Polymer mass concentration

Turbidity has proven to be especially useful in studies of protein polymerization, where one can demonstrate that the turbidity is directly proportional to the polymer mass concentration. This is illustrated in the following plot (Fig. 1) obtained for assembled microtubules. 

Figure 1. Top Turbidity, measured at 350 nm, as a function of microtubule polymer mass concentration (expressed as mg/mL polymerized tubulin). Tubulin solutions of varying concentrations were polymerized until they reached stable plateau values in a Cary 118C spectrophotometer. Each sample was then transferred to an ultracentrifuge tube, and microtubules were pelleted, separated from the unpolymerized tubulin in the supernatant fraction, and then resuspended for protein concentration determination. The corresponding turbidity and polymer mass concentrations are plotted here. Bottom Time-course of tubulin polymerization assayed by turbidity.Repro-duced from MacNeal and Purich with permission from the American Society for Biochemistry and Molecular Biology.

Now we compare the above osmotic pressure data with the scaled particle theory. The relevant equation is Eq. (27) for polydisperse polymers. In the isotropic state, it can be shown that Eq. (27) takes the same form as Eq. (20) for the monodisperse system though the parameters (B, C, v, and c ) have to be calculated from the number-average molecular weight M and the total polymer mass concentration c of a polydisperse system pSI in the parameters B and C is unity in the isotropic state. No information is needed for the molecular weight distribution of the sample. On the other hand, in the liquid crystal state2, Eq. (27) does not necessarily take the same form as Eq. (20), because p5I depends on the molecular weight distribution. 

Here c(r) is the polymer mass concentration at a radial distance r from the axis of rotation, 0p/0c the specific density increment of polymer at constant T and p0, and co the angular velocity. 

The osmotic pressure it of a dilute solution of a monodisperse polymer with molecular weight M is expressed as a power series of polymer mass concentration c (weight of polymer per unit volume of solution) as... 

Polymerization reactions require stringent operating conditions for continuous production of quality resins. In this paper the chain-growth polymerization of styrene initiated with n-butyllithium in the presence of a solvent is described. A perfectly mixed isothermal, constant volume reactor is employed. Coupled kinetic relationships descriptive of the initiator, monomer, polystyryl anion and polymer mass concentration are simulated. Trommsdorff effects (1) are incorporated. Controlled variables include number average molecular weight and production rate of total polymer. Manipulated variables are flow rate, input monomer concentration, and input initiator concentration. The... 

Body force of component i Polymer mass concentration Macroscopic diffusion coefficient Cooperative diffusion coefficient Stokes-Einstein diffusion coefficient Rouse diffusion coefficient Self diffusion coefficient... 

Usually, C is assumed to depend on polymer mass concentration c and temperature T, unless the chain is too short. It can be adequately formulated by free volume theory [3]. On the other hand, Fg is assumed to be a function of c and N (or molecular weight M). The central theme in polymer self-diffusion studies is to evaluate the latter by theory or experiment for a variety of chain architectures and solvent conditions. 

Figure 9.5, which also shows that the type of pol)mier influences the particle size, at constant polymer mass concentration. 

Figure 9.13 shows the reasonable agreement that this model gives to experimental data on two polystyrene (PS) melt of low molecular weights. The moduli in this fignre are normalized with pRTIM where p is the polymer mass concentration and the freqnency is normalized with the terminal (i.e., longest) relaxation time, Note that the nnmerator in Eqnation 9.50 can be expressed as the product of Na that represents the mean-sqnared end-to-end distance of the molecule and that repre-... 

In these equations, h is the refractive index of the solution, (8h/8c) the specific refractive index increment, Ig the wavelength of incident light in vacuum, Ca and Cb the polymer mass concentrations at the meniscus and the cell bottom, respeaively, Ca and Cb the radial distances from the center of rotation to the meniscus and the cell bottom, respectively, Cg the initial polymer mass concentration, [dp 8c) the density increment, and c the mean concentration defined by (Ca-rcb)/2. In eqns [41]-[43], the solution is assumed to be incompressible. Furthermore, to apply eqn [43], sedimentation experiment has to be performed at a low rotor speed with a short solution column. Note that both light scattering and sedimentation equilibrium give dfigldc)T,p. 

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