Journal of Molecular Liquids

Journal of Molecular Liquids 161 (2011) 153 157 ontents lists available at ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq Effect of temperature on the intrinsic viscosity of poly(ethylene glycol) in water/dimethyl sulfoxide solutions Abbas Mehrdad a,, Lotf Ali Saghatforoush b, Gamar Marzi c a Department of Physical hemistry, Faculty of hemistry, University of Tabriz, Tabriz, Iran b Department of Physical hemistry, Payame Noor University, Khoy, Iran c Department of Physical hemistry, Payame Noor University, Urmia, Iran article info abstract Article history: Received 2 January 2011 Received in revised form 25 April 2011 Accepted 24 May 2011 Available online 7 June 2011 Keywords: Polymer solution Poly(ethylene glycol) Intrinsic viscosity Expansion factor In this work, the intrinsic viscosities of poly(ethylene glycol) with molar mass of 20 kg mol 1 were measured in water/dimethyl sulfoxide solutions from (298.15 to 318.15) K. The expansion factors of the polymer chains were calculated from the intrinsic viscosity data. The expansion factor were decreased by increasing temperature; therefore the chain of PEG shrinks and the end-to-end distance become smaller by increasing temperature. Perhaps the interactions of segment segment are favored toward segment solvent by increasing temperature; therefore the hydrodynamic volumes of the polymer coils become smaller by increasing temperature. The thermodynamic parameters (entropy of dilution parameter, the heat of dilution parameter, theta temperature and polymer solvent interaction parameter) were derived by the temperature dependence of the polymer chain expansion factor. The thermodynamic parameters indicate that the interactions of segment segment were increased by increasing temperature. 2011 Elsevier B.V. All rights reserved. 1. Introduction One of the most important transport properties in polymerization processes is the viscosity of polymer solutions [1]. Polymer solvent and polymer polymer mixture viscosity is an important physical property in polymer research, development, and engineering [2]. When high molecular weight nonionic polymer molecules dissolve in a fluid, they typically expand to form spherical coils. In dilute solutions, the volume associated with each polymer coil contains one polymer molecule surrounded by a much larger mass of solvent. A polymer coil's hydrodynamic volume depends upon the polymer molecular weight and its thermodynamic interaction with the solvent. Favorable polymer solvent interactions increase the hydrodynamic volume of the polymer coil. When the polymer solvent interactions are unfavorable, the polymer coil volume is decreased. With unfavorable polymer solvent interactions, polymer coils can completely collapse and become insoluble in the fluid. Polymer solvent interactions depend upon the polymer molecular structure, chemical composition, solution concentration, solvent molecular structure, and the solution temperature [3]. Viscosity is a transport property (not thermodynamic). In activated processes as viscosity the temperature dependence of the viscous flow is given as η = A expðe=rtþ where E is activation energy which can be obtained from thermodynamic data; therefore viscosity of fluid can be studied using thermodynamic. But the intrinsic viscosity and expansion factor orresponding author. Fax: +98 411 3340191. E-mail address: a_mehrdad@tabrizu.ac.ir (A. Mehrdad). of polymer chain are hydrodynamic parameters (not transport property) which are related to the polymer polymer and polymer solvent interactions; and polymer polymer and polymer solvent interactions have close relevance to the thermodynamic parameters; therefore thermodynamic parameters can be concluded from intrinsic viscosities data. Poly(oxyethylene), an industrially important polymer, has unique solubility properties, dissolving in water in all proportions at moderate temperatures and in a very wide range of degrees of polymerization, contrary to other structurally similar polyethers, which are all insoluble in water. The poly(oxyethylene) has two names. The low and high molecular weights of poly(oxyethylene) are named poly(ethylene glycol) (PEG) and poly(ethylene oxide) (PEO), respectively. It is expected that the structure of water would affect the conformation of poly(oxyethylene) in aqueous solution, and play an important role in the physico-chemical properties of the solution [4]. Therefore, a significant amount of research has been conducted with regard to studying poly(oxyethylene) solutions which majority of these studies are in water and aqueous salts solutions [4 10]. The previous findings indicate that water is a good solvent for poly (ethylene oxide) at low temperatures, and water approaches a theta solvent for poly(ethylene oxide) with increasing temperature [11 13]. The previous findings indicate that a water/ethanol mixture is a poorer solvent than pure water for poly(ethylene oxide) [9,14,15]. The aim of this study was to determine the effect of temperature on the intrinsic viscosities of PEG in mixtures of water/dimethyl sulfoxide and calculate some of the thermodynamic parameters by temperature dependence of expansion factor of the polymer chain. 0167-7322/$ see front matter 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2011.05.013

154 A. Mehrdad et al. / Journal of Molecular Liquids 161 (2011) 153 157 2. Experimental 2.1. Materials The poly(ethylene glycol) used in this study was purchased from Merck hemical o. and had a reported nominal molar mass of 20 kg mol 1. Dimethyl sulfoxide (DMSO) was purchased from Merck hemical o. and had a reported mass fraction purity of 0.99. Poly (ethylene glycol) and DMSO were used without further purification. Distilled water was used for preparation of solutions. 2.2. Apparatus and procedure Gel permeation chromatography (GP) which was kindly performed by Jahad-e-Keshavarzi Engineering Research enter, gave an average molar mass of 21.2 kg mol 1 with polydispersity index 1.20 for PEG. PEG solutions were prepared gravimetrically by an analytical balance (Sartorius P224 S) with an uncertainty ±2 10 7 kg. The polymer solutions were prepared by dispersing the polymer powder into prepared DMSO aqueous solutions with volume fractions of DMSO, ϕ DMSO =0.05, 0.10, 0.15 and 0.20. The uncertainties of the DMSO volume fractions and concentration of polymer solutions are ±0.2% and ±2 10 3 kg m 3, respectively. The polymer solutions were filtered before use by a filter with aperture 75 μm and their viscosities were measured using a jacketed Ubbelohde viscometer with 0.4 mm capillary. The temperature of solutions was kept constant by a temperature controller (Lab. ompanion, RW-0525 G, Jeio tech o.) with an uncertainty ±0.05 K. Densities were measured with a U-tube vibrating densimeter (Kyoto Electronic DA-210) with an uncertainty ±3 10 2 kg m 3. The flow times for solutions which used in this work were never less than 190 s. The flow times were determined from an average three reading with uncertainty of ±0.2 s. 3. Theoretical The relative viscosity, η r, and specific viscosity, η sp, of dilute macromolecular solutions were calculated by Eqs. (1) and (2). η r = η η 0 = td t 0 d 0 η sp = η r 1 where t and t 0 are the flow time for the given polymer solution, d and d 0 are the density for the given polymer solution and the solvent. The reduced viscosity of dilute macromolecular solutions, η red,is calculated by Eq. (3). η red = η sp where is solution concentration. The plot of reduced viscosity versus concentration in dilute solution often gives a straight line and Huggins [16] proposed Eq. (4). η red = ½ηŠ + k H ½ηŠ 2 where [η] and k H are intrinsic viscosity and Huggins constant, respectively. Some other equations for the determination of [η] are Schultz Blaschke [17] and Martin [18] equations: η red = ½ηŠ + k SB ½ηŠη sp η red = ½ηŠ expðk M ½ηŠÞ ð6þ where k SB and k M are Schultz Blaschke and Martin constants, respectively. ð1þ ð2þ ð3þ ð4þ ð5þ In a good solvent the polymer molecule expands. Flory [19] suggested that the expansion factor, α, which describes the excluded volume effect, is calculated by Eq. (7). E1 0:5 α = @ A ð7þ 0 where and 0 the mean square end-to-end distance of a polymer chain in expanded and in unperturbed chain, respectively. Flory and Fox [20] suggested that the Mark Houwink equation can be put in the form: ½ηŠ = KM 0:5 α 3 where M is molecular weight of polymer and K is calculated by Eq. (9). E1 K = Φ@ A Mα 2 1:5 = Φ@ E 1 0A M 1:5 where Φ is the Flory constant. The Flory constant is equal 2.8 10 20 [3]. Therefore substitute Eq. (9) in Eq. (8) yields: α 3 = ½ηŠM Φ 1:5 0 Table 1 Densities, d, of PEG in mixture of water and DMSO at different (kg m 3 ) ð8þ ð9þ ð10þ T=298.15 K T=303.15 K T=308.15 K T=313.15 K T=318.15 K ϕ DMSO =0.05 0.00 1.00391 1.00224 1.00059 0.99875 0.99654 4.53 1.00481 1.00297 1.00130 0.99961 0.99748 6.81 1.00519 1.00329 1.00159 0.99999 0.99791 10.99 1.00592 1.00395 1.00215 1.00071 0.99867 13.89 1.00639 1.00444 1.00256 1.00119 0.99919 17.56 1.00697 1.00499 1.00312 1.00171 0.99977 20.14 1.00740 1.00546 1.00356 1.00216 1.00020 22.56 1.00779 1.00583 1.00393 1.00253 1.00057 ϕ DMSO =0.10 0.00 1.01100 1.00927 1.00733 1.00517 1.00301 4.49 1.01175 1.01011 1.00812 1.00601 1.00394 6.78 1.01209 1.01048 1.00847 1.00641 1.00434 9.09 1.01244 1.01084 1.00885 1.00676 1.00472 11.39 1.01279 1.01117 1.00918 1.00715 1.00512 13.51 1.01311 1.01151 1.00953 1.00751 1.00547 15.72 1.01345 1.01185 1.00985 1.00782 1.00585 17.75 1.01375 1.01215 1.01017 1.00814 1.00616 20.30 1.01413 1.01258 1.01056 1.00853 1.00655 ϕ DMSO =0.15 0.00 1.01839 1.01648 1.01433 1.01209 1.00966 4.52 1.01924 1.01728 1.01516 1.01313 1.01064 6.93 1.01962 1.01769 1.01559 1.01358 1.01109 8.80 1.01993 1.01799 1.01596 1.01392 1.01142 11.25 1.02039 1.01844 1.01639 1.01439 1.01189 13.70 1.02086 1.01886 1.01686 1.01486 1.01236 16.45 1.02139 1.01942 1.01738 1.01538 1.01288 18.45 1.02176 1.01983 1.01776 1.01577 1.01326 20.87 1.02221 1.02028 1.01823 1.01625 1.01373 ϕ DMSO =0.20 0.00 1.02598 1.02377 1.02149 1.01906 1.01640 4.57 1.02693 1.02494 1.02251 1.02031 1.01767 7.05 1.02739 1.02548 1.02303 1.02085 1.01824 9.42 1.02783 1.02593 1.02348 1.02133 1.01878 11.49 1.02823 1.02633 1.02388 1.02173 1.01918 13.77 1.02866 1.02676 1.02431 1.02216 1.01961 15.97 1.02908 1.02718 1.02473 1.02258 1.02003 18.74 1.02961 1.02774 1.02529 1.02321 1.02063 20.63 1.02998 1.02811 1.02568 1.02355 1.02109

A. Mehrdad et al. / Journal of Molecular Liquids 161 (2011) 153 157 155 Table 2 The relative viscosities, η r, of PEG in mixture of water and DMSO at different (kg m 3 ) T=298.15 K T=303.15 K T=308.15 K T=313.15 K T=318.15 K ϕ DMSO =0.05 4.53 1.1839 1.1784 1.1708 1.1644 1.1584 6.81 1.2854 1.2738 1.2622 1.2536 1.2441 10.99 1.4767 1.4604 1.4416 1.4269 1.4126 13.89 1.6210 1.6002 1.5810 1.5556 1.5355 17.56 1.8126 1.7959 1.7611 1.7301 1.7037 20.14 1.9544 1.9253 1.8871 1.8552 1.8232 22.56 2.1046 2.0654 2.0208 1.9852 1.9451 ϕ DMSO =0.10 4.49 1.1763 1.1700 1.1638 1.1584 1.1528 6.78 1.2736 1.2639 1.2532 1.2460 1.2383 9.09 1.3789 1.3630 1.3497 1.3394 1.3276 11.39 1.4861 1.4641 1.4492 1.4362 1.4196 13.51 1.5926 1.5633 1.5448 1.5297 1.5121 15.72 1.7048 1.6735 1.6488 1.6335 1.6084 17.75 1.8136 1.7795 1.7515 1.7334 1.7068 20.30 1.9524 1.9113 1.8822 1.8568 1.8293 ϕ DMSO =0.15 4.52 1.1752 1.1684 1.1634 1.1573 1.1529 6.93 1.2767 1.2671 1.2590 1.2505 1.2425 8.80 1.3573 1.3490 1.3342 1.3218 1.3128 11.25 1.4700 1.4535 1.4454 1.4284 1.4136 13.70 1.5851 1.5674 1.5542 1.5328 1.5193 16.45 1.7335 1.7098 1.6910 1.6672 1.6445 18.45 1.8309 1.8056 1.7841 1.7550 1.7329 20.87 1.9706 1.9418 1.9174 1.8825 1.8583 ϕ DMSO =0.20 4.57 1.1723 1.1683 1.1626 1.1580 1.1528 7.05 1.2747 1.2672 1.2591 1.2526 1.2429 9.42 1.3771 1.3674 1.3575 1.3473 1.3357 11.49 1.4737 1.4546 1.4463 1.4293 1.4210 13.77 1.5818 1.5604 1.5491 1.5327 1.5187 15.97 1.6853 1.6688 1.6483 1.6315 1.6152 18.74 1.8235 1.8000 1.7860 1.7646 1.7412 20.63 1.9270 1.9002 1.8790 1.8532 1.8307 In the random flight chains model with restricted bond angles φ but rotations about the bonds are not restricted, 0 is calculated by Eq. (11). D E = 1 cosφ 1+ cosφ 0 Nl2 1+ cosφ +2l2 cosϕ ð ÞN ð11þ ð1+ cosφþ 2 where N and l are the number of bonds existing in polymer chain and the bond length, respectively. However, in the case PEG φ=109.5 and the value of N is threefold of ratio molecular mass of polymer to mass of monomer, because there are three linkages in each monomer of PEG. Table 4 The intrinsic viscosities, [η], and Schultz Blaschke constant, k SB, of PEG in various mixture of water and DMSO at different 298.15 0.03919 0.03779 0.03718 0.03645 303.15 0.03781 0.03639 0.03586 0.03544 308.15 0.03627 0.03500 0.03470 0.03429 313.15 0.03497 0.03387 0.03346 0.03330 318.15 0.03375 0.03271 0.03244 0.03214 k SB 298.15 0.224 0.261 0.260 0.257 303.15 0.237 0.261 0.276 0.261 308.15 0.247 0.277 0.295 0.284 313.15 0.254 0.295 0.304 0.292 318.15 0.260 0.304 0.315 0.315 The value of l in the case of PEG is derived by taking average from bonds length for ( ) and ( O) The used bonds length are l =0.153 and l O =0.143 nm [8]. Therefore substitute Eq. (11) in Eq. (10) yields:! α 3 = ½ηŠM 1 cosφ 1+ cosφ Φ Nl2 1+ cosφ +2l2 cosφ ð 1:5 ÞN ð12þ ð1+ cosφþ 2 Flory and Fox [20] further suggested that the temperature dependence of the expansion factor as Eq. (13).! E 1 α 5 α 3 2 27 ν R 2 = @ 0A 2 1:5 π 1:5 N A V s M 1:5 ΨM 0:5 1 θ T ð13þ where V s, ν, N A and T are the molar volume of solvent, the partial specific volume of the polymer, Avogadro's number and absolute temperature, respectively. On the other hand, the relation of Ψ and κ is given by Eq. (14). κ = θψ T ð14þ where thermodynamic parameters Ψ, κ and θ are the entropy of dilution parameter, the heat of dilution parameter and theta temperature, respectively. The polymer solvent interaction parameter, χ, can be expressed in terms of entropy and heat of dilution parameter as Eq. (15). χ =0:5 +κ Ψ ð15þ Table 3 The intrinsic viscosities, [η], and Huggins constant, k H, of PEG in various mixture of water and DMSO at different 298.15 0.03862 0.03717 0.03657 0.03589 303.15 0.03724 0.03584 0.03524 0.03491 308.15 0.03573 0.03445 0.03405 0.03371 313.15 0.03445 0.03331 0.03284 0.03274 318.15 0.03326 0.03217 0.03183 0.03155 Table 5 The intrinsic viscosities, [η], and Martin constant, k M, of PEG in various mixture of water and DMSO at different 298.15 0.03893 0.03749 0.03690 0.03617 303.15 0.03754 0.03613 0.03557 0.03519 308.15 0.03601 0.03474 0.03439 0.03401 313.15 0.03472 0.03361 0.03317 0.03303 318.15 0.03351 0.03246 0.03216 0.03185 k H 298.15 0.298 0.352 0.351 0.343 303.15 0.318 0.347 0.376 0.347 308.15 0.331 0.371 0.407 0.385 313.15 0.341 0.399 0.418 0.396 318.15 0.346 0.411 0.434 0.433 k M 298.15 0.256 0.301 0.299 0.296 303.15 0.272 0.298 0.320 0.299 308.15 0.284 0.318 0.344 0.329 313.15 0.292 0.340 0.353 0.338 318.15 0.298 0.350 0.366 0.367

156 A. Mehrdad et al. / Journal of Molecular Liquids 161 (2011) 153 157 Table 6 The expansion factor, α, of PEG in various mixture of water and DMSO at different 298.15 1.856 1.833 1.824 1.812 303.15 1.834 1.811 1.801 1.795 308.15 1.809 1.787 1.781 1.775 313.15 1.787 1.768 1.760 1.758 318.15 1.766 1.747 1.742 1.737 Table 7 The heat of dilution parameter, κ, in various mixture of water and DMSO at different 298.15 0.7124 0.7223 0.7503 0.7422 303.15 0.7007 0.7104 0.7379 0.7299 308.15 0.6893 0.6988 0.7259 0.7181 313.15 0.6783 0.6877 0.7143 0.7066 318.15 0.6677 0.6769 0.7031 0.6955 On the other hand, the temperature dependence of the polymer solvent interaction parameter is as Eq. (16). χ = χ s + χ h T ð16þ where χ s and χ h are the entropic and enthalpic contribution of polymer solvent interaction parameter, respectively. 4. Results and discussion The flow times and densities of PEG solutions in mixed water/ DMSO with volume fractions of DMSO, ϕ DMSO =0.05, 0.10, 0.15 and 0.20 were measured at various temperatures and concentrations of polymer. The densities in various conditions are listed in Table 1. From the flow times and densities data, relative viscosities, η r,are calculated. The calculated relative viscosities in various conditions are listed in Table 2. According to the Huggins equation the intrinsic viscosity of the polymer can be obtained by extrapolation of reduced viscosity to zero polymer concentration. The obtained intrinsic viscosities according to the Huggins equation and Huggins constants are listed in Table 3.For flexible polymer molecules Huggins constant is expected to be about 0.35 in good solvents, but higher in poor solvents [21]. The Huggins constant may be influenced by branching of the polymer, by aggregation in solution, as well as by the shear rate during measurement. Our pervious data reveals that the Huggins constant for PEG in pure water are less than 0.2 [13]. Our data reveals that the Huggins constants for PEG in mixed water/dmso are higher than those in pure water. Nevertheless the mean value of Huggins constants for PEG in mixed water/dmso is 0.37 which is around the expected value (0.35). According to the Schultz Blaschke equation the intrinsic viscosity of the polymer is obtained by extrapolation of reduced viscosity to zero specific viscosity. The obtained intrinsic viscosities according to the Schultz Blaschke equation and Schultz Blaschke constants are listed in Table 4. For an ideal solution of spherical solute particles, the value of Schultz Blaschke constant is 0.4, while for a real solution, taking into account the frictional coefficient, this value is less than 0.4 [4]. Our data reveals that the mean value of Schultz Blaschke constants for PEG in mixed water/ DMSO is 0.274. Also According to the Martin equation the intrinsic viscosity of the polymer is obtained by extrapolation of Ln(η red )to zero polymer concentration. The obtained intrinsic viscosities according to the Martin equation and Martin constants are listed in Table 5. The results of Tables 3 5 reveals that the Huggins, Schultz Blaschke and Martin constants are increased by increasing volume fractions of DMSO. It seems likely that this increment arise from aggregation of polymer molecules. omparison the results of Tables 3 5 reveals that the obtained intrinsic viscosities from Huggins, Schultz Blaschke and Martin equations are comparable. The obtained intrinsic viscosities of PEG are decreased by increasing temperature. Therefore, mixed water/dmso solutions were changed to the weak solvents for PEG by increasing temperature. The values of expansion factor were calculated using average intrinsic viscosities which obtained on the basis mentioned equations. The calculated expansion factors of PEG at different temperatures and various volume fractions of DMSO are listed in Table 6. The data of Table 6 indicate that the values of expansion factor were decreased by increasing temperature; therefore the chain of PEG shrinks and the end-to-end distance become smaller by increasing temperature. This behavior is maybe due to effect of temperature on the interactions of segment segment and segment solvent. Perhaps the interactions of segment segment are favored toward segment solvent by increasing temperature; therefore the hydrodynamic volumes of the polymer coils become smaller by increasing temperature. For evaluating of theta temperature and entropy of dilution parameter, the values of (α 5 α 3 ) plotted versus 1/T. The plots of (α 5 α 3 ) versus 1/T are presented in Fig. 1. From the intercept and slope of these plots the values of theta temperature and entropy of dilution parameter were calculated. The obtained values of theta temperature for PEG in mixed water/dmso with volume fractions of ϕ DMSO =0.05, 0.10, 0.15 and 0.20 are 394.7, 399.0, 404.4 and 416.1 K, respectively. The obtained values of entropy of dilution parameter for PEG in mixed water/dmso with volume fractions of ϕ DMSO =0.05, 0.10, 0.15 and 0.20 are 0.5381, 0.5397, 0.5532 and 0.5319, respectively. The obtained values of entropy of dilution parameter indicate that the entropy of dilution parameter is negative for PEG in all volume fractions of DMSO that is, solvent molecules are ordered by Table 8 The polymer solvent interaction parameter, χ, in various mixture of water and DMSO at different Fig. 1. The changes of (α 5 α 3 ) versus 1/T for PEG in water/dmso;, ϕ DMSO =0.05;, ϕ DMSO =0.10;, ϕ DMSO =0.15;, ϕ DMSO =0.20. 298.15 0.3257 0.3174 0.3029 0.2897 303.15 0.3374 0.3294 0.3153 0.3019 308.15 0.3488 0.3409 0.3273 0.3138 313.15 0.3598 0.3520 0.3389 0.3252 318.15 0.3705 0.3628 0.3501 0.3363

A. Mehrdad et al. / Journal of Molecular Liquids 161 (2011) 153 157 157 PEG was increased by increasing the volume fraction DMSO. According to Eq. (16) the plots of χ versus 1/T gives the values of χ s and χ h. The plots of χ versus 1/T are presented in Fig. 2. The obtained values of χ s for PEG in mixed water/dmso with volume fractions of ϕ DMSO = 0.05, 0.10, 0.15 and 0.20 are 1.038, 1.040, 1.053 and 1.032, respectively. The obtained values of χ h for PEG in mixed water/dmso with the volume fractions of ϕ DMSO =0.05, 0.10, 0.15 and 0.20 are 212.4, 215.3, 223.7 and 221.3 K, respectively. The obtained absolute values of χ h for PEG in mixed water/dmso is higher than of that in pure water ( 186.7) which reported previously [13]. 5. onclusion Fig. 2. The changes of χ versus 1/T for PEG in water/dmso;, ϕ DMSO =0.05;, ϕ DMSO =0.10;, ϕ DMSO =0.15;, ϕ DMSO =0.20. PEG. However, the absolute value of entropy of dilution parameter for PEG in mixed water/dmso is higher than of that in pure water ( 0.4813) which reported previously [13]. This behavior is maybe due to the interaction of PEG-DMSO stronger than interaction of PEGwater; therefore the DMSO molecules rather than water are ordered by PEG. The heat of dilution parameter for PEG in various volume fractions of DMSO and temperatures were calculated by Eq. (14).The values of the heat of dilution parameter for PEG in various volume fractions of DMSO and temperatures are listed in Table 7. The obtained results indicate that of heat of dilution parameter is negative for PEG in all volume fractions of DMSO that is, interactions of segment solvent is favored toward segment segment in PEG. However, the absolute value of heat of dilution parameter for PEG in mixed water/dmso is higher than of that in pure water which reported previously [13]. This behavior is maybe due to the interaction of segment-dmso is stronger than its segment-water. The polymer solvent interaction parameter was calculated by Eq. (15). The values of polymer solvent interaction parameter are listed in Table 8. The results of Table 8indicate that polymer solvent interaction parameter for PEG in all volume fractions of DMSO are increased by increasing temperature. Polymer solvent interaction parameter is related to the thermodynamic quality of solvent in polymer solutions. A good solvent has a low value of polymer solvent interaction parameter, while a poor solvent has a high value of polymer solvent interaction parameter; therefore the results of Table 8 indicate that the quality of mixed water/dmso for PEG were decreased by increasing temperature. Also the results of Table 8 indicate that the thermodynamic quality of mixed water/dmso for In this work, the effect of temperature on the intrinsic viscosity of poly(ethylene glycol) in mixed water/dmso was investigated. Our results indicate that the values of intrinsic viscosity were decreased by increasing temperature and volume fractions of DMSO. The values of expansion factor were calculated using intrinsic viscosities. The obtained data indicate that the values of expansion factor were decreased by increasing temperature and volume fractions of DMSO; therefore the chain of PEG shrinks and the end-to-end distance become smaller by increasing temperature volume fractions of DMSO. The polymer solvent interaction parameter was calculated by the temperature dependence of the polymer chain expansion factor. The obtained polymer solvent interaction parameters indicate that the thermodynamic quality of mixed water/dmso for PEG was decreased by increasing temperature. References [1] Y. 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