If the two polymers are miscible, you can use the Flory-Fox equation as a first approximation (based on the free volume theory). You will see the shift if the amount of the second component is significant. If the two components are immsicible you may see even two seprate Tg-s. You may also try TSC (thermally stimulated currents) as this is very sensitive to the appearance of second phase. Tg, by itself does not tell you too much about the structure (graft copolymer, blend etc.). For that you need morphological studies, maybe IR or Raman microscopy. At the molecular level you may need C13NMR. Selectrive dissolution may also help.

for homogeneous blends and statistical polymers you might use the Flory-Fox equation to predict Tg. In my experience it is a good indication. So, if no phase-separation occurs (in which case you would measure two distinctive Tg's) in the copolymer you prepare. If you plan to make a material out of this polymer (or if this is feasible) determination by means of DMTA is more accurate compared to DSC. Often, the max of the tan delta is often used to determine the Tg.

The Tg will shift towards the second polymer, depending on the composition. There is a standard equation related mass of each polymer and Tg. Polymer physics book might help you.

F Khan

If the two polymers are miscible, you can use the Flory-Fox equation as a first approximation (based on the free volume theory). You will see the shift if the amount of the second component is significant. If the two components are immsicible you may see even two seprate Tg-s. You may also try TSC (thermally stimulated currents) as this is very sensitive to the appearance of second phase. Tg, by itself does not tell you too much about the structure (graft copolymer, blend etc.). For that you need morphological studies, maybe IR or Raman microscopy. At the molecular level you may need C13NMR. Selectrive dissolution may also help.

By drs, dmta, dsc, tsdc

You can use the Fox equation: 1/Tg=w1/Tg1+w2/Tg2......Valid for copolymers.

Where w1 and w2 are weight fractions of components 1 and 2, respectively.

Thanks and all suggestions and explanations are useful for me. I will try DTA to compare if we will get a consistent Tg with DSC. We have seen one transition by DSC, so it may be a miscible copolymer blend. I may try to employ Flory-Fox eq. to estimate the resulting Tg of copolymer.

Another concern is that if we changed grafting in molar stoichiometry of copolymer, does it still follow Flory-Fox's Eq. ?

The general rule is that the glass transition will be between the glass transition of the components. For the compatible case, you expect a single TG somewhere between the TG of components, with a position controlled by the weight fraction of the components. Refined theories add expansion coefficients of these components.

For the incompatible case you obtain two glass transition temperatures identical to the TGs of the homopolymers. For interactions is obtained two glass transition temperatures in between the two TGs. In certain extreme cases you may go (at least theoretically) beyond the range defined by the two glass transition temperatures.

I would not use DSC which has a reduced resolution. If possible try DMA for the location of the glass transition(s).

Are there not exceptions to the general rule?

I cannot cite a concrete example, but in principle if the two molecules interact strongly thus making the resulting structuremore rigid than any of the components, the Tg value may even arise (simlarly to the boiling points of miscible liquids). Probably there are sevral other possible reasons for deviation form the rule - that's why most responding colleagues emphaiszed that "generally" "as rule" the Tg-s of miscible polymer blends or copolymers are lower than that obtained form a linear mixture rule.

Predicting Tg is, in fact, still an assumption. Flory-Fox equation could be used for thermodynamically miscible polymer blends. But application of such equation can be limited to the preparation condition of blends. Blends prepared in solution casting can exhibit large difference with the blends prepared in melt blending. However, a large number of litteratures can be found where Fox equation is used for predicting Tg in blends, irrespetive to the understanding of molecular structure and blend preparations. Gordon-Taylor euqation can also be useful in such case. Moreover, predicting can only give a way to compare the experimental value with the theoretical one. In practical sense or in more logical manner a good correlation between morphology of blends and its thermal transition could be more useful in understanding the origin of such Tg in blends. however, Tg in polymer or in blends still a never ending debate!

Could the excess Gibbs Free Energies of the two polymers be used for the calculation of resultant Tg?

Gibb's free energy could be used to calculate the miscibility of blends.

The use of thermodynamics in relation to glass temperature is not very sound approcah, as the glass transition itself in not an equilibrium phenomenon (see an earlier discussion whether glass transition can be regarded as a second order thermodyanmic transition or not). My impression is that the free volume theory provides a sounder framework to describe the glass transition. Cast and melt blending may result in different glass transitions for blends exactly because both are formed under non-equilibrium conditions, but these conditions are different.

As others have mentioned, Flory-Fox equation indeed would give you a "rule-of-thumb" estimate of Tg of polymer based on % grafting. Such an estimate works very well if you are comparing within a single set of grafting units, for example, if you graft polymer A with different %s of polymer B, most likely you will find a good correlation between Tg and % of A (or B). However, extrapolating that to a different polymer C for a combination of A and C will be a stretch (exceptions apply). On top of the assumptions that A, B and C are miscible, and do not "phase - separate" in and around Tg ( you measurement temperature) and as Gyorgy stated, they are also non-interacting. Interaction between them will completely change the free volume scenario and hence the predictability. I would not necessarily look for any sort of thermodynamic picture related to Tg; also if there is any dependency on the processing conditions (for example, melt vs solution processed), that is mostly because differences in resulting homogeneity. (Can't help putting my 2-cents! :)).

Predictions such as those proposed herein are well used and functional methodologies. Nevertheless beware with your results since you are landing into the colligative forces world, thus predictions need to be taken with really care. As stated by many of our colleagues herein, this property is highly dependent on how the chemically coupled blocks interact among each other. If they strongly interact hence the Tg would be higher due to the fact that they are better supramolecularly assembled (VDW, London forces, etc.). Expect also an increase in DeltaH in the latter case. I suggest to develop theoretical calculations of variable sections of your interacting blocks, and if the obtained energy in the minimization is lower hence your Tg should increase in a factor and you can correlate that by varying the lengths of interaction to predict a certain property such as Tg. Have luck in your determinations. Hope this helps.

You might also take a look at the predictive model described by Brostow et. al in Materials Letters 2008, Prediction of glass transition temperatures: Binary blends and copolymers. The article is available here http://www.unt.edu/LAPOM/publications/pdf%20articles/TgML.pdf

Thanks to Haley

You can use positron annihilation life time spectroscopy (PALS )to evaluate glass transition with high accuracy which depend on study of free volume size

If each polymer polymer self assemble in "sufficiently" large domains, you should be able to visualize both Tgs using regular DSC technique.

I think it depends on the grafting density and also the length of the grafts. Considering that Tg is related to the molecular movement is small scales (can imagine in order of 50 C-C bonds), we can see that you need high grafting density to affect Tg. About the graft length, if your grafted chain exceeds certain length (lets say 50 C-C bond), then I expect that you will see two Tgs, one related to the backbone and the other one related to the grafts.

It really depends on if your polymers form interphase or phase-separation. For the first case, Fox equation can give you a rough estimate. Otherwise, you will see two distinct Tgs if they are far enough from each other.

If the sample is blend of two polymers, then it is probable two Tg will appear in DSC. But if there is any interactions (hydrogen bonding, cross linkage etc) between two types of polymer chains it will change the Tg. It will depends on the nature of polymer grafted. e.g. If branching is to lesser extent it will lower the Tg. but if branching is to greater extent it will create hindrance in the segmental movements and result in increase in Tg.