Polymer mass balance

To describe the MWD for live polymer, mass balances for polymeric radicals are written ... 

The monomer and polymer mass balance in the reactor allows cumulative and instantaneous monomer conversion to be defined, and permits computation of and [q] from light scattering, viscosity, and concentration data, mft) is the cumulative (or total) mass of monomer plus polymer in the reactor, which is the sum of initial monomer mass in the reactor and that flowed in from the external reservoir, minus the amount flowed out for ACOMP sampling. This is found from ... 

In the above reactions, I signifies an initiator molecule, Rq the chain-initiating species, M a monomer molecule, R, a radical of chain length n, Pn a polymer molecule of chain length n, and f the initiator efficiency. The usual approximations for long chains and radical quasi-steady state (rate of initiation equals rate of termination) (2-6) are applied. Also applied is the assumption that the initiation step is much faster than initiator decomposition. ,1) With these assumptions, the monomer mass balance for a batch reactor is given by the following differential equation. 

Note that in the component mass balance the kinetic rate laws relating reaction rate to species concentrations become important and must be specified. As with the total mass balance, the specific form of each term will vary from one mass transfer problem to the next. A complete description of the behavior of a system with n components includes a total mass balance and n - 1 component mass balances, since the total mass balance is the sum of the individual component mass balances. The solution of this set of equations provides relationships between the dependent variables (usually masses or concentrations) and the independent variables (usually time and/or spatial position) in the particular problem. Further manipulation of the results may also be necessary, since the natural dependent variable in the problem is not always of the greatest interest. For example, in describing drug diffusion in polymer membranes, the concentration of the drug within the membrane is the natural dependent variable, while the cumulative mass transported across the membrane is often of greater interest and can be derived from the concentration. 

Material Balances. The material (mass) balances for the ingredients of an emulsion recipe are of the general form (Accumulation) = (Input) - (Output) + (Production) -(Loss), and their development is quite straightforward. Appendix I contains these equations together with the oligomeric radical concentration balance, which is required in deriving an expression for the net polymer particle generation (nucleation) rate, f(t). 

Experimentally, the adsorbed amount is usually expressed as T i.e. mass polymer/area of surface. This is usually obtained from a mass balance technique, after analysing the equilibrium solution, r a 0ex> but an exact correlation is difficult to establish. 

The determination of adsorption isotherms at liquid-solid interfaces involves a mass balance on the amount of polymer added to the dispersion, which requires the separation of the liquid phase from the particle phase. Centrifugation is often used for this separation, under the assumption that the adsorption-desorption equilibrium does not change during this process. Serum replacement (6) allows the separation of the liquid phase without assumptions as to the configuration of the adsorbed polymer molecules. This method has been used to determine the adsorption isotherms of anionic and nonionic emulsifiers on various types of latex particles (7,8). This paper describes the adsorption of fully and partially hydrolyzed PVA on different-size PS latex particles. PS latex was chosen over polyvinyl acetate (PVAc) latex because of its well-characterized surface PVAc latexes will be studied later. 

The amount of polymer adsorbed in gramsper gram Aerosil can be calculated from the mass balance, according... 

Table 1 presents the results of fractionations of the DOM. The result of mass balance calculation of the DOC system shows that more than 55 % of the total DOC was retained by XAD-8 resin column, involving the portions of Ho A and HbN/B, and DOC concentrations of the portion eluted by blackwashing (HoA) accounted for 47.4 % of total DOC, as compared with 26.25 % hydrophilic acids (HiA) of the total DOC. More than 11% of the total DOC passed through two resin columns, indicating that small molecular weight polar components were not absorbed onto by XAD-8 and XAD-4. The fractionation did cause potential loss of organic matter by permanent adsorption onto resin s polymers, which were 8.34 % for the XAD-8 resin and 6.41 % for the XAD-4 resin, respectively. 

Within either of the polymer-rich phases, borate esters and diesters of the functional groups are assumed to form with the same association constants as observed for the independent functional groups in aqueous solution. The resulting equations simply describe the borate ester association constants as well as mass balances on boron and polymer-bound functional groups. Wise and Weber used the model to estimate association constants for the borate esters formed with the diols in PVA and to predict the gelation of PVA-borate solutions. As we have independently measured the association constants for the borate esters formed in this work, we have used the model to estimate the radius of gyration of the GP3 dendrimer and to predict both the boron speciation in borate/GP3 solutions and the efficacy of PAUF using these functional dendrimers. 

The thermal energy balance, expressed per unit polymer mass, may be written as ... 

Through the analysis of the particular selected examples it was shown that it is possible to get a good description of temperature and conversion profiles generated during the cure of a thermosetting polymer. Thermal and mass balances, with adequate initial and boundary conditions, may always be stated for a particular process. These balances, together with constitutive equations for the cure kinetics and reliable values of the necessary parameters, can be solved numerically to simulate the cure process. 

Solvent transport in organic polymer matrices is usually depicted as a two-step mechanism. The first step is the dissolution of the solvent in the superficial polymer layer. This process, which can be considered almost instantaneous in the case of water, creates a concentration gradient. The second step is the diffusion of the solvent in the direction of the concentration gradient. This process may be described by a differential mass balance (often called Fick s second law), which, in the unidimensional case, may be written as... 

In order to relate the thickness of the coating to R and U, we must perform a mass balance on the region starting at the exit of the die and ending where the fluid has reached the same velocity as the wire. Here, we must assume that the polymer density is constant, although the melt undergoes density changes as it solidifies. The mass balance is written as... 

By pressing the bar against the plate, a radial velocity profile will be induced in the melt film, thus removing the newly melted polymer from the location of melting, and draining it. The mean radial velocity at any location r, vr can be expressed in terms of (the yet unknown) velocity by a simple mass balance... 

The mass balance is written using as state variables the amount of initiator I (kmol), monomer M (kg) and polymer P (kg). The reaction rates are in kmol/s, and kmol/m3, respectively. Subscripts 1 and 2 refer to the monomer-rich and polymer-rich phases, respectively. For clarity, we will use symbols as cKj to denote the concentration (kmol/m3) of species FCin phase j. 

An important quantity which can be calculated at equilibrium conditions is the amount of substance migrated into the food or food simulant at equilibrium, mF,e. Provided that the migration potential in the polymer, i.e. the initial amount of migrant dissolved in the polymer, mP0, is known then from mass balance calculations the following equation can be derived ... 

The use of these diffusion models to progress the evaluation process of a food packaging plastic will be discussed shortly. In those cases where assessment by mass balance considerations under equilibrium conditions, including partitioning effects, does not provide a clear picture of the plastics conformity status, then the different diffusivities of polymer types and the influence of the migrant molecule size or its molecular weight on its mobility within a plastic can be taken into account to achieve more distinguished views on QM/SML ratios. 

The simplest estimation of migration is to use the mass balance calculation shown in Eq. (14-1) below. This equation assumes that all of the styrene found in the polymer will migrate into the food instantly. This is of course not realistic but the estimation gives an upper limit to the possible migration that could occur at the end of the product s shelf life. 

It is possible that styrene will never reach the mass balance migration limit specified by Eq. (14-1) in certain foods because of partitioning effects. The systems most likely to have partitioning effects, i.e. when K 1, are those for styrene between aqueous foodstuffs and PS. Migration is usually highest into fats and oils since styrene is readily soluble in both the fats and polymers so that K < 1. 

Diffusion controlled migration results in step 3 compared to the results in step 4 assuming a mass balance, show that the diffusion of the styrene in the polymer acts to slow down mass transfer into the product. These calculations also show that the relationship in Eq. (14-1) is still valid (mass balance calculations represent the maximum possible amount of migration). 

---