Journal of Biomaterials and Nanobiotechnology, 2011, 2, 301-310
doi:10.4236/jbnb.2011.23037 Published Online July 2011 (http://www.SciRP.org/journal/jbnb)
301
Crystallization Kinetics of
Poly(3-Hydroxybutyrate) Granules in
Different Environmental Conditions
Michael M. Porter, Jian Yu
Hawai’i Natural Energy Institute, University of Hawai’i at Mānoa, Honolulu, Hawai’i.
Received February 4th, 2011; revised May 4th 2011; accepted June 1st, 2011.
ABSTRACT
Poly(3-hydroxybutyrate) (PHB) is a natural biopolyester accumulated in microbial cells as tiny amorphous granules.
The nano- micro-particles have a variety of potential applications and behave differently in different environments. In
this work, the in situ crystallization of native PHB granules was investigated under different environmental conditions.
The isothermal crystallization kinetics of the granules was shown to follow Avrami’s equation. The model parameter
describing crystal growth is a function of temperature or pH and estimated from in situ crystallization measurements
with attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy. Empirical equations describing
crystal growth are derived for the parameter values. PHB granules heated at 80˚C - 140˚C in acidic solution (pH 2) up
to 4 hr showed an increase in crystallinity from about 5% to 35% and moderate particle aggregation. PHB granules
suspended in alkaline solutions (pH 9-12) at room temperature up to 4 hr showed an increase in crystallinity up to 45%
and very little particle aggregation. It was found that the amorphousness of PHB granules in vivo is stabilized by water,
lipids and proteins. Upon removal of these impurities, partial crystallization is induced which may inhibit extensive
particle aggregation.
Keywords: Avrami Model, Crystallization Kinetics, PHA, PHB Granules, Biopolyester Particles
1. Introduction
Poly(3-hydroxybutyrate) (PHB) is a representative, natu-
rally occurring bacterial polyhydroxyalkanoate (PHA)
that can be produced from renewable feedstocks as an
eco-friendly bioplastic [1,2]. In nature, PHB biopoly-
esters are accumulated in microbial cells as tiny intracel-
lular amorphous granules (0.2 - 0.5 μm in diameter) (see
Figure 1(a)) [1-5]. PHB granules can be extracted from
microbial cells and purified by a number of different re-
covery processes [6-9]. During recovery, the environ-
ment of the amorphous granules changes and may cause
the nano- micro-particles to crystallize [10-12]. Interest-
ingly, in different environmental conditions the rate and
extent of PHB crystallization varies, which may affect
the degree of particle aggregation, resulting in different
size and morphology of the biopolyester granules. Puri-
fied PHB particles may be useful in a variety of applica-
tions because PHB is completely biodegradable and bio-
compatible [2,4,5].
The crystallization of PHB is an energetically favor-
able process that may be induced by its environment.
Purified PHB granules become a semi-crystalline mate-
rial (~60% crystallinity) [13-15]. When pure PHB is
heated above its melting point (~180˚C), it becomes a
fully amorphous melt [14,16-20]. Upon cooling, the PHB
molecules crystallize, forming antiparallel helical chains
linked by C – H ··· O hydrogen bonds between the car-
bonyl (C=O) and methyl (CH3) groups of the polyester
backbone [18,21,22]. Crystallization begins as groups of
amorphous molecules aggregate into tiny clusters form-
ing nuclei [19,23]. Then, sheet-like structures known as
lamellae grow radially outward from the nuclei in the
form of spherulites [19,23]. The kinetics of PHB crystal-
lization depend on the thermodynamics of phase change
(i.e., amorphous to crystalline), the nature of nucleation
and spherulitic crystal growth, and environmental factors
such as temperature and chemical potential [19,23,24].
In vivo, PHB granules are fully amorphous and sur-
rounded by a monolayer membrane composed of phos-
pholipids and proteins [3,10,11,25]. The amorphousness

Crystallization Kinetics of Poly(3-Hydroxybutyrate) Granules in Different Environmental Conditions 302
of native PHB in vivo is likely stabilized by a small
amount of water (5% - 10%) contained within the gran-
ules and the monolayer membrane surrounding the gran-
ules [2,3,10]. In different environmental conditions, na-
tive PHB granules may undergo varying degrees of par-
tial crystallization, which may be attributed to the re-
moval of intra-granule water and the membrane lipids
and proteins [10-12]. The rate and extent of in situ crys-
tallization in the granules is a function of the environ-
ment, such as temperature or pH. Understanding the
crystallization kinetics of the PHB granules in situ is
useful to help understand the processes of particle ag-
gregation and the resulting size and morphology of the
biopolyester particles.
This work shows that the in situ crystallization kinetics
of native PHB granules in different environmental condi-
tions can be modeled similar to that of pure PHB cooled
from melt. The in situ crystallization of native PHB
granules is shown to be induced or driven by the tem-
perature or pH of the granule environment and dependent
on environmental factors, such as granule impurities (i.e.,
non-PHB biomass and water) and particle morphology
(i.e., aggregation). Such environmental factors may pro-
mote or inhibit PHB crystallization by changing the free-
energy barrier required for crystal growth or the number
of nucleation sites available for crystal growth.
2. Materials and Methods
2.1. PHB Granules
In this work, Ralstonia eutropha cells containing 60 - 70
wt% PHB were stored at room temperature (~23˚C) in
solutions of 0.2 M sulfuric acid (H2SO4). The slurry con-
tained 150 - 250 g dry cell mass/liter. Three aqueous so-
lutions of PHB-containing cells were prepared as con-
trolled samples of different crystallinity:
 Native amorphous PHB granules that were suspended
in acidic solution (pH 2) as described above (see Fig-
ure 1(b));
 PHB granules heated in acidic solution with moderate
crystallinity, where the native granule slurry was heated
in glass test tubes at 80˚C - 140˚C and maintained for 0
- 4 hr, then set at room temperature for several months
for the apparent crystallinity to stabilize;
 PHB granules in solutions of varying pH with high
crystallinity, where the pH of the native granule slurry
was increased from 2 to 12 by adding equal volumes
of varying concentrations of sodium hydroxide (NaOH)
to the native slurry at room temperature.
2.2. Purified PHB
Pure PHB was extracted from the microbial cells for
comparison. The cells were freeze dried, suspended in
500 nm500 nm
(a) (b)
Figure 1. TEM images of PHB-containing cells: (a) in neu-
tral solution (pH 7); (b) in acidic solution (pH 2). The bar is
500 nm.
hot chloroform, and filtered to separate the polymer solu-
tion from the residual cell mass. Pure PHB was precipi-
tated from the chloroform solution by adding hexanes.
The precipitates were filtered, washed, and dried. The
purified PHB was then dissolved in hot chloroform and
cast on a clean glass surface as a thin film (~0.2 mm
thickness).
2.3. Attenuated Total Reflectance Fourier
Transform Infrared Spectroscopy
The infrared absorption spectra of the pure PHB and the
PHB-containing cells were recorded with a Nicolet Ava-
tar 370 FTIR spectrometer (Thermo Electron Co., Madi-
son, WI). All measurements were taken in ambient con-
ditions on a germanium crystal window of micro-hori-
zontal attenuated total reflectance (ATR). A total of 32
scans were averaged for measurement of a single sample
over 1 min.
For time-resolved measurements describing the crys-
tallization of pure PHB, the sample was first melted at
180˚C, then placed directly on the ATR window at 0 min
and allowed to cool at room temperature (~23˚C). Ab-
sorption spectra were collected every 1 - 2 min over the
duration (30 min) of the process. The crystallinity of PHB
was monitored at the wavenumber 1184 cm–1 and scaled
by the reference peak 1382 cm–1 according to crystalline
measurements of pure PHA [21,26-28]. An absorption
index AI defined below (1) is a relative measurement of
the degree of PHB crystallinity:
1184
1382
A
AI A  (1)
where v
A
 is the infrared absorption intensity of PHB at
wavenumber v . The actual crystallinity of PHB was
determined through a correlation of DSC measurements
with the ATR-FTIR absorption spectra of three PHA
samples of different crystallinity (data not shown here).
The following linear correlation (2) was derived and used

Crystallization Kinetics of Poly(3-Hydroxybutyrate) Granules in Different Environmental Conditions 303
to calculate the crystallinity from the absorption index:
2.91 3.04XAI (2)
where X is the apparent crystallinity of PHB.
For in situ measurements of the PHB-containing cells,
a small drop (~2 μL) of aqueous solution was placed di-
rectly on the ATR window and allowed to evaporate at
room temperature. During water evaporation, the PHB-
containing cells deposited onto the window via sedimen-
tation and absorption spectra were collected every 1 - 2
min for the duration (30 min) of the process. The absorp-
tion spectra were divided into three distinct stages: an
initial scattering stage predominated by water absorption,
a stable secondary stage representing the true, in situ
crystallinity, and a final “artificial” crystallization stage
caused by excess dehydration. The apparent, in situ crys-
tallinity was measured during the stable, secondary stage
of the measurement at the wavenumber 1184 cm–1,
scaled by the reference peak 1382 cm–1 [21,26-28]. Spec-
tral interference from background absorptions caused by
water and other non-PHB cellular components were de-
termined to be constant (data not shown here) and sub-
tracted from the total absorption spectra. The in situ PHB
crystallinity measurements were quantified using the
same DSC/ATR-FTIR correlation mentioned above in (1)
and (2).
2.4. Transmission Electron Microscopy
The transmission electron microscopy (TEM) images
were viewed on a LEO 912 EFTEM (Zeiss, Germany) at
100 kV and photographed with a frame-transfer CCD
camera (Proscan, Germany). The cells were fixed with
glutaraldehyde and calcium chloride in a sodium caco-
dylate buffer, then post-fixated with osmium tetroxide,
stained with uranyl acetate, dehydrated with ethanol and
embedded in epoxy. Ultrathin (60 - 80 nm) sections were
obtained on an Ultracut E ultramicrotome (Reichert,
Austria), double stained with uranyl acetate and lead cit-
rate.
2.5. Environmental Factors and Kinetics
Modeling
To determine the factors that may stabilize amorphous
PHB granules, aqueous solutions of PHB-containing
cells were dehydrated by freeze-drying and acetone ex-
traction. The in situ crystallization behavior of the native
granules in different environmental conditions was in-
vestigated by suspending PHB-containing cells in an
acidic solution (pH 2) at high temperatures (80˚C - 140˚C)
or in aqueous solutions of increasing pH (2 - 12) in am-
bient conditions.
The crystallization of pure PHB from melt was ana-
lyzed and compared to the in situ crystallization of the
PHB granules. Crystallinity measurements were obtained
via ATR-FTIR and fit to Avrami’s Equation (3) [21,28,
29]:
1exp n
X
kt

 

(3)
where X is the crystallinity, t is the crystallization time, k
is a rate constant dependent on the formation of nuclei
and spherulitic crystal growth, and n is Avrami’s expo-
nent dependent on the nature of nucleation and geometry
of crystal growth. Empirical equations to describe the
growth rate parameter (k) as a function of temperature or
pH were derived. Based on the crystallization kinetics of
polymers similar to PHB, the growth rate parameter may
be described by the Arrhenius Equation (4) as a function
of temperature [29,30]:
1exp na
o
E
kk RT





(4)
where a E

is the crystallization activation energy, R is
the gas constant (8.314 J/K·mol), ko is a pre-exponential
factor independent of temperature, and T is the isother-
mal crystallization temperature in Kelvin. The growth
rate parameters and Avrami’s exponents were estimated
by fitting the measured values to the empirical equations
and discussed in terms of thermodynamic energy, gran-
ule geometry, spherulitic growth rate, and the nature of
nucleation. Transmission electron microscopy (TEM)
images of the granules in different environments were
taken to show the extent of granule aggregation.
3. Results
3.1. Crystallization of Pure PHB from Melt
Figure 2(a) shows a time development of the infrared
absorption spectra illustrating the crystallization of pure
PHB cooled from an amorphous melt at 180˚C (solid line)
to a semi-crystalline solid at room temperature (dashed
line) over 30 min in ambient conditions. As seen in the
figure, the absorption intensity at 1184 cm–1 decreases
with time, while the absorption intensity at 1382 cm–1
does not change with time and is taken as the reference
peak [31]. Using the data from Figure 2(a) with (1) and
(2), the corresponding crystallinity of PHB versus cool-
ing time is plotted in Figure 2(b). Primary crystallization,
which includes nucleation and spherulitic crystal growth,
is represented by the solid data points and occurs be-
tween 2 - 15 min. Secondary crystallization, or the rear-
rangement of PHB molecules into more energetically
favorable structures, is represented by the hollow data
points and occurs after 15 min. The initial data points (0 -
2 min) are neglected in this analysis because the thermal
history of the sample may be unstable and is not known.

Crystallization Kinetics of Poly(3-Hydroxybutyrate) Granules in Different Environmental Conditions 304
(a)
(b)
Figure 2. (a) Time development of the infrared absorption
spectra of pure PHB, illustrating the crystallization due to
cooling from an amorphous melt at 180˚C (solid line) to a
semi-crystalline solid at room temperature (dashed line); (b)
Crystallinity versus cooling time of pure PHB cooled from
melt at 180˚C to room temperature, illustrating primary
crystallization (solid data points) and secondary crystalliza-
tion (hollow data points).
3.2. Crystallization of Native PHB Granules
The native PHB-containing cells stored in acidic solution
(pH 2) exhibited no biological activity. The mild acidic
conditions caused some damage to the cell walls as seen
in Figure 1(b), but did not significantly change the na-
ture of the native PHB granules.
Figure 3(a) shows a time development of the infrared
absorption spectra of the native PHB granules in micro-
bial cells suspended in acidic solution. In 30 min of mea-
surement, a spectral pattern is observed that resembles
the crystallization of pure PHB seen in Figure 2(a). Ini-
tially, the absorption spectrum of the solution is domi-
nated by water (dotted line). As water evaporates in ap-
proximately 5 min, a secondary spectrum of the PHB
granules and other cellular components emerges due to
sedimentation (solid line). This spectrum represents the
true, instantaneous crystallinity of the native granules.
After 15 min, the spectra changes due to excess dehydra-
tion, becoming fully developed, but no longer represents
the true, instantaneous crystallinity of the native granules
(dashed line).
The in situ crystallinity of the native PHB granules
versus measurement time corresponding to Figure 3(a) is
plotted in Figure 3(b). As mentioned, the instantaneous
crystallinity was measured during the stable secondary
stage (5 - 15 min), after the initial scattering stage pre-
dominated by water (0 - 5 min), and before the final arti-
ficial stage due to excess dehydration (15 - 30 min). Af-
ter 15 - 30 min the PHB crystallinity increased up to 32%,
corresponding to a water content of less than 20%. The
true, instantaneous crystallinity of the native granules av-
eraged over the secondary stage (5 - 15 min) is 4.89% ±
1.84%.
(a)
(b)
Figure 3. (a) Time development of the infrared absorption
spectra of PHB-containing cells suspe nded in acidic solution
(pH 2), illustrating the initial spectrum dominated by water
at 0 mins (dotted line), the secondary spectrum characteris-
tic of the instantaneous crystallinity after 10 mins (solid
line), and the final spectrum caused by extensive dehydra-
tion after 30 mins (dashed line); (b) In situ crystallinity ver-
sus measurement time for native PHB granules in acidic
solution at room temperature, illustrating the instantaneous
crystallinity at 5 - 15 mins (Xi = 4.89 ± 1.84%). The final
crystallinity (32%) is attributed to excess dehydration.

Crystallization Kinetics of Poly(3-Hydroxybutyrate) Granules in Different Environmental Conditions 305
In further analysis, dehydration of the PHB-containing
cells was observed to induce partial crystallization in the
native granules. Cells freeze-dried for 3 hr exhibited a
slow crystallization of PHB, increasing up to 33% over
the first 24 hr after drying. In contrast, cells dehydrated
with acetone extraction showed a much faster crystalliza-
tion of PHB up to 52% after 24 hr. The increased crystal-
linity observed from acetone extraction is attributed to
the simultaneous removal of water, as well as, lipids
from the granules.
3.3. Crystallization of PHB Granules Subjected
to High Temperatures
PHB-containing cells heated to and maintained at 80˚C -
140˚C for 0 - 4 hr in acidic solution (pH 2) showed an
increase in PHB crystallization and granule aggregation
with increasing temperature and exposure time. A sig-
nificant increase in crystallinity observed (20% - 35%) in
the granules heated above 80˚C suggests that heating the
cell slurry may have induced partial crystallization where
intra-granule water, proteins and lipids were displaced
from the PHB particles. Figure 4(a) contains a represen-
tative TEM image of the granules heated at 120˚C for 1
hr in acidic solution (pH 2). As seen in the figure, heating
the PHB-containing cells induced moderate granule ag-
gregation. The instantaneous crystallinity of the PHB
granules at 120˚C for 1 hr, for instance, reached 22.52%.
3.4. Crystallization of PHB Granules Subjected
to Varying pH
Raising the pH of the PHB-containing cells from 2 to 12
in ambient conditions showed an increase in granule
crystallinity with increasing pH. Increasing the pH, how-
ever, did not seem to induce granule aggregation and the
in situ crystallization of the PHB granules seemed to oc-
cur instantaneously. Most likely, increasing the pH may
have dissolved lipids and proteins from the granule
membranes, inducing a quick partial crystallization at the
particle surfaces where the granule membranes were re-
moved. Figure 4(b) contains a representative TEM im-
age of the granules at pH 12 for 1 hr in room temperature.
As seen in the figure, increasing the pH of the PHB-con-
taining cells induced very little granule aggregation. The
instantaneous crystallinity of the PHB granules at pH 12
for 1 hr, for instance, reached 40.59%.
3.5. Modeling the Crystallization Kinetics of
PHB
The crystallization of PHB is well described by Avrami’s
Equation (3) for isothermal crystallization, and is con-
veniently rewritten in linear form (5) [21,28,29]:


 
logln 1loglog
X
kn t  (5)
500 nm
500 nm
(a) (b)
Figure 4. TEM images of PHB granules. (a) heated in acidic
solution (pH 2) at 120˚C for 1 hr; (b) suspended in alkaline
solution (pH 12) at room temperature for 1 hr. The bar is
500 nm.
Referring to Figure 2(b), the primary crystallization
stage (2 - 15 min) of pure PHB can be fit to Avrami’s
equation by plotting



logln 1
X
 versus


log t.
Figure 5 contains a log-log plot for the crystallization of
pure PHB from melt. Numerical values of Avrami’s ex-
ponent and the growth rate parameter were obtained from
the slope and intercept to be n = 1.5010 and k = 0.0118,
respectively. When compared to published results, these
values are close to the documented range (n = 1.58 – 1.92;
k = 0.04 – 0.13) for the isothermal crystallization of neat
PHB [31].
Similar to the crystallization of pure PHB, the in situ
crystallization of PHB granules subjected to heating or
varying pH can be modeled by Avrami’s Equation (3),
where X is the in situ crystallinity of the PHB granules
and t is the period of time the granules are exposed to the
different environmental conditions.
Table 1 gives the values of n and k obtained from lin-
ear correlations of the crystallinity data from the Avrami
analysis of the PHB granules heated at 80˚C - 140˚C for
0 - 4 hr in acidic solution (pH 2). Table 1 also shows the
measured in situ crystallinity of the granules after 4 hr of
heating at each temperature. From observation it is ap-
parent that Avrami’s exponent remains constant with
temperature, so that n = 0.2140. Further analysis shows
that the crystallization growth rate parameter increases
with temperature and may follow the Arrhenius equation
previously mentioned (4). Rewriting the Arrhenius equa-
tion in linear form (6) [29,30]:


11
ln lna
o
E
kk
nRT




(6)
and plotting




1lnnk
versus 1T, as seen in Figure
6, the pre-exponential factor and activation energy were
found from the linear correlation to be o
k = 78.73 min–1
and a
E

= 48.82 kJ/mol, respectively. When compared
to the activation energy of polypropylene (163 kJ/mol),

Crystallization Kinetics of Poly(3-Hydroxybutyrate) Granules in Different Environmental Conditions 306
Table 1. Crystallization of PHB granules heated in acidic
solution (pH 2).
T (˚C) X (%) after 4 hr n k (min–1) R2
25 4.89 --- --- ---
80 21.00 0.2159 0.0711 0.9915
100 23.26 0.1922 0.0904 0.9806
120 27.19 0.2018 0.1042 0.9274
140 35.54 0.2459 0.1200 0.9754
AVG --- 0.2140 --- ---
STD --- 0.0234 --- ---
Figure 5. Determination of the crystallization rate constant
k and the Avrami exponent n for the crystallization of pure
PHB at room temperature during primary crystallization
(2 - 15 min).
Figure 6. Crystallization growth rate parameter k as a
function of temperature for heated PHB granules.
the activation energy determined for the heated PHB
granules (48.82 kJ/mol) is much lower, but of similar
magnitude [29].
Table 2 contains the values of n and k obtained from
linear correlations of the crystallinity data from the
Avrami analysis of the PHB granules suspended in solu-
tions of varying pH (2-12) for 0 - 4 hr at room tempera-
ture. Table 2 also shows the in situ crystallinity of the
PHB granules averaged over the 4 hr of exposure time.
The value of the Avrami exponent (n) was found to be
around zero. As previously mentioned, raising the pH of
the cell slurry caused the PHB granules to crystallize
nearly instantaneously. Therefore, the in situ crystallinity
was assumed to be independent of the exposure time.
Figure 7 contains a plot of the term

 
logln 1
X

from Avrami’s equation versus pOH (= 14 – pH). From
the log plot in Figure 7, it is apparent that the PHB crys-
tallinity is linearly correlated to the pOH of the cell
slurry, such that:





logln 1pOHX


 
(7)
where the constants

= –0.0891 and

= –0.1219.
Then combining (5) and (7) with the observation that N =
0, the growth rate parameter is expressed as:


10 OHk

 

 (8)
where OH




 is the concentration of hydroxide ions in
the solution. No temperature dependence appears in this
empirical relation because the pH of the granules was
adjusted at a constant room temperature (~23˚C).
Table 3 outlines the kinetics models describing the
crystallization of pure PHB cooled from melt, PHB
granules heated in acidic solution, and PHB granules of
Table 2. Crystallization of PHB granules in solutions of
varying pH at room temperature (~23˚C).
pH X ± STD (%) n k (min–1)
2.00 6.99 ± 1.41 0.00 0.0645
3.55 7.61 ± 1.36 0.0886
9.30 26.70 ± 0.52 0.2881
11.06 28.43 ± 2.65 0.4133
11.80 41.14 ± 1.96 0.4811
12.12 41.25 ± 4.63 0.5137
Figure 7. Log plot illustrating the linearity of in situ crystal-
lization versus pOH of PHB granules suspended in solutions
of varying pH.

Crystallization Kinetics of Poly(3-Hydroxybutyrate) Granules in Different Environmental Conditions 307
Table 3. Crystallization models of pure PHB and PHB granules in different environmental conditions by Avrami analysis.
Pure PHB PHB Granules (Heat) PHB Granules (pH)
Crystallinity 1exp n
Xkt  

1expn Xkt 



 1expn
Xkt  

1exp na
o
E
kk
R
T









10 OHk

 


Growth Rate Parameter 1exp
na
o
E
kk
R
T





ko = 78.73 min–1; a
E

= 48.82 kJ/mol

= –0.0891;

= –0.1219
n 1.5010 0.2140 0
k (min–1) 0.0118 0.0725 - 0.1215a 0.0428 - 0.7553b
R2 0.9761 0.9903 0.9727
aRange of k for temperatures 80˚C - 140˚C; bRange of k for pH 0 - 14.
varying pH. Table 3 also includes numerical values of
the empirical constants, Avrami exponents (n), and growth
rate parameters (k) determined for each of the three
cases.
4. Discussion
4.1. Stabilizing Factors of Amorphous PHB
Granules
According to the observation on dehydration of the na-
tive PHB granules, removal of water from the granules,
as well as, removal of lipids from the granule membranes
induced some partial crystallization. It is widely accepted
that PHB granules are fully amorphous in vivo having a
crystallinity of 0% in a neutral culture medium (pH 7) [3,
10]. When partially isolated and/or subjected to varying
environmental conditions, however, the PHB granules
undergo varying degrees of in situ crystallization [10-12].
As expected, the mild acidic solution (pH 2) used to store
the PHB-containing cells triggered very minuscule
changes in crystallinity (~5%). It seems that the intra-
granule water and granule membranes remained largely
intact, stabilizing the native PHB granules in a mostly
amorphous state. Furthermore, the crystallization that
occurred due to excess dehydration during ATR- FTIR
measurement and dehydration by freeze-drying the cells
did not exceed 35%. Hence, the remaining granule mem-
branes obviously kept the PHB granules from reaching a
fully crystalline state (~60%). When dehydrated with
acetone, on the other hand, the native granules became
highly crystalline (~ 52%) in 24 hr, further suggesting
that the lipids dissolved in acetone stabilized the native
granules in a prior amorphous state.
The crystallization of PHB is primarily driven by C –
H ··· O hydrogen bonding between the C = O and CH3
groups in PHB [18,21,22]. Weakening the hydrogen
bonds by melting or disrupting the hydrogen bonds with
environmental impurities may inhibit the crystallization
of PHB [10,13-15]. As noted, the amorphousness of na-
tive PHB granules in vivo must be stabilized by the
monolayer membrane surrounding the particles and in-
tra-granule water [2,3,10]. The 5% - 10% of water pre-
sent in the granules is thought to act as a plasticizer,
forming hydrogen bonds with the C=O and CH3 groups
of the biopolyester backbones [10]. These hydrogen
bonds prevent strong intra- and intermolecular interac-
tions from occurring between the C=O and CH3 groups
in PHB [3,10,12]. Similarly, the granule membranes pre-
vent strong interactions from occurring between PHB
molecules in adjacent granules. Removal of the in-
tra-granule water or the granule membrane promotes in
situ crystallization due to increased C–H ··· O hydrogen
bonding, which is analogous to the cooling crystalliza-
tion process in pure PHB [10]. If there is very little or no
granule crystallization, regions of particles without gran-
ule membranes tend to aggregate.
4.2. Interpretation of Avrami Exponents and
Growth Rate Parameters
Table 3 contains the equations and empirical constants
determined from the Avrami analyses for the crystalliza-
tion of pure PHB, PHB granules heated in acidic solution
(pH 2), and PHB granules in solutions of varying pH at
room temperature. As previously shown, Avrami’s equa-
tion can be used to describe the crystallization of pure
PHB, as well as, the in situ crystallization of native PHB
granules in different environmental conditions. Differ-
ences in the Avrami exponents (n) and the growth rate
parameters (k) for each condition provide the insight
necessary to understand the different crystallization proc-
esses. To help visualize the geometric nature of crystal-
lization, it is useful to introduce a theoretical size pa-
rameter (w) describing crystal growth:
n
s
r
wr

(9)

Crystallization Kinetics of Poly(3-Hydroxybutyrate) Granules in Different Environmental Conditions 308
and the critical nuclei radii (cr r) required to overcome
the free energy barrier for nucleation [23,24]:
2
cr
v
rG



(10)
where the average radii of the nuclei and corresponding
spherulites are n
r and
s
r, and the surface and volumet-
ric energies associated with nucleation are

and v G

,
respectively.
The Avrami exponent (n) is a measure of the geomet-
ric constraints associated with isothermal crystallization,
describing the type of crystal growth (i.e., geometry of
spherulites) and the nature of nucleation (i.e., number
and size of nucleation points). A large Avrami exponent
(1n) signifies relatively large spherulite growth from
infinitesimal, point-source nuclei (0w), as seen in the
observation of pure PHB where n = 1.5010. Because pure
PHB is a neat homopolymer, it undergoes favorable,
homogeneous nucleation, in which volumetric energy
dominates, so that ncr
rr [23,24]. A small Avrami
exponent (1n), represents small spherulite growth
from tiny, surface-source nuclei (01w), as seen in
the heated granules where n = 0.2140 and the granules at
high pH where n = 0. This heterogeneous nucleation
phenomenon most likely occurs at interfacial surfaces
created by the removal of non-PHB biomass and water,
lowering the free energy barrier and allowing a greater
number of smaller nuclei to crystallize, so that ncr
rr.
As the Avrami exponent approaches zero (0n), the
size of spherulites may be restricted by material avail-
ability (i.e., amount of PHB per granule) or the im-
pingement of adjacent crystallites, and unable grow be-
yond the size of the initial nuclei (1w). This behavior
is seen in the granules at high pH where n = 0, which is
indicative of nearly instantaneous, time independent
crystal growth where crystalline regions are composed of
several tiny crystallites roughly the size of individual
nuclei.
The growth rate parameter (k) is a measure associated
with the frequency of nucleation (i.e., number of nuclei)
and subsequent spherulitic crystal growth. That is, a ma-
terial exhibiting a small growth rate parameter may crys-
tallize from very few nucleation points into relatively
large spherulites. Conversely, a material exhibiting a
larger growth rate parameter may crystallize from several
nucleation points into many tiny spherulites. As seen in
Tables 1-3, the growth rate parameter is smallest for
pure PHB where k = 0.0118 and increases with increas-
ing temperature (0.1215k) and increasing pH
(0.7553k). This suggests that, although the average
growth rate of an individual spherulite of PHB may not
differ in varying environments, the overall crystallization
growth rate of PHB is affected by the frequency of nu-
cleation; which, in pure PHB is significantly less than
that of the heated granules and the granules at high pH.
The growth rate parameter describing the heated granules
increases with temperature most likely because hetero-
geneous nucleation is more favorable at higher tempera-
tures. The granules at high pH, on the other hand, show
increasing growth rate parameters with increasing pH
because the removal of lipids and proteins from the
granules create surfaces where heterogeneous nucleation
is more favorable. Referring to Figure 4, the heated
granules were generally less than 2 μm in diameter (Fig-
ure 4(a)), while the granules at high pH were generally
less than 0.5 μm in diameter (Figure 4(b)). The relative
size of the PHB granules is dependent on the extent of
particle aggregation, which occurs only at regions where
PHB is amorphous and intermolecular entanglement can
easily take place. With more surface area favorable for
heterogeneous nucleation (ncr rr) than a sample of pure
PHB, the frequency of nucleation in smaller PHB gran-
ules is much greater, resulting in larger values of the
growth rate parameter.
5. Conclusions
The in situ crystallization of PHB in its native form is
similar to that of pure PHB and can be modeled by
Avrami’s equation under isothermal conditions. The
growth rate parameter (k) is dependent on the crystalliza-
tion environment (i.e., temperature and pH) and de-
scribes the frequency of nucleation and subsequent
spherulitic crystal growth. The Avrami exponent (n) is
dependent on the geometric nature of crystallization and
is related to the number and size of nucleation points and
spherulites.
In summary, the empirical values of n and k increase
and decrease respectively, with the amount of available
material (i.e., amount of PHB per crystal/granule) for
nucleation and crystal growth. Pure PHB crystallized into
large spherulitic structures from homogeneous nuclei (n
= 1.5010) at a low growth rate (k = 0.0118). PHB gran-
ules heated (80 - 140˚C) in acidic solution (pH 2) crystal-
lized into partial spherulitic structures from heterogene-
ous nuclei (n = 0.2140) at moderate growth rates (k =
0.0725 - 0.1215). PHB granules suspended in solutions
of increasing pH (2-12) at room temperature crystallized
instantaneously from heterogeneous nuclei at granule
surfaces (n = 0) and high growth rates (k = 0.0428-
0.7553).
6. Acknowledgements
This work is partially supported by the Consortium for
Plant Biotechnology Research (CPBR) and the U.S. De-
partment of Energy.

Crystallization Kinetics of Poly(3-Hydroxybutyrate) Granules in Different Environmental Conditions 309
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