Dear Dr Prabhu,

which viscosity you mean, solution or melt viscosities. In general, chain length (molecular weight) has a strong influence on viscosity, though other factors are also playing important roles. Regards

I need to control, final viscosity of the co polymer

I am using free radical polymerization technique

can u please let me know, how to control molecular weight of the above said monomers and viscosity parameters in the aqeous medium

and how to caliculate Mn values of the polymer theoriatically

Regards

Charan

Dear Prabhu Charan Reddy;

in its simplest way, the viscosity in solution may be controlled by concentration.

In free radical polymerization process there are two strategies. The classical way is to use transfer agents such as mercaptans. The advanced way is to synthesis your copolymer via one of the living/controlled polymerization processes.

Of course the word control has many meanings!!!!

There is a Mark-Houwink-Sakurada Equation which allows to get the molecular weight from viscometry using an Ubelohde viscometer. Regards

You may possibly be interested at a reasonable mixture rule formula that may allow to estimate the viscosity of the co-polymer after that of the separated polymerized components. Direct application of a simply mixture rule to either dynamic or kinematic viscosity is not advisable. The SI unit of kinematic viscosity (ν) is m2/s, while that of thermal conductivity (k) is watts per meter-kelvin (W/(m·K)). The k/ν ratio has the SI unit of (J/(m3·K)), being therefore given as a specific quantity on a volume basis. The following mixing-rule can be used to estimate the k/v ratio for the (binary) co-polymer from that of its polymerized components ('1' and '2') of given volume ratios (f1 and f2 = 1 - f1) which translate their relative contribution for the co-polymer: k/ν = f1·k1/ν1 +  f2·k2/ν2. This formula could be obviously generalized for more than two components. It states that the k/ν ratio for the co-polymer can be estimated after the arithmetic mean of the corresponding ratios for the separated polymerized components ─ weighted by volume fraction. It can be easily understood that k/v tends to be fairly stable if k1/ν1~ k2/ν2, although these ratios are likely to be different for most practical co-polymer formulations.

The above mixture-rule formula was given in a volume fraction basis. It may be convenient, however, to consider a comparable formula, but given in a mass fraction basis. This is the subject now bring to discussion. It can be noticed that the k/(ν·ρ) ratio, where ρ stands for density (kg/m3), has the SI unit of (J/(kg·K)), being therefore given as a specific quantity on mass basis. This is also the ratio between thermal conductivity (k) and the dynamic viscosity (μ = ν·ρ). The following mixing-rule can be used to estimate the k/(ν·ρ) ratio for the (binary) co-polymer from the corresponding ratios that would apply to its (conceivably separated) polymerized components ('1' and '2') of given mass ratios (R1 and R2 = 1 - R1): k/μ = R1·k1/μ1 + R2·k2/μ2. Again, this formula is of obvious generalization for extra components. It states that the k/μ ratio for the co-polymer can be estimated after the arithmetic mean of the corresponding ratios for the separated polymerized components ─ weighted by mass fraction.

We may be interested at the temperature dependency of the viscosity of the co-polymer, after somehow accessing the temperature dependency that would apply to the polymerized components (here denoted ‘α’ and ‘β’), conceptually taken as isolated. To address this problem, the following correlation can be proposed, modified from the well-known Williams-Landel-Ferry viscosity model (*) μ/k = (μº/kº)·exp [-C1·ΔT / (C2 + ΔT)]. Here μº and kº stand for the dynamic viscosity and thermal conductivity of the co-polymer at the reference temperature, Tº ≥ Tg, while μ and k refer to the actual temperature considered (T). The actual temperature is taken as exceeding Tº by a ΔT gap (ΔT = T-Tº), while C1 and C2 are empiric parameters. These parameters can be estimated for the co-polymer by mixture-rule formulas given in terms of mass ratios (Rα and Rβ = 1 - Rα), meaning C1= Rα·C1α + Rβ·C1β and C2= Rα·C2α + Rβ·C2β. We can also adopt the mixture-rule equation given with the above answer to estimate μº/kº: μº/kº = 1 / (Rα·kαº/μαº + Rβ·kβº/μβº). We can now estimate μ/k for the co-polymer as a function of the temperature. As easily understood, μº/kº would be fairly stable against compositional variation if kαº/μαº ~ kβº/μβº.

(*)https://en.wikipedia.org/wiki/Temperature_dependence_of_liquid_viscosity