Dear Swapnil,

To determine the cross-link density, you must first define cross-link density. If you define the cross-link density as the inverse of the molecular weight between cross-links (Mc), then the cross-link density can be determined by the equation

Ge = pRT/Mc,  

where Ge is the equilibrium modulus as determined by a temperature sweep in dynamic mechanical analysis, p is the density (which can be determined by Archimedes method), R is the universal gas constant in J/mol*K and T is absolute temperature in K. Once you find Ge and p experimentally, then you can calculate Mc and then finally calculate the cross-link density.

I hope this helps.

Best,

Nick

Dear Swapnil,

Cross-linked polymers do not soluble in any solvent. But in my opinion, if it is slightly cross-linked, it may show state which is close to soluble, in actual it may be gel or swollen transparent soft matter and not solution. If it is completely soluble, then it may be branched polymer. 

Dear Swapnil,

If you are interested in branching polymers. You can determine “branching factor” of polymers. You can read this paper. “S.Alli, A.Alli and B.Hazer, Journal of Applied Polymer Science, 124, 536-548, 2012.

If you have crosslinked polymers. You can determine Mc values. Mc of a network is a main characteristic parameters that serves as a reference in describing a network structure.

The polymer-solvent interaction parameters can be determined using the VPO (vapour pressure osmometer) method. Although VPO is not an absolute equilibrium method the determine the molar mass of the polymer , and consequently the thermodynamic data on polymer - solvent system, it has been reported that the obtain by the VPO are satisfactorily in agreement with the data obtained by the other absolute and equilibrium techniques such as membrane osmometer and Cahn electrobalance.

I recomment you to read this paper. “B.Hazer, et all. Polymer Bulletin 46, 389–394 (2001)”

Dear

you can see the the attached files.

Best regards

Reza 

Dear Swapnil,

To determine the cross-link density, you must first define cross-link density. If you define the cross-link density as the inverse of the molecular weight between cross-links (Mc), then the cross-link density can be determined by the equation

Ge = pRT/Mc,  

where Ge is the equilibrium modulus as determined by a temperature sweep in dynamic mechanical analysis, p is the density (which can be determined by Archimedes method), R is the universal gas constant in J/mol*K and T is absolute temperature in K. Once you find Ge and p experimentally, then you can calculate Mc and then finally calculate the cross-link density.

I hope this helps.

Best,

Nick

To calculate the cross-link density You can read this paper. “F. Abd-El Salam, M. H. Abd-El Salam, M. T. Mostafa, M. R. Nagy, M. I. Mohamed, Journal of Applied Polymer Science, 90 (2003) 1539-1544.

"Effect of the vulcanizing system on the mechanical properties of butyl rubber/ ethylene propylene diene monomer – carbon black blends."

Dear Swapnil,

Rheological analysis could help you determine whether your polymer is cross-linked or not and also help compare the range of cross-link densities you may have. You could do this by looking at the complex viscosity and dynamic moduli curves.

Kind regards,

Cat

you can see the the attached files.

Best regards

I am trying to solv the same problem. Acording my up till now experience ansver follow:

Crosslink density you can estimate only in crosslinked insoluble polymer acording earlier ansvers exploating mechanical properties.

Another method is from the degree of swelling of the crosslinked polymer.

From the changes of the molecular weight prior the gel formation you mai estimate gel point.

The very first method to measure the degree of crosslinking is the soxhlet extraction process. The non-linked polymer should be leach or dissolve, so the weight difference between inital and final weight should give the non-link amount.

Dear Nicholas,

thanks for your suggestion,

Swapnil 

A crosslinked polymer cannot dissolve in organic solvents because the crosslinks (even if they are small in number) will join the macromolecules by primary "covalent bonds" which do not allow the macromolecules to get apart for dissolution. For sulfur-crosslinked natural rubber, my students used to determine the percentage of sulfur incorporated by dividing the number of moles of sulfur on the number of moles of N.R which in turn is found by dividing the mass of N.R on the mass of the CRU "constitutional repeating unit" of N.R. Note that all sulfur is used up as if it is a limiting reactant.

thanks to all for valuable suggestions

Swapnil

In the case of vulcanized rubber, the Flory-Rehner equation is used to determine the crosslink density of the vulcanized rubber. You just choose the suitable solvent to soak your sample. Then, you just calculate the crosslink density according to the Flory-Rehner equation.

Mc= 3ρRT/E' - we have determined  Mc by DMA analysis ( from log E`versus T) . E` is the constant storage modulus  after Tm; then, crosslinking density is defined as ρ/Mc - for chemically crosslinked polymers

Hi Swapnil: For crosslinked materials that do dissolve in organics you can indirectly make comparisons and measure the swelling ratio of samples immersed in hot ortho-xylene. *This is a technnique used with polyethylene per NIST Test Method F 2214. Hope that helps you out.

How can i know the reason of decrease in nitrogen sorption during de-protection of hydroxyl group in a powdered form polymer. Can i measure the cross linking density before and after the de-protection reaction. DMA of powdered form polymers is possible? any other technique? please suggest

Is there anyone who can help me to answer my question. Recently i do the crosslinking of quinone molecules which consist some double bond position favorable for cross- linking.  after the crosslinking reaction with Fecl3,  I facing problem to completely remove Fecl3 even after 48 hour of soxhlet washing. when i exposed the same material with 1 mol HCl washing, i found that the material could be dissolved 90%. however, I noticed that the starting monmer is facing resistance to solublity even in concentrated Hcl.  Hope someone can help me.

thank you

Is there any ASTM or ISO standard to calculate the crosslinking percentage? 

Hi, the formula given by E'=3.R.T.Ro/Mc can only be applied for a homogenous polymeric system. So for a composite material what should we use?

Thank you