Macromolecules 1980, 13, 734-741 P. J. Flory, B. E. Eichinger, and R. A. Orwoll, Macromolecules,
(1968).
T. Shiomi, K. Fujisawa, F. Hamada, and A. Nakajima, J. Chem. SOC.,Faraday Trans. 2, submitted. J. S. Rowlinson, Discuss. Faraday SOC.,49, 30 (1970). N. S. Snider and T. M. Herrington, J. Chem. Phys., 47, 2248 (1967); T. W. Leland, J. S. Rowlinson, and G. A. Sather, Trans. Faraday SOC.,64, 1447 (1968); M. L. McGlashan, ibid., 66, 18 (1970); K. N. Marsh, M. L. McGlashan, and C. Warr, ibid., 66,
T. Okazawa and M. Kaneko, Polym. J., 2, 747 (1971). R. A. Orwoll and P. J. Flory, J. Am. Chem. SOC.,89, 6814
P. H. C. Lin, Ph.D. Thesis, Washington University, Missouri,
1, 287 (1968).
B. E. Eichinger and P. J. Flory, Trans. Faraday SOC.,64, 2053 (1968).
B. E. Eichinger and P. J. Flory, Trans. Faraday SOC.,64,2061 (1968).
B. E. Eichinger and P. J. Flory, Trans. Faraday SOC.,64,2066
2453 (1970). 1970.
(1967).
K. Kubota, Y. Kim, K. Kubo, and K. Ogino, Rep. Prog. Polym. Phys. Jpn., 20, 43 (1977). K. Kubota, Doctoral Thesis, Tokyo University, Tokyo, 1979. I. C. Sanchez and R. H. Lacombe, J . Phys. Chem., 80, 2352
F. Hamada, K. Fujisawa, and A. Nakajima, Polym. J., 4, 316 (1973).
P. J. Flory and H. Hocker, Trans. Faraday SOC.,67, 2251 (1971); H. Hocker and P. J. Flory, ibid., 67, 2270 (1971); H. Hocker, H. Shih, and P. J. Flory, ibid., 67, 2275 (1971); A. Nakajima, F. Hamada, K. Yasue, K. Fujisawa, and T. Shiomi, Makromol. Chem., 175, 197 (1974). P. J. Flory and H. Shih, Macromolecules, 5, 761 (1972). R. Chahal, W. Kao, and D. Patterson, J. Chem. SOC.,Faraday Trans. 1. 69. 1834 (1973). K. Sugkiya, N. Kuwahara, and M. Kaneko, Macromolecules,
(1976).
S. Morimoto, J . Polym. Sci., Part A-I, 6, 1547 (1968). B. E. Eichinger and P. J. Flory, Trans. Faraday SOC.,64,2035 (1968).
P. J. Flory, “Statistical Mechanics of Chain Molecules”, Interscience, New York, 1969. R. L. Scott and P. H. van Konynenburg, Discuss. Faraday SOC.,49, 87 (1970). W. C. Roth, J . Am. Chem. SOC.,69, 474 (1947). C. H. Baker, W. B. Brown, G. Gee, J. S. Rowlinson, D. Stubley, and R. E. Yeadon, Polymer, 3, 215 (1962). W. R. Krigbaum and P. J. Flory, J. Am. Chem. SOC.,75,1775
7, 66 (1974). T. Shiomi. Z. Izumi. F. Hamada. and A. Nakaiima. “ , Macro-
molecules,’submitted. T. Shiomi, Y. Kohra, F. Hamada, and A. Nakajima, Macromolecules, submitted. E. A. Guggenheim, Trans. Faraday SOC.,44, 1007 (1948); “Mixtures”, Oxford University Press, London, 1952. K. Fujisawa, T. Shiomi, F. Hamada, and A. Nakajima, Polym. Bull., submitted.
(1953).
P. J. Flory and H. Daoust, J. Polym. Sci., 25, 429 (1957).
Conformational Characteristics of Poly(viny1 fluoride), Poly(fluoromethylene), and Poly(trifluoroethy1ene) Alan E. Tonelli Bell Laboratories, Murray Hill, New Jersey 07974. Received October 29, 1979 ABSTRACT: Conformational energy estimates are employed t o determine the conformational characteristics of poly(viny1 fluoride) (PVF), poly(fluoromethy1ene) (PFM), and poly(trifluoroethy1ene) (PTF,). Effects of stereoconfiguration and, in the case of P V F and PTF,, the presence of head-to-head:tail-to-tail (H-H:T-T) defect structures are considered. Rotational isomeric state models are developed for these polymers and used t o calculate their unperturbed dimensions, dipole moments, and conformational entropies. T h e calculated results are compared t o corresponding values found for poly(viny1idene fluoride), poly(tetrafiuoroethylene), and polyethylene, and the equilibrium flexibilities of PVF, PFM, and PTF, are discussed on this basis.
During the course of our studies concerning the 13C NMR chemical shifts of vinyl polymers we became interested in understanding the 13C chemical shifts observed in the fluorinated polymers poly(tetrafluoroethy1ene) (PTFE), poly(viny1idene fluoride) (PVFJ, poly(viny1 fluoride) (PVF), poly(fluoromethy1ene) (PFM), and poly(trifluoroethylene) (PTF,). We have demonstrated in hydrocarbon polymers, such as poly(propylene),’r2 ethylene-propylene copolymer^,^^^ poly~tyrene,~ etc., and in a chlorine-substituted vinyl polymer [poly(vinyl ~hloride)~], that the chemical shift of a given carbon atom depends on the frequency with which it is involved in three bond gauche or y interactions7-’l with other carbon or chlorine atoms. Each y interaction produces an upfield chemical shift on the order of 3-5 ppm. Enumeration of the number and kind of y interactions involving a given carbon atom permits1’ a determination of its relative 13C chemical shift. Bond rotation probabilities obtained from the rotational isomeric state (RIS) mode112J3of a polymer chain lead to just such an accounting of possible y interactions. With knowledge of the conformational characteristics of these polymers it was possible to understand their stereosequence-dependent 13C chemical shifts. Before the 0024-9297/80/2213-0734$01.00/0
same approach can be attempted for fluorinated polymers, we must possess information concerning their conformational characteristics. The conformational characteristics of PTFE14 and PVF215have been determined through approximate potential energy estimates16 and checked against experimentally determined unperturbed d i m e n ~ i o n s ’ ~and J~ dipole mornent~.’~ However, neither PVF nor PFM nor PTF, have been studied from a conformational point of view. Such a study is described in this report, where the conformational energies of PVF, PFM, and PTF3 chain fragments of various stereosequence are calculated, and where the possibility of head-to-head:tail-to-tail (H-H:T-T) addition of monomer units in PVF and PTF3is permitted and considered. From the conformational energies, RIS models are developed, and the conformationally sensitive properties (r2),, and ( P ~ ) i.e., ~ , the mean-square unperturbed dimensions and dipole moments, and the conformational entropies, S,, are calculated.
Conformational Energy Calculations Portions of PVF (PTF,) and PFM chains whose conformations depend on one or both of two neighboring bond rotation angles are illustrated in Figure 1. For PVF
0 1980 American Chemical Society
Conformational Characterisics of Poly(viny1 fluoride) 735
Vol. 13, No. 3, May-June 1980
320xJ4
H - H: T - T
H - T
240 H
F
H (FHF)
F
H (HHF)
F
s" H F
H
H
H
F
(HFH)
F
H
H
H (HFF)
0
00
160
240
320
+, Figure 1. (a) PVF (PTFJ chain fragments. CH2are replaced by CF2 for PTFB. (b) PFM chain fragments.
- -
-
-
(PTF3)both head-to-tail (H-T) HFH,FHF (FHF,HFH) HFF,HHF F H H (HHF and H-H:T-T F F H FHH,FFH HFF) chain fragments were considered. Conformational energies were calculated for each of these fragments as a function of the rotation angles $1 and &, using the approximate potential energy f u n c t i o n ~ ' ~ J ~ previously employed14J5in the analysis of the conformational characteristics of PVFz and PTFE. An intrinsic threefold torsional potential with a barrier height of 3.0 kcal/mol is assumed to separate three rotational minima a t & or c $ ~ = 0 (trans, t), 4~120' (gauche *, g*). A 6-12 potential describes nonbonded van der Waals interactions, and partial charged5 of f0.2 esu are assigned to the C and F atoms, respectively, terminating C-F bonds to account for nonbonded electrostatic interactions. A dielectric constant E = 6 was selected15 to mediate the electrostatic interactions. Bond lengths of 1.53, 1.36, and 1.10 A were used for C-C, C-F, and C-H bonds, and the valence anglesz0LCCC = 112 (PVF), 116 (PTF3), 117.5' (PFM), LHCF = LFCF = 106', and LHCH = 109.5' were employed. Both rotation angles were stepped in 20' increments over their entire ranges. Evaluation of RIS Models Statistical weights SW,, were evaluated for each of the nine pair-wise dependent rotational states CUP = tt,tg*g*tg*g*, and g'g' from the calculated conformational energies. As an example,
SW,.,
=
180'
60"
C
C exp[-E(+d~J/RTl
+,=60° $2=-60° 340' 340'
C
+1=0 &=0
exp[-E(@l,&)/RTl
where the sums in both numerator and denominator contain only terms whose energies E(&,&) are within 5.0 kcal/mol of the lowest energy conformation (&,&) found.
Figure 2. Conformational energy map for the HFH fragment in H-T PVF. Contours are in kcal/mol of fragment relative to the lowest energy conformation denoted by X.
Statistical weight matrices U were then constructed at a given temperature. For PVF, as an example, g'
One such statistical weight matrix was constructed for each different chain fragment (see Figure 1)considered in PVF, PFM, and PTF, at T = 0,50,100,150, and 200 'C. These matrices define the RIS model appropriate to each polymer.
Calculation of Dimensions, Dipole Moments, and Conformational Entropies Matrix multiplication technique^'^ were used to calculate mean-square end-to-end distances ( r2)o,dipole moments ( F * ) ~ and , conformational entropies S , of isolated and unperturbed PVF, PFM, and PTF3 chains. A C-F bond dipole momentz1 of 1.8 D was used in the calculation of (p2),,. Chains of 400-500 backbone bonds were considered. Each chain was generated a bond at a time by Monte-Carlo techniques and checked for the effects of stereosequence and (H-H:T-T) defect content at each bond addition. Ten Monte-Carlo chains were generated for each defect content and each degree of stereoregularity, and (r2)o,( F ' ) ~ ,and S , were averaged over the same ensemble of chains. Calculated Results Figures 2-6 present conformational energy maps for representative fragments of the PVF and P F M chains. Statistical weight matrices for all possible PVF, PFM, and PTF3 chain fragments are given in the Appendix at T = 0, 50, 100, 150, 200 'C. The dimensions and dipole moments presented as the ratios (r2)o/n12and ( ~ ~ ) ~ / n r n ~ , where n is the number of bonds in the chain, l2 is the square of the C-C bond length, and m2 is the square of the C-F bond dipole moment (l/z and 3 / 2 the square for PVF and PTF3), appear in Tables I and 11. Temperature
736 Tonelli
Macromolecules
”
s”
160
240
320
0
9,
80
160
240
320
”
41
F i g u r e 3. Same as Figure 2 except replace HFH with FHF.
F i g u r e 4. Same as Figure 2 except replace HFH with FFH and H-T with H-H:T-T.
TABLE I “ ~
ni2 and
3mx
”
nm2
cdlculdted for 400-500 Bond PVF dnd PTF, Chdlns d S d Function Of Stereoreguldritv dnd H-H T - T Defect Content PVF
PTF,
< w 2 > ,/nm’
1 7 Ib6.1‘ 7.7 80 6 54 ~
,
l.28b 123 I20
’
1
~
I 15‘ I12 I10
~
9gb 1103 105
8 9‘ 90 90 90 90 89 95 93 94 94 95 94 99 95 97 97 99 99 10 4 99 98 IO I IO 3 IO 2
~
~1
:
6
(i 76
163
~
62
4 6
a
-
b
-T
=
50°C
c
.T
=
ISOT
Probability 01
72 71 70 71 74 74 71
60 59 58 I 6 0 60 ‘ 5 9
~
I05 I08 0 90 I08 1 00 0 93 0 91 0 93 0 79 0 94 0 94 0 87 0 80 0 19
I06
~
~
0 99 I02 0 90 I02 0 95 0 92 0 89 0 92 0 80 0 91 0 93 0 85 0 82 0 82
II 0 ~~
10.7 II 6 IO 6
II I II 6 11 8 II 5 ~
~
~
12 4 II 3 II 3 II 9 I2 4 I2 3
-
~
0 54b 0 56 0 57 0 57 0 56 0 54 0 43 0 48 0 48 0 47 0 47 0 44 0 35 0 43 0 42 0 40 0 38 0 37 __ 0 30 0 36 0 37 0 36 0 33 0 30 ~
~
0 52‘ 0 52 0 52 0 52 0 52 0 52 0 43 0 46 0 45 0 43 0 44 0 44 0 37 0 42 0 40 0 38 0 38 0 36 0 32 0 36 0 37 0 35 0 32 0 32
240
9,
~
F i g u r e 5. Same as Figure 4 except replace F F H with FHH. Table I1 tr2),/n12and (fiZ),/nm2 Calculated for 400 Bond PFM Chains as a Function of Stereoregularity (r2),/nl2 (fi’),,/nm Pma 50°C 150°C 50°C 150°C 2.1 1 1.67 13.3 10.4 0 1.39 8.54 1.58 0.2 10.5 1.07 7.30 1.17 0.4 8.57 0.86 0.83 6.06 0.6 7.07 5.13 0.58 0.60 0.8 5.81 0.40 4.95 0.36 1 .o 5.01
meso (GI dyad (see Figure l ( a ) )
coefficients of ( r 2 ) oand ( F ~are) presented ~ in Tables I11 and IV. Discussion and Results Both the calculated dimensions and dipole moments of PVF are virtually independent of stereosequence. Fur-
a
Probability of a meso ( m ) dyad (see Figure l b ) .
Conformational Characterisics of Poly(viny1 fluoride) 737
Vol. 13, No. 3, May-June 1980
Table V Comparison of Unperturbed Dimensions
TABLE I l l dl n < r2 > ,/dT
PE P ;IF PVFIC PFM PTF, PTFE'
and dln,/dT for PVF and PTF, Chains of 400-500 Bonds of Varying Stereoregulariiies and H-H:T-T Defect Contents '%H-T:T-T
Pm"
(din< r2>o/dT)h,K-
'
d In tr'),/dT
CRa
polymer
6.1 6.0 5.9 4.5-10.5 9.5 30
-0.0011 -0.0020 -0.0013 -0.0012-0.0024d -0.0020 -0.0009
a T = 150 "C. Calculated for d T = 150 - 50 = 100 "C. Experimentally confirmed . I 3 Range corresponds to P , = 1.0-0.0. 914,1'
PVF
PVF
0
0 2 4 6 8
IO 0
IO
2 4 6
8 I O 0 2 4 6 8 I O 0 2 4 6 8 I O
20
30
a
-
- 0017 - 0018 - 0021 - 0022 - 0021 - 0017 - 0018
- 0019
- 0020 - 0021 - 0019 - ooia - 0017 - 0019 - 0020
- 0020 - 0021 .0018
- ooia - 0019 - ooia - 0021 - 002 1 - 0018
Probability of meso
b - dT
=
150-50
=
(E)
- 001 I - 0013 - 0015 ~
0015
- 0013 - 001 I - 0013 - 0012 - 0015 - 0017 - 0015 - 0013
- 0016
- 001 1 - 0013 - 0018 - 0018 - 0015 - 0018 - 0013 - 0014
- 0016 - 0019 - 0019
- 0010 .0009 . 0009 - 0010 - 0009 - 0010 - 0006 - 0006 - 0007 - 0004 - 0006 - 0006 00 .0006
- 0004 .0007 - 0009
- 0009 - 0007 - 0004 00 0004 - 0006 ~
- 0001
- 0009 - 0007 00 0006 - 0002 - 0005 - 0005
- 0001
00 - 0003
- 0005
- 0002
+ 0001 . 0003
- 0001 - 0002
+ 0002
+ 0004
+
+ 0006 00 00 - 0003 - 0003 + 0006
dyad (see Figure 1 ( a ) )
IOO"C
Table IV d In (r'),/dT and d In ( p 2 ) , / d T for 400 Bond PFM Chains of Differing- Stereoregularity -
a
PrlQ
d In (r')o/ d T , b K"
d In ( M ' ) , / dT,b K - '
0 0.2 0.4 0.6 0.8 1.0
-0.0024 -0.0021 -0.0018 -0.0015 -0.0012 -0.0012
-0.0023 -0.0013 -0.0009 -0.0004 t 0.0003
+0.0011
Probability of meso ( m )dyad (see Figure l b ) .
dT=
150 - 50 = 100 "C.
thermore the dimensions are also insensitive to the level of H-H:T-T addition. The characteristic ratios CR = (r2)o/n12calculated for PVF do not vary more than 10-15% over the entire spectrum of stereoregularity even allowing for as many as 30% H-H:T-T additions. Dipole moment ratios CM = (k2)o/nm2, although independent of stereosequence, do decrease 20-25% as the H-H:T-T content reaches 20-30%. Neither property can be usefully employed to determine PVF stereoregularity, and they both fail to exhibit any marked degree of sensitivity to H-H:T-T defect content. These two conformational properties cannot be expected to characterize the microstructure of PVF.
Table VI Conformational Entropies Calculated at 150 "C polymer
S,, eu/( mol bonds)
PE PVF PVF, PFM PTF, PTFE
(2.1-2.3)" 2.0 (1.9-2.6)b (1.8-2.0)'
1.8
1.4
a Corresponds to P , = 0.0-1.0 and 0% H-H:T-T addiCorresponds t o tion. Corresponds to P, = 1.0-0.0. P, = 1.0-0.0 and 0% H-H:T-T addition.
Both CR and CM are sensitive to chain stereoregularity in PFM. As the probability of meso ( m )dyad placement decreases from 1.0 to 0.0, CR and CM increase 2-3- and 4-6-fold, respectively. Clearly, either property can be expected to successfully characterize the stereoregularity of P F M chains. Neither CR nor CM are sensitive to chain stereoregularity in PTF3 As for PVF chains, only CM is significantly affected by H-H:T-T addition and may possibly be used to characterize the defect content of PTF, chains. Inspection of the statistical weight matrices of PVF (see Appendix) indicates that several conformations, or pairs of bond rotations, are likely regardless of stereosequence or defect content. Also note the similarities among the conformational energy maps of PVF fragments (Figures 2-5) corresponding to both H-T and H-H:T-T addition of monomer units. The similar degree of conformational diversity among all possible PVF chain fragments produces the nearly constant dimensions calculated for PVF chains of any likely structure. These comments are also applicable to PTF,, with the additional observation that the larger dimensions [CR = 9.5 (PTF,), 6.0 (PVF)] result from a significant increase in the probability of the all-trans ( t ) ,planar zigzag conformation. The PFM chain, on the other hand, increasingly prefers the extended tt conformation as the meso ( m )placement of dyads decreases. (The all-meso chain prefers the tg*g*t conformations, which result in compact chain conformations.) Hence, the all-racemic (r) chain has dimensions 2-3 times as large as all-meso ( m )PFM. PVF, PFM, and PTF, are all expected to contract with increasing temperature as indicated by the temperature coefficients of the dimensions, d In (r2)o/dT,presented in Tables I11 and IV. Stereosequence and defect content have little effect on the ability of these polymer chains to adopt more compact conformations as the temperature is raised. It may be of interest to compare the conformational characteristics of PVF, PFM and PTF, with those of PVF2, PTFE, and polyethylene (PE) to learn how the increasing
738 Tonelli
Macromolecules
?, '/
I,,
F , H #2
':
1
C / k % d rX % C\
-i
C
hX F
320
0
80
160
320
240
4, Figure 6. Conformational energy map for the r, m chain fragment of PFM. Contours are in kcal/mol of fragment relative to the lowest energy conformation denoted by X.
fluorination of PE affects equilibrium chain extension. In Table V the calculated dimensions (CR)and their temperature coefficients are presented for PE, PVF, PFM, PVF,, PTF3, and PTFE. With the exceptions of the completely fluorinated member (PTFE) and predominantly isotactic P F M chains (with P M = 0.0-0.2), all members of this polymer series have dimensions which are remarkably similar, i.e., CR = 5-9. In addition, each polymer chain contracts with increasing temperature to adopt more compact conformations. This chain contraction is characterized by d In (P),/dT = -(0.0014.002) K-' for each of these polymers. Although the conformational characteristics of PVF, PFM, and PTF3chains remain to be tested experimentally, it would appear that except for PTFE all of the polymers in this series possess comparable equilibrium extensions as manifested by their unperturbed dimensions. In addition, Table VI presents conformational entropies, s,, c a l c ~ l a t e at d ~150 ~ ~"C ~ ~for each polymer. Conformational entropy provides a measure of the number and frequency of occurrence of the various bond rotational states. Thus, CR and S,, which are two distinctly differentz4probes of polymer chain conformations, both indicate that this series of polymers, with the exception of PTFE, possesses similar conformational characteristic^.^^
Acknowledgment. Happy Birthday Professor Flory.
Appendix: Statistical Weight Matrices+ for PVF, PFM, and PTF3 Chains at 0,50, 100, 150, and 200 "C PTF3 (H-T)
PVF (H-T)
61\42
g'
FHF(dd) =
.179
g-
,167 .116 ,118 . I 19 ,119 ,119
, I 14 ,115 ,115 ,114 ,113 ,068 ,074 ,078 ,082 ,085 .01 I ,016 ,021 ,026 ,030
41\62
g-
.202 ,188
t
,179 ,172 .167 ,067 ,077 ,082 ,086 ,089 ,067 ,073 ,078 ,081 ,083
HFH(dd) =
g+
g-
t
.358a .333b ,313' .297d .284e ,051 ,064 ,075 ,084 ,091 ,261 ,253 ,245 ,236 ,229
g+
g-
,261 ,253 ,244 ,235 .227 ,009 ,015 ,021 ,027 ,032 ,001 ,003 ,005 ,008 ,010
,051 ,064 ,075 ,084 ,091 0.0 0.0 ,001 ,001 ,002 ,009 ,015 ,021 ,027 ,032
a b c d
- T = - T = - T = - T = e - T =
0°C 50°C 100°C 150°C 200°C
Vol. 13, No. 3, May-June 1980
Conformational Characterisics of Poly(viny1 fluoride) 739
61\42 t
g-
t
g+
g-
,347 ,301 .271 ,249 ,233 ,120 ,125 ,127 ,128 ,129 ,099 ,105 ,108 . I IO , I 12
,118 .122 .I25 ,126 ,127 .I12 ,114 ,115 ,115 ,115 ,037 ,046 ,052
,092 .096 .099 ,102 ,103 ,043 ,053 ,060 ,065 ,068 ,032 ,038 .043 ,047 ,051
61\02 t
HFH (dl) = g+
g-
,058 .062
t
g+
g-
,629 ,539 ,472 ,423 ,386 ,082 ,099 . I 12 ,120 ,126 ,065 ,082 ,095 ,103 ,110
,082 ,099
,065 ,082 ,095 ,103 ,110 ,001 ,002 .003 ,005 ,007 ,074 ,094 ,107 ,116 ,122
. I 12 ,120 ,126 ,001 ,002 ,004 ,006 ,008 ,001 ,001 .003 ,004 ,006
41\42 t
HFH(d)= g+
61\62 FHF(d)=
t
g+
g-
t
g+
g-
,314 ,276 ,251 ,235 ,223 ,160 ,162 ,161 ,159 ,156 . I 14 ,122 .I26 ,129 ,130
,147 ,148 .I47 ,145 ,143 .047
,163 ,165 ,164 ,162 ,160 ,009 ,014 ,020 ,025 .030 .041 ,050 ,057 ,062 ,067
t ,151 ,151 ,149 ,149 ,148
,215 ,201 ,192 ,184 ,178 ,075 ,083 ,088 ,093 ,096
,055 .062 ,067 ,071 ,005 ,008 ,012 ,016 ,202
g'
,151 ,147 ,144
,140 ,137 ,066 ,076 ,084 ,089 ,092 ,003 ,005 ,008 .01 1 ,014
g,219 ,205 ,195 ,187 ,181 ,021 ,030 ,037 ,044 ,050 ,099 ,102 ,104 ,104 ,105
Interchanging the second and third columns and rows of F H F ( d d ) , FHF(dl), and H F H ( d ) yields FHF(II1, F H F ( l d ) , and HFH(I), respectively. Interchange H and F for PTF, PVF (H-H:T-T)
61\62 .t
FFH (dl) = 9+
t
g+
,195 .I84 ,176 ,171 ,167 ,146 ,144 ,142 ,140 ,139 ,199 ,188 ,181 ,175 ,170
. I 14
61\42
g-
,098 ,118 ,100 ,120 ,101 , 1 2 2 ,101 ,123 ,101 ,126 ,017 ,125 ,023 , 1 2 4 ,029 ,123 ,034 , 1 2 2 ,038 ,053 ,052 ,061 ,057 ,067 ,060 ,071 ,063 ,074 ,066
t
FFH(dd)
=
&+
g-
t
,268 ,245 ,228 ,215 ,206 .I 11 . I 15 . I 18 .I20 ,121 ,145 ,152 ,154 ,155 ,155
g'
,061 ,074 ,079 ,083 ,086 ,060 ,065 ,069 ,072
g-
,239 ,217 ,202 ,191 ,183 ,039 ,048 ,056 ,062 ,074 ,066 ,013 ,058 ,019 ,065 ,024 ,070 ,028 ,074 ,032 ,077
740 Tonelli
Macromolecules
PTF:, (H-H:T-T)
41\42 t
HHF(dl) = g+
g-
t
.255 .246 .238 -230 .224 .094 .lo7 .I16 .122 ,127 .294 ,275 ,259 ,246 ,235
8+
.288 .274 .261 .249 .239 .009 .015 .021 ,027 ,033 .003 ,007 .011
g-
t
,018 ,027 .035 .042 .049 0.0 0.0 ,001
g+
.399 .357 .326 .302 .284 ,230 .225 .219 ,213 .207 ,086 .097 .lo5 ,110 .114
.001
,002 ,039 ,050
,060 .067 .020 .073 ,015
g-
.lo7 ,117 ,124 ,128 .131 .005 ,010 ,015 ,020 .024 0.0 0.0
.119 .126 ,131 ,134 .136 .002 .004 ,006 .009 ,012 .052 ,065 ,001 .074 .002 .082 ,002 ,088
Interchanging the second and third columns and rows of FFH(dl) and FFH(dd) yields FFH(Id) and FFH(1I). Each of the H F F matrices can be obtained from the appropriate FFH matrix via total interchange of elements. As an example, FHH(dd) [I,Jl =FFH(dd) [J,Il. Interchange H and F for PTF3.
d,\4* t
FHH(d)
=
g+
g-
t
,270 .245 ,226 .213 ,203 ,143 ,140 ,138 ,136 ,135 ,122 , I 17 , I 14 , I 13 , I 12
g+
,116 ,118 ,119 .I19 ,120 .074
t
g-
,140 ,143 .143 ,142 ,140 ,025 .081 ,033 ,086 ,041 ,090 .047 .092 ,052 ,025 ,085 ,033 ,090 ,040 ,093 ,046 ,094 ,051 ,095
t
HFF(d)
=
g'
g-
,432 ,382 ,345 ,317 ,295 ,122 ,132 ,137 ,141 ,143 ,172 ,175 ,176 .I74 ,173
g'
.I57 ,164 ,166 ,167 ,166 ,009 ,014 ,020 ,026 ,031 ,003 ,005 ,008 ,012 ,015
g-
,067 ,080
,089 .096 ,102 ,001 ,003 ,005
,007 ,009 ,037 ,046 ,054 .061 ,067
FHH(I) is obtained from F H H ( d ) by interchanging second and third columns and rows, and H H F ( d ) and HHF(I) are obtained by a total interchange (I,J-J,I) of the elements of F H H ( d ) and FHH(I). Interchange H and F for PTFJ.
Conformational Characterisics of Poly(viny1 fluoride) 741
Vol. 13, No. 3, May-June 1980
PFM
41\62 t
Ill =
g+
g-
41\62 t
Idd
=
g-
t
g+
.036 .045 ,053 ,059 .065 .314 ,283 ,259 ,241 .227 ,042 .052 ,060 ,066 .071
.028 .037 .045 .052 ,058 ,074 ,083 .090 .095 .098 .003
t
,005
.008 .011 .014 g+
.312 .283 ,262 .245 .233 .183 ,177 .172 ,166 .161 .069 ,080 .lo5 ,088 ,108 .094 ,110 ,098
.218 .207 .198 ,191 .184 ,024 .032 .040 .046 ,051 ,093 .lo0
61\42
g-
.257 .237 .221 .208 ,198 .161 ,165 .166 ,166 ,165 ,085 ,097 .098 .IO2 ,104
t
Id1
.129 ,134 .137 ,138
g-
,119 ,123 ,125 .125
=
g-
61\42
g-
.084 .093 ,098 ,102 .lo5 .006 ,011 ,015 .020 .025 .011 ,017 .022 ,028 .033
g+
t
,321 .291 .268 ,251
t
Idd = g+
g-
,009 .013 ,017 .021 ,030 ,039 ,046 ,052
,014 .170 .021 ,167 ,028 ,164 ,034 ,039 ,056 t
g+
.214 ,205 .197 .190 ,184 .355 .319 ,293 ,274 .258 .120 .126 ,129 .131 ,132
,016 ,023 .029 ,035 ,039 .156 .154 ,150 ,146 ,142 ,006 ,010 .015 ,019 ,024
g,060
,071 ,079 ,085 ,090 ,061 ,073 .083 ,090 ,095 .012 ,019 ,025 .030 ,036
Interchanging second and third columns and rows of 111, Idl, Idd, and Ild yields ddd, dld, dll, and ddl, respectively. -I- In the calculation of conformational entropies,
s,,
all elements of each statistical weight matrix must be divided by the largest element corresponding to a given temperature. As a n example, the elements of FHF(dd) (PVF) must be divided by ,153, , 1 5 1 , ,149, ,148, and ,147 when calculating a t T = 0, 50, 100, 150 and 200OC. respectively.
s,
References and Notes (1) A. E. Tonelli, Macromolecules, 11, 565 (1978).
A. E. Tonelli, Macromolecules, 12, 83 (1979). A. E. Tonelli, Macromolecules, 11, 634 (1978). A. E. Tonelli, Macromolecules, 12, 255 (1979). A. E. Tonelli, Macromolecules, 12, 252 (1979). A. E. Tonelli, F. C. Schilling, W. H. Starnes, Jr., L. Shepherd, and I. M. Plitz, Macromolecules, 12, 78 (1979). (7) H. Spiesecke and W. G. Schneider, J . Chem. Phys., 35, 722 (1961). (8) D. M. Grant and E. G. Paul, J . Am. Chem. SOC.,86, 2984 (1964). (9) L. P. Lindeman and J. Q. Adams, Anal. Chem., 43, 1245 (1971). (10) F. A. Bovey, “Proceedings of the International Symposium on Macromolecules”, E. B. Mano, Ed., Rio de Janeiro, July 26-31, 1974, Elsevier, Amsterdam, 1975, p 169. (11) A. E. Tonelli, unpublished results cited in ref 10. (12) M. V. Volkenstein, “Configurational Statistics of Polymeric Chains”, Interscience, New York, 1963. (13) P. J. Flory, “Statistical Mechanics of Chain Molecules”, Interscience, New York, 1969, Chapters 11-V. (2) (3) (4) (5) (6)
(14) T. W. Bates and W. H. Stockmayer, Macromolecules, 1,12,17 (1968). (15) A. E. Tonelli, Macromolecules, 9, 547 (1976). (16) T. W. Bates, Trans. Faraday SOC.,63, 1825 (1967). (17) R. C. Doban, A. C. Knight, J. H. Peterson, and C. A. Sperati, 130th National Meeting of the American Chemical Society, Atlantic City, N.J., Sept. 1956. (18) G. J. Welch, Polymer, 15, 429 (1974). (19) D. A. Brant, W. G. Miller, and P. J. Flory, J . Mol. Biol., 23,47 (1967). (20) The A - C - C = 117.5’ in PFM is taken as the average of the LC-CF,-C = 118.5’ and A-CH,-C = 116.5’ in PVF,.15 (21) V. I. Minkin, 0. A. Osipov, and Yu. A. Zhdanov, “Dipole Moments in Organic Chemistry”, Plenum, New York, 1970. (22) A. E. Tonelli, J . Chem. Phys., 53, 4339 (1970). (23) A. E. Tonelli, “Analytical Calorimetry”, R. S. Porter and J. F. Johnson, Eds., Plenum, New York, 1974, p 89. (24) J. E. Mark, Acc. Chem. Res., 12, 49 (1979). (24) Note Added in Proof: After completion of the present work the author discovered conformational energy calculations performed previously on PTF, by R. R. Kolda and J. B. Lando [J.Macromol. Sci., Phys., 11, 21 (1975)l. These authors treated helical conformations only and the effects of H-H:T-T defects on helix stability.
