# Study of Interfacial Rheology of Human Serum Albumin Microcapsules using
Electrodeformation Technique

Sneha Puri and Rochish M. Thaokar
E-mail<EMAIL_ADDRESS>
Phone: +91 (22) 2576 7241 Fax: +91 (22) 2572 6895
Department of Chemical Engineering,
Indian Institute of Technology Bombay, Mumbai-400076

###### Abstract

Understanding the mechanical characterization of microcapsules is critical for
their precise applications, such as in pharmaceuticals, cosmetics,
agriculture, food industries, etc. Microcapsules synthesized from different
materials show distinct mechanical characteristics. It is therefore necessary
to study these systems considering their respective micro-physics for an exact
theoretical model suitable to these systems. In the present work, we conducted
mechanical characterization of the membrane of human serum albumin (HSA)
microcapsules using the electrodeformation technique. Proteins are widely used
as encapsulating materials for many biomedical and food industries. Relating
the microstructure to the mechanical properties of a protein-membrane is a
challenge owing to its complex structure and sensitivity towards different
environmental conditions such as pH, temperature, and solvents. Interfacial
rheology of human serum albumin microcapsules studied using the
electrodeformation technique shows that HSA capsules are strain-softening in
nature. The viscoelasto-electrohydrodynamic model was utilized to understand
the creep mechanism in the human serum albumin capsules. The effect of
different reaction parameters such as protein concentration and pH on the
morphology of the capsule membrane was investigated, and an attempt has been
made to correlate microstructure with the mechanical properties. The pH has a
remarkable effect on the morphology of HSA microcapsules which is also
reflected in their mechanical characteristics. The capsule synthesized with
carbonate buffer shows very distinct morphology with pores on the membrane
surface, making the membrane less elastic with significant nonrecoverable
creep. The capsules synthesized with different protein concentrations at the
same pH condition show different morphology and thus different rheological
properties. Capsules with a low concentration of HSA show smooth membrane
structure with higher Young’s modulus than the capsules synthesized at a very
high concentration which show a rough folded wavy structure with low membrane
elastic modulus. The effect of frequency on the interfacial rheological
properties of human serum albumin capsules was studied using a frequency sweep
test using the electrodeformation technique. The rheological properties were
computed incorporating the viscoelasto-electrohydrodynamic model for the
oscillatory response of capsules. The results show that the elastic response
dominates in the high-frequency regime. Thus the electrodeformation technique
allows studying the effect of very high-frequency 1 Hz to 1 kHz, which is
otherwise not possible with the conventional rheometers.

##  1 Introduction

A microcapsule is a liquid droplet covered with a thin sheet (shell) of self-
assembled or crosslinked particles or polymers of a few 10s of microns in
size. Common examples of natural microcapsules include red blood cells, fat
globules in milk, etc. Synthetic microcapsules made up of crosslinked polymers
find tremendous use in several applications. Specifically, crosslinked
proteins as the shell material have attractive applications in the biomedical,
pharmaceuticals, cosmetics and food industries. This paper demonstrates an
electrodeformation technique to study the interfacial rheology of human serum
albumin microcapsules. HSA is a biocompatible protein and having a very
attractive binding capacity to many drugs. Below we briefly discuss the
studies on the characterization of human serum albumin microcapsules.

The fourier transform infrared (FTIR) spectroscopic studies on HSA capsules
synthesized by the emulsification method showed the participation of amino,
hydroxyl, and carboxyl functional groups of albumin in the formation of the
crosslinked HSA microcapsules [levy1991fourier]. The extent of involvement of
these functional groups depends on the reaction conditions during the capsule
synthesis process. levy1991fourier studied the chemical characterization of
HSA capsules using FTIR spectroscopy and TNBS titration techniques. Their
method was focused on the determination of the amount of free amino groups of
the microcapsules, using the TNBS titration method to understand the degree of
crosslinking, and the FTIR technique for the involvement of various functional
groups at different reaction conditions.

Proteins are known to be sensitive to pH and acquire a configuration that
depends upon the protonation/deprotonation of amino groups and ionization of
their carboxylic group present on the amino acid side groups
[dumetz2008effects]. At low pH, the involvement of only free amine groups is
seen, whereas, for high pH, carboxyl and hydroxyl groups also participate in
the reaction. Moreover, at a higher pH, the ionization of the amine groups is
suppressed, thereby favoring the amide reaction with the reducing agent. HSA
capsules synthesized with phosphate buffer in the pH range between 5.9 to 8
yielded larger-sized microcapsule aggregates with smooth morphology that
collapsed after drying. However, with a similar reaction condition,
microcapsules prepared with a carbonate buffer (pH 9 to 11) resulted in
smaller, pale yellow, rough individual spherical capsules [levy1991fourier].

In yet another study, it was found that the acylation of amino groups of HSA
is more intense with acetate buffer than with the phosphate buffer at the same
pH of 5.9 [edwards1993determination]. This gives the advantage of increasing
crosslinking density of the membrane of HSA microcapsules without raising the
pH. The difference between acetate and carbonate buffers was attributed to the
difference in the ionic concentration of the two buffers. The exact reason for
why the higher ionic concentration of the acetate buffer favors acylation of
the amino groups at the same pH though is unclear.

Increasing reaction time shows a similar effect as upon increase in pH on
membrane morphology of the capsules. At pH 9.8 (carbonate buffer) with 2 min
reaction time, bigger $\sim$ 30 $\mu m$ capsules with smooth membrane
morphology is formed, while as the reaction time increases, smaller
microcapsules with rough morphology are obtained. Initially, only free amines
participate in the reaction, and as the reaction time increases, more
functional groups are involved in the reaction producing rough and more
granular microcapsules [levy1995fourier]. Similarly, with the increase in the
concentration of crosslinker, a rough membrane is formed, showing a higher
degree of crosslinking [levy1995fourier, levy1991fourier].

To summarize, the literature survey about the synthesis of HSA capsules
indicates that two types of capsules can be synthesized by tuning the
different reaction parameters.

  1. 1.

Poorly crosslinked type-1 capsules that show smooth membrane morphology and
involve mainly the reaction of free amines; can be synthesized either at low
pH, at low TC concentration (2.5 percent), or with a short reaction time at
high pH. The extent of crosslinking is much lower in this case.

  2. 2.

Highly crosslinked type-2 capsules are smaller in size with rough morphology
and involve the formation of more $\beta$ sheets, ester, and anhydride bonds
and can be synthesized by intensifying the reaction by increasing one of the
reaction parameters; pH, reaction time, or TC concentration.

Designing a microcapsule with desired mechanical characteristics is a
challenge in microencapsulation technology. The capsules prepared with
different materials, such as chitosan, alginate, and proteins, show distinct
membrane mechanical properties. For example, HSA-alginate capsules show strain
hardening [carin2003compression] behavior while serum albumin (HSA/BSA)
capsules exhibit strain-softening nature [gires2014mechanical,
gubspun2016characterization]. The reaction parameters and fabrication
techniques can also significantly affect the membrane properties of
microcapsules synthesized with the same system. Therefore it is often
necessary to study their properties on a case-by-case basis to understand
their characteristics that are relevant to their applications.

Mechanical characterization of water-in-water albumin capsules using the
microfluidic technique has been reported in several studies [de2014mechanical,
de2015stretching, gires2016transient, gubspun2016characterization]. Various
theoretical models such as Hooke’s law, Neo-Hookean, and Skalak law describe
the 2D membrane characteristics of elastic microcapsules. Most of the
literature studies considered strain-softening Neo-Hookean law to compute
mechanical properties of albumin capsules [gubspun2016characterization,
gires2014mechanical], barring the study about stretching of HSA capsules in
planar elongation flow by de2015stretching which reports that these capsules
follow generalized Hooke’s law with Poisson’s ratio of 0.4 [de2015stretching].

The deformation study of HSA capsules in elongational flow and the atomic
force microscopy (AFM) technique allowed the estimation of surface shear
modulus and 3-D Young’s modulus in the small deformation limit. A combination
of these two methods revealed that Young’s modulus and membrane thickness both
increase with the HSA concentration and size of the capsule
[de2014mechanical]. Studies on the influence of protein concentration and the
size of the microcapsule on the mechanical properties of the HSA microcapsule
membrane using the microfluidic technique suggest that as the size and the HSA
concentration increase, the shear modulus also increases [gires2014mechanical,
gubspun2016characterization, de2016tank]. Simultaneous fabrication and
characterization of HSA microcapsules using a microfluidic (double flow-
focusing setup) technique have been reported in the literature; however, it is
difficult to remove the excess unreacted precursor and to make stable capsules
with this technique. The study also showed that as the reticulation time
increases, the shear modulus also increases [chu2013fabrication].

Studies have been conducted on ovalbumin capsules to understand their
mechanical characteristics. The study of the deformation of ovalbumin capsules
under shear flow through a cylindrical microchannel at different flow rates
showed that the use of a Neo Hookean law gave a constant value of shear
modulus in the low deformation regime [lefebvre2008flow]. The study comparing
the mechanical and chemical characterization of ovalbumin capsules, done using
the microfluidic technique and combined with determining free amino groups
using the TNBS method, shows that the shear modulus and the amino groups are
nearly constant with the reaction pH for the capsules fabricated after 5 min
of reticulation. The shear modulus increases with the reaction time, while the
$NH_{2}$ content decreases with it, indicating the conversion of progressive
amines to amides. An overall increase in shear modulus with pH is also
observed for ovalbumin capsules, similar to the HSA capsules
[chu2011comparison], but with an unexpected rise in $NH_{2}$ content.

Very few studies have been conducted on the viscoelastic characterization of
microcapsules. The theoretical studies considered the Kelvin-Voigt model to
describe the viscoelastic properties of the membrane under shear flow
[barthes1985role, yazdani2013influence]. An experimental study was performed
by chien1978theoretical on the erythrocyte membrane in which the Kelvin-Voigt
model was used to find the membrane viscosity using the micropipette
technique. Recently, alginate-coated chitosan capsules were studied using the
microelectromechanical (MEMS) microgripper technique, and the Kelvin model was
used to find the viscoelastic characteristics of these microcapsules
[kim2009elastic]. The viscoelastic properties of oil-in-water vitamin A
capsules coated with starch were studied using the four-element Burger model
[zhang2019effect]. Similarly, urea-formaldehyde microcapsules showed
viscoelastic characteristics, and the relaxation was described by the three-
element Maxwell model [han2019investigation]. Recently, a novel method has
been developed, by integrating a deep convolutional neural network with a
high-fidelity mechanistic capsule model, to predict the membrane viscosity and
elasticity of a microcapsule from its dynamic deformation when flowing in a
branched microchannel [lin2021high].

Only a few studies have been reported on the viscoelastic properties of water-
in-water HSA microcapsules. The study of tank treading motion of HSA
microcapsules indicates that these capsule membranes are viscoelastic in
nature, and the membrane viscosity was computed from the measurement of the
period of rotation of the membrane [de2016tank]. The transient response of
cross-linked HSA capsules was studied by flowing capsules through a sudden
expansion, and comparing the characteristic time scales of the capsule
relaxation with a complete numerical model of the relaxation of a capsule
flowing in a rectangular channel. The study shows that the crosslinked HSA
membrane is viscoelastic and that the relaxation is solely a function of the
ratio of the relaxation time to the flow convective time [gires2016transient].

In the present work, we use the electrodeformation technique to study the
viscoelastic properties of HSA microcapsules using creep and oscillatory
tests. An elasto-electrohydrodynamic model is used to compute the membrane
elasticity and viscosity by corelating the fitted parameters of five element
spring dashpot model. The dynamics of the deformation of the capsule was
studied at constant electric stress for different frequencies to study the
effect of frequency on membrane rheological properties. The electrodeformation
method allows interfacial rheological studies at very high frequencies, not
easily accessible in conventional interfacial rheometers.

##  2 Materials and methods

Human serum albumin protein standard (P8119), span 85, chloroform,
terepthyalyolchloride, and silicone oil (350 cSt) were obtained from Sigma
Aldrich. Cyclohexane was obtained from Imparta chemicals, and pH 7.4 PBS
buffer from LOBA chemicals. All the chemicals were used as procured.

(a)

(b)

Figure 1: Schematic representation of (a) reaction mechanism (b) membrane
formation mechanism for HSA microcapsule (not to the scale) Figure 2:
Methodology for the synthesis of human serum albumin microcapsules

###  2.1 Methodology for synthesis of HSA capsules

Figure 1 shows the probable reaction mechanism for the formation of the
membrane of HSA microcapsules. HSA from the aqueous phase adsorbs at the oil-
water interface and subsequently unfolding of proteins can occur, making the
buried functional groups, amine, ester, and hydroxylic of proteins present in
the aqueous phase available for reaction with the chloride group of the
crosslinker terephthaloyldichloride present in the oil phase, to form amide,
ester, and anhydride bonds. Adsorption and unfolding phenomenon of a protein
depend on the reaction parameters, such as protein concentration and pH. At a
high concentration of HSA, there might be competition between adsorption and
the unfolding process resulting in the multilayer film formation. The
hydrophobic $\beta$-sheets would mostly be on the oil side and the
$\alpha$-helix would be on the aqueous side of the membrane.

The HSA microcapsules were synthesized by the conventional method of
interfacial polymerization of HSA using the emulsification technique with
terephtyalyol chloride as the crosslinking agent [levy1991fourier] as shown in
Figure 2. The lyophilized HSA was dissolved in the phosphate (pH 7.4) or
carbonate (pH 9.2) buffer to make solutions of different [10, 20, and 30
percent (weight/volume)] concentrations of HSA. Note, % w/v= 100 gms of
solute/100 ml of solution. Thus, a 10% HSA solution had 0.1 gms of HSA/100 ml
of solution, or 100 mg/ml of HSA. Around $100\mu l$ of the HSA solution was
then added to cyclohexane containing 5 percent (volume percent) span 85 and
stirred at a constant speed of about 600 rpm for 5 min, to produce an emulsion
of aqueous droplets containing HSA dispersed in cyclohexane. The cross-linker
terepthylyoldichloride (0.25 percent weight/volume), dissolved in (1:4)
chloroform cyclohexane mixture, was then added to this emulsion, and the
polymerization reaction was stopped after 15 min by dilution of the reaction
media. The capsules were washed gently thrice with an organic phase to remove
the excess crosslinker.

In the present work, we use the notations $HSA_{10}$, $HSA_{20}$, and
$HSA_{30}$ to represent capsules synthesized with PBS buffer at pH 7.4 with
concentrations of 10, 20, and 30 percent HSA respectively. A HSA capsule
synthesized with carbonate buffer at pH 9.2 for 20 percent HSA is represented
as $HSA_{20},pH9.2$. Poly-dispersed microcapsules were formed by this method
in the size range of 10 $\mu m$ to $400$ $\mu m$. Any one of these capsules
from the emulsion was then used for more detailed interfacial study and the
size of such a capsule was estimated from images obtained using light
microscopy. The size distribution of the suspension of capsules (See Figure
LABEL:fig:size_distribution provided in Supplementary Information) was studied
using instrument particle size analyzer (Horiba LA 960). It should be noted
here that for size measurement using the particle size analyzer, the capsules
were resuspended in water, by removing the organic solvent using excess water.
Thus the size of the capsules obtained using the Horiba (LA 960) are only
indicative of the actual water-in-oil, crosslinked capsules, synthesized using
the water-in-oil emulsion (For details see Supplementary Information).

###  2.2 Scanning electron microscopy (SEM) studies for HSA capsules

The morphology of microcapsules was studied using the scanning electron
microscopy (SEM) technique. Freshly synthesized capsules were placed on an
aluminum foil using the drop-casting method and the organic phase was
evaporated at room temperature to get the dry sample. The samples were coated
with platinum for 60 s. Imaging was carried out in the dry mode at 5 kV with
various magnifications ranging from 45X to 50,000X.

###  2.3 FTIR studies on capsules

The seccondary structure of proteins has been widely studied using the FTIR
spectroscopic technique, especially the Amide-I, Amide-II band
[singh1993fourier, usoltsev2020ftir, yang2015obtaining, usoltsev2020ftir]. The
microcapsules synthesized using the method described, were centrifuged and
washed thrice with the organic phase and thrice with deionized water, and
finally suspended in deionized water. The lyophilized microcapsules were then
studied using the standard procedure for a wavelength range of 6250 to 5882 nm
using the FTIR (Bruker, Germany, 3000 Hyperion Microscope with Vertex 80 FTIR
System) instrument.

###  2.4 Experimental set-up for electrodeformation study:

Figure 3: Electrodeformation experimental set-up

The experimental set-up (see Figure 3) consisted of two copper electrodes of
$45$ mm in height, 1 mm in thickness, and 1 cm wide, attached to the inner
sidewalls of a plastic cuvette. The distance between the copper electrodes was
kept as $4$ mm. A required voltage difference was applied across the copper
electrodes with the help of a function generator (33220A Agilent Technologies
Pvt. Ltd., USA) that had a voltage range of $0-20$ V. The frequency of the ac
voltage used in this work, was in the range of (1Hz-1kHz). The function
generator was connected to a high voltage amplifier TREK (model 20/20C-HS) of
fixed gain $2000$ $V/V$ to generate the desired amplified voltage.

For the mechanical characterization, a single microcapsule was manually placed
in the cuvette containing 350 cSt silicone oil with the help of a
micropipette. As the electric field was applied, the capsule deformed into an
ellipsoidal shape in the direction of the field. The complete
electrodeformation video (when the field is switched on and also after
switching off the field) was recorded with the help of a high-speed
videography (by Phantom V12 camera), attached to a stereo-microscope (Leica
z16AP0) at $200-70000$ frames per second. A light source (Nikon) was used for
illumination and image analysis was performed using the ImageJ software
(https://imagej.nih.gov/ij/).

The deformation of the microcapsules was estimated by defining a modified
Taylor parameter.

$D=\dfrac{((l/L)-(b/B))}{((l/L)+(b/B))}$ (1)

Where L, B, l, and b are the initial major and minor axes of the original
undeformed and deformed capsule before and after the application of the
electric field respectively. The surface Young’s modulus is calculated using
Eq.2 (See [karyappa2014deformation] for details), which relates electric
capillary number ($Ca_{e}$) to deformation (D), as expressed below.

$D=\dfrac{16}{45}Ca_{e}$ (2)
$Ca_{e}=\dfrac{aE_{o}^{2}\epsilon\epsilon_{o}}{E_{s}}$ (3)

Here, $E_{o}$ is the RMS value of the applied electric field, a is the radius
of a capsule, $\epsilon_{o}$ is permittivity of free space, $\epsilon$ is the
dielectric constant of the medium and $E_{s}$ is the surface Young’s modulus
of a membrane (N/m).

###  2.5 Viscoelastic model for the study of rheological properties of
microcapsules

(a)

(b)

Figure 4: (a) Schematic of spring-dashpot visco-elastic model (b)
Corresponding schematic of stress-strain constitutive equation for elasto-
electro-hydrodynami model

In the present work, we describe the rheological characteristics of the human
serum albumin capsules using the five-element Burger model. The five-element
viscoelastic model (Figure 4) consists of two Kelvin-Voigt elements and one
dash-pot arranged in series used for fitting the deformation versus time data
for creep experiments. The complete response, that is deformation with respect
to time, for a step-stress is proportional to $a\epsilon\epsilon_{e}E_{o}^{2}$
for $t<t_{o}$ is given by,

$D(t)=\left(\frac{1}{k_{1}}\left(1-e^{-t/\tau_{1}}\right)+\frac{1}{k_{2}}\left(1-e^{-t/\tau_{2}}\right)+\frac{t}{\eta_{o}}\right)a\epsilon\epsilon_{o}E_{o}^{2}$
(4)

and for $t>t_{o}$

$D(t)=\left(\frac{1}{k_{1}}\left(e^{-(t-t_{o})/\tau_{1}}-e^{-t/\tau_{1}}\right)+\frac{1}{k_{2}}\left(e^{-(t-t_{o})/\tau_{2}}-e^{-t/\tau_{2}}\right)+\frac{t_{o}}{\eta_{o}}\right)a\epsilon\epsilon_{o}E_{o}^{2}$
(5)

where $\tau_{1}=\eta_{1}/k_{1}$ and $\tau_{2}=k_{2}/\eta_{2}$.

Note that the elastic and viscous constants $k_{1}$ , $k_{2}$, $\eta_{1}$,
$\eta_{2}$, in the spring-dashpot model, do not exactly represent membrane
elasticity and viscosity. It is expected that $\eta_{1}$, $\eta_{2}$ should
represent the solution viscosity $a\mu_{e}$ shown in Figure 4 (b)) and
membrane viscosity $\eta_{m}$, respectively, with $k_{1}$, $k_{2}$,
representing the membrane surface elasticity. A more accurate way is to have
these spring-dashpot constants expressed as equivalent frame invariant stress-
strain measures, which when solved in the spherical coordinate system, yield
non-trivial geometry and property dependent parameters (such as viscosity
ratio etc).

Therefore an viscoelasto-electrohydrodynamic model developed in our earlier
work [puri2022study] which relates the parameters of the spring dash-pot model
with the elasticity, membrane viscosity and solution viscosity as mentioned
earlier, that is $\eta_{1}\sim\mu_{e}a$ and $\eta_{2}\sim\eta_{m}$, while
$k_{1}\sim E_{s}$ and $k_{2}\sim E_{y}$ is used. The interfacial stress-strain
relationship for this 4-element linearised elastic model is given by,

$\displaystyle\tau_{\theta\theta}^{el}+2\frac{E_{s}\eta_{p}+E_{s}\eta_{m}+E_{2}\eta_{p}}{E_{s}E_{2}}\frac{\tau_{\theta\theta}^{el}}{dt}+\frac{\eta_{m}\eta_{p}}{E_{s}E_{2}}\frac{d^{2}\tau_{\theta\theta}^{el}}{dt^{2}}=\eta_{p}\frac{d\epsilon_{\theta\theta}}{dt}+\frac{\eta_{m}\eta_{p}}{E_{2}}\frac{d^{2}\epsilon_{\theta\theta}}{dt^{2}}$
(6)
$\displaystyle\tau_{\phi\phi}^{el}+2\frac{E_{s}\eta_{p}+E_{s}\eta_{m}+E_{2}\eta_{p}}{E_{s}E_{2}}\frac{\tau_{\phi\phi}^{el}}{dt}+\frac{\eta_{m}\eta_{p}}{E_{s}E_{2}}\frac{d^{2}\tau_{\phi\phi}^{el}}{dt^{2}}=\eta_{p}\frac{d\epsilon_{\phi\phi}}{dt}+\frac{\eta_{m}\eta_{p}}{E_{2}}\frac{d^{2}\epsilon_{\phi\phi}}{dt^{2}}$
(7)

where subscripts "$\phi\phi$" and "$\theta\theta$" represent the azimuthal and
meridional quantities, and $\epsilon_{\theta,\theta},\epsilon_{\phi,\phi}$
represent the linearised strain. This coupled with the electric and
hydrodynamic stresses yields a relationship between the capsule deformation
and the elastic, electric, and hydrodynamic parameters. The detailed model
derivation is described in the Supplementary Information of our previous work
[puri2022study].

The equations (4, 5) were fitted (Figure 12) using the MATLB2019a and the
parameters $k_{1},k_{2},\eta_{1},\eta_{2}$, and $\eta_{o}$ were estimated. The
estimated fitting parameters are related to the elasticity, membrane
viscosity, solution viscosity by the detailed viscoelasto-electrohydrodynamic
model as mentioned in the Eq. 8.

$\displaystyle{k_{1}}=\frac{16{E_{s}}}{45}\text{;}\,\,\,\,\,{k_{2}}=\frac{16{E_{y}}}{45}\text{;}\,\,\,\,\,{\eta_{1}}=\frac{64a{\mu_{e}}}{105}\,\,\,\,\,{\eta_{2}}=\frac{32{\eta_{m}}}{45}\text{;}\,\,\,\,\,{\eta_{o}}=\frac{32{\eta_{p}}}{45}\text{;}$
(8)

###  2.6 Viscoelasto-electrohydrodynamic model for oscillatory test

The effect of frequency on the viscoelastic properties such as elasticity and
membrane viscosity was studied by applying an oscillatory (ac) electric field,
of varying frequencies, to the HSA microcapsules. The equations can be solved
using the Laplace Transform technique when a sinusoidal electric field is
applied. The equivalence between the complete hydrodynamic model and the
spring-dashpot Burgers model is again found to exist similar to that of step
stress case and the response is given by

$\displaystyle(D/a\epsilon\epsilon_{o}E_{o}^{2})=\frac{1}{2{k_{1}}}+\frac{1}{2{k_{2}}}+\frac{t}{2{\eta_{3}}}-\frac{2{\tau_{1}}^{2}\omega^{2}e^{-\frac{t}{{\tau_{1}}}}}{4{k_{1}}{\tau_{1}}^{2}\omega^{2}+{k_{1}}}-\frac{2{\tau_{2}}^{2}\omega^{2}e^{-\frac{t}{{\tau_{2}}}}}{4{k_{2}}{\tau_{2}}^{2}\omega^{2}+{k_{2}}}-$
$\displaystyle\left(\frac{1}{2\left(4{k_{1}}{\tau_{1}}^{2}\omega^{2}+{k_{1}}\right)}+\frac{1}{2\left(4{k_{2}}{\tau_{2}}^{2}\omega^{2}+{k_{2}}\right)}\right)\cos(2\omega
t)+$
$\displaystyle\left(-\frac{1}{4{\eta_{3}}\omega}-\frac{{\tau_{1}}\omega}{4{k_{1}}{\tau_{1}}^{2}\omega^{2}+{k_{1}}}-\frac{{\tau_{2}}\omega}{4{k_{2}}{\tau_{2}}^{2}\omega^{2}+{k_{2}}}\right)\sin(2\omega
t)$ (9)

where the relationship between the parameters of the spring dashpot Burgers
model to that of the full viscoelasto-electrohydrodynamic model remains the
same.

The above expression can be used to fit and estimate the
$E_{s},E_{y},\eta_{m}$ and $\eta_{p}$ values from the deformation time series
for each frequency.

###  2.7 Methodology for estimation of model parameters and confidence bounds

The variation of J(t) (ratio of deformation to electric stress) with time was
fitted using the equations 4, 5 and 8 to estimate the model parameters using
MATLAB R2019a and Fminsearchbnd [d2012fminsearchbnd] method for each capsule.
The rheological properties of HSA capsules was estimated by fitting the mean
deformation of all capsules for estimating the rheological properties from the
fitting of plotted mean deformation with respect to stress. The confidence
bounds were estimated for the parameters estimated from mean deformation of
all capsules. We computed the confidence bounds for the estimated parameters
using the F test [namdeo2022palladium].

##  3 Results and discussion:

###  3.1 Different time scales in the system

The formation of a cross-linked protein film at an oil-water interface
proceeds through several steps at different rates. When proteins are dispersed
in an aqueous solution, they can self-aggregate. The time scale of self-
aggregation of HSA molecules to form oligomers seems to be of the order of few
microseconds, indicating that the formation is instantaneous, and aggregate
sizes of around a few hundred nanometers have been
reported[chubarov2020reversible]. The aggregated and non-aggregated protein
molecules then migrate to the oil-water interface over time scales of
$a^{2}/D\sim(300\mu m)^{2}/(6\times 10^{-11})\sim 1500s$. The time scale
though could be shorter because of convection in the system on account of
stirring as well as very high concentrations of HSA used in this work, which
can effectively decrease intermolecular and interaggregate distance as well as
their distance from the interface.

The second relevant time scale is that of adsorption of proteins on the
surface. This is reported to be of the order of $1$ s [yano2012kinetics]. This
is followed by protein unfolding, at the oil-water interface, which is known
to occur over time scales of few seconds to minutes. Finally the crosslinking
is expected to be instantaneous due to very fast reaction. Further, growth of
the interfacial film can occur due to diffusion-controlled reaction since the
HSA present inside the drop phase needs to overcome the barrier of the
polymeric membrane formed to react further with the cross-linker present on
the oil side. The other time scale of relevance, which is the diffusion time
of TC to arrive at the interface is expected to be very short.

###  3.2 Characterization of capsules using Fourier transform infrared
spectroscopy (FTIR) technique:

Figure 5: Comparison of secondary structure of original HSA and HSA capsules
synthesized at different conditions

The amide -I band (1600–1700 cm–1), which has contributions from the $C=O$
stretching due to vibration of the amide group, the in-phase bending of the
N-H bond and the stretching of the C-N bond, is the most sensitive spectral
region representing changes in secondary structure of proteins
[yang2015obtaining]. Amide-II is derived mainly from in-plane N-H bending and
the C-N stretching vibrations and is more complex than Amide-I. Although this
band is conformationally sensitive, it has not been commonly used for
describing changes in protein structures. The other amide bands are rarely
used to study protein structure due to their complexity and dependence on the
details of the force field, the nature of side chains, and hydrogen
bonding[yang2015obtaining].

Figure LABEL:fig:ftir provided in Supplementary Information shows FTIR spectra
in full-range for pure HSA and cross-linked HSA microcapsules studied in the
present work. We analyzed the Amide-I band in detail to understand the
microstructure of the membrane of the microcapsules using quantitative
analysis of the Amide-I band contour, employing curve fitting, second
derivative, and Fourier self-deconvolution methods. A Gaussian curve-fitting
was conducted on deconvoluted spectra using OriginPro 2019b software. The
peaks obtained by deconvolution of the amide-I band are assigned to specific
types of secondary structure based on the known correlations between different
secondary structures ($\alpha$ helix, $\beta$ sheets, random coil) of proteins
and their FTIR spectra [levy1991fourier, litvinov2012alpha, singh1993fourier].

From Figure LABEL:fig:ftir (See Supplementary Information), it is clear that
there is a significant difference in the spectral peaks for uncrosslinked HSA
in aqueous solution and cross-linked capsules. The deconvoluted Amide-I
bandwidth spectra fitted for different cases of capsules as well as that of
lyophoilized uncrosslinked HSA is shown in Figure LABEL:fig:ftir_o and
LABEL:fig:FTIR_fit provided in Supplementary Information. Figure 5 shows
percentages of different elemental structures such as $\alpha$-helix,
$\beta$-sheets and random coils present in the capsules for different cases
considered in the present study. It is important to note here that although
the aqueous HSA molecules contain no $\beta$-sheets and have a completely
helical structure, the lyophilized HSA used in our FTIR study showed a
significant percentage of $\beta$-sheets. Infact, Figure 5 indicates that the
pure lyophilized HSA contains more $\beta$-sheets than the crosslinked HSA
capsules. It is known that lyophilization of protein leads to unfolding and
changes in their secondary structure, which upon rehydration in an aqueous
buffer, might be again refolded entirely or partially [lin2000stability].

The capsules synthesized with pH 9.4 buffer showed more $\beta$-sheet
formation than the capsules synthesized with PBS 7.4 buffer. This could be
attributed to greater disruption of the native structure at higher pH due to
charge repulsion. It is should be noted that the FTIR study was done on
lyophilized capsules with polydispersed capsules synthesized by the emulsion
technique. Therefore the variation of $\beta$ sheets with concentration at pH
7.4 can not be accounted due to polydispersity in the size of capsules. The
results of FTIR studies for different concentrations of HSA should be analyzed
with caution. The FTIR studies were conducted on a collection of capsules of
varying sizes, as obtained in the emulsion technique. As shown later in the
studies, the radius of the capsule can affect the crosslinking significantly.
The different percentages of $\alpha$-helix, $\beta$-sheets, and random coil
in capsules can result in different membrane surface morphologies, which
ultimately affect their mechanical properties. At low pH, free amines
participate in the reaction while at higher pH, the carboxylic groups can
ionise and participate in anhdyride bond formation along with ester bonds
formed by acylation of hydroxyl groups [levy1991fourier]. The involvement of
different functional groups in the crosslinking could affect the crosslinking
degree and formation of secondary protein structure.

###  3.3 Scanning electron microscopic results for membrane surface morphology

(a)

(b)

(c)

Figure 6: Scanning electron microscopy images for capsules prepared with 15
min reaction time with phosphate pH 7.4 buffer for (a) $HSA_{10}$ (b)
$HSA_{20}$ (c) $HSA_{30}$

(a)

(b)

Figure 7: Scanning electron microscopy images of HSA capsules synthesized with
carbonate buffer at pH 9.2 (a) 10 percent HSA, 20 min reaction (b)15 percent
HSA, 20 min reaction

Figure 6 shows the surface morphology of the microcapsule membrane for
different pH and concentrations of HSA studied in the present work using SEM
images. The different morphologies of capsules for different HSA
concentrations could be due to the fact that the interfacial adsorption and
unfolding phenomena depend upon the pH and concentration of HSA. These factors
affect the cross-linking and thereby, the membrane morphology. The degree of
cross-linking reaction and membrane microstructure depends upon the
availability of buried functional groups of a protein at the interface. This
in turn depends upon the protein conformational changes induced by a change in
interface environments such as pH, HSA molecules per unit area, and the nature
of the interface (aqueous, organic, air).

Figure 6 indicates that $HSA_{10}$ capsules show relatively smoother
morphology than that for the other cases. SEM images showed that tiny
microcapsules are adsorbed on the surface of bigger microcapsules in the case
of $HSA_{10}$. The adsorbed smaller capsules show very smooth membrane surface
morphology. This is possibly because the surface concentration of the protein
$\Gamma=4/3\,a\,C$, where $C$ is the bulk HSA concentration for a capsule with
size $a$. Thus reduction in size leads to lower surface concentration, lower
reaction rates, and thereby lower crosslinking and a smoother surface, aided
by lower surface concentration. It should be mentioned here that the capsules
synthesized with the emulsification method give a wide range of size
distribution, and hence the smaller and larger microcapsules prepared with the
same HSA concentration showed different morphology. Similar to $HSA_{10}$,
smaller microcapsules with $HSA_{20}$ also showed relatively smoother membrane
morphology than bigger microcapsules.

In the case of $HSA_{20}$ (Figure 6 b), for the similar sized capsules, the
capsules showed a rougher membrane surface than for the case of $HSA_{10}$,
possibly due to higher concentration of HSA. The microcapsules synthesized
with $30\%$ HSA concentration showed a much different microstructure ( Figure
6 c) than for the other two cases ($HSA_{10}$ and $HSA_{20}$). For the case of
$HSA_{30}$, the capsules showed a wavy folded structure. Few microcapsules of
$HSA_{30}$ case showed pores on their membrane surfaces. The change in the
morphology for $HSA_{30}$ could be attributed to the formation of larger
oligomeric structures in the bulk at such high concentrations. These
oligomeric structures can assemble at the interface and form porous, weakly
crosslinked structures.

Capsules synthesized with carbonate buffer at pH 9.2 showed a very rough,
granular membrane surface with bigger pores ( Figure 7), identical to those
seen for $HSA_{30}$. It is known that HSA changes its configuration from
native form to a basic structure when pH changes from 7 to 9. This N-B
transition; results in exposure of the buried residues, leading to an increase
in exchangeable hydrogen and an increased bulk aggregation despite increased
charge stability. This is supported by the greater conversion of
$\alpha$-helix to $\beta$-sheets for pH 9.4 as seen in the FTIR studies. The
assembly of these bulk oligomers at the interface can lead to a porous
membrane morphology. Thus both high pH and high concentration can lead to
increased hydrophobicity and formation of oligomers in the bulk aqueous
solution. Further, we investigate the rheological properties of HSA capsules
using the electrodeformation technique.

###  3.4 Justification for the five-element Burger model:

The dynamic deformation of HSA capsules studied at different applied stresses
shows an instantaneous deformation followed by slow time-dependent
deformation. The instantaneous deformation can be related to the spring
element $k_{1}$, associated with the solution viscosity giving a fast
timescale. The $k_{2}$ and membrane viscosity ($\eta_{2}$), correspond to a
slow creep response. The nonrecoverable creep deformation, is captured by the
extra dashpot in series ($\eta_{o}$). From a microstructural viewpoint, the
occurrence of the elasticity can be attributed to the existence of
intermolecular bondings. It has been suggested in the literature that the
protein molecule exists on the surface in an unfolded structure, probably in
the form of straightened $\beta$-configuration resulting in the instantaneous
elastic response [inokuchi1953rheology]. The extent of various secondary
structural units such as $\alpha$-helix, $\beta$\- sheets, and random coils
and their conformational arrangements in cross-linked protein can result in
the different rheological properties of the membrane.

The literature does not present enough evidence on structure-rheology
relationships for crosslinked proteins. For example, it is unclear from the
literature if the proteins at the interface are folded or unfolded and the
extent of conversion of $\alpha$ helices into $\beta$ sheets, as well as the
percentage of intermolecular and intramolecular crosslinking. Based on the
limited literature [zhang2017self, brown1963physical, chan2020spider,
debenedictis2019mechanical, choe2005elasticity, hsin2011molecular,
buehler2008elasticity, ahmad2005guanidine] about the relation between
different structural units of protein with the mechanical characteristics, for
an interfacially crosslinked protein network, we propose a microstructure for
the microcapsules as follows:

  1. 1.

The interface is laden with proteins adsorbed from the bulk, either as single
molecules or as oligomers.

  2. 2.

The protein molecules then can unfold to varying degrees, typically, the
domains I, II, and III could break the quaternary structures without
significantly affecting their individual tertiary and secondary structures.

  3. 3.

Increased conversion of the $\alpha$-helix to the $\beta$-sheets indicates
increased hydrophobicity. This could lead to a higher oligomerization in the
bulk, or indicate a higher amount of unfolding at the interface, with
hydrophobic parts residing in the oil phase.

  4. 4.

The unfolded structures could get crosslinked, most likely in the bulk, with
the hydrophobic regions of the proteins anchored in the oil phase.

  5. 5.

The interfacial film is typically multi-layered. The microstructure of the
interfacial film and its crosslinking determines the rheological properties of
the microcapsule. Multilayered and thick films are known to have lower
rheological properties [puri2019study, jancar2008thickness].

One then expects two sources of elasticity. The anchored hydrophobic parts of
the proteins in the oil phase yield an elastic response, which is resisted by
the viscosity of the oil. This is expected to result in an instantaneous
deformation, which could be attributed to the stretching of $\beta$-sheets.
The subsequent creep could be because of the uncoiling of $\alpha$-helices and
random coil structure and the viscous resistance arising out of internal
friction of the protein domains, giving the viscoelastic effect. The secondary
structure can rearrange with the conversion of $\alpha$-helix into
$\beta$-sheets during the deformation, and hence the plastic deformation
(unrecoverable creep) can be attributed to the irreversible changes in the
secondary structure of a protein membrane.

###  3.5 Estimation of rheological characteristics of microcapsule membrane

Figure 8: Dynamic deformation response HSA capsule for different electric
stresses

(a)

(b)

Figure 9: Deformation with respect to electric capillary number for HSA
microcapsules synthesized with different HSA concentrations at pH 7.4 (a)
$HSA_{10}$, (b)$HSA_{20}$

(a)

(b)

(c)

Figure 10:  Interfacial rheological properties (a) elasticity, (b) membrane
viscosity, and (c) unrecoverable creep at different stresses obtained from
model fitting

(a)

(b)

Figure 11: Dynamic deformation for HSA microcapsules suspended in 350 cSt
silicone oil at constant electric field (1kHz) synthesized at pH 7.4 with 10
percent HSA concentration Figure 12: Creep compliance fitted with respect to
time for HSA microcapsules at constant applied electric field at 1 kHz (solid
line shows model fitted)

We first investigated surface elasticity using the approximate analysis method
from the small deformation theory. In any typical electrohydrodynamic
experiment, a single capsule was suspended in pure silicone oil (350 cSt) in a
plastic cuvette, with copper electrodes attached at its inner sidewalls, and a
uniform electric field (1 kHz) was applied for about 2 s. As the electric
field was switched on, the capsule was deformed to an ellipsoidal shape in the
direction of an applied electric field while, after switching off the electric
field, it relaxed back as shown in Figure 8. The dynamics of the deformation
was studied at different electric fields until the capsule burst. The temporal
data of deformation clearly shows signature of creep (Figure 8). The surface
Young’s modulus was calculated using the small deformation theory from the
linear regime of deformation versus electric capillary number plot as shown in
the Figure 9. Since the temporal deformation data shows significant creep, as
a preliminary approach, we considered steady deformation value at the end of
signal that is at 2 sec for computing surface elasticity by using the Eq. 2
(See [karyappa2014deformation] for details), which relates the electric
capillary number ($Ca_{e}$) to deformation (D).

Figure 9 clearly shows that the HSA capsules exhibit strain-softening, for
both $HSA_{10}$ and $HSA_{20}$, as indicated by deviation of the $D$ vs
$Ca_{e}$ curve from linearity at higher capillary numbers. This is in
agreement with the observation from other studies about HSA capsules in the
literature [gires2014mechanical, gubspun2016characterization]. A more accurate
way of analysis is to fit the viscoelastic spring dashpot model to the dynamic
deformation curve. Therefore, for each of the experiments in the $D$ vs
$Ca_{e}$ data, a 4 element Burger model was fitted to the temporal data of
deformation, and the variation of $E_{s},E_{y},\eta_{m}$ and $1/\eta_{p}$
(unrecoverable creep) are plotted (Figure 10). The results indeed show strain
softening ($E_{s}$, $E_{y}$ decrease with the electric stress).

For a more detailed analysis of the viscoelastic properties of the HSA
capsules, we performed creep tests using the electrodeformation method, and
the Burger model described previously was fitted to compute their rheological
properties. The creep tests were performed at very low electric stress (left
side of dotted lines shown in the Figure 9) to ensure that the experiments
were in the linear viscoelastic regime. To get the estimate of the duration of
application of electric stress required to study creep in capsules till it
reaches the secondary stage, we applied constant low electric stress for the
different duration as shown in Figure 11. The results indicate that applying
stress for 10 sec was sufficient to study creep behaviour. Increasing the time
of application of electric field could lead to large deformations, and
rendering the system non-linear.

For the creep test, a low electric stress (0.0024-0.0045 $N/m$) was applied to
the capsule suspended in 350 cSt silicone oil for 10 s. We continued video
recording of electrodeformation experiments for further 10 s to capture creep
recovery after switching off the field. For each experiment, a new capsule was
used. The creep compliance J(t), which is the ratio of deformation to stress,
is plotted with respect to time for three sample data sets. The five-element
spring dashpot model was fitted individually for each capsule using the
MATLAB2019a as shown in Figure 12 and an excellent fit with the theoretical
model was observed. The correlation between the fitted model parameters with
the viscoelasto-electrohydrodynamic model was used to compute the interfacial
rheological properties of HSA capsules. Following this methodology, around 76
capsules were studied using the creep test, and each data point reported was
averaged over around 3-8 capsules.

(a)

(b)

Figure 13:  Interfacial rheological properties elasticity ($E_{s}$, $E_{y}$)
membrane viscosity ($\eta_{m}$), and unrecoverable creep ($1/\eta_{p}$)
obtained from model fitting for (a) capsules synthesized with different HSA
concentrations (b) for different capsule sizes and HSA concentrations.