Glass Transition - Science topic

Why glass transition and crystallization peak and associated temperature is shifted with heating rates. Explain?

Dear Researchers, I recently went through my DTA analysis for my sample. In that, I found the sample weight is increasing with temperature increase. I never found like that graph in any literature. How do I understand the data? Can heat flow with a temperature graph be useful?

What can we calculate using TGA data?

Is it possible to calculate the glass transition temperature?

Please guide

Thanks in advance

Why heating-cooling-heating cycle used as compared to normal heating cycle to calculate glass transition temperatures of food protein and starches ?

I performed DMA tests on a standard polycarbonate (PC) material using the following conditions on a TA instrument:

1. Dual cantilever clamp, 0.1% strain, 1 Hz, 3°C/min, and obtained a Tg of 160°C (tan delta peak).

2. Tension clamp, 0.1% strain, 1 Hz, 3°C/min, and obtained a Tg of 180°C (tan delta peak).

Is it normal to observe a difference in Tg for the same material under identical testing conditions but with different clamps? If so, what causes this discrepancy?

Also, why on increasing scan rate, glass transition temperature is not much changing if we take sample in less amount and thermal lag is decreased.

I am performing a temperature sweep from -100 to 100C at a 3deg/min rate to determine Tg of elastomer samples using the DMA 850 model. The data doesn't begin collecting at -100C (attached data here doesn't start until -40C) and it doesn't collect continuously until after the glass transition temperature. This behavior is consistent with other elastomers of different formulas. Is there an error in sample loading? Does anyone have advice to get smoother data collection? I don't know if I can trust this data.

I am working on modifying polymer membranes with surfactants to improve their pervaporation performance. I noticed that the glass transition temperature (Tg) of the membranes decreased as the permeation increased, indicating that the polymer became more rubbery. On the other hand, the X-ray diffraction (XRD) and positron annihilation lifetime spectroscopy (PALS) measurements showed that the free volume of the membranes decreased, suggesting that the polymer chains became more compact. I am wondering how these two phenomena are related and what is the role of the surfactant in this process. Does the surfactant act as a plasticizer or an antiplasticizer for the polymer? How does the surfactant affect the molecular interactions and chain mobility of the polymer? I would appreciate any insights or references on this topic. Thank you.

I have two DSC curves, attached below. One of them shows an endothermic peak at 90 and another one at 71⁰C. Are these two peak shapes glass transition temp (considering enthalpy relaxation process)?

Moreover, in the high temp region if 314 and 157⁰C are considered to be melting temp of the compds what could be the possible processes involved for the other two peaks at 337 and 231⁰C?

Any suggestions are appreciated.

-Bidyut

The glass transition temperature of a polymer can vary from one experiment to another based on the parameters used in the synthesis and the synthesis route. I would like to know how much this oscillation range is. Sludos

Is there any procedure for determining melting point and glass transition temperature of TKX 50?

full explanation required

I have a query is that after crystallization peak point some of other noise type peaks occur in DSC scan for (Se78-xTe20Sn2Znx) x=2 and x=6 ,this peak shown the material property or due to atmospheric condition. Please explain me.

and I have another question about the DSC peak. Can you please explain me, is glass transition peak represents the material's rigidity or it signifies something else?

If a doped a material in a matrix. Its glass transition temperature and crystallization temperature decreases compared to the matrix but activation energy increases (Kissinger, Moynihan). Please give me the explanation for increased activation energy with decreased Tg and Tc.

I have doubts regarding finding the glass transition temperature for neat epoxy and epoxy composites reinforced with bamboo fibers. Anyone having knowledge about it, kindly help.

I have the graphs showing DSC-TGA simultaneously but I want to find the glass transition temperature and degree of crystallinity too. Is there some way to calculate or find them from the graphs or data?

What are the importance of glass transition temperature to surfactant role in detergency?

Why does the glass transition temperature of PCL between (-65)-(-60)?

Please see the figure in PDF attached herewith.

Good day dear all

I want to calculate the glass transition temperature of different systems of polymer/nanoparticles to study the effect of the NPS in the tg of polymer matrix

I try to use scrip in material studio software for that .but I got many problems and syntax.

Please. who can help me to attain my objective ??

Hi all,

I am finding polymer like PMMA and PC.

It should meet several conditions,

1. Transparent, high transmittance in visible light.

2. Tg is higher than room temperature.

3. Degree of crystallinity is very law.

I have found several qualified copolymer,

but I want to find a qualified polymer that has more simple structure.

Thank you very much.

Welcome everybody!

I've made PLA thin films from previously prepared granules of PLA. 8 types of thin films were obtained.

LT - pure PLA, LT2 - PLA with 0,2% Natamycin, LT6 - PLA with 0,6% Natamycin, LT10 - PLA with 1% Natamycin.

LT-PEG, LT2-PEG, LT6-PEG and LT10-PEG. PLA samples were plasticized with 5% (weight%) PEG1500.

DSC results are shown in table, and graphs.

Questions:

why there is no cold crystalization peak, when PEG is added?

can natamycyn act as plasticizing agent? (Tg is decreased with natamycin% is rising)

degree of crystallinity is rising in both cases, why?

Thank you in advance, PG.

I am looking to melt extrude PLA and a microcellulosic filler in a single screw extruder. The concern is insufficient back pressure due to low polymer viscosity before the compression zone. I want the polymer to be softened up instead of losing viscosity. This is the context in which I want to ask if Tg and softening temperatures are the same or different. If so, can a test method for gauging the softening point (temperature) of semicrystalline polymers and composites be shared?

Info: I was using Tzero Pan and Tzero lid, and around 8 mg of (powdery) material per pan.

Observation: The pan comes out of the measurement showing a slightly opened lid and some material overflow.

My question: From the graphs, how can I determine at what temperature did this occur? In other words, can I recognise from looking at the graph only, when some material overflows my pan?

Example: Looking at the heat flow below: Is it correct to analyse that the pan opened at the 160°C mark, and can be shown by a sudden sharp endo-thermal event in the heat flow.

Hello! I have a co-amorphous system with API-Tryptophan and API-Phenyalalnine obtained milled. Amino acids could not be transformed into an amorphous form via ball milling, so I cannot get the glass transition temperature of pure amorphous amino acids. So the questions are:

1.Where then to take the glass transition temperature for amino acids?

2. To determine the constant, it is necessary to know the density of amorphous substances. In the literature, I found that the density of a crystalline substance is used, as far as this is correct?

I would be very grateful for an explanation of this issue. Thanks in advance

I want to proceed the experiment using optical fiber. However, there is a problem. In one of the processes, the temperature reaches almost 600 degrees(Celsius). I know that the glass transition temperature of the soda lime glass is around 600 degrees.

In addition, the commercial glass optical fiber is consisting of 3 parts, core(pure silica) cladding(doped silica),and buffer layer(polyimide). The company says that this fiber can endure even at 400 degrees because of the polyimide, which is heat-resisting polymer. But, I think that it can endure up to 600 degrees if there is no polymer. Is it true? I will use the fiber as just a substrate, so I don't need any other layer except the core.

After I etch the polymer, what is the limit temperature for the glass optical fiber? 

My DSC curve (Figure1) do not show a horizontal shape. It may be related to the calibration, even though we recently calibrated the instrument.

In any case, the software offers an option in the settings tab: DSC/DTA Horizontal on/off (Figure 2). Using this mode, the curve changes to what I would expect and what is reported in the literature (Figure 3). Does this setting affect my analysis (glass transition, ...)? Can I rely on this setting to perform my analysis?

The glass transition isn't clearly visible in my curve (Figure 1), but when I apply DSC horizontal mode, I can clearly see it (Figure 3).

If I can use this setting, how/where should I set the segment (Figure 4)??

Qualitatively at a certain temperature the higher the viscosity the higher the GFA. I wonder whether there is any theoretical or empirical equation describe this relation.

In the Gordon-Taylor equation, the values of Tg1 and Tg2 correspond to the glass transition temperature of the two components. I have a polymer flavonoid suspension (Soluplus-quercetin). In the DSC soluplus curve, glass transition is observed but no glass transition in quercetin (temperature range 25-350 ° C).

How can I use the Gordon Taylor equation in this case?

The Tg can be obtained from three regions from a DMA test result.

1. Onset point of Storage modulus(E')

2. Peak point of Loss modulus(E")

3. Peak point of Damping coefficient(Tan Delta)

Which Tg is taken for analysis?

If there are any conditionals for selecting one of these, what are they?

Thanks in advance.

How to find the glass transition temperature of the polymer, if the corresponding step transition is so small that it is difficult to locate properly in the DSC curve?

I have a DSC curve from an amorphous material. I doubt that I can accurately determine the glass transition temperature. In reviewing the literature, I see that the glass transition temperature is chosen based on visual analysis. But if there are several thermal events or the crystallization peak greatly changes the scale of the curve? Is there a computer program (open access) that can determine the glass transition temperature from the analysis of the DSC curve? Or other Jedi tricks?

Thanks in advance

To evaluate the miscibility of a binary blend, two experimental methods are often used.

1. Phase morphology: whether it is homogeneous down to the molecular level. SEM can be used for the determination of phase morphology.

2. Glass transition temperature: whether the blend exhibits a single Tg. DSC is often used to evaluate the Tg values of a binary blend.

Furthermore, the crystallizable part in the polymers affects the phase separation.

Can anyone suggest literature (book, article...) to this topic, please?

It is also welcome to write detailed information on crystallization-induced phase separation in a polymer blend here.

Thank you in advance.

What is the glass transition temperature (Tg) for self reinforced polypropylene (SRPP) thermoplastic composite. In some references Tg for polypropylene is about -20 ̊c. Does Tg for SRPP different with that? Is there any reference for this?

I am researching a project where I am trying to create a co amorphous ternary drug-drug mixture of(warfarin-Naproxen-Benzamide)

N: B: All samples were heating up to 180 and cooled all the sampled 20 per minute.

Sometimes I am unable determine the required temperature to melt the glass composition. Is there any formula to estimate the glass transition temperature as a function of composition?

The polymer is Polyethylene and the forcefield being used is Dreiding.

Polymer gets softened at glass-transition temperature (Tg), so the bonding of two polymeric layers is possible.

What are the operating procedures for thermally bonding PDMS to PMMA?

I have made a UMAT subroutine to describe the mechanical behaviour of a shape memory alloy (SMA) following the Brinson model. However, I don't know how to make the Abaqus software know the original shape of a shape memory part so that when the glass transition temperature is applied, the SMA is able to recover its original shape.

Does anyone know how to make a part for example with a V shape (shape previously modified by applying a pressure to the part at the glass transition temperature) become completely straight, when the shape memory is applied?

Hello!

Kinetic research in the field of curing process is of great interest for me. It is okay, when some of epoxy resin based systems can be described in terms of usual second (n) order reaction models with additional autocatalysis and/or deceleration terms. Sometime we need to use so called diffusion factor function if reaction is complicated by glass transition temperature and deceleration term in usual from doesn‘t give us a good result of fitting.

Hello,

I'm trying to model a transient heating process in COMSOL with a thin metal film on a polymer substrate. I'm trying to gain intuition into the mechanical and thermal properties as a function of temperature. In particular, how do the heat capacity and Young's modulus of polyimide change with temperature especially near or above the glass transition temperature.

Regards,

Adam

The image is taken From Callister's Materials Science and Engineering.

After glass transition, the polymer chains are mostly free to rotate and wiggle, but cannot slide past each other until close to melting point. So, with temperature, why there is no continuous decrement of viscoelastic modulus (for a fixed applied strain, after same time)? Is this because the chain "freeing for movement" and "fleeing for sliding past" are kinetically activated sharply beyond a certain temperature (say, Arrhenius kinetics), and in the plateau zone the glass-transition related chain "free to movement" activation is virtually close to 100% while melting related "free to slide past" activation is virtually zero?

We have multiple samples of PHA polymers that are prepared differently. We would need Tg values with sufficient precision in order to compare the different samples, which will have relatively close Tg values. I believe values to at least 1^oC would be sufficient.

I have been recommended to perform DSC testing at a heating rate of 1^oC/min, performing multiple passes and repeating the test with replicate specimens to get the most accurate Tg. As far as I'm currently aware it isn't feasible to slow down the heating rate.

Are there any other ways of performing this test to ensure we have values precise enough for comparison or is performing multiple passes the best way of determining these values?

Nowadays, prediction of some physical properties of glasses, namely, density, Young's modulus, shear modulus, hardness, glass transition temperature, thermal expansion coefficient, liquidus temperature, and refractive index. Using (AI) become one of the effective methods to know more and more about the structure of the glass nature.

Hi I was wondering if anyone could help with the interpretation of this DSC curve obtained for PLA powder. I'm unsure as to why there is a peak located at 113.9C. Most of the curves I see in literature show an exothermic event. 

The powder is being used used for additive manufacturing, with the addition of a filler, the powder is very prone to warping even when processed at temperatures close to the onset of melting. I believe that this is linked to stresses caused by crystallization, but from the DSC it shouldn't be crystallising at the temperatures im processing it at. If anyone can enlighten me as to what might be occurring i'd be really grateful! 

Would Tg, glass transition temperature remain constant at different applied %Strain?

I know the approximate folding and unfolding rate constants, but not the exact concentrations or anything like that. Is there a way to determine a very coarse approximation for the relaxation time when the temperature is increased 2 degrees celcius? Two minutes or ten minutes or an hour?

Kfold=10^5.8

Kunfold=10^-4.1

Hello everyone

I have done a DSC test on the poly-lactic acid by Mettler DSC set-up. As the result shows, there are three endothermic peaks in the red curve that I marked by the black color. It is obvious that peak number one belongs to the glass transition temperature, and peak number three is the melting temperature, but I don't know exactly what is the type of peak number two. I have this concern that the second peak might be the effect of impurity or a metastable modification in the polymer tested.

Any guidance, suggestion, or opinion would be helpful.

Best regards.

Hello all,

If we consider a polymer is heated till glass transition temperature at atmospheric pressure. Can we call it Enthalpy of Fusion ( Latent Heat of Fusion). I am confused, as on the internet there is nothing mentioned about transition point.

Thank you

Rajesh

Hello all,

I have a two graph ( TGA and DSC) of a biopolymer that I see decomposition starts around 170C. However once I run the DSC I do not see any melting or crystallization peak. Why?

Dear friends

As we know, in real applications we must use GRE materials under the glass transition temperature (Tg). I have a E-glass Epoxy composite pipe and i'm working on the effect of hygrothermal conditions on it's performance. I'll do test on the different temperature below Tg. But which method can i use to determine Tg exactly ?

DSC or DMA ?

Which method is more confident?

I could not find suitable reference for this answer.

Can anyone help me on this ?

thanx

I want to use pa6 for additive manufacturing. My goal is to use the components above 200 degrees celsius. My part has be dimensionally stable at 200 degrees celsius. I am confused between Tg and Tm. I know that i can use pa6 above Glass transition temperature because it semi crystalline polymer but i want to know till what temperature i can use it.

I'm trying to make some 3D printed microfluidic chambers on glass slides by using fused deposition modeling and printing directly on the glass. The problem of course is that due to differences in thermal expansion/contraction, the PLA falls off as soon as the glass/PLA interface cools due to thermal stresses. I've tried typical adhesives for printing like hairspray, etc. but these only really give a temporary bond until the material cools.

Are there any sprayable adhesives that could easily bond glass to PLA that I could use in a step by step mask method (printing the inside of the microfluidic chamber, spray the adhesive, remove the inside, print the outside chamber, etc.)?

Is there another way to get this to occur? I thought about poly-l-lysine treated glass as well, but I haven't had a chance to try that yet.

Is it possible for more than one glass transition range for a thermoplastic polymer. If so why and how? I need the exact answer of this question. Please help.

Dear all,

I conducted a differential scanning calorimetry (DSC) to investigate the miscibility of polylactic acid/polypropylene carbonate (PLA/PPC) blends. The blends were prepared by using the internal mixer with different time of mixing and rotational speed. (condition A : mixing time 5 minutes with speed 60 rpm; condition B: mixing time 10 minutes with speed 50 rpm). The results showed 2 glass transition temperature (Tg) on PLA/PPC (sample prepared in condition A), meanwhile, one Tg PLA/PPC for sample prepared by using condition B. My question is, does the conditions of sample preparation affect the miscibility of the polymer blends? is there any reference that I can rely on?

its a silicone based soft denture lining material(polydimethylsiloxane) with 3 triaminomethylsiloxane ionic liquid. please explain in detail the difference between the control and experimental groups.

Hello all,

I did DMA test on several unsaturated polymers and am currently having problem interpreting the data. So I have determined the glass transition temperatures, the loss factor i.e. tan δ and also have the loss factor and storage modulus plotted against temperature. I know than high tan δ and low storage modulus correspond to good damper but I can't seem to draw a conclusion on what value do I consider as low when the moduli are plotted over temperature. Do I consider the value at the glass transition temperature? Also, other than dampening property I can't really decide on what other properties I should elaborate about. I have been reading some papers to help but I still can't really find a solution. Please help me, much appreciated!

There are different values for Tg of PE in the literature. The values are (-78, -110, -125 deg C). Are these correct. As I ran a DSC for my HDPE sample (1mm and 3mm) and got this curve. As per my understanding, there is no transition for Tg. Looking for your expert opinion.

Attached is the file.

I have polymerized emulsions consisting of Methyl Methacrylate, Butyl Acrylate and Methacrylic Acid (around 20 degrees C Glass transition temperature) in various surfactant systems. I have found that Phosphate Esters give higher gloss levels in coatings than Sulfated Nonylphenol Ethoxylates. I also found that a smaller particle size does not necessarily mean higher gloss. What plays the biggest role in achieving higher gloss levels?

Are two glass transition temperatures possible for a polyimide?

I am using CF/epoxy (thermoset) and CF/PEEK (thermoplastic) composite for some thermal related research. The glass transition temperature of the epoxy is 165 ℃ and that of PEEK is 143℃. According to the literature, both thermoset and thermoplastic polymer can undergo a 'softening' period when the temperature reaches Tg. But what is the difference of the thermal response of thermoplastic and thermoset polymer when the temperature is around Tg? Is there any quantitative or qualititive conclusion with regard to the module loss of the two material? Looking forward to some discussion.

I am strugling a bit with filtration of air containing a sticky dust. It consists of polymer, water and some triethyl citrat. (current Tg around 20°C).

I would like to make air less sticky by forcing the polymer dust to be below the Tg for easier handling and dealing with hard/glass polymer? (To get Tg above 40°C)

As it is a waste, what compound should be mixed to achieve that?

Understanding the mechanism behind the glass transition is one of those old problems that has resisted massive efforts and huge grants. Many different models have been invented and discussed and, with time, different schools of thought emerged (among theoreticians) to understand the glass transition. Two notable examples are the school of Kinetically Constrained Models (KCM) and the school of the Random First Order Transition (RFOT).

A huge part of the (theoretical) literature in the previous recent years, focuses either on the debate between these two visions, or on the many problems each of them finds in its own way after each step. This is why it is very difficult to find ideas detached from a given school of thought (at least in recent literature).

As a theoretician, I am naturally interested on the technical developments behind these approaches, nevertheless, I'm also curious about the original problem. So, if one could answer this question without any reference to the pre-existing theories and to their constructions, what are the empirical facts that any successful theory of the glass transition must be able to explain?

Could it be a few maximums in polymer molecular weight distribution?

I am modeling a hygroscopic (i.e. moisture-induced) swelling of the hydrogel matrix. The water from outside enters the hydrogel domain through diffusion. As the hydrogel will swell, the elastic modulus (E) of the hydrogel will keep on decreasing. I want to know whether there is any way I can computationally predict the change in the elastic modulus value using some relation.

I know there exists a relation between temperature-induced swelling and elastic modulus which is discussed in equation 11 (file attached). Please help?

Further adding to this question, if I know the change in glass transition temperature of hydrogel with moisture content, can I calculate the elastic modulus from there? Or is there a relation between glass transition temperature and elastic modulus?

Thankyou

I am curious what it means when the loss modulus, E", never peaks during a DMA test (increasing temp / constant frequency). I would imagine that this material never dissipates energy over the course of the test, which seems odd. I would imagine there is some point where the energy put in would cause the chains to move. There is a clear tan delta peak as well, so there is definitely a Tg. What am I missing?

Also, just to make sure I am understanding a DMA run correctly. Another run did show the loss modulus spike about 30 C lower than the Tg (Here is a pic of the run: https://imgur.com/a/KMK47kT). This is an acrylate cured urethane elastomer. Does this means the energy being put in is enough to cause the chains to disassociate, but not enough to cause them to completely move around? I usually see the loss modulus spike near the Tg, but this sample is quite a bit lower. What would be the cause for the large gap between the loss modulus peak and the tan delta peak? Are the backbone chains moving, but the hydrogen bonded links still solid and finally break at the Tg?

Any insight you can share would be greatly appreciated.

Thanks!

The question is coming because for the two phase transitions, one is characterized by sharp changes in enthalpy & the other stays as a diffused broad change (e.g., glass transition). Is it also possible that such phenomena are strongly material dependent? I mean, the same melting or glass transition would show exceptional changes in enthalpy as one changes the system of materials. Please send me some relevant research papers or book references on this topic. 

I am doing the DSC of my compounds (small molecule, no polymer) before the decomposition temperature and I dont understand the non reversible peak I obtained on the first cycle. I also observe glass transition only in the following cycles.

Any idea on what does this mean ?

below : Two DSC curves corresponding to two slightly similar aromatic molecule with just different halogens group.

as i understand by increase the molecular weight of the polymer ,glass transition ( Tg ) increases but

why some polymer have high molecular weight but it is glass transition is lower than another polymer that have lower molecular weight

for example poly (hexyl methacrylate) have lower Tg than poly ( methyl methacrylate)

if we consider molecular weight we will find that poly (hexyl methacrylate) have higher molecular weight than poly ( methyl methacrylate)

I was wondering what the difference is between the glass transition temperature and the ductile/brittle transition temperature? I know that Tg is the temperature where a polymer will go from a glassy state to a viscoelastic state. From my understanding when a polymer is under the Tg value it will be brittle and glassy. When a polymer is above the Tg value it will act rubbery and ductile. Is this correct?

I also know that the ductile/brittle transition temperature is the minimum temperature in which a material has the ability to absorb a specific amount of energy without fracturing. In other words it is the temperature in which a material will fail and crack because it has become so brittle.

I am just getting confused because I am trying to determine the temperature at which polyethylene will crack in the freezer and I don't know which value to use. For example, polyethylene has a glass transition temperature of -90°C, but it can crack if it is in a temperature of -70°C (DBTT). It does not make sense to me that polyethylene would crack while it is still in the viscoelastic state.

If anyone can explain the difference and clarify this up for me that would be great. Also, if anyone knows what value I should use to determine the cracking point of polymers due to freezing please let me know. Thanks!

I'm studying the low temperature resistance elastomers. But I didn't find any good method to decrease Tg of the materials, by chemical modifications or by reinforcement. I need help.

I have DSC thermograms that have already being plotted. At specific points on the graph, values denoted as Integral in mJ, onset, peak and endset in oC are provided. While I understand that the values in J/g represent enthalpy what does the integral value in mJ denote. Is it possible to have more than one glass transition temperature on the same thermogram?

Hi, I'm planning to make some ionic liquid gated transistor.

But the problem is famous ionic liquid, DEME-TFSI has a glass transition below 180K.

But I need to lower the temperature till 70K.

Is there any other option that i can choose for the ionic liquid?

I am getting slightly different values of Tg from both DSC and DMA. The DMA results are giving me higher values of Tg compared to DSC. Which values should I trust?

I am actually working on pharmaceutical formulations with thermoplastic polymers such as "copovidone or Kollidon VA64 and active ingredients like "Paracetamol". When i was running DSC with pure polymers, i used to do heat-cool-heat cycle (25-250 at 10°C/ min) in order to obtain the glass transition temperature (103 °C). Now, I am producing extrudates of KVA64 with Paracetamol and I am trying to determine solid state change of the Paracetamol (which is crystalline and have melting peak at 170°C) and check if I obtained a solid amorphous dispersion. However, by applying the heat-cool-heat cycle method to the physical mixture or the extrudates, i only fitnd in the 2nd heat a glass transition temperature without the melting peak characteristic of the Paracetamol even though on XRD there a some cristalline peaks. I think during the 1st heating, I amorphized the Paracetamol within the copovidone and the 2nd heating displays the thermal profile of this in-situ solid amorphous dispersion and not my original product. Could you suggest me some solutions to this issue? Thanks in advance

I am currently doing some work on sub-Tg physical ageing of polymers, and doing my modeling using the TNM framework.

I have been successful in implementing the TNM model in the non-isothermal case, but I am struggling to implement the isothermal case (see attached -. Eq. 4 from Journal of Non-Crystalline Solids, 378 (2013) 186-195). The issue that I am having trouble understanding is how the Tf evolves during this isothermal step - because this is isothermal, won't the summation of "delta T_j" multiplied by the nested summation (relaxation term) always equal to zero, given that delta T during an isotherm is equal to zero?

I am implementing the model in Matlab. If anyone could give me some insight here and help point me in the right direction, I would be extremely grateful!

Dear All,

I'm working on matrix encapsulation with different polysaccharides and especially Acacia gum (also called Arabic gum) and Maltodextrine at different DE values.

After research on Internet and in scientific journals, I didn't find a Handbook or a database of the Tg value of polysaccharides?

Have you these data? If yes, can you share them with me or the reference of the publication where I can find them?