The Cluster Size and Change of Water Molecules in Poly(vinyl alcohol) Film by Heating

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1 Transaction The Cluster Size and Change of ater Molecules in Poly(vinyl alcohol) Film by Heating Saori Tamura 1,# and Ryo Oono 1 1 Graduate School of Home Economics, Kyoritsu omen s University, 2-2-1, Hitotsubashi, Chiyoda-ku, Tokyo , Japan Abstract: The cluster size of water molecules in poly(vinyl alcohol) (PVA) film was determined using the cohesive energy equation and the heat of evaporation of water. On the heating process of PVA film, the mass of evaporated water was measured by thermogravimetric analysis (TGA) and the heat of evaporation was measured by differential scanning calorimetry(dsc). The evaporation energy and the cluster size are closely related each other, and the size was calculated using the equation of cohesive energy which contains surface energy. As a result, the size of water cluster in 0% relative humidity (RH) film was about 13.2 molecules, 40% RH film was 6.6 molecules and 80% RH film was 3.5 molecules, respectively. The cluster size in 0% RH and 40% RH films are likely to contain errors caused by the overestimation of evaporation energy. In the film of 80% RH, the clusters of 3.5 molecules were absorbed at a ratio of one cluster per 5.3 repeating units of PVA chain. The cluster size was calculated at various temperatures in the order of evaporation. The average cluster size in 80% RH film was about 1-2 molecules on the film surface and it was about 3.5 molecules in the inside of film. (Received 25 January, 2015 ; Accepted 14 July, 2015) 1. Introduction The physical properties of polymer strongly depend on the amount of absorbed water. Therefore, it is very important to reveal the amount of absorbed water and the binding state between polymer and water. According to the previous papers on binding states, it is considered that there are three types of bound water, intermediate water and liquid water.[1-4] Bound water directly bind to the hydrophilic group of polymer in amorphous region and have properties that are completely different from the liquid water. Intermediate water bind indirectly to the polymer by binding to the bound water and liquid water move freely outside of the intermediate water. Similarly, poly(vinyl alcohol) (-CH2-CHOH- PVA) film contains three types of water. Another indication reveals that the characteristics of absorbed water may be understood by examining the size of water cluster. Because the cluster size corresponds to the binding state of absorbed water. So far, the size of water cluster in polymer has been estimated mainly using the Flory-Huggins theory and the Zimm-Lundberg theory.[5,6] The experimentally determined adsorption isotherm curves can be explained well based on these theories. [7-13] However, it is important to analyze also using the other theories. This paper reports the cluster size of # corresponding author absorbed water in PVA film which was analyzed by the cohesive energy equation. e assumed that the cluster is the aggregation of water molecule. Generally, a decrease in the cluster size causes an increase in the surface area and a decrease in the cohesive energy. The equation used in this study represents the total cohesive energy of a cluster as a function of a molecule number and surface area.[14,15] This equation was firstly applied to the melting and evaporation of Ar clusters and secondly applied to the aggregation of Ag atoms.[16] In this study, we applied this equation to the evaporation of the water cluster in PVA film. 2. Experimental 2.1 Materials PVA was purchased from Junsei Chemical Co., Ltd. (Tokyo, Japan) and had a 99.0% degree of hydrolysis, an average degree of polymerization of PVA film with a thickness of about 100 µm was prepared from a 4% aqueous solution of the polymer by pouring onto the polyethylene dishes, and then water was evaporated at 23 C under 40% RH during 3 days. After evaporation, the sample films were set under the humidity of 0%, 40%, 80% RH for 2 weeks at 23 C, and they reached to the equilibrium adsorption of water. Humidity conditioning of 0% RH film was performed with a vacuum dryer, and conditioning of 40% RH, 80% RH films were performed

2 by a humidity chamber (IG400, Yamato Scientific Co., Ltd., Tokyo, Japan). 2.2 Thermogravimetric analysis (TGA) The mass of water evaporated from the PVA film was measured by a thermogravimetric analysis instrument (2960SDT, TA Instruments, Delaware, U.S.A.). PVA films of approximately 10 mg were placed in an aluminum open cell on the sample stage and the temperature was raised from room temperature to 250 C at a rate of 1 C/min. The furnace was purged with nitrogen gas at the flow rate of 30 ml/min. 2.3 Differential scanning calorimetry (DSC) analysis The heat of evaporation of water cluster was investigated by a differential scanning calorimeter (DSC- 60, Shimadzu Corporation, Kyoto, Japan) under the same conditions as TGA measurement. 2.4 Fourier transform infrared (FTIR) analysis The degree of crystallinity of PVA films was measured by an infrared spectrometer (FTIR-610, JASCO Corporation, Tokyo, Japan) with heating unit. The crystallinity was calculated using the equation reported by Tretinnikov et al.[17] The equation consisted of the ratio of the intensities of the peaks at 1144 cm 1 and 1094 cm 1. The thickness of sample films was about 8 μm and the experiment was carried out in the temperature range of C. 3. Results and discussion 3.1 eight loss of PVA film by the evaporated water Fig. 1 shows TGA heating curves of PVA films. The weight loss due to evaporation strongly depended on the film thickness and the heating rate of temperature. By trial and error, the errors for both the TGA and DSC measurements were found to be the smallest for films with a thickness of 100 μm and a heating rate 1 C/min. The weight loss of PVA film decreased initially between room temperature and 150 C, stayed constant values between C, and decreased abruptly over 200 C. eight loss between room temperature and 150 C was due to the evaporation of water from PVA film.[18,19] This weight loss progressed monotonously and did not exhibit discontinuous change at the boiling point of at 100 C. It indicated that the water in PVA film do not boil because of the small amount of water in PVA film. These clusters may be consisted of bound water and intermediate water, and did not include free water which shows a boiling. In the constant weight range between C, the weight losses were 4.26 wt %, 5.50 wt %, and 12.3 wt % for the films stored at 0%, 40%, and 80% RH, respectively. The weight loss of 0% RH film was not zero, even if it was placed for more than two weeks in a vacuum chamber. These weight loss values correspond to the water content of PVA. eight loss over 200 C is due to thermal degradation and it was very large. Fig. 1 TGA heating curves of PVA films. Fig. 2 shows the derivative curves at the evaporation range in Fig. 1, i.e., the weight loss of PVA film per minute (=1 C). The shape of differential curves resemble a normal distribution. The curve of 0% RH could be approximated perfectly to the normal distribution with mean (μ) of 100 and standard deviation (σ) of The curve of 40% RH also could be approximated to the normal distribution with mean (μ) of 96 and standard deviation (σ) of There was only a slight difference at low temperature sides in two curves of 0% RH and 40% RH. The curve of 80% RH was asymmetric and could not be approximated to a normal distribution. The curves exhibited a nested structure each other, as the 0% RH curve is inside of the 40% RH and the 40% RH curve is inside of the 80% RH. The clusters on the surface of a film are likely to evaporate first and those at the center are likely to evaporate at the end. As mentioned above, this theory was assumed the simplify model. The nested structure of curves was relevant to the order of evaporation of water clusters. Fig. 2 Derivative curves of weight loss in the evaporation range in Fig. 1.

3 3.2 Heat of evaporation of water clusters from PVA film Fig. 3 shows the DSC curve of 40% RH film and it showed two endothermic peaks in the wide range of C and a melting peak at 228 C. The broad peak of C was due to the evaporation of water from the film. A small endothermic peak appeared at about 37 C before the evaporation in the curves of 0% RH and 40% RH. This peak was not observed in the curve for the 80% RH film. PVA does not have a specific temperature such as the glass transition in the vicinity of 37 C. If this peak was caused by the evaporation of water, it would also appear on the derivative curves of Fig. 2. However, the peak did not appear on the derivative curve. hile structural distortion caused by the drying process of the film may be considered to be one of the causes of the peak, the exact origin of the peak is uncertain. Fig. 3 DSC curve of 40% RH film during heating process. Fig. 4 shows the endothermic curves of the PVA films in the evaporation range obtained by DSC measurement and the curves were very similar in shape to those of Fig. 2. It indicated that the mass of evaporated water was nearly proportional to the amount of absorbed heat. The three curves differed significantly in the low temperature sides, but they were similar at temperatures above the peak temperature. The clusters near the film surface are likely to evaporate at lower temperature and those at the center are likely to evaporate at higher temperature. Therefore, the results indicate that the water clusters in 0% RH and 40% RH films were trapped mainly inside the film than those of 80% RH film. From the mass of evaporated water and the absorbed heat, the latent heat of evaporation, i.e., the endothermic heat divided by the weight loss, could be calculated. This latent heat is likely to include errors associated with the energy other than the energy for separating the water molecules from each other. One of the errors is the hydrogen bonding between water molecules and hydroxyl groups of the PVA molecular chain. Other errors may be caused by the passage of water molecules in the film, such as opening the closed pore or passing through at long distance. These errors will be discussed in a later section. Fig. 4 DSC curves of the PVA film in the evaporation range. Fig. 5 shows the latent heats of the evaporation of water clusters from PVA films, which were calculated using Fig. 2 and Fig. 4. A straight line in the upper part of the graph indicates the heat of evaporation of liquid water, which has been provided for comparison.[20] The heat of evaporation was high in the temperature range of C, and was low at the beginning and end of evaporation. The energy curves of 0% RH and 40% RH films were similar to each other, except at around 80 C. The maximum values of the heat of evaporation for the various films were ranked in the following order : 0% RH > 40% RH > 80% RH. This result contradicts the prediction, since both the cluster size and the heat of evaporation increase with increase in environmental humidity. It is believed that this contradictory result is caused by energy contributions other than the energy required to separate water molecules from each other. 3.3 Binding energy equation of a cluster From the heat of evaporation shown in Fig. 5, it was possible to calculate the size of water clusters. The total Fig. 5 Latent heat of the evaporation of water cluster from PVA film.

4 cohesive energy of a cluster is represented by the surface energy of fine particles using the following equation. 2 E( N)= NEb 4πR γ (1) here E (N ) is the total binding energy of a cluster as a function of particle number N. N is the cluster size ( = the number of particles in a cluster ) which is related to the cluster radius as R =rsn 1/3. Eb is the bulk binding energy per atom, and γ is the surface tension. rs is the radius of a sphere corresponding to the volume of one atom in bulk. This equation was originally applied to the analysis of melting and evaporation of Ar clusters.[14] Subsequently, it was applied to the surface energy of Ag nanoparticles. [16] e apply this equation to the evaporation of water clusters from PVA film. In this case, an Ar atom was replaced with a water molecule, and the surface energy and the binding state of water clusters were assumed to be equivalent to those of liquid water. Furthermore, each term of this equation was multiplied by the factor 1/(NMw) to convert the energy unit from per N molecules to per gram of water. In the multiplying factor, Mw is the mass of a water molecule, i.e., Mw=18.015/( )g. EN ( ) Eb rs = 4 2 π γ 13 / NM M N M here the left-hand side term E (N )/(NM) is the evaporation energy per gram of water in PVA film (J/g), and the value obtained from Fig. 5 was used for this term. Eb/Mw is the evaporation energy per gram of liquid water (J/g) and was approximated by the following formula at a temperature T C, based on the literature.[21] E M b T T = ( ) πrs 2 in the second term in right-hand side of Eq.2 is the cross area of a water molecule. However, a water molecule is not spherical like an Ar atom. Therefore, the volume of a water molecule was approximated by a cube of one side length of 1/(d/Mw) 1/3. d is the density of water, and the cross area of a water molecule was approximated by πrs 2 =( Mw/d ) 2/3. e used the equation of d reported by G. S. Kell.[22] The surface tension γ of water was represented by the equation reported by Vargaftik, et al.[23] 3.4 Calculation of a cluster size This equation was first applied to determine the total heat of evaporated water from PVA film. The mass loss of the 0% RH film was 4.26 wt % per gram of PVA film and its heat of evaporation was J/g. hen this (2) (3) value is converted to per gram of water, this heat is equivalent to the evaporation energy E (N )/(NM) of 1926 J/g. Although evaporation occurred in the temperature range between room temperature and 150 C, we assumed that all of evaporation occurred at 100 C, in order to simplify the calculations. At 100 C, the other values are as follows. The energy of evaporation of liquid water Eb/ Mw was J/g, density of water dwas g/cm 3, cross area of a water molecule πrs 2 was cm 2, surface energy γ was J/cm 2. As a result, the calculated cluster size N of 0% RH film was 13.2 molecules and this size could be regarded as an average value throughout the entire evaporation process. hen we calculated in the same manner, the mass loss of the 40% RH film was 5.50 wt %. The heat of evaporation from PVA film was J/g and this value was equivalent to the evaporation energy E (N )/(NM)of 1840 J/g. The cluster size N of 40% RH film was 6.6 molecules. Similarly, the mass loss of the 80% RH film was 12.3 wt %, heat of evaporation from PVA film was J/g. This heat was equivalent to the evaporation energy E (N )/(NM) of 1742 J/g and the cluster size N was 3.5 molecules. This cluster size of 3.5 molecules is overestimation, owing to the calculation at 100 C. Because the center of distribution of evaporated mass was located at about 80 C, as evident from Fig. 2. Cluster size decreased with increase in the environmental humidity of film. This result is in conflict with previous papers.[10, 11] e discussed later. Next, we considered the cluster size in detail at various temperatures. Fig. 6 shows the logarithm of the size N of water cluster calculated similarly as the above. N was logarithmic notation since N was distributed widely over the range of The cluster size was small at the beginning and end of evaporation and had the maximum value at C. The maximum size of 0% RH film was 209 molecules at 80 C, 40% RH film was 27 molecules at 100 C and 80% RH film was 3.5 molecules at 100 C, respectively. ater cluster is likely to evaporate in the order from small clusters near the surface of a film. Therefore, it is improbable for 0% RH film to have the maximum cluster at 80 C in the early stage of evaporation. Evaporation energy from the PVA film of 0% RH contains energy other than the hydrogen bond between water molecules which cause errors. Other types of energy include those associated with a weak bond between methylene group of PVA and water, hydrogen bond between hydroxyl group of PVA and water, hydrogen bond between hydroxyl groups of PVA, the movement of the segment of PVA molecular

5 chain, the passing energy of trapped water molecules, and so on. Of these energy contributions, factors associated with dry are the hydrogen bond between hydroxyl groups of PVA chains and the passing energy of trapped water molecules. Therefore, the increase in N due to drying of the film may be caused by hydrogen bonding between hydroxyl groups of PVA chains formed with traces of evaporated water and by the passing energy of trapped water molecules. Fig. 7 Degree of crystallinity of PVA film measured by FTIR. Fig. 6 Cluster size of water in PVA film. This phenomenon corresponds also to the degree of crystallinity of PVA film, as evident from Fig. 7. The degree of crystallinity of three samples were constant until 80 C and increased monotonously with increase in temperature between C. In Fig. 5 the evaporation energy of 0% RH film exhibits a peak at 80 C and this is a boundary temperature. This boundary temperature of 80 C is the glass transition temperature of PVA.[24] In this way, the movement of the segment of PVA chains depend strongly on temperature and water content. This constraint of the movement of the segment caused the differences in curves in Fig. 6 and Fig. 7. The movement of the segment is mainly restrained by the hydrogen bonding between hydroxyl groups of PVA chains in amorphous region.[4,25] The evaporation energy is large, especially when water molecules pass through closed pores below the glass transition temperature. The constraint by the hydrogen bonding between hydroxyl groups was weakest for 80% RH film, because its water content was the highest in three films. Therefore, 80% RH film exhibited the lowest energy and the flat peak in Fig. 5. The result of 80% RH film was most accurate and those of 0% RH and 40% RH films contained errors. From the above results, the state of water molecules absorbed in a PVA film were examined. Since the PVA film of 0% RH had a degree of crystallinity of 33.1% and water content of 4.26 wt % at room temperature, it was calculated that a PVA chain in amorphous region absorbed the cluster of average 13.2 molecules per 81.2 repeating units of PVA. Similarly, the PVA film of 40% RH had a degree of crystallinity of 33.0% and water content of 5.50 wt %. A PVA chain in amorphous region absorbed the water cluster of 6.6 molecules per 30.9 repeating units. The film of 80% RH had a degree of crystallinity of 47.8% and water content of 12.3 wt %. A PVA chain absorbed the water cluster of average 3.5 molecules per 5.3 repeating units. In details of various temperatures, the cluster size in 80% RH film in Fig. 6 was about 2 molecules until 70 C and was about 3 molecules between C. The increase in cluster size at 80 C may be caused by the change in evaporation from near the film surface to inside according to the weight distribution of Fig. 2. The average size of 2-3 molecules is likely to contain bound water and intermediate water, but free water is likely to be a little. Fig. 8 shows the mass distribution of cluster size of 80% RH film estimated by Fig. 2 and Fig. 6. Although particle number is integer, the distribution is shown with the number of decimal point for accuracy. Although the size of cluster is expected to be exhibit a continuous distribution with one peak, it is found to be a discontinuous distribution with two peaks. One of these peaks is 2 molecules and another peak is 3.5 molecules. The exact cause of the two peaks is unknown, but the peak of 2 molecules may be due to clusters near the surface and the peak of 3.5 molecules may be due to clusters inside the film. This conclusion based on the fact that the step at 80 C in the 80% RH curve in Fig. 6 became a boundary with 2 molecules and 3 molecules. Another feature of this distribution is that there is no cluster containing over 3.5 molecules. Large cluster in fact, contained a few. The equations for cohesive energy and surface energy can be used to calculate only the average cluster size. For this reason, a cluster containing more than 3.5 molecules was probably truncated.

6 in PVA film of 80% RH contained an average of 3.5 molecules per 5.3 repeating units of PVA. e could calculate the cluster size at various temperatures in the order of evaporation. The average cluster size was found to be about 1-2 molecules on the film surface and about 3.5 molecules from inside. References Fig. 8 Distribution of cluster size of 80% RH film. e have compared the results with that of wood reported by Rawat et al.[10] The cluster size of water in wood by the analysis based on the Zimm-Lundberg theory was 1-2 molecules up to 90% RH and reached 10 only at 98% RH. Haxaire et al. reported on the hydration of hyaluronan polysaccharide, and showed that they absorbed water molecules as the sigmoid curve of environmental humidity.[11] Our results showed that the cluster size decreased with an increase in the environmental humidity. This discrepancy arises mainly from our estimation of evaporation energy, which contains other energies rather than that dissociated the water molecules from each other. Another reason for the discrepancy may be the measurement of sorption isotherms based on the Zimm-Lundberg theory, where only molecules near the film surface are accounted for and molecules trapped inside the film are not considered. However, if the result for 80% RH films is correct, we can say that the cluster size calculated based on different theories are in good agreement. 4. Conclusions On the heating process, the water cluster size in PVA film was calculated using the evaporation energy of water and the cohesive energy equation. The mass loss of evaporated water was measured by TGA and the heat of evaporation was measured by DSC. The evaporation energy of water cluster per gram was calculated as the heat of evaporation divided by the loss of mass. Although DSC is not generally suitable for precise measurements of evaporation energy, we got the results with low errors, by choosing the appropriate film thickness and the heating rate of temperature. As a result, the cluster size in 0% RH film was about 13.2 molecules, 40% RH was about 6.6 molecules and 80% RH film was about 3.5 molecules, respectively. The cluster sizes in 0% RH and 40% RH films are likely to contain errors caused by the overestimation of evaporation energy. The water clusters 1. Lee, H. B., Jhon, M. S. and Andrade, J. D. J. Colloid Interface Sci., 51, (1975). 2. Scherer, J. R., Bailey, G. F., Kint, S., Young, R., Malladi, D. P. and Bolton, B. J. Phys. Chem., 89, 312 (1985). 3. Ping, Z. H., Nguyen, Q. T., Chen, S. M., Zhou, J. Q. and Ding, Y. D. Polymer, 42, (2001). 4. Sekine, Y. and Fukazawa, T. I. J. Chem. Phys., 130, (2009). 5. Flory, P. J. J. Chem. Phys., 9, (1941). 6. Zimm, B. H. and Lundberg, J. L. J. Phys. Chem., 60, (1956). 7. Starkweather, H.. Polym. Lett., 1, 133 (1963). 8. Starkweather, H.. Jr. Macromolecules, 8, (1975). 9. Hartley, I. D., Kamke, F. A. and Peemoeller, H. ood Sci. Technol., 26, (1992). 10. Rawat, S. P. S. and Khali, D. P. J. Polym. Sci. Part- B, 36, (1998). 11. Haxaire, K., Maréchal, Y., Milas, M. and Rinaudo, M. Biopolym. Biospectrosc., 72, (2003). 12. Olek,., Majka, J. and Czajkowski, L. Holzforschung, 67, (2013). 13. Davis, E. M. and Elabd, Y. A. J. Phys. Chem. B., 117, (2013). 14. Rytkönen, A., Valkealahti, S. and Manninen, M. J. Chem. Phys., 106, (1997). 15. Rytkönen, A., Valkealahti, S. and Manninen, M. J. Chem. Phys., 108, (1998). 16. Nanda, K. K., Maisels, A., Kruis, F. E., Fissan, H. and Stappert, S. Phys. Rev. Lett., 91, (2003). 17. Tretinnikov, O. N. and Zagorskaya, S. A. J. Appl. Spectrosc., 79, (2012). 18. Tsuchiya, Y. and Sumi, K. J. Polym. Sci. A-1, 7, (1969). 19. Thomas, P. S., Guerbois, J. P., Russell, G. F. and Briscoe, B. J. J. Therm. Anal. Cal., 64, (2001). 20. In CRC Handbook of Chemistry and Physics 85th Ed., David, R. L., Ed., CRC Press, New York, p 6-3 (2004).

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