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# Applications of calorimetry

Calorimetry is a method to measure the heat effect of a process,which could  be physical changes, such as melting, evaporation, dehydration (could also be defined as chemical change), or it can be a chemical change, such as acid-base neutralization, dissolving, solid-state reaction, and crystal phase transition. Calorimeter is an instrument which determines heat effect in it by directly measurement of temperature. Calorimetry is well applied in thermochemistry field, by determining the enthalpy formation trends, phase stability, heat capacity, surface effect, etc. This content contains theory, introduction of different calorimeters, and will focus on the application of high temperature oxide melt solution calorimetry in the study of different materials, such as nanomaterial, ceramics, zeolite.

### Theory

Although matters prefer to exist in energetic stable state which obeys the lowest energy principle, they actually can have various energetic states. Natural occurrence, polymorph, reactivity and different physical properties (photo, electrical, magnetic) have a common profound implication of energy difference. From another standpoint, if we can understand and establish the correspondence relationship, we can predict natural occurrence, polymorph, reactivity and physical properties based on energy measurement. The thermodynamic research provides a direct way to study the relationship among energy (enthalpy, entropy, and free energy), structure and properties.

Enthalpy is the heat at constant pressure, which is defined as H=U+PV (U is internal energy, P is pressure of the system, V is volume of the system)[1]. Enthalpy of formation are related with the stability and thermal properties of chemicals. For inorganic material, especially solid crystalline materials, ΔS is relatively small. So free energy change ΔG=ΔH-TΔS is mainly dependent on the enthalpy changes.Thus the enthalpy changes normally can be used directly to study thermodynamic effects of solid material.

Based on heat transfer theory, the relations between the heat effect generated and the quantity measured in the calorimeter known as the heat balance equation is established, which expresses the change of temperature directly as a function of the heat produced in a calorimeter and is applied to design different types of calorimeters.

### Instrument: Introduction of different calorimeter

All the calorimeter measurement applies three different techniques: temperature change (either adiabatic or isoperibol)in which the temperature change of calorimeter measuring cell can be converted to heat change of the reaction occurring in the calorimeter; power compensation (often called isothermal)in which reaction and controlled heater as two heating sources are kept at same heating power so the heat change is equal to the integration of the controlled heater power over the measurement time;and heat conductionin which the very temperature change caused by the heat produce in a reaction was recorded as a small voltage through  heat flow sensors. The calorimeters can be classified on the basis of different criteria.

By the opening state of system, calorimeter can be divided into adiabatic and non-adiabatic calorimeter. Adiabatic calorimeter directly measures the temperature changing in a heat insulated system. While Non-adiabatic calorimeter measure the heat flow of the system, in which heat would transfer to the surrounding environment[2]. In terms of different working conditions, it can be classified as constant pressure calorimeter and constant volume calorimeter, or high temperature calorimeter and low temperature calorimeter.

In terms of construction principle, it can be classified into single calorimeter and twin calorimeter. Other types of calorimeters have also been developed for more flexible application, such as DSC (Differential Scanning Calorimetry), solution calorimetry. Following is the introduction of four typical calorimeters: coffee cup calorimeter, bomb calorimeter, solution calorimeter and scanning calorimeter.

## Coffee Cup Calorimeter (Calorimetry with constant pressure)

Figure 1: Coffee cup calorimeter

As a simple calorimeter for thermochemistry lab, coffee cup calorimeter uses Styrofoam cups with insulated lid to prevent the heat lose and thermometer to measure the temperature changing. It works at atmosphere pressure which is assumed as a constant. Since the enthalpy changing is equal to heat transfer at constant pressure(ΔH=qp), this calorimeter can be used easily to measure the enthalpy change of some simple processes, like fusion enthalpy, dissolving enthalpy,and determine the heat capacity (Cp) of material, such as metals. This calorimeter usually works with well heat conducting solvents for measure convenience, such as water and must be calibrated by a material with known heat capacity. In this type of calorimeter, heat is a function of temperature difference, which can be written in formula:

$ΔH=q_p=mcΔT\ tag{1}$

In which: ΔH is the enthalpy change; qpis heat at constant pressure(J), m is mass(g), c is specific heat capacity of the material (J/k·g), ΔT is the temperature difference(k).

## 2.2 Bomb Calorimetry (Calorimetry with constant volume)

Fig.2 Bomb calorimeters

Bomb calorimeter is an isolated system and has constant volume. The bomb is a sealed container for the reaction occurring, and the heat of reaction will transfer to the water or oil in the inner container. The temperature changing of the water is used to calculate the heat of reaction. Bomb calorimeter is suitable for study of combustion reaction. The ignition of sample will be done by electricity connecting to the sample holder in the bomb[3]. This system is adiabatic, so there is no heat transfer between calorimeter and surrounding, q=0. For a process of combustion, the initial temperature is T1 and the final temperature is T2.

Then the overall change of internal energy of system is ΔUoverall=0

So the change of internal energy of combustion of sample ΔU1 and changing of internal energy of water ΔU2 are related by:

ΔU1+ΔU2=0

ΔU1 =-ΔU2

Since the process is at constant volume, Cv is the constant heat capacity of calorimeter and water.

ΔU2=CvΔT

The enthalpy of combustion can be calculated by:

ΔHc=ΔU1+ΔPV= -ΔU2+ΔnRT

In which Δn is the change of moles of gas during the combustion. Thus, by measuring the heat change of water, enthalpy of combustion can be obtained.

#### Solution calorimetry

Solution calorimeter keeps the reaction in solution, either low temperature in aqueous or high temperature in oxide melt solvent. High temperature calorimeter which works above 400°C is used to measure reaction heat at high temperature.[2] According to Hess’s law,once different chemicals can reach same final state, they can relate each other with the enthalpy of different processing, such as phase transition, formation and reaction can be calculated through thermocycle.

High temperature drop solution calorimeter

The high temperature drop solution calorimeter developed by Professor Navrotsky in UC Davis work sat 700˚C and 800˚C using sodium molybdate, lead borate and alkali borate as solvents. It’s been used to measure the heat contents, enthalpy of formations, enthalpy of phase transitions, enthalpy of dehydration, enthalpy of oxidation for different of oxides, solid solution, and minerals.

Fig.3 High temperature oxides melt solution calorimeter

The instrument is shown above.The solid samples with mass range from 5 mg to 15 mg can be dropped into high temperature solvent through the dropping tube. Three melt salt solvents(sodium molybdate, lead borate, and alkali borate)are usually used. The heat released by the dissolving process contains heat content and heat of solution. The heat flow was measured by thermopiles, which is surrounded by inconel block and heaters are kept in the insulation. Thermopile is analloy material which can convert heat to emf(electromotive force) and quantify the heat of a process. The integral of the heat flow within every minute through reaction time will give out the sum of enthalpy of solution and heat content. The result of the data will be recorded by the program on computer. In some situation, bubbling tube will be used to help sample dissolving when necessary. And flushing tube will be used when gas evolution is occurred during the process to keep the pressure constant. The calorimeter also need to calibrate use a known heat content material, such as Pt, Al2O3, TiO2[4][5].

The formation enthalpy of sample (ΔHf) can be calculated by a designed thermocycle by using the data of drop solution enthalpy (ΔHdr). For example, assuming M1 and M2 are two metal elements, Oxygen has molar number of x, and the material has a formula M1M2Ox.  The thermocycle is can be written by:

M1M2Ox(25˚C,solid)→ M1M2Ox(700˚C,soln)   ΔH1

M1O(25˚C,solid)→ M1O(700˚C,soln)       ΔH2

M2O(25˚C,solid)→ M2O(700˚C,soln)     ΔH3

M1O(25˚C,solid)+ M2O(25˚C,solid)→ M1M2Ox(25˚C,solid)   ΔH4

Where ΔH1, ΔH2, ΔH3 are drop solution enthalpy measured by calorimetry, ΔH4 is formation enthalpy of material M1M2Ox from oxides. Cause:

ΔH4= ΔH2+ ΔH3- ΔH1

Notice that all of the equation must be balanced and all samples mustcompletely dissolve in solvent, so that M1M2Ox (700˚C,soln) and M1O(700˚C,soln)+ M2O(700˚C,soln) are in equallydissolved states.[6]

#### The acid solution calorimeter (low temperature calorimeter)

Low temperature calorimeter is used to measure the heat of process at low temperature, such as freezing and crystallization. The temperature range is from -200°C to 200°C[2]. Instead of using solid solution as the solvent, aqueous acid and base are used as solvents in this solution calorimeter, such as HCl and NaOH aqueous solution. The applied scope includes aqueous ion enthalpy and formation enthalpies of carbonates and organic containing material, which can dissolved in aqueous acid or base at room temperature.

The instrument is also open to the ambient pressure, the aqueous solvent is filled in a Dewar and the sample is filled in the small Teflon dish hold by the sample bell. By operating the push rod, the sample can be dumped and mixed with the solvent. The temperature change will be probed by the micro thermometer or thermistor. The enthalpy of reaction also can be calculated by:

ΔHr=Qp=CpΔT

In which Cp is a constant heat capacity for the calorimeter and solvent. It is also a calibration factor for each of calorimeter which can obtain by measure those samples whose enthalpy of reaction with the solvent is known.

### Scanning calorimetry

Differential Scanning Calorimetry(DSC)

In 1920’s, the first differential calorimeter was developed by measuring the micro voltage[7]. That means calorimeter can be made to be more precise and smaller scale. Nowadays, Differential Scanning Calorimeter is the most common calorimetry insolid material laboratory for many advantages, such as measuring fast, precisely and little sample needed. It is convenient to probe thermo properties of material within a temperature range. The instrument is just as big as a printer, with two sample holders surrounded with thermo sensor sitting in a mobile furnace. Temperature can be gradually increased and decreased when sample and reference sample (high temperature resistant material, such as sapphire) were put in the furnace. Then thermal behavior due to the temperature difference between sample and reference sample will be recorded by data analysis system during the process[8].DSC can be combined with TG (Thermo gravimeter) to measure the weight change during the heating which correspond to the water content or other changes involved. The combined instrument is known as DSC/TG.

Fig.4 Sketch of  differential scanning calorimeter

In an example of analysis of differential scanning calorimetry for hydrated Copper acetate(CuAc), the sample went through dehydration and decomposition at the DSC curve range from 25˚C to 700˚C. The DSC curve first comes outan endothermic peak at 145˚C, corresponding toa weight loss of 11.9% on the TG curve(water loss processing) which is followed bya small exothermic peak at 245˚C.Thenan endothermic peak at 270˚C, companied with huge weight loss 68.1%, is the decomposition of CuAc. The third broad peak from 450˚C to 700˚C without weight change is the reaction of Cu, CuO, and Cu2O[9]. However, the DSC/TG needswork wit XRD to figure outthe product at each stage.

### Gas/Water adsorption calorimetry

Fig.5 Sketch of gas adsorption microcalorimetry.

Gas adsorption calorimetry is a method designed to measure the enthalpy of adsorption, such as water adsorption enthalpy. The instrument is a combination of three systems: surface area analyzer, gas dosing system and a micro calorimeter. It enables to measure the enthalpy change of an adsorption process: volume controlled dosing gas adsorped by the surface area of known sample. A commercial micromeritics ASAP2020 which is used to measure surface area by BET (Branuer-Emmet-Teller) method is used as a surface analyzer, and a water bulb with turbo pump are used as water dosing system ( Fig.5). The calorimeter is a calvet-type microcalorimeter Setaram DSC111. The experiment is worked in this sequence: at first slowly removing all of the surface water or gases without change the structure; then measuring the surface area;finally starting to involve the calorimeter with the volumetric dosing system and measuring the heat change of the adsorption process.

### Applications

This part will mainly focus on the application of high temperature oxide melt solution calorimeter whichhas been applied in study of several kinds of material, such as nano-material, ceramic,zeolite. The applied scope of this calorimeter covers most solid materials in inorganic and material field [11].

#### Nanomaterials

Nano particle (<100nm) material has larger surface area and surface energy than bulk materialenable it has unique properties[12]. High temperature oxide melt solution calorimetry can be used to determine surface energy by comparingthe formation enthalpy of nano particle and formation enthalpy of bulk material.

##### ZnO

Nano particle has highersurface activity than bulk materials due to surface effectwhich has been exploredand used to explain many novel properties of material in nano-scale. Various methods have been developed to control the morphology of nano material,such as nano porous, nano rods, and nano tetrapods, nano needle, and nano particle. But there is rare research about the difference among variousmorphologies in nano-scale.Do these nano ZnO of different shapes have different surface energies? In the study of Surface enthalpies of nano phase ZnO by using high temperature oxide melt solution calorimetry, this question was answered. The result showed that all anhydrous ZnO samples have larger surface enthalpies than that of hydrous phase. Both in hydrated state or anhydrous state, the results showed nanorod and nanotetrapod have similar surface enthalpy; nanoparticle and nanoporous have similar surface enthalpy; and the former two morphologies have much larger surface enthalpy than the later two morphologies. Combined with others’ research, the author came to the conclusion that this difference was derived from exposing different planes on surfaces in these morphologies. [13]

##### Nano TiO2

The study on Titania oxide has revealed the relationship between polymorphs and surface energy. The three polymorphs of TiO2 rutile, brookite, and anatase can transform to each other. The question is what the driving force of the transformation is. High temperature oxide melt solution calorimetry and water adsorption calorimetry have been applied to three polymorphs of TiO2 with different particle size. The result showed that the three polymorphs of TiO2 have different surface energy. Anatase has larger surface energy than brookite, and rutile has least surface energy[14]. That’s the reason why rutile is asstable as bulk material and anataseis the least stable one as nano size. Other nano oxides have also been studied for their surface effect, such as Al2O3, ZrO2, and Fe2O3. [15]

#### Ceramics

The energetic study of ceramics or solid solution is able to reveal information about the thermodynamicsand properties of material and furtherprovideinstructions to the synthesis and application.

##### YDC-YSZ solid solution

For example, high temperature oxide calorimetry was used to measure the enthalpy of formation of xCe0.8Y0.2O1.9-(1-x)Zr0.8Y0.2O1.9 solid solution system with different x content from 0 to 1. The calculated enthalpies of formations referredto the oxide Ce0.8Y0.2O1.9 and Zr0.8Y0.2O1.9 showed that as the content changes, the formation enthalpies varies with a trend in three parts: x from 0 to 0.4,increasing,  0.4 to 0.6, decreasing and 0.6 to 1 slightly deceasing [16]. Comparing the result with other YSZ (Yttria stabilized zirconia) system and YDC (yttria doped ceria), the researchers found out an important stabilizing mechanism: structure of oxygen vacancies near Zr4+ is energy favorable than it nears Y3+. This is because oxygen vacancies near Zr4+ will form 7-coordinate monoclinic zirconia which is a stable phase. While the Ce4+ cannot attract the oxygen vacancies around Y3+, but only stablize YDC by diluting the vacancy defect.

By relating the result trend with the structure and ionic properties of Zr and Ce, the researcher verified that Zr4+ can stabilize the end member Zr0.8Y0.2O1.9 and cancelle size mismatch effect by attracting oxygen vacancies from Y3+ to near the Zr4+ site, which is called “scavenging effect”. The study also estimated that 20YDC-20YSZ (20% of Yttia in YSZ and YDC) is only stabilized in a range of 0 to 37.5% of YSZ based on the scavenging effect.

##### SixOyCz polymer-like amorphous

Another study of ceramics is silicon-oxycarbide (SiCO), a high temperature resistant material which can stay amorphous at up to 1000˚C[17]. A series of SixOyCz and related oxideswith controlled x, y, z ratio were applied to high temperature oxide solution calorimeter. It results a nagative formation enthalpy relative to crystalline form SiO2, SiC, and C explained the properties of crystalline resistance of SiCO. The result indicates that the amorphous silicon-oxycarbide is more stable than the crystalline phase due to its lower formation enthalpy and free energy[18]. The researcher demonstrated such low free energy is because the graphene nanodomain structure in the amorphous phase hampered the movement of Silica.

The two examples have somedifferencein methodology because the element Carbon in SiCO has different final state in the high temperature oxide solution calorimeter. Unlike metal elements which can dissolve in solvent, carbon with turn to be CO2 which is a gas and will escape from the solvent. The data of heat effect of CO2 gas phase is neededcalculateformation enthalpy from oxide.

#### Zeolites and framework material

Zeolite beta

The structure of Zeolite featured with pores, framework, metal cation for charge balance. The properties of zeolites which have wide application in petrochemical industry and water treatment were ascribed to it structure features[19].  The energetic trend for different cation is been studied using calorimeter.

The formation enthalpy study of other kinds of cation (Li, Na) exchanged zeolites has reveals a trend: higher formation enthalpy as cation radius larger. High temperature oxide melt solution calorimeter was used to study the energetic of Li and Na containing zeolite beta. Formation enthalpy from oxide study has proved the same trend again. Na zeolite beta showed larger formation enthalpy than Li zeolite beta[20]. The formation enthalpy of zeolite with various water contents fits a quadratic relationship with the water content. Dehydration enthalpy was also studied for Li and Na zeolites with different contents of water. The results showed partial molar dehydration enthalpy decreased as the water contents increased which indicated a kinetic effect--water is tighter bound at less water contents. Dehydration of Li zeolite showed higher endothermic effect than that of Na zeolite.

Zeolite beta with different cation (Mg, Ca, Sr, Ba) showedan increasing trend of formation enthalpy versus average ionic potential for both hydrous and anhydrous phase[21], which means the bigger the cation is, the more unstable the zeolite is. Comparison amongsame cation zeolite with different Al/Si ratioindicated the higher Si content zeolite is less endothermic, thus more stable. This maybe related with the structure defect level. That also implied it is more difficult to synthesize low silica zeolite beta with cation Mg and Ca than high silica zeolite beta.

### Conclusion

Calorimetry builds up a bridge between chemical/physical process and heat change which is fundamental to understand chemical reactivity and physical property. DSC-TG which is a general tool in chemical lab provides a convenient way to track possible phase change, dehydration and structure collapse. High temperature oxide melt solution calorimeteris a powerful tool to explore thermodynamic factor to drive chemical/physical change in solid material and explanation for difference of stability and properties. The development of oxide melt solution with higher temperature will further broad its application.

### Reference:

1. [1] Svein Stølen, Tor Grande. Chemical thermodynamics of materials: macroscopic and microscopic aspects. John Wiley. 2004. Page: 4-9
2. [2] Hemminger, W., and G. Höhne. Calorimetry – Fundamentals and Practice. Verlag Chemie, Weinheim.1984. Page: 275-279
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