1. Introduction
Emulsion polymerization processes are one of the most common polymerization processes to produce high-solid-content polymer dispersions. In contrast to suspension polymerization, emulsion polymerization promotes higher solid contents, better heat transfer, faster polymerization rates, and better colloidal stability. A vast variety of polymers and stabilizers are already well-characterized. Accessible products range from low to high density polymers, branched and stretched, and homo- as well as co-polymers. Given the great variety of polymers, many different types of products and different product applications can be achieved [
1,
2].
The precise analysis of particle size and particle size distribution (PSD) is of the utmost importance for liquid polymer dispersions. These properties play an important role as they define the usage and applications of polymer dispersions, e.g., the fluidity and stability of high-solid-content polymer dispersions [
3]. The mean particle size of polymers depends on many thermodynamic and kinetic factors during their synthesis, like the solubility of the monomer–polymer, composition of the reactants, temperature, solvent-to-medium ratio, or even reactor geometry [
2,
4]. The final mean particle size and PSD during emulsion polymerization are further influenced by the monomer amount introduced and the capability of the stabilizer in the dispersion to sustain the colloidal stability of the particles growing. The amount of stabilizer added accounts for the amount of particles formed and, therefore, also the final mean particle size [
5].
To access the mean particle size in high-solid-content polymer dispersions and to determine the PSD, different techniques are known and promoted like turbidimetry, fiber-optic quasi-elastic light scattering or focused beam reflectance measurement, and particle vision and measurement technology. Online measurements in undiluted processes are particularly challenging due to the high turbidity, high number of particles, and multiple scattering [
6,
7,
8,
9,
10,
11]. Most commonly, offline PSD analysis is used. However, offline techniques require extensive sample preparation like dilution, are time consuming, and are not easy to handle. Additionally, dilution always induces a change in the particle system, whose effects on the measurement are not well-known. Analysis of nanoparticle size distribution is possible by multiple techniques. Laser light-scattering techniques are shown to deliver reliable results; however, adding to the extensive sample preparation and dilution, the results are influenced strongly and shifted by the fractions of bigger particles in the sample. For multimodal or very polydisperse samples, light-scattering techniques lack resolution [
12,
13,
14,
15].
Input parameters for measurements like the solvent viscosity, the refractive index, the sample concentration, and the sample temperature play a significant role and are compulsory. Necessary sample dilution evidently affects these factors and provokes falsified results. For dynamic light scattering (DLS) measurements, the dilution of the sample affects the autocorrelation function and the resulting particle size. For samples with high particle concentration, i.e., high solid contents, the Stokes–Einstein equation is no longer valid and diffusion coefficients yield wrong hydrodynamic radii [
16,
17,
18,
19]. Photon density wave (PDW) spectroscopy offers dispersion analysis of highly turbid particle systems or emulsions without dilution by the independent experimental determination of the optical coefficients, reduced scattering coefficient and absorption coefficient, respectively [
20,
21,
22,
23]. This technique is used in this study to determine the PSD in undiluted concentrated polymer dispersions and compared to the DLS, Static Light Scattering (SLS), and Electron Microscopy (EM) analysis of diluted samples.
In this work, two polymer systems are produced and thoroughly analyzed—polystyrene (PS) particles, stabilized by sodium dodecyl sulfate (SDS), and polyvinyl acetate (PVAc), stabilized by poly (vinyl alcohol, PVA). The respective chemical structures of the polymers and stabilizers used in this study are shown in
Figure 1. Stabilizers are shown in their deprotonated form. It is reported in literature that PS and SDS are not prone to incorporating water, due to their hydrophobic character, whereas PVAc and PVA, due to their significantly more hydrophilic character, especially PVA with plenty of accessible hydroxyl groups also shown in
Figure 1, are not only known to bind water loosely by van der Waals interactions, but are also able to build hydrogen bonds, which bind the water strongly to the hydrophilic sites [
24,
25,
26,
27]. Due to the polarizability of SDS, it is possible that water molecules attach to the surfactants surrounding the polymer, but the amount and effect on the particle will be significantly lower than for the PVA stabilized particles. The hydrophobic aklylchains will attach to the polymer and few loose interactions happen with the surrounding media and water.
Three states of bound water were found to be present in PVA: free water, bound–freezable, and bound–non-freezable water, which has nearly the same characteristics as bulk water [
28,
29,
30]. The amount of freezable water accounts only for a very small percentage and is, therefore, complicated to detect. Only a combination of different thermal analyses may be able to determine the amount of water in the PVAc-PVA particle [
31,
32,
33]. It is assumed that the PVAc-PVA particles are swollen with water and also have a swollen emulsifier shell around the PVAc particle core. The degree of swelling is hard to determine due to the different kinds of water-binding mechanisms. The swelling of the polymer particle has a significant influence on the density and refractive index of the particle as well as the solid content and the volume ratio between the PVAc polymer core, polymer shell, and medium in the dispersion. These are the main factors that have a great influence on the PSD measurements. A lot of data on polymer swelling in literature concentrates on the swelling of dry polymer films in water or the swelling of hydrogels [
34,
35,
36]. In this study, undiluted measurements of PVAc-PVA particles are analyzed regarding the swelling of the particle with the medium in high-solid-content dispersions.
For both systems, PS-SDS and PVAc-PVA, particles with various mean particle sizes and PSD can be obtained by emulsion polymerization [
5,
37,
38]. The polymers can be produced in numerous shapes, co-monomer compositions, and sizes from a few nanometers to the upper micrometer size regime [
5,
39,
40]. To produce mean particle sizes between 50 and 500 nm, seeded emulsion polymerization was performed. Seeded emulsion polymerization is a well-known method to produce monodisperse PS dispersions.
Starved-feed emulsion polymerization was used to produce PVAc-PVA particles between 100 and 500 nm mean particle size [
20,
41,
42].
2. Materials and Methods
All chemicals were used and handled as described. Styrene was purchased from different suppliers throughout the experiments (104.15 g mol−1, ≥99.5%, Carl Roth, Karlsruhe, Germany and Merck, Darmstadt, Germany). Sodium dodecyl sulfate (SDS, 288.38 g mol−1, Carl Roth, Karlsruhe, Germany), di-sodiumtetraborate decahydrate (Na-Tetra Borate, 381.37 g mol−1, ≥99.5%, Carl Roth, Karlsruhe, Germany), sodium hydroxide (NaOH, 40.0 g mol−1, ≥99%, Carl Roth, Karlsruhe, Germany), aluminum hydroxide (AlOH3, dried gel, 78.01 g mol−1, 99%, abcr GmbH, Karlsruhe, Germany), and potassium peroxodisulfate (KPS, 270.32 g mol−1, ≥99%, Carl Roth, Karlsruhe, Germany) were used as purchased.
Prior to use, the styrene was destabilized by filtering over granulated AlOH3 in a flash column and, afterwards, washed repeatedly in 1 M NaOH using a separating funnel. The styrene showed a light transparent-yellowish color and was further handled at room temperature. Monomer vinyl acetate (VAc, 86.09 g mol−1, ≥99%, Sigma-Aldrich, Darmstadt, Germany) was purged with N2 (Nippon Gases, Duesseldorf, Germany) for 30 min prior to synthesis. Redox initiator pair ascorbic acid (AA, 176.12 g mol−1, 99%, Acros Organics, Geel, Belgium) and sodium persulfate (NaPS, 238.10 g mol−1, ≥99%, Carl Roth, Karlsruhe, Germany) and catalyst ammonium iron (III) sulfate hexahydrate (FAS, 392.14 g mol−1, 99+%, Acros Organics, Geel, Belgium) were used as purchased. Mowiol® 4-88 (polyvinyl alcohol, approx. 31,000 g mol−1, Sigma-Aldrich, Darmstadt, Germany) was used as purchased.
2.1. Synthesis
Preparation of solutions was performed with analytical grade Milli-Q® water from an in-house Milli-Q® water dispenser (Milli-Q®, Integral 5, Merck Millipore, Darmstadt, Germany). An automated lab reactor (OptiMax 1001, Mettler Toledo, Gießen, Germany) at approx. 1 L reaction scale was used for synthesis. Produced polymer dispersions were stored in airtight containers and showed no sign of destabilization for over twelve months.
2.1.1. PS Seed Synthesis
Batch emulsion polymerization was used to produce PS particles with a narrow size distribution to be used further as seed particles. The recipe for the seed synthesis is given in
Table 1.
Emulsion polymerization was started by charging 500 g of Milli-Q® water in the 1 L batch reactor. Under stirring at 100 rpm and N2 purging, the initial charge (iC) was heated to 100 °C for 60 min to degas. Temperature was reduced to 55 °C over 45 min. At 55 °C reaction temperature, 135 g styrene, 6.2 g SDS in water, and 0.125 g of Na-Tetra Borate were added. After a short waiting period for the emulsion to form, 30 mL of a 5% KPS solution were added automatically via a computer-controlled dosing unit at 6 mL min−1. Simultaneously, the stirrer was ramped to 200 rpm. The emulsion was left to polymerize at 55 °C reaction temperature for 24 h. After 24 h, a post-polymerization step at 83 °C for 3 h was initiated. The system was cooled to 20 °C over 30 min.
2.1.2. PS-Seeded Emulsion Polymerization
To produce PS nanoparticles of different mean particle sizes, seeded emulsion polymerization was performed. A small amount of the PS seed produced after
Table 1 was taken and the particles were grown to various mean particle sizes, as shown in
Table 2.
2.1.3. Emulsion Polymerization of Polyvinyl Acetate Dispersions
Recipe for the produced PVAc-PVA dispersions is shown in
Table 3 with determined density of the pure polymer and gravimetrically derived solid content after at least 48 h drying at 74 °C in an oven. Details on the emulsion polymerization process can be found in Schlappa et al. [
20].
2.2. Dispersion Analysis
After completion of a synthesis, offline sample analysis was performed. After approx. 400-fold dilution with Milli-Q® water to visual transparency, three repetition measurements of each sample were performed by DLS analysis (Zetasizer Ultra, Malvern Panalytical, Worcestershire, UK), at measurement angle of 173°, in disposable 4 mL PS cuvettes, at 25 °C measurement temperature. Samples for SLS measurements (LS13320, Beckman Coulter, Brea, CA, USA) were manually diluted approx. 1:125 with Milli-Q® water and charged to the SLS sample chamber until a polarization intensity differential scattering (PIDS) signal of approx. 40% was achieved. Obscuration values lower than 2% were retained. Results shown for PSDs obtained by light-scattering techniques are mean values of three measurements. Out of the three individual measurements, the mean value is plotted with one standard deviation as error bars. For electron microscopy (EM) analysis, samples were diluted approx. 1000-fold with Milli-Q® water and a drop of sample was placed onto a copper-coal mesh (Plano GmbH, Wetzlar, Germany). The sample was left to dry for an hour at ambient conditions. Quanta FEI 250 electron microscope was used for analysis in STEM mode.
2.3. PDW Spectroscopy Dispersion Analysis
Photon density wave (PDW) spectroscopy is among few techniques which offers dispersion analysis by the determination of the optical coefficients of a highly turbid particle system without dilution even at high solid contents of the dispersed species. The PDW spectroscopy device used here is self-built (University of Potsdam—innoFSPEC, Potsdam, Germany). No sample preparation is needed as the optical fibers can directly be inserted into the dispersion for measuring. Two optical fibers are immersed into the undiluted dispersion. These fibers act as light emission and detection source for intensity-modulated laser light. The detection fiber is mounted to a precision translations stage which moves in scalable distances to and from the emission fiber. Fibers used in this set-up have a 600 µm core diameter. Intensity-modulated laser light (10–1210 MHz) is guided into the sample via the emission fiber and interacts with the sample regarding the samples’ absorption and scattering properties. Due to the multiple scattered light, a PDW is expressed. A small portion of the PDW light is guided to an avalanche photo diode by the detection fiber. The electronic signal is amplified and then analyzed by a network analyzer with respect to phase shift and amplitude. The change in amplitude and phase in dependency of the distance between the emission and detection fiber and the modulation frequency can be related to the absorption coefficient µa and reduced scattering coefficient µs’ of the sample. These optical coefficients can be obtained for different wavelengths one after another.
The reduced scattering coefficients are used to determine the mean particle size and particle size distribution, with the help of the Mie theory and the theory of dependent scattering [
22,
43]. Highly turbid polymer samples have already been successfully analyzed and characterized by PDW spectroscopy regarding their mean particle diameter and PSD [
44,
45,
46,
47]. Inline monitoring of emulsion polymerization processes has also been successfully reported [
20,
21,
48,
49,
50].
In this study, two polymer systems were evaluated, one which is not prone to incorporating water and one where water swelling of the particles is common, to show the differences in analyzing the particle size by PDW spectroscopy if water swelling of particles occurs. To determine the mean particle size and PSD, theoretical µs’ values are calculated that match the experimentally determined µs’ values by the applied PDW spectroscopy algorithm. If experimental and theoretical values agree well with each other, it can be assumed that the swelling, and particle characteristics represent the actual situation in the dispersion. To theoretically reproduce the experimentally determined µs’, the refractive index, and density of the polymer and medium as it is present in the dispersion, as well as the solid content, an assumption of the mean particle diameter and width of a normal logarithmic Gauss distribution are necessary for a data fit. In a first step, the solid content will be determined gravimetrically. A small weighted sample is placed in a drying cabinet at low temperature (74 °C) in order to keep the polymer intact. Drying was achieved over a period of time >72 h to evaporate the medium and bound water inside the polymer. The dry weight is measured at mass consistency, and the solid content calculated.
A concentration series of 30% (
w/
w), 20% (
w/
w), 10% (
w/
w), 1% (
w/
w), and 0.1% (
w/
w) of each polymer dispersion was used to determine the density of the polymer particles. Each sample was measured at 20 °C with a densitometer (DM45 Delta Rage, Mettler Toledo, Gießen, Germany). Density analysis of the particles for the pure polymer (100% (
w/
w)) was performed by [
49]:
with
ρDisp,
ρD, and
ρP as densities of the dispersion, the dispersant, and the polymer and the solid content
w of the dispersion. The density of pure water was considered for zero polymer content (0% (
w/
w)). The density of the polymer was obtained from the slope of a linear fit; the error was obtained via error propagation.
The same samples were also used for refractive index measurements with a multi-wavelength refractometer (DRS-λ, Schmidt + Haensch, Berlin, Germany) at 20 °C at seven different wavelengths between 403 and 938 nm. The measured refractive indices are extrapolated to the refractive index of the particles using the Newton equation and, afterwards, inter- or extrapolated to the wavelengths of PDW spectroscopy by a Cauchy formula [
49,
51].
To speed up the PDW calculations, estimates of the mean particle size and PSD can be introduced based on offline reference methods or theoretical particle size considerations. With these parameters, a first PDW spectroscopy fit is obtained within a few minutes.
In the case that this first fit of theoretical
µs’ does not match the experimental results, high error values
Χ2 for the
µs’ fit are given by the software. The value of
Χ2 expresses how well the theoretically calculated values agree with the experimentally determined values and is a measurement of the fit quality. If
Χ2 values are high, modifications of the input parameters are necessary, as the particle in solution expresses different properties as determined by this first rough estimation of its physical properties. Literature data already suggest that the bound water inside the PVAc-PVA polymer cannot be dried off completely by only drying in an oven. A combination of different thermogravimetric techniques is necessary to determine the exact water content, which is very time consuming, costly, and complicated. The water-swollen polymer in solution does not express the same properties like in a dried state. To validate the mean particle diameter and PSD measurement by PDW spectroscopy, iterative steps of water swelling
θswollen are assumed, affecting the density
, refractive index
, and volume fraction
of the polymer to a great extent. Various percentages of water swelling
θswollen in 0.05 steps (from 0% to 50%) are assumed and added to the experimentally derived solid content. A new volume fraction for the particle affected by water swelling is calculated:
with this new volume fraction of the swollen polymer
, adjusted values for the density (Formula (1)) and refractive index (Formula (3)) are recalculated.
with the recalculated refractive index of water-swollen polymer as
nP,swollen, the increased volume fraction
φP,swollen, and the refractive index of the non-swollen particle
nP and dispersant
nD. These recalculated values are used with the assumed mean particle size and PSD to recalculate
µs’ by the automated PDW spectroscopy algorithm. The resulting
µs’ values are compared to the experimental values again and the
X2 error parameter for the fit of theoretical-to-experimental
µs’ is analyzed. The smaller the
X2, the better the agreement between experimental and theoretical values, meaning the better the fit quality, and the water-swelling factor
θswollen is assumed to represent the real properties of the particles in the analyzed dispersion.
This iterative approach is carried out for several percentages of water swelling until the lowest possible X2 value is found, starting with 10% water-swelling steps, finding the lowest X2 and minimizing the steps up to 1%. A parabola fit is used to find the minimum of X2 of the theoretically determined PDW spectroscopy fits. This percentage of water swelling represents the experimental data best and it can be assumed that the polymer is swollen with water by the derived percentage.
For comparison between size distribution data from DLS, SLS, and PDW spectroscopy, the mean particle diameter calculated from the volume frequency distributions are normalized regarding the bin width. PSDs are usually shown in different types of distributions. Most common types include intensity, number, and volume-based PSDs. PDW spectroscopy provides a volume-based PSD with a mean particle diameter comparable to the so-called De Brouckére mean (
d43). The DLS measurement used for comparison gives a PSD in volume from measuring the hydrodynamic radius, calculated from an intensity weighted measurement [
52,
53,
54]. To compare particle size distributions derived from PDW spectroscopy to distributions derived from offline, dilution-based techniques, an area normalization of the distribution is done. Normalization results in volume frequency distributions per nanometer (
f3) for every measurement method.