Major references of literature for development of DSC Curve Solutions are listed as follows:

J. Cao; "Numerical simulation of DSC and TMDSC curves as well as reversing and non-reversing curve separation",

*Journal of Applied Polymer Science*, Vol. **106**, 3063-3069 (2007)
**ABSTRACT:** The basic physical meaning of temperature modulation for DSC is an arguable research topic,
and its interpretation affects the development of thermal analysis and polymer science. This article studies the basic
physical meaning of TMDSC by numerical simulation. DSC and TMDSC output curves are computed for a sample with step
changes in its specific heat and for a sample with crystallites melting over the temperature range. The TMDSC curves
are further analyzed to obtain the reversing and nonreversing components. It is shown that separation of the reversing
and nonreversing components from the underlying heat flow cannot be justified. Some common misconceptions regarding
TMDSC are discussed as well.
**Keywords:** TMDSC; reversing component; nonreversing component; phase lag

J. Cao; "Mathematical studies of modulated differential scanning calorimetry - I. Heat capacity measurements",

*Thermochimica Acta*, Vol. **325**, 101-109 (1999)
**Abstract:** The mathematical bases for modulated differential scanning calorimetry (MDSC) have been discussed.
It is found that the amplitude of heat flow is a non-linear function of the thermal transfer coefficient, λ,
the modulation period, *p*, the heat capacity of reference, *C*_{pr}, and the heat capacity of a sample,
*C*_{ps}. Therefore, the quantitative determination of the heat capacity of a sample is rather difficult
if not impossible. From this point of view, MDSC does not offer any advantage over a conventional DSC.

**Keywords:** Temperature modulation; Differential scanning calorimetry; Heat capacity; Amplitude; Phase lag

J. Cao; "Mathematical studies of modulated differential scanning calorimetry - II. Kinetic and non-kinetic components"

*Thermochimica Acta*, Vol. **329**, 89-95 (1999)
**Abstract:** Further to Part I of this study (Vol. 325, pp. 101-109), this article describes the mathematical
expression of MDSC by taking melting, crystallization as well as the temperature dependence of the heat capacity of a
sample into consideration. A numerical method has been established and found to be suitable for the simulation of MDSC
thermograms. It is found that a non-kinetic thermal event results in changes in the amplitude of heat flow of the
thermogram of MDSC, but a kinetic thermal event causes no change in the amplitude of heat flow. A quantitative separation
of the kinetic and non-kinetic components is, however, problematic since there is no linear relationship between
the amplitude and the thermal parameters of a sample.

**Keywords:** Temperature modulation; DSC; Reversing component; Kinetics; Numerical simulatation

J. Cao, Yu Long and R.A. Shanks; "Experimental Investigation into the Heat Capacity Measurement Using an Modulated DSC";

*Journal of Thermal Analysis*, Vol. **50**, 365-373 (1997)
**Abstract:**
Experiments using a commercial modulated DSC (MDSC) for the measurement of specific heat capacity of a sample
have been carries out. It is found that because the ampliltutde of heat flow of MDSC is a complicated non-linear
function of various experimental conditions such as the modulation frequency and the heat capacities of a sample
and pan, the methodology of heat capacity determination using an MDSC in a single run has not been justified.
The experimental results, on the other hand, agree with the theoretical equation of one of the authors. It is therefore
conculude that the capabilities of MDSC should be further examined.

**Keywords:** DSC; Heat capacity; Indium; Linearity; Modulated DSC

J. Cao and I. Sbarski; "Determination of the enthalpy of solid phase transition for isotactic polypropylene using a
modified DSC technique"

*Polymer (Communications)*, Vol. **47**, 27-31 (2006)
**Abstract:**
This paper investigates the enthalpy of solid phase transition of isotactic polypropylene from the mesomorphic phase
to the monoclinic crystal form using DSC. iPP fibres with either monoclinic crystal form or mesomorphic phase were
obtained by varying the conditions of melt spinning. XRD and mechanical tests were used to confirm the crystal forms.
It is found that conventional DSC techniques fail to detect the transition enthalpy; a technique using silicon oil
as the thermal medium was then employed to determine the transition enthalpy, which is of 3% the melting enthalpy
for crystallites with monoclinic form, or 6.1 J/g on 100% crystallinity basis.

**Keywords:** Polypropylene; Solid phase transition; Enthalpy

J. Cao and F. Leroy; "Depression of the Melting Temperature by Moisture for es in Human Hair Keratin",

*Biopolymers*, Vol. **77**, 38-43 (2005)
**Abstract:**
DSC thermal analysis has been carried out for human hair samples with various moisture contents to investigate
the melting temperature depression behavior of alpha-form crystallites in human hair. This is achieved by adopting a
novel technique using silicon oil as the thermal medium, which permits hair samples to retain a range of moisture contents in
between completely dry and fully saturated. The results show that the melting temperature of the -form crystallites in human
hair varies with moisture content from 205°C for dry hair to 155°C for the hair sample with moisture content of 23%.
These experimental results are particularly useful for clarification of the conceptual ambiguities associated with the
molecular properties of alpha-helices and alpha-form crystallites. Furthermore, the Flory-Huggins theory was employed to
determine the water-helix interaction parameter and the alpha-form crystallinity of human hair (22%), a figure consistent
with that obtained by the XRD method (21%).

**Keywords: **alpha-helix; crystal; thermodynamics; human hair; keratin; DSC; moisture

J. Cao, A.N. Buckley and L.J. Lynch; "Measurement of an Intrinsic Softening Temperature for Coal-tar Pitches by Proton
Magnetic Resonance Thermal Analysis"

*Carbon*, Vol. **32**, 493-497 (1994)
**Abstract:**
The measurement of the softening temperature of the amorphous continuous phase in a composite by means of proton
magnetic resonance thermal analysis (PMRTA) is described. A coal-tar pitch with various quinoline insoluble (QI)
particles levels was used to demonstrate that PMRTA can be used to obtain an intrinsic softening point of the amorphous
continuous phase. Standard methods for measuring a softening point for pitch determine a value influenced by the
presence of the QI particles.

**Keywords: **softening temperature, glass transition temperature, melting temperature, coal-tar pitch, molecular
mobility, nuclear magnetic resonance.

J. Cao, T. Kikutani, A. Takaku and J. Shimizu; "Non-isothermal Orientation Induced Crystallization in Melt Spinning of
Polypropylene",

*Journal of Applied Polymer Science*, Vol. **37**, 2683-2697 (1989)
**Abstract:**
Two kinds of polypropylene with different molecular weight (MI = 15 and 30) were melt-spun at the spinning temperatures
of 210-290°C and take-up velocities of 0.15-3 km/min. In the cases of the spinning temperatures of 270 and 290°C for MI15
and 250 and 290°C for MI30, the density showed a minimum with increasing take-up velocity at around 0.5-1 km/min. This
result suggests that crystallization behavior is influenced by two competitive effects, i.e., cooling rate and
crystallization rate both of which are enhanced by the increase in take-up velocity. Crystal structures of slightly
oriented monoclinic, slightly oriented pseudohexagonal, highly oriented pseudohexagonal, and highly oriented monoclinic
were successively observed with increasing take-up velocity. The change of crystallization temperature may result in the
different kinds of crystal modifications. Numerical calculations on nonisothemal orientation-induced crystallization in the
melt spinning process and experimental results showed qualitative agreement in the change of crystallinity with take-up velocity,
spinning temperature, and molecular weight.

J. Cao; "Re-examination of a Proposed Method to Obtain Avrami Parameters from Non-isothermal Crystallization Data",

*Polymer (Communications)*, Vol. **33**, 3520-3521 (1992)
**Abstract:**
This communication is a theoretical re-examination of the method to obtain Avrami parameters directly from non-isothermal
crystallization data proposed by Dutta.

**Keywords: **crystallization; non-isothermal; Avrami parameters; PET

J. Cao; "A Weight-Averaged NMR Spin-Spin Relaxation Time Constant and Its Determination",

*Journal of Magnetic Resonance*, Vol. **B103**, 296-298 (1994)
**Abstract:**
Proton magnetic resonance thermal analysis (PMRTA) has been proven to be a convenient yet powerful tool for detecting molecular
mobility as a function of temperature for a hydrogen-containing organic and polymeric material. This technique essentially
records the proton magnetic resonance (1H NMR) spin-spin relaxation signal of a sample at various temperatures. The signal
decays rapidly for rigidly bound molecules, but more slowly as molecular mobility is acquired, usually with an associated shift
in signal shaper from the exponential type to the Gaussian type.

...

It will be shown in the following that the normalized signal area itself, i.e., the area encompassed by a relaxation signal
and the intensity axis and zero line of the signal divided by the initial intensity of the signal, could be a quantitative measure
of molecular mobility.

T. Hashimoto, J. Cao, and A. Takaku; "Thermal Diffusivity Measurements for Thin Films by the Photoacoustic Effect",

*Thermochimica Acta*, Vol. **120**, 191-201 (1987)
**Abstract:**
When the thermal diffusivity of materials is measured by using the photoacoustic effect method, a sound wave interference
effect will inevitably occur. This interference effect causes an extra phase lag between the modulated light and the. sound
signal detected with a microphone. A theoretical expression has been developed to relate the phase lag caused by the sound
interference effect to the modulation frequency of the incident light. Simulation results of the theoretical expression show
good agreement with the experimental results. In some cases, it is convenient to use a reference film to revise the measured results.
Furthermore, some theoretical relations between the phase lag and the chopping frequency as well as the thermal diffusivity
of a sample have been recast according to the Rosencwaig-Gersho theory

J. Cao, "Interferential formulization and interpretation of the photoacoustic effect in multi-layered cells,"

*J. Phys. D: Appl. Phys.*, Vol. **33**, 200-206 (2000)
**Abstract:**
Mathematical formulization of the thermal response in a two-layer photoacoustic cell, where the interference of thermal waves
in a sample is compounded by the inter-layer interference effect, has been carried out by employing the thermal-wave interference
theory. The physical meanings of the obtained formulae are then discussed in terms of the thermal-wave interference to explain
the origin of the thermal phase lag for various cases. In addition, it is found that the inter-layer thermal-wave interference
results in an extra phase lag.

J. Cao, "OBTAINING THE CRITICAL DRAW RATIO OF DRAW RESONANCE IN MELT SPINNING FOR POWER LAW POLYMER FLUIDS,"

*Chinese Journal of Polymer Science*, Vol. **25**, 501-507 (2007)
**Abstract:**
A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial
differential equations of melt spinning, and to determine the critical draw ratio for draw resonance. The results show
that for shear thin fluids, the logarithm of the critical draw ratio has a well defined linear relationship with the power
index for isothermal and uniform tension melt spinning. When the power index approaches zero, the critical draw ratio points at
unity, indicating no melt spinning can be processed stably for such fluids. For shear thick fluids, the critical draw ratio
increases in a more rapid way with increasing the power index.

**Keywords: **Draw resonance; Mel Draw resonance; Melt spinning; Power law fluid; Numerical simulation

J. Cao, "OBTAINING PRECISE CRITICAL DRAW RATIO OF DRAW RESONANCE IN MELT SPINING BY NUMERICAL SIMULATION OF DIFFERENCE EQUATIONS,"

*Chinese Journal of Polymer Science*, Vol. **23**, 311-318 (2007)
**Abstract:**
Direct difference methods have been used to solve the simultaneous non-linear partial differential equations for melt spinning
without recourse to linearisation or perturbation approximation. The stability of each difference schemes was studied by error
analysis using the Taylor series, and by comparison of the results obtained from numerical simulation with the logical value
in melt spinning. It is found that computation with 19 digit long double precision has significantly simplified the stability
problem of difference equations. Using this method, the precise critical draw ratio of draw resonance in an isothermal and uniform
tension spinning of Newtonian fluids can be obtained in between 20.218 and 21.219, a figure consistent with 20.218 which was
obtained by a linear perturbation approximation method by Kase and Denn. It thus has paved the way to computation of full information
for unsteady melt spinning processes using the difference method.

**Keywords: **Draw resonance; Mel Draw resonance; Melt spinning; Newtonian fluid; Numerical simulation

J. Cao, "Studies on the Mechanism of the Instability of Polymers in Tensile Testing,"

*Journal of Applied Polymer Science*, Vol. **45**, 2169-2179 (1992)
**Synopsis:**
This study deals with the mechanism of the instability of tensile force occurring in tensile testing for polymer materials.
It was found that through a proper transformation of inertia coordinates, a tensile test can be described in the same governing
differential equations with the same boundary conditions as those employed in melt spinning. This fact suggests that the nature
of the instability is simply due to draw resonance rather than any other cause. The effects of extension rate in tensile testing
and the specimen dependence on the instability of tensile force were experimentally investigated by using specimens with various
molecular orientations. The results are interpreted by applying the principles of draw resonance in melt spinning.

J. Cao, "Numerical Simulations of Draw Resonance in Melt Spinning of Polymer Fluids,"

*Journal of Applied Polymer Science*, Vol. **49**, 1759-1768 (1993)
**Synopsis:**
This artical deals with numerical simulations of draw resonance of polymer fluids by employing direct difference methods to solving
the governing equations in melt spinning. The stability of each difference method was studied by a comparison of the results
obtained from simulations with the theoretical solutions or values. The numerical simulation confirms that the critical draw
ratio of draw resonance in an isothermal and uniform tension spinning of a Newtonian fluid is between 20 and 21.
The cross-sectional area of a spinline in draw resonance was found to decrease monotonically from a spinneret toward a
take-up bobbin, although the taken-up filament shows periodical variation. This study has also illustrated the mechanism of
draw resonance previously proposed by the author.

To visit DSC Curve Solutions (DCS ®), click links shown in naviation bar.