Dilute solution general features

Models of the polymer coil are based on the end-to-end distance, which is generally not directly available as a quantitative feature. Coils in dilute solution can be characterized in terms of the radius of gyration, Rg, which is a statistical measure of the distribution of mass about the center of gravity or in terms of the hydrodynamic radius, Rh, that is usually determined through the use of Stokes law and a measurement of a drag coefficient or friction factor, /drag/ for the coil,... 

For different applications, water-soluble neutral and ionic comonomers can be incorporated into or attached to the PNIPAM chain backbone to form amphiphilic PNIPAM copolymers via free-radical copolymerization. In this section, we will use the folding of neutral PNIPAM amphiphilic copolymer chains in extremely dilute solutions ( pg/mL) to illustrate a general feature of the folding of hydrophilically modified copolymer chains. 

Order-Disorder Transitions. General Features, Experimental data are summarized in Table II, and representative thermochromic behaviors are shown in Figure 2. For the dialkyl-substituted polysilylenes the transition is very sharp, with a barely discernible coexistence region and an approximate isosbestic point. On the other hand, the asymmetrically substituted polymers, except poly(n-dodecylmethylsilylene), display very smooth behavior only in n-hexane solution and a broad but clearly discernible transition in dilute toluene solution. The transition width (ATc) in toluene solution was taken to be the interval between departure from the extrapolated, smooth, high-temperature behavior and the onset of peak absorption wavelength saturation at low temperature. The transition temperature (Tq) is defined arbitrarily as the midpoint of this region. 

Probably the most important structural feature of the titanium and other alkoxides is that, although monomeric species can in certain cases exist, especially in very dilute solution, these compounds are in general polymers. Solid Ti(OC2H5)4 is a tetramer, with the structure shown in Fig. 25-A-l. This compact structure neatly allows each Ti atom to attain octahedral coordination. However, in benzene solution, Ti(OR)4 compounds are trimeric for primary alkoxides10 but are unassociated when made from secondary and tertiary alcohols.11 The alkoxides are often referred to as alkyl titanates and under this name are used in heat-resisting paints, where eventual hydrolysis to TiOz occurs. 

The present chapter aims to describe some typical contributions from recent studies on stiff polymers in dilute solution. We will be mainly interested in (1) applicability of the wormlike chain model to actual polymers, (ii) validity of the hydrodynamic theories [2-4] recently developed for this model, and (iii) the onset of the excluded-volume effect on the dimensions of semi-flexible polymers. Yamakawa [5, 6] has generalized the wormlike chain model to one that he named the helical wormlike chain. In a series of papers he and his collaborators have made a great many efforts to formulate its static and dynamic properties in dilute solution. In fact, the theoretical information obtained is now comparable in both breadth and depth to that of the wotmlike chain (see Ref. [6] for an overview). Unfortunately, however, most of the derived expressions are too complex to be of use for quantitative anal) sis and interpretation of experimental data. Thus, we only have a few to be considered with reference to the practical aspects of the helical wormlike chain, and have to be content with mentioning the definition and some basic features of this novel model. 

Figure 6 shows the dependence on concentration and temperature of the molar conductivity of 1,2-dimethoxyethane solutions of LiBF4 from infinite dilution to saturation. The plots of A versus show a minimum at moderate concentrations and a maximum at high concentrations. Although the minimum is only weakly dependent on temperature, the maximum exhibits a strong displacement. The minimum is a general feature of bilateral triple-ion formation ... 

The proton is generally a less important species in melts, although it features prominently in molten bisulfates and hydroxides, as well as in dilute solutions of water and, for example, HCl, in anhydrous molten salts. Generally,... 

Equivalent phase diagram for a gelating system in semi-dilute solutions with a good solvent, is the monomer concentration (and each monomer is polyfunctional). is an equivalent temperature, which decreases from infinity to low values when the chemical reaction progresses. The particular model used in the text assumes instant reaction between monomers which are in contact. But the qualitative features of the diagram are more general. 

The accurate prediction of material properties of specific polymers is only one kind of the many tasks that one may wish to solve by MC simulation another task is to elucidate some universal predictions of general features of polymers that should hold irrespective of their chemical structure. For example, for polymers in dilute solution under good solvent conditions, nontrivial universal exponents V and y describe the scaling of the gyration radius, Rg, and the configural free energy, Fconf, with the degree of polymerization, n. ... 

A remarkable feature about resistivity changes is that for dilute solutions, the resistivity (p) increases linearly with concentration (x) at a rate that is entirely characteristic of the particular solute in a given alkali metal. This can be defined in terms of a resistivity coefficient dp/dx, which expresses the increase in resistivity (S2m x 10 ) caused by solution of 1 mol% of the solute. Some values are given in Table VII, and a few broad generalizations are possible. Thus, coefficients increase with increase in ionic radius of the dissolved atom or ion, so that the size of a dissolved species is more important than its charge in determining the resistivity coefficient. The coefficients are largely independent of the alkali metal used as solvent. 

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