Solutions of Low Molecular Weight Substances

When spraying solutions of substances of low molecular weight, a first drying step occurs above the solubility limit of the solute, and the drop reduces in size until the solubility limit is reached. For this first step, which is usually called the first or constant rate period (CRP), the drying velocity, that is, the solvent mass evaporated per unit time, is given by the vapor pressure of the solution at the drop surface, p s, and the vapor pressure in the vicinity of the particle, pv.oo. The vapor pressure at the surface depends - assuming a well-mixed state within the droplet - on the drop temperature and on the water activity within the solution. The surface temperature remains low in the CRP as the solvent, due to its heat of evaporation Ah uses up the sensible heat (expressed by the specific heat capacity Cp of the air-vapor mixture) transferred to the particle by the gas in a hot atmosphere. The particle surface temperature Ts is more or less close to the wet bulb temperature of pure water, depending on the water activity in the case of dissolved matter (see Eq. 5.44 in Volume 1 of this series). The dependence of the vapor pressure of the solvent on the surface temperature Ts may be expressed by the Antoine or Clausius-Clapeyron equation, as 

High solute and air temperature usually mean higher solubility and higher mass content before the onset of crystallization. (However, some materials do not show increased solubility with increased temperature, as e.g., NaCl). High solubility also means a late onset of crystallization and low solvent content. Due to this fact, particles should form a shell with a thick wall. Materials with low solubility, but still sprayed into the dryer as a solution, are expected to form a thinner shell. However, the nudeation properties, such as nudeation rates and the growth rates of crystals, also play a major role. Some materials do not form crystals but solidify in an amorphous or glassy state. A typical example is lactose, for example, sprayed as a 20 wt% solution into air at an air exit temperature of 90 °C, as shown in Fig. 6.3. 

In Brenn et al. (2001) a proposal is presented for distinguishing between the formation of hollow beads and compact particles obtained from crystallizing substances by means of the parameter 

The model was validated on NaCl solutions. In Eq. 6.3, Di is the diffusion coefficient of the solute in the liquid phase, Dg is the diffusion coefficient of the solvent vapor in the gas phase, Qi and pg are the liquid and gas densities, respectively. Sh is the dimensionless mass transfer rate in the vapor phase. This modified Sherwood number, that accounts for the film thinning effect of Stefan flow, lies typically in the range 2 Sh 5. The quantity Bm is the Spalding transfer number according to Abramzonand Sirignano (1989) (Sirignano (1999), compare with Eq. 1.66 in Volume 

Many materials such as salts, for example, Na2S04, show different stable modifications for given temperatures with different content of crystal water. Usually, a stable modification is formed first, at the given drop or particle temperature. The hygroscopic property of the product may then be the result of a subsequent transformation into a different modification stable at ambient temperature and humidity. As the lattice of the crystals is restructured during uptake of water from the ambient air, the strength of the particle may diminish and dust can be formed. 

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The expoimental data on the non-steady state Ken effect of flexible-chain polymers dissolved in solvents with moderate viscosities reveal that at frequences up to lO Hz no dispersion of B is observed (just as in solutions of low molecular weight substances and monomers). This is also an indication of mutually independent orientation of single monomer units in the electric field which is only sightly related to the structure and conformation of the polymer chain as a whole. 

The addition of solute(s) further complicates rheology beeause in sueh mixtures solvents may not only interact among themselves but also with the solute(s). There are also interactions between solutes and the effect of ionized species with and without solvent participation. Only very dilute solutions of low molecular weight substances exhibit Newtonian viscosity. In these solutions, viscosity is a constant, proportionality factor of shear rate and shear stress. The viscosity of these solutions is usually well described by the classical, Einstein s equation ... 

The number of papers concerning the viscosity of binary mixtures of solutions of low molecular weight substances is considerable. In spite... 

We are better provided for in regard to the viscosity of suspensions, and, since solutions of high polymers represent transition stages between solutions and suspensions, we shall first discuss solutions of low molecular weight substances, then suspensions and, finally, high polymers. 

Changes in reactivity and reaction kinetics in comparison to conversions of low-molecular-weight substances can also be attributed to the fact that macromolecules in solution are in a more or less coiled state. During the course of a reaction this state changes through alteration of the solubility parameters, thus facilitating or aggravating conversion. Finally one observes in-... 

Crude experiments were performed in the laboratory with substances unlikely to show significant weight change by adsorption of water or oxygen and sufficiently volatile for loss to be recorded conveniently on an ordinary balance. Petri dishes (41 sq. cm. area) were used to contain the substances, mostly liquids and used in the pure state. Two solids were included p-dichlorobenzene and naphthalene. These were layered in coarse powder form, and the surface was sprayed with a solution of low molecular weight polyisobutene in petroleum ether until it was sticky enough to prevent blowing of the powder in the wind it was intended to use. 

Electric birefringence (EB) or the Kerr effect is widely used in molecular optics as a method for the investigation of the molecular structure of low molecular weight substances. The study of the Kerr effect in the gas phase or in solutions in combination with other methods, such as refraction, light scattering, dielectric measurements etc. permits to ascertain the spatial arrai ement of atoms in the molecule and thus to calculate the main values of the polarizability tensor of the molecule and to obtain information about the value and direction of its dipole moment ... 

Hemicelluloses have traditionally been defined by extraction procedures, i. e., hemicelluloses are those polysaccharides extracted by alkaline solutions from plant tissues after removal of low-molecular-weight substances with hot aqueous alcohol, removal of waxes and other lipid-soluble substances, delignification, and removal of pectin with an aqueous solution of a calcium ion chelator. The most abundant hemicelluloses in the primary cell walls of dicotyledons are xyloglucans. Xyloglucans have a backbone chain whose chemical stmcture is identical to that of cellulose. About 75% of the 8-D-glucopyranosyl units in that chain are substituted... 

The comparison of permeability values of low-molecular-weight substances diffusing into hydrophobic polymers from water solutions to those from the dry gaseous phase (e.g., HCl, NH3, CO2, SO2) showed that these values were commensurate, providing that the vapor elasticity over the solution and its partial pressure in the gaseous phase were equal. It is believed that volatile electrolytes are transferred in hydrophobic polymers in the form of non-dissociated molecules devoid of hydrate shells. 

Nevertheless, studies of adsorption and release of low-molecular weight substances by PEMs are limited to such dyes as fluorescein [7], 9-aminoacridine [7], methylene blue [5], TMPyP [6]. In an alkaline solution, some dyes can be rapidly loaded into PEMs and rapidly released, while in an acidic solution this process can be repeated several times [6]. The amount of an adsorbed dye depends not only on pH, but also on the nature of the dye, PEM s composition and film thickness [5,7]. 

Here we have a heat of mixing differing from zero, while the entropy of mixing retains as before the ideal value. Such mixtures which are realizable in great number in the domain of low molecular weight substances, Hildebrand has termed regular solutions. 

Dispersed systems are common aqueous solutions of low molecular weight compounds, salts, amino acids, mono- and oligosaccharides (such as sodium chloride, glycine and saccharose), as they contain at least two types of particles (molecules of the water-dispersion medium and the ions or molecules of the substance-dispersed phase). These systems are monodispersed systems because their components contain particles of about the same size with a certain relative molecular weight (in daltons. Da) or molar weight (in kilogram per mole, kg/mol, or gram per mole, g/mol). 

There are several noteworthy and important features that are characteristic of polymer crystallization from dilute solution. A derived Avrami equation fits the isotherms over almost the complete transformation. Except for very low molecular weights, this is contrary to the results for bulk crystalUzation.(37) The reason for this difference and the crystallinity level that is attained will be discussed shortly. The crystallization of polymer from dilute solution can be considered to be ideal, since the kinetics resemble the crystallization of low molecular weight substances. 

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