The system poly(4-hydroxystyrene)/poly(vinyl acetate)/acetone: An experimental and theoretical study

Macromol. Chem. Phys. 195, I043 -1062 (1994) 1043

The system poly(4-hydroxystyrene)/(poly(vinyl acetate)/ acetone: an experimental and theoretical study

Gustavo Luengo, Ramon G. Rubio

Department of Physical Chemistry, University of Complutense, 28040 Madrid, Spain

Isaac C. Sanchez

Department of Chemical Engineering, University of Texas at Austin, Austin, TX 78712, U. S. A.

Constantinos G. Panayiotou *

Department of Chemical Engineering, University of Thessaloniki, 54006 Thessaloniki, Greece

(Received: May 18, 1993; revised manuscript of June 21, 1993)

SUMMARY In an effort to assess the intermolecular interactions between poly(4-hydroxystyrene) a) (P4HS)

and poly(viny1 acetate) (PVAc), two types of experimental measurements were conducted: volumetric properties and vapor pressures of solutions in a common solvent (probe). The PVT measurements for a 50 : 50 (w/w) binary polymer mixture were conducted over a pressure range from 0 to 100 MPa and a temperature range from 350 to 470 K. The vapor pressures of acetone over a series of ternary systems acetone/P4HS/PVAc, and for four intermediate weight ratios PVAc/P4HS, were measured at 298,15 K, 308,15 K and 318,15 K. PVAc and P4HS interact primarily through hydrogen bonding. The probe molecule (acetone) on the other hand interacts also through hydrogen bonding with P4HS. A recent equation-of-state theory of hydrogen bonding has been used to correlate these measurements. Application of the theory was requiring the knowledge of the volumetric behavior of pure P4HS. Extensive PVT measurements for this polymer have also been conducted. The PVT measurements for the polymer mixture were used in order to estimate the hydrogen bonding parameters for the hydroxyl-ester pair. The vapor pressures of the system acetonelP4HS were used in order to estimate the hydrogen bonding parameters of the hydroxyl-carbonyl pair. On the basis of this information the theory was used to predict the vapour pressures of the ternary system. The theoretical predictions are in quantitative agreement with the experiments.

Introduction

The role of specific interactions in the enhancement of polymer-polymer miscibility has been very much appreciated in recent years -4). In this respect hydrogen bonding has attracted particular attention from both the academic and the technological view- point2-6). In the majority of applications the proton donor was a hydroxyl group which was incorporated in the principal polymer chain via copolymerization of the main monomer with monomers containing hydroxyl or groups easily transformed to

a) IUPAC name: poly(4-vinylphenol).

0 1994, Hiithig & Wepf Verlag, Basel CCC 1022-1 352/94/$08.00

1044 G. Luengo, R. G. Rubio, I. C. Sanchez, C. G. Panayiotou

hydroxyl. Although the variety of the proton acceptor groups is much larger, the ester group seems to have an especially high position from the technological standpoint.

A common solvent is often used in an early phase in the polymer blending process. The thermodynamics of these ternary systems and in particular the relative strength of the intermolecular interactions involved is of much interest since the very compatibility of the two polymers may depend on the common solvent from which they are cast7-*).

The use of a common solvent to probe the intermolecular interactions in polymer blends is also a rather well established techniqueg-"). It should be kept in mind, however, that the success of the technique resides heavily upon the theoretical model which is used to extract the information on the interaction between the polymer pair from the experimental data for the ternary solvent/polymer/polymer system.

The system of interest in the present paper is a ternary solvent/polymer/polymer system, the acetone/poly(4-hydroxystyrene) (P4HS)/poly(vinyl acetate) (PVAc) system. In every repeating unit of P4HS there is a hydroxyl group which self-associates and cross-associates with the ester group of PVAc or the carbonyl group of acetone. Due to the chain character of the associated components, the association complexes formed are essentially three-dimensional in character. Since the hydrogen bonds are formed and disrupted continuously, the system is in a sense a dynamic physical (hydrogen- bonded) network. It is obvious then that the appropriate theory for the present case should be a thermodynamic theory of polymer mixtures which takes into account in a consistent manner this network character of the hydrogen-bonded system.

The principal attempt towards establishing such a theoretical framework is that of Coleman, Painter and coworkers summarized in a recent monographI2). It is a semi- empirical extension of the widely used Flory approach of consecutive linear association 13). The problems associated with the consistent extension of this approach to hydrogen-bonded networks are indicated in a recent publication 14). At present this extension in a fundamentally correct manner remains a challenging problem.

Polymer scientists have appreciated in recent years the value of the equation-of-state theories of polymer solutions, especially their capacity to explain the universal lower critical solution temperature (LCST) behavior of polymer solutions and polymer mixtures. Having taken this into account, Panayiotou and Sanchez have presented recently Is) a general equation-of-state theory of hydrogen bonding which is valid for linearly associated systems as well as for hydrogen-bonded networks. As with all widely used theories of associated solutions, the basic premise of this theory is the division of intermolecular interactions into physical (or van der Waals) and chemical (or hydrogen bonds). This division of interactions leads to two separable factors in the partition function - a physical and a chemical factor. In the case of non-associated systems the model reduces to the lattice fluid theory of fluids16-'8). Details of the formalism of the model as applied to the ternary system of our interest are given below in the section on the theory. Because of its equation-of-state character the theory when applied to pure associated fluids requires, besides the hydrogen-bonding parameters, three equation-of-state of lattice-fluid parameters, which in the case of polymers are usually obtained from the volumetric properties of the polymer.

The rest of the paper is organized as folllowing: The experimental measurements along with the experimental methods used are presented in the next section. In the

The system poly(4-hydroxystyrene)/(poly(vinyl acetate)/acetone . . . 1045

subsequent section are presented the essentials of the theory for the hydrogen-bonded polymer/polymer/solvent system Is). In the section on applications, the theory is used to correlate and predict the volumetric properties and the vapor pressures of acetone in the P4HS/PVAc/acetone system.

Experimental part

The following properties have been measured: 1) Vapor pressures of solutions of acetone with pure poly(4-hydroxystyrene) (P4HS), pure poly(viny1 acetate) (PVAc), and four mixtures of the polymers with weight ratios of PVAc to P4HS of 0,241, 0,618, 1,511 and 3,829. 2) PVT data for pure P4HS and for a 50 : 50 (w/w) binary mixture of the polymers. All these measurements are presented in this work except for the vapor pressures of acetone/P4HS which have been published previously ").

Materials

Acetone was from Carlo Erba (RPE) and was used without purification, except for being kept over 0,4 nm molecular sieves. The density of acetone at 293,15 K was 0,791 g/cm3, which compares well with the value reported in the literature") (0,790 g/cm3).

P4HS samples used in the vapor pressure measurements were obtained from Polysciences (U. K.) (a, = 1000-7000). Vapor pressure osmometry of P4HS dissolved in 1,4-dioxane gave M,, = 1 500. Gel permeation chromatograhy (Shimadzu LC-9A GPC, solvent tetrahydrofuran, calibration with polystyrene standards from Polymer Laboratories) revealed a polydispersity ratio M,/M,, = 2. The P4HS samples used in the PVT measurements were obtained from Shell Development Co. (aw P 6200, density 1,16 g/cm3 at 20 "C). PVAc was obtained from Polyscien- ces Inc. (a, = 90000, density 1,19 g/cm3). The polymer mixtures were obtained by casting from solution using acetone as the common solvent. Removal of the solvent in the later stages of sample preparation was done in a vacuum oven for two days at 80°C and with a nitrogen bleed.

Vapor pressure measurements

In a previous publication ") we have presented details of the procedure for the measurement of vapor pressures in the acetone/P4HS system. The same procedure was used for all solutions of the present work. The polymer of polymer mixture was degassed by keeping it under high vacuum for 24 h; afterwards the cell was sealed and observed during a week for the appearance of any desorbed gas in the cell. Acetone was degassed according to the procedure described previously2'). The amounts of polymer in the cell and of acetone in each ampule were known to within * 0,03 mg. The temperature was kept constant within +3 mK and mesured with a calibrated thermistor, the uncertainty in T being < +8 mK. The heights of the menisci in the manometers were read with a cathetometer precise to + 5 pm. Under the above conditions the precision in the vapor pressure was +2,2. Torr fo rp I 150 Torr and +6,0. lo-* Torr for higher pressures. Each vapor pressure was the average of three measurements that agreed within experimental error.

In Tab. 1 are reported the experimental vapor pressures for the system acetone/PVAc at 25, 35 and 45 "C. In Tab. 2 are reported the experimental vapor pressures for the system acetone/P4HS/ PVAc at the above three temperatures and for four weight ratios of the two polymers.

PVT measurements

In order to determine the equation-of-state parameters of pure P4HS its volumetic (PVT) properties have been measured in a Gnomix Research (Colorado, USA) PVT equipment from 0 to 100 MPA and from 74 to 200OC. Much care was exercised in the preparation of the polymer specimens for not trapping any air bubbles in the close packed pellets. The P4HS was compression molded at 190 'C (well above the glass transition temperature) into very brittle bars (100 x 30 x


Tab. 1 . Vapor pressures of the system poly(viny1 acetate)/acetone at different temperatures. ( W3 is the weight fraction of acetone)

w3 Vapor pressure in Torr at

298,15 K 308,15 K 318,15 K

0,4154 0,4568 0,4958 0,5466 0,6079 0,6386 0,67 18 0,7032 0,7454 0,7554 0,7837 0,8178 1 .OOo

210,56 216,00 219,17 222,68 225,42 226,97 227,77 228,77 229,02 229,56 229,78 229,80 230,50

- 325,05 330,67 336,09 340,14 342,30 344,15 345,65 346,66 346,61 346,93 347,05 348,90

- 476,74 483,40 493,76 500,18 503,76 505,49 506,58 508,05 508,67 510,13 509,00 512,lO

5 mm) using a two heat plates compressor. A total of 300 experimental data have been obtained and are presented in Tab. 3. PVT measurements have also been conducted for a 50 : 50 (w/w) binary mixture of the two polymers. The temperature range was from 78 to 200 "C and the pressure range from 0 to 100 MPa. The polymer mixture was prepared as described previously. A total of 3 12 experimental data were obtained for this system too and are presented in Tab. 4. Experimental uncertainties in temperature and pressure during PVTmeasurements were ?0,2 K and +0,2%, respectively. The sensitivity in specific volume of the instrument is +0,0002 cm3/g while the absolute accuracy of the reported specific volume data are estimated to be better than *0,002 cm3/g.

Theory

The general thermodynamic theory for hydrogen-bonded systems and the detailed derivations are exposed in the original paper15). In this section we will present the formalism for the case of a ternary system consisting of a polymer (component 1) with d l proton-donor and a1 (=dl ) proton-acceptor groups, a polymer (component 2) with a2 proton-acceptor groups, and a solvent (component 3) with one proton acceptor group. The correspondence to the components of the system P4HS/PVAc/acetone is obvious as the hydroxyl groups of P4HS are both donors and acceptors while the ester groups of PVAc and the carbonyl group of acetone are only acceptors.

Consider then a system of Nl, N2 and N3 molecules of components 1, 2 and 3, respectively, at temperature T and external pressure Z? Following the nomenclature of ref. 15), let molecules of type 1, 2, 3 be characterized by r l , r,, r3 number of segments per molecule, respectively. Similarly let the hard-core volumes per segment be ut, v r and uf and the average intermolecular interaction energies per segment E:, E?, ~ f , respectively. The molecules are assumed arranged on a quasi-lattice of N, sites, No of which are empty. The N, sites are given by

The system poly(4-hydroxystyrene)/(poly(vinyl acetate)/acetone . . .

Besides mole fractions

Ni - _ - Ni x . = I N , f N2 f N3 N

also segment fractions

i = 1 , 2 , 3

1047

will be used repeatedly in the followings. They should be distinguished, however, from the site fraction f, given by

and for the fraction of the empty sites

i = 1 , 2 , 3 (4)

= l/fi is the reduced density (fi being the reduced volume) which is obtained from the equation of state given later.

As already mentioned the canonical partition function of our system, in its maximum term approximation, is considered to be separable into two factors, one physical, QP, and one chemical, QH or

Q = Q P ' Q H (6)

the physical factor QP is approximated in this work by the lattice-fluid partition

where wi is a constant characteristic of the fluid i, which will cancel out in all applications of our interest; ELF is the total potential energy of the system, arising from physical intermolecular interactions, and is given by

-ELF = rN/je* (8)

For simplicity we will not differentiate here surface fractions from segment fractions. The full surface fraction formalism has been presented previously Is). In the one-fluid approximation then the average interaction energy per segment in the mixture is assumed to be given by the following combining and mixing rules ''3


( E Z = ti*). Cii in Eq. (10) is a dimensionless binary parameter expected to have values close to unity. For simplicity, tii was set equal to one throughout this work.

Let us now concentrate on the chemical factor QH of the partition function. Contrary to the majority of association theories in current use the present development does not invoke explicitly and a priori the existence of association complexes. Following

Tab. 2. tone(3). ( Wi denotes the corresponding weight fractions)

Vapor pressures of the system poly(4-hydroxystyrene)(l)/poly(vinyl acetate)(2)/ace-

WZ/WI w3 w2 Vapor pressure in Torr at

298,15 308,15 K 318,15 K

0,241 3 0,3755 0,4488 0,5536 0,6713 0,7483 0,8028 0,8421 0,8703

0,6184 0,3697 0,4361 0,5371 0,6385 0,7161 0,7690 0,8110 0,8418

1,5113 0,3815 0,4205 0,4849 0,5568 0,6375 0,7117 0,7760 0,8206

3,8286 0,3121 0,4387 0,5597 0,6608 0,7379 0,7876 0,8217 0,8488

0,1214 0,1072 0,0868 0,0639 0,0489 0,0383 0,0307 0,0252

0,2408 0,2155 0,1769 0,1381 0,1085 0,0883 0,0722 0,0604

0,3722 0,3487 0,3100 0,2667 0,2182 0,1735 0,1348 0,1080

0,5454 0,445 1 0,3491 0,2690 0,2078 0,1684 0,1414 0,1199

175,26 195,53 213,42 223,ll 226,49 227,99 228,98 229,79

187,45 200,12 214,31 222,48 226,29 227,39 228,29 228,87

200,70 205,23 214,ll 220,53 224,86 227,21 228,86 229,99

189,30 211,60 222,25 226,93 228,75 229,56 229,80 230,04

264,52 294,76 322,56 337,70 342,56 344,87 246,40 347,06

282,52 302,51 324,41 336,49 342,62 343,95 345,34 346,09

300,50 310,94 323,76 333,67 340,36 344,87 346,17 347,30

283,28 319,31 336,40 343,19 346,28 347,27 347,88 348,14

385,82 432,24 473,78 495,76 502,82 506,26 508,39 509,42

411,58 443,82 476,36 494,18 502,02 505,12 506,96 508,19

438,35 455,09 475,40 489,58 499,37 505,34 508,29 509,81

411,65 467,36 493,77 503,76 508,15 509,70 510,57 511,07

The system poly(4-hydroxystyrene)/(poly(vinyl acetate)/acetone . . .

Tab. 3. Experimental volumetric properties of poly(4-hydroxystyrene)

1049

P/MPa v/(cm3/g) Tin "C WMPa v/(cm3/g) T i n "C P/MPa v/(cm3/g) Tin "C

10,O 0,8715 10,O 0,8720 10,O 0,8729 10,O 0,8737 10,O 0,8747 10,O 0,8757 10,O 0,8763 10,O 0,8778 10,O 0,8784 10,O 0,8796 10,O 0,8807 10,O 0,8816 10,O 0,8826 10,O 0,8837 10,O 0,8844 10,O 0,8856 10,O 0,8863 10,O 0,8870 10,O 0,8880 10,O 0,8900 10,O 0,8910 10,O 0,8916 10,O 0,8922 10,O 0,8936 10,O 0,8953 10,O 0,8960 10,O 0,8970 10,O 0,8985 10,O 0,8998 10,O 0,9003 10,O 0,9016 10,O 0,9024 10,O 0,9042 10,O 0,9046 10,O 0,9061 10,O 0,9067 10,O 0,9081 10,O 0,9089 10,O 0,9105 10,O 0,9114 10,O 0,9125 10,O 0,9130 10,O 0,9143 10,O 0,9162 10,O 0,9175 10,O 0,9184 10,O 0,9197 10,O 0,9201 10,O 0,9207 10,O 0,9240 10,O 0,9251

130,8 133,l 135,3 137,7 139,9 142,l 144,3 146,5 148,6 150,8 153,O 155,2 157,3 159,5 161,7 163,9 166,l 168,3 170,4 172,6 174,9 177,O 179,2 181,4 183,5 185,7 187,7 190,O 192,l 194,3 196,5 198,7 200,9 203,l 205,2 207,3 209,5 21 1,6 213,7 215,8 217,9 220,l 222,2 224,4 226,5 228,7 230,9 233,O 235,O 239,3 241,4

10,O 0,9256 10.0 0,9271 10,O 0,9284 10,O 0,9294 10,O 0,9296 10,O 0,9289 20,O 0,8684 20,O 0,8693 20,O 0,8696 20,O 0,8702 20,O 0,8711 20,O 0,8726 20,O 0,8736 20,O 0,8745 20,O 0,8756 20,O 0,8763 20,O 0,8771 20,O 0,8779 20,O 0,8787 20,O 0,8806 20,O 0,8807 20,O 0,8819 20,O 0,8830 20,O 0,8837 20,O 0,8844 20,O 0,8868 20,O 0,8868 20,O 0,8883 20,O 0,8888 20,O 0,8897 20,O 0,8906 20,O 0,8913 20,O 0,8936 20,O 0,8939 20,O 0,8946 20,O 0,8954 20,O 0,8963 20,O 0,8971 20,O 0,8979 20,O 0,8987 20,O 0,9021 20,O 0,9028 20,O 0,9053 20,O 0,9057 20,O 0,9066 20,O 0,9073 20,O 0,9089 20,O 0,9098 20,O 0,9105 20,O 0,9118 20,O 0,9129

243,5 245,8 247,8 249,5 250,5 250,7 140,6 142,7 144,9 147,2 149,4 151,6 153,7 155,8 158,l 160,3 162,5 164,7 166,9 169,2 171,4 173,5 175,7 177,9 180,l 182,2 184,s 186,6 188,8 190,9 193,2 195,4 197,5 199,5 201,6 203,7 205,8 207,9 210,l 212,l 218,5 220,6 222,7 224,8 227,O 229,2 231,3 233,4 235,6 237,8 239,9

20,O 0,9139 20,O 0,9148 20,O 0,9157 20,O 0,9170 20,O 0,9178 20,O 0,9182 20,O 0,9184 40,O 0,8628 40,O 0,8635 40,O 0,8642 40,O 0,8649 40,O 0,8658 40,O 0,8669 40,O 0,8678 40,O 0,8686 40,O 0,8696 40,O 0,8704 40,O 0,8713 40,O 0,8719 40,O 0,8731 40,O 0,8736 40,O 0,8752 40,O 0,8755 40,O 0,8766 40,O 0,8775 40,O 0,8784 40,O 0,8793 40,O 0,8802 40,O 0,8810 40,O 0,8818 40,O 0,8824 40,O 0,8838 40,O 0,8845 40,O 0,8854 40,O 0,8868 40,O 0,8877 40,O 0,8883 40,O 0,8891 40,O 0,8905 40,O 0,8911 40,O 0,8920 40,O 0,8931 40,O 0,8939 40,O 0,8945 40,O 0,8952 40,O 0,8964 40,O 0,8974 40,O 0,8991 40,O 0,8999 40,O 0,9007 40,O 0,9017

242,1 244,3 246,5 248,85 250,0 250,8 250,7 146,0 148,2 150,5 152,7 155,1 157,3 159,6 161,8 164,0 166,0 168,2 170,3 172,4 174,6 176,7 178,9 181,1 183,3 185,5 187,7 189,9 192,1 194,3 196,5 198,6 200,7 202,8 204,9 207,0 209,2 211,2 213,3 215,5 217,7 219,7 221,8 224,0 226,2 228,3 230,4 232,7 234,9 237,1 239,3


Tab. 3. Continued

P/MPa u/(cm3/g) Tin "C WMPa u/(cm3/g) Tin "C P/MPa u/(cm3/g) Tin "C

40,O 0,9022 40,O 0,9036 40,O 0,9044 40,O 0,9050 40,O 0,9064 40,O 0,9068 40,O 0,9072 40,O 0,9072 60,O 0,8571 60,O 0,8577 60,O 0,8582 60,O 0,8596 60,O 0,8600 60,O 0,8611 60,O 0,8617 60,O 0,8626 60,O 0,8632 60,O 0,8644 60,O 0,8652 60,O 0,8658 60,O 0,8669 60,O 0,8676 60,O 0,8686 60,O 0,8695 60,O 0,8706 60,O 0,8712 60,O 0,8719 60,O 0,8723 60,O 0,8740 60,O 0,8750 60,O 0,8756 60,O 0,8762 60,O 0,8773 60,O 0,8778 60,O 0,8792 60,O 0,8798 60,O 0,8806 60,O 0,8814 60,O 0,8819 60,O 0,8833 60,O 0,8838 60,O 0,8852 60,O 0,8862 60,O 0,8868 60,O 0,8878 60,O 0,8888 60,O 0,8893 60,O 0,8898 60,O 0,8911

241,5 243,8 245,9 248,l 249,9 251,l 251,7 251,l 149,2 151,4 153,7 155,7 158.0 160,2 162,5 164,7 166,8 169,O 171,l 173,4 175,6 177,8 179,9 182,l 184,2 186,4 188,6 190.7 192,9 195,O 197,2 199.4 201,5 203,7 205,8 207,9 210,o 212.1 214.2 216,3 218,6 220,7 222,7 224,8 227,O 229,2 23 1,4 233,6 235,9

60,O 0,8918 60,O 0,8921 60,O 0,8943 60,O 0,8950 60,O 0,8963 60,O 0,8971 60,O 0,8978 60,O 0,8982 60,O 0,8979 80,O 0,8518 80.0 0,8522 80,O 0,8531 80,O 0,8542 80,O 0,8552 80,O 0,8561 80,O 0,8565 80,O 0,8573 80,O 0,8585 80,O 0,8594 80,O 0,8598 80,O 0,8605 80,O 0,8611 80,O 0,8621 80,O 0,8633 80,O 0,8640 80,O 0,8647 80,O 0,8658 80,O 0,8663 80,O 0,8670 80,O 0,8676 80,O 0,8682 80,O 0,8693 80,O 0,8703 80,O 0,8709 80,O 0,8721 80,O 0,8727 80,O 0,8734 80,O 0,8745 80,O 0,8758 80,O 0,8762 80,O 0,8766 80,O 0,8778 80,O 0,8789 80,O 0,8798 80,O 0,8805 80,O 0,8812 80,O 0,8820 80,O 0,8825 80,O 0,8831

238,l 240,4 242,6 244,7 246.8 248,9 250,7 251,8 252,l 155,O 157,2 159.3 161.4 163,6 165,8 168,2 170,4 172,5 174,8 177.1 179,2 181,4 183,6 185,8 187,9 190,l 192,2 194,5 196,6 198,7 201 ,o 203,l 205,2 207,3 209,4 211,5 213,6 215,8 217,9 220,l 222,2 224,4 226,6 228,7 230,9 233,l 235,3 237,5 239,7

80,O 0,8842 80,O 0,8850 80,O 0,8856 80,O 0,8872 80,O 0,8875

100,O 0,8473 100,O 0,8483 100,O 0,8486 100,O 0,8494 100,O 0,8506 100,O 0,8513 100,O 0,8516 100,O 0,8534 100,O 0,8537 100,O 0,8540 100,O 0,8554 100,O 0,8564 100,O 0,8570 100,O 0,8574 100,O 0,8578 100,O 0,8583 100,O 0,8601 100,O 0,8610 100,O 0,8617 100,O 0,8621 100,O 0,8629 100,O 0,8634 100,O 0,8641 100,O 0,8646 100,O 0,8665 100,O 0,8673 100,O 0,8670 100,O 0,8678 100,O 0,8689 100,O 0,8698 100,O 0,8706 100,O 0,8711 100,O 0,8725 100,O 0,8728 100,O 0,8731 100,O 0,8736 100,O 0,8755 100,O 0,8767 100,O 0,8766 100,O 0,8768 100,O 0,8784 100,O 0,8792 100,O 0,8798 100,O 0,8802

241,9 244,0 246,2 248,3 250,3 157,6 159,8 162,0 164,2 166,3 168,5 170,7 172,7 174,9 177,1 179,3 181,4 183,7 185,9 188,0 190,1 192,3 194,4 196,5 198,7 201,0 203,0 205,2 207,3 209,3 211,3 213,4 215,6 217,7 220,0 222,2 224,5 226,7 229,0 23 1,2 233,3 235,4 237,6 239,7 242,0 244,1 246,2 248,4 250,4


Tab. 4. acetate) 50: 50 (w/w)

P/MPa u/(cm3/g) Tin "C P/MPa v/(cm3/g) Tin "C P/MPa v/(cm3/g) Tin "C

Experimental volumetric properties of the mixture poly(4-hydroxystyrene)/poly(vinyl

10,O 0,8653 10,O 0,8661 10,O 0,8666 10,O 0,8673 10,O 0,8689 10,O 0,8702 10,O 0,8709 10,O 0,8722 10,O 0,8728 10,O 0,8732 10,O 0,8751 10.0 0,8761 10,O 0,8767 10,O 0,8777 10,O 0,8787 10,O 0,8793 10,O 0,8808 10,O 0,8815 10,O 0,8831 10,O 0,8840 10,O 0,8848 10,O 0,8854 10,O 0,8861 10,O 0,8882 10,O 0,8891 10,O 0,8895 10,O 0,8913 10,O 0,8821 10,O 0,8827 10,O 0,8946 10,O 0,8956 10,O 0,8964 10,O 0,8971 10,O 0,8977 10,O 0,8996 10,O 0,9003 10,O 0,9010 10,O 0,9016 10,O 0,9045 10,O 0,9053 10,O 0,9103 10,O 0,9111 10,O 0,9119 10,O 0,9128 10,O 0,9134 10,O 0,9184 10,O 0,9192 10,O 0,9199 10,O 0,9206 10,O 0,9213

74,9 77,2 79,6 82,O 84,2 86,5 88,9 91,2 933 95,9 98,2 100,5 102,s 105,l 107,3 109,7 111,9 114,2 116s 118,8 121,o 123,4 125,7 128,l 130,4 132,7 134,9 137,2 139,4 141,6 143,8 145,9 148,2 150,4 152,6 154,8 157,O 159,3 163,6 165,8 172,3 174,4 176,7 178,9 181,2 187,6 189,7 191,9 193,9 195,3

10,O 0,9217 10,O 0,9231 20,O 0,8622 20,O 0,8630 20,O 0,8645 20,O 0,8656 20,O 0,8664 20,O 0,8676 20,O 0,8685 20,O 0,8693 20,O 0,8700 20,O 0,8707 20,O 0,8722 20,O 0,8733 20.0 0,8738 20,O 0,8747 20,O 0,8755 20,O 0,8764 20,O 0,8773 20,O 0,8787 20,O 0,8797 20,O 0,8807 20,O 0,8813 20,O 0,8828 20,O 0,8836 20,O 0,8842 20,O 0,8856 20,O 0,8869 20,O 0,8877 20,O 0,8883 20,O 0,8895 20,O 0,8909 20,O 0,8917 20,O 0,8923 20,O 0,8939 20,O 0,8948 20,O 0,8954 20,O 0,8970 20,O 0,8976 20,O 0,8983 20.0 0,9002 20,O 0,9013 20,O 0,9022 20,O 0,9032 20,O 0,9056 20,O 0,9059 20,O 0,9069 20,O 0,9078 20,O 0,9094 20,O 0,9106

196,2 196,2 76,8 79,2 813 84,O 86,4 88,9 91,2 93,6 96,O 98,2 100,5 102,8 105.1 107,4 109,8 112,l 114,4 116,5 119,l 121,3 123,8 126,l 128,4 130,8 133,O 135,2 137,4 139,6 141,8 143,9 146,l 148,3 150,4 152,6 154,8 156,9 159,2 161,4 163,6 165,9 168,l 170,3 172,4 174,7 177,l 179,4 181,7 183,7

20,O 0,9115 20,O 0,9123 20,O 0,9130 20,O 0,9147 20,O 0,9156 20,O 0,9163 20,O 0,9167 20,O 0,9169 40,O 0,8569 40,O 0,8576 40,O 0,8583 40,O 0,8593 40,O 0,8603 40,O 0,8611 40,O 0,8620 40,O 0,8628 40,O 0,8638 40,O 0,8647 40,O 0,8654 40,O 0,8663 40,O 0,8674 40,O 0,8681 40,O 0,8688 40,O 0,8699 40,O 0,8706 40,O 0,8716 40,O 0,8725 40,O 0,8736 40,O 0,8744 40,O 0,8753 40,O 0,8762 40,O 0,8771 40.0 0,8783 40,O 0,8792 40,O 0,8799 40,O 0,8817 40,O 0,8821 40,O 0,8828 40,O 0,8839 40,O 0,8850 40,O 0,8858 40,O 0,8868 40.0 0,8874 40,O 0,8889 40,O 0,8897 40,O 0,8911 40,O 0,8921 40,O 0,8930 40,O 0,8936 40,O 0,8951

185,8 187,9 190,1 192,1 194,1 195,6 196,6 196,1 80,0 82,3 84,7 87,0 89,4 91,8 94,1 96,4 98,8 101,1 103,4 105,7 107,9 110,3 112,6 114,9 117,3 1193 121,8 124,1 126,5 128,9 131,3 133,7 135,9 138,1 140,4 142,5 144,8 147,1 149,2 151,4 153,7 155,8 158,1 160,3 162,6 164,8 167,0 169,2 171,4 173,6


Tab. 4. Continued.

P/MPa u/(cm3/g) T in 'C P/MPa u/(cm3/g) Tin "C P/MPa u/(cm3/g) Tin "C

40,O 0,8958 40,O 0,8970 40,O 0,8982 40,O 0,8990 40,O 0,8999 40,O 0,9012 40,O 0,9023 40,O 0,9033 40,O 0,9040 40,O 0,9050 40,O 0,9056 40,O 0,9059 40,O 0,9059 60,O 0,8535 60,O 0,8542 60,O 0,8549 60,O 0,8559 60,O 0,8567 60,O 0,8573 60,O 0,8583 60,O 0,8593 60,O 0,8600 60,O 0,8608 60,O 0,8617 60,O 0,8624 60,O 0,8635 60,O 0,8641 60,O 0,8648 60,O 0,8658 60,O 0,8667 60,O 0,8677 60,O 0,8685 60,O 0,8692 60,O 0,8700 60,O 0,8710 60,O 0,8720 60,O 0,8729 60,O 0,8735 60.0 0,8746 60,O 0,8755 60,O 0,8763 60,O 0,8772 60,O 0,8780 60,O 0,8787 60,O 0,8802 60,O 0,8811 60,O 0,8816 60,O 0,8831 60,O 0,8841 60,O 0,8849 60,O 0,8857 60,O 0,8863 60.0 0,8880 60,O 0,8893

175,8 177,9 180,l 182,4 184,8 187,O 189,l 191,3 193,5 195,4 196,7 197,3 197,O 84,7 87,l 89,4 91,8 94,l 96,6 98,9

101,l 103,5 105,9 108,2 110,5 112,8 115,O 117,4 119,7 122,o 124,4 126,7 129,O 131,2 133,5 135,8 137,9 140,3 142,5 144,7 147,O 149,2 151.4 153,6 155,8 158,O 160,2 162,4 164,6 166,8 169,O 171,2 173,4 175.6

60,O 0,8902 60,O 0,8911 60,O 0,8912 60,O 0,8923 60,O 0,8933 60,O 0,8939 60,O 0,8946 60,O 0,8953 60,O 0,8971 60,O 0,8974 60,O 0,8979 60,O 0,8978 80,O 0,8504 80,O 0,8516 80,O 0,8521 80,O 0,8525 80,O 0,8544 80,O 0,8548 80,O 0,8553 80,O 0,8557 80,O 0,8577 80,O 0,8580 80,O 0,8586 80,O 0,8596 80,O 0,8606 80,O 0,8612 80,O 0,8624 80,O 0,8631 80,O 0,8636 80,O 0,8649 80,O 0,8660 80,O 0,8668 80,O 0,8675 80,O 0,8678 80,O 0,8688 80,O 0,8707 80,O 0,8705 80,O 0,8714 80,O 0,8721 80,O 0,8727 80,O 0,8749 80,O 0,8752 80,O 0,8753 80,O 0,8765 80,O 0,8771 80,O 0,8778 80,O 0,8787 80,O 0,8801 80,O 0,8807 80,O 0,8815 80,O 0,8826 80,O 0,8839 80,O 0,8844 80,O 0,8852

177,8 180,O 182,3 184,4 186,6 188,9 191,2 193,5 195,5 197,O 197,8 197,7 91 ,O 93,3 95,6 98,O

100,2 102,5 104,9 107,3 109,6 111,9 114,3 116,6 118,9 121,2 123,5 125,8 128,2 130,5 132,8 135,O 137,3 139,6 141,8 144,l 146,4 148,7 150,9 153,l 155.2 157,3 159,6 161,8 164,O 166,2 168,4 170,5 172,8 175,l 177,3 179.6 181,9 184,2

80,O 0,8866 80,O 0,8878 80,O 0,8880 80.0 0,8886 80,O 0,8901 80,O 0,8906 80,O 0,8909 80,O 0,8914

100,O 0,8462 100,O 0,8472 100,O 0,8480 100,O 0,8481 100,O 0,8497 100,O 0,8499 100,O 0,8509 100.0 0,8521 100,O 0,8521 100,O 0,8526 100,O 0,8539 100,O 0,8546 100,O 0,8550 100,O 0,8559 100,O 0,8569 100,O 0,8574 100,O 0,8586 100,O 0,8590 100,O 0,8596 100,O 0,8613 100,O 0,8615 100,O 0,8620 100,O 0,8633 100,O 0,8641 100,O 0,8646 100,O 0,8652 100,O 0,8660 100,O 0,8670 100,O 0,8678 100,O 0,8689 100,O 0,8694 100,O 0,8704 100,O 0,8708 100,O 0,8719 100,O 0,8728 100,O 0,8746 100,O 0,8749 100,O 0,8764 100,O 0,8773 100,O 0,8779 100,O 0,8791 100,O 0,8795 100,O 0,8806 100,O 0,8815 100,O 0,8822 100,O 0,8831

186,2 188,5 190,8 193,1 195,1 196,9 197,9 198,3 93,6 95,7 98,0

100,4 102,6 104,9 107,3 109,6 111,9 114,3 116.5 118,9 121,3 123,5 125,8 128,2 130,4 132,7 135,1 137,3 139,5 141.8 144,0 146,4 148,5 150,7 152,9 155,2 157,4 159,6 161,9 164,0 166,3 168,5 170,7 175,2 177,5 179,8 182,0 184,2 184,4 188,6 190,8 193,0 195,0 196,7


the ideas of Levine and Perram22), of Luck23) and of Veytsmanu), the focus is on the equilibrium of creation and rupture of hydrogen bonds throughout the system rather than on the formation of a priori specified multimolecular entities.

It should be stressed, once again, that the interaction energies giving rise to the QH factor are in excess of the above physical interactions. The ternary system of our interest here is the simple case where each type of molecules has different types of proton donnor and/or acceptor groups. The general formalism of ref. Is) is considerably simplified in this case.

Let E t be the favorable energy change upon hydrogen bond formation between a donor group i and an acceptor group j . There are N, such bonds in the system and, thus, the total hydrogen bonding energy of the system is

3 E , = Nlj .E? j

j = 1

Throughout we adopt the convention that the inner index refers to the donnor and the outer index refers to the acceptor group. The number of ways Q of distributing the Nil bonds among the functional groups of the system is given byI5p2') (cf. Eq. (24) of ref. Is))

where N,, is the number of donors of type 1 and Noj is the number of acceptors of type j that are not hydrogen bonded:

P , j in Eq. (12) is the mean field probability that a specific acceptor j will be proximate to a given donor 1 and is given byt5)

P l j = c exp(SYj/R)/(rN) (15)

where SYj is the entropy loss associated with the formation of an 1 j hydrogen bond. With these definitions the canonical partition function for hydrogen bonding in its

maximum term approximation can now be written as

where

1054

and

G. Luengo, R. G. Rubio, I. C. Sanchez, C. G. Panayiotou

FY, = E : j - TSYj (1 8 )

Having defined QP and QH we may write for the Gibbs partition function in the maximum term approximation

Y = Qp. QH. exp ( -PY / (m) ) (19)

V is the system volume and is given by

V = rNGv* + N , , . VYj (20) i

V?, is the volume change accompanying the formation of the hydrogen bond I j . u* is the average close-packed volume per segment in the mixture and, in the one-fluid approach, is assumed to be given by

v* = c I p i . v t (21) i

The Gibbs free energy of the system is

G = -RTInY = G,, + G H (22)

The reduced volume ij (or the reduced density f i ) and the number of hydrogen bonds N , at equilibrium are obtained from the free energy minimization conditions

Eq.

where

(23) yields the equation of state

the reduced pressure, is defined by

the reduced temperature, 2 by

- T R T T = - = - F &*

The system poly(4-hydroxystyrene)/(poly(vinyl acetate)/acetone . 1055

and a modified average chain length, i, by

where vH is the fraction of hydrogen bonds in the system. Eq. (25) is identical in form to the orignal lattice-fluid equation of stateI6) except that l / i replaces the usual l / r term.

The second minimization conditions, Eq. (24), yields

where

N j 0 y . = - NIO v,o = - N I j v,, = - r N rN 'O r N

and

GYj = EYj + PVyj - TS?j

j = 1,2,3

Eq. (29) is a set of three simultaneous quadratic equations in v I (or N , j ) . Notice that these three equations and the equation of state (25) have to be solved simultaneous- ly in order to obtain the four coupled order parameters v I 1 , vIz, vI3 , and 6.

From the full partition function, Eq. (19), one obtains in the usual way all basic thermodynamic quantities. For each such quantity of the real mixture there is one contribution arising from physical interactions and one contribution arising from hydrogen bonding. The quantity of prime interest in this work is the chemical potential for which we may write

where the physical or LF contribution is

1- + (i; - 1) ln(1 - ij) + - r rk 1 @k rk - p + Pi; [ ?k

' k ~ ' - In- + 1 - - + r k ' RT w k

where

Ef + &I' - 2 & $ x.. = R T


and the chemical or hydrogen bonding contribution is

v d (=N, d l / ( rN) ) is the average number of proton-donor groups per segment in the system.

In the treatment of vapor pressure data, the chemical potential of the solvent (component 3) will be needed. In this case Eqs. (33) and (35) give

and

Application of the theory to the experimental data

We will, now, apply the theory of the preceding section to our experimental data. Prior to the application of the theory to the mixture data we must notice that the poly(4-hydroxystyrene) molecule self-associates in the pure state. Thus, the pure- component equation of state properties of P4HS should be determined by taking into account the hydrogen bonding of the molecule. As usual, the experimental data used for obtaining the scaling constants of the polymer are extensive volumetric data of the melt. There are three equation of state parameters to be determined (e. g. F, P*, and p* or r ) and three hydrogen bonding parameters for the hydroxyl-hydroxyl bond (e. g. Eo, So and Vo). These hydrogen bonding parameters for this particular molecule should not be very different from the corresponding parameters for phenol. As an approximation they are set equal to the latter, namely, E o = -21,8 kJ/mol, So = -26,5 J/(K . mol), and V o = 0,O cm3/mol which are obtained from an overall fit of experimental vapor pressures, densities and heats of vaporization of phenol25). The LF scaling constants of PVPh reported in Tab. 3 were obtained by the classical least squares fitting procedure applied to the experimental PVTdata reported in the (Exptl. part). As mentioned there the molecular weight of the P4HS sample used for the PVT measurements was 6200, i. e., the average number of hydroxyl groups per molecule was 5 1,6. In Fig. 1 are shown the experimental and the calculated specific volumes of P4HS over an extended range of temperature and pressure.

The P4HS sample used in the vapor pressure measurements had an average molecular weight a,, = 1500, i. e., the average number of hydroxyl groups per molecule was 12,5. The LF scaling constants reported in Tab. 5 were used for this sample as well to a rather good approximation. The LF scaling constants for acetone and PVAc reported in Tab. 5 were obtained previously 16, ").


Fig. 1. Experimental and calculated (solid lines) specific volumes of poly(4-hydroxystyrene) melt at various pressures: (0), 10 MPa; (o), 20 MPa; (V), 40 MPa; (V) 60 MPa; (0) 80 MPa; (m) 100 MPa

0.91 \

5 I

2 0.92

0.90

0.88

L L

0 c

500 2

400

300 Fig. 2. Vapor pressures of the system poly(4-hydroxystyrene)/acetone at three temperatures. Solid lines were calculated by the present hydrogen- bonding model. Dashed lines were calculated by the plain Sanchez-La- combe theory "). W , is the weight fraction of

200

acetone 100

0.81 ' 50 100 150 200

Temp in OC

J

0.2 0.4 0.6 0.8 1.0 w3

nYo sets of hydrogen bonding parameters are needed in order to apply the theory to our ternary system, one for the hydroxyl-ester and the other for the hydroxyl-carbonyl (acetone) interaction. Parameters for dispersive interactions are not adjusted in this approach. For the hydroxyl-carbonyl interaction the experimental vapor pressures of


Tab. 5.

Liquid F / K P*/MF% p*/( kg/m 3,

Acetone 484 533 917 Poly(4-hydroxystyrene) 750 441 1240 Poly(viny1 acetate) 590 509 1283

Lattice fluid scaling constants of pure liquids

the acetone-P4HS mixture') at 25 "C were used in order to determine the energy and entropy of the interaction. The values obtained are Eo = -21,75 kJ/mol, S o =

- 12,9 J/(K. mol). For lack of any volumetric data for this system the hydrogen bonding volume V o was set equal to zero. These parameters were subsequently used with the theory in order to calculate the vapor pressures at other temperatures. These predictions are compared with the experimental data in Fig. 2.

Having determined the hydrogen bonding parameters for the hydroxyl-carbonyl interaction we are now left with the corresponding parameters for the hydroxyl-ester interaction. For their determination we have used the experimental PVT data for the binary mixture of the two polymers reported in the Exptl. part. From this fitting procedure, however, result numerous sets of parameters fitting equally the experimental data. Not all of them are adequate for reproducing the experimental vapor pressures in the ternary system. Since we did not want to adjust any other parameters we have selected the following set Eo = -18,4 kJ/mol, S o = -12,8 J/(K.mol), V o =

4,O cm3/mol, which reproduces adequately the vapor pressures at 25 "C of the ternary mixture with a weight ratio of the two polymers P4HS/PVAc equal to 0,2413. This set was subsequently used in order to calculate the vapor pressures at all other conditions of temperature and composition. In Fig. 3 are compared the experimental and

n 0.91 \

E

2 0.92 -

0.90

0.88

0.86

0.81

Fig. 3. Experimental and calculated specific volumes of the blend poly(4-hydroxystyrene)/poly(vinyl acetate) (50 : 50) (w/w). Symbols are as in Fig. 1

100 150 200 250 300 Temp. in O C


calculated PVT data for the binary polymer mixture. In Figs. 4 to 7 are compared the experimental data with the theoretical predictions. For completeness, in Fig. 8 are shown the experimental and predicted vapor pressures for the acetone/PVAc system. No binary parameters were adjusted for this system. In all cases the binary parameters [ of Eq. (10) was set equal to one.

500

LOO

300

200

100 0.2 0.6 1.0 0.2 0.1 0.6 0.8 1.0

w3 w3

Fig. 4. Fig. 5 .

Fig. 4. Vapor pressures of the ternary system poly(4-hydroxystyrene)(l)/poly(vinyl acetate)(2)/ acetone(3) with weight ratio Wz/W, = 0,241 at three temperatures. Solid lines were calculated by the present hydrogen-bonding model

Fig. 5 . Vapor pressures of the ternary system with weight ratio Wz/W, = 0,618 at three temperatures. Solid lines were calculated by the present hydrogen-bonding model

Discussion and conclusions

The experimental data reported in this work are a fairly complete set for testing equation of state theories of hydrogen bonded polymer solutions once the hydrogen bonding parameters of the theories are known. Direct measurements of the degrees of hydrogen bonding, which would lead to an independent assessment of these parameters, have not been conducted. For the model used in this work the only known parameters were for the hydroxyl-hydroxyl interaction. The vapor pressure data for the

1060 G. Luengo, R G. Rubio, I. C. Sanchez, C. G. Panayiotou

L L

0 + 2 500

400

300

200

100 I 0.2 0.4 0.6 0.8 1.0

w3

Fig. 6.

.

0.2 0.4 0.6 0.8 1.0 w3

Fig. 7.

Fig. 6. temperatures. Solid lines were calculated by the present hydrogen-bonding model

Fig. 7. peratures. Solid lines were calculated by the present hydrogen-bonding model

Vapor pressures of the ternary system with weight ratio Wz/W, = 1,511, at three

Vapor pressures of the ternary system with weight ratio Wz/W, = 3,829, at three tem-

acetone/P4HS system were rather sufficient for a n estimation of the energetic parameters for the hydroxyl-carbonyl interaction. However the PVT data for the polymer mixture may not be sufficient for estimating the parameters for the hydroxyl- ester interaction. In fact the hydrogen bonding volume makes a not too large contribution to the specific volume of the mixture. For such a set of experimental data it is obvious that the least squares minimization procedure cannot give a unique estimate within the appropriate confidence limits. Although the selection of the final set of the parameters was aided with some vapor pressure data of the ternary system, this set may not be the best one. Caution should be then exercised in transferring this set to other systems with hydroxyl-ester interactions. Nevertheless, the estimated hydrogen-bonding parameters are within the range of expected values for comparable systemsz6). On the other hand a knowledge of these parameters would allow an estimation of the physical and chemical contributions to the various thermodynamic


Fig. 8. Experimental and calculated (solid lines) vapor pressures of system poly(viny1 acetate)/acetone at three temperatures

L L

0 t-

500

LOO

300

200

100

35oc

25OC

properties of the mixture. We have initiated a program in our laboratories for making an independent estimation of the above type of parameters aided by literature data and carefully designed experiments.

Aside from these problems, the calculations in this work show that the theoretical model used is a useful and quite versatile model for correlating satisfactorily thermodynamic data in rather highly non-ideal systems with a minimum of parameter adjustment.

Financial support for this work has been provided by DGICYT (Spain) contract NO. PB89094, the Air Force Office of Scientific Research, and the General Secretariat for Research and Technology of Greece (STRIDE HELLAS 348), the Welch Foundation and the Texas Advanced Research Projects Agency.

’) 0. Olabisi, L. M. Robeson, M. T. Shaw, ‘%lymer-Polymer Miscibility”, Academic Press,

*) E. M. Pearce, T. K. Kwei, B. Y. Min, J Macromol. Sci.-Chem. A21, 1181 (1984) 3, R. A. Weiss, C. Beretta, S. Sasongko, A. Garton, 1 Appl. Polym. Sci. 41, 91 (1990) 4, M. M. Coleman, C. J. Serman, D. E. Bhagwagar, P. C. Painter, Polymer 31, 1187 (1990) 5 , C. C. Han, Ed., ‘%lymer Blends and Composites in Multiphase Systems’: Adv. Chem. 206,

American Chemical Society, Washington, DC 1984 6, L. A. Utracki, “Polymer Alloys and Blends”, Hanser Publishers, Munich 1989 ’) C. S. Su, D. Patterson, Macromolecules 10, 708 (1977)

New York 1979


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lo) Y. H. Cheng, D. C. Bonner, J. Appl. Polym. Sci. 19, 2457 (1975) “) C. Panayiotou, J. H. Vera, Polym. J . 16, 89 (1984) 12) M. M. Coleman, J. F. Graf, P. C. Painter, “Specific Interactions and the Miscibility of

1 3 ) P. J . Flory, J . Chem. Phys. 12, 425 (1944) 14) C. Panayiotou, I. C. Sanchez, Macromolecules 24, 6231 (1991) ‘9 C. Panayiotou, I. C. Sanchez, J . Phys. Chem. 95, 10090 (1991) 16) I. C. Sanchez, R. Lacombe, J. Phys. Chem. 80, 2568 (1976) ”) I. C. Sanchez, R. L. Lacombe, Macromolecules 11, 1145 (1978) Is) C. Panayiotou, Macromolecules 20, 861 (1987) ”) G. Luengo, G. Rojo, R. G. Rubio, M. G. Prolongo, R. M . Masegosa, Macromolecules24,1315

20) J. A. Riddick, N. B. Bunger, “Organic Solvents”, Wiley-Interscience, New York 1970 ’I) R. G. Rubio, J. A. R. Renuncio, M. Diaz Pena, J. Chem. Ermodyn. 14, 983 (1982) 22) S. Leine, J. W. Perram, in “Hydrogen Bonded Solvent Systems”, A. K . Covington, P. Jones,

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The system poly(4-hydroxystyrene)/poly(vinyl acetate)/acetone: An experimental and theoretical study

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Transcript of The system poly(4-hydroxystyrene)/poly(vinyl acetate)/acetone: An experimental and theoretical study