Specific volume concentration dependence

The critical micelle concentration (CMC) and the partial specific volume, F, depend on the temperature. The relationship between k and K is represented as... 

The specific volume of solutions flowing in a two stage CSTR depends on the concentrations according to... 

V, is the molar volume of polymer or solvent, as appropriate, and the concentration is in mass per unit volume. It can be seen from Equation (2.42) that the interaction term changes with the square of the polymer concentration but more importantly for our discussion is the implications of the value of x- When x = 0.5 we are left with the van t Hoff expression which describes the osmotic pressure of an ideal polymer solution. A sol vent/temperature condition that yields this result is known as the 0-condition. For example, the 0-temperature for poly(styrene) in cyclohexane is 311.5 K. At this temperature, the poly(styrene) molecule is at its closest to a random coil configuration because its conformation is unperturbed by specific solvent effects. If x is greater than 0.5 we have a poor solvent for our polymer and the coil will collapse. At x values less than 0.5 we have the polymer in a good solvent and the conformation will be expanded in order to pack as many solvent molecules around each chain segment as possible. A 0-condition is often used when determining the molecular weight of a polymer by measurement of the concentration dependence of viscosity, for example, but solution polymers are invariably used in better than 0-conditions. 

What this comparison indicates is that as a first approximation, the terms A and B in equation (45) are not strongly dependent upon temperature and concentration. The pressure dependence of K for electrolyte solutions can be thus estimated from the properties of pure water. Since K = 1/B , the reciprocal of the 1 atm compressibility, it thus becomes possible to make reasonable estimates of vp from 1 atm specific volume data (v°) and compressibility data (B ). 

These techniques are of particular interest in that they provide a means of separating molecular species which are difficult to separate by other techniques and which may be present in very low concentrations. Such species include large molecules, sub-micrometre size particles, stereo-isomers and the products from bioreactors (Volume 3). The separations can be highly specific and may depend on molecular size and shape, and the configuration of the constituent chemical groups of the molecules. 

The concept of a unique hydrodynamic volume for all rodlike polymers was derived from examination of the Mark-Houwink constants, K and a, of the equation [rj ] = KMa. Macromolecules with values of a greater than unity are commonly accepted to be stiff or rigid rods. However, it was also found that such molecules (even for values of a less than unity) obey a relation illustrated by close concordance with the curve in Fig. lb (13) flexible, branched or otherwise irregular polymers, on the other hand, show dispersion around the upper part of the curve. The straight line curve in Fig. lb implies that the constants K and a are not independent parameters for the regular macromolecules to which they apply. Poly (a- and polyQJ-phenylethyl isocyanide) fall on this line the former has a value of a > 1 while the latter has a value a < 1 (14) both polymers give linear concentration dependence of reduced specific viscosity for fractionated samples... 

The sedimentation equilibrium experiment requires much smaller volumes of solution, about 0.15 ml. With six-hole rotors and multichannel centerpieces (41) it is potentially possible to do fifteen experiments at the same time. For situations where the photoelectric scanner can be used one might (depending on the extinct coefficients) be able to go to much lower concentrations. Dust is no problem since the centrifugal field causes it to go to the cell bottom. For conventional sedimentation equilibrium experiments, the analysis of mixed associations under nonideal conditions may be virtually impossible. Also, sedimentation equilibrium experiments take time, although methods are available to reduce this somewhat (42, 43). For certain situations the combination of optical systems available to the ultracentrifuge may allow for the most precise analysis of a mixed association. The Archibald experiment may suffer some loss in precision since one must extrapolate the data to the cell extremes (rm and r6) to obtain MW(M, which must then be extrapolated to zero time. Nevertheless, all three methods indicate that it is quite possible to study mixed associations. We have indicated some approaches that could be used to overcome problems of nonideality, unequal refractive index increments, and unequal partial specific volumes. 

Where EDTA is used, the typical cleaning product starting point is commercially available as a 38% w/w concentrated liquid solution, which requires 10 to 15 ppm of product for every 1 ppm of cation to be removed, on a weight-per-weight basis. (The specific requirement is dependent on which cations, e.g., Ca/Fe, are predominant.) As a result, and when making due additional allowance for soluble cations, fairly high volumes of product are needed. 

Sample molecules that are too large to enter the pores of the support material, which is commercially available in various pore dimensions, are not retained and leave the column first. The required elution volume Ve is correspondingly small. Small molecules are retained most strongly because they can enter all the pores of the support material. Sample molecules of medium size can partly penetrate into the stationary phase and elute according to their depth of penetration into the pores (Fig. 7.3). No specific interactions should take place between the molecules of the dendrimer sample and the stationary phase in GPC since this can impair the efficiency of separation by the exclusion principal. After separation the eluate flows through a concentration-dependent detector (e.g. a UV/VIS detector) interfaced with a computer. One obtains a chromatogram which, to a first approximation, reflects the relative contents of molecules of molar mass M. If macromolecules of suitable molar mass and narrow molar mass distribution are available for calibration of the column, the relative GPC molar mass of the investigated dendrimer can be determined via the calibration function log(M) =f( Vc). 

The viscosity starts to increase above the CMC and it is well established that the viscosity of a colloidal solution can give information on size and shape of the particles. From studies of the viscosity as a function of micellar concentration, the intrinsic viscosity may be obtained by extrapolation. The intrinsic viscosity depends on a shape factor, and the micelle specific volume and viscosity studies are therefore used to determine micelle shape and hydration. In many cases, these factors appear to be quite constant over a wide concentration range above the CMC. In other cases, such as hexadecyltrimethylammonium bromide (Fig. 2.9), dramatic increases in viscosity are observed at higher concentrations35). Studies of surfactants with low... 

The introduction forms Chapter 1 of this survey. Chapter 2 deals briefly with various approaches to the description of the concentration dependence of the viscosity of disperse systems, including the transition region from fluid to solid-like systems. Chapter 3 describes viscosity from the standpoint of the free volume theory and the specific features of the transition from mobile to glasslike systems. Chapter 4 presents the concept of the free volume of disperse systems developed by us as well as the results of experiments illustrating it Chapter 5 contains the pertinent generalizations and conclusions. 

The specific volume vk does not depend on the concentration in an ideal system. 

Numerical validation for pesticide movement addresses the question of whether the results generated from the model predict actual experimental values. A few models have been validated by correlating the estimated airborne pesticides and/or the amount on room materials with actual measurements in certain specific cases, van Veen et al. (1999) reported an experiment to validate a painting model of CONSEXPO which describes concentrations of a volatile solvent in room air both during and after the application. The concentrations depended on evaporation, initial concentration of solvent in two layers of paint, volume of paint and removal of solvent by ventilation from the room. Model parameters were either measured from the room before the experiment (ventilation rate, room size, physico-chemical parameters, etc.) from the act of painting (surface painted and amount of paint used), or fixed in advanced (relative size of the two layers of paint, transfer rate between the layers, etc.). The model predicted room concentrations that were within 80 % of the actual measured concentrations (Figure 6.1). Important with respect to the evaporation term is that peak concentrations could be predicted very well, so indicating that the source term is appropriate. 

Joosten et al.51 found that for a given stirrer power inpul and superficial gas velocity, the volumetric mass-transfer coefficient first increased relative to the value of the clear (no solid) liquid when small volume fraction of solids was added. While this is in qualitative agreement with the observations of Slesser et al.l2fi and Chandrasekaran and Shama,14 unlike these authors. Joosten et al.51 found the increase to be rather small (between 10 and 20 percent). Furthermore, as more solids were added, the volumetric mass-transfer coefficient remained constant at first, and then started to decline at a specific concentration depending on solid type and particle size. These data are illustrated in Fig. 9-15. 

Lundberg. Bull s data at T = 298.15 K have been used for the activity of water in this system." Starkweather has determined the activity of water in the concentration range 0 volume fraction as ai = 12 1, the expression that was used in our calculations. The molecular weight and the partial specific volume of collagen were taken from ref 41. The results of the calculations are presented in Figures IB, 2B, and 3B. In contrast to the toluene + polystyrene mixture, the solvent (water) is in deficit around a central water molecule but in excess around a protein molecule. 

Variables of the kind with which the phase rule is concerned are called phase-rule variables, and they are intensive properties of the system. By this we mean properties that do not depend on the quantity of material present. If you think about the properties we have employed so fer in this book, you have the feeling that pressure and temperature are independent of the amount of material present. So is concentration, but what about volume The total volume of a system is called an extensive property because it does depend on how much material you have the specific volume, on the other hand, the cubic meter per kilogram, for example, is an intensive property because it is independent of the amount of material present. In Chap. 4 we take up additional intensive properties, such as internal energy and enthalpy. You should remember that the specific (per unit mass) values of these quantities are intensive properties the total quantities are extensive properties. 

Most laboratory analysis methods measure concentration. The choice of units for concentration depends in part on the medium and in part on the process that is being measured or described. In water, a common expression of concentration is mass of chemical per unit volume of water. Many naturally occurring chemicals in water are present at levels of a few milligrams per liter (mg/liter). The fundamental dimensions associated with such a measurement are [M/L3]. The letters M, L, and T in square brackets refer to the fundamental dimensions of mass, length, and time, which are discussed further in the Appendix. For clarity in this book, specific units, such as (cm/hr) or (g/m3), either are free-standing or are indicated in parentheses, not in square brackets. 

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