Could you present the experimental result? The temperature is definitely too low for silica glass Tg. Or modification means polymer coating? Even with a polymer you would observe such a transition only for elastomer-like substances. Is the effect reversible? Did you dry the material carefully?

Modification with glycidyl methacrylate, what do you mean about reversible? Material was dry but not completely, what is the effect of water on transition?

I meant by reversibility that repeated heating-cooling-reheating results in the same curve with identical tarnsition. If there is post-curing or water desorption, the second heating curev will be different. Glycidy methacrylate: did the unsaturation react (polymerize)? Then the observed second order transition might be glass transition - although in the case of acrylates it should be much above room temperature.

No, GMA is not polymerized on the surface of Silica. double bond of GMA-silica is used in preparation of nanocomposite that chemicaly bonded to polymer.

It's a mistake to describe the glass transition as second-order. Classically, a second-order transition has a discontinuity in the second derivative of free energy with respect to the order parameter, and a glass transition does not have such a discontinuity. In mean field theory, the glass "transition" would more correctly be described as a "crossover," similar to a second-order transition in the presence of a symmetry breaking field.

cp and the thermal expansion coefficient do show a stepwise change at the glass transition, dont they? The first is detected by DSC the second one by dilatometry. The only argument against regarding the glass transition as a second order transition is that it has strong kinetic aspects (related to volume and enthalpy realxation). I read somewhere that it is better to talk about a second order transition lying behind the glass transition, but this transition temperature can only be achieved by infinitely slow cooling. At least this is read about in silicate and polymer glasses. Spin glasses may be somethig different - I do not know them well enough.

Water will cause some artifacts at about 100°C. You could use an special crucible cover having a very small pinhole, this way water will be released during the first heating, even thought this is not the main purpose of such cover.

Essentially, the argument against the glass transition being a phase transition per se is that it is not associated with a change of symmetry, or a change in the number of stable phases (e.g. consolute point at the top of a miscibility gap). Hence the rounded character of the specific heat peak.

The following references all regard Tg as a second order transition:

http://www.colby.edu/chemistry/PChem/lab/DiffScanningCal.pdf

http://onlinelibrary.wiley.com/doi/10.1002/%28SICI%291097-4628%2819990103%2971:1%3C143::AID-APP17%3E3.0.CO;2-I/abstract

http://www.files.chem.vt.edu/chem-dept/marand/MEScchap7-1c.pdf

http://www.weizmann.ac.il/condmat/superc/pdfs/Phys.Rev.Lett.95,257004,pp.1-4%282005%29.pdf

http://old.iupac.org/polyedu/page36/page19/page22/files/Hess%20Lecture.pdf

You cannot expect a change in symmetry in a system which lacks symmetry both above and below the transition temperature (e.g. atactic polystytrene).

Thank you for the references, I'll try to give them a read. Which is best to start with?

BUT, I doubt they will make a compelling case. Classically (Ehrenfest), a second-order transition has a discontinuity in the second derivative of free energy with respect to the order parameter. More recently, Michael Fisher (Can't find the reference, but maybe it is also in Rev. Mod. Phys. 46, 597- 1974) suggested calling such transitions "critical" because they are associated with critical points.

It's clearly wrong to say, "You cannot expect a change in symmetry in a system which lacks symmetry..." in reference to a glassy system, because the symmetry is C_infinityV, and can be reduced by ordering; e.g. to a smectic (or other) ordered liquid crystal phase.

I'm sure your right - I am not a physicist, only a poor chemist. I was simply surprized by your note because in the physical chemistry of polymer sand silicate glasses the association of the glass trasition with a second order transition is taken almost granted. I know that there is some debate, i.e. whether it is a "real" second order transition or is only "behind it". It is also well known that the experimentally determined transtion is a kinetic phenomenon inflenced by the cooling rate. Nevertheless it is usually assumed in the free volume theory (see e.g. http://www.ims.uconn.edu/~avd/class/2006/cheg351/lec6.pdf) that there is a limiting Tg which is not kinetically determined, and THAT is supposed to be a thermodynamically determined transition.

Regarding point groups it was many many years ago that I had to deal with them in IR and Raman spectroscopic calculations. But I am curious. C_infinityV means that you have infinite mirror planes around an axis isn't it? (It is the case of cylinders). But this is not he case with atactiv polystyrene molecule (http://en.wikipedia.org/wiki/Tacticity) - a typical glassy material - even if the molecule is stretched out. In the case of nematic ordering OK, you have isotropically oriented cylinders in the disorederd liquid state and more or less parallel ones in the nematic state the center of gravity remaining disporeder. But this is not possible with atactic polymers. Liquid crystalline polymers do exist (both main chain and side chain liquid crystals), but even these have glass (and sometimes crystalline) transitions separate form the liquid crystalline transitions. Thank you for instructing me.

I'm not a physicist either, rather a lapsed mineralogist. I have spent a lot of time thinking about solid-solid phase transitions, but have neglected the literature on the glass transition. So, I'm not familiar with the "behind it" second-order transition idea. I'll try to look at the references you cite.

By C_infinityV I meant to imply spherical symmetry (maybe C_infinityV is not the correct terminology). I assume the atactiv polystyrene system you refer to is one in which both the liquid and glass have spherical symmetry; therefore no change in symmetry. SO, that would be one in which I would say there could be no phase transition.

If I remember well, the supposed transition is where the free volume reaches its possible minimum for the given system, and from that point on the thermal expansion coefficient becomes "solid-like". Above that temperature the thermal expansion coefficient has two components: the solid-lie and that of the free volume - causing liquid-like expansion coefficient. The free volume thory also explains the pressure dependence of the glass transition temperature well observable experimentally. Why is necessary to assume a change in symmetry for a second order transition?

It's not necessary to have a change of symmetry; e.g. the critical point at the crest of a miscibility gap is an isolated point of (classically) second-order transition. It is also, however, a point at which two phases change into one, or vice versa. I'm not familiar with free volume theory...more to learn.

If I know well, the free volume concept was introduced by Russian physicst Frenkel to explin the viscosity of fluids. Free volume is the additional volume above the volume of the molecules themselves. The viscosity can be expressed as a function of the free volume and the dependence of free volume on temperature and pressure can be estimated using various models. See the uconn reference cited in one of my earlier notes.

I had a quick and superficial look at the sites and paper you referenced, and my impression is as follows:

1) phenomenology of the glass transition is like that of a second-order transition in a field. In principle the field may be arbitrarilly weak; i.e. the system may be arbitrarilly close to a second-order transition. The presence of the field, however weak, changes the transition to a crossover, i.e. eliminates the transition point. As the field becomes very weak the distinction between a phase transition and a crossover may begin to sound a bit theological, but I don't think it is.

2) Plots of actual data, in the references you list, are always permissive of a smooth curve in isothermal compressibility as opposed to a discontinuity. Of course this is always the case, but none of the figures I recall were compelling.

3) The authors of those refs. either assume a second-order transition, or actually say that there is no transition per se (http://www.colby.edu/chemistry/PChem/lab/DiffScanningCal.pdf).

It's interesting. You should write an article on this topic to a polymer journal - it may induce and intense discussion with "better equipped" polymer pyhsicists than myself. If you do so I would suggest you the journal eXPRESS Polymer Letters, where I am involved as executive editor. I mean it sincerely!

Before I do anything that rash, I should chat with Jack Douglas who is the NIST expert on polymer-physics theory. I'll let you know how it turns out.

OK, I'm looking forward to it. Anyway, it was an interesting discussion. I wonder what "crossover" exactly means in this context and what it the difference between a crossover process and phase transition.