• 沒有找到結果。

Specific interactions in miscible polymer blends of poly(2-hydroxypropyl methacrylate) with polyvinylpyrrolidone

N/A
N/A
Protected

Academic year: 2021

Share "Specific interactions in miscible polymer blends of poly(2-hydroxypropyl methacrylate) with polyvinylpyrrolidone"

Copied!
7
0
0

加載中.... (立即查看全文)

全文

(1)

DOI: 10.1002/pi.1271

Specific interactions in miscible polymer

blends of poly(2-hydroxypropyl methacrylate)

with polyvinylpyrrolidone

Shiao-Wei Kuo,

1

Chien-Chou Shih,

2

Jye-Shiou Shieh

1

and Feng-Chih Chang

1∗

1Institute of Applied Chemistry, National Chiao Tung University, Hsin Chu, Taiwan

2Chemical Systems Research Division, Chung Shan Institute of Science and Technology, Lungtan, Taoyuan, Taiwan

Abstract: The miscibility behaviour and hydrogen-bonding interaction in blends of poly(2-hydroxypropyl methacrylate) (PHPMA) with polyvinylpyrrolidone (PVP) were characterized using differential scanning calorimetry and Fourier-transform infrared spectra. This polymer blend was miscible over the whole composition range and an unusually large positive deviation of Tgfrom the linearity rule was observed, indicating strong hydrogen bonding between the hydroxyl group of PHPMA and the carbonyl group of PVP. Infrared spectroscopic analysis provided positive evidence for the intra-molecular hydrogen bonding of PHPMA and inter-molecular hydrogen bonding between PHPMA and PVP at various compositions and temperatures. Furthermore, equilibrium constants and enthalpies of self-association and inter-association between functional groups in the blend of PHPMA and PVP were calculated to explain the results.

 2004 Society of Chemical Industry

Keywords: miscibility behaviour; hydrogen bonding; PHPMA; PVP

INTRODUCTION

Miscible polymer blends have been of great interest to material scientists as a result of improved or modified physical properties of the individual constituent poly-mers. However, from a thermodynamic viewpoint, miscibility behaviour is rarely achieved in polymer blends owing to the high degree of polymerization that provides a small entropy change. As a result, the for-mation of miscible polymer blends can be achieved through specific interactions, such as hydrogen bonding,1 – 3ionic interaction,4 – 6charge-transfer

com-plex formation, and a copolymer repulsion effect.7 – 9

In general, hydrogen-bonding interaction is consid-ered to be the driving force for miscibility and its important role in the miscibility of polymer blends has been widely described. In earlier studies,1 – 3

hydrogen-bonded donor polymers can be divided into two cate-gories. The first category is the simple self-association polymers, such as nylons and polyurethanes, which have both donor and acceptor functional groups. The two-equilibrium-constant model for self-association polymers gives rise to the second category of poly-mers, such as polyvinylphenol (PVPh), phenolic resin, phenoxy resin and poly(vinyl alcohol), because the self-association equilibrium constant describing dimer formation should be different from that for multimer formation, based on infrared spectra analysis.1

Poly(2-hydroxypropyl methacrylate) (PHPMA) has a special chemical structure that includes the hydroxyl donor group and the carbonyl acceptor group. We consider that this polymer is a simple self-association polymer, like the nylons or polyurethanes. As far as we know, few studies have been reported concerning the hydrogen bond that exists between the PHPMA and second functional polymers. Goh and coworkers10

studied the PHPMA complexation with three ter-tiary amide polymers containing poly(N-methyl-N-vinylacetamide), poly(N,N-dimethylacrylamide) and poly(2-ethyl-2-oxazoline). Katime and coworkers11

also studied the hydrogen bonding between PHPMA and polyvinylpyridines. However, the self-association equilibrium constant of PHPAM and the inter-association equilibrium with the functional group of the second polymer have not been investigated. In this present study, we determine the self-association equi-librium constant of PHPMA and the inter-association equilibrium constant between the PHPMA and the polyvinylpyrrolidone (PVP).

Polyvinylpyrrolidone is a water-soluble tertiary amide and a strong Lewis base that possesses good biocompatibility, and devices based on hydrogels of this material have found several medical applications. PVP was chosen for this study because the amide group is known to be a stronger hydrogen-bond acceptor

Correspondence to: Feng-Chih Chang, Institute of Applied Chemistry, National Chiao Tung University, Hsin Chu, Taiwan

E-mail: [email protected]

Contract/grant sponsor: National Science Council, Taiwan, Republic of China; contract/grant number: NSC-91-2216-E-009-018 (Received 31 October 2002; accepted 20 March 2003)

(2)

than the carbonyl group of poly(methyl methacrylate) (PMMA) or the ether group of poly(ethylene oxide) (PEO). It has been shown to form miscible blends with a large number of polymers such as polyvinylphenol,12

phenoxy resins,13 poly(vinyl alcohol),14 poly(vinyl

fluoride)15and poly(vinyl chloride).16In our previous

study, we have found that the wavenumber and half-width of PVP absorptions in the infrared spectral analysis are sensitive to the dipole interaction or hydrogen bonding with molecules or polymer chains. Furthermore, the glass transition temperatures of PVP-based polymer blends or copolymers have a good correlation with these specific interactions.17

In this study, the polymer blend of PHPMA with PVP was investigated using differential scanning calorimetry (DSC) and Fourier-transform infrared spectrum (FTIR). In addition, equilibrium constants and enthalpies of self-association and inter-association between functional groups in blends of PHPMA and PVP were calculated to explain the experimental results of these blends.

EXPERIMENTAL Materials

The poly(2-hydroxypropyl methacrylate) (PHPMA) was purchased from Aldrich Chemical Company with molecular weights of Mn= 24 000 and Mw=

32 700 g mol−1. The polyvinylpyrrolidone (PVP) with molecular weight of Mw= 58 000 g mol−1 was

pur-chased from Acros Chemical Company, Inc.

Preparation of polymer blends

Solution blends (5% wt/vol) of PHPMA and PVP in N,N-dimethylformamide were prepared by mixing appropriate amounts of each polymer. Each solution was allowed to evaporate slowly at 50◦C for 1 day. The film of each blend was then dried at 80◦C for 2 days to ensure total elimination of solvent.

Thermal analysis

Differential scanning calorimetry was performed with a Du-Pont (DSC-9000) instrument. Sample weights of 5 – 10 mg, and a heating rate of 20◦C min−1 were used. The sample was first heated from 30◦C to 210◦C and kept at that temperature for 10 min. It was then quickly cooled to 30◦C in the DSC cell and maintained at that temperature for another 3 min. The glass transition temperature was then obtained as the inflection point of the increase in heat capacity with a scan rate of 20◦C min−1 temperature range of 30 to 250◦C.

FTIR spectroscopy

Infrared spectra were measured on a Nicolet Avatar 320 FTIR spectrophotometer and 32 scans were collected with a spectral resolution 1 cm−1. Infrared spectra of polymer blend films were determined by using the conventional NaCl disk method. The DMF solution containing the blend was cast onto

a NaCl disk and dried under conditions similar to those used in the bulk preparation. Films used in the FTIR measurements were sufficiently thin to be within the absorbance range where the Beer – Lambert law was obeyed. IR spectra recorded at elevated temperatures were obtained by using a cell mounted inside the temperature-controlled compartment of the spectrometer.

RESULTS AND DISCUSSION Thermal analysis

The most widely used criterion for the judgment of the miscibility behaviour of polymer blend is the existence of a single glass transition temperature. The Tg dependence on composition is shown in

Fig 1. All PHPMA/PVP blends have only a single

Tg, suggesting that these are fully miscible blends with

a homogeneous amorphous phase. Moreover, a single

Tg higher than that of either individual polymer was

observed. This large positive deviation reveals that strong hydrogen bonding must exist between these two polymers. It has been generally suggested that the Tgrelationship to the composition of the miscible

polymer blends follows the Kwei equation:18

Tg=

W1Tg1+ kW2Tg2

W1+ kW2

+ qW1W2 (1)

where w1 and w2 are weight fractions of the

components, Tg1and Tg2represent the corresponding

glass transition temperatures, and k and q are fitting constants. In this study, k= 1 and q = 130 were

Glass transition temperature (

°C) PHPMA fraction Experimental data Kwei equation k = 1, q = 130 Linearity rule 160 150 140 130 120 110 100 90 80 1.0 0.8 0.6 0.4 0.2 0.0

Figure 1. Tgversus composition curves based on: () experimental

(3)

obtained from the non-linear least-squares ‘best fit’ values. Here q is a parameter corresponding to the strength of hydrogen-bonding in the blend, reflecting a balance between the breaking of the self-association and the forming of the inter-association hydrogen bonding. In this study, a positive q value of 130 was obtained, indicating a strong intermolecular interaction between PHPMA and PVP. In our previous study,12 we found that the q value of

PVPh/PVP blend was 140; we therefore expect that the hydrogen bonding strength of the PHPMA/PVP blend is slightly weaker than that of the PVPh/PVP blend.

Infrared spectroscopy analysis

The chemical structure of the pure PHPMA has both a donor hydroxyl group and an acceptor carbonyl group. If we can make a suitable infrared measurement using the pure PHPMA, the self-association equilibrium constant of pure PHPMA can be determined by using the following simple equation:1

KB=

fHB

(fF)2

(2)

where the KB is the self-association equilibrium

con-stant of pure PHPMA, and fHB and fF represent

the fractions of hydrogen-bonded and free carbonyl groups of the PHPMA, respectively. Figure 2 illus-trates the FTIR spectra of the pure PHPMA measured at temperatures from 130◦C to 180◦C. We chose these high temperatures because they are above the glass transition temperature of the PHPMA, so that equilibrium conditions can be retained. Figure 2(a) shows the hydroxyl-stretching region of the pure PHPMA at various temperatures. The pure PHPMA shows a narrow half-width hydroxyl stretching, reveal-ing that the hydrogen-bonded conformation is simpler between the hydroxyl and the carbonyl of the PHPMA.

In contrast, the pure phenolic resin or polyvinylphenol shows a very broad hydroxyl stretching region (the two-equilibrium-constant model for self-association polymers). The half-width of hydroxyl-stretching of the pure PHPMA is similar to that of nylon 6 or polyurethanes (simple self-association polymers) showing a very narrow absorption.1 In addition, the hydrogen-bonded hydroxyl band of the pure PHPMA tends to shift to a higher frequency, from 3512 cm−1 to 3532cm−1, with increasing temperature, indicating that the hydrogen bonding is decreased with increasing temperature, and this has been well documented.

Figure 2(b) shows that the carbonyl-stretching frequency of the pure PHPMA splits into two bands,9 absorptions by the free and hydrogen-bonded carbonyl groups at 1730 and 1710 cm−1, respectively. These two bands can easily be resolved into two Gaussian peaks, as shown in Fig 2(c), and the ratio of these two absorptivities (a= a2/a1) is

equal to 1.5, according to previous infrared studies of hydroxyl – carbonyl inter-association.1 The

curve-fitting results are summarized in Table 1, indicating that the hydrogen-bonded fraction of the carbonyl groups decreased with the increase of temperature. Therefore, the self-association equilibrium constant of pure PHPMA can be determined using eq (2), and its corresponding hydrogen-bonding enthalpy can be determined by the Van’t Hoff relationship

K= −h

RT + C (3)

Meanwhile, the self-association equilibrium constant in this temperature range based on the Van’t Hoff expression can be calculated and extrapolated to room temperature as shown in Fig 3. We obtained the self-association equilibrium constant at 25◦C (KB)

of the pure PHPMA as 3.17 and its hydrogen-bonding enthalpy (h) as −3.16 Kcal mol−1. The

(4)

Table 1. Curve-fitting of fraction of hydrogen-bonding results of the pure PHPMA at various temperatures Free C=O H-bonded C=O Pure PHPMA ν (cm−1) W1/2(cm−1) Af(%) ν (cm−1) W1/2(cm−1) Ab(%) fb(%)∗ 130 1729.6 20.0 56.85 1710.0 23.2 43.15 33.60 140 1729.5 20.2 58.00 1710.0 23.3 42.00 32.56 150 1729.3 20.5 59.82 1709.7 22.8 40.18 30.94 160 1729.3 20.8 61.26 1709.9 23.0 38.74 29.67 170 1729.2 21.1 62.13 1709.8 22.9 37.87 28.90 180 1728.9 21.6 64.93 1709.3 22.6 35.07 26.50

fb: fraction of hydrogen bonding.

relatively smaller self-association equilibrium constant observed for the pure PHPMA compared with the pure polyvinylphenol (KB = 66.8)1 reveals a greater

steric-hindrance effect in the pure PHPMA.

We now turn our attention to the hydrogen-bonded blends of PHPMA/PVP; Fig 4 shows a scale-expanded infrared spectrum in the range 2700 – 4000 cm−1 of a PHPMA/PVP blend at room temperature. The pure PHPMA shows two bands in the hydroxyl-stretching region of the infrared spectrum, corre-sponding to free hydroxyl at 3525 cm−1 and the hydrogen-bonded hydroxyl – carbonyl of the PHPMA at 3430 cm−1, respectively. The frequency difference between the hydrogen-bonded hydroxyl absorption and free hydroxyl absorption (υ) is a rough esti-mate of the average hydrogen-bonding strength and its enthalpy in a hydrogen-bonding blend system.19

Com-pared with the polyvinylphenol/poly(methyl methacry-late) blend system, the υ is about 125 cm−1,1 corresponding to a hydrogen-bonding enthalpy of −3.75 Kcal mol−1. In this study, the υ of the pure

PHPMA is 95 cm−1, corresponding to a hydrogen-bonding enthalpy of about −3.16 Kcal mol−1, which is in good agreement with previous infrared spectra analysis, with measurement at various temperatures.

Figure 4 also illustrates that the hydrogen-bonded hydroxyl and carbonyl group absorbance of PHPMA shifts to a lower wavenumber with increase of the PVP content. Concurrently, the intensity of the free hydroxyl group decreases gradually with an increase of PVP content, as would be expected. This

Figure 3. The Van’t Hoff relationship for pure PHPMA.

Figure 4. FTIR spectra recorded at room temperature in the

4000–2700 cm−1region for PHPMA/PVP blends.

result reflects a new distribution of hydrogen bond formation resulting from the competition between the hydroxyl – carbonyl group of pure PHPMA and the hydroxyl of PHPMA and the carbonyl of PVP. It also reveals that the interaction of the hydroxyl of PHPMA and the carbonyl of PVP become dominant in PVP-rich blends. Therefore, it is reasonable to assign the band at 3350 cm−1 to the hydrogen-bonding interaction between the hydroxyl of PHPMA and carbonyl group of PVP. Hydrogen-bonding interaction between hydroxyl of PHPMA and carbonyl of PVP (υ= 175 cm−1) is stronger than the hydroxyl – carbonyl interaction of the pure PHPMA (υ= 95 cm−1) and this is consistent with the observed positive q value in the Kwei equation. In the PVPh/PVP blend, the υ is 325 cm−1, which provides even stronger hydrogen-bonding interaction

(5)

than that of the PHPMA/PVP blend, which is also consistent with the q value difference in the Kwei equation. The υ of PHPMA/PVP blend is 175 cm−1, which is equal to the υ of the pure PVPh.12

Therefore, the inter-association hydrogen-bonding enthalpy of PHPMA/PVP is about −5.2 Kcal mol−1 from this relationship.

Figure 5 shows infrared spectra of the carbonyl stretching recorded at room temperature, ranging from 1600 to 1780 cm−1 for the blends with various compositions. There are numerous possible interactions involved and the four most important are summarized in Scheme 1. As mentioned above, the carbonyl stretching of pure PHPMA splits into two bands, absorption by the free and hydrogen-bonded carbonyl groups at 1730 and 1710 cm−1, respectively. Meanwhile, the carbonyl stretching of PVP also splits into two bands at 1680 and 1665 cm−1, corresponding to the free and the hydrogen-bonded carbonyl groups, which can also be well fitted to a Gaussian function. The fraction of hydrogen-bonded carbonyl group of PVP can be calculated by using an appropriate absorptivity ratio (aR= aHB/aF= 1.3)

which has been discussed in our previous study.12 Table 2 summarizes results from these curve fittings, indicating that the carbonyl hydrogen-bonded fraction of PVP increases with the increase of the PHPMA content. Furthermore, the carbonyl of PVP shifts to only about 1665 cm−1, which is a smaller frequency than that of the PVPh/PVP blend (1660 cm−1). This result is also consistent with the

Kwei equation and analysis of infrared spectra on hydroxyl-stretching. Here, we need to emphasize that the fraction of hydrogen-bonded carbonyl of PHPMA cannot be calculated due to the overlapping with the

Figure 5. FTIR spectra recorded at room temperature in the

1780–1600 cm−1region for PHPMA/PVP blends.

free carbonyl of the PVP. However, we expect that the hydrogen-bonded carbonyl fraction will decrease with the increase of PVP content because most hydroxyl groups of the PHPMA will interact with the carbonyl

C C CH3 C C C CH3 C O O CH2 C CH3 HO Free carbonyl at 1730 cm−1 O O CH2 C CH3 O H Hydrogen-bonded carbonyl at 1710 cm−1 Free PVP carbonyl in pure PVP homopolymer 1680 cm−1 C N O CH2 CH CH2 CH C N O CH2 C C O O C O H CH3 CH2 CH3 Hydrogen-bonded carbonyl of PHPMA/PVP blend at 1665 cm−1 Scheme 1.

(6)

Table 2. Curve fitting of fraction of hydrogen-bonding results of the PHPMA/PVP blends at room temperature Free C=O H-bonded C=O PHPMA/PVP ν (cm−1) W1/2(cm−1) Af(%) ν (cm−1) W1/2(cm−1) Ab(%) fb(%)∗ 80/20 1682.7 16.3 10.07 1663.5 22.0 89.93 87.30 70/30 1684.5 12.5 14.53 1663.6 27.1 85.47 81.91 60/40 1683.7 16.3 24.07 1661.7 25.0 75.93 70.82 50/50 1684.4 14.5 33.46 1665.0 24.7 66.54 60.48 40/60 1684.1 15.5 32.97 1663.9 27.1 57.03 50.52 30/70 1683.7 16.8 53.31 1663.4 21.5 46.69 40.26

fb: fraction of hydrogen bonding.

Figure 6. Experimental values of hydrogen-bonded carbonyl group of PVP and the theoretical curves obtained by using different values of KA.

of PVP. From Table 2, we can calculate the inter-association equilibrium constant of the PHPMA/PVP blend. This investigation attempted to use the approximate method proposed by Coleman et al to obtain the KAvalue, expressed by eqns (4) and (5):1

B= B1 (1− KBB1)2  1+KA0A r  (4) A= 0A  1+ KAB1 (1− KBB1)  (5)

where Aand Bare volume fractions of the

non-self-associated species A and the self-associating species B, respectively. 0A and B1 are the corresponding

vol-ume fractions of isolated PVP and PHPMA segments, respectively, and r is the ratio of molar volumes,

VA/VB. The self-association equilibrium constants

(KB), describe the formation of hydrogen bonding.

Finally, the KAis the equilibrium constant

describ-ing the association of A with B. In the first place, we calculated the theoretical fraction of hydrogen-bonded carbonyls in the blend from eqns (4) and (5) by using different values of KA. We then plotted such values

as a function of the blend composition and com-pared them with the experimental data from Table 2. Figure 6 shows that a reasonable value of KA of 30

is obtained from the data-fitting of the theoretical prediction by using Miscibility Guide & Phase Calcu-lator (MG&PC) Software package.1Table 3 lists these

equilibrium constants and their enthalpies, molar vol-umes, molecular weights, and solubility parameters of PHPMA and PVP required by the Painter – Coleman equation to estimate thermodynamic properties for the polymer blend. The path from the hydrogen-bonding equilibrium concentrations through to the fraction of hydrogen bonded carbonyl has been widely described by Coleman et al.1These results reveal that the inter-association hydrogen bonding between the hydroxyl group of PHPMA and carbonyl group of the PVP is stronger than the self-association hydrogen bond-ing between the hydroxyl and carbonyl group of the pure PHPMA, which is consistent with previous Kwei equation and infrared spectrum analysis.

Figure 7(b) shows the FTIR spectra of the PHPMA/PVP= 50/50 blend measured at tempera-tures from 25◦C to 180◦C, revealing that the fraction

(7)

Table 3. Summary of the self-association and inter-association parameters of PHPMA/PVP blend Equilibrium constant K (25◦C) Enthalpy, h (Kcal mol−1) Self-association of PHPMA1 3.17 −3.16

Inter-association between PHPMA and

PVP1 30.0 −5.20 Polymer Molar volume (ml mol−1) Molecular weight (g mol−1) Solubility parameter (cal ml−1)0.5 Degree of polymerization DP PHPMA2 108.4 143.2 9.4 170 PVP2 73.6 115.1 11.0 500 1In this study.

2Estimated using a group contribution method proposed by Coleman et al.1

Figure 7. FTIR spectra recorded at various temperatures for

PHPMA/PVP= 50/50 blend.

of hydrogen-bonded carbonyl group decreases with the increase of temperature at the same composi-tion. Figure 7(a) also shows the hydroxyl-stretching region of PHPMA/PVP= 50/50 at various temper-atures. The hydrogen-bonded hydroxyl – carbonyl of the PHPMA shifts to a higher frequency obviously with increase of temperature, suggesting that the inter-association hydrogen bonding between PHPMA and PVP becomes weaker with the temperature increase. Furthermore, the change in total area is thus explained on the basis of the difference in the average absorp-tion coefficients for the free and hydrogen-bonded hydroxyl-stretching vibration.

CONCLUSIONS

PHPMA/PVP blends are totally miscible over the entire composition range based on DSC analysis and the Kwei equation can accurately predict Tg values

from experimental results due to the existence of hydrogen bonding between the hydroxyl group of PHPMA and the carbonyl group of PVP. Infrared spectra provides positive evidence of the hydrogen bonding at various compositions and with various and intra-molecular interactions. The inter-association constant for the PHPMA/PVP blend is

significantly higher than the self-association constant of pure PHPMA, revealing that the tendency toward hydrogen bonding of the PHPMA and PVP dominates the intra-hydrogen bonding of the pure PHPMA in the mixture based on FTIR and DSC analysis.

ACKNOWLEDGMENTS

The authors would also like to thank the National Science Council, Taiwan, Republic of China for financially supporting this research under Contract No NSC-91-2216-E-009-018.

REFERENCES

1 Coleman MM, Graf JF and Painter PC, Specific Interactions

and the Miscibility of Polymer Blends, Technomic Publishing:

Lancaster, PA, USA (1991).

2 Coleman MM and Painter PC, Progr Polym Sci 20:1 (1995). 3 Painter PC and Coleman MM, Polymer Blends Vol 1, ed by

Paul DR and Bucknall CB, John Wiley & Sons: New York (2000).

4 Eisenberg A, Smith P and Zhou ZL, Polym Eng Sci 22:929 (1982).

5 Smith P and Eisenberg A, J Polym Sci Polym Lett Ed 21:223 (1983).

6 Russell TP, Jerome R, Charlier P and Foucart M,

Macro-molecules 21:1709 (1988).

7 Paul DR and Barlow JW, Polymer 25:4870 (1984). 8 Panayiotou C, Makromol Chemie 188:2733 (1987).

9 Merfeld GD and Paul DR, Polymer Blends Vol 1, ed by Paul DR and Bucknall CB, John Wiley & Sons: New York (2000). 10 Dai J, Goh SH, Lee SY and Siow KS, J Appl Polym Sci 53:837

(1994).

11 Cesteros LC, Meaurio E and Katime I, Macromolecules 26:2323 (1993).

12 Kuo SW and Chang FC, Macromolecules 34:5224 (2001). 13 Martinez A, Iruin JJ and Fernazdez-Berridi MJ, Macromolecules

28:3707 (1995).

14 Thyagargian G and Janarthanan V, Polymer 30:1797 (1989). 15 Ceccorulli G, Pizzoli M, Scandola M, Alfonso G and

Tur-turro A, Polymer 27:1195 (1989).

16 Guo Q, Makromol Chem Rapid Communications 11:279 (1990). 17 Kuo SW, Huang CF and Chang FC, J Polym Sci Polym Phys Ed

40:2313 (2002).

18 Kwei TK, J Polym Sci Polym Lett Ed 22:307 (1984).

19 Moskala EJ, Varnell DF and Coleman MM, Polymer 26:228 (1985).

數據

Fig 1. All PHPMA/PVP blends have only a single
Figure 2. FTIR spectra recorded at various temperatures for pure PHPMA.
Table 1. Curve-fitting of fraction of hydrogen-bonding results of the pure PHPMA at various temperatures Free C =O H-bonded C =O Pure PHPMA ν (cm −1 ) W 1/2 (cm −1 ) A f (%) ν (cm −1 ) W 1/2 (cm −1 ) A b (%) f b (%) ∗ 130 1729.6 20.0 56.85 1710.0 23.2 43.1
Figure 5 shows infrared spectra of the carbonyl stretching recorded at room temperature, ranging from 1600 to 1780 cm −1 for the blends with various compositions
+3

參考文獻

相關文件

Evaluation of the association between t he characteristics of physicians and th eir practices with the availability of electronic health records.. Association with the availability

You are given the wavelength and total energy of a light pulse and asked to find the number of photons it

Teachers may consider the school’s aims and conditions or even the language environment to select the most appropriate approach according to students’ need and ability; or develop

Wang, Solving pseudomonotone variational inequalities and pseudocon- vex optimization problems using the projection neural network, IEEE Transactions on Neural Networks 17

volume suppressed mass: (TeV) 2 /M P ∼ 10 −4 eV → mm range can be experimentally tested for any number of extra dimensions - Light U(1) gauge bosons: no derivative couplings. =>

We explicitly saw the dimensional reason for the occurrence of the magnetic catalysis on the basis of the scaling argument. However, the precise form of gap depends

First Taiwan Geometry Symposium, NCTS South () The Isoperimetric Problem in the Heisenberg group Hn November 20, 2010 13 / 44.. The Euclidean Isoperimetric Problem... The proof

(c) Draw the graph of as a function of and draw the secant lines whose slopes are the average velocities in part (a) and the tangent line whose slope is the instantaneous velocity