the experimental (fee) energy minimum modification (Vo), the interatomic distances in the open packed ff-B structure become very short, and the structure is more than 80 kJ mol-1 less stable than the fee close packing. However, when the volume is relaxed the ff-B structure is rapidly stabilized. The optimum volume lies near V/Vo = 1.4, corresponding to an expansion of about 40% with respect to the energy minimum volume. At this volume the Al-Al distances within the Al icosahedra are 264 pm, which compares... 

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