CHINESE JOURNAL OF PHYSICS
VOL. 27, NO. I
FEBRUARY 1989
Optical Mixing Spectroscopic Studies of Gelatin Solution
*J.S.Hwang(~iEj$-&),H.J.Gi(#$!~E$2)
S. N. Chen ( j$#s$j )
*Department of Physics, National Cheng Kung University, Tainan,
Taiwan, R. 0. C.
Department of Chemistry, National Cheng Kung University, Tainan,
Taiwan, R. 0. C.
(Received December 17, 1988)
Monodisperse gelatin solutions have been analyzed by optical
mixing spectroscopy (OMS). OMS is a new analytical technique for the
diffusion coefficient and particle sizes. Autocorrelation functions were
measured at 24’C at 90” scattering angle. Calculations of the translational diffusion coefficients (D,) and radius (R) of the particles in the
gelatin solution from the measured autocorrelation functions of
Rayleigh scattered light have been carried out. OMS is a very rapid and
direct method to determine the translational diffusion coefficients and
particle sizes. Our results are that D, is 1.04 X IO-” ml/s and R is
2 1 .O M-I in the dilute solution.
INTRODUCTlON
Gelatin systems have been extensively investigated by osmotic pressure and sedimentation methods. Pouradiar and Venet’?’ measured the osmotic pressure of alkali-precursor
calf skin gelatin in aqueous solutions containing various reagents. They found that the
number-average molar mass varied from 608OOg in distilled water to 666008 in 4.0 M urea
solvent and that the gelatin was molecularly dispersed in each of the solvent systems. The
most common characteristics obtained from light scattering studies are the mass-average
molar mass M and the radius of gyration of the molecule Rs. Boedtker and Doty3 used
light-scatteringwtechniques to study properties of an ossein gelatin and its gel. They found
that the gelatin molecules have a random coil-like shape with mean configuration comparable to those of typical synthetic polymers and mass-average molar masses of 9600g in 2 M
KCNS solvent. They also found that, at all temperatures below the equilibrium melting
temperature, aggregates of gelatin molecules were readily discernible, even in extremely
dilute solutions that were incapable of gelitrn. The aggregate size, however, was related to
50
J. S. HWANG, H. C. GI, S. N. CHEN
.
51
the temperature and the thermal path by which the gelatin solution was brought to the
measurement temperature. William4 et al from sedimentation analysis obtained the weight
average end-to-end chain extension of 25.8 nm by assuming a random coil model.
Gallop’ carried out the denaturation of ichthyocal and made a variety of physical
chemical measurements on sedimentation coefficients, diffusion coefficients, particle
specific volume and intrinsic viscosity of the parent gelatin in sodium citrate buffer at pH
3.7. He also obtained a mass-average molar mass 1.7 X 1 O6 g and 70000g for collagen and
gelatin respectively, using light scattering measurements. Boedtker and Doty6 repreated
Gallop’s study and obtained number-average molar masses 345000g and 138000g for
coliagen and gelatin respectively. Extensive studies of sedimentation and ultracentrifuge
measurements were later made to clarify different components in the parent gelatin from
collagen.
Counts and Stainsby studied the gelatin from ox-hide limed collagen and found the
molar masses ranged from 320000 to 64000g depending on the solvent system and gelatin
concentrations. Veis8~g~10~‘1~‘2 studied gelatin from unlimed purified steer hide corium
collagen by various short neutral or acid extractions. Molar masses were found to range
from 8.3 X lo6 to 0.2 X lo6 g in various fractions.
The results from the optical mixing spectrosocpy (OMS) studies indicated that gelatins
are extremely heterogeneous with molar mass varying over a fiarly wide range up to values
greater than lo6 g and a single configuration model is unable to represent all gelatins.
Gelatin is commonly used to suppress polarographic maxima. The mechanism of suppressing polarographic maxima is uncertain and it is difficult to study gelatin solution by electrochemical methods. Based on these reasons, we studied the distribution of gelatin molecules
in aqueous solution by OMS.
EXPERLMENTAL DETAlLS
(A) Gelatin Solutions
The gelatin solid was provided by Wako Chemical. Various amounts of dried gelatin
solid were added to 60 mL Hz 0 to make up gelatin solutions of different concentrations.
The mixture was stirred by .a magnetic stirrer at 60°C for 20 min and then were added
various amounts of NaClO, to the gelatin solutions. The sampel was cooled to room
temperature 24°C . The solution was diluted to 100 ml and then centrifuged with an
acceleration 5200 g for 10 min. at the same temperature. Thus we obtained gelatin solutions with varied concentration.
(B) Optical Mixing Spectroscopy
The arrangement for optical mixing spectrosocopy, shown in Fig. 1, is fairly standard.
The light beam of an Argon ion laser (coherent 90) passed through a Glan-Thomson prims;
OPTIC AL MIXING SPECTROSOPIC STUDIES OF GELATIN SOLUTION
52
~-___________________________‘________;@
MIRRUR
47 x/2 PLATE.
GLAN-THUHSCIM
$ PRISI.!
SAMPLE CELL
BEAM STOP
FIG. 1
.
Block diagram of apparatus used for the optical mixing spectroscopic measurements.
then it was focused by a lens into the scattering cell. The scattered light passed through two
pinholes and fell on to the photocathode of a photon-counting photomultiplier tube (EM1
9863B). The photon-counting photomultiplier produced a train of standardized pulses in
response to the detected intensity. Its output was amplified by an amplifier-discrirnantor,
and fed into a digital correlator l3 . The standardized pulses produced from photomultiplier
tube were accumulated in a high-speed pulse counter which was under clock control of the
timer, so that the photocountes in successive and equal sample time intervals were
measured. Data were accumulated and correlated in blocks of 1000 successive sample intervals until the correlation function is sufficiently smooth. From a multichannel analyzer
(NS-700) interfaced to the correlator, we obtained the correlation function. Data were
transferred to the IBM 80286 computer for analysis and. printing the correlation function.
(C) Data Analysis
The principle of diffusion measurement by light scattering is most easily explained by
considering the first-order autocorrelation function G’ (7).
G(~)(T) = N < 1 a l2 > < exp[-i q ax(r)] >
(1)
in which N is the number of identical particles in a scattering volume V, q are the scattering
vectors and AX(~) is the average particle displacement in the delay time 7. Equation (1)
depends on the delay time through the average particle displacement AX(T) only, which
Einstein found to be normally distributed with varianceI
< AXE > = 2D,7
(2)
-.
J.S. ~'ANG,H.C.GI.S.N.CHEN
53
This relation is true for delay times large compared with hydrodynamic relaxation times.
Computation of the average in equation (1) thus amounts to taking the Fourier transform
into q-space of gaussian particle displacement density and yields15
G(~)(T) = N < I a I* > exp (-q’ Dtr)
(3)
which is an exponential decay with a time constant from which we may obtain the translational diffusion coefficient Dr. This expoential correlation corresponds to a lorentzian distribution.
All photon correlation experiments easily yield the second-order autocorrelation function, G2 (r), that is
(4)
.
The small g denotes normalized correlations.
For identical, independent particles, equation (4) predicts a single exponential decay
also for the second-order autocorrelation function,
gc2)(,) =
1 + exp(-2q2 Dt r)
(5)
Comparison with the first-order autocorrelation function, equation (5) shows an additional
background and a decay that is more rapid by a factor 2.
In real experiments the finite coherence at the detector produces lower constant in the
signal and leads to a reduced second-order autocorrelation function
gc2)(r) = 1 + p exp (-2q2 Dt T)
(6)
Even though the intercept p may be computed from the optical setup, it is commonly
determined from the actually measured correlation diagram. Linear fits of ln[g2(r)-l/p] vs
r thus give the slope as -2Dtq2 from which the translational diffusion coefficient D, can be
found. From the Stokes-Einstein equation
D,
=kT
61777 R
(7)
in which k is the Boltzmann constant, T is absolute temperature and TJ is the viscosity of the
solvent, we obtain the radius R of particles.
d._
-f.
OPTICAL MIXING SPECTROSOPIC STUDIES OF GELATIN SOLUTION
54
RESULTS AND DISCUSSION
To check that no counts were lost, we shave light from a Spectral Physics model 155
He-Ne laser on the pinhole in front of the correlator. The autocorrelation function of
g(*)(T) - l/p . T is shown in Fig. 2. Fig. 2 shows the resultant I g(l)(r) I2 which was just
the expectec? result produced from a totally uncorrelated signal. We analyzed the light
.
FIG. 2
Autocorrelation function of He-Ne laser light
960 P rcc/div
scattered from the water solution of standardized polystyrene latex spherical particles,
which were supplied by Dow Chemical, with diameter 0.234 pm at 24” C and 90” scattering
angle. Its second-order autocorrelation function is shown in Fig. 3. Linear fit’s of ln[g(*)(T)
- 1 /p] vs. T then gave the slope as -2Dtq2 from which the translational diffusion coefficient
D, was found. Combined with equation (7), we obtained the radius of the latex particle to
be 0.120 pm which was reasonably close to the standard value 0.117pm. Based on these
test results, we proved that our correlator performed properly.
FIG. 3
Autocorrelation function of light scattered by the solution of polystyrene latex at scattering
angle = 75”. The dots are the values of the first 1 lo-channel and line is the fitted curve.
The second-order autocorrelation functions oi‘ gelatin solutions with various NaClO,
concentrations were measured at 24°C and 90” scattering angle. Using the same method, we
-
J.
FIG. 4
s. I-IN'ASG,
I(.
c. GI. s. s. CliEN
55
Concentration dependence of particle radius of gelatin solutions in 0.00(l), 0.05(2), 0.10(3),
0.20(4), and 0.30 M(5) NaC104 after being centrifiuged.
obtained the translational diffusion coefficients D, and.radii of gelatin particles shown in
Fig. 4 and 5, respectively. When the solution concentration is less than the crossover concentration, the micelles formed from gelatin solution are far enough apart that the effect of
interactions between gelatin micelles is small and can be negected, and each micelle exercises
its invidual Brownian motion characterized by free translational diffusion coefficient D, independent of the solution concentration, and the radius R of the gelatin micelle remains
constant. We obtained that D, is 1.04 X lo-” mz /s and R is 21 .O nm. From the equation
M =-
4n R3 Na
37
(8)
in which Na is avogadro’s number and 7 is its specific volume, we can obtain the average
molar mass M. The method to calculate the specific volume is described in Ref (16). The
average molar mass is 1.08 X 10’ g.
i C-”-r------c
--- -7
_
I
FIG. 5
Concentration dependence of diffusion coefficient of gelatin solutions in 0.00(l) and 0.05 M(2)
NaC104 after being centrifuged.
-_.‘_
..I.
56
OPTIC.AL S1IXING SPECTROSOPIC STCDIES OF GELXTIS SOLUTION
As the solution concentration is increased, the micelles start to interact by the
coulombic interaction which forms hydrogen bonds between gelatin micelles and produces
the excluded volume effect. The translational diffusion coefficient D, and the radius R of
the particle are dependent on the solution concentration. We obtained that the radius is
appraximately proportional to the solution concentration.
Fig. 6 contains plots of the radii R of gelatin micelles V S. NaClO, concentration at
different gelatin concentrations larger than the crossover concentration. The decrease in the
radius of the particle as the NaClO, concentration is increased indicates that the polar
groups of a gelatin micelle distribute on the surface of the gelatin micelle. At small NaClO,
concentrations, the chance of hydrogen bond formed between the micelles is so large that
gelatin micelles aggregate easily. However, as the NaClO, concentration increases, the
coulombic interactions are screened more and more completely by the charges on the ions
and the radius of the particle decreases with increase of NaClO, concentration.
FIG. 6 Effect NaC104 concentration on the particle radius of lOO( l), 75(2), W3) and 25 mdmJ44)
gelatin solutions.
CONCLUSION
At small gelatin concentrations, gelatin micelles in solution undergo free diffusion.
The translational diffusion coefficient is thus independent of the concentration. However,
as the gelatin concentration exceeds than crossover concentration, the diffusion coefficient
of gelatin micelle decreases as the concentration increases. This behaviour is due to the
increasing effects of interparticle interactions when the interparticle spacing becomes com-
J. S. HN'ANG. H. C. GI.
S. N. CHEN
51
parable to the particle size and the gelatin micelles in solution form a polymer network.
This phenomenon is however inhibited by the presence of NaClO, .
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