Martin equations

Fig, 5.3. Viscosity at various concentrations and molecular weights in the low to moderate concentration range. Polystyrene-decalin and polymethyl methacrylate-xylene are theta or near-theta systems the remainder are good solvent systems (121,177). Note that the c[i/] reduction is somewhat better in theta solvents, and that the Martin equation [Eq. (5.9)], which would give a straight line in the figure, is a somewhat better representation for... 

Let us suppose that the experimental contribution of polymer to solution viscosity at low concentration, rj0 — t]s, can be represented to a sufficient approximation by the Martin equation [Eq.(5.9)]. An alternative which is presumably always available to the solution is free draining behavior [Eq.(4.16)]. As concentration is increased, then, according to the minimum dissipation principle, the behavior would be expected to change from the Martin form to the free draining form in the range where the two expressions for rj0 — rjs become equal ... 

The retention factors of the polymers in 60 % THF were calculated from gradient elution and discussed together with those directly measured for oligomers with 2-12 repeat units or 2000, 4000, and 9000 g/mol molar mass. On a lOOnm-pore packing, the Martin equation was fulfilled for n = 19 repeat units. At higher values, the curve... 

Different empirical equations relating the viscosity ratio excess to the intrinsic viscosity were tested, and the Martin equation (50) correlated the data with an error of 1% with respect to the results obtained using Equation 43 ... 

Martin equation, 235 Mass transfer, 28, 29, 32 Mesh sizes, 115 Micellar LC, 224 Microbore columns in LC, 200 Molecular sieves, 46, 47, 117 Molecular weight chromatograph, 83 Multipath term in rate equation, 31... 

By comparing RM values of compounds that differ by only a methylene group or a functional group, a table of RM values can be compiled. Since they are proportional to the free energies for these groups, they should be additive, and the total RM value for any analyte can be predicted by summing the values for the groups of which the molecule is composed. This idea is known as the Martin equation ... 

Example 12.2. Potential mass transfer-induced instability in olefin hydroformylation [14]. The rate of olefin hydroformylation with cobalt hydrocarbonyl catalysts in a liquid phase obeys in good approximation the Martin equation... 

The above-given Martin equation form the basis for the Kovats retention index system in gas chromatography as well as for several HPLC retention prediction schemes. It must be noted here that the relationships between retention parameters and carbon numbers are usually linear at some limited range of the aliphatic chain length up to 6-8 carbon atoms in reversed-phase HPLC [491. 

The solution viscosity is calculated using the Martin equation... 

The Es value is usually about 10 to 20 kJ/mol. For low-concentrated solutions of polymers with moderate molecular masses, the difference between these two activation energies, AE = Ep - E does not exceed usually 10 kJ/mol. For low-concentrated solutions of certain polymers in thermodynamically bad solvents negative AE values were reported. The Newtonian viscosity of solution related to the polymer concentration can be evaluated, for example, using Martin equation ... 

Martin equation is usually valid in the range of redueed eoneentrations, c < 10. For evaluation of [r ], the Mark-Houwink relationship is reeommended... 

The Martin equation (also known as the Bungenberg-de Jong equation) utilizes the common logarithm of the reduced viscosity ... 

For concentrated polymer solutions, the Martin equation is applicable ... 

This equation—sometimes referred to as the Martin equation—has been applied by Chauveteau (1982) in correlating the viscosity-concentration behaviour of xanthan in the semi-dilute regime. A number of other empirical equations which correlate polymer viscosity over a wide range of concentrations are reviewed by Ott (1955). 

---