Relative chain length

Figure 5.1 Schematic representation of relative chain lengths of molecules of ...

The saponification value is the amount of alkali required to saponify a defined amount of sample. It is expressed in mg potassium hydroxide (KOH) per g sample. The procedure involves the use of excess alcoholic KOH, which catalyzes the saponification/release of the free fatty acids from the glycerol backbone. The unreacted KOH is then back-titrated with standardized hydrochloric acid (HC1) using phenolphthalein as the indicator. The amount and normality of the HC1 used for neutralization can then be used to calculate the saponification value. The saponification value provides evidence as to the relative chain lengths of the fatty acids in the system. 

M and v are the molecular weight and the partial specific volume of the polymer, jjo p are the viscosity and the density of the solvent, respectively, and P and O are functions of relative chain length L/A and of the parameter of hydrodynamic interaction, d/A, respectively. These functions have been represented in an analytical form and tabulated over a wide range of changes in the L/A and d/A parameters At extremely high molecular weights (at IVA -> ), functions P and ap oach an asymptotic limit P— Po = 5.11 — 4>, = 2.862 x 10 (the Flory constant). This corresponds to the conformation of a hydrodynamically undrained Gaussian coil. 

Equation (32) uniquely relates the asymmetry of the shape of a worm-like chain Px to the relative chain length x and the asymmetry of the chain shape p in the conformation of a Gaussian coil. 

Fig. 15. Plot of relative anisotropy of a worm-like chain yj - yjIffA vs. relative chain length x = 2 L/A 1 In a system of coordinates of the first chain element in accordance with Eq. (39) 2 In a system of coordinates of the middle chain element according to Eq. (40), 3 In a system of coordinates of vector h according to Eq. (47)...

The initial molecular weight is important for the rate of decrease of the relative chain length in unzipping as well as random scission polymers. For the latter, the molecular weight ratio is ... 

Depending on the stoichiometry of the mixture (the relative concentrations, the relative chain lengths, and charge densities), one observes mainly two types of complex formations a macroscopic phase separation between the solvent and the polymers or a partial aggregation of the polymer chains. The complex formation observed from our earlier studies between chitosan and gum karya... 

We consider a quasi-binary solution of q + 1 components. When q = 1, the system will be referred to as binary. We designate the solvent as component 0 and q monodisperse homologous homopolymers as components 1, 2,..., q in the order of increasing relative chain length. Here, the relative chain length Pi of component i is defined by... 

We denote AG per unit volume of solution by AG. Thermodynamics tells us that AG of a quasi-binary solution is a function of T, p, and 4>i. For a given polymer species it also may depend on the distribution of relative chain length in the polymer mij re. Thus, when the pressure effect is not considered, the basic variables for AG of quasi-binaiy solutions are T, , and /(P) as the basic variables. For a paucidisperse polymer, q is finite and /(P) is represented by q delta functions with different strength, while for a truly poly-disperse polymer, q is infinitely large and /(P) becomes a continuous function of P. Thus, AG for quasi-binary solutions of a truly polydisperse polymer is a functional with respect to /(P), and requites sophisticated mathematics for its treatment. 

For a binary solution the function f(P) reduces to a single parameter P, the relative chain length of the polymer, so that or x depends on T, , and P. The basic task in the thermodynamic study of binary solutions is to find this dependence by appropriate experiments. 

Dispersibility and retention Relative chain length of trunk polymer Relative grafts length Relative number of grafts... 

If the relative chain lengths are chosen correctly, this can result in separated zones of glassy polystyrene in a continuous matrix of polyisoprene. The polystyrene phase can be spheres, cyhnders or laminae (sheets), again depending on the relative volume fractions of the two types of chain (Figure 7.12). 

The FHS model relates the relative chain length, m, to molar mass M by... 

Block copolymers can solubilize homopolymers up to a certain amount, beyond which phase separation occurs. This ability to continuously swell block copolymer microstructures is the basis of a number of potential and actual applications in optoelectonics where the periodicity of the block copolymer structure is extended up to 0.1-1 /xm, which corresponds to wavelengths for reflection or guiding of light. The limit for macrophase separation in blends of block copolymer with homopolymer depends on the relative chain lengths, i.e. on a = Np /N c> where Np is the degree of polymerization of the homopolymer (A) and Aac is the degree of polymerisation of the same component of the... 

Fig. 7.6. Distribution of relative chain lengths of tie molecules in the amorphous regions of 6 polyamide fibers as obtained from numerical evaluation of step-strain ESR data [4, 71.

Fig. 7.7. Distributions of relative chain lengths shown as histograms of free radical concentrations obtained in step-straining of 6 polyamide fibers at (a) -25 °C, (b) room temperature, (c) + 50°C, and (d)+100°C [4, 5].

Then, particle growth is carried out by one of the procedures already described in section 17.3.1. The size and the shape of the particles can be modulated with the precursor/polymer ratio, the molecular weight of the polymer, and the relative chain length in block copolymers. 

---