Polymer Solidification under Pressure and High Cooling Rate

V. La Carrubba                                                   1. Introduction                                                                       Page 7 
fields, high thermal gradients and high pressures, the development of a model 
able to describe polymer behaviour turns out to be really complex, due to the 
large variety of parameters that must be accounted for. If the studied material 
is a semicrystalline polymer, this analysis is also complicated by the 
occurrence of the crystallisation phenomenon, that needs to be properly 
described and quantified. One of the process variables really difficult to 
predict is the volumetric shrinkage related to the solidification; this shrinkage 
turns out to be more relevant if the polymer crystallizes, and also depends on 
the amount of molten polymer involved during the solidification process. In 
any case there is an enormous interest towards polymer crystallization, 
especially in order to predict the PVT behaviour during material 
solidification for processing operations involving a moulding step, such as 
injection moulding. 
Since normal techniques industrially employed to obtain polymeric 
products are very often carried out under high pressure conditions and rapid 
cooling rates, it is easy to understand that the analysis of the relationships 
between process conditions and morphology of the sample obtained is a 
crucial point in plastic materials characterisation. As a matter of fact, the 
main purpose of research in this field is to obtain polymeric products 
matching the required properties. Due to the experimental difficulties, any 
investigation of polymeric structure dependence upon pressure and cooling 
rate has been mainly performed using conventional techniques, such as 
dilatometry and differential scanning calorimetry under isothermal conditions 
or non isothermal conditions but at cooling rates several orders of magnitude 
lower than those experienced in industrial processes. 
Relevance of crystallization kinetics has been widely recognized. 
Unfortunately the lack of information on the influence of processing 
conditions on crystallization kinetics restricts the possibilities of modelling 
and simulating the industrial material transformation processes, since the 
development of a model able to describe polymer behaviour under drastic 
solidification conditions turns out to be really complex. 
In order to understand the complexity of the physical and chemical 
transformation that the polymer undergoes during processing operations, it 
could be interesting to analyse as an example injection moulding, the most 
widely employed transformation operation. During injection moulding 
polymer solidification occurs through drastic pressure and cooling rate 
conditions. As a matter of fact the material, after injection under pressures of 
several decades of MPas, is rapidly cooled down by the cold mould wall. 
Additionally, crystallization occurs under the influence of a flow field.  
For sake of completeness, it should be confessed that the complexity of 
the investigation concerning polymer solidification under processing 
V. La Carrubba                Polymer Solidification under pressure and high cooling rates                            Page 8 
conditions is even deeper if the wide latitude of morphologies achievable is 
considered.  Generally speaking, polymer crystallization under processing 
conditions cannot be considered an “equilibrium” phenomenon, since it is not 
possible to separate thermodynamics from kinetics of processes. Furthermore 
polymeric materials crystallization is always limited by molecular mobility, 
and very often leads to metastable phases, as recently shown by Strobl [1]. 
From this general background it should not result surprising the lack of 
literature data in this particular field of investigation, due to the complexity 
of the subject involved.  
The major task to tackle is probably the attempt to individuate the 
rationale behind the multiform behaviour observed in polymer solidification, 
with the aim of finding out the basic functional relationships governing the 
whole phenomenon. Therefore a possible approach, along this general 
framework, consists in designing and setting-up model experiments with the 
aim to isolate and study the influence of some experimental variables on the 
final properties and on the final morphology. Thus a systematic investigation 
on polymer solidification under processing conditions should start on the 
separate study of the influence of flow, pressure and temperature on 
crystallization kinetics. The first successful attempt was devoted to determine 
how the final properties of a product depends upon cooling rate, that 
represents the most relevant parameter governing the polymer solidification. 
In the last few years a special equipment has been developed and widely 
tested in order to quench polymeric samples in a wide range of experimental 
conditions up to very high cooling rates (up to 2000 °C/s) under quiescent 
conditions: it has been possible to collect many information about the 
influence of cooling rate on the final properties of some widely used 
polymer, such as iPP, PET, PA6 [2, 3, 5, 49-53, 55]. 
One of the other relevant variables affecting the final characteristics of 
the obtained product is the pressure at which the solidification process is 
performed. Up to now only few works have been focused on the influence of 
pressure on the mechanical and physical properties, due to experimental 
difficulties. Additionally, the majority of studies at high pressure have 
concentrated on one polymer, polyethylene, dealing with the formation of 
extended chain crystals, as shown by Wunderlich and coworkers [56-63]. 
The pressure associated with such investigations tends to be extremely high 
(typically 500 MPa) with respect to the pressures normally used in industrial 
processes; furthermore, the experimental conditions normally investigated 
were quasi-isothermal. This implies that the obtained results may not be 
applied to of polymer processing, involving very high thermal gradients. 
As for the kinetics associated with polymer solidification, relevance of 
crystallization kinetics has been widely recognised as the large research work 
V. La Carrubba                                                   1. Introduction                                                                       Page 9 
devoted to this topic witnesses [66]. In any case, the application of a model 
describing crystallization kinetics requires a large availability of 
experimental results in order to check the reliability of the theoretical 
modelling and of the predicted results. 
 
1.3 Morphology and properties of polymers crystallized from the melt. 
When studying the behaviour of polymer materials, it is necessary to 
underline the large variety of morphology that can develop after 
solidification from the melt during industrial transformation processes. This 
aspect is highly relevant, since morphology developed during crystallization 
determines also mechanical and physical properties of the manufact. As a 
matter of fact, mechanical behaviour of polymers depends on crystallinity in 
the sense that crystalline zones impart ductility to the material; as a 
consequence of that, a high crystallinity implies a high resistance to the 
impact, and a stress-strain curve showing the yielding phenomenon. By 
studying the distribution of properties on a local scale it would be possible to 
predict the final material properties. 
Morphology of polymers is characterized by the presence of 
spherulites. These are complex entities constituted of tri-dimensional 
aggregates of crystal units radially developing. They are typical of 
crystallization from the melt. Furthermore polymer morphology depends 
upon the cooling rate and the field of pressure applied; other factors could 
also affect the resulting morphology, such as impurities and nucleating 
agents.  
When cooling rate decreases the crystalline entities formed result more 
ordered. As a matter of fact crystallinity tends to higher values. More 
complex is to analyse the effect of pressure, since the physical and chemical 
properties of the examined polymer, and their dependence upon pressure 
must be accounted for. 
Last but not least, the very high complexity of an accurate 
morphological study of polymer should be pointed out, due to the complexity 
of the operating conditions imposed by the typical transformation processes. 
Let us consider as an example once more the case of injection moulding. 
During injection the molten polymer, flowing though the cavity, is cooled 
down by the mould wall; the final result is a cooling rate distribution along 
the manufact, which in turns determines a non-uniformity of crystallinity and 
final properties. The molten material is subjected to a heat transfer with the 
cold mould by conduction along the thickness; this creates a solidified layer 
facing the mould wall. Since the velocity profile on the solid layer shows a 
discontinuity, a “shear flow” develops along the cavity.  
V. La Carrubba                Polymer Solidification under pressure and high cooling rates                            Page 10 
To sum up, it should be clear that in this process solidification occurs 
under non-isothermal conditions and under the influence of a very complex 
flow field. Pressure gradients make it also more complicated an accurate 
comprehension of the transformations that the polymer is subjected to. 
 
1.4 Objectives of the present work 
The major aim of the present investigation was to highlight as 
accurately as possible the dependence of the final property distribution (in 
terms of mechanical properties, volumetric properties and final morphology) 
upon the experimental conditions adopted throughout the solidification. 
Specifically, the simultaneous effect of high pressures and high cooling rates 
has been deeply studied. A model experiment able to achieve these goals 
under controlled conditions was designed, set-up and optimised in our 
laboratory. The methodological approach of recording the thermal histories 
of samples cooled under pressure and then analysing the resulting 
morphology and properties was adopted. All the available data concerning 
polymer crystallization under very high cooling rates at ambient pressure 
were extensively used as a starting point to evaluate the effect of pressure 
when superimposed to the one of cooling rate. 
Secondly, the present research allowed one to gain information on 
crystallization kinetics under pressure. Indeed, if the cooling rates applied are 
sufficiently high to lead to samples showing a low crystallinity and a reliable 
crystallization kinetics model is available, non-isothermal crystallization 
behaviour can be determined as function of the applied pressure.  
Thirdly, by means of the results provided by this study it will be 
possible to add new knowledge about PVT time dependent polymer 
behaviour by including data obtained under high cooling rate, which are 
closer to industrial processing conditions.  
In order to generalise the results achievable with the help of this 
proposed experimental approach, three different polymers that covers a large 
variety of application fields has been adopted: isotactic PolyPropylene (iPP), 
PolyEthyleneTerephtalate (PET) and PolyAmmide6 (PA6). The study of 
three very different polymers, as far as their chemical and physical features 
are concerned, could be helpful for successive modelling of polymer 
behaviour during crystallization under processing conditions. 
Additionally, a large number of complementary analysis technique 
were used, with the aim of achieving many experimental results and establish 
a qualitative and quantitative comparison of the data obtained. Although the 
non-mutual linearity of the data obtained with different techniques makes 
sometimes the interpretation of the results very hard, the set of information 
V. La Carrubba                                                   1. Introduction                                                                       Page 11 
collected is a good starting point for an accurate description of the 
phenomena involved during the process.  
Finally, crystallisation kinetics under pressure was studied for iPP and 
PA6 adopting an extension of the classical Kolmogoroff-Avrami-Evans 
(KAE) approach. In the case of iPP and PET a master curve approach was 
also proposed. The general aim was to find out some simple equations able to 
provide a quantitative description of the effect of cooling rate and pressure on 
final polymer properties, first of all density. The basic assumption was to 
consider superimposed the effect of pressure to the one of cooling rate. Then 
a “transformation function” which converts a pressure effect into a cooling 
rate effect was assessed. A so-called “equivalent cooling rate” was defined, 
which correctly accounts for the real cooling rate and the solidification 
pressure. 
 
1.5 Outline of the present work 
In order to achieve the goal of studying the crystallization of polymer 
when quenched under pressure, a new equipment has been developed and 
improved. In that way it has been possible to study the simultaneous effect of 
pressure and high cooling rate on polymer structure and properties. The 
experimental apparatus was essentially constituted of an injection moulding 
machine, used as a source of molten polymer supplied at a pre determinable 
and maintainable pressure; the injection moulding machine was coupled with 
a special “injection mould”, specifically designed for our purposes.  
The experimental methodology of following the thermal history of 
rapidly cooled samples and then analysing the resulting sample morphology 
has been adopted throughout the present work. Thus polymer samples could 
be cooled at a known cooling rate and under a known pressure. 
Density, Micro Hardness (MH), Wide Angle X-ray Scattering 
(WAXS), Small angle X-ray Scattering (SAXS), Polarized Optical 
Microscopy (POM), Infra Red (IR) measurements, PVT dilatometry and 
annealing measurements were then used to determine the obtained sample 
morphology.  
A heat transfer model of the cooling inside polymer has been 
developed, considering a simplified uni-axial symmetry and neglecting the 
latent heat of crystallization and transport and physical properties changes 
with temperature. This model provided qualitative and quantitative 
information on the temperature profile inside the sample; by means of this 
model it was possible to calculate the cooling rate distribution across the 
sample depth. Additionally a simplified balance equation was assessed in 
order to estimate the heat transfer coefficient at water-polymer surface. 
V. La Carrubba                Polymer Solidification under pressure and high cooling rates                            Page 12 
A deconvolution technique of WAXS patterns was also used to 
evaluate the final phase content of samples and to assess a crystallization 
kinetics behaviour.  
The classical KAE kinetic approach was applied in describing 
crystallisation kinetics of iPP and PA6. For iPP and PET a master curve 
approach was successfully applied to the obtained density and Micro 
Hardness results. 
 
V. La Carrubba                                                   1. Introduction                                                                       Page 13 
1.6 The material studied throughout this work: general features and 
fields of application 
1.6.1 Isotactic PolyPropylene (iPP) 
Isotactic polypropylene (iPP) is a polymer of particular interest due its 
quite high commercial value both as a virgin polymer and as a recyclable 
polymer. It is a polymer not smelling, colourless, and very easy to colour. 
Between its features it should be underlined the resistance to the impact, the 
low density, the electrical and insulation properties, the resistance to folding 
and to chemical attack. 
Modern production techniques and new catalysts have lead to 
production of a greater variation of molecular weight and particle structure, 
making it possible to tailor the structure of iPP to specific requirements, i.e. 
to produce the so called “engineering grades”, which in turns has lead to a 
vast increase in iPP being used in engineering applications, particularly in the 
car industry. 
It tends easily to crystallise and it forms several different crystalline 
structures. In the case of very high cooling rates it may give rise to the 
formation of a metastable phase, indicated in literature like a “mesomorphic 
phase”. This is a disordered phase, characterized in WAXS patterns by the 
presence of two broaden peaks that demonstrates the presence of very small 
domains.  
 
1.6.2 PolyEthyleneTeraphtalate (PET) 
PolyEthyleneTeraphtalate (PET) is the Polyester industrially employed 
the most. It is a cyclolinear polymer and it can be prepared by direct 
esterification of terephtalic acid and ethylene glycol or by transesterification 
of dymethyl terephtalate with ethylene glycol. It is a semicrystalline polymer; 
its molecular structure is described by the fringed-micelle model, where the 
polymer exists as an imperfect two-phase system of interconnected 
crystalline and amorphous domains. The way these domains are distributed in 
the solid polymer depends on the stresses and temperature used during 
processing. It is a strong, flexible thermoplastic that readily crystallizes, can 
be oriented and also heat stabilized. For this reason, it has various uses as an 
amorphous, partially crystalline, or highly crystalline material. Its most 
important features are: 
a) Crystallizability 
b) Orientability 
c) High melting point 
d) Excellent strength, creep resistance, impact resistance, clarity 
barrier properties (especially when oriented). 
V. La Carrubba                Polymer Solidification under pressure and high cooling rates                            Page 14 
For its versatility and excellent physical properties, PET can be 
processed in many different ways, giving rise to several categories of 
manufacts that are widely used in a variety of application. The application for 
which PET is nowadays well known is the production of containers for 
beverages, where it has replaced glass and other polymeric materials. 
Many researches regarding PET have tried to understand the influence 
of the operating condition on its final crystallinity. As a matter of fact, 
although PET has been used widely used in industry, crystallization kinetics 
of this material has not been explored sufficiently. For this reason PET 
behaviour under pressure and high cooling rates has been explored 
throughout this work. 
 
1.6.3 PolyAmmide6 (PA6) 
PolyAmmide6 (PA6) is a versatile polymer, characterized by a 
temperature of use quite higher than that of polymers commonly employed. It 
has also a very high resistance to impact and abrasion, an excellent 
workability and stiffness, for which it is used in techno-mechanical 
applications [6].  
An other important feature is resistance to fatigue, due to the high 
stiffness combined with a high elasticity. Finally, its good resistance to gas 
permeability could make PA6 as a material to use in food industry. 
The reasons for which PA6-based products did not widely penetrate in 
industrial applications must be found in its high cost and technological 
processing difficulties. A particular problem is the high absorption of 
humidity, that makes this material subjected to degradation, combined with a 
dimensional instability of the final product [7]. It crystallizes in two 
crystalline modifications, the monoclinic α structure, and the pseudo-
hexagonal γ phase, characterized by a higher grade of disorder [8]. It could 
be easily understood that PA6 is a polymer of a great engineering interest, 
and its characterization under processing conditions turns out to be a 
necessary step in order to predict new possible application fields. 
 
V. La Carrubba                                                         2. State of the Art                                                          Page 15 
2. State of the Art 
Many researches have been carried out in the recent years concerning 
polymer solidification under pressure and several fields of research have 
been explored. A great amount of data about solidification behaviour of many 
polymers is available in literature. Most of the experiments were performed 
under isothermal conditions, or non-isothermal but under cooling rates up to 
few °C per second, which are several orders of magnitude lower than the 
cooling rates normally experienced by polymeric materials during 
transformation processes. 
 
2.1 Density and PVT data 
The largest number of results reported in literature is represented by density 
(or equivalently specific volume) measurements. Two methods are typically 
used to measure polymer specific volume: dilatometry and density gradient 
column. In the case of dilatometric measurements polymer specific volume is 
measured directly when the material is still under pressure, even in the solid 
phase. The first limit of this equipment is its relatively huge mass (necessary 
to apply very high pressure to the polymer) that limits the maximum 
achievable cooling rates to few degrees °C per minute. Secondly, a problem 
of great relevance of dilatometric experiments is the difficulty to produce and 
maintain and hydrostatic pressure field in the solid state. If this major 
requirement is not fulfilled, all the measurements performed may not to be 
reliable, due to the possible pressure gradients in the polymer sample. 
Thirdly, dilatometric measurements, since are evaluating the polymer 
specific volume while the material is maintained under pressure, does not 
allow one to predict the polymer behaviour once the pressure has been 
released. Although this observation could sound captious, it is worthwhile 
reminding that polymeric materials, after the forming processes, are normally 
used at ambient pressure. As a consequence of that, a detailed knowledge of 
how the pressure conditions adopted during the forming stage influences the 
final properties at the pressure of usage is definitely missing when invoking a 
set of dilatometric experimental results.  
On the opposite, density gradient column measure sample density, 
crystallized under pressure, at atmospheric pressure. In this case the limit is 
the impossibility of measuring directly density in situ, i.e. during 
solidification, like in a dilatometer. In other words, the material is first 
solidified under some processing conditions (thermal history, pressure), and 
then the effect of these variables is evaluated by means of density 
measurements. In this way it is possible to measure density of samples 
solidified under more drastic conditions, at cooling rates up to 2000 °C/s. 
V. La Carrubba                Polymer Solidification under pressure and high cooling rates                            Page 16 
The main purpose of researches on polymer behaviour under pressure was 
generally to perform experiments leading to reliable PVT time dependent 
data for polymers. Although many works have demonstrated that it is 
possible to cover a very wide pressure range (from 0.1 MPa to several 
hundreds of MPa), only few experiments have been performed under cooling 
rates higher than 2-3 °C/s, due to typical constraints imposed by the 
apparatus employed. Data presented in Termodinamik [9] represent a very 
interesting source of information on PVT behaviour of polymeric materials 
(amorphous and semicrystalline) under medium cooling rates, although the 
experimental apparatus used deserves some reasonable doubts about the 
possibility of applying a hydrostatic pressure on the solid, belonging to the 
“piston-die” category.  
As a matter of fact, when volume changes need to be measured, two methods 
are widely practised: “the piston-die technique” and the “confining fluid 
technique”. In the piston-die technique, the material is confined in a cylinder, 
which it must fill completely. Then a pressure is applied to the sample by a 
piston, and the displacement of the piston is used to calculate the volume 
change of a sample, and consequently, the sample specific volume. The 
fundamental problem of this apparatus is that the state of stress for a solid 
sample in this type of apparatus is not hydrostatic, i.e. the true pressure 
experienced by the sample is unknown. A mathematical analysis of the state 
of stress experienced by a solid polymeric sample loaded axially in a cylinder 
[23], leads to the conclusion that this type of dilatometer can only measure 
volume under “pressure” when the shear modulus of the sample is very much 
smaller then its bulk modulus. This is certainly the case for liquids, including 
polymer melts. When the degree of crystallinity increases, however, the 
material starts to behave like a rubber/solid and measurements could become 
unreliable. To sum up, the use of such a dilatometer for getting information 
on specific volume in the solid state could lead to nonsensical results. Results 
of dilatometric measurements using a “piston die type” dilatometer are 
reported by Chang [69]. To overcome these hardships, Zoller et al. [24, 25] 
developed a “confining fluid” dilatometer. In this kind of technique a 
material is surrounded at all times by a confining fluid, often mercury, and 
the combined volume changes of sample and confining fluid are measured by 
a suitable method as a function of temperature and pressure. The volume of 
the sample is determined by subtracting the volume change of the confining 
fluid. The advantage of this technique is that the sample is under hydrostatic 
pressure at all times, and that there are neither friction nor leakage problems. 
The only possible problems encountered when applying this technique rely 
on the possible interactions of the confining fluid with the polymeric sample. 
V. La Carrubba                                                         2. State of the Art                                                          Page 17 
As for the experimental works devoted to study the PVT behaviour of 
polymers, many studies should be mentioned. Hyun and Spalding [10] have 
studied the dependence of bulk density on temperature and pressure for some 
polymeric resins. Materials employed where in form of pellet and powder. 
The explored temperature range was from ambient temperature up to T
g
 for 
amorphous polymers, or near the melting point T
m
 for semicrystalline 
polymers. The presented results show that amorphous polymers compact very 
little with pressure for temperatures between ambient and about 20°C below 
the glass transition temperature T
g
. On the opposite semicrystalline polymers 
compact readily at all temperatures between ambient and the melting 
temperature. Similar studies have been carried out by Smith and Parnaby 
[11] on Low Density PolyEthylene (LDPE) and High Density PolyEthylene 
(HDPE).  
A numerical representation of the specific volume together with its 
dependence upon the variables of interest has been attempted throughout the 
years. The traditional Tait equation, used also by Zoller [70], is based on the 
assumption that specific volume can be considered only as a function of 
pressure and temperature. Some corrections to the original Tait equation in 
order to take into account the effects of low cooling rate (up to 10°C/min) 
were proposed by Chang for amorphous polymers [69]; on the other hand 
Zoller [71] showed that the Tait equation yields a good representation only of 
semicrystalline polymer melts (such as iPP and PB-1), while the description 
of the compressibility behaviour of solid semi-crystalline polymers is quite 
unsatisfactory. Dee and al. [15] obtained PVT data for an extensive series of 
PolyTetraFluoroEthylenes (PTFEs) and PTFE oligomers, determining also 
crystallinities by ambient densities of the solids and also by DSC heat of 
fusion. 
Bhatt and Mc Carthy [16] studied the PVT behaviour of LDPE, PolyStyrene 
(PS) and poly Acrylonitrile Butadiene Styrene (ABS) filled and unfilled, in 
order to calculate thermal diffusivity values in the melt phase. For their 
experiments a standard capillary rheometer was used. Rodriguez and Filisko 
[17] applied a rapid hydrostatic pressure field on HDPE and LDPE samples 
under adiabatic conditions. The temperature changes were reported as a 
function of pressure and temperature by using a curve fitting analysis based 
on an empirical equation. Then data were analysed by determining the so 
called “thermoelastic coefficient” derived from the Thomson equation. Other 
studies on PolyEthylene-co-VinylAcetate were performed by Busch et al. 
[18], that used a “vibrating titanium tube” in order to measure sample 
density. As a matter of fact, sample density is proportional to the square of 
the period of vibration. The density dependence on pressure and temperature 
found by the authors on Poly(ethylene-con-vinylacetate) is in agreement with 
V. La Carrubba                Polymer Solidification under pressure and high cooling rates                            Page 18 
literature results. A Tait equation was used by the authors for describing the 
PVT behaviour of Poly(ethylene-con-vinylacetate). Chiu and Liu [19] 
developed a method for measuring PVT relationships of thermoplastic 
materials using an injection moulding machine. PolyStyrene (PS), 
Acrylonitrile-Butadiene-Styrene resin (ABS) and LDPE were investigated by 
using an empirical correlation based on Tait equation. Their results displays 
that, in the low pressure region the specific volume determined from this 
method and from a dilatometric apparatus are close to each other, whereas at 
higher pressures the results obtained by the two methods do not match. 
Barlow [20] obtained PVT data for cis-1,4 Poly-Butadiene used to calculate 
the related physical properties, such as the thermal expansion coefficient, and 
the compressibility coefficient. In the same sphere of research fall all 
investigations made by Leute et al. [21], that studied the dependence of 
thermal properties for PE, iPP and Poly-Ethylene-Oxide (PEO) on pressure. 
It is worth noticing that they worked at very low cooling rates (few °C per 
hour). Kogowski and Filisko [22] measured densities versus time profiles at 
various annealing temperatures for polystyrene (PS) glasses vitrified at 
various pressures and cooling rates. They solidified PS samples under 
pressures from 69 to 276 MPa, applying two different cooling rates, 0.2 
°C/min and 300 °C/min respectively. Then pressure was released and 
samples were subjected to annealing (for temperatures of 65, 80 and 95 °C) 
and the density versus log of time pattern was recorded, by using a gradient 
column whose set temperature was 23°C. Samples solidified under pressure 
show an initial decrease of density with time, the rate of which increases with 
solidification pressure and cooling rate. Then all samples tend to the same 
final density value, independently on the solidification pressure. Furthermore, 
in the case of annealing at 80°C, there is a minimum in density, or 
“undershoot”, the magnitude of which increases with solidification pressure 
and cooling rate. The same results of annealing at 80°C show a density 
decrease on increasing pressure, justified according to the authors by the 
kinetics of transformation that becomes more rapid when pressure increases. 
Density measurements on iPP performed in this work show many analogies 
with these results last mentioned. This work [22] however shows that the 
variation of density takes place as a consequence of complex mechanisms 
involving the internal structure of material determined by the application and 
release of pressure.  
Zoller and Fakhreddine [24] and elsewhere Zoller [25] employed a 
"confining fluid dilatometer" by GNOMIX Inc. in order to measure the 
specific volume of some semicrystalline polymers, such as isotactic 
PolyPropilene (iPP), Polyammide66 (PA66), PolyEthyleneTherephtalate 
(PET). The volume of the sample was determined by subtracting from the 
V. La Carrubba                                                         2. State of the Art                                                          Page 19 
total volume change the volume change of the confining fluid. In their 
measurements the samples were cooled under a constant slow cooling rate 
(1.5 °C/s) under a constant pressure. At the end of the test pressure was 
reported to 10 MPa and the value of density read. They found a decrease of 
final solid density with increasing pressure for iPP, while they noticed an 
increase of density with pressure for PA66 and PET. Furthermore they notice 
the anomalous behaviour of iPP also in the isobars reporting the specific 
volume as a function of temperature, as shown in fig. 5.1.8. The figure 
reports the melting curves and the solidification curves for different 
pressures. It should be noticed that the final specific volume in the solid state, 
recorded at the end of solidification curve, is systematically higher than the 
one measured in the melting curve. This last indicates that the process of 
solidification under pressure, determined a structural transformation that 
could justify the final lower density. The authors try to explain the density 
decrease of iPP with the appearing of the γ phase, which is less dense than 
the α phase. Being the γ phase less dense than the α phase, this explanation 
turns out to be qualitatively consistent with the observed decrease of density 
with pressure. From a quantitative point of view, however, assuming that at 
200 MPa an upper limit of nearly 20% of the α phase is substituted by the γ 
phase, the calculated decrease of density related to this effect turns out to be 
lower than the one experimentally measured (ca. 0.1 %). This indicates that 
some other effects should be accounted for in order to justify the iPP density 
decrease with solidification pressure. However in the experiments shown in 
this thesis there is no evidence of γ phase, being the maximum adopted 
pressure 40 MPa.  
Additionally He and Zoller [25] carried out measurements of crystallization 
kinetics at high pressure. They found an increase of crystallization rate under 
isothermal conditions at the same undercooling. Generally speaking, 
experiments performed under isothermal conditions are made at very low 
undercoolings if solidification must take place during the isotherm and not 
during the cooling ramp to obtain isothermal conditions. Therefore the 
kinetic constant calculated using these data refers to a temperature interval 
(around 130°C) that is far away from the temperature region where the 
maximum crystallization rate falls, around 70°C for iPP, where diffusion 
control of crystallization becomes significant. For these reasons He and 
Zoller’s kinetic results, based on isothermal experiments, may not be directly 
compared to the data here presented obtained under high cooling rates and 
high undercoolings. Other interesting PVT measurements have been carried 
out by Zoller on LDPE [26] and by Schneider [27] on amorphous and atactic 
polymers under similar conditions. 
V. La Carrubba                Polymer Solidification under pressure and high cooling rates                            Page 20 
Fleischmann and Koppelmann [28] modified the PVT diagram of iPP by 
accounting for crystallization induced by the flow field, which the material is 
subjected to in an injection moulding process. They also take into account the 
influence of cooling rate. This investigation shows that a modification of 
PVT diagrams is necessary to obtain a better description of the melt 
behaviour under injection moulding conditions. At the end of the cooling 
phase, the calculated pressure differs from the measured pressure, due to the 
volume change of the mould caused by the high internal pressure. 
On the other hand, many studies have concentrated on modelling the PVT 
behaviour of polymeric materials, in order to predict some relevant physical 
properties, such as compressibility and thermal expansion coefficient. Parekh 
and Danner [12] tried to predict the PVT behaviour of polymers by using a 
technique called “Group Contribution Lattice – Equation Of State”, (GCL 
EOS). This model requires only the structure of the molecule as input 
information. The results show that this method can be successfully applied in 
the prediction of PVT behaviour for a large variety of homopolymers, 
random copolymers and polymers blends.  
Sanchez et al. [101] showed that the compression response of many polymer 
liquids satisfies a temperature-pressure superposition principle. This is in 
agreement with the “pressure-cooling rate superposition” that is here 
proposed for iPP and PA6 in the solid state. The authors developed a new 
isothermal equation of state and extended its range of applicability to a wide 
range of temperatures. This result was achieved by means of the empirical 
observation that in polymers both the density and the bulk modulus are 
almost linear functions of temperature. For every polymer a characteristic 
temperature, pressure and density were defined, having some simple physical 
interpretation.  
Ito et al. [73] modified the equation proposed by Spencer and Gilmore for 
PolyStyrene [72], assessing an equation of state for describing specific 
volume of iPP; their approach suggested the individuation of two main zones 
(melt and solid zone) with an intermediate crystallisation zone whose shape 
is a function of the crystallisation kinetics. Hieber [13] used a modified two-
domain Tait equation so as to interpolate a series of experimental curves of 
melting and crystallization of isotactic PolyPropylene (iPP). He also 
employed the Nakamura equation in order to predict the density versus 
temperature isobars for semicrystalline polymers, obtaining a good matching 
with experiments only in a few cases. The author has also noticed that iPP, at 
a cooling rate of 120 °C/min, has a specific volume in the solid state 
systematically larger than the one predicted by the model based on the two-
domain Tait equation. He tried to interpret this observation in terms of a 
smaller absolute crystallinity due to a kinetics-limiting situation. Although 
V. La Carrubba                                                         2. State of the Art                                                          Page 21 
this suggestion is in agreement with the experimental results presented along 
this work, it should be pointed out that Hieber’s work was only a modelling 
of literature PVT data. 
Similarly Olabisi and Sihma [14] extended the same investigation to Poly-
Methyl-MethAcrylate (PMMA), Poly-nButil-MethAcrylate (PnBMA), Poly-
Cyclo-Hexyl-MethAcrylate (PCHMA), High Density Poly-Ethylene (HDPE) 
and Low Density Poly-Ethylene (LDPE). Analytical representations of the 
equation of state were obtained and the resulting thermal expansivities and 
compressibilities compared with each other and with the result of previous 
investigations for similar polymeric systems. 
 
2.2 Mechanical Properties and Micro Hardness 
Some other studies have concentrated on investigating the dependence of the 
mechanical properties of materials on solidification pressure during 
transformation processes. Shlykova et al. [29] have studied the effect of 
injection moulding at high pressures (up to 500 MPa) on some relevant 
properties for HDPE. Density, ultimate tensile stress and shrinkage were 
measured as a function of the injection moulding pressure. Their results show 
that the global effect of an increase of pressure is an improvement of the 
mechanical properties of material (dimensional stability, strength, heat 
stability). Several studies have investigated the stress strain behaviour of 
semicrystalline polymers under hydrostatic pressure. As far as iPP is 
concerned, Mears et al. [97] have shown that under hydrostatic pressures up 
to 210 MPa the ultimate strains are large, but decrease gradually with an 
increase in pressure. At higher pressures, the ultimate strains decrease 
abruptly. Consequently, the nature of deformation is changed. While at 
atmospheric pressure a neck occurs and distributes, at higher pressures the 
neck becomes faintly pronounced and a quasi-brittle failure takes place. 
Furthermore Mears et al. [97] have shown that the dependence of iPP yield 
strength upon pressure is linear. Silano et al. [98] and Zihlif [99] investigated 
the dependence of stress on deformation and pressure for iPP. Their results 
show that the dependence of shear modulus on pressure breaks for pressures 
above 200 MPa. The dependence of yield strength on pressure may be 
considered to be linear. As for the influence of molecular parameters, Pae et 
al. [100] have shown that, at the same pressure, Young’s modulus is higher 
in specimens with a smaller molecular mass. Additionally Pae et al. [93] 
have also shown that the dependence of Young’s modulus upon pressure is 
similar for many semicrystalline polymers. As a matter of fact, the E(P) plots 
consist in two almost linear sections. The first section (at low pressure) is 
characterised by a stronger dependence of the modulus of elasticity on 
pressure than the second one (at high pressure).